Computational Biology: New Research

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COMPUTATIONAL BIOLOGY: NEW RESEARCH No part of this digital document may be reproduced, stored in a retrieval system or transmitted in any form or by any means. The publisher has taken reasonable care in the preparation of this digital document, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained herein. This digital document is sold with the clear understanding that the publisher is not engaged in rendering legal, medical or any other professional services.

COMPUTATIONAL BIOLOGY: NEW RESEARCH

ALONA S. RUSSE EDITOR

Nova Science Publishers, Inc. New York

Copyright © 2009 by Nova Science Publishers, Inc.

All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Russe, Alona S. Computational biology : new research / Alona S. Russe. p. cm. ISBN 978-1-60876-545-4 (E-Book) 1. Computational biology. I. Title. QH324.2.R87 2008 570.285--dc22 2008035979

Published by Nova Science Publishers, Inc. 

New York

CONTENTS Preface Expert Commentary

ix Expressed Sequence Tags in Cancer Genomics Vincent Navratil and Abdel Aouacheria

Short Commentaries Short Commentary A

Short Commentary B

Short Commentary C

1 9

Protein Bioinformatics for Drug Discovery Concavity Druggability and Antibody Druggability Hiroki Shirai, Kenji Mizuguchi, Daisuke Kuroda, Haruki Nakamura,, Shinji Soga, Masato Kobori and Noriaki Hirayama A Linkage Disequilibrium-Based Statistical Approach to Discovering Interactions Among SNP Alleles at Multiple Loci Contributing to Human Skin Pigmentation Variation Sumiko Anno and Takashi Abe Sufficient Conditions for Exact Penalty in Constrained Optimization on Complete Metric Spaces Alexander J. Zaslavski

11

19

29

Short Commentary D

How to Create a Computational Medicine Study Viroj Wiwanitkit

39

Short Commentary E

Identifying Related Cancer Types C. D. Bajdik, Z. Abanto, J. J. Spinelli, A. R. Brooks-Wilson, and R. P. Gallagher

47

Research and Review Studies Chapter 1

Sample Size Calculation and Power in Genomics Studies Danh V. Nguyen, Damla Şentürk Danielle J. Harvey and Chin-Shang Li

57 59

vi Chapter 2

Chapter 3

Chapter 4

Contents Coupling Computational and Experimental Analysis for the Prediction of Transcription Factor E2F Regulatory Elements in the Human Gene Promoter Kenichi Yoshida Solving a Stochastic Generalized Assignment Problem with Branch and Price David P. Morton, Jonathan F. Bard and Yong Min Wang Reconstruction and Analysis of Large-Scale Phylogenetic Data, Challenges and Opportunities Toni Gabaldón, Marina Marcet-Houben and Jaime Huerta-Cepas

Chapter 5

Chromatin Fiber: 30 Years of Models Julien Mozziconacci and Christophe Lavelle

Chapter 6

Fast Modelling of Protein Structures Through Multi-level Contact Maps Davide Baù, Ian Walsh, Gianluca Pollastri and Alessandro Vullo

Chapter 7

Coarse-Grained Structural Model of Protein Molecules Kilho Eom and Sungsoo Na

Chapter 8

Differentiating Superficial and Advanced Urothelial Bladder Carcinomas Based on Gene Expression Profiles Analyzed Using Self-Organizing Maps Phei Lang Chang, Ke Hung Tsui, Tzu Hao Wang, Chien Lun Chen and Sheng Hui Lee

Chapter 9

Chapter 10

Chapter 11

Full Sibling Reconstruction in Wild Populations From Microsatellite Genetic Markers Mary V. Ashley, Tanya Y. Berger-Wolf, Isabel C. Caballero, Wanpracha Chaovalitwongse, Bhaskar DasGupta and Saad I. Sheikh Recent Issues and Computational Approaches for Developing Prognostic Gene Signatures from Gene Expression Data Seon-Young Kim and Hyun Ju Kim Comparison of Φ-Values and Folding Time Predictions by Using Monte-Carlo and Dynamic Programming Approaches Oxana V. Galzitskaya and Sergiy O. Garbuzynskiy

89

99

129

147

165

193

215

231

259

277

Contents Chapter 12

Chapter 13

Computational Methods for Protein Structural Class Prediction Susan Costantini and Angelo M. Facchiano

315

Fundamentals of Natural Computation in Living Systems Abir U. Igamberdiev

341

Chapter 14

Extraction of Position-Sensitive Promoter Constituents Yoshiharu Y. Yamamoto and Junichi Obokata

Chapter 15

Deconvolution of Positional Scanning Synthetic Combinatorial Libraries: Mathematical Models and Bioinformatics Approaches Yingdong Zhao and Richard Simon

Chapter 16

Chapter 17

Index

vii

361

375

Scripting of Molecular Structure Viewer for Data Analysis Using Lua Language Interpreter Yutaka Ueno

389

Computational Medicine Research in Hematology: A Study on Hemoglobin and Prothrombin Disorders Viroj Wiwanitkit

407 419

PREFACE Expert Commentary - Expressed sequence tag (EST) databases are a well established and continuously growing source to study gene expression, alternative splicing, genome sequences, gene-associated polymorphisms and sequence homologies through bioinformatic approaches. Here, the authors examine recent efforts to identify and characterize cancer genes and tumor markers using ESTs. Limitations of EST mining strategies and directions for future research are also summarized. Short Commentary A - The field of protein bioinformatics analyzes the sequence and structure of protein; it plays a critical role in the discovery of small therapeutic agents as well as protein drugs. Here the authors present our recent progress in this field, including the new concepts of concavity druggability and antibody druggability, which are expected to raise the drug discovery success ratio. Short Commentary B - Linkage disequilibrium (LD), the nonrandom association of alleles from different loci, can provide valuable information about the structure of human genome haplotypes. Because haplotype-based methods offer a powerful approach for disease gene mapping, this information may facilitate studies of the association between genomic variation and human traits. Single nucleotide polymorphism (SNP) alleles at multiple loci produce an LD pattern resulting from gene–gene interactions that can provide a foundation for developing statistics to detect other such interactions. Although several studies have used LD to address the role of gene interactions in various phenotypes and complex diseases, the current lack of formal statistics and the potential importance of data resulting from this research have motivated us to develop LD-based statistics. The authors chose to examine skin pigmentation because it is a complex trait, and SNP alleles at multiple loci may play a role in determining normal variation in skin pigmentation. The main purpose of this chapter is to outline the development of LD-based statistics for detecting interactions among SNP alleles at multiple loci that contribute to variation in human skin pigmentation. To accomplish this, the authors developed a general theory to study LD patterns in gene-interaction trait models. They then developed a definition of gene interaction and a measure of interactions among SNP alleles at multiple loci contributing to the trait in the framework of LD analysis. Short Commentary C - In this paper, the authors use the penalty approach in order to study two constrained minimization problems on complete metric spaces. A penalty function is said to have the generalized exact penalty property if there is a penalty coefficient for which approximate solutions of the unconstrained penalized problem are close enough to

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approximate solutions of the corresponding constrained problem. In this paper they establish sufficient conditions for the generalized exact penalty property. Short Commentary D - With the advent of computational research, several applications in science can be seen. The application in medicine is also documented. Computational medicine study can help answer a complicated query in medicine within a short period. How to create a computational medicine study is a common question from the beginner. In this article, the author will describe the steps for creating computational medicine research. Briefly, a simple process as that for simple in vivo and in vitro research can be used. The setting up of a conceptional framework based on literature review is the first necessary step. Next, selection of the proper database and tool for manipulation is needed. Simulating based on the designed framework can help one reach the answer. These steps must be thoroughly followed to complete computational medicine research. Short Commentary E - Background: Human cancer is often classified according to the anatomic site at which it occurs, and researchers are often taught these cancer types are actually a spectrum of disease. A review in 2000 (Hanahan and Weinberg; Cell 2000 100:5770) reported that all cancers share six characteristics: (1) self-sufficiency in growth signaling, (2) the ability to ignore external anti-growth signals, (3) the ability to avoid apoptosis, (4) sustained angiogenesis, (5) the capacity for limitless reproduction and (6) the ability to invade tissue and spread to other anatomic sites. Our goal was to identify related cancer types using different observational strategies. Methods: The authors employed one method that used textmining of online information about genes and disease. A second method used medical records of patients in British Columbia who were diagnosed with multiple cancer types between 1970 and 2004. A third method correlated Canadian provincial cancer rates for various cancer types. Results: Several pairs of related cancer types were identified using each method, although no pair was identified by all three strategies. The pairs of cancer types lung/bladder and lung/kidney were both identified by the text-mining and correlation studies. Esophageal cancer and melanoma were identified as related cancer types by both the analysis of patients with multiple primary cancers and the correlation study. Discussion: If cancer types are related, patients with one cancer might increase surveillance for other related cancer types, and drugs that are effective for treating one cancer might be successfully adapted for the related cancer types. Chapter 1 - High-throughput laboratory measurement technologies, including microarrays for genomics and proteomics, are now typically used in biomedical studies ranging from animal models to human clinical trials. These methods, such as gene expression microarrays, aim to capture the global expression patterns of thousands of genes or proteins simultaneously. A common feature is the high-dimensionality of the resulting data. Post-study analytical challenges involve methods to extract the meaningful information from the millions of data points. However, there is a need to develop systematic approaches to planning such studies. In this work, the authors provide a synthesis of the available and current trends in sample size and power analysis for genomics studies. Their emphasis will be on clarifying assumptions of the available methods as well as their applicability in practice, including the assumption of independent gene expression. The authors also emphasize emerging sample size design methods that focus on the false discovery rate (FDR) over the traditional familywise error rate as a criterion. Chapter 2 - Completion of the human genome sequencing has provided us with opportunities to understand the molecular complexity of the human body. The transcriptional

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regulatory circuits of gene expressions are one of the most promising matters to be resolved by exploring the human genome sequence. The authors have been interested in human cell fate regulated by the transcription factor E2F. To accelerate the investigation, the authors need to develop a strategy that can efficiently identify E2F target genes. Basically, their approach is to combine computational and experimental analysis. Annotated data of gene expression profiles deposited in the public database and knowledge accumulated in the published literature are a treasure-house of E2F candidate target genes. Next, a promoter region based on the information of the transcriptional start site can be used for motif searching of E2F regulatory elements. Finally, a set of predicted E2F regulatory elements are tested by molecular biological and biochemical assays. In this chapter, the author gives a basic introduction of our recent strategy for computational and experimental analysis for the prediction of transcription factor E2F regulatory elements in the human gene promoter. In addition, recent progress in unrevealing E2F functions achieved by genome wide approaches is discussed. Chapter 3 – In this chapter, the authors investigate the generalized assignment problem with the objective of finding a minimum-cost assignment of jobs to agents subject to capacity constraints. A complicating feature of the model is that the coefficients for resource consumption and capacity are random. The problem is formulated as a stochastic integer program with a penalty term associated with the violation of the resource constraints and is solved with a branch-and-price algorithm that combines column generation with branch and bound. To speed convergence, a stabilization procedure is included. The performance of the methodology was tested on four classes of randomly-generated instances. The principal results showed that the value of the stochastic solution (VSS), i.e., the gap between the stochastic solution and the expected value solution, was 35.5% on average. At the root node of the search tree, it was found that the linear programming relaxation of the master problem associated with column generation provided a much tighter lower bound than the relaxation of the original constraint-based formulation. In fact, two thirds of the test problems evidenced no gap between the optimal integer solution and the relaxed master problem solution. Additional testing showed that (1) initializing the master problem with a feasible solution out performs the classical big-M approach; (2) SOS type 1 branching is superior to singlevariable branching; and, (3) variable fixing based on reduced costs provides only a slight decrease in runtimes. Chapter 4 - The analysis of the evolutionary relationships among biological sequences, known as phylogenetics, constitutes one of the most powerful tools of computational biology. Besides its classical use to ascertain the evolution of a group of species, phylogenetics has many other applications such as the prediction of the function of a protein and the detection of genes under specific selective constrains. The advent of the genome era has brought about the possibility of extending such analyses to larger sets comprising thousands of sequences from complete genomes. The use of whole genomes, rather than that of reduced sets of genes or proteins, opens the door to a wide range of new possibilities. On the other hand, however, it poses many conceptual and technical challenges that require the development of new algorithms to interpret and manipulate large-scale phylogenetic data. Here the authors survey recent progress in the development of automated pipelines to reconstruct and analyze large collections of phylogenetic trees and provide some examples of how they have been used to address important biological questions.

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Chapter 5 - A thorough understanding of electrostatic, elastic and topological behaviour of DNA has provided some relevant mechanistic insights into the regulation of genetic expression. Although this approach has proved valuable for the study of many biological processes, it is limited by the simple description level represented by DNA. Indeed, genomic DNA in eukaryotic cells is basically divided into chromosomes, each consisting in a single huge chromosomal fiber hierarchically supercoiled. Since this organisation plays a critical role in all processes involved in DNA metabolism, tremendous efforts have been done to build relevant models of chromatin structure and dynamics. Namely, by shifting from a DNA (as a simple molecular polyelectrolyte) point of view to a chromatin (as a polymorph supramolecular nucleoprotein complex) point of view, we should go towards more efficient mechanistic framework in which the control of genetic expression and other DNA metabolism processes could be interpreted. This review gives an historical overview of the progresses that have been done during the last 30 years in this field, and discusses what the most challenging outcomes are now. Chapter 6 – The authors present an algorithm to reconstruct protein Cα traces from 4class distance maps, and benchmark it on a non-redundant set of 258 proteins of length between 51 and 200 residues. They first represent proteins as contact maps, and show that even when exact maps are available, only low-quality models can often be obtained. The authors then adopt a more powerful simplification of distance maps: multi-class contact maps. They show that the reconstructions based on 4-class native maps are significantly better than those from binary maps. Furthermore, the authors build two predictors of 4-class maps based on recursive neural networks: one ab initio, or relying on the sequence and on evolutionary information; one in which homology information is provided as a further input, showing that even very low sequence similarity to PDB templates yields more accurate maps than the ab initio predictor. They reconstruct Cα traces based on both ab initio and homology-based 4class map predictions. The authors show that homology-based predictions are generally more accurate than ab initio ones even when homology is dubious. Chapter 7 - Understanding the protein mechanics is a priori requisite for gaining insight into protein’s biological functions, since most protein performs its function through the structural deformation renowned as conformational change. Such conformational change has been computationally delineated by atomistic simulations, albeit the mechanics of large protein structure is computationally inaccessible with atomistic simulation such as molecular dynamics simulation. In a recent decade, normal mode analysis with coarse-grained modeling of protein structures has been a computational alternative to atomistic simulations for understanding large protein mechanics. In this review, the authors delineate the current stateof-art in coarse-grained modeling of proteins for normal mode analysis. Specifically, the pioneered coarse-grained models such as Go model and elastic network model as well as recently developed coarse-grained elastic network model are summarized and discussed for understanding large protein mechanics. Chapter 8 - The aim of this study was to differentiate between superficial and advanced bladder cancers by analyzing the gene expression profiles of these tumors by using the selforganizing maps (SOMs). The authors also used the GoMiner software for the biological interpretation of 473 interesting genes. Materials and Methods: Between December 2003 and November 2004, 17 patients with urothelial bladder cancers who were admitted to the Chang Gung Memorial Hospital for

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transurethral resection of the tumor were included in this study. The gene expression data included 7400 cDNAs in 17 arrays. The software, GeneCluster 2.0, was used for analyzing gene expression data by using SOMs. The authors used a 2-cluster SOM to cluster automatically a set of 17 tissues samples into superficial and advanced bladder cancers based on the gene expression patterns. The authors also used the GoMiner software for the biological interpretation of top 473 interesting genes. Results: Patients included 11 males and 6 females. Pathological studies confirmed the presence of superficial tumors in 9 patients and advanced tumors in 8 patients. Of the 7400 genes analyzed, 473 genes showed significant changes in their expression. Of these 268 were up-regulated, and 205 were down-regulated. Using the top 473 genes, SOMs were used to differentiate between the gene expression patterns of superficial and advanced bladder cancer tissue samples. The patient tissue samples were clustered into 2 groups, namely, superficial and advanced bladder cancers, comprising 10 and 7 samples, respectively. Only one patient tissue sample with advanced bladder cancer was clustered into the superficial bladder cancer group. This analysis had a high accuracy rate of 94% (16/17). The top 473 genes also were classified into biologically coherent categories by the GoMiner software. The results revealed that 452, 435, and 452 genes were associated with biological processes, cellular components, and molecular functions, respectively. Conclusion: Based on the authors’ results, they believe that superficial and advanced urothelial bladder cancers can be differentiated by their gene expression profiles analyzed by SOMs. The SOM method may be used on microarray data analysis to distinguish tumor stages and predict clinical outcomes. The genes that are uniquely expressed in either stage of bladder cancer can be considered as possible candidates for biomarkers. Chapter 9 - New technologies for collecting genotypic data from natural populations open the possibilities of investigating many fundamentalbiological phenomena, including behavior, mating systems, heritabilities of adaptive traits, kin selection, and dispersal patterns. The power and potential of genotypic information often rests in the ability to reconstruct genealogical relationships among individuals. These relationships include parentage, full and half-sibships, and higher order aspects of pedigrees. Some areas of genealogical inference, such as parentage, have been studied extensively. Although methods for pedigree inference and kinship analysis exist, most make assumptions that do not hold for wild populations of animals and plants. In this chapter, the authors focus on the full sibling relationship and first review existing methods for full sibship reconstructions from microsatellite genetic markers. The authors then describe our new combinatorial methods for sibling reconstruction based on simple Mendelian laws and its extension even in the presence of errors in the data. They also describe a generic consensus method for combining sibling reconstruction results from other methods. They present experimental comparison of the best existing approaches on both biological and simulated data. The authors discuss relative merits and drawbacks of existing methods and suggest a practical approach for reconstructing sibling relationships in wild populations. Chapter 10 - Microarray gene expression profiling, which monitors the expression of tens of thousands of genes simultaneously, is a promising tool for developing prognostic markers for cancer patients. Many researchers have applied microarray gene expression profiling in order to develop better prognostic markers, and have demonstrated promising results in many types of cancer. Unfortunately, there are concerns regarding the premature clinical use of newly-developed prognostic gene signatures, as problems associated with their application

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remain unresolved, diminishing the reliability of their intended results. This review first discusses these presently unsolved problems in the development of prognostic gene signatures. Recent computational approaches to circumventing these problems are then presented, and therein the authors discuss these approaches in the categorized framework of mechanism-derived bottom-up approaches, meta-analytic approaches, integrative approaches that combine genomics and clinical data, and sub-type-specific analysis approaches. The authors believe that recent bioinformatics approaches, which integrate rapidly accumulating genomics, clinical, and other forms of data, will help overcome current problems, and will help realize the successful application of prognostic gene signatures in personalized medicine. Chapter 11 - The authors calculate time of folding and explore the transition state ensembles for ten proteins with known experimental data at the point of thermodynamic equilibrium between unfolded and native state using a Monte Carlo Gō model and Dynamic programming where each residue is considered to be either folded as in the native state or completely disordered. The order of events in folding simulations has been explored in detail for each of the proteins. The times of folding for ten proteins which reach the native state within a limit of 108 Monte Carlo steps are in a good correlation with experimentally measured folding time at mid-transition point (the correlation coefficient is 0.71). A lower correlation was obtained if to use Dynamic programming approach (the correlation coefficient is 0.53). Moreover, Φ-values calculated from the Monte Carlo simulations for ten proteins correlate with experimental data (the correlation coefficient is 0.41) practically at the same level as Φ-values calculated from Dynamic programming approach (the correlation coefficient is 0.48). The model provides good prediction of folding nuclei for proteins whose 3D structures have been determined by X-ray, and exhibits a more limited success for proteins whose structures have been determined by NMR. Chapter 12 - The structural class of a given protein represents the first level in the hierarchical structural classification. Its knowledge starts the progressive identification of the next levels, which allows to relate the protein to a family, in evolutionary as well as functional terms. A number of computational methods have been proposed to predict the structural class based on primary sequences. Most of the prediction methods use simple sequence representations such as composition vectors and polypeptide composition or also more advanced representations that combine physico-chemical properties and sequence composition. Moreover, different classification algorithms, including neural network, rough sets and logistic regression, and the application of complex classification models, such as ensembles, bagging and boosting, have been recently used. However, the accuracy of all these methods is strongly affected by sequence similarity. Some algorithms were tested on small datasets with high sequence identity percentage, which results in an overestimated prediction accuracy. On the other hand, low similarity sequences pose a substantial challenge. The main aim of this paper is to present the state of the art in this field, describing some methods developed in the last years for the prediction of the protein structural class and underlining the need of using protein datasets of varying similarity and new testing procedures in order to evaluate correctly the quality and the accuracy of new prediction methods. Chapter 13 - The computational process is based on the fundamental semiotic activity linking mathematical equations to the materialized physical world. Its limits are defined by the set of imposed physical values constituting the background structure of the Universe.

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Computation becomes a direct consequence of semiosis, in the case where the arbitrariness of semiotic signs appears strictly defined in the semiotic context. This results in emergence of an internal formal structure of the system that can be modeled and computed. The authors consider formalization of the Peircean semiotics in the framework of Peirce algebra as a prerequisite of the understanding of fundamentals of computation. In reproducible semiotic structures such as biological entities, the factor that makes these systems “closed to efficient causation” (in Robert Rosen’s sense) is a basic element of the Peirce algebra that provides semantic closure to the system via introduction of the parameter of organizational invariance. Approaches to define this factor as a set of dual components, related both to relations and sets, are discussed in the frames of the semiotic interpretation of quantum mechanics where actualization is explained as a signification process within the network of quantum measurements. In this framework, enzymes are molecular automata, the set of which maintains highly ordered robust coherent state of the quantum computer, and genome concatenates error-correcting codes into a single reflective set that can be described by the Peirce algebra. The biological evolution can be viewed as a functional unfolding of the organizational invariance constraints in which new limits of iteration emerge, possessing criteria of perfection and having selective values. Chapter 14 - Extraction of functional sequences from promoters has been achieved with alignment-based motif search algorithms, but recently, several new approaches have been developed. In this review, I would like to introduce a methodology called as the LDSS (Local Distribution of Short Sequences) analysis. This approach evaluates distribution profiles of short sequences along the promoter region, and sequences that preferentially appear at specific promoter regions are extracted. Application of this strategy to human, mouse, Drosophila, C. elegans, Arabidopsis, rice, and also yeast resulted in successful extraction of both well known promoter elements and also novel putative elements. This method is so sensitive that various kinds of minor elements can be simultaneously detected by analysis of all the promoters of a genome as one batch. However, the LDSS analysis does not detect all the elements involved in transcriptional regulation, but position-insensitive elements are out of range of the analysis. No need of microarray data for the analysis enables its application to wide range of species beyond the model species. Chapter 15 - Combinatorial peptide library technology has been proven to be a powerful approach to both T-cell epitope determination and analysis of TCR specificity and degeneracy. During the past ten years, the authors have developed mathematical models and bioinformatics approaches for deconvolution of positional scanning synthetic combinatorial libraries (PS-SCL). PS-SCL are composed of trillions of peptides systematically arranged in mixtures with defined amino acids at each position. Starting from the mathematical model building to deconvolute the spectrum of PS-SCL, the authors proposed a biometrical approach using the score matrix to systematically search the protein databases for putative antigenic peptide candidates. The authors then evaluated of the assumption of independent contribution of the side chains of the amino acids in peptides and applied more sophisticated machine learning algorithms to improve the prediction accuracy based on synthesized peptide data. Finally, they implemented the above approach into a web based tool for searching protein database for T-cell epitopes based on experimental data from PS-SCL with the website employed a strong statistical analysis package, relational database and Java applets. The authors’ work has provided a sound basis for PS-SCL data analysis and has been proven efficient and successful for identifying target antigens and highly active peptide mimics.

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Chapter 16 - To improve the flexibility and extensibility of application programs, a method to support scripting function by embedding a Lua language interpreter is described. Using this approach, variations of input data and parameters for calculations are supported by a script file without rewriting the application program. For instance, the script information is supplied to the program and internal data can also be exported to a script for extended calculations. This chapter summarizes the basic framework of embedding this scripting language to interact with existing codes using the application programming interface provided by Lua. The method was applied to the molecular structure viewer program MOSBY to support additional visualizations and calculations from atomic coordinate data by script programs. Atomic structure data in the original C structure were mapped to a Lua script by using a mechanism called "metamethod" in Lua. In addition, the table data type in Lua provides a simple database useful for a configuration of molecular graphics. The design of a “domainspecific language” in biocomputing is discussed with reference to other scripting languages. Chapter 17 - At present, the third wave of medical experiments, in silico or computational simulating, is accepted as a powerful tool to drive the medical society into the new post genomics phase. Computational biology research is an important facet of bioinformatics. In this article, the author presents the concept and shares the experience in computational hematology research. Cases on hemoglobin and prothrombin disorders are demonstrated. Briefly, the computational research can help understand the genome, proteome and expression of hemoglobin and prothrombin disorders.

In: Computational Biology: New Research Editor: Alona S. Russe

ISBN: 978-1-60692-040-4 © 2009 Nova Science Publishers, Inc.

Expert Commentary

EXPRESSED SEQUENCE TAGS IN CANCER GENOMICS Vincent Navratil1 and Abdel Aouacheria2 1

INRA, Université de Lyon 1, Ecole Nationale Vétérinaire de Lyon, UMR754, IFR 128biosciences, Lyon, F-69007, France 2 Apoptosis and Oncogenesis Laboratory, IBCP - Institut de Biologie et Chimie des Protéines, UMR 5086 CNRS/UCBL - Université Claude Bernard Lyon 1, IFR128, 7 passage du Vercors, Lyon, F-69367, France

Abstract Expressed sequence tag (EST) databases are a well established and continuously growing source to study gene expression, alternative splicing, genome sequences, gene-associated polymorphisms and sequence homologies through bioinformatic approaches. Here, we examine recent efforts to identify and characterize cancer genes and tumor markers using ESTs. Limitations of EST mining strategies and directions for future research are also summarized.

Introduction The purpose of this short commentary is to present a snapshot of the current use of Expressed Sequence Tags (ESTs) in modern cancer research. ESTs are short (usually about 200-600 bp), single-pass DNA sequences corresponding to a fragment of a complimentary DNA (cDNA) molecule, which may be expressed in a cell at a particular time. ESTs reflect the transcriptome of the material from which they were generated. To date (April 2008), the human subset of EST database (dbEST) contains more than 8 million sequences - having doubled in size since 2002, see Figure 1 - with >100 different tissues and cell types. As exemplified herein, groups of genes or mutations that are characteristic of cancer cells (and may also be driving the disease process) can be identified using EST-based approaches. The preferred approach is to identify biomarkers from tissue-wide or genome-wide screening and then focus on a limited subset of candidates for further validation or in-depth investigation.

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Figure 1. Number of human Expressed sequence tags (ESTs) from dbEST (1992-2008). This plot shows the rapid growth of human EST data.

Gene expression Since EST clone frequency is roughly proportional to the corresponding gene expression level in a given tissue, ESTs are useful for profiling genes expressed in various tissues, cell types or developmental stages. Based on EST frequencies from different cDNA libraries, one of the many interesting applications of the publicly available EST databases is therefore ‘expression profiling’, i.e. identifying the various mRNA expressed in one or more biological samples (from cancer and non-cancer tissues). A key benefit of EST profiling techniques is to allow ‘computer-based differential display’ (also referred to as ‘digital differential display’, 'in silico subtraction' or 'electronic northern'). During the past decade, this procedure was used by several groups (Dahl et al., 2005; Grutzmann et al., 2003; Schmitt et al., 1999) and international initiatives like CGAP (Cancer Genome Anatomy Project) (Lal et al., 1999) to identify transcripts preferentially expressed or repressed in the tumor context by comparing selected cancerous libraries (present in dbEST) against ‘control’ libraries. Care should be taken in such comparisons to use non-normalized, non-subtracted and reasonably sized EST libraries to prevent artifactual gene expression profiles. Mindful of these considerations, analysis of EST data has proven to be an effective method of identifying and characterizing genes expressed in a variety of malignancies including prostate, breast, ovary colorectal and gastric cancer (Asmann et al., 2002; Chakrabarti et al., 2002; Dahl et al., 2005; Kim et al., 2004; Lu et al., 2006; Shen et al., 2005), as well as in the tumour endothelium (Herbert et al.,

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2008). A number of attempts were also made to apply in silico transcriptomics to genomewide and multi-tissue screening of cancer genes (Aouacheria et al., 2006; Baranova et al., 2001; Brentani et al., 2003; Campagne and Skrabanek, 2006; Helftenbein et al., 2008; Scheurle et al., 2000). Other reports focused on the discovery of novel splice forms in tumor cells that are distinct from the predominant forms in normal tissues (Xu and Lee, 2003) or on cancer-specific transposable element fusion transcripts (Kim et al., 2007). Due to the increasing availability of transcribed sequences (Figure 1), we predict growth in the number of EST mining project for cancer research.

SNPs ESTs resources can also be exploited to reveal genetic variation within genes. A Single Nucleotide Polymorphism (SNP) is a DNA sequence variation occurring when a single nucleotide - adenine (A), thymine (T), cytosine (C) or guanine (G) - in the genome differs between individuals, or between homologous chromosomes within an individual. SNPs are the most frequent variation in the human genome, occurring every ~2000 bp throughout the genome (Sachidanandam et al., 2001). SNPs can be identified directly from alignments of ESTs sequenced from different alleles (Huntley et al., 2006; Picoult-Newberg et al., 1999). The in silico procedure identifies SNPs where, at the same base call, discrepancy occurs in multiple EST sequences, assuming that redundant discrepancies represent actual SNPs rather than simply sequencing errors. Using EST sequences from cancer EST libraries and from normal tissue EST libraries, genetic variants associated with cancer (i.e. those that are statistically over-represented in ESTs derived from cancerous libraries) can be detected (Buetow et al., 1999; Clifford et al., 2000; Irizarry et al., 2000). In a recent series of genomewide scale in silico analyses, ESTs have been used to predict SNPs related to the cancer phenotype (Aouacheria et al., 2005; Qiu et al., 2004), including SNPs located in micro-RNA (Yu et al., 2007) or 5’/3’ untranslated regions of transcripts (Aouacheria et al., 2007) that exhibit an aberrant allele frequency in tumours. EST sequence analysis tentatively detected genes with a signature of positive selection in tumours (genes with a significant excess of non-synonymous substitutions over synonymous substitutions in cancer ESTs compared to normal ESTs) (Babenko et al., 2006). Although ESTs could also be mined for small insertion/deletion events (indels), there has been no study reporting candidate cancerassociated indels in human EST data.

Databases A number of bioinformatics databases and web servers have been developed for performing digital expression analysis across normal and cancer tissues based on EST data. Aside from the NCI Cancer Genome Anatomy Project (http://cgap.nci.nih.gov), there are many websites with searchable databases including GeneHub-GEPIS (Zhang et al., 2007), DigiNorthern (Wang and Liang, 2003), Digital Differential Display (DDD) (http://www.ncbi.nlm.nih.gov/UniGene/info_ddd.html), cDNA Digital Gene Expression Displayer (DGED) (http://cgap.nci.nih.gov/Tissues/GXS) and xProfiler (http://cgap.nci.nih. gov/Tissues/xProfiler). Candidate SNPs identified in human EST data could be picked up

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using CASCAD (Guryev et al., 2005), QualitySNP (Tang et al., 2006), HaploSNPer (Tang et al., 2008) and DigiPINS (Navratil et al., 2008), this latter tool offering additional access to the polymorphisms related to cancer.

Advantages and Limitations As they take advantage of pre-existing sequence resources generated for gene discovery rather than marker discovery, EST projects are extremely cost-efficient. Furthermore, ESTs are easily produced and, since they represent coding sequences, they directly identify genes of interest. Another advantage of the EST-based approach is that it can identify common sequence variations within the human genome and, more and more, uncommon sequence variations also, as the number of cDNA libraries continues to increase. Moreover, ESTs provide the opportunity to detect genetic variation and to profile expression for nearly all genes, either annotated or entirely novel (i.e. predicted) (Krukovskaja et al., 2005) in a quantitative and straightforward way. General limitations associated with the use of EST databases include poor sequencing depth of the libraries, and differences in library sizes and uncertainty concerning the origin of the samples. One related problem is that many cell types are often pooled together during the preparation of EST libraries. As more EST data become available, it will be possible to perform expression profiling in more detailed tissue subtypes. ESTs (as single pass reads) are also prone to sequencing errors. Moreover, all EST-based strategies are biased towards the 3’ ends of transcripts and towards highly-expressed genes. Despite the obvious benefits of cost and time savings, it is clear that laboratory techniques (such as real-time RT-PCR, western blotting and site-directed mutagenesis) are required to validate computational predictions. The results obtained through the use of ESTs may also be compared to results from other experimental platforms such as SAGE and microarrays, despite their own limitations or biases. Thus, EST libraries should be considered as a starting point for detecting differential expression and DNA sequence polymorphisms.

Conclusions After candidate genes or SNPs have been identified via computational methods into the ocean of sequence data available, the next step is to use bioinformatics to further down-select data. One route is to use functional annotations of the candidate set to dissect biological pathways, functional groups and molecular modules of interest. As we move toward such a “systems biology” approach in cancer genomics, the integration of logical databases such as GO, KEGG, REACTOME, OMIM will be of vital importance in the future. The clear goal is not only to identify biomarkers, but also to identify biologically relevant patterns in data that can serve to understand the underlying molecular mechanisms and pathways of cancer. Ultimately, an understanding of the molecular behaviour of tumours would help their molecular classification and also provide a basis for future patient-specific therapeutic approaches.


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Acknowledgement This work was supported by grants from La Ligue Contre le Cancer (Comités de la Drôme et du Rhône).

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SHORT COMMENTARIES



Short Commentary A

PROTEIN BIOINFORMATICS FOR DRUG DISCOVERY CONCAVITY DRUGGABILITY AND ANTIBODY DRUGGABILITY Hiroki Shirai1,*, Kenji Mizuguchi2, Daisuke Kuroda3,4, Haruki Nakamura3,, Shinji Soga1, Masato Kobori1 and Noriaki Hirayama5 1: Advanced Genomics, Molecular Medicine Research Laboratories, Astellas Pharma Inc., 21 Miyukigaoka, Tsukuba, Ibaraki 305-8585, Japan 2: National Institute of Biomedical Innovation, 7-6-8 Asagi, Saito, Ibaraki-city, Osaka 567-0085, Japan 3: Institute for Protein Research, Osaka University., 1-3 Yamadaoka, Suita-city, Osaka 565-0871, Japan 4: Graduate School of Frontier Biosciences, Osaka University, 1-3 Yamadaoka, Suita-city, Osaka 565-0871, Japan 5: Tokai University School of Medicine, 143 Shimokasuya, Isehara, Kanagawa 259-1143, Japan

Abstract The field of protein bioinformatics analyzes the sequence and structure of protein; it plays a critical role in the discovery of small therapeutic agents as well as protein drugs. Here we present our recent progress in this field, including the new concepts of concavity druggability and antibody druggability, which are expected to raise the drug discovery success ratio.

Key words: concavity druggability, antibody druggability, protein bioinformatics, drug discovery

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Hiroki Shirai, Kenji Mizuguchi, Daisuke Kuroda et al.

Introduction Currently, the two in silico technologies, bioinformatics and computational chemistry, are effectively used for drug discovery[1-6]. Bioinformatics plays various roles in drug discovery at multiple stages: target discovery, target validation, building a screening system, and analysis of the mechanism of diseases as well as that of compounds[1-3]. It also contributes to the generation of protein drugs and small therapeutic agents. It comprises four components: information technology (IT), information science, theoretical biology, and theoretical biochemistry, although the boundaries between them are obscure. The IT aspect of bioinformatics includes the construction and maintenance of an information infrastructure (hardware, software, network systems, and in-house database). Various kinds of biological data are collected and entered into the in-house database to yield a user-friendly interface and easily accessible data. The information science aspect of bioinformatics is the analysis of microarray and other biological data using sophisticated data mining approaches. Text mining, which extracts useful information from literature, falls into this category. The theoretical biology aspect of bioinformatics, sometimes called pathway bioinformatics, is used to determine which genes are involved in physiological functions. The theoretical biochemistry aspect of bioinformatics, which is almost the same as protein bioinformatics, includes the analysis of protein sequence or structure in order to elucidate its molecular function. In addition, protein bioinformatics naturally plays a critical role in protein drug discovery. Despite the importance of protein bioinformatics, inefficient information-sharing between industrial and academic researchers in this field could prevent the development of more useful tools for real drug discovery. The surrent status of protein bioinformatics and problems therewith are summarized and addressed below. Just ten years ago, there were still significant difficulties with generating a lead compound via docking studies between compounds and a target protein. The improvement of software and hardware as well as the rapid increase in protein/compound interaction data over the past decade have enabled us to obtain lead compounds in many projects. In addition to docking studies, other technologies involving computational chemistry effectively contribute to drug discovery at various stages[4-6]. The structure-activity relationship is used for lead optimization, ADME and toxicity prediction for lead evaluation, and chemoinformatics for clustering and the rational selection of compounds. More importantly, the generation of the “druggability of small compounds” concept and its suitability as an indicator for lead compound evaluation changed the general flow of drug discovery. However, despite efforts made based on computational chemistry, compounds are often dropped for various reasons. Researchers try to reduce the risk of this happening by evaluating ADME and toxicity at an earlier stage, increasing the variety of lead compounds, and optimizing as many of them as possible. However, it should be noted that the use of computational chemistry alone would reduce only some specific risks and generate a limited variety of lead compounds. A combination approach, such as with bioinformatics, is more desirable as it is expected to reduce different types of risks while increasing lead compound variety. Bioinformatics and computational chemistry are currently used independently for drug discovery; however, if used in combination, a synergistic effect is expected. Protein

Protein Bioinformatics for Drug Discovery Concavity Druggability…

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bioinformatics is considered to be a way to combine these two in silico technologies; thus, it plays a key role in the creation of an integrated solution, which may improve the next generation drug discovery success ratio. Effective usage of sequence and structure analysis could reduce side effects. This matter is described in detail in the next section. In addition, we recently proposed a new concept, concavity druggability, which is expected to increase the variety of lead compounds (described in section II).

I) Protein Sequence and Structure Analysis The efficiency of protein bioinformatics in drug discovery is illustrated below by introducing our work with the guanidino-group modifying enzyme (GME) superfamily[7-9]. The GME superfamily consists of enzymes (GMEs) that catalyze the modification of guanidino groups[7]. This superfamily includes many key metabolic enzymes, some of which are already recognized as attractive drug targets. GMEs adopt a unique tertiary structure known as the α/β propeller, which can accommodate a diverse set of sequences. The aminoacid sequence identities among GMEs are from 8% to 23%. Amidinotransferase (AT) is the first enzyme of this superfamily to have its structure determined. It catalyzes the transfer of amidino group from amino acid arginine to another substrate. The crystal structure of AT revealed a barrel-shaped fold with a cavity on one side where the substrate arginine binds. The chemical reaction is catalyzed by a Cys-His-Asp catalytic triad at the bottom of this cavity. Our first project dealing with the protein bioinformatics of GME was to propose the existence of the GME superfamily itself[8]. Before our proposal, despite the functional similarity, the low sequence similarities among the enzymes and the lack of the structural information except for AT prevented the researchers from understanding their evolutionarily relatedness (homology) for a long time. FUGUE is the sophisticated fold recognition software which one of the authors (Kenji Mizuguchi) developped[10]. By using FUGUE, we predicted three other enzyme families to be homologous to AT and share similar catalytic mechanisms[8]. These are dimethylarginine dimethylaminohydrolase (DDAH), Arginine deiminase (ADI) and Porphyromonasgingivalis peptidyl-arginine deiminase (PPAD) and related hypothetical proteins showing weak similarity to it (which we called PPADH). After our prediction, the structures of DDAH, ADI and PPADH were determined by X-ray crystallography, and confirmed our hypothesis[11-13]. The second GME project was the prediction of succinyl arginine dihydrolase (AstB) as a new member of the GME superfamily[9]. After prediction, the structure of AstB was determined by X-ray crystallography, which confirmed our hypothesis[14]. The useful information obtained from these two drug discovery projects are summarized as follows: i) Structures useful in docking studies for determining compounds that block GME can be predicted. ii) Catalytic residues of DDAH, ADI, PPAD, PPADH, and AstB; this information is valuable for validating protein as a drug target as well as useful for setting up an assay system. iii) Identification of PPADH proteins as new drug targets. They would have some enzymatic activity in common with GME, and produce ammonia. Proteins that generate ammonia sometimes act as virulence factors in pathogenic microorganisms, thus the PPADH from Helicobacter pylori might act as such by generating ammonia from the abundant peptides in the stomach. iv) Catalytic mechanisms of DDAH, ADI, PPAD and AstB. These

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catalytic mechanisms are valuable for the design of chemical compounds at the lead optimization step. The sequence analysis aspect of protein bioinformatics could extract these pieces of valuable information prior to structure determination by X-ray crystallography. Mammalian peptidyl-arginine deiminase (PAD) is a metallo-enzyme that had been considered unrelated to GME until the crystal structure of human PAD was determined[15]. The structure of PAD is composed of several domains, one of which is the α/β propeller. The overall structural similarity, the conservation of catalytic residue, and the similarity of function confirmed that it is another member of the GME superfamily. Its relatedness could not be predicted prior to structural determination; therefore it is necessary to improve the sensitivity of the fold recognition tools. After many GME structures had been determined, we conducted a third GME project[7]. Structural superposition and structure-based alignment could identify new key GME residues involved in catalysis and substrate binding. We found that conserved guanidino-carboxyl interactions are used in two different ways: acidic residues in the catalytic site form hydrogen bonds to the substrate guanidino group, and the enzyme Arg residues at several key positions recognize the carboxyl group of the substrate and fix its orientation. Based on this observation, we proposed rules for classifying the GME sequences and predicting their molecular function from the conservation of the key acidic and Arg residues. The useful predictive tools generated by this third drug discovery project are summarized below. i) The GME commonality and diversity information extracted allows for the design of a compound with high selectivity. ii) The proposed rules allow for the prediction of pathogenic organism unannotated gene function and the proposal of new drug targets. Importantly, protein bioinformatics can be used to extract valuable information even after structural determination by X-ray crystallography. Generally, if a compound binds to its target protein, it can also bind to the homologues of the target, which would eventually generate a side effect. For this reason, we usually screen not only for the target protein, but also counter-screen for its homologues to select compounds with both high affinity and selectivity. Selecting the homologues to be checked is crucial, but there is some controversy over whether it is necessary to check remote homologues or not. Since remote homologues are so different, some researchers insist that only close homologues need to be checked, while others insist that all should be. We feel that checking depends on the features of the superfamily to which the target protein belongs. For example, the GME superfamily comprises enzymes capable of a diverse array of reactions (transferase, hydrolase, and dihydrolase), and whose substrates are the same or similar to each other (arginine or related ligands). Despite the very low sequence similarity among GMEs, they are considered to bind to the same or similar compounds. Thus, if finding a compound that blocks a certain GME with high selectivity is desired, the selectivity of remote homologues should also be checked. In contrast, the acyl-CoA N-acyltransferase (NAT) superfamily comprises enzymes whose substrates are diverse, but whose reactions are the same (acyl transferase)[9]. For this reason, NATs are not considered to easily bind to the same or similar compounds. Thus, if a compound that blocks a certain NAT with high selectivity is desired, checking the selectivity of remote homologues is not likely to be necessary. Using protein bioinformatics is expected to reduce the number of different types of side effects that must be tackled with computational chemistry.


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II) Concavity Druggability Using protein bioinformatics, we proposed a new concept, “concavity druggability”, and developed a method to evaluate druggability from the amino-acids present in the concavity on the protein surface[16,17]. The specific binding of a ligand to its target protein is the key to drug action. The surface of a target protein usually possesses multiple concavities where small molecules may bind. However, each ligand binds preferentially to a specific concavity. We defined druggable concavity as the concave surface where drug-like molecules are highly inclined to bind. Drug targets that can be modified by a small molecular drug need to be identified for each disease phenotype. Thus, finding a druggable concavity in disease-related proteins is a crucial step towards validating new drug targets. It is also important for increasing the chance of obtaining a drug-like compound and for understanding the function of a given protein. Since the binding site of a drug is considered to be highly specific to its molecular characteristics, the binding concavity must have a distinct character significantly different from those of similar concavities on protein targets. One of the authors (Noriaki Hirayama) recently established a profile for determining the “drug-likeness” of a compound, which comprises multiple molecular descriptors to determine how much like a drug the molecule is[18]. We evaluated the drug-likeness of ligands, which was determined while their structures were complexed with proteins from the Protein Data Bank (PDB). The amino acid compositions around the binding sites for drug-like ligands in well-qualified X-ray structures were analyzed in detail. The analysis revealed a remarkable propensity for the presence of specific amino acids at the binding site of each drug-like compound. From this data, a simple discrimination index called Propensity for Ligand Binding (PLB) was developed, which allows the druggability of concavities on a given protein surface to be evaluated. Importantly, the PLB index can be used to identify druggable concavities in homology models. Use of the PLB index to find new druggable concavities would increase the variety of lead compounds that would be obtained if computational chemistry alone was used.

III) Antibody Modeling and Druggability Protein bioinformatics contributes to the generation of protein drugs as well as small compound drugs. Recently, more antibody drugs are expected to be developed because of their low toxicity and high efficiency. Establishing high affinity binding is crucial for expanding detection limits, extending dissociation half times, decreasing drug dosage, and increasing drug efficacy[19]. Affinity maturation of antibodies in vivo often fails to generate antibody drugs of the targeted potency, which makes it necessary to perform further affinity maturation in vitro using directed evolution or rational design via protein bioinformatics. For rational design, a tertiary structural model of an antigen binding site needs to be constructed from its amino acid sequence. The efficiency of in silico design depends on the accuracy of the model. An antigen-binding site is composed of six complementaritydetermining regions (CDRs). Five of these CDRs (CDR-L1, L2, L3, H1, and H2) have a limited number of canonical structures; however, the third CDR of the heavy chain (CDR-H3) shows substantial diversity in length, sequence, and structure. In addition, CDR-H3 sometimes changes its conformation depending on the existence of an antigen. Importantly, it

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lies in the centre of the antigen-binding site and generally plays a dominant role in antigen recognition. Thus, building a model of CDR-H3 is the most important and the most difficult step. After examination of the qualified crystal structures of the antibody, we proposed empirical rules for predicting the structural features of CDR-H3 from its amino-acid sequence (H3-rules)[20,21]. Essentially the same proposal was also made by a different group[22]. We recently revised the rules (H3-Rules 2007) to apply only to the analysis of newly determined structures[23]. Multicanonical molecular dynamics simulation is one of the algorithms for enhanced conformational sampling[24]. We found it is quite useful for building an accurate model and capturing the structural variety of CDR-H3s[25,26]. At present, the usage of revised H3-rules and multicanonical molecular dynamics simulation provides the best approach for determining the antigen binding site. However, it remains difficult to predict the structure of long CDR-H3s, the non-canonical structures of the other five CDRs, and the dimerization angle of the H chain and L chains. Thus, the methods of antibody model building need to be improved. Current drug discovery practice uses the druggability of small compounds as an indicator of lead compound potential. However, a similarly rational approach has not yet been established for antibody evaluation. However, such rational approaches have not yet been established for antibody evaluation. We recently proposed a new concept, “antibody druggability”[23]. We examined the CDR-H3 structures of 12 antibody drugs and found the common structural features. Antibody druggability would be effectively applied to rational antibody design and selection.

Conclusion Although protein bioinformatics plays a critical role in drug discovery, the inefficiency of information-sharing between industrial and academic researchers in this field could prevent the development of more useful tools for real drug discovery. In this review, our recent progress in protein bioinformatics was presented, and the current status of this field, along with associated problems that may be experienced by pharmaceutical companies, were summarized. It is our hope that more useful tools will be developed in this field to increase the success ratio of drug discovery even further.

References [1] Chen YP, and Chen F. Identifying targets for drug discovery using bioinformatics. (2008) Expert Opin Ther Targets 12:383-389. [2] Mizuguchi K. (2004) Fold recognition for drug discovery. Drug Discovery Today: Targets;3:18-23. [3] Yan Q. (2008) The integration of personalized and systems medicine: bioinformatics support for pharmacogenomics and drug discovery. Methods Mol Biol.;448:1-19. [4] Mohan CG, Gandhi T, Garg D, and Shinde R. (2007) Computer-assisted methods in chemical toxicity prediction. 1: Mini Rev Med Chem. 7:499-507.


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[5] Tropsha A, and Golbraikh A. (2007) Predictive QSAR modeling workflow, model applicability domains, and virtual screening. Curr Pharm Des.;13:3494-3504. [6] Taft CA, Da Silva VB, Da Silva CH. (2008) Current topics in computer-aided drug design. J Pharm Sci. 97:1089-1098. [7] Shirai H, Mokrab Y, and Mizuguchi K. (2006) The guanidino-group modifying enzymes: structural basis for their diversity and commonality. Proteins. 64:1010-1023. [8] Shirai H, Blundell TL, and Mizuguchi K. (2001) A novel superfamily of enzymes that catalyze the modification of guanidino groups. Trends Biochem Sci. 26:465-468. [9] Shirai H, and Mizuguchi K. (2003) Prediction of the structure and function of AstA and AstB, the first two enzymes of the arginine succinyltransferase pathway of arginine catabolism. FEBS Lett. 555: 505-510. [10] Shi J, Blundell TL, and Mizuguchi K. (2001) FUGUE: sequence-structure homology recognition using environment-specific substitution tables and structure-dependent gap penalties. J Mol Biol. 310: 243-257. [11] Murray-Rust J, Leiper J, McAlister M, Phelan J, Tilley S, Santa-Maria J, Vallance P, and McDonald N. (2001) Structural insights into the hydrolysis of cellular nitric oxide synthase inhibitors by dimethylarginine dimethylaminohydrolase. Nat Struct Biol. 8: 679-683. [12] Das K, Butler GH, Kwiatkowski V, Clark AD Jr, Yadav P, and Arnold E. (2004) Crystal structures of arginine deiminase with covalent reaction intermediates; implications for catalytic mechanism. Structure 12: 657-667. [13] Galkin A, Kulakova L, Sarikaya E, Lim K, Howard A, and Herzberg O. (2004) Structural insight into arginine degradation by arginine deiminase, an antibacterial and parasite drug target. J Biol Chem. 279: 14001-14008. [14] Tocilj A, Schrag JD, Li Y, Schneider BL, Reitzer L, Matte A, and Cygler M. (2005) Crystal structure of N-succinylarginine dihydrolase, AstB, bound to substrate and product, an enzyme from the arginine catabolic pathway of Escherichia coli. J Biol Chem. 280: 15800-15808. [15] Arita K, Hashimoto H, Shimizu T, Nakashima K, Yamada M, and Sato M. (2004) Structural basis for Ca(2+)-induced activation of human PAD4. Nat. Struct. Mol. Biol. 11: 777-783. [16] Soga S, Shirai H, Kobori M, and Hirayama N. (2007) Use of amino acid composition to predict ligand-binding sites. J Chem Inf Model. 47:400-406. [17] Soga S, Shirai H, Kobori M, and Hirayama N. (2007) Identification of the druggable concavity in homology models using the PLB index. J Chem Inf Model. 47:2287-2292. [18] Horio K, Muta H, Goto J, and Hirayama N. (2007) A simple method to improve the odds in finding 'lead-like' compounds from chemical libraries. Chem. Pharm. Bull. 55: 980-984. [19] Lippow SM, Wittrup KD, and Tidor B. (2007) Computational design of antibodyaffinity improvement beyond in vivo maturation. Nat. Biotechnol. 10: 1171-1176. [20] Shirai H, Kidera A, and Nakamura H. (1996) Structural classification of CDR-H3 in antibodies. FEBS Lett. 399: 1-8. [21] Shirai H, Kidera A, and Nakamura H. (1999) H3-rules: identification of CDR-H3 structures in antibodies. FEBS Lett. 455: 188-197.

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[22] Morea V, Tramontano A, Rustici M, Chothia C, and Lesk AM. (1998) Conformations of the third hypervariable region in the VH domain of immunoglobulins. J Mol Biol. 275: 269-294. [23] Kuroda D, Shirai H, Kobori M, and Nakamura H. (2008) Structural classification of CDR-H3 revisited: A lesson in antibody modeling. Proteins inpress. [24] N. Nakajima, H. Nakamura and A. Kidera (1997) Multicanonical ensemble generated by molecular dynamics simulation for enhanced conformational sampling of peptides. J. Phys. Chem B101: 817–824 [25] Shirai H, Nakajima N, Higo J, Kidera A, and Nakamura H. (1998) Conformational sampling of CDR-H3 in antibodies by multicanonical molecular dynamics simulation. J Mol Biol. 278: 481-496. [26] Kim ST, Shirai H, Nakajima N, Higo J, and Nakamura H. (1999) Enhanced conformational diversity search of CDR-H3 in antibodies: role of the first CDR-H3 residue. Proteins. 37: 683-696.



Short Commentary B

A LINKAGE DISEQUILIBRIUM-BASED STATISTICAL APPROACH TO DISCOVERING INTERACTIONS AMONG SNP ALLELES AT MULTIPLE LOCI CONTRIBUTING TO HUMAN SKIN PIGMENTATION VARIATION Sumiko Anno1 and Takashi Abe2 1

2

School of Engineering, Shibaura Institute of Technology School of Bio-Science, Nagahama Institute of Bio-Science and Technology

Abstract Linkage disequilibrium (LD), the nonrandom association of alleles from different loci, can provide valuable information about the structure of human genome haplotypes. Because haplotype-based methods offer a powerful approach for disease gene mapping, this information may facilitate studies of the association between genomic variation and human traits. Single nucleotide polymorphism (SNP) alleles at multiple loci produce an LD pattern resulting from gene–gene interactions that can provide a foundation for developing statistics to detect other such interactions. Although several studies have used LD to address the role of gene interactions in various phenotypes and complex diseases, the current lack of formal statistics and the potential importance of data resulting from this research have motivated us to develop LD-based statistics. We chose to examine skin pigmentation because it is a complex trait, and SNP alleles at multiple loci may play a role in determining normal variation in skin pigmentation. The main purpose of this chapter is to outline the development of LD-based statistics for detecting interactions among SNP alleles at multiple loci that contribute to variation in human skin pigmentation. To accomplish this, we developed a general theory to study LD patterns in gene-interaction trait models. We then developed a definition of gene interaction and a measure of interactions among SNP alleles at multiple loci contributing to the trait in the framework of LD analysis.

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Sumiko Anno and Takashi Abe

Introduction Industrial activity has increased the rate at which ozone is being depleted and has led to higher levels of exposure to ultraviolet (UV) rays-conditions to which humans have not had time to adapt. To properly adjust to heightened UV exposure, it will be necessary to understand how the environment exerts pressures and effects on portions of the genome encoding complex human phenotypes such as pigmentation [1]. Over the course of their evolution, humans have adapted to complicated and challenging environments by evolving new traits and abilities. Human skin color variation, regulated by melanin expression, is an adaptation to different levels of environmental UV exposure. For example, people indigenous to Northern Europe have pale skin, while people indigenous to Africa have dark skin. At lower latitudes, melanin production is increased to protect against high levels of UV irradiation, while at higher latitudes, melanin production is decreased, which allows the body to synthesize more vitamin D. Increased vitamin D synthesis provides a variety of health benefits, including protection against rickets (osteomalacia) [1–3]. Although variations in human skin color are known to occur in connection with environmental factors such as UV radiation, the genetic background of human skin color is still unclear. Several studies of skin pigmentation have reported polymorphisms associated with skin color at various loci such as melanocortin 1 receptor (MC1R), oculocutaneous albinism II (OCA2), and agouti signaling protein (ASIP). Human skin color variation is thought to be controlled by interactions among multiple loci at alleles known to contain single nucleotide polymorphisms (SNPs) [4–11]. SNP alleles at multiple loci produce a linkage disequilibrium (LD) pattern resulting from gene–gene interactions; such patterns can provide a foundation for developing statistics to detect similar interactions. Although several studies have used LD to address gene interactions, the current lack of formal statistics and the potential of this information have motivated us to develop LD-based statistics. Because pigmentation is a complex trait, SNP alleles at multiple loci may play a role in determining normal variation in skin pigmentation. The main purpose of this chapter was to develop LD-based statistics for detecting interactions among SNP alleles at multiple loci that contribute to human skin pigmentation variation, in order to clarify the molecular basis of the genetic background of human skin color. To accomplish this, we developed a general theory to study LD patterns using geneinteraction trait models. We then developed a definition of gene interactions and a measure of interactions contributing to the trait among SNP alleles at multiple loci within the framework of LD analysis.

Materials and Methods Samples were collected from 122 Caucasoid participants in Toledo, Ohio and 100 Mongoloid participants in Japan. Sample collection was conducted in accordance with a protocol approved by the Human Subjects Research Committee of the Shibaura Institute of Technology, Japan. Participants gave informed consent for the collection of buccal samples, which were anonymously coded [12]. We extracted DNA from the buccal samples using the ISOHAIR kit (NIPPON GENE COMPANY Chiyoda-ku, Tokyo, Japan). To provide sufficient genomic DNA for SNP

A Linkage Disequilibrium-Based Statistical Approach to Discovering Interactions… 21 genotyping, we amplified whole genomic DNA using the REPLI-g Kit (QIAGEN, Chuo-ku, Tokyo, Japan). Next, ASIP, tyrosinase-related protein 1 (TYRP1), tyrosinase (TYR), MC1R, OCA2, microphthalmia-associated transcription factor (MITF), and myosin VA (MYO5A) genes were selected as candidate genes for human skin pigmentation [4–11, 13–17]. Twenty SNPs in the loci of the candidate genes that had been registered for the dbSNP database [18] were selected: rs819136, rs1129414, rs2075508, rs10960756, rs3793976, rs2298458, rs3212363, rs1805008, rs3212371, rs2279727, rs4778182, rs1800419, rs2311843, rs1800414, rs1800404, rs7623610, rs704246, rs16964944, rs1724577, and rs4776053. PCR was performed to amplify the regions containing the SNPs of interest within the DNA samples. The PCR products were electrophoresed on 2% agarose gels to verify that the expected single-band product was generated. The verified PCR products were purified with ExoSAPIT (Amersham Pharmacia Biotech, Piscataway, New Jersey, USA). The allele discrimination assay consisted of PCR amplification of multiple SNP alleles at a particular locus using specific primers with tags differing in molecular weight. For this assay, the purified PCR products were combined with two hemi-nested allele-specific primers and two universally tagged Masscode oligonucleotide primers (Qiagen). Each tag was covalently attached to the 5′ end of an oligonucleotide primer via a photolabile linker. Following PCR amplification, the SNP-specific PCR products were passed through a QIAquick 96 silica-based filter membrane to remove unincorporated tagged primers. The filtered PCR products were exposed to a 254-nm mercury lamp to cleave the incorporated tags, and the tags were analyzed using an optimized Agilent 1100 single quadrupole mass spectrometer. The presence of a particular tag indicated the presence of the corresponding SNP allele in the genomic DNA sample. Genotype data were reported in a comma-delimited flat-file format that contained the SNP and sample identifiers for each allele detected. Alleles were reported using a binary nomenclature in which l represented wild-type alleles and 2 represented variant alleles. The SNP allele was classified into three types: wild-type homozygous, variant-type homozygous, and heterozygous. Thus, a homozygous wild-type allele was designated 1,1, and a heterozygous allele was designated 1, 2 [19–20]. The following analyses were conducted with the data obtained from the results of the SNP genotyping of Caucasoid and Mongoloid participants,.

Genotype and allele frequencies for the 20 SNPs in the two populations The genotype and allele frequencies of the 20 SNPs observed in the Caucasoid (n = 122) and Mongoloid (n = 100) participants were calculated to determine racial differences.

Cluster analysis We conducted cluster analysis for genetic differentiation of the SNP genotyping results by condensing the genotype assignment for each SNP allele into a single numeric value as follows: homozygous wild type 1,1 = 0, heterozygous 1,2 = 0.5, and homozygous variant 2,2 = 1. An unweighted pair group method with arithmetic mean (UPGMA) dendrogram was constructed based on the genotyping data using the euclidean distance. UPGMA is one of the simplest and most commonly used hierarchical clustering algorithms. As input, it receives a

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set of components and a distance matrix, which contains pairwise distances between all components, and constructs a hierarchical dendrogram from this set.

Linkage disequilibrium (LD) generated by gene-gene interactions contributes to two racial groups To examine the contribution of nonrandom associations of SNP alleles at multiple loci to racial differences, we examined the associations between the 20 SNP alleles at various candidate-gene loci in the genome. LD serves as a measure of gene–gene interactions among unlinked loci [21]. LD is the association between the qualitative random variables corresponding to SNP alleles at different polymorphic sites, not necessarily on the same chromosome [22–23]. LD provides important gene-mapping information when used as a tool for fine mapping of complex disease genes and also in proposed genome wide association studies. LD is also of interest because of what it may reveal about the evolution of populations. The concept of LD in this chapter is as it was defined by Richard Lewontin in one of the earliest measures of disequilibrium to be proposed (symbolized by D) [24]. When measuring LD, D quantifies disequilibrium as the difference between the observed frequency of a two-locus haplotype and the frequency it would be expected to show if the alleles are segregating at random. Consider two markers, with alleles A, a and B, b. Their haplotype frequency can be described as fAB, fAb, faB, and fab. The discrepancy of the distribution under LD can be measured by D = fABfab – fAbfaB. Measures of LD are defined as the standardized values of D. Two common such measures are R2 = D2/(fAB + fAb)(fAB + faB)(faB + fab)(fAb + fab) and D′ = D/Dmax, where Dmax is min((fAB + fAb)(fAb + fab), (fAB + faB)(faB + fab)) when the numerator is positive, and min((fAB + fAb) (fAB + faB), (fAb + fab)(faB + fab)) otherwise. The case of D′ = 1 is known as complete LD. Values of D′ < 1 indicate that the complete ancestral LD has been disrupted. The magnitude of values of D′ < 1 has no clear interpretation. The definition of R2 can be understood by considering the alleles as realizations of quantitative random variables (with values 0 and 1), from among which we can calculate a correlation coefficient. LD can be analyzed with software such as the EH program [25], Haploview [26], R statistical software [27], and others. To examine the contribution of nonrandom associations of SNP alleles at multiple loci to racial differences, we calculated the LD statistic and significance levels for all possible SNP allele pairs. Significant levels were calculated using a χ2 test on the two-by-two table of the haplotype frequencies. The P value of LD was determined with a χ2 test; statistical significance was set at 0.05. Combinations of SNP alleles at multiple loci under LD were jointly tested for association with Caucasoid or Mongoloid race by performing a χ2 test for independence. Only data that followed the conditions of Hardy-Weinberg equilibrium were used in the analysis.

Results Table 1 shows the genotypes and allele frequencies for the 20 SNPs in the Caucasoid and Mongoloid groups. We also observed some allele frequencies in the Caucasoid samples that differed from the Mongoloid samples (Figure 1). The 20 SNPs that we used in this study were

A Linkage Disequilibrium-Based Statistical Approach to Discovering Interactions… 23 assumed to contribute to racial differences in skin color. Cluster analysis showed that each racial group formed a separate cluster except for one Mongoloid participant, who fell into the Caucasoid cluster [12]. Table 1. Genotypes and allele frequencies for 20 SNPs in the Caucasoid and Mongoloid populations

The allele combination rs1800419-C/rs1800414-G/rs1800404-G was associated with the Mongoloid group (p = 5.39 × 10−20). These alleles are found in OCA2 on chromosome 15, and formed a haplotype [12]. OCA2 controls the transport of tyrosine, a precursor of melanin, into the melanosome for melanin synthesis. The allele combination rs2311843-C/rs1800404-A/rs4776053-C was associated with the Caucasoid group (p = 5.51 × 10−33). These alleles are found in OCA2 and MYO5A on chromosome 15, and formed a haplotype [12]. MYO5A functions in vesicle transport, and mutations in this gene confer a lighter skin color due to defects in actin-based pigment granule transport within melanocytes. The pigmentation variation is believed to be due to abnormal distribution of melanosomes along the dendrites of melanocytes [28]. There were significant differences in the allele combinations (i.e., haplotypes) between the two racial groups. The allele combination rs2311843-C/rs1800404-A/rs4776053-C was associated with the Caucasoid group. The one of the allele of the combination was rs4776053 in MYO5A found in only the Caucasoid group; and the other of the allele of the combination were rs2311843 and rs1800404 in OCA2 found in both the Mongoloid and the Caucasoid groups. Thus, the rs4776053 associated with the Caucasoid group only could be considered to

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confer lighter skin color. The rs4776053 allele varies as C/T. The allele frequencies for this genotype were 83.2/16.8 (C/T) for the Caucasoid group and 76.0/24.0 (C/T) for the Mongoloid group. The higher frequency of the C variant among the Caucasoid group indicates that rs4776053-C could be a SNP allele that confers lighter skin color. This result suggests that the lighter skin pigmentation observed in Caucasoid populations is the result of positive selection on different loci in different human populations [4, 12].

Figure 1. Comparison of allele frequencies in Mongoloid and Causcasoid populations. Allele frequencies of Mongoloid samples plotted against allele frequencies of Caucasoid samples. Note: only SNPs that vary substantially between the populations are labeled.

Conclusion The results of the LD analysis of the Caucasoid and Mongoloid groups show that the SNP alleles at multiple loci that contribute to racial differences are on the same chromosome and are likely to form the haplotype [12]. Every gene has variable SNPs, and these may constitute haplotypes; some haplotypes are present in all populations, while some are population specific [29]. Haplotypes associated with skin color differences between Caucasoid and Mongoloid persons are populationspecific haplotypes. For most genes, haplotypes represent an opportunity for functional adaptation and diversification [29]. The haplotypes identified in this study are most likely the result of adaptation to different UV ray intensities. This study adds to the growing evidence of genetic variability with regard to skin color in different geographically isolated populations [12].

A Linkage Disequilibrium-Based Statistical Approach to Discovering Interactions… 25 Several studies have searched the Perlegen and HapMap datasets for signatures of selection using nucleotide diversity or similar measures [30–31]. While these studies have concentrated on SNP diversity, LD-based measures may also be used to search for positiveselection signatures [32–33]. Our results verify that LD-based approaches can be used to identify regions with the highest variation and are a powerful means of detecting active selection prior to allelic fixation or selection acting on existing genetic variation [12, 34]. Confirmation of these findings requires further study involving more ethnic groups, such as a Negroid population, to analyze the associations between SNP alleles at multiple loci and racial differences in skin color. Clarifying these associations will not only elucidate an interesting physiological trait, but may also provide a model or test system for gene discovery in other polygenic traits (such as complex diseases) that have greater environmental sources of variation [6]. There is a clear justification for adopting an evolutionary approach to exploring the genetics of human pigmentation. Such studies have already revealed the trait to have a highly dynamic and complex evolutionary past and have pointed to the molecular mechanisms underlying phenotypic variability [6]. This was demonstrated most recently by the identification of the selection signatures of the functionally important SLC24A5 and POMC genes [35–36]. The identification and analysis of additional genes involved in human skin pigmentation, along with functional characterization of the allelic variants at the candidate loci presented here, will help to clarify the nature and extent of skin pigmentation adaptation in human populations [4, 12].

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[9] Naysmith, L; Waterston, K; Ha, T; Flanagan, N; Bisset, Y; Ray, A; Wakamatsu, K; Ito, S; Rees, JL. Quantitative measures of the effect of the melanocortin 1 receptor on human pigmentary status. J Invest Dermatol. 2004; 122(2): 423-428. [10] Ancans, J; Flanagan, N; Hoogduijn, MJ; Thody, AJ. P-locus is a target for the melanogenic effects of MC-1R signaling: a possible control point for facultative pigmentation. Ann N Y Acad Sci. 2003; 994: 373-377. [11] Rees, JL. Genetics of hair and skin color. Annu Rev Genet. 2003; 37: 67-90. [12] Anno, S; Abe, T; Yamamoto, T. Interactions between SNP Alleles at Multiple Loci Contribute to Skin Color Differences between Caucasoid and Mongoloid Subjects. Int J Biol Sci. 2008; 4: 81-86. [13] Tadokoro, T; Yamaguchi, Y; Batzer, J; Coelho, SG; Zmudzka, BZ; Miller, SA; Wolber, R; Beer, JZ; Hearing, VJ. Mechanisms of Skin Tanning in Different Racial/Ethnic Groups in Response to Ultraviolet Radiation. J Invest Dermatol. 2005; 124: 1326-1332. [14] Bonilla, C; Shriver, MD; Parra, EJ; Jones, A; Fernández, JR. Ancestral proportions and their association with skin pigmentation and bone mineral density in Puerto Rican women from New York city. Hum Genet. 2004; 115: 57-68. [15] Shriver, MD; Parra, EJ; Dios, S; Bonilla, C; Norton, H; Jovel, C; Pfaff, C; Jones, C; Massac, A; Cameron, N; Baron, A; Jackson, T; Argyropoulos, G; Jin, L; Hoggart, CJ; McKeigue, PM; Kittles, RA. Skin pigmentation, biogeographical ancestry, and admixture mapping. Hum Genet. 2003; 112: 387-399. [16] Hoggart, CJ; Parra, EJ; Shriver, MD; Bonilla, C; Kittles, RA; Clayton, DG; McKeigue, PM. Control of confounding of genetic associations in stratified populations. Am J Hum Genet. 2003; 72: 1492-1504. [17] Sturm, RA; Teasdale, RD; Box, NF. Human pigmentation genes: identification, structure and consequences of polymorphic variation. Gene. 2001; 277: 49-62. [18] [Internet] National Library of Medicine: Searchable NCBI site for Single Nucleotide Polymorphisms. http://www.ncbi.nlm.nih.gov/projects/SNP/ [19] Kokoris, M; Dix, K; Moynihan, K; Mathis, J; Erwin, B; Grass, P; Hines, B; Duesterhoeft, A. High-throughput SNP genotyping with the Masscode system. Mol Diagn. 2000; 5(4): 329-340. [20] Ogata, K; Ikeda, S; Ando, E. QIAGEN Genomics Inc. A study of SNP genotyping using Masscode™ technology. Shimadzu Hyoka. 2002; 58(3/4): 125-129 [In Japanese]. [21] Zhao, J; Jin, L; Xiong, M. Test for interaction between two unlinked loci. Am J Hum Genet. 2006; 79(5): 831-845. [22] Jorde, LB. Linkage Disequilibrium and the Search for Complex Disease Genes, Genome Res. 2000; 10: 1435-1444. [23] Pritchard, JK; Przeworski, M. Linkage Disequilibrium in Humans: Models and Data, Am J Hum Genet. 2001; 69:1-14. [24] Lewontin, RC. The interaction of selection and linkage.I. General considerations; heterotic models. Genetics. 1964; 49: 49-67. [25] Terwilliger, J; Ott, J. Handbook of Human Genetic Linkage. Johns Hopkins University Press, Baltimore. 1994. [26] Barrett, JC; Fry, B; Maller, J; Daly, MJ. Haploview: analysis and visualization of LD and haplotype maps, Bioinformatics. 2005; 21: 263-265. [27] Warnes, G; Leisch, F. Genetics: Population genetics [computerprogram]. R package version 1.2.0. 2005. Available: http://cran.r-project.org/src/contrib/PACKAGES.html.

A Linkage Disequilibrium-Based Statistical Approach to Discovering Interactions… 27 [28] Libby, RT; Lillo, C; Kitamoto, J; Williams, DS; Steel, KP. Myosin Va is required for normal photoreceptor synaptic activity. J Cell Sci. 2004; 117: 4509-4515. [29] Stephens, JC; Schneider, JA; Tanguay, DA; Choi, J; Acharya, T; Stanley, SE; Jiang, R; Messer, CJ; Chew, A; Han, JH; Duan, J; Carr, JL; Lee, MS; Koshy, B; Kumar, AM; Zhang, G; Newell, WR; Windemuth, A; Xu, C; Kalbfleisch, TS; Shaner, SL; Arnold, K; Schulz, V; Drysdale, CM; Nandabalan, K; Judson, RS; Ruano, G; Vovis, GF. Haplotype variation and linkage disequilibrium in 313 human genes. Science. 2001; 293: 489-493. [30] Eberle, MA; Rieder1, MJ; Kruglyak, L; Nickerson, DA. Allele Frequency Matching Between SNPs Reveals an Excess of Linkage Disequilibrium in Genic Regions of the Human Genome. PLoS Genetics. 2006; 2: e142. [31] Nielsen, R; Williamson, S; Kim, Y; Hubisz, MJ; Clark, AG; Bustamante, C. Genomic scans for selective sweeps using SNP data. Genome Res. 2005; 15: 1566–1575. [32] Voight, BF; Kudaravalli, S; Wen, X; Pritchard, JK. A map of recent positive selection in the human genome. PLoS Biol. 2006; 4: e72. [33] Sabeti, PC; Reich, DE; Higgins. JM; Levine, HZ; Richter, DJ; Schaffner, SF; Gabriel, SB; Platko, JV; Patterson, NJ; McDonald, GJ; Ackerman, HC; Campbell, SJ; Altshuler, D; Cooper, R; Kwiatkowski, D; Ward, R; Lander, ES. Detecting recent positive selection in the human genome from haplotype structure. Nature. 2002; 419: 832–837. [34] Przeworski, M; Coop, G; Wall, JD. The signature of positive selection on standing genetic variation. Evol Int J Org Evol. 2005; 59: 2312–2323. [35] Lamason, RL; Mohideen, MA; Mest, JR; Wong, AC; Norton, HL; Aros, MC; Jurynec, MJ; Mao, X; Humphreville, VR; Humbert, JE; Sinha, S; Moore, JL; Jagadeeswaran, P; Zhao, W; Ning, G; Makalowska, I; McKeigue, PM; O'donnell, D; Kittles, R; Parra, EJ; Mangini, NJ; Grunwald, DJ; Shriver, MD; Canfield, VA; Cheng, KC. SLC24A5, a putative cation exchanger, affects pigmentation in zebrafish and humans. Science. 2005; 310: 1782-1786. [36] Millington, GWM. Pro-opiomelanocortin (POMC): the cutaneous roles of its melanocortin products and receptors. Clin Exp Dermatol. 2006; 31: 407-412.


ISBN: 978-1-60692-040-4 c 2009 Nova Science Publishers, Inc.

Short Commentary C

S UFFICIENT C ONDITIONS FOR E XACT P ENALTY IN C ONSTRAINED O PTIMIZATION ON C OMPLETE M ETRIC S PACES Alexander J. Zaslavski∗ Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel

Abstract In this paper we use the penalty approach in order to study two constrained minimization problems on complete metric spaces. A penalty function is said to have the generalized exact penalty property if there is a penalty coefficient for which approximate solutions of the unconstrained penalized problem are close enough to approximate solutions of the corresponding constrained problem. In this paper we establish sufficient conditions for the generalized exact penalty property.

1.

Introduction

Penalty methods are an important and useful tool in constrained optimization. See, for example, [1-4, 6-11] and the references mentioned there. The notion of exact penalization was introduced by Eremin [6] and Zangwill [7] for use in the development of algorithms for nonlinear constrained optimization. Since that time exact penalty functions have continued to play a key role in the theory of mathematical programming. For discussions and various applications of exact penalization to various constrained optimization problems see [1, 2, 4]. In this paper we use the penalty approach in order to study constrained minimization problems with lower semicontinuous constraints in complete metric spaces. A penalty function is said to have the exact penalty property [1, 2, 4] if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem. We study two constrained minimization problems with lower ∗

E-mail address: [email protected]

30

Alexander J. Zaslavski

semicontinuous objective functions. The first problem is an equality-constrained problem in a complete metric space with a lower semicontinuous constraint function and the second problem is an inequality-constrained problem in a complete metric space with a lower semicontinuous constraint function. In [8] we considered these two problems in a Banach space with locally Lipschitzian constraint and objective functions and established a very simple sufficient condition for the exact penalty property. In particular, the problem f (x) → min subject to g(x) = c possesses the exact penalty if the real number c is not a critical value of the function g. In other words the set g −1 (c) does not contain a critical point of the function g. Usually the exact penalty property is related to calmness of the perturbed constraint function. In [8-11] and here we use assumptions of the different nature which is not difficult to verify. Note that in [8] we used the following notion of a critical point of a Lipschitzian function: A point z is a critical point of the function g if 0 ∈ ∂g(z) where ∂g(z) is Clarke’s generalized gradient of g at z [3]. In [11] we extended the results of [8] to the equality-constrained problem and the inequality-constrained problem in an arbitrary complete metric space with locally Lipschtz constraint and objective functions. In the present paper we extent the results of [11] to the equality-constrained problem and the inequality-constrained problem in a complete metric space with lower semicontinuous constraint and objective functions assuming that all closed bounded subsets of the complete metric space are compact. We use the convention that ∞ + c = ∞ for any real number c and that the sum over an empty set is zero. Let (X, ρ) be a metric space. Assume that U is a nonempty open subset of X. A function f : U → R1 is called Lipschitzian if there exists c > 0 such that |f (x1 ) − f (x2)| ≤ cρ(x1, x2) for each x1, x2 ∈ U. In order to study our minimization problems we need the notion a critical point of a Lipschitz function introduced in [11]. Let a function f : U → R1 be Lipschitzian. For each x ∈ U define Ξf (x) = lim sup[ lim inf (f (z) − f (y))(ρ(z, y))−1] y→x

z→y,z6=y

(1.1)

[11]. Clearly, Ξf (x) is well-defined for all x ∈ U . A point x ∈ U is called a critical point of f if Ξf (x) ≥ 0 [11]. A real number c ∈ R1 is called a critical value of f on U if there is a critical point x ∈ U of f such that f (x) = c [11]. For each x ∈ X and each r > 0 set B(x, r) = {y ∈ X : ρ(x, y) ≤ r}.

(1.2)

A set D ⊂ X is called bounded if there exist x ∈ X and r > 0 such that D ⊂ B(x, r). In [11, Proposition 1.1] it was pointed out that the following proposition holds. Proposition 1.1 A point x ∈ U is a critical point of f if and only if there exist a ∞ sequence {xk }∞ k=1 ⊂ U and a sequence {rk }k=1 ⊂ (0, 1) such that ρ(xk , x) → 0 as

Sufficient Conditions for Exact Penalty in Constrained Optimization...

31

k → ∞ and that for each integer k ≥ 1, B(xk , rk ) ⊂ U and f (z) ≥ f (xk ) − ρ(z, xk )k−1 for all z ∈ B(xk , rk ). In view of the definition (1.1) the following proposition holds. Proposition 1.2 [11, Proposition 1.2] Let x ∈ U , {xi }∞ i=1 ⊂ U and let lim ρ(xi, x) = 0.

i→∞

Then Ξf (x) ≥ lim supi→∞ Ξf (xi ). Corollary 1.1 [11, Corollary 1.1] Let x ∈ U , {xi }∞ i=1 ⊂ U , limi→∞ ρ(xi , x) = 0 and let lim sup Ξf (xi ) ≥ 0. i→∞

Then x is a critical point of f . The analog of the notion of a critical point of f introduced above were used in [8] in the case when X is a Banach space. Now we compare the notion of a critical point introduced above and the notion of a critical point used in [8] when X is a Banach space. Assume that (X, ||·||) is a Banach space, (X ∗, ||·||∗) is its dual space and that ρ(x, y) = ||x − y||, x, y ∈ X. Let f : U → R1 be a Lipschitzian function defined on a nonempty open subset U of X. For each x ∈ U let f 0 (x, h) = lim sup [f (y + th) − f (y)]/t, h ∈ X t→0+ ,y→x

be the Clarke generalized derivative of f at the point x [3], let ∂f (x) = {l ∈ X ∗ : f 0 (x, h) ≥ l(h) for all h ∈ X} be Clarke’s generalized gradient of f at x [3] and set ˜ f (x) = inf{f 0 (x, h) : h ∈ X and ||h|| = 1} Ξ [8]. ˜ f (x) ≥ Ξf (x). Proposition 1.3 [11, Proposition 1.3] For each x ∈ U , Ξ ˜ f (x) ≥ 0 and that a real number c is In [8] we say that x ∈ U is a critical point of f if Ξ a critical value of f if there is a critical point x ∈ U of f such that f (x) = c. Proposition 1.3 implies that if x ∈ U is a critical point of f according to the definition given in this paper, then x is also a critical point of f in the sense of the definition given in [8]. Proposition 1.3 also implies that if c ∈ R1 is a critical value of f according to the definition given in this paper, then c is also a critical value of f in the sense of the definition given in [8].

32

2.


The main results

Let (X, ρ) be a complete metric space. For each function f : X → R1 ∪ {∞} and each nonempty set A ⊂ X put inf(f ) = {f (z) : z ∈ X} and inf(f ; A) = inf{f (z) : z ∈ A}. For each x ∈ X and each B ⊂ X put ρ(x, B) = inf{ρ(x, y) : y ∈ B}. We assume that any nonempty closed bounded subset of (X, ρ) is compact. Fix θ ∈ X. Let g : X → R1 ∪ {∞} be a lower semicontinuous function, c ∈ R1 and let f : X → R1 ∪{∞} be a lower semicontinuous bounded from below function which is not identically ∞ and such that (2.1) lim f (x) = ∞. ρ(x,θ)→∞

We consider the equality-constrained minimization problem f (x) → min, g −1 (c)

(Pe )

such that g −1 (c) 6= ∅ and g is finite-valued and continuous function and the inequalityconstrained minimization problem f (x) → min, x ∈ g −1 ((−∞, c])

(Pi )

such that g −1 ((−∞, c]) 6= ∅. With these two problems we associate the corresponding families of unconstrained minimization problems f (x) + λ|g(x) − c| → min, x ∈ X (Pe,λ) and f (x) + λ max{g(x) − c, 0} → min, x ∈ X

(Pi,λ)

where λ > 0. The following two theorems which are proved in Section 3 are the main results of the paper. Theorem 2.1 Assume that g −1 (c) 6= ∅, the function g is finite-valued and continuous, inf(f ; g −1(c)) < ∞ and that the following assumptions hold: (A1) for each x ∈ g −1 (c) satisfying f (x) = inf(f ; g −1(c)) there is ∆x > 0 such that the restrictions of the functions f and g to the ball B(x, ∆x) are finite-valued and Lipschitz; (A2) if x ∈ g −1 (c) satisfies f (x) = inf(f ; g −1(c)), then x is not a critical point of the function g and is not a critical point of the function −g.


33

Then there exists Λ > 0 such that for each > 0 there exists δ ∈ (0, ) such that the following assertion holds. If λ ≥ Λ and if x ∈ X satisfies f (x) + λ|g(x) − c| ≤ inf{f (z) + λ|g(z) − c| : z ∈ X} + δ, then there is y ∈ g −1(c) such that ρ(x, y) ≤ and f (y) ≤ inf(f ; g −1(c)) + δ. Theorem 2.2 Assume that g −1 ((−∞, c]) 6= ∅, inf(f ; g −1((−∞, c])) < ∞ and that the following assumptions hold: (A3) for each x ∈ g −1((−∞, c]) satisfying f (x) = inf(f ; g −1((−∞, c])) there is ∆x > 0 such that the restrictions of the functions f and g to the ball B(x, ∆x ) are finitevalued and Lipschitz; (A4) if x ∈ g −1 ((−∞, c]) satisfies f (x) = inf(f ; g −1((−∞, c])), then x is not a critical point of the function g. Then there exists Λ > 0 such that for each > 0 there exists δ ∈ (0, ) such that the following assertion holds. If λ ≥ Λ and if x ∈ X satisfies f (x) + λ max{g(x) − c, 0} ≤ inf{f (z) + λ max{g(z) − c, 0} : z ∈ X} + δ then there is y ∈ g −1((−∞, c]) such that ρ(x, y) ≤ and f (y) ≤ inf(f ; g −1((−∞, c])) + δ. Theorems 2.1 and 2.2 imply the following result. Theorem 2.3 1. Assume that g −1(c) 6= ∅, the function g is finite-valued and continuous, inf(f ; g −1(c)) < ∞ and that the assumptions (A1) and (A2)hold. Then there exists Λ > 0 such that for each λ ≥ Λ and each sequence {xi }∞ i=1 ⊂ X which satisfies lim [f (xi) + λ|g(xi) − c|} = inf{f (z) + λ|g(z) − c| : z ∈ X}

i→∞

−1 there exists a sequence {yi }∞ i=1 ⊂ g (c) such that

lim f (yi ) = inf(f ; g −1(c)), lim ρ(yi , xi) = 0.

i→∞

i→∞

2. Assume that g −1 ((−∞, c]) 6= ∅, inf(f ; g −1((−∞, c])) < ∞

34


and that the assumptions (A3) and (A4) hold. Then there exists Λ > 0 such that for each λ ≥ Λ and each sequence {xi }∞ i=1 ⊂ X which satisfies lim [f (xi) + λ max{g(xi) − c, 0})] = inf{f (z) + λ max{g(z) − c, 0} : z ∈ X}

i→∞

−1 there exists a sequence {yi }∞ i=1 ⊂ g ((−∞, c]) such that

lim f (yi ) = inf(f ; g −1((−∞, c])), lim ρ(yi , xi) = 0.

i→∞

3.

i→∞

Proofs of Theorems 2.1 and 2.2

We prove Theorems 2.1 and 2.2 simultaneously. Put A = g −1(c)

(3.1)

A = g −1((−∞, c])

(3.2)

in the case of Theorem 2.1 and

in the case of Theorem 2.2. Clearly, A is a nonempty closed set. For λ > 0 put ψλ (x) = f (x) + λ|g(x) − c|, x ∈ X

(3.3)

in the case of Theorem 2.1 and ψλ (x) = f (x) + λ max{g(x) − c, 0}, x ∈ X

(3.4)

in the case of Theorem 2.2. Clearly, for any λ > 0, ψλ : X → R1 ∪ {∞} is a lower semicontinuous bounded from below function such that inf(ψλ) < ∞. We show that there exists positive number Λ such that the following property holds: (P1) for each > 0 there exists δ ∈ (0, ) such that for each λ ≥ Λ and each x ∈ X satisfying ψλ(x) ≤ inf(ψλ) + δ there is y ∈ A ∩ B(x, ) such that ψλ (y) ≤ ψλ (x). It is not difficult to see that the existence of a positive number Λ for which (P1) holds implies the validity of Theorems 2.1 and 2.2. Let us assume that there is no positive number Λ such that (P1) holds. Then for each natural number k there exist k ∈ (0, 1), λk ≥ k, xk ∈ X

(3.5)

ψλk (xk ) ≤ inf(ψλk ) + 2−1 k k−2 ,

(3.6)

such that

Sufficient Conditions for Exact Penalty in Constrained Optimization... {z ∈ A ∩ B(xk , k ) : ψλk (z) ≤ ψλk (xk )} = ∅.

35 (3.7)

Let k be a natural number. It follows from (3.6) and Ekeland’s variational principle [5] that there is yk ∈ X such that (3.8) ψλk (yk ) ≤ ψλk (xk ), ρ(yk , xk ) ≤ (2k)−1k ,

(3.9)

ψλk (yk ) ≤ ψλk (z) + k−1 ρ(z, yk ) for all z ∈ X.

(3.10)

By (3.7), (3.8) and (3.9), yk 6∈ A for all natural numbers k.

(3.11)

In the case of Theorem 2.2 it follows from (3.2) and (3.11) that g(yk ) > c for all natural numbers k.

(3.12)

In the case of Theorem 2.1 it follows from (3.2) and (3.11) that for any natural numbers k, either g(yk ) > ck or g(yk ) < ck . Extracting a subsequence and re-indexing and replacing g by −g and c by −c if necessary we may assume without loss of generality that (3.12) holds for all natural numbers k in the case of Theorem 2.1 two. By (3.3), (3.4), (3.5), (3.6) and (3.8) for all natural numbers k, f (yk ) ≤ ψλk (yk ) ≤ ψλk (xk ) ≤ inf(ψλk ) + 2−1 k k−2 ≤ inf(f ; A) + 2−1 k−2 .

(3.13)

In view of (3.13) and (2.1) the sequence {yk }∞ k=1 is bounded. Extracting a subsequence and re-indexing we may assume without loss of generality that there exists y∗ = lim yk in (X, ρ). k→∞

(3.14)

Let us show that y∗ ∈ A. By (3.12), (3.3), (3.4), (3.8), (3.13), (3.5) and (3.6) for each integer k ≥ 1 0 < λk (g(yk ) − c) = ψλk (yk ) − f (yk ) ≤ ψλk (yk ) − inf(f ) ≤ ψλk (xk ) − inf(f ) ≤ inf(ψλk ) + 1 − inf(f ) ≤ inf(f ; A) + 1 − inf(f ). Together with (3.5) this implies that lim |g(yk ) − c| = 0.

k→∞

(3.15)

Relations (3.15), (3.14), (3.1) and (3.2) imply that y∗ ∈ A. In view of (3.13) and (3.14) f (y∗ ) ≤ inf(f ; A).

(3.16)

36


Combined with (3.16) this implies that f (y∗ ) = inf(f ; A).

(3.17)

By (3.16), (3.17), (3.1), (3.2), (A1) and (A3) there is ∆ > 0 such that the restrictions of f and g to B(y∗ , ∆) are finite-valued and Lipschitz. Thus there is L0 > 1 such that |f (y1) − f (y2 )|, |g(y1) − g(y2)| ≤ L0 ρ(y1, y2) for all y1 , y2 ∈ B(y∗ , ∆).

(3.18)

By (3.14) there is a natural number k0 such that ρ(y∗, yk ) < ∆/2 for all integers k ≥ k0.

(3.19)

Let k ≥ k0 be an integer. In view of (3.18) and (3.19) there is a number ∆1 ∈ (0, ∆/4)

(3.20)

g(z) > c for all z ∈ B(yk , ∆1).

(3.21)

such that

It follows from (3.10), (3.8), (3.6), (3.3), (3.4), (3.21), (3.20), (3.19), (3.18) and (3.5) that for each z ∈ B(yk , ∆1), −k−1 ρ(z, yk ) ≤ ψλk (z) − ψλk (yk ) = f (z) − f (yk ) + λk (g(z) − g(yk )) and −1 −1 g(z) − g(yk ) ≥ −λ−1 k k ρ(z, yk ) + λk (f (yk ) − f (z))

≥ −k−2 ρ(z, yk ) − k−1 L0 ρ(z, yk ). Combined with (1.1) this implies that Ξg (yk ) ≥ −k−2 + k−1 L0 . This implies that lim inf Ξg (yk ) ≥ 0. k→∞

(3.22)

By (3.22), (3.14), (3.18) and Proposition 1.2 Ξg (y∗) ≥ 0.

(3.23)

Relations (3.16), (3.17), (3.23), (3.1) and (3.2) contradict (A2) in the case of Theorem 2.1 and contradict (A4) in the case of Theorem 2.2. The contradiction we have reached proves that there exists Λ > 0 such that (P1) holds. This completes the proofs of Theorems 2.1 and 2.2.


37

References [1] D. Boukari and A.V. Fiacco, Survey of penalty, exact-penalty and multiplier methods from 1968 to 1993, Optimization 32, 301-334 (1995). [2] J. V.Burke, An exact penalization viewpoint of constrained optimization, SIAM J. Control Optim. 29, 968-998 (1991). [3] F. H. Clarke, Optimization and Nonsmooth Analysis , Willey Interscience (1983). [4] G. Di Pillo and L. Grippo, Exact penalty functions in constrained optimization, SIAM J. Control Optim. 27, 1333-1360 (1989). [5] I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47, 324-353 (1974). [6] I. I. Eremin, The penalty method in convex programming, Soviet Math. Dokl. 8, 459462 (1966). [7] W. I. Zangwill, Nonlinear programming via penalty functions, Management Sci. 13, 344-358 (1967). [8] A. J. Zaslavski, A sufficient condition for exact penalty in constrained optimization, SIAM Journal on Optimization 16, 250-262 (2005). [9] A. J. Zaslavski, Existence of exact penalty for optimization problems with mixed constraints in Banach spaces, J. Math. Anal. Appl. 324, 669-681 (2006). [10] A. J. Zaslavski, Existence of exact penalty for constrained optimization problems in Hilbert spaces, Nonlinear Analysis 67, 238-248 (2007). [11] A. J. Zaslavski, Existence of exact penalty for constrained optimization problems in metric spaces, Set-Valued Analysis 15, 223-237 (2007).



Short Commentary D

HOW TO CREATE A COMPUTATIONAL MEDICINE STUDY Viroj Wiwanitkit Wiwanitkit House, Bangkok Thailand 10160; Visiting professor Hainan Medical College China

Abstract With the advent of computational research, several applications in science can be seen. The application in medicine is also documented. Computational medicine study can help answer a complicated query in medicine within a short period. How to create a computational medicine study is a common question from the beginner. In this article, the author will describe the steps for creating computational medicine research. Briefly, a simple process as that for simple in vivo and in vitro research can be used. The setting up of a conceptional framework based on literature review is the first necessary step. Next, selection of the proper database and tool for manipulation is needed. Simulating based on the designed framework can help one reach the answer. These steps must be thoroughly followed to complete computational medicine research.

Introduction With the advent of computational research, several applications in science can be seen. The application in medicine is also documented. The expectations of computational biology to command a leading role in drug discovery and disease characterization is a present focus [1, 2]. Computational medicine study can help answer a complicated query in medicine within a short period. These forces have moved much of life sciences research almost completely into the computational domain [2]. How to create a computational medicine study is a common question from the beginner. Importantly, educational training in computational medicine has been limited to students enrolled in the life sciences curricula, yet much of the skills needed to succeed in biomedical informatics involve or augment training in information technology curricula [2]. In this article, the author will describe the steps for creating computational medicine research.

40

Viroj Wiwanitkit

Research Design: The First Step It is accepted that science is based on evidence. Proof or verification is necessary in science. Although computational biology is a new science, it still follows the basic scientific principle of other sciences. Briefly, a simple process as that for simple in vivo and in vitro research can be used. Setting up the question has to be the primary step before beginning any other activities. How to set up a good question is a hard step for any beginner. The best way is to base the question on collected evidence. There are many ways to collect evidence, such as the following: 1. Primary data collection: This is the primary way, with the data personally collected by the researcher conducting the scientific project. The collection may be obtained via survey or by several techniques. However, the main pitfall of this technique is its time-consuming nature. It requires a lot of time to collect all data that are statistically satisfied for further implementation. 2. Secondary data collection: This is a faster way. This makes use of others’ work as a baseline for the generation of ideas. However, there is a main problem with this technique: the reliability of the data source. The verification of the primary data in the literature has to be done before further generalization into the study question. Nevertheless, this technique is presently widely used due to its convenience. The setting up of a conceptional framework based on literature review is the first necessary step. There are several tools for a literature search, but the two most famous databases are PubMed (www.pubmed.com) and Scopus (www.scopus.com). PubMed was developed by the National Center for Biotechnology Information (NCBI) at the National Library of Medicine (NLM), located at the U.S. National Institutes of Health (NIH). It provides access to citations from biomedical literature. Scopus is a newer database. This database covers more literature than PubMed. It covers both medical and non-medical journals. After searching the data and getting the complete necessary documents, one can set up the research question. The conceptual framework must be set because it will be the guideline for further processes. If there is no clear concept, the research might be run in the wrong way. The definition of the study must be clearly defined. It is a requirement to know what you will do in the future before you actually do it. The design of computational medicine research can be either prospective or retrospective. For the retrospective ones, data mining is the best example. For the prospective ones, computation prediction is the best example.

Database and Tool for Manipulation After the research question and conceptual framework have been set up completely, the next step is to select the equipment as armor to conquer or to reach the research question. Unlike in vivo or in vitro studies, the in silico computational medicine research makes use of the computer as equipment. Based on mathematical principles, computers are developed and become necessary tools for present scientific research. In computational medicine, the role of the computer is very great. There are two main groups of computer facilities for

How to Create a Computational Medicine Study

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computational medicine research. First is the database, which is the collection of data that is required for further analysis. Second is the tool, which is any interactive computational program that can be used for mathematical prediction or the simulating of input data or phenomena. There are a number of available databases at present. Some are publicly accessible; others are private. The usage of a public database in medicine can enhance the quality and effectiveness of patient care and the health of the public. Renschler said that publications could be retrieved and downloaded anywhere and any time with the introduction of electronic publishing and full text databases becoming available [3]. In addition, study groups for practice-based learning can prepare themselves for discussions of their problems or of simulated cases systematically provided by central organizations with experts using information technology [3]. Renschler also mentioned that a pilot study showed great interest in the application of information technology: 80% of the responding colleagues showed interest in occasional or regular use of medical or non-medical full text databases, preferably using their own computers [3]. However, Keller noted that the variations of medical practice of private doctors could be due to a difference in data they received from public databases [4]. Therefore, it is necessary to learn and know many databases in order to choose the best selection. Some examples will be further described. 1. Swiss-Prot protein knowledgebase [5] The Swiss-Prot protein knowledgebase (http://www.expasy.org/sprot/ and http://www.ebi.ac.uk/swissprot/) connects amino acid sequences with the current knowledge in the Life Sciences [5, 6]. Each protein entry provides an interdisciplinary overview of relevant information by bringing together experimental results, computed features and sometimes even contradictory conclusions [5, 6]. The Swiss-Prot protein knowledgebase provides manually annotated entries for all species, but concentrates on the annotation of entries from model organisms to ensure the presence of high quality annotation of representative members of all protein families [5]. The Expert Protein Analysis System (ExPASy) Web site might help to identify and reveal the function of proteins [5]. 2. UniProt [7, 8] UniProt provides a comprehensive, fully classified, richly and accurately annotated protein sequence knowledgebase, with extensive cross-references and query interfaces [7, 8]. The central database will have two sections, corresponding to the familiar Swiss-Prot (fully manually-curated entries) and TrEMBL (enriched with automated classification, annotation and extensive cross-references) [7, 8]. For convenient sequence searches, UniProt also provides several non-redundant sequence databases [7, 8]. The UniProt NREF (UniRef) databases provide representative subsets of the knowledgebase suitable for efficient searching. The comprehensive UniProt Archive (UniParc) is updated daily from many public source databases. The UniProt databases can be accessed online (http://www.uniprot.org) [7, 8]. 3. Gene Ontology Annotation Database [9] The Gene Ontology Annotation (GOA) database (http://www.ebi.ac.uk/GOA) aims to provide high-quality electronic and manual annotations to the UniProt Knowledgebase

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Viroj Wiwanitkit (Swiss-Prot, TrEMBL and PIR-PSD) using the standardized vocabulary of the Gene Ontology (GO) [9]. As a supplementary archive of GO annotation, GOA promotes a high level of integration of the knowledge represented in UniProt with other databases [9]. GOA provides annotated entries for nearly 60,000 species (GOA-SPTr) and is the largest and most comprehensive open-source contributor of annotations to the GO Consortium annotation effort [9].

There are also many useful tools for computational medicine research. Some of the most widely used tools will be hereby presented. 1. Pegasys [10] This tool includes numerous tools for pair-wise and multiple sequence alignment, ab initio gene prediction, RNA gene detection, masking repetitive sequences in genomic DNA as well as filters for database formatting and processing raw output from various analysis tools [10]. It enables biologists and bioinformaticians to create and manage sequence analysis workflows [10]. 2. GeneViTo [11] This tool is a JAVA-based computer application that serves as a workbench for genome-wide analysis through visual interaction [11]. The application deals with various experimental information concerning both DNA and protein sequences (derived from public sequence databases or proprietary data sources) and meta-data obtained by various prediction algorithms, classification schemes or user-defined features. Interaction with a Graphical User Interface (GUI) allows easy extraction of genomic and proteomic data referring to the sequence itself, sequence features, or general structural and functional features [11]. 3. BioBuilder [12] This tool is a Zope-based software tool that was developed to facilitate intuitive creation of protein databases [12]. Protein data can be entered and annotated through web forms along with the flexibility to add customized annotation features to protein entries [12]. A built-in review system permits a global team of scientists to coordinate their annotation efforts [12]. 4. DBParser [13] This tool is for rapidly culling, merging, and comparing sequence search engine results from multiple LC-MS/MS peptide analyses [13]. It employs the principle of parsimony to consolidate redundant protein assignments and derive the most concise set of proteins consistent with all of the assigned peptide sequences observed in an experiment or series of experiments [13]. 5. UniHI [14] UniHI provides researchers with a flexible integrated tool for finding and using comprehensive information about the human interactome [14]. UniHI is available at http://www.mdc-berlin.de/unihi [14]. At present, it is based on 10 major interaction maps


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derived by computational and experimental methods. It includes more than 150,000 distinct interactions between more than 17 000 unique human proteins [14].

Simulation Experiment Simulation is the heart of computational medicine research. There are many kinds of simulating. The main types of simulation experimental medicine are: 1. Interaction Interaction simulation means the simulating focuses on the phenomenon that occurs after the interaction of two molecules. There are several techniques to reach this result. One of the most famous techniques is molecular docking. Docking involves the development of computer algorithms that evaluate the binding modes of putative ligands in receptor sites [15]. This technique can be used for designing combinations between molecules. Over the past year there have been some interesting and significant advances in computer-based ligand-protein docking techniques and related rational drug-design tools, including flexible ligand docking and better estimation of binding free energies and solvation energies [16]. There are many techniques for molecular docking. An interesting computational molecular technique is PatchDock [17], which can be used for modeling the recombination. PatchDock is a computational molecular technique for molecular docking based on shape complementarity principles [17]. The input is two molecules of any type: proteins, DNA, peptides, drugs [17]. The output or result can be further processed to be in the format of three-dimension (3D) molecular structure through the Swiss PDB Viewer (GlaxoSmithKline R&D & the Swiss Institute of Bioinformatics). The property as well as geometry of the derived complex can also be studied by the Swiss PDB Viewer. Another interesting technique is pathway mapping. This technique is according to systomics and systemic biology. This makes use of pathway identification and creation of the new overall summative pathway. 2. Mutation Mutation simulation means the simulating focuses on the phenomenon that occurs after changes, either minor increases or decreases, within molecules. The basic mutating is based on the knowledge of the coding for nucleic acids and amino acids. Simulating manipulation on the wild type codes can be easily performed and the mutant can be further used. Here are several techniques to reach this result. One of the most famous techniques is ontology. Gene ontology is the new “logy” for this purpose. Gene ontology is a scientific term used to describe the biology of a gene product in any organism. It also describes the molecular functions of gene products, the corresponding placement in and as cellular components, and the participation in biological processes [18]. Since much of biology works by applying prior knowledge to an unknown entity, the application of a set of axioms that will elicit knowledge and the complex biological data stored in bioinformatics databases are necessary [19]. These often require added knowledge to specify and constrain the values held in that database, and a way of capturing knowledge within bioinformatics applications and databases is through the use of ontologies [19]. At the beginning of this century, the Gene Ontology (GO) Consortium was founded. The

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Viroj Wiwanitkit aim of the GO Consortium is to provide a framework for both the description and the organization of such information [20].

References [1] [2] [3] [4] [5]

[6]

[7]

[8]

[9]

[10]

[11] [12]

[13]

Pons T, Montero LA, Febles JP. Computational biology in Cuba: an opportunity to promote science in a developing country. PLoS Comput Biol. 2007 Nov;3(11):e227. Kane MD, Brewer JL.An information technology emphasis in biomedical informatics education.J Biomed Inform. 2007 Feb;40(1):67-72. Renschler HE. Rational continuing medical education. Schweiz. Rundsch. Med. Prax. 1991;(19):515-23. Keller RB. Public data and private doctors: Maine tackles treatment variations. J. State Gov 1991; 64(3):83-6. Schneider M, Tognolli M, Bairoch A. The Swiss-Prot protein knowledgebase and ExPASy: providing the plant community with high quality proteomic data and tools. Plant Physiol Biochem. 2004 Dec;42(12):1013-21. Boeckmann B, Bairoch A, Apweiler R, Blatter MC, Estreicher A, Gasteiger E, Martin MJ, Michoud K, O'Donovan C, Phan I, Pilbout S, Schneider M. The SWISS-PROT protein knowledgebase and its supplement TrEMBL in 2003. Nucleic Acids Res. 2003 Jan 1;31(1):365-70. Apweiler R, Bairoch A, Wu CH, Barker WC, Boeckmann B, Ferro S, Gasteiger E, Huang H, Lopez R, Magrane M, Martin MJ, Natale DA, O'Donovan C, Redaschi N, Yeh LS. UniProt: the Universal Protein knowledgebase. Nucleic Acids Res. 2004 Jan 1;32(Database issue):D115-9. Bairoch A, Apweiler R, Wu CH, Barker WC, Boeckmann B, Ferro S, Gasteiger E, Huang H, Lopez R, Magrane M, Martin MJ, Natale DA, O'Donovan C, Redaschi N, Yeh LS. The Universal Protein Resource (UniProt). Nucleic Acids Res. 2005 Jan 1;33(Database issue):D154-9. Camon E, Magrane M, Barrell D, Lee V, Dimmer E, Maslen J, Binns D, Harte N, Lopez R, Apweiler R. The Gene Ontology Annotation (GOA) Database: sharing knowledge in Uniprot with Gene Ontology. Nucleic Acids Res. 2004 Jan 1;32(Database issue):D262-6. Shah, S.P., He, D.Y., Sawkins, J.N., Druce, J.C., Quon, G., Lett, D., Zheng, G.X., Xu, T., and Ouellette, B.F., 2004, Pegasys: software for executing and integrating analyses of biological sequences. BMC Bioinformatics. 5(1):40. Parkinson J, Anthony A, Wasmuth J, Schmid R, Hedley A, Blaxter M. PartiGene— constructing partial genomes. Bioinformatics. 2004; 20(9):1398-404. Kousthub PS, Deshpande N, Shanker K, Pandey, A. BioBuilder as a database development and functional annotation platform for proteins. BMC Bioinformatics. 2004; 5(1):43. Yang X, Dondeti V, Dezube R, Maynard DM, Geer LY, Epstein J, Chen X, Markey SP, Kowalak JA. DBParser: web-based software for shotgun proteomic data analyses. J. Proteome. Res. 2004; 3(5):1002-8.


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[14] Chaurasia G, Iqbal Y, Hänig C, Herzel H, Wanker EE, Futschik ME. UniHI: an entry gate to the human protein interactome. Nucleic Acids Res. 2007 Jan;35(Database issue):D590-4. [15] Jones G, Willett P. Docking small-molecule ligands into active sites. Curr Opin Biotechnol. 1995 Dec;6(6):652-6. [16] Schneidman-Duhovny D, Inbar Y, Polak V, Shatsky M, Halperin I, Benyamini H, Barzilai A, Dror O, Haspel N, Nussinov R, Wolfson HJ. Taking geometry to its edge: fast unbound rigid (and hinge-bent) docking. Proteins 2003; 52: 107-12. [17] Lybrand TP. Ligand-protein docking and rational drug design. Curr Opin Struct Biol. 1995 Apr;5(2):224-8. [18] Stevens R, Goble CA, Bechhofer S. Ontology-based knowledge representation for bioinformatics. Brief. Bioinform. 2000; 1(4):398-414. [19] Ashburner M, Lewis S. On ontologies for biologists: the Gene Ontology--untangling the web. Novartis Found Symp. 2002; 247:66-80 [20] Takai T, Takagi T. Introduction to gene ontology. Tanpakushitsu Kakusan Koso. 2003; 48(1):79-85.



Short Commentary E

IDENTIFYING RELATED CANCER TYPES C. D. Bajdik1,2, Z. Abanto1, J. J. Spinelli1,2, A. R. Brooks-Wilson1,3,4, and R. P. Gallagher1,2 1

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Cancer Control Research Program, BC Cancer Agency School of Population and Public Health, University of British Columbia 3 Canada’s Michael Smith Genome Science Centre, BC Cancer Agency 4 Department of Medical Genetics, University of British Columbia

Abstract Background: Human cancer is often classified according to the anatomic site at which it occurs, and researchers are often taught these cancer types are actually a spectrum of disease. A review in 2000 (Hanahan and Weinberg; Cell 2000 100:57-70) reported that all cancers share six characteristics: (1) self-sufficiency in growth signaling, (2) the ability to ignore external anti-growth signals, (3) the ability to avoid apoptosis, (4) sustained angiogenesis, (5) the capacity for limitless reproduction and (6) the ability to invade tissue and spread to other anatomic sites. Our goal was to identify related cancer types using different observational strategies. Methods: We employed one method that used text-mining of online information about genes and disease. A second method used medical records of patients in British Columbia who were diagnosed with multiple cancer types between 1970 and 2004. A third method correlated Canadian provincial cancer rates for various cancer types. Results: Several pairs of related cancer types were identified using each method, although no pair was identified by all three strategies. The pairs of cancer types, lung/bladder and lung/kidney, were both identified by the text-mining and correlation studies. Esophageal cancer and melanoma were identified as related cancer types by both the analysis of patients with multiple primary cancers and the correlation study. Discussion: If cancer types are related, patients with one cancer might increase surveillance for other related cancer types, and drugs that are effective for treating one cancer might be successfully adapted for the related cancer types.

Introduction Cancer is often classified according to the site at which it occurs, and different cancer types are sometimes considered a spectrum of disease. This classification system closely corresponds to systems for diagnosing and treating cancer. Stomach cancer is often diagnosed

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C. D. Bajdik, Z. Abanto, J. J. Spinelli et al.

by a gastroenterologist, whereas skin cancer is often diagnosed by a dermatologist. The healthcare professionals, and sometimes entire clinics, that treat and diagnose stomach cancer patients are often different than those who treat and diagnose melanoma. Despite the benefits that come from considering different cancer types as different diseases, there are several things that all cancer types have in common. In their landmark review, Hanahan and Weinberg summarized six characteristics that all cancers share: (1) self-sufficiency in growth signaling, (2) the ability to ignore external anti-growth signals, (3) the ability to avoid apoptosis, (4) sustained angiogenesis, (5) the capacity for limitless reproduction and (6) the ability to invade tissue and spread to other anatomic sites. (Hanahan and Weinberg 2000) We suspect that some cancer types are related in additional ways. The identification of related cancer types could lead to better therapies for treating a cancer based on the success of a therapy for a related cancer type. The identification of related cancers also might lead to improved surveillance strategies in cancer patients and their families. Finally, the identification of related cancer types is expected to provide insight regarding cancer etiology, and therefore might ultimately lead to prevention measures. Our goal was to identify related cancer types using different observational strategies. This paper describes three analyses to identify related cancer types: (Study 1) text-mining information about genetic factors, (Study 2) summarizing medical records observations of people with multiple primary cancers, and (Study 3) correlating cancer rates in nine Canadian provinces.

Methods Cancer types were defined according to the categories specified by the National Cancer Institute of Canada in their 2007 publication of Canadian cancer rates. (CCS/NCIC 2007) The 22 categories are somewhat arbitrary and defined in Table 1. Those categories are based on anatomic sites, and defined using the topology and cell histology codes described by the International Coding of Diseases for Oncology system. (Fritz et al 2000) We excluded the cancer type “liver” because the original versions of Study 1 and Study 2 (described below) did not consider liver cancer. We performed three studies that used different strategies to identify related cancer types. Each study used observational or publicly-accessible data. We provide a list of related cancer pairs that were identified by each study, and compare the results. The methods for each study are briefly described below. Each study used slightly different criteria to determine whether a cancer pair was significant, but we consistently relied on two-sided confidence intervals and p-values, and did not correct for multiple testing. Readers are advised to consult the original publications from each study for further information.

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Table 1. Definitions of 23 cancer types according to anatomic site and cell histology codes of the International Classification of Diseases for Oncology, Third Edition (ICDO3) (Fritz et al 2000). Cancer type definitions are taken from the 2007 National Cancer of Canada summary (NCIC 2007).

* excluding cervix

Study 1: Text-mining Online Mendelian Inheritance in Man (OMIM; www.ncbi.nlm.nih.gov/omim) is a computerized database of information about genes and heritable traits in human populations, based on information reported in the scientific literature. (Hamosh et al 2002) We developed an automated text-mining system for OMIM to identify genetically-related cancers, and

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developed the computer program CGMIM to search for entries in OMIM that are related to one or more cancer types. (Bajdik et al 2005) The software considers all cancer types in Table 1, but did not separate Hodgkin and Non-Hodgkin lymphomas because it is difficult to distinguish them in text-mining analyses. For pairs of cancer types, CGMIM generates a table with rows and columns for each cancer type, and cells containing the number of OMIM gene entries that mention an association with those cancers. If several OMIM entries mention one type of cancer, and several entries mention another type of cancer, then some entries will mention both types of cancer by chance. If the mention of different cancers occurred at random, the expected number of genes in OMIM that mention two specific types of cancer can be estimated as the total number of genes related to cancer, multiplied by the probabilities that an OMIM entry mentions each individual cancer type. The latter probabilities are estimated as the proportion of genes in OMIM that are related to each cancer type. CGMIM results are posted regularly and the source code is available from the BC Cancer Research Centre website (http://www.bccrc.ca/ccr/CGMIM). An approximate two-tailed 95% confidence interval for the ratio of expected number of cases (E) and observed cases (O) is O/E ± (1.96/√E). We defined a pair of cancer types to be significantly-related if the number of observed cases exceeded the number of expected cases, and the confidence interval for their ratio excluded 1. CGMIM results from March 31, 2008 were used to identify pairs of cancer types that are significantly-related for Study 1.

Study 2: Analysis of medical records from patients with multiple primary cancers We considered an analysis of people diagnosed with multiple cancer types in British Columbia, Canada between 1970 and 2004. (Bajdik et al 2006) The analysis used data recorded in the BC Cancer Registry (BCCR) and considered all of the cancer types in Table 1. In people with two or more cancer types, the probability of a specific type was determined as the number of diagnoses for that cancer type divided by the total number of cancer diagnoses. If two types of cancer occur independently of one another, then the probability that someone will develop both cancers by chance is the product of the individual probabilities for each type. The expected number of people with both cancers is the number of people at risk multiplied by the separate probabilities for each cancer. An approximate two-tailed 95% confidence interval for the ratio of expected number of cases (E) and observed cases (O) is O/E ± (1.96/√E). For Study 2, we defined a pair of cancer types to be significantly-related if the number of observed cases exceeded the number of expected cases, and the 95% confidence interval for their ratio excluded 1.

Study 3: Correlation of regional cancer incidence rates We considered correlations between the 2007 Canadian provincial rates for the incidence of various cancer types. The analysis used annual age-standardized incidence rates per 100,000 as reported by the National Cancer Institute of Canada. (CCS/NCIC 2007) Data was reported for 16 female cancer types and 15 male cancer types from Table 1. We did not use reported data from the province of Newfoundland and Labrador because those rates are likely to be

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underestimated. (CCS/NCIC 2007) We did not use the reported prostate cancer incidence rate for the province of Quebec because of the same problem. (CCS/NCIC 2007) In females and males separately, we considered the Pearson correlation for each pair of cancer types. For Study 3, we defined a pair of cancer types to be significantly-related if the Pearson correlation was positive and the 2-tailed p-value was less than 0.05 .

Results Study 1: Text-mining On March 31, 2008, CGMIM identified 2147 genes related to cancer. There were 38 pairs of cancer types with significantly more related genes than would be expected (Table 2). For example, there were 41 genes related to cancer of the esophagus and 138 genes related to cancer of the stomach. Assuming the cancers are independent, about three gene entries in

Table 2. Pairs of cancer types for which there are significantly more related genes as would be expected if the cancer types were independent. Results are based on textmining of genetic information about cancer as reported in Online Mendelian Inheritance in Man (OMIM; www.ncbi.nlm.nih.gov/omim accessed March 31, 2008).

* excluding cervix

OMIM should mention both. In reality, there were 21 gene entries in OMIM that mention both stomach and esophageal cancer, and the seven-fold discrepancy indicates that these cancers types may be genetically related. The order of anatomic sites for each pair reported in

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Table 2, and the order of pairs in Table 2, is an alphabetic one. The “groups” of pairs in the table were used to ease reading, and do not imply the quantity of a site’s mention, the degree of supporting evidence for a related pair, nor the importance of a particular site/pair. Recall that this study did not distinguish Hodgkin and Non-Hodgkin Lymphoma, and could not identify related pairs for males and females separately. A related pair of cancer types identified by this study was that of cancers affecting the ovary and the prostate. It is unlikely that anyone is diagnosed with both of these cancers, but the types might be related through a factor that affects both genders. (E.g., hormone exposure.)

Study 2: Analysis of medical records for patients with multiple primary cancers In the BCCR data, there were records for 28,159 people with records of multiple primary cancers that were diagnosed from 1970 to 2004, including 1,492 people with between three and seven diagnoses. There was only one pair of cancer types that occurred significantly more often than expected among females, and eight pairs of cancer types that occurred significantly more often than expected among males (Table 3). As in the previous table, the order of anatomic sites in each pair and the order of pairs in Table 3 is alphabetic. The order does not imply the degree of supporting evidence for a related pair nor the site’s or pair’s importance. Table 3. Pairs of cancer types among females and males for which there was significantly more people diagnosed with both cancers than expected. Results are based on analysis of people in British Columbia diagnosed with more than one type of primary cancer between 1970 and 2004 (Bajdik et al 2006).

Study 3: Correlation of regional cancer incidence rates The analysis of 2007 cancer incidence rates for Canadian provinces suggested several pairs of related cancer types (Table 4). The analysis indicates two significantly-related pairs of cancer types among females, and nine significantly-related pairs of cancer types among males. In addition to evidence of related pairs, stomach cancer and melanoma incidence rates were negatively correlated for females (p µ0 ) based on n = 16 observations at level

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Danh V. Nguyen, Damla S¸entürk, Danielle J. Harvey and Chin-Shang Li

α = 0.05. The test statistic is based on the sample mean T =

X − µ0 √ σ/ n

(1)

which equals 4X in this example. Under H0 , T ∼ N (0, 1) and one rejects H0 if T ≥ z1−α where z1−α is the (1 − α)th quantile of the standard normal distribution; i.e. Φ(z1−α) = 1 − α. Note that Pr(Type I error) = Pr(reject H0 |H0 true) = Pr(T > z1−α ) = 1 − Φ(z1−α) = α. Suppose that we observe x = 0.64 so our observed test statistic is t = 4(0.64) = 2.56. The p-value for a test statistic is the probability that one observes a test statistic (T ), under H0 , as extreme or more extreme that what was observed (i.e. more extreme than t = 2.56). There are various ways to compute this probability. When the sampling distribution of T is known, as it is in this case, it can be obtained directly as p = Pr(T > 2.56) = 0.0052. If the assumed probability model for the data (the Xi ’s) leads to a test statistic T whose sampling distribution is unknown, the p-value can be obtained using simulation, for instance. This approach is useful when the form of T is particularly complex, with unknown exact or approximate sampling distribution. In this example (although P not needed), based on B = 10000 simulations p = B −1 B b=1 I{tb > 2.56} = 0.0048, where tb is the observed test statistic based on the bth simulated data. Throughout, we denote the indicator function I(A) or I{A} for event A to be I(A) = 1 if A is true and I(A) = 0 otherwise. In the two-sample problem, such as comparing the gene expression levels among n1 diseased and n2 non-diseased individuals, the two-sample t-statistic, namely T = (X 1 − X 2 )/s can be used to test H0 : µ1 = µ2 versus H1 : µ1 6= µ2 . Here X k (k = 1, 2) is the sample mean of group k and s = {(s21 /n1) + (s22 /n2 )}1/2 where s2k is the sample variance for group k. In this case, the distributional assumption of T (or equivalently of the underlying data Xki ’s) can be avoided in computing the p-value by using random permutations of the data and repeatedly computing the test statistic T . Denoting tb to be the observed test statistic for the bth permutation of the data, an estimate of the p-value is P p = B −1 B b=1 I{|tb | > |t|} where t is the observed test statistic based on the original (unpermuted) data. The power function of a test of the null hypothesis H0 , denoted by h(n, θ) is a function of the sample size n and of a parameter of interest, denoted by θ. In the above one-sample problem, θ = µ, the mean, for instance. When comparing competing test statistics, it is appropriate to fix n and compare their respective power. For the sample size calculation to plan/design a study at a desired level of power, h(n, θ) is fixed at a given power and the root of the function can then be solved to obtain the required n. Therefore, a sample size n can be obtained to achieve a desired level of power, typically set at 80% or higher in clinical studies and with a fixed Type I error probability of α. Continuing with the onesample problem described above, we have that h(n, ∆) = Pr(T > z1−α |H1 ) = Pr(T ∗ > √ √ z1−α + nδ/σ) = 1 − Φ(z1−α + nδ/σ), where T ∗ ∼ N (0, 1), δ = µ0 − µ1 , and δ/σ is the (standardized) effect size. For example, to obtain the sample size required to detect an effect size ∆ (e.g. µ1 = 1, µ0 = 0, σ = 1, ∆ = 1) with 90% power (β = 0.1) a solution to h(n, ∆) = 0.9

(2)

Sample Size Calculation and Power in Genomics Studies 65 √ is needed to find n. Equation (2) is the same as Φ(z1−α + nδ/σ) = β, where β = 0.1. √ Thus, z1−α + nδ/σ = zβ = −z1−β , and so n = σ 2(z1−α + z1−β )2 /δ 2. For example, with ∆ = 1 and type I error of α = 0.05 the needed sample size to achieve 90% power is n = (z0.95 + z0.9 )2 = (1.645 + 1.282)2 = 8.57 ≈ 9 samples. √ We note that the power function h(n, ∆) = 1 − Φ(z1−α + nδ/σ) in this case can be √ obtained explicitly since the distribution of the test statistic T = n(X − µ0 )/σ is known due to the normality assumption for the data model. However, when the normal model is not assumed, the power function h(n, ∆) is approximate when n is large. The sensibility of a model assumption will depend on the specific application. For gene expression data, the distribution of raw expression is typically not symmetric and so one can justify such a methodological assumption after a suitable transformation to the original/raw expression data, such as a logarithm. Note also that we have considered an example with a one-sided alternative hypothesis (e.g. H1 : µ1 > µ0 ). For a two-sided test of H0 : µ = µ0 versus H1 : µ 6= µ0 the null hypothesis H0 is rejected given the extremes T ≤ −z1−α/2 or T ≥ z1−α/2 √ √ and the power functon is h(n, ∆) = 1 − Φ(z1−α/2 + nδ/σ) + Φ(−z1−α/2 + nδ/σ) where δ = µ0 − µ and therefore n = σ 2 (z1−α/2 + z1−β )2/δ 2 . In the case of two-group comparisons based on the data {(X1i, X2j ), i = 1, . . ., n1 , j = 1, . . . , n2}, the tests of H0 : µ1 = µ2 versus H1 : µ1 6= µ2 , H1 : µ1 > µ2 , or H1 : µ1 < µ2 correspond to alternative hypotheses of no differential expression, up-regulation or down-regulation relative to condition 1, respectively. In the hypothesis of no differential expression under the normal distribution assumption (with equal group variances σ12 = σ22 = σ 2 known), the sample size per group is n = 2σ 2(z1−α/2 + z1−β )2 /δ 2. As mentioned earlier, when h(n, ∆) (or a function of it) cannot be solved analytically to obtain the sample size, numerical methods can be used. Alternatively, (Monte Carlo) simulation can be utilized based on an explicit probability model to generate the data and to evaluate the resulting power as a function of n for a given test statistic of interest. The advantage of a simulation approach is that a more complex model, which may better reflect the real data, can be used for sample size planning. The main consideration in using a simulation model then is to assess/justify the model used. As is usually the case, pilot data or data from previous similar studies are helpful in making this assessment. Simulation models that use the real (e.g. pilot) data aim to address this issue.

2.2.

Introduction to multiple testing and false discovery rate

We next provide an introduction to multiple hypothesis testing and the relevant concepts, including results on the false discovery rate (FDR). Because of the large number of hypothesis tests carried out in genomics expression data, the use of FDR as a measure of error

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has been popular and it is particularly useful in exploratory studies, such as those using microarrays. A common application in microarray studies is to identify differentially expressed genes among two or more groups (experimental conditions), as illustrated in the Introduction section with the colon cancer initiation and progression in the rat example. Assuming that 1 be each array hybridization (sample) is from a unique animal, let {(X1i1, . . ., X1im)}ni=1 the m gene expression levels for animals in group 1 (e.g. animals on n-3 PUFAs diet) and 2 similarly let {(X2i1, . . ., X2im)}ni=1 be the m levels for animals in group 2 (e.g. animals on n-6 PUFA diet). If one is interested in identifying genes over-expressed in the n-3 PUFA group, the corresponding hypothesis for gene j is H0j : µ1j = µ2j versus H1j : µ1j > µ2j , for j = 1, . . ., m. These m hypotheses are typically dependent in practice, as in array data, although independence is often assumed as an approximation. As we will describe later, some methods for sample size incorporate simple dependence structures that are tractable. Simulation studies can also be used to assess the assumptions of independence as well as specific dependence structures. When testing these m hypotheses, the possible outcomes are summarized in Table 2. Among m hypothesis tests (m genes), m0 and m1 denote the number of truly unexpressed and truly expressed genes, respectively. The number of rejections (“discoveries”) is R and the number of non-rejections is W (= m − R). Note that only R, W and m are observable from Table 2. The proportion of genes truly unexpressed is denoted by π0 ≡ m0 /m. From Table 2, note that V /m0 = Proportion of genes declared significant among genes actually not DE S/m1 = Proportion of genes declared significant among genes actually DE 1 − V /m0 = U/m0 = T N/m0 = specificity V /R = Proportion of false discoveries S/R = Proportion of true discoveries U/W

= T N/(T N + F N ) = Negative predictive value

(U + S)/m = Accuracy.

Table 2. Possible outcomes of testing m hypotheses. The proportion of true null hypotheses is π0 ≡ m0 /m and FDR = E( VR I{R>0}).

Null true (Truly unexpressed) Alternative true (Truly expressed) Total

Accept (Declare unexpressed) U (True Negative/TN) T (Error II, False Negative/FN) W

Reject (Declare expressed) V (Error I, False Positive/FP) S (True Positive/TP) R

Total m0 m1 m

Sample Size Calculation and Power in Genomics Studies

67

The conventional criteria for controlling error in multiple testing is to control the familywise error rate (FWER), which is Pr(V ≥ 1). This is the probability of making at least one false positive error. Testing each of the m hypotheses at the comparison-wise error rate (CWER) of α (e.g. α = 0.05) does not control (guarantee) the FWER at level α. The simplest method to control the FWER at level α is to test each hypothesis at the CWER of α∗ = α/m, which is the well-known Bonferroni correction. This approach is not reasonable when m is large (since for array data m ∼ 1000 − 50000) which would require testing each hypothesis at a level α∗ that is too small. For reasonable levels of CWER, Pr(V ≥ 1) is large for m in the order typical of array experiments. Improvements on the Bonferroni correction that still control the FWER, based on multi-step procedures, were proposed by Holm (1979) and Hochberg (1988), although (1) dependency of the test statistics is not used and (2) the gain is modest, particularly for m in the order of microarray applications. An alternative criteria that is widely used in genomics studies for error-control is the false discovery rate (FDR). Although FDR was proposed by Benjamini and Hochberg (1995) in a different context of application, it has been found to be useful in genomics, imaging and other high-dimensional data. In the context of multiple testing, as summarized in Table 2, FDR is the expected proportion of false discoveries among the R discoveries or rejections. More precisely, FDR (Benjamini and Hochberg, 1995, herein BH) is defined as V V I R > 0 Pr(R > 0). (3) =E FDR = E R {R>0} R Denoting the ordered observed p-values as p(1), . . . , p(m), the BH FDR controlling procedure is to find ˆBH = max{j : p(j) ≤ (j/m)α} (4) k and reject p(1), . . . , p(kˆBH) . The pre-specified FDR target control level is α ∈ (0, 1). It was shown by BH that FDR ≤ π0 α ≤ α in the FDR controlling procedure (4), where in the last inequality π0 is set to 1. FDR controlling procedure (4) was later shown by Finner and Roters (2001) to control the FDR at exactly level π0 α. Refinement by an adaptive control was proposed in Benjamini and Hochberg (2000). Thus, this approach is a conservative procedure and improved power results from incorporating an estimate of π0 into the FDR controlling procedure (4). This was recognized in the context of genomics data and new methods that aim to estimate π0 for FDR estimation were proposed by Storey (2002; 2003) and Storey and Tibshirani (2003), although improvement due to estimating π0 (or m0) in multiple testing has previously been recognized (e.g. Schweder and Spjøvtoll, 1982). The effect of estimating π0 on the improvement in power to detect DE was examined by Nguyen (2004a,b, 2005) among others. Storey (2002) introduced an alternative direct approach to the BH sequential FDR procedure (4); see also Storey (2003) and Storey et al. (2004). This approach involves first estimating π0. We briefly review this estimation procedure, assuming independent test statistics (or equivalently p-values). Large p-values, say pi > λ, 0 < λ < 1, suggest that the observed data is more compatible with true null hypotheses; i.e. more consistent with H0j for gene j. Estimation of π0 can be based on the set of large p-values falling into the upper interval (λ, 1]. Also, note that If no genes are differentially expressed then null p-values are uni-

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formly distributed, denoted P ∼ U(0, 1), and Pr{P ∈ (λ, 1]} = Pr(P > λ) = 1 − λ. Therefore, the expected number of null p-values that would fall into the interval (λ, 1] is (1 − λ)m0. If the number of null p-values in (λ, 1], namely #{Null pj > λ}, is unknown, an unbiased estimate of π0 is π ˆ0(UB) =

#{Null pj > λ} , m(1 − λ)

(5)

since E[ˆ π0(UB)] = m0/m = π0 . Because the numerator in (5) is not observable, replacing the numerator with #{pj > λ}, an observable quantity, leads to a conservatively biased estimate of π0 : W (λ) #{pj > λ} = . (6) π ˆ0(λ) = m(1 − λ) m(1 − λ) The estimator π ˆ0 (λ) is conservatively biased since #{pj > λ} = #{Null pj > λ} + π0(λ)] ≥ E[ˆ π0(UB)] = π0 . Note that #{Alt. pj > λ} ≥ #{Null pj > λ} and, thus, E[ˆ as λ approaches 1, #{pj > λ} consists mostly of truly null p-values, therefore, the bias decreases. At the same time, due to the resulting small interval 1 − λ (as λ → 1), the variance increases. Thus, λ, serves as a tuning parameter that balances bias and variance. Storey (2002) and Storey and Tibshirani (2003) proposed the following automatic algorithm for choosing the optimal λ to minimize the mean squared error of π ˆ0 (λ). The ˆ0(OPT) ≡ limλ→1 π ˆ0 (λ). For example, applicaoptimal estimator of π0 is defined as π tion to the colon cancer data gives the estimated proportion of non-differentially expressed genes between-3 PUFA and n-6 PUFA enriched diets to be π ˆ0 (OPT) = 0.758. ˆ0 (λk ). 1. For each λk ∈ R = {0, 0.01, 0.02, . . ., 0.95} compute π 2. Fit a natural cubic spline with 3 degrees of freedom, fˆ, through the data points ˆ0(λk )}96 {λk , π k=1 . The data points are weighted by 1 − λk . ˆ0 (OPT) = fˆ(1). 3. Estimate π0 by π Thus, the FDR controlling procedure incorporating π ˆ0 (λ) is α ˆλ = max j : p(j) ≤ j . k m π ˆ0(λ)

(7)

Note that taking π ˆ0 (λ) ≡ 1 gives the BH procedure (4). In addition to the estimation of the proportion of null hypotheses, the following basic results on direct estimation of the FDR (due to Storey, 2002; Storey et al., 2004) are useful for sample size calculations that aim to control FDR (described in subsequent sections). Storey (2002) introduced the positive FDR (pFDR), V |R > 0 = FDR/ Pr(R > 0) (8) pFDR = E R and showed that pFDR(γ) =

π0 γ π0 Pr(P ≤ γ|H = 0) = Pr(P ≤ γ) Pr(P ≤ γ)

(9)


69

for independent p-values, where γ is the rejection threshold corresponding to a fixed rejection region [0, γ], and H = I(alternative is true) (Storey, 2003; Theorem 1). The denomic ≤ γ) = R(γ)/m, where R(γ) = #{pi ≤ γ}. nator, Pr(P ≤ γ), can be estimated by Pr(P c > 0), Since pFDR is conditioned on R(γ) > 0 and Pr(R(γ) > 0) ≥ 1 − (1 − γ)m ≡ Pr(R Storey (2002) proposed the following conservatively biased estimator of pFDR: d λ(γ) = pFDR

W (λ)γ π ˆ0(λ)γ , = c ≤ γ)Pr(R c > 0) (1 − λ){R(γ) ∨ 1}{1 − (1 − γ)m} Pr(P

(10)

where R ∨ 1 = max{R, 1}. Thus, by dropping the estimate of Pr(R > 0) from (10), we obtain a direct estimator of FDR: d λ (γ) = FDR

W (λ)γ . (1 − λ){R(γ) ∨ 1}

(11)

d λ(γ)] ≥ FDR(γ) The estimate (11) is conservatively designed in the sense that E[FDR for all γ and π0 (Storey, 2002; Theorem 2). As we will describe in Section 4., sample size calculation methods use the result (9) and relation between FDR and pFDR when the number of hypotheses m is large. Because the lower bound Pr(R(γ) > 0) ≥ 1−(1−γ)m ≈ 1 for m large, as in array data, from definition (8), pFDR ≈ FDR. It is also convenient to express result (9) equivalently in terms of test statistics, instead of p-values. In terms of the independent test statistics T1, . . . , Tm and rejection region Γ = [0, γ], (9) is equivalent to pFDR(Γ) =

π0 Pr(T ∈ Γ|H = 0) = Pr(H = 0|T ∈ Γ), Pr(T ∈ Γ)

(12)

with Pr(T ∈ Γ) = π0 Pr(T ∈ Γ|H = 0) + π1 Pr(T ∈ Γ|H = 1) (Storey, 2002; Theorem 1). Thus, to control FDR at level α (when pFDR ≈ FDR), (12) is set to be less than or equal to α, i.e. Pr(T ∈ Γ|H = 0) α π1 . (13) ≥ 1 − α π0 Pr(T ∈ Γ|H = 1) We note here that although the BH method for FDR control was originally shown for independent p-values, it has been shown to also hold for a certain class of dependency, such as positive regression dependency (Benjamini and Yekutieli, 2001). Estimation of FDR under dependence is also proposed in Storey and Tibshirani (2003).

3.

General simulation-based approaches to sample size and power planning

In the past decade there have been unprecedented transcriptomic data from microarray experiments generated, ranging from laboratory to clinical studies and in various genomes. Human array data is particularly abundantly available from individual investigator databases that are open to the public and also from more formal public repositories, including the National Center for Biotechnology Information (NCBI) Gene Expression Omnibus (GEO; http://www.ncbi.nlm.nih.gov/geo/). These data can be selected and combined to form pilot

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data to estimate model parameters (e.g. variability) in defining effect sizes for sample size and power analysis. The abundance of “pilot” data provides a platform for consideration of more complex models for gene expression from which the determination of sample size and power can be based (e.g. see Page et al., 2006). The availability of data coupled with modest computational requirements makes these simulation-based approaches to sample size and power planning feasible. k Consider the case of a two group comparison with pilot data {(Xki1, . . . , Xkim)}ni=1 for groups k = 1, 2. One can consider a parametric model, such as the normal distribution, for processed gene expression with gene-specific parameters based on the pilot data. For instance, in the case of independent gene expression, Li et al. (2005) considered Xkij ∼ N (0, σ ˆ j2) for the m0 unexpressed genes (j ∈ M0 ). For DE genes, the mean difference for the experimental group relative to the control (reference) group, for instance, can be σj , σ ˆ j2), for j ∈ assumed to be in units of the standard deviation from pilot data: X2ij ∼ N (δˆ M1. The set of DE, namely M1, can be selected at random from the pilot data. Data sets can be generated from this parametric simulation model that allow for gene-specific effects. Note that if the gene-specific parameters are not obtained from the pilot data, the data can be generated to be within a target range of effect sizes. The BH or Storey and Tibshirani (ST) FDR controlling procedure can then be applied to each of the simulated data sets to estimate power and sample size. This approach may be generalized to comparisons among more than two groups as well as other hypothesis tests of interest, including linear regression models or mixed-effects regression models. For example, in the colon cancer example in the introduction, gene-specific fixed effects parameters as well as variance components from the pilot data can be used as input parameters into the normal model for a linear mixed-effects model to simulate expression data. An important challenge in sample size calculations (as well as in other methods for the analysis of gene expression data) is the generation/simulation of expression data that reflects characteristics of real expression data. A key step is to relax the artificial assumption of independence and to incorporate into the data generation model the correlation structure of genomics data. The transcriptional state of the repertoire of genes under a given condition is a coordinated, complex process. Dependence among gene expression, whether among individual genes or within cluster/family of related functional members, has been shown from numerous microarray experiments. The important issue of incorporating the dependence structure of gene expression data, addressed by Li et al. (2005), arises in the simulation of gene expression data for two group comparisons. Their procedure involves three parts: (1) removing the potential (observed) differences between groups in the pilot data; (2) resampling from the data; and (3) randomly selecting DE genes by adding a mean difference between the two groups, δˆ σj , to each resampled data set. Although mean differences between the two groups are removed, the correlation structure is retained. More precisely, these steps are as follows: 1. Let xk1 , . . ., xknk be the original m-vectors of expression data for groups k = 1, 2. Remove systematic differences in gene expression between groups not due to noise by taking x∗ki ≡ xki − xk + z, i = 1, . . . , nk , where xk = (xk1 . . . , xkm )T is the vector of average expression for the m genes in group k and z is vector of overall averages over the two groups combined.


71

2. New expression data for group k are then generated by repeatedly resampling (with k . replacement) from {x∗ki }ni=1 3. DE genes can then be (randomly) selected and a mean difference between the two groups is assigned to be δˆ σj . The number of DE genes is set at m1 . Suppose that steps (2)-(3) are repeated ND times (e.g. ND = 1000) resulting in ND simulated data sets. The BH and ST FDR procedures are then applied to each generated data set, which retains the original correlation structure, from which power and sample size can be determined. Because typically π0 , the number of null genes (non-DE genes), is unknown, its effect on sample size and power should be assessed in the simulation and this is done by simply varying m1 in step (3); i.e. repeat the simulation for various values of m1. Nguyen et al. (2007) also proposed a simulation-based approach to determine sample size and power using the ST FDR controlling algorithm, where the model for gene expression incorporates both additive and multiplicative measurement errors, xk = µk eη + ,

k = 1, . . ., K,

(14)

where xk is the observed (gene expression) intensity measurement and µk is the true (unknown) gene expression (Rocke and Durbin, 2001) in group k. For two comparison groups, K = 2. The gene expression measurement error model (14) has been widely adopted and provides a reasonable approximation to empirical data (see, for example, Rocke and Durbin, 2001; Zien et al. 2003; Huber et al., 2002 and references therein). In the above error model, the additive and multiplicative measurement error models are ∼ N (0, σ2)

and

η ∼ N (0, ση2).

(15)

These terms represent the error associated with genes that are not expressed or expressed at low levels and the multiplicative (proportional) error for genes expressed at high levels. Model (14) is a two-component error model which approximates a constant standard deviation for low expression levels and a constant coefficient of variation for higher expression levels. More specifically, the following lognormal model of gene expression for µk is adopted (Zien et al. (2003), µk = µ∗k eβ ,

k = 1, . . ., K,

(16)

where β ∼ N (0, σ 2), µ∗k is the mean gene expression level in group k, and the parameter σ represents the standard deviation of the biological variability. The family of lognormal distributions has been used as a model for gene expression (Nguyen and Rocke, 2004; Zien et al., 2003; Nguyen, 2004a,b; Konishi, 2004, among others). See Limpert et al. (2001) for a general introduction to the use of the lognormal distribution in the sciences. For two comparison groups, the fold ratio of expression between groups 1 and q 2 for gene j is θj ≡ ∗ ∗ µ1j /µ2j . The signal to noise ratio, averaged over groups 1 and 2, is µ∗1j µ∗2j /σ . Simulated data allowed for varying levels of fold changes in Nguyen et al. (2007). Alternatively, with pilot data, the effects sizes can be directly estimated from the data as in the work of Li et al. (2005) described above. The measurement error parameters (σ and ση2) can be generally estimated based on an array with technical replicates (e.g. Bartosiewicz et al. (2000), Stuart et al. (2001), and Lemon et al. (2002) among others). The following procedure is then applied to the ND simulated data sets :

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0.07

1

0.06 0.8

0.04 FDR

0

Power P(n, π )

0.05 0.6

0.4

0.03 0.02

0.2 0.01 0 30

0 30 25

1

20

0.8

15

0.6 10

1

20

0.8

15

0.6 10

0.4 5

Sample size ni

25

0

0.4 5

0.2 0

π

Sample size n

o

i

0.2 0

0

πo

Figure 2. Expected power and FDR control. (Left) The power surface, P (n, π0) as a function of sample size n and π0 , and (Right) the expected FDR control, set at level α = 0.05. Adopted from Nguyen et al. (2007).

1. Specify the desired FDR control level α ∈ (0, 1). 2. Compute the test-statistics, denoted by t1 , . . . , tm and their corresponding p-values by p1, . . . , pm corresponding to null and alternative hypotheses, H0j and H1j , for genes j = 1, . . ., m. 3. Apply the ST FDR controlling method. 4. Generate power surface, h(n, π0) for determining power and sample size. The power corresponding to each sample size n and π0 , the proportion of truly non-DE genes −1 PND is obtained as ND l=1 (sl /m1 ). It is the average proportion of the true alternative hypotheses correctly identified (discovered), averaged over the ND data sets (simulations). For example, Figure 2 displays the estimated power and FDR control for the two comparison groups case under the measurement error model above. Due to the complexity of the model, possibly with general dependence structure, it is important to check the FDR control from the simulation. The average proportion of false rejections, averaged over the −1 PND ND simulations are obtained as ND l=1 vl / max{rl , 1} (right plot in Figure 2). Li et al. (2005) provide a careful study of FDR control in the data-based simulation model and found that the actual FDR is under-controlled with correlated gene expression. Because FDR controlling procedures (e.g. BH) have been shown to hold under independence and some special dependence structures, an examination of FDR control is needed as general dependence is the case with real array data.

4.

Methods assuming independence in gene expression

Many sample size calculation methods assume independent test statistics. These approaches are based on the result of Storey (2002, Theorem 1), where all tests are assumed to be


73

independent and identically distributed and the null hypothesis H0 is true with probability π0 . This is the result described by (12), i.e. pFDR(Γ) =

π0 Pr(T ∈ Γ|H = 0) = Pr(H = 0|T ∈ Γ). Pr(T ∈ Γ)

(17)

As described in Section 2.2., since Pr(R > 0) ≈ 1 in microarray applications because the probability of no significant discoveries among thousands of genes monitored is close to zero. Thus, pFDR(Γ) ≈ FDR(Γ) and result (17) can be used to determine the sample size. These approaches, utilizing the simplifying assumption of independence and identical tests were developed by Liu and Hwang (2007) and Jung (2005). More precisely, controlling FDR at level α, i.e. FDR ≤ α, is equivalent to ∆≥

Pr(T ∈ Γ|H = 0) , Pr(T ∈ Γ|H = 1)

(18)

α π1 where ∆ = 1−α π0 . Note that α, the desired level of FDR control, is to be specified by the investigator and the level of control will depend on the type of experiment. The proportion of null genes π0 is best estimated when pilot data is available; otherwise its specification is also required. A rejection region Γ is chosen to satisfy the boundary of (18). Considerq the two-group comparison based on the t-statistic for gene j, namely Tj =

−1 0 1 (X 1j − X 2j )/ s2j (n−1 1 + n2 ) to test Hj : δj = 0 versus Hj : δj 6= 0, where δj =

µ1j − µ2j , s2j = (n − 2)−1 {(n1 − 1)s21 ) + (n2 − 1)s22)}, and nk (k = 1, 2) are the group sample sizes with n = n1 + n2 . The null hypothesis H0j is rejected when |Tj | > cj , for the threshold constant cj . Thus, application of (18) to the two-group comparison gives ∆=

Pr(|Tj | > cj |H = 0) , Pr(|Tj | > cj |H = 1)

(19)

where cj is the critical value corresponding to gene j. When H0j holds (gene j is not DE), then Pr(|Tj | > cj |H = 0) = 2t(n − 2; −cj ), where t(d; c) denotes the cumulative distribution function for the central t-distribution with d degrees of freedom (DF). Under the alternative hypothesis, H1j , Tj ∼ t(n − 2, θj ), the non-central t-distribution with q −1 −1 non-centrality parameter θj = δj / σj n1 + n2 . Thus, the denominator in (19) is Pr(|Tj | > cj |H = 1) = 1 − t(n − 2, θj ; cj ) + t(n − 2, θj ; −cj ). Note that for (normalized and) log (base 2) transformed data, a two-fold change for gene j corresponds to δj = 1. Also, although not much of practical interest, δj = δ and σj = σ correspond to the case where the differential expression and variability in gene expression are identical for each gene. Clearly, other test statistics T in (18) with known sampling distribution can be used in other designs or hypothesis tests. This includes the multi-group comparison using the F-test, as described in Liu and Hwang (2007). For instance, in a (simple single) loop design (see e.g. Yang and Speed (2003), Smyth (2004) and references therein) with three groups/treatments (G1 → G2 → G3 → G1), the design matrix   1 0 X =  −1 1  0 −1

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compares group 1 to 2 and group 2 to 3, based on a single set of experiments with three arrays (e.g. in a two-color cDNA array). Liu and Hwang (2007) proposed to determine the number of sets of slides for a given design to control the FDR based on a linear model for each set i (i = 1, . . ., n), Yij = Xβj + ij ,

j = 1, . . . , m.

(20)

Here β j is a vector of size p for gene j , Yij is the expression measures of gene j over the ith replicate set and eij is the corresponding random error. A null hypothesis test of interest pertaining to gene j can be formulated as H0j : Lβ j = 0 versus H1j : Lβ j 6= 0, where L is an r × p (r ≤ p) matrix of coefficients consisting of contrasts/comparisons of interests (see, with variance σ 2 , e.g. Seber, 1977). Assuming that the error eij is normally distributed P ˆj )T [L(XT X)−1LT /n]−1 (Lβ ˆj )}/{ n eT eij /d(n)}, the F-test of H0j is Tj = {r−1(Lβ i=1 ij ˆ where eij = Yij − Xβj , d(n) is the degrees of freedom depending on the sample Pn T −1 T ˆj = size n, and β i=1 (X X) X Yij /n is the least squares estimator of β j . Un0 der the null hypothesis Hj : Lβ j = 0, the test statistic Tj is distributed as a central F-distribution with r and d(n) DF, denoted by F (r, d(n)). Under the alternative hypothesis H1j : Lβ j 6= 0, Tj is distributed as a non-central F-distribution, denoted F (r, d(n), λ), where λ = (Lβ j )T Σ−1 (Lβ j ) and Σ = σ 2L(XT X)−1 L/n. To determine the sample size n, the probability of rejection under the null and alternative hypothesis is based on the central and non-central F-distribution, respectively, to solve (18), ∆=

1 − F (r, d(n); cj ) Pr(Tj > cj |H = 0) = . Pr(Tj > cj |H = 1) 1 − F (r, d(n), λ; cj)

(21)

Here, F (df1 , df2 , λ; c) denotes the cumulative distribution function of the F-distribution. Numerical integration methods are needed to solve (17) generally and to accommodate different effect sizes (e.g. δj ) and gene-specific characteristics (e.g. σj ), Liu and Hwang (2007) suggested modelling the distribution of gene-specific parameters parametrically or nonparametrically (e.g. fˆ(δj , σj )) from pilot data. Sensitivity of these proposed methods to dependence in gene expression has not been assessed. Under the independence assumption, Jung (2005) provided a similar approach to sample size calculation, controlling FDR for the two-group comparison. The method is based on the relation m0 γ P , (22) FDR(γ) = m0 γ + j∈M1 Pr(Pj ≤ γ|H1j ) (Storey, 2002; see (12) in Section 2.2.), where M1 is the set of truly DE genes. Jung (2005) considered the two-sample comparison test statistic for gene j, Tj = (X 1j − q −1 X 2j )/ sj n−1 . Although not a justifiable assumption in genomics applica1 + n2 tions, assuming that the sample size is large ( nk , large for k = 1, 2), Tj ∼ N (0, 1) under H0j : δj = 0. This assumption together with the assumption of equal/constant effect size leads to a simple closed-form solution for sample size based on (22). As for the more realistic cases, numerical methods are needed to obtain a solution for sample size. For illustration, consider the one-sided test (e.g. up- or down-regulation) with alternative H1j : δj > 0. Then

Sample Size Calculation and Power in Genomics Studies √ under the alternative, Tj ∼ N (δj na1 a2 /σj , 1), where ak = nk /n. Thus, m0 γ P . FDR(γ) = √ m0γ + j∈M1 [1 − Φ(z1−γ − δj na1 a2 /σj )]

75

(23)

Note that this is a specific application of (18). The expected number of true rejections (discoveries) at the single test significance level γ is X √ [1 − Φ(z1−γ − δj na1 a2 /σj )] (24) E{S(γ)} = j∈M1

and a common measure of power is the expected proportion of true discoveries, E(S/m1), for multiple testing. Thus, given the specified expected number of true discoveries that one wants to detect, say E{S(γ)} = s (s ≤ m1 ) at the CWE level of γ, and the FDR control set at level α, then (23) becomes α = m0 γ/(m0γ + s), which gives the modified single-gene significance level (Type I error) of γ ∗ = (s/m0)[α/(1 − α)] needed to detect s discoveries on average with FDR controlled at level α. Thus, upon substituting the new γ ∗ and the expected number of true discoveries desired into (24), the sample size needed can be obtained by solving h(n, ∆) = 0, where X √ [1 − Φ(z1−γ ∗ − δj na1 a2/σj )] − s (25) h(n, ∆) = j∈M1

and ∆ = (δ1 /σ1, . . . , δm /σm ). Jung (2005) proposed using the bisection method to solve h(n, ∆) = 0 and for the unrealistic case of equal effect sizes for all genes ( δj /σj = δ/σ for all j = 1, . . . , m), n = {σ 2(z1−γ ∗ + z1−β ∗ )2/(a1a2 δ 2 )} + 1, where β ∗ = s/m1. For two-sided tests of no differential expression for each gene, γ ∗ and δj in (25) are replaced by γ ∗/2 and |δj |. To avoid a large sample (nk → ∞), Jung also considered replacing the normal distribution by the non-central t-distribution to compute Pr(Pj ≤γ|H1j ) in (22), as was done in Liu and Hwang (2007). (See earlier discussion.) As discussed earlier, the gene-specific effect sizes can be easily estimated based on similar pilot data in most cases. However, the effect dependence in gene expression on sample size and power estimation is important and has been recognized. There have been some approaches to incorporate the dependence structure and we discuss some of these approaches next.

5.

Methods accounting for dependence in gene expression

A method for sample size calculation based on fixing the expected number of false positives E(V ) using a small individual CWER (1/1000 or 2/1000) was proposed by Tsai et al. (2005) and Wang and Chen (2004). First, consider the case of independent gene expression and denote P 1 the outcome of the test for gene j by Sj , then the number of true discoveries S = m j=1 Sj ∼ Bin(m1 , 1 − β), where (1 − β) is the probability that a truly DE gene is declared significant. (Note that this is assumed to be constant from gene to gene.) Tsai et al. defined the family-wise power of identifying s out of m1 truly DE genes for a given CWER level α as the probability of at least s true discoveries, m1 X m1 (1 − β)l β m1 −l . (26) φ ≡ Pr(S ≥ s) = l l=s

76


The sample size formula for testing no differential expression of a single gene is n=

2σ 2(z1−α/2 + z1−β )2 . δ2

(27)

For multiple genes with equal effect size, from (26) one can see that for even a very low probability (i.e. family-wise power) of detecting all m1 differentially expressed genes one would need to have the comparison-wise power (1 − β) to be close to one. Thus, Wang and Chen (2004) and Tsai et al. (2005) suggested the following modification. Consider the sensitivity measure λ = s/m1 . To detect at least the fraction λ of truly DE genes at familywise power level φλ, one can solve for the required comparison-wise error (1 − β) from (26) with s = [m1λ] denoting the largest integer less than m1 λ. Thus, given the solution for (1 − β) and given α and a fixed effect size δ, the sample size can be obtained from (27). Other criterion, besides the sensitivity, including the proportion of true discovery ( s/r) or the accuracy [(m0 − v + s)/m] can be used for λ as well. The equal effect size for each gene is needed for the proposed method (i.e. for expression (26) ), although this is clearly not a realistic assumption. Dependence between genes can be modelled naively by making the simplifying assumption that DE genes are equally correlated; i.e. Corr(Si , Sj ) = θ. The quantity of interest S, an sum of Bernoulli variates, is then modeled as a beta- binomial distribution and so the family-wise power φ = Pr(S≥s) is obtained by summing the individual probabilities from s to m1 . This is simply (26) with the binomial distribution replaced by the beta-binomial distribution. The issue of sample size calculation under dependence adjustment is taken up in more details by Shao and Tseng (2007). In addition to the need for adjusting for dependence in gene expression, this resulting dependence among the test statistics also has affected the measure of power. More precisely, under dependence, the commonly used measure of power is an “average power”, r1, and it is the expected proportion of true discoveries, among all m1 true alternatives, ¯ r1 = E[S/m1] = 1 − β.

(28)

Under dependence, the variability of U is more than when the test statistics are independent, and the achieved proportion of true discoveries is more variable. Thus, Shao and Tseng (2007) among others, considered determining the sample size to achieve a probability that at least a fraction r1 of truly DE genes are identified. More precisely, this probability is Ψ = Pr([S/m1] ≥ r1 )

(29)

and the overall power is specified by the pair (Ψ, r1). Shao and Tseng (2007) considered the following approach to incorporate dependence into sample size calculations using the Pm overall power criterion for the two-sample comparison. Let R ≡ R(γ) = j=1 Rj (γ) ij and denote the correlation between Ri ≡ Ri(γ) and Rj ≡ Rj (γ) by θR = Corr(Ri , Rj ). P 1 ij Also, let Sj = I(pj ≤ γ), S = m j=1 Sj , and ρS be the correlation between the (normal) test statistics for gene i and j. Using the result in Ahn and Chen (1995), the correlation ij θS = Corr(Si , Sj ) can be expressed as a function of the CDF of a standard bivariate m1 normal distribution, ρij S , βi and βj . Also, define the average correlation among {Sj }j=1

Sample Size Calculation and Power in Genomics Studies 77 P as θS = (m1(m1 − 1))−1 i6=j θSij . The variance of S, σS2 , can be obtained as a function ¯ of βi and θSij , and under the assumption of equal effect sizes ( δj all equal, βj = β = β) 2 ¯ ¯ σS = m1 β(1 − β)[1 + θ S (m1 − 1)]. The calculation of sample size (and power) is based on a normal approximation for the distribution of S, depending on the parameters m1, β¯ and σS2 . That is, ¯ σ2 ) S ∼ N (m1(1 − β), S

(30)

approximately for “small dependent blocks in the arrays” (see Shao and Tsing (2007) based on Billingsley (1968)). Also, with the assumption that both m0 and m1 are large, we ¯ for can obtain the per gene comparison level γ as γ = {α/(1 − α)}(m1/m0 )(1 − β), sample size calculations (where α is the specified FDR control level). For example, with equal effect size (δj equal, βj = β), for average power r1 and overall power of 0.5, Ψ = Pr(S ≥ m1 r1) = 0.5 does not depend on σS2 . The sample size (for one-sided alternatives) is n = σ 2(z1−γ + z1−β )2/(a1a2 δ 2 ). When the overall power Ψ > .5, which is the case of interest in practice, β¯ can be obtained from the normal approximation (30) and σS2 needs to be estimated based on pilot data, for instance. See Shao and Tseng (2007) for details on this estimation as well as the case of unequal effect sizes and extensions to two-sided alternative hypothesis. We briefly note here that the approximation (30) may require assessment as well as the assumption that m1 is large. For array experiments, m1 may not be large, in the 1-5% in many experiments. Clearly, exceptions are experiments that include conditions in which cells are subject to broad changes, such as a carcinogen or irradiation.

6.

Methods for controlling family-wise error

Microarray experiments are exploratory in nature, examining thousands of gene expressions simultaneously. Thus, a less strict criterion, like the FDR, is more suitable for exploratory search of DE genes. See Nguyen (2004a,b, 2005) for more discussion. However, some methods for controlling FWER have been proposed, based on the step-down p-value adjustment work of Westfall and Young (1993). See also Dudoit et al. (2003). We briefly review here the study of Jung, Bang and Young (JBY, 2005) for sample size determination in the two-group comparison setting, with emphasis on the assumptions of the methodologies. We further note that such methods are rarely used, at least for the initial stage of microarray experiments. However, these methods may be suitable for follow-up microarray experiments, where a smaller subset of candidate genes are further studied. Thus, a more strict criterion, like the FWER may be more suitable. Again, let Tj be the t-statistic for gene j testing H0j : δj = 0 versus H1j : δj > 0 for j = 1, . . . , m. A one-sided test is considered here for convenience. The null hypothesis is rejected if Tj > c, for some critical value c, and the FWER is defined as α = Pr(T1 > c or T2 > c, . . . , or Tm > c|H0 ) = Pr( max Tj > c|H0 ), 1≤j≤m

(31)

0 where H0 : δj = 0 for all j (i.e H0 = ∩m j=1 Hj ). The Bonferroni adjustment takes c = cα = tn−2,α/m , the upper α/m-quantile of the t-distribution with n − 2 DF. JBY considered estimating the distribution of W = max1≤j≤m Tj under H0 using permutation.

78


The adjusted p-value is defined as Pr(max1≤j 0 ≤m Tj 0 ≥ tj |H0 ), where tj is the observed t-statistic of Tj from the original data. The single-step procedure for estimating the adjusted p-value, based on B (random) permutations of the original data is p˜j = B −1

B X

I{wb ≥ tj },

j = 1, . . ., m,

(32)

b=1 (b)

(b)

where wb = max1≤j≤m tj , tj is the computed t-statistic based on the bth permutation of the original data (b = 1, . . ., B). All hypotheses with p˜j < α are rejected. (For two-sided tests, tj is replaced by |tj |.) The step-down procedure for adjusting the observed p-values as proposed by Westfall and Young (1993) and adopted by Dudoit et al. (2003) is provided in JBY (see Algorithm 2, p. 160). They proposed an algorithm to find the sample size by solving the power equation h(n) = 1 − β, where √ h(n) = Pr(max1≤j≤m (ej + δj na1 a2 /σj ) > cα), (e1, . . . , em ) ∼ N (0, R) and R denotes a m × m correlation matrix. This is based on JBY’s result that the distribution of (T1, . . . , Tm) has approximately the same distribution as (e1, . . . , em ) ∼ N (0, R) under √ the null hypothesis and (ej + δj na1 a2 /σj ) under the alternative hypothesis when nk ’s √ are large. Because the distribution of max1≤j≤m ej and max1≤j≤m (ej + δj na1 a2/σj ) are unknown, solving h(n) = 1 − β is non-trivial and JBY proposed using simulation. However, to be able to simulate the needed distribution, further simplifying assumptions are made, including equal correlation between genes (e.g. block compound symmetry). Such a correlation structure is at best poor models for the observed data. In addition, the distribution result upon which the power function h(n) is based is derived from assuming large sample size, which is not justified for gene expression data as the sample size should be fixed and small. Although computationally more intensive, direct simulation of the underlying model with parameters estimated from pilot data (see Section 3.) can be applied in this setting to relax many of the simplifying, but poorly justified, assumptions from real data perspectives.

7.

Other approaches and relevant literature

One of the early works on power and sample size consideration for DNA microarray studies is that of Lee and Whitmore (2002), where various error controls were discussed in the context of multiple testing, including FDR, and the use of E(S)/m1, the expected proportion of truly expressed genes, as a measure of power. Pawitan et al (2005) considered a mixture model for the distribution of the t-statistics, and emphasized the need to also consider the sensitivity/false negative rate in conjunction with the false discovery rate. Pan et al. (2002) and Lin and Le (2002) also used a mixture model approach. Pounds and Cheng (2005) considered the problem of k-group comparison, also using the FDR criterion; see also Hu et al. (2005). Yang et al. (2003) used a conservative bound for FDR for calculating sample size and considered this issue in the context of serial time points experiments (within groups) based on a mixed model where time and treatment are fixed effects and subject is a single random effect. Tibshirani (2006) proposed a simple approach where the gene score from the SAM (significance analysis of microarray, Tusher et al., 2001) is used and the null distribution of the scores is estimated based on permutation. Muller et al. (2004) considered sample


79

size calculation based on a hierarchical Bayes model under a decision-theoretic framework. Black and Doerge (2002) considered a requirement for the number of spots within the array for detection significant of fold change; see also Lee et al. (2000). Wei et al. (2004) examined factors affecting size and power and compared the relative sample size requirement for humans and inbred animals studies to detect fold changes. Although we have focused on sample size and power considerations for the identification of DE genes, some work has been done on sample size determination for classification studies as well. One area of application is the classification among tumor issue/cell types or between normal and cancer cells (e.g. see Alizadeh et al., 2000; Golub et al., 1999; Alon et al., 1999; Nguyen and Rocke, 2002a,b,c, 2004). Sample size requirements for designing classification can be found in Hwang et al. (2002), Mukherjee et al. (2003), and Dobbin and Simon (2007). Hua et al. (2005) examined the number of features, as a function of sample size, in various classifiers.

8.

Discussion

In recent years, there have been increased interests in the design issues, including sample size and power, at the initial study planning stage of genomics studies. Because of the large number of probes monitored in microarrays or other high-throughput assays, the FDR criterion has been preferred as the measure of error. Thus, much research have been devoted to methods for determining sample size/power for controlling FDR and FDR-related criterions. As we have emphasized here, various assumptions made are for mathematical convenience and their consequences need better assessment. A key assumption is the independence of gene expression. Under dependence, the effects on FDR control assuming independence, is not negligible and should be carefully assessed and quantified. This also applies to models that over-simplify the dependence structure by assuming, for instance, a single common correlation among all genes. In these cases, it is informative to compare their performance/sensitivity to the case of more general dependence structure, which can be based on the observed dependence structures across many real data sets. We note also that through such studies, some assumptions made for mathematical convenience that are not critical for modelling real expression data can be identified. Finally, we note that the sample size and power results are critically dependent on the proportion of null genes π0 . Depending on the type of genomics experiments or the area of application (e.g. highdimensional data in MS or MRI studies) a suitable range of π0 should be chosen. Pilot data or previous similar studies are informative for determining the range of π0 of interest in practice. Sensitivity of the assumptions, such as independence or a specific type of dependence structure among genes, needs to be assessed in the appropriate range of π0 .

Acknowledgment Support for this work includes the National Institute of Health (NIH) grants UL1RR024922, RL1AG032119 and RL1AG032115, National Institute of Child Health and Human Development grant HD036071, NIEHS grant P01-ES011269-06 and grant UL1 RR024146 from the National Center for Research Resources, a component of NIH.

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Chapter 2

COUPLING COMPUTATIONAL AND EXPERIMENTAL ANALYSIS FOR THE PREDICTION OF TRANSCRIPTION FACTOR E2F REGULATORY ELEMENTS IN THE HUMAN GENE PROMOTER Kenichi Yoshida∗ Department of Life Sciences, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki, Kanagawa 214-8571, Japan

Abstract Completion of the human genome sequencing has provided us with opportunities to understand the molecular complexity of the human body. The transcriptional regulatory circuits of gene expressions are one of the most promising matters to be resolved by exploring the human genome sequence. We have been interested in human cell fate regulated by the transcription factor E2F. To accelerate the investigation, we need to develop a strategy that can efficiently identify E2F target genes. Basically, our approach is to combine computational and experimental analysis. Annotated data of gene expression profiles deposited in the public database and knowledge accumulated in the published literature are a treasure-house of E2F candidate target genes. Next, a promoter region based on the information of the transcriptional start site can be used for motif searching of E2F regulatory elements. Finally, a set of predicted E2F regulatory elements are tested by molecular biological and biochemical assays. In this chapter, I give a basic introduction of our recent strategy for computational and experimental analysis for the prediction of transcription factor E2F regulatory elements in the human gene promoter. In addition, recent progress in unrevealing E2F functions achieved by genome wide approaches is discussed.

∗

Correspondence: Kenichi Yoshida, Department of Life Sciences, Meiji University, 1-1-1 Higashimita, Tama-ku, Kawasaki, Kanagawa 214-8571, Japan. Tel. & Fax.: +81-44-934-7107. E-mail: [email protected]

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Introduction The human genome sequence can provide us with huge volumes of information on gene structure such as coding and promoter regions. At the same time, however, recent highthroughput experimental technologies have provided us with such a plethora of complex information that understanding it becomes a major problem. To overcome these phenomena, computational biology that can create new values just from DNA sequences or expression data derived from genome wide experiments has been evolved. Deeper genome annotation within the ENCODE regions, which span 1% of the human genome sequence, make it possible to assess the accuracy of the computationally created information [Guigó et al., 2006; Gerstein et al., 2007]. Currently, our approach is simply to identify transcription factor E2F target genes by bioinformatics and then set out to elucidate the E2F target genes in a functional manner in the cellular context. E2F plays pivotal and unique roles in cell cycle regulation as well as carcinogenesis, differentiation, and development [Blais and Dynlacht, 2004; Bracken et al., 2004; Yamasaki and Pagano, 2004; Korenjak and Brehm, 2005]. Therefore, a state-of-the-art strategy combining computational and experimental approaches to identify E2F target genes could be applied to other cell cycle regulators, with the aim of eventually unraveling the complexity of gene regulation.

1. DNA Microarray and Bioinformatics Data for global gene expression changes monitored by DNA microarray have been produced in large amounts. Technologically, the DNA microarray itself became the classic one. Generally, the transcriptional control network model has been well established in the yeast cell cycle regulation rather than mammalian cell cycle regulation [Futcher, 2002]. So far, several studies have reported on E2F target genes and their function by analyzing microarray data in mammalian cells [Ishida et al., 2001; Ma et al., 2002; Stanelle et al., 2002; Huang et al., 2003; Vernell et al., 2003; Young et al., 2003; Black et al., 2005; Jamshidi-Parsian et al., 2005]. Basically, E2F over-expression by conditional regulation or knock-down facilitated through the use of short interfering RNA (siRNA) was employed to prepare mRNAs to be tested with the DNA microarray technique. As E2F is negatively controlled by association with the retinoblastoma (pRb) pocket binding protein [Korenjak and Brehm, 2005], some reports preferred siRNA-mediated gene silencing of pRb to activate the E2F function. Collecting unique patterns of expression changes can be applied for prognostic purpose of certain illnesses, and can be effective in the selection of suitable treatment strategies in the clinically challenged. Towards this purpose, one might think whether these E2F target genes identified by the DNA microarray are real targets or not. To our perplexity, accumulating bodies of evidence suggest a pivotal role of microRNAs (miRNAs) in human carcinogenesis as unique oncogenes or tumor suppressors [Kent and Mendell, 2006; Zhang et al., 2007]. Microarray analysis revealed down-regulation of the E2F pathway by miR-34a [Tazawa et al., 2007], indicating the importance of miRNA function to be taken into account for E2F target genes. Indeed, miR-17-5p and miR-20a, both of which are transcriptional targets of the cMyc oncogene, negatively regulated E2F [O’Donnell et al., 2005]. Endogenous E2F1, E2F2, and E2F3 could directly bind to the promoter of the miR-17-92 cluster, and miR-20a, a member of the miR-17-92 cluster, modulated the translation of the E2F2 and E2F3 mRNAs

Coupling Computational and Experimental Analysis…

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[Sylvestre et al., 2007]. The E2F3 protein was also confirmed to be down-regulated by miR210 [Giannakakis et al., 2008]. Therefore, we need to know E2F target miRNAs and then which miRNAs can regulate the E2F activity. For this purpose, the adenoviruses Ad-Control, as an empty vector, and Ad-E2F1, containing the E2F1 cDNA, were used. For the infection, A549 human lung carcinoma cells were infected by adding the adenoviral vectors at a MOI (multiplicity of infection) of 100 plaque-forming units per cell. Cells were collected after 24 hours virus infection and total RNA containing miRNA was recovered with a miRNeasy Mini Kit (Qiagen, Valencia, CA). The miRNA processing and hybridization to a human miRNA microarray, which contains 470 mature miRNAs, and data acquisition and analyses was performed according to the manufacture’s miRNA microarray system protocol Version 1.0, April 2007 (Agilent Technologies, Santa Clara, CA) [Wang et al., 2007]. Surprisingly, no miRNAs were up-regulated in Ad-E2F1-infected A549 cells, whereas only 10 miRNAs including miR-202 (0.57-fold), miR-330 (0.59-fold), miR-501 (0.62-fold), miR-509 (0.63fold), miR-601 (0.66-fold), miR-575 (0.67-fold), miR-636 (0.69-fold), miR-149 (0.72-fold), miR-610 (0.73-fold), and miR-583 (0.75-fold) were down-regulated in Ad-E2F1-infected cells compared to Ad-Control-infected cells. We do not have any clues about the functional relationship between E2F and these miRNAs at present.

2. Computational Prediction of E2F Binding Site Locations As described above, one can easily access many candidate genes to be regulated by E2F. Tracing gene lists published in the literature is a reliable method. Another way is to search the public database. The Gene Expression Omnibus (GEO) at the National Center for Biotechnology Information (NCBI) is the most popular public database (http://www.ncbi.nlm.nih.gov/geo/) storing DNA microarray data [Barrett and Edgar, 2006; Edgar and Barrett, 2006; Barrett et al., 2007]. In addition, we have been collecting E2F target genes by over- or down-regulating E2F expression in human cells [Goto et al., 2006]. Although computational methods that can predict the transcriptional start site are available [Zhang, 2007], we searched transcriptional start sites of candidate genes at the NCBI Map Viewer (http://www.ncbi.nlm.nih.gov/projects/mapview/) [Wheeler et al., 2007]. The core promoter is often defined as minimal required sequences, approximately 80~100 base pairs (bp) surrounding the transcriptional start site, which can drive a reporter gene at a basal level. On the other hand, the proximal promoter can be defined as 250~1,000 bp upstream of the core promoter. We usually focus on the 700 bp upstream and 300 bp downstream of transcriptional start sites, -700/+300, in which the transcription start sites, designated as + 1, are forwarded to a transcription factor binding site search. In silico identification of E2F binding site locations is accomplished by searching assembled collections of experimentally defined transcription factor binding sequences. To the best of our knowledge, the largest and most commonly used matrix library collection is the TRANSFAC database for eukaryotic transcription factors [Stormo, 2000; Matys et al., 2003; Matys et al., 2006]. This binding specificity of transcription factors is usually obtained from SELEX (Systematic Evolution of Ligands by Exponential Enrichment) and Chromatin immunoprecipitation (ChIP)-on-chip. Several sets of optimized matrix cut-off values are built in to the TRANSFAC database to provide a variety of search modes of different stringencies. The user simply inputs DNA sequences of their interest into the system with matrices including default or user-defined cut-

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off values. We normally use a cut-off score of 85 for E2F binding site prediction. For more accuracy, it is recommended to perform a double check with another system, such as a MatInspector [Cartharius et al., 2005].

3. Experimental Verification of E2F Binding Site Locations There are a few essential biological assays such as gel shift or ChIP assay for experimentally testing that the computationally identified sequences are really bound by transcription factors. Before this stage, we normally check the identified putative E2F regulatory sequences with a luciferase-based reporter assay. Briefly, a promoter fragment is cloned upstream of the firefly luciferase reporter gene in the pGL3-Basic (Promega, Madison, WI). pRL-TK (Promega), a plasmid that contains the Renilla luciferase gene under the cytomegalovirus promoter, is utilized as an internal control to normalize the effects of the transfection efficiency. A Dual Luciferase Reporter Assay Kit (Promega) is used for the luciferase reporter assay. Light intensity was quantified in a luminescence reader (GloMax 20/20 Luminometer, promega). In our experience, gene promoters that include predicted E2F regulatory elements sometimes failed to be up-regulated by E2F1 co-expression in human cell culture. For example, a TRANSFAC search revealed that upstream of human histone acetyltransferase, MYST2 (a histone acetyltransferase binding to ORC1: hereafter we call this gene HBO1) possesses a putative E2F regulatory element (cut-off score 86). Moreover, HBO1 was selected as candidate gene for an E2F target, because HBO1 has been shown to bind to DNA replication factors ORC1 and MCM2 [Iizuka and Stillman, 1999; Burke et al., 2001]. DNA replication factors are known as classic targets of E2F [Ren et al., 2002]. Indeed, ORC1, MCM5, and MCM6 have been shown to be regulated by E2F1 [Ohtani et al., 1996; Ohtani et al., 1999]. These pieces of evidence favored by bioinformatics strongly suggested that HBO1 potentially is a novel target of E2F. To make sure, we cloned the -270/-1 region of the HBO1 sequence (RefSeq Accession NM_007067), including the predicted E2F regulatory element, into the pGL3-Basic vector upstream of the luciferase coding region, and analyzed the promoter activity of the vector with firefly luciferase as the reporter gene transiently transfected into human culture cells. Co-expression of the E2F1 expression vector with the pGL3-HBO1 270/-1 failed to induce the reporter gene activity under the control of the putative HBO1 promoter (unpublished data). Therefore, this step is very important when determining whether candidate genes are really worth forwarding to the next experimental steps such as RT-PCR, gel shift, and ChIP assays.

4. ChIP-on-Chip Recent progress in genomic microarray technology has allowed researchers to identify the exact location of the chromatin to be bound by transcription factors. The combination of chromatin immunoprecipitation followed by hybridization to tiled arrays (ChIP-on-chip or ChIP-chip) analysis is one of the most powerful tools of the genomic microarray [Lieb, 2003; Ren and Dynlacht, 2004; Blais and Dynlacht, 2005a]. Because cell cycle regulation is strictly regulated by a couple of transcription factors, it is absolutely ideal to be analyzed by ChIPon-chip [Blais and Dynlacht, 2005b; Wu et al., 2007]. Among cell cycle regulators at


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transcriptional levels, E2F has unique roles not also in the G1 to S phase progression but also DNA replication, DNA damage repair, differentiation and development [Cam and Dynlacht, 2003; Bracken et al., 2004]. Therefore, ChIP-on-chip analysis has been employed to identify E2F target genes [Blais and Dynlacht, 2004]. Among ~1,200 genes expressed during cell cycle entry, it was found that the promoters of 127 genes were bound by E2F4, partly in common with E2F1, in human primary fibroblasts. Remarkably, this experiment revealed that E2F could regulate the genes involved in chromatin assembly/condensation, chromosome segregation, and the mitotic spindle checkpoint [Ren et al., 2002]. Using a human CpG microarray, ChIP analysis revealed that E2F4 could bind to 68 unique targets involving genes encoding proteins involved in DNA repair or recombination [Weinmann et al., 2002]. Other report using the ChIP approach urged that E2F and nuclear respiratory factor-1 cooperatively regulate E2F target genes in particularly for mitochondrial biogenesis and metabolism [Cam et al., 2004]. ChIP-on-chip analyses of approximately 24,000 promoters indicated that more than 20% of the promoters were bound by E2F1 [Bieda et al., 2006]. Interestingly, within 30 mega-bp of the human genome, more than 80% of E2F1 binding sites are estimated to be located within core promoters and that 50% of the E2F1 binding sites overlapped with transcription start sites [Bieda et al., 2006]. Recently, the binding patterns of E2F1, E2F4, and E2F6 were assayed by ChIP-on-chip in normal and cancerous cells [Xu et al., 2007], demonstrating that three members share common target promoters and are located within 2 kilo-bp of a transcription start site of the target genes. Epigenetics should be considered to account for spatial regulation of chromatin by E2F. It is recognized that silent and active chromatin loci in eukaryote genome, namely controlling the balance between methylation and acetylation of histone H3 lysine 9, are important in E2F-dependent promoter regulation [Nicolas et al., 2003].

5. Systems Biology The circadian rhythm is a set of biological rhythms that have a periodicity of around 24 hours. Systemic biological approaches partly succeeded in understanding that mammalian circadian clocks consist of complex integrated feedback loops of transcription factors [Hayes et al., 2005; Kronauer et al., 2007]. Interestingly, a recent finding in cyanobacteria strongly indicates that circadian clocks are regulated through transcriptional-translational feedback regulation, especially regulated by phosphorylation of a key clock protein [Iwasaki et al., 2002; Naef, 2005]. This tendency is true of cell cycle regulation. The cell cycle is also a set of biological rhythms that have a periodicity of around 24 hours. The cell cycle holds not only complex integrated feedback loops of transcription factors but also protein-protein interaction. E2F1 itself is known to be modified at a post-translational level. For instance, E2F1 is phosphorylated in response to DNA damage [Stevens et al., 2003]. Stabilized E2F1 can change the transcriptional targets from cell cycle progression to apoptosis genes in response to DNA damage [Pediconi et al., 2003]. The cell cycle database (http://www.itb.cnr.it/cellcycle/) is a useful bioinformatics tool [Alfieri et al., 2008] to help with understanding the cell cycle gene ontology. A recent data-driven mathematical approach to understanding the G1 cell cycle progression revealed that cyclin E/Cdk2 activation is independent of cyclin D/Cdk4/6 in mammalian cells [Haberichter et al., 2007]. Cyclin D/Cdk4/6 and cyclin E/Cdk2 complexes are upstream regulators of E2F; therefore a data-

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driven mathematical approach could be applicable to understand the transcriptionaltranslational feedback regulation as well as redundant E2F members in the context of cell cycle regulation. Apparently, E2F cannot stand alone during the cell cycle regulation. The crossover and information exchange among E2F, p53, and c-Myc for the regulation of the cell cycle and carcinogenesis has been well documented [Matsumura et al., 2003; Stanelle and Pützer, 2006]. A systemic biological approach demonstrated that p53-mediated transcriptional repression of several target genes is dependent of the activities of E2F [Tabach et al., 2005]. E2F1 is known to be involved in both cell cycle and apoptosis [La Thangue, 2003; Bell and Ryan, 2004]. The regulation of how these functions can be separately exerted at a molecular level remains however uncertain [Knezevic and Brash, 2004]. In addition to feedback regulation of transcription factors, apoptosis induced by E2F1 is roughly divided into the p53dependent or p53-independnet types [Stanelle and Pützer, 2006]. These issues are the most challenging case to be solved by a systemic biological approach in the near future.

Conclusion In the future, transcriptional complexity will be more unraveled under close scrutiny by methodological improvements. At present, we can summarize transcriptional complexity at a unicellular level, but eventually it has to be unraveled at tissue or multicellular organism levels. Understanding the full spectrum of the gene regulatory networks will allow us to add or withdraw certain factors from the well-established systems. This type of simulation could be a powerful tool to predict or simulate the pathological conditions of gene regulatory malformation frequently seen in cancerous or disease cells. Stimuli or genes which can affect the robustness of networks can be used for better tools to heal human disease.

Acknowledgement This work was supported in part by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology in Japan (MEXT).

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Iizuka M, Stillman B: Histone acetyltransferase HBO1 interacts with the ORC1 subunit of the human initiator protein. J Biol Chem 1999, 274:23027-23034. Ishida S, Huang E, Zuzan H, Spang R, Leone G, West M, Nevins JR: Role for E2F in control of both DNA replication and mitotic functions as revealed from DNA microarray analysis. Mol Cell Biol 2001, 21:4684-4699. Iwasaki H, Nishiwaki T, Kitayama Y, Nakajima M, Kondo T: KaiA-stimulated KaiC phosphorylation in circadian timing loops in cyanobacteria. Proc Natl Acad Sci USA 2002, 99:15788-15793. Jamshidi-Parsian A, Dong Y, Zheng X, Zhou HS, Zacharias W, McMasters KM: Gene expression profiling of E2F-1-induced apoptosis. Gene 2005, 344:67-77. Kent OA, Mendell JT: A small piece in the cancer puzzle: microRNAs as tumor suppressors and oncogenes. Oncogene 2006, 25:6188-6196. Knezevic D, Brash DE: Role of E2F1 in apoptosis: a case study in feedback loops. Cell Cycle 2004, 3:729-732. Korenjak M, Brehm A: E2F-Rb complexes regulating transcription of genes important for differentiation and development. Curr Opin Genet Dev 2005, 15:520-527. Kronauer RE, Gunzelmann G, Van Dongen HP, Doyle FJr, Klerman EB: Uncovering physiologic mechanisms of circadian rhythms and sleep/wake regulation through mathematical modeling. J Biol Rhythms 2007, 22:233-245. La Thangue NB: The yin and yang of E2F-1: balancing life and death. Nat Cell Biol 2003, 5:587-589. Lieb JD: Genome-wide mapping of protein-DNA interactions by chromatin immunoprecipitation and DNA microarray hybridization. Methods Mol Biol 2003, 224:99-109. Ma Y, Croxton R, Moorer RLJ, Cress WD: Identification of novel E2F1-regulated genes by microarray. Arch Biochem Biophys 2002, 399:212-224. Matsumura I, Tanaka H, Kanakura Y: E2F1 and c-Myc in cell growth and death Cell Cycle 2003, 2:333-338. Matys V, Fricke E, Geffers R, Gössling E, Haubrock M, Hehl R, Hornischer K, Karas D, Kel AE, Kel-Margoulis OV, et al: TRANSFAC: transcriptional regulation, from patterns to profiles. Nucleic Acids Res 2003, 31:374-378. Matys V, Kel-Margoulis OV, Fricke E, Liebich I, Land S, Barre-Dirrie A, Reuter I, Chekmenev D, Krull M, Hornischer K, et al: TRANSFAC and its module TRANSCompel: transcriptional gene regulation in eukaryotes. Nucleic Acids Res 2006, 34:D108-110. Naef F: Circadian clocks go in vitro: purely post-translational oscillators in cyanobacteria. Mol Syst Biol 2005, 1:2005.0019. Nicolas E, Roumillac C, Trouche D: Balance between acetylation and methylation of histone H3 lysine 9 on the E2F-responsive dihydrofolate reductase promoter. Mol Cell Biol 2003, 23:1614-1622. O'Donnell KA, Wentzel EA, Zeller KI, Dang CV, Mendell JT: c-Myc-regulated microRNAs modulate E2F1 expression. Nature 2005, 435:839-843. Ohtani K, DeGregori J, Leone G, Herendeen DR, Kelly TJ, Nevins JR: Expression of the HsOrc1 gene, a human ORC1 homolog, is regulated by cell proliferation via the E2F transcription factor. Mol Cell Biol 1996, 16:6977-6984.


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ISBN 978-1-60692-040-4 c 2009 Nova Science Publishers, Inc.

Chapter 3

S OLVING A S TOCHASTIC G ENERALIZED A SSIGNMENT P ROBLEM WITH B RANCH AND P RICE David P. Morton∗ Graduate Program in Operations Research Department of Mechanical Engineering The University of Texas Austin, TX 78712-0292, 512-471-4104 USA Jonathan F. Bard† Graduate Program in Operations Research Department of Mechanical Engineering The University of Texas Austin, TX 78712-0292, 512-471-3076 USA Yong Min Wang‡ American Airlines, 333 Amon Carter Blvd. MD 5358 Fort Worth, TX 76155-2664 USA

Abstract In this chapter, we investigate the generalized assignment problem with the objective of finding a minimum-cost assignment of jobs to agents subject to capacity constraints. A complicating feature of the model is that the coefficients for resource consumption and capacity are random. The problem is formulated as a stochastic integer program with a penalty term associated with the violation of the resource constraints and is solved with a branch-and-price algorithm that combines column generation with branch and bound. To speed convergence, a stabilization procedure is included. The performance of the methodology was tested on four classes of randomlygenerated instances. The principal results showed that the value of the stochastic solution (V SS), i.e., the gap between the stochastic solution and the expected value solution, was 35.5% on average. At the root node of the search tree, it was found that the linear programming relaxation of the master problem associated with column ∗

E-mail address: [email protected] E-mail address: [email protected]. Corresponding author. ‡ E-mail address: [email protected] †

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David P. Morton, Jonathan F. Bard and Yong Min Wang generation provided a much tighter lower bound than the relaxation of the original constraint-based formulation. In fact, two thirds of the test problems evidenced no gap between the optimal integer solution and the relaxed master problem solution. Additional testing showed that (1) initializing the master problem with a feasible solution outperforms the classical big-M approach; (2) SOS type 1 branching is superior to single-variable branching; and, (3) variable fixing based on reduced costs provides only a slight decrease in runtimes.

Key words: stochastic integer programming, generalized assignment problem, branch and price

1.

Introduction

The generalized assignment problem (GAP) is a classical example of a difficult combinatorial optimization problem that has received considerable attention over the years due to its widespread application. In many instances, it appears as a substructure in more complicated models, including routing problems [11], facility location models [21], and computer networking applications [2]. In the deterministic version of the problem, the objective is to assign jobs to agents at minimum cost, subject to capacity constraints. Despite its simplicity, the GAP is strongly NP-hard [18] and can only be solved to optimality for a few hundred agents and jobs. Recently, the GAP has been extended to capture uncertainty, often an important factor in real-world applications [1, 25, 26]. A stochastic GAP can arise when an agent’s capacity and/or coefficients for resource consumption are known only imprecisely. The purpose of this research is to investigate a stochastic GAP in which both of these sets of coefficients are random. To find solutions, we have developed a branch-and-price algorithm that makes use of a stabilization procedure to speed convergence. Experimental results are presented for instances with up to 20 agents, 60 jobs, and 100 scenarios. In the next section, the relevant literature is reviewed. Section 3. introduces a constraintbased stochastic integer programming formulation for the stochastic GAP, which is reformulated as a set partitioning problem in Section 4. as the first step in column generation. Our branch-and-price algorithm is described in Section 5., followed by our computational experience in Section 6.. Insights gained from model development and testing are summarized in Section 7..

2.

Literature Review

Most exact methods for solving the GAP are based on branch and bound (B&B), beginning with the work of Ross and Soland [20]. Improved relaxations were developed by Fisher et al. [11] and Martello and Toth [17]. In both of these papers, the job assignment constraints are relaxed and placed in the objective function as a penalty term giving rise to a Lagrangian formulation, which is solved with a dual-ascent procedure. The approach proposed in [11] is extended in [14] by allowing temporary primal infeasibility and by adding surrogate constraints whenever such violations occur. However, the performance of the corresponding

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algorithm was seen to degrade as the ratio of the number of agents to the number of jobs grew. Often, exact solutions are not necessary and near-optimal solutions that can be obtained quickly suffice. Most such heuristics for the GAP are based on its linear programming (LP) relaxation. In [27] for example, the LP relaxation is repeatedly solved and decision variables taking 0 or 1 values are fixed. In the implementation, the fixing can occur with a probability less than one. Narciso and Lorena [19] describe a second heuristic rooted in Lagrangian relaxation that makes use of a subgradient algorithm to improve the multipliers. Relative to the deterministic GAP, stochastic variants have received much less attention. Random yes-no demand for individual jobs is modeled via Bernoulli random variables for resource consumption in [1]. In this stochastic program, job-agent assignments are made in the first stage, and after the resource-consumption coefficients are realized, reassignments are made in the second stage to deal with overloaded agents. When the resourceconsumption coefficients are independent of the agents, the combinatorial reassignment problem is totally unimodular. This convexity property allows the authors to employ an L-shaped decomposition method with binary first stage variables and continuous second stage variables. (The L-shaped method [28] generates cutting planes in a manner similar to Benders’ decomposition.) The standard deterministic GAP involves a set of agents, each with a single resourceconsumption constraint, but is extended to agents with multiple resources in [12]. A stochastic variant of the multi-resource GAP is developed in [26], where the resourceconsumption coefficients are deterministic but the agents’ resource capacities are random. Like the model in [1], job-agent assignments are made prior to the realization of the random parameters. To correct any violations of the capacity constraints that may result, three recourse alternatives are discussed: (i) penalize the magnitude of the total violation, (ii) penalize the number of violated resource constraints, or (iii) cancel jobs (and incur a penalty) to satisfy the resource constraints. Bimodal, exponential, and normally-distributed resourcecapacity distributions were considered. Lagrangian relaxation bounds were iteratively tightened and used with a B&B algorithm to solve these models. A model for a stochastic GAP model is presented by Spoerl and Wood [25] in which the resource-consumption coefficients are independent and normally distributed. The normality assumption is exploited in developing an equivalent deterministic model. Under the additional assumption that the resource-consumption coefficients for an agent all have a common mean-to-variance ratio, a smaller deterministic equivalent model is derived. Dantzig-Wolfe decomposition [6, 7] exploits specially-structured linear programs using a reformulation with exponentially-many columns. These columns are iteratively generated and added to a master program as needed by solving a so-called pricing subproblem to identify columns with attractive reduced costs. More generally, a column-generation (CG) method is a way to approach a mathematical program with an excessive number of columns. In some integer programs like the GAP, CG is applied to a reformulation with exponentiallymany columns because more compact formulations have weaker LP relaxations. (In other circumstances, such formulations may be the only model available.) Often, CG is applied only at the root node of the B&B tree for the purpose of obtaining a tight initial LP bound. When the approach is applied at all nodes of the search tree the full methodology is called branch and price (B&P) [4, 29]. In recent decades, B&P has been

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used with considerable success on a variety of problems, including the GAP [23], facility location problems [24], vehicle routing problems [8], and scheduling problems [3, 9]. Effective CG depends on being able to solve the pricing subproblem quickly and on the overall algorithm converging in a reasonable number of iterations. However, since its early application to cutting-stock problems [13], CG has had a reputation of slow convergence, which is attributable in part to multiple optimal dual solutions of the master problem. In response, stabilization methods have been developed that attempt to limit the distance between the dual solutions from one iteration to the next. The primary means of accomplishing this is by slightly relaxing the master problem constraints and penalizing “infeasibilities.” This has the effect of placing bounds on the dual variables. These bounds and associated penalties are typically updated dynamically [10]. Other approaches resolve multiple optimal dual solutions by using an interior point method to solve the master problem [22] or by using a weighted average of previously generated solutions and the current dual solution [30]. For more detail, see [15]. In this chapter, we consider a stochastic GAP that has random resource capacities and random resource-consumption coefficients. We penalize, in expectation, a weighted sum of the magnitudes of resource-constraint violations and then develop a B&P algorithm that includes a stabilization feature along with several other computational enhancements. To the best of our knowledge, no version of the stochastic GAP has been solved by B&P in the literature, although we note that the possibility was discussed in [24].

3.

Mathematical Formulation

We begin by presenting the standard model of the deterministic GAP. Let i ∈ I index the set of agents and j ∈ J index the set of jobs. The goal of the GAP is to find a minimumcost assignment, using binary decision variables xij , of all jobs j ∈ J to agents i ∈ I. The problem can be formulated as follows XX cij xij (1a) min x

s.t.

i∈I j∈J

X

xij = 1,

j∈J

(1b)

i∈I

X

dij xij ≤ bi,

i∈I

(1c)

j∈J

xij ∈ {0, 1},

i ∈ I, j ∈ J

(1d)

where cij is the cost of assigning job j to agent i, bi is the capacity of agent i and dij is the amount of that capacity consumed when job j is assigned to agent i. Constraints (1b) and (1d) ensure that each job is assigned to exactly one agent and constraints (1c) ensure that the resource capacity of agent i is obeyed. The objective function (1a) minimizes the total cost of assigning all jobs to agents. Now let us consider uncertainty in the resource-capacity and resource-consumption co˜ ˜ ˜ efficients. Let ξi = (dij )j∈J , bi denote the random vector of coefficients associated with agent i, and let ξiω = (dωij )j∈J , bωi be its realizations indexed over the sample space,


103

ω ∈ Ωi , where it is assumed that |Ωi| is finite. Let pωi = P (ξ˜i = ξiω ), ω ∈ Ωi , be the corresponding probability mass function and let ξ˜ = (ξ˜i )i∈I be the vector of all the random coefficients. As we describe below, however, our model’s objective function is separable in the subvectors ξ˜i , i ∈ I, and hence the dependency structure among these subvectors is irrelevant. Restated, an optimal solution to our model is optimal for all dependency structures between these subvectors. As with all the stochastic GAP models referenced in the previous section [1, 25, 26], our model first assigns jobs to agents subject to constraints (1b) and (1d) and with costs as indicated in (1a). Then we observe a realization of ξ˜ and penalize the sum of the magnitudes of violations in constraints (1c) over all agents with respective unit penalties qi ≥ 0. We add to the costs already incurred in the objective function (1a), the expected value of this penalty function given as follows.  +  + X X X X qi  = qi Eξ˜i  d˜ij xij − ˜bi d˜ij xij − ˜bi  Eξ˜ i∈I

j∈J

i∈I

j∈J

X

=

i∈I

X

qi

ω∈Ωi

 + X pωi  dωij xij − bωi 

(2)

j∈J

Here, (·)+ = max(·, 0). Linearizing the “max” terms with the help of the continuous variables yiω , which denote the magnitude of the constraint violations, leads to X X XX cij xij + qi pωi yiω (3a) z ∗ = min x,y

s.t.

i∈I j∈J

X

i∈I

xij = 1,

ω∈Ωi

j∈J

(3b)

i∈I

X

dωij xij − yiω ≤ bωi ,

ω ∈ Ωi , i ∈ I

(3c)

j∈J

xij ∈ {0, 1}, yiω

≥ 0,

i ∈ I, j ∈ J

ω ∈ Ωi , i ∈ I

(3d) (3e)

The objective function in (3a) minimizes the job assignment costs as in (1a) plus the expected cost of violating the resource-capacity constraints. Constraints (3c) and (3e) achieve the desired linearization of (2), while constraints (3b) and (3d) are identical to (1b) and (1d).

4.

Reformulating the Stochastic GAP

We begin this section by reformulating model (3) so that it has a column orientation. The motivation for doing so is that the LP relaxation of the constraint-based formulation (3) gives weak lower bounds on z ∗ , resulting in excessive runtimes when B&B is applied directly. (We revisit this issue in Section 6..) After reformulating model (3), we describe how to obtain upper and lower bounds on z ∗ that can be used to reduce the size of the search tree. Finally, we augment our reformulation to help stabilize the CG iterations within the B&P algorithm.

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4.1.

Formulation

Let xi = (xij )j∈J denote the vector of job assignments to agent i, and let xki , k ∈ Ki , index all 2|J| such assignments ranging from agent i having no assignments to being assigned all P + ω k ω d x − b . jobs from J. Given assignment xki and scenario ω ∈ Ωi , let yiωk = i j∈J ij ij With yik = yiωk ω∈Ω , we have the pairs (xki , yik ) over k ∈ Ki, i ∈ I, representing all i P P feasible solutions to (3). Defining cki = j∈J cij xkij + qi ω∈Ωi pωi yiωk , i.e., the expected cost of assignment xki , we can reformulate model (3) as follows. z ∗ = min λ

s.t.

XX

cki λki

(4a)

i∈I k∈Ki

XX

xkij λki = 1,

j∈J

(4b)

i∈I k∈Ki

X

λki = 1,

i∈I

(4c)

k∈Ki λki ∈

{0, 1},

k ∈ Ki , i ∈ I

(4d)

Constraints (4c) and (4d) ensure exactly one set of jobs is assigned to each agent and the objective function gives the expected cost of that assignment. Constraint (4b) is then equivalent to (3b), i.e., each job is done once. Problem (4) is called the full master problem (MP). Of course, it is neither practical nor desirable to explicitly enumerate all feasible assignments of Ki , i ∈ I. Instead we start with modest-sized subsets Ki0 ⊂ Ki, i ∈ I, that have the property that each job j ∈ J can be covered by at least one of the agents, i.e., constraints (4b) - (4d) are feasible when Ki is replaced by Ki0. This leads to the so-called restricted master problem (RMP). z¯ = min λ

s.t.

XX i∈I

k∈Ki0

i∈I

k∈Ki0

XX X

cki λki

(5a)

xkij λki = 1,

λki = 1,

j∈J

i∈I

(5b) (5c)

k∈Ki0

ˆ = Let λ

ˆk λ i

k∈Ki0 , i∈I

λki ∈ {0, 1},

k ∈ Ki0, i ∈ I

be a feasible solution to the LP relaxation of model (5).

îj = Then (ˆ xij , yîω )ω∈Ωi ,i∈I,j∈J is a feasible solution to the LP relaxation of (3), where x P P k k ω ωk k ˆ ˆ î = k∈K 0 yi λi . The first stage decision is binary, and the following k∈Ki0 xij λi and y i ˆ and x proposition characterizes the relationship between λ ˆ. ˆ = (λ ˆ k )k∈K 0 ,i∈I be an optimal solution to the LP Proposition 1. (Savelsbergh [23]) Let λ i i ˆ k is fractional for some i, then there must be a j such that x îj = relaxation of (5). If λ i P k k ˆ k∈K 0 xij λi is fractional. i


105

The proof of this proposition in [23] is for the deterministic GAP, but hinges on the assumption that there are no duplicate columns in the (restricted) master problem. This assumption is valid for our (restricted) master problem so Savelsbergh’s proof carries over directly to (5). Consider the LP relaxation of (5) and let πj , j ∈ J, and αi , i ∈ I, be optimal dual variables associated with constraints (5b) and (5c), respectively. The reduced cost for λki is then c¯ki = cki − =

X

X

πj xkij − αi

j∈J

(cij − πj ) xkij + qi

j∈J

X

pωi yik,ω − αi

ω∈Ω

The optimal dual multipliers from the RMP are defined over the problem with columns Ki0 , i ∈ I. Consider the problem of solving mink∈Ki c¯ki , i.e., finding a column for agent i with the smallest reduced cost over the set Ki . Such a column can be found by solving the following pricing problem for agent i.

vi = min xi ,yi

s.t.

X X (cij − πj )xij + qi pωi yiω j∈J

X

ω∈Ωi

dωij xij

−

yiω

≤

bωi ,

ω ∈ Ωi

(6)

j∈J

xij ∈ {0, 1}, yiω ≥ 0,

ω ∈ Ωi , j ∈ J

î = (ˆ xij )j∈J and yî = (ˆ yiω )ω∈Ωi . If vi − αi ≡ Let (ˆ xi , yî ) solve (6), where x îj to the RMP with objective function comink∈Ki c¯ki 3). Therefore, using multi-class contact maps is expected to improve the resolution of reconstruction algorithms on geometrical constraints. Moreover, if a suitable set of distance thresholds is chosen, the number of instances in each class may be kept approximately balanced, which in turn may improve generalisation performances of learning algorithms over the (normally unbalanced) binary prediction case. For our experiments, we derived a set of five distance thresholds to define multi-class contact maps based on four distance intervals. As shown in Figure 5, the four classes are empirically chosen from the distribution of distances among amino acids in the training set, ignoring trivial pairs |i − j| ≤ 3 and by trying to keep informative distance constraints and the classes as balanced as possibile. The resulting set of thresholds is {0, 8, 13, 19, ∞}, which defines suitable distance intervals corresponding to short ( [0, 8)), medium ([8, 13), [13, 19)) and long-ranged interactions among amino acids. A potential improvement beyond this choice is to automatically determine an optimal set of thresholds based on some criteria, e.g. the reconstruction ability on a set of benchmarking proteins.

3.

Modelling Structures with Contact Maps

We predict protein models by solving a global optimisation problem, where a function (pseudo-energy) is minimised by searching the configurational space of 3D structures. The pseudo-energy function we use to guide the search is designed in a way that allows us to

Fast Modelling of Protein Structures Through Multi-level Contact Maps

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solve an unconstrained minimisation problem by a simple simulated annealing protocol. More specifically, the pseudo-energy function measures the degree of match of a protein conformation to the constraints encoded in the contact map (binary or multi-class) predicted in the first stage. In the following, we describe the set of moves used to explore the configurational space and the different forms of potential functions used respectively for binary and multi-class contact maps.

3.1.

Optimisation Algorithm

The algorithm we use for the reconstruction of the coordinates of protein C α traces is organised in two sequential phases, bootstrap and search. The function of the first phase is to generate an initial physically realisable configuration. A random structure is created using a self-avoiding random walk and explicit modelling of predicted helices, by adding C α positions one after the other until an initial draft of the whole backbone is obtained. More specifically, this part runs through a sequence of N steps, with N being the length of the r where input chain. At stage i, the position of the i-th Cα is computed as ri = ri−1 + d |r| d ∈ [3.733, 3.873] and r is a random direction vector. Both d and r are uniformly sampled. If the i-th residue is predicted at the beginning of an helix, all the following residues in the same segment are modelled as an ideal helix with random orientation. In the search step, the algorithm refines the initial bootstrapped structure by global optimisation of a pseudo-potential function using local moves and a simulated annealing protocol. Simulated annealing is a good choice in this case, since the constraints obtained from various predictions are in general not realisable and contradictory. Hence the need for using a “soft” method that tries to enforce as many constraints as possible never terminating with failure, and is robust with respect to local minima caused by contradictions. The search strategy is similar to that in [4], but with a number of modifications. At step t of (t) the search, a randomly chosen Cα atom at position ri is displaced to the new position (t+1) by a crankshaft move (Figure 6), leaving all the other C α atoms of the protein in their ri original position. Secondary structure elements are displaced as a whole, without modifying their geometry (Figure 7). The move in this case has one further degree of freedom in the helix rotation around its axis. This is assigned randomly, and uniformly distributed. A new set of coordinates S (t+1) is accepted as the best next candidate with probability (t) p = min(1, e∆C/T ) defined by the annealing protocol, where ∆C = C(S (t), M) − C(S (t+1), M) and T (t) is the temperature at stage t of the schedule.

3.2.

Pseudo-energy Function

Let Sn = {ri}i=1...n be a sequence of n 3D coordinates, with ri = (xi , yi , zi) the coordinates of the i-th Cα atom of a given conformation related to a protein p. Let DSn = {dij }i<j , dij = kri − rj k2, be the corresponding set of n(n − 1)/2 mutual distances between Cα atoms. A first set of constraints comes from the (predicted) contact map and depends on the type of contact maps, i.e. binary (see section 3.2.1.) or multi class maps (see section 3.2.2.). The representation of protein models induces the constraints B = {dij ∈ [3.733, 3.873], |i − j| = 1}, encoding bond lengths, and another set

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Davide Baù, Ian Walsh, Gianluca Pollastri et al.

(t)

Figure 6. Crankshaft move: a randomly chosen C α atom at position ri is displaced to the (t+1) leaving all the others C α atoms of the protein in their original position. new position ri

Figure 7. Secondary structure elements are displaced as a whole, without modifying their geometry.

C = {dij ≥ DHC , i 6= j} for clashes. The set M = C ∪ B ∪ C defines the configurational space of physically realisable protein models. 3.2.1. Binary Contact Map Constraints When using binary contact maps the set of contraints coming from the predicted maps can 2 be represented as a matrix C = {cij } ∈ {0, 1}n . Let F0 = {(i, j) | dij > dT ∧ cij = 1} denote the pairs of amino acid in contact according to C (binary case) but not in Sn (“false negatives”). Similarly, define F1 = {(i, j) | dij ≤ dT ∧ cij = 0} as the pairs of amino acids in contact in Sn but not according to C (“false positives”). The objective function is then defined as: X X (dij /DT )2 + (dij − DB )2 } C(Sn, M) = α0 {1 + (i,j)∈F0

+ α1 |F1| + α2

X

(i,j):dij 6∈C

(i,j):dij 6∈B (DHC −dij )

e

(1)


175

3.2.2. 4-class Contact Map Constraints In the case of 4-class contact maps, the constraint derived from the predicted map assumes a slightly different form. Since contacts between pairs of C α are here predicted in four classes, a contact is penalised not only if it is not present in the predicted map, but also depending on its distance to the boundaries of the correspoding class: Fk = {(i, j) | Dk < dij < Dk+1 ∧ cij 6= k} with Dk being the distance thresholds that define the classes. 0 Let Dk = (Dk + Dk+1 )/2, then the objective function is defined as: C(Sn , M) = α0 {1 + +

X X

X

k (i,j)∈Fk

(dij − DB )2} + α1

(i,j):dij 6∈B

3.3.

0

(dij /Dk )2 X

e(DHC −dij )

(2)

(i,j):dij 6∈C

Experiments and Results

The protein data set used in reconstruction simulations consists of a non redundant set of 258 protein structures (S258) showing no homology to the sequences employed to train the contact map predictors (see below). This set includes proteins of moderate size (51 to 200 amino acids) and diverse topology as classified by SCOP (Structural Classification of Proteins database) [27] (all-α, all-β, α/β, α + β, surface, coiled-coil and small). No two proteins in this set share more than 25% sequence identity. In all the experiments, we run the annealing protocol using a non linear (exponential decay) schedule with initial (resp. final) temperature proportional to the protein size (resp. 0). Pseudo energy parameters are set to α0 = 0.2 (false non-contacts), α1 = 0.02 (false contacts) and α2 = 0.05 (clashes) for binary maps and α0 = 0.005 and α1 = 0.05 (clashes) for multi-class maps, so that the conformational search is biased towards the generation of compact clash-free structures and with as many of the predicted contacts realised. In the first set of simulations we compare the quality of reconstructions based on binary maps and multi-class maps for the case in which experimental constraints are known, that ˚ , since these are more informative than is the maps are native. We use binary maps at 12 A a number of alternative we tested (tests not shown). In order to assess the quality of predictions, two measures are considered here: root mean square deviation (RMSD) and TM-score [28] between the predicted structure and the native one. For each protein in the test set, we run 10 folding simulations and select the best one. The results for the best simulations are then averaged over all the 258 proteins in the set and are reported in Table 1.

4.

Contact Map Prediction

Only a small number of algorithms have being developed for the prediction of distance maps [11, 29]. Far more common are methods for the prediction of binary contact maps ˚ , 8A ˚ , 10A ˚ , or 12A ˚ usually chosen to define the [18–24], with distance cutoffs of 6 A

176


Table 1. Reconstruction algorithm results for the best models derived from binary and multi-class true contact maps. Maps Binary 4-Class

RMSD 4.01 2.23

TM-score 0.65 0.83

threshold between a contact and a non-contact. At the Critical Assessment of Protein Struc˚ between ture Prediction, CASP [30], maps are evaluated with a distance threshold of 8 A Cβ atoms (Cα in the case of Gly). There is a wide range of machine learning techniques for predicting contacts: hidden markov models [31], recursive neural networks [9], multi-layer perceptrons [18, 19, 24], support vector machines [22, 23], and self-organizing maps [21] are just a few. Predictors of contact maps are virtually always ab initio, meaning that they do not rely directly on similarity to proteins of known structure. In fact, often, much care is taken to try to exclude any detectable similarity between training and test set instances when gauging predictive performances of structural feature predictors. The method we present here is based on recursive neural networks, in particular 2dimensional recursive neural networks (2D-RNNs). We predict both binary and multi-class maps. The system presented is an update of the system which took part in CASP7 [30]. The most significant update is the addition of homology information from the PDB [32]. In the following sections we give a detailed overview of the system and show that homology information greatly increases the performance of the predictor, even in the difficult [0,30)% sequence identity homology zone.

4.1. 2D-RNNs 2D-RNNs were previously described in [20] and [33]. This is a family of adaptive models for mapping two-dimensional matrices of variable size into matrices of the same size. If oj,k is the entry in the j-th row and k-th column of the output matrix (in our case, it will represent the estimated probability of residues j and k belonging to a particular class), and ij,k is the input in the same position, the input-output mapping is modeled as: (1) (2) (3) (4) oj,k = N (O) ij,k , hj,k , hj,k , hj,k , hj,k (1) (1) (1) (1) (1) hj,k = N (1) ij,k , hj−1,k , .., hj−s,k , hj,k−1 , .., hj,k−s (2) (2) (2) (2) (2) hj,k = N (2) ij,k , hj+1,k , .., hj+s,k , hj,k−1 , .., hj,k−s (3) (3) (3) (3) (3) hj,k = N (3) ij,k , hj+1,k , .., hj+s,k , hj,k+1 , .., hj,k+s (4) (4) (4) (4) (4) hj,k = N (4) ij,k , hj−1,k , .., hj−s,k , hj,k+1 , .., hj,k+s j, k = 1, . . ., N s = 1, . . . , S


177

(n)

where hj,k for n = 1, . . . , 4 are planes of hidden vectors transmitting contextual information from each corner of the matrix to the opposite corner. We parametrise the output update, and the four lateral update functions (respectively N (O) and N (n) for n = 1, . . . , 4) using five two-layered feed-forward neural networks, as in [33]. Stationarity is assumed for all residue pairs (j, k), that is the same parameters are used across all j = 1, ..., N and k = 1, ..., N . Each of the 5 neural network contains its own individual parameters, that are not constrained to the ones of the other networks. We use 2D-RNNs with shortcut connections. The best way to think of shortcuts is to think of a simple recurrent network in a 1-dimensional (1D) case. The standard definition of 1D recurrent neural networks prescribe an explicit dependency between the input being processed now (here), at time (position) j, and the item processed previously, j − 1, resulting in an implicit dependency between j and all previous items. Most algorithms lack the power to extract information from the implicit dependencies (especially when using gradient learning) beyond the span of a few steps, because of the well known problem of vanishing gradient [34]. Therefore allowing shortcuts is an extension of this idea where in addition to simply having a a direct dependency on the previous item, j − 1, there is also a direct dependency on the previous j − s for all s > 1, ..., S. Indeed, shortcut connections can be placed at any of the previous inputs j − s for any s ∈ 1, .., S. The latter placement of shortcuts between j and S was used to produce near perfect secondary structure predictions in a bidirectional recurrent neural network when (j, s) are native contacts [35]. Notice that increasing the number of shortcuts increases the parameters resulting in a model that may overfit on the data. Extending this idea to the 2D case in any direction in the matrix is straightforward (in fact any dimension can be processed). Shortcut directions and patterns are not strictly constrained (so long as cycles are not introduced in the directed graph representing the network) and may even be learned. With the addition of shortcuts the span of contextual information analysed by a recursive network can be extended, although this may come at the price of increased noise reaching the input, and increased potential for overfitting the examples. The choice of input ij,k is an important factor for the algorithm. In the case of contact map prediction the simplest input is the amino acid symbols at (j, k). Different input signals can be constructed to improve the algorithm. For example, contact density was used in [8] to improve contact map prediction accuracy significantly. In section 4.4 the design of the input will be discussed.

4.2. Training Learning proceeds by gradient descent by minimising the relative cross entropy between target and output. Careful management of the gradient must take place, not letting it be too small or too large: the absolute value of each component of the gradient is kept within the [0.1,1] range, meaning that it is set to 0.1 if it is smaller than 0.1, and to 1 if it is greater than 1. The learning rate is set to 0.3 divided by the the total number of proteins in the dataset. The weights of the networks are initialised randomly. Learning is slow due to the complexity of the problem. Each 2D-RNN contains 5 neural networks, replicated N 2 times for a protein of length N . During each training epoch forward and back-propagation has to occur in each of the 5×N 2 networks, for all P proteins in

178


the training set. The neural network forward and back-propagation have a complexity proportional to O(θ) where θ is the number of parameters in the network. Learning generally converges at about 300-350 epochs. Although the complexity of an epoch is polynomial at O(θN 2 P ), the large size of the training set, and especially the quadratic term in the length of the proteins make learning quite time-consuming. Training of all systems (binary, multiclass; ab initio, template-based) took approximately three months on a cluster of 10 2.8GHz CPUs. However, during prediction only one forward propagation needs to run for each instance, meaning that predictions for a set may be run in roughly 3 orders of magnitude less time than a training on the same set. For instance, maps for 1000 proteins of average length 120 amino acids can be predicted in approximately 13 hours on a single 2.8GHz CPU, and genomic-scale predictions are possible even on a small cluster of machines.

4.3. Architecture In each of the 5 neural networks used to parameterise the functions, N (O) and N (n) for n = 1, . . . , 4, we use a single hidden layer. Let Nhh and Nho denote the number of units associated with the hidden layer and the output layer of the hidden contextual networks respectively. From the definition of the 2D-RNN we see that each hidden network has I regular input units and 2 × Nho + S × Nho contextual inputs, where S are the total number of shortcuts allowed. Thus, including the usual bias terms in each layer, the total number of parameters in one of the four hidden networks is: (I + 2 × Nho + S × Nho ) × Nhh + Nhh + Nhh × Nho + Nho . The output network also contains I regular inputs but it takes contextual inputs from the four hidden networks 4 × Nho resulting in: (I + 4 × Nho ) × Nh + Nh + D × N h + D parameters, where Nh are the number of units in the hidden layer of the output network and D is the number of classes. The activation functions used are softmax and tanh. Only the output units of the output network have softmax functions in order to estimate Bayesian posterior probability of class membership. All other units have tanh transfer functions. No overfitting avoiding techniques such as early stopping or weight decay were applied given the very large size of the datasets, and the fact that we ensemble many networks in the final predictor (see section 4.5.2). Due to the large computational power needed to train one model we ensemble networks both from different trainings and from different stages of the same training. Networks are saved every 5 epochs, and for each training the last 3 networks are ensembled. Three networks with different architectural parameters (Nhh = Nho = Nh = 13, 14, 15) are trained for each predictor. Results for network performances in this work are reported for these ensembles of 3 × 3 = 9 models. Ensembling leads to significant classification performance improvements over single models. All results are in 5-fold cross validation, meaning that, in fact, 5 times 9 models are available for each system. For the reconstruction results (see next section) only the final networks for each training are ensembled, for a total of 1 × 3 × 5 = 15 for each system. The number of classes is D = 2 or D = 4 depending on the problem (binary vs. multiclass). For all networks the number of shortcuts is S = 2, with more sophisticated shortcut placements to be investigated in the future.


179

4.4. Input Design Input ij,k associated with the j-th and k-th residue pair contains primary sequence information, evolutionary information, structural information, and direct contact information derived from the PDB templates: (E)

(T )

ij,k = (ij,k , ij,k )

(3)

where, assuming that e units are devoted to evolutionary sequence information and structural information in the form of secondary structure [36, 37], solvent accessibility [36, 38] and contact density [8]: (E)

(1)(E)

ii,j = (ij,k

(e)(E)

, . . . , ij,k

)

(4)

)

(5)

Template information is placed in the remaining t units: (T )

(1)(T )

ij,k = (ij,k

(t)(T )

, . . ., ij,k

Hence ij,k contains a total of e + t components. As in [8] e = 418, consisting of a sparse 20 × 20 matrix corresponding to the frequency of all pairs of amino acids observed in the two columns j and k of the multiple sequence alignment - this was chosen in order to capture information about correlated mutations. Structural information in the form of secondary structure (three classes), solvent accessibility (two classes), and contact density (four classes) for residue j and k are placed in the remaining 6,4 and 8 input units respectively. For the template units we use t = 3 for binary maps and t = 5 for multi class maps, representing weighted contact class information from the templates and one template quality unit. For example, in the case of multi class maps the first four input units contain the weighted average contact class frequency in the PDB templates, while the last unit encodes (p) the average quality of the template column. Assume that dj,k is a 4-component binary vector encoding the contact class of the j-th and k-th residue pair in the p-th template. Then, if P is the total number of templates for a protein: (1)(T ) (4)(T ) (ij,k , . . . , ij,k )

=

PP

(p) p=1 wp dj,k PP p=1 wp

(6)

where wp is the weight attributed to the p-th template. If the sequence identity between template p and the query is idp and the quality of a template (measured as X-ray resolution + R-factor/20 or 10 for NMR hits, as in [39]) is qs , then the weight is defined as: wp = qp id3p

(7)

Taking the cube of the identity between template and query allows to drastically reduce the contribution of low-similarity templates when good templates are available. For instance a 90% identity template is weighed two orders of magnitude more than a 20% one. In preliminary tests (not shown) this measure performed better than a number of alternatives.

180


The final unit of ij,k , the quality unit, encodes the weighted average coverage and similarity of a column of the template profile as follows: PP (5)(T ) p=1 wp cp (8) ij,k = PP p=1 wp where cp is the coverage of the sequence by template p (i.e. the fraction of non-gaps in the alignment). Encoding template information for the binary maps is similar. (E) Ab initio based predictions use only the first part of the input, ij,k from equation 4, including secondary structure, solvent accessibility and contact density, although these are predicted ab initio. The template based predictions use the complete ij,k as input.

4.5. Experiments 4.5.1. Problem Definition The main objective of the experiments is to compare ab initio systems (PDB templates are assumed unavailable) and template-based systems. When very reliable PDB information (e.g. sequence identity to the query greater than 30-35%) is available we expect templatebased predictions to be substantially better, and in fact, to nearly exactly replicate the maps of the best template. More interesting questions are: whether template-based predictions improve on ab initio ones in the so called twilight zone of sequence similarity (less than 30%); whether, in this same region, template-based predictions are better than can be obtained by simply copying the map of the best template, or a combination of the maps of the templates. ˚ contact maps ˚ ab intio contact maps (12AI ), 12 A The 4 systems that we test are 12 A with templates (12T E ), multi-class ab intio (MAI ) and multi- class with templates (MT E ). 4.5.2. Dataset The dataset used in the present simulations is extracted from the December 2003 25% pdb select list 1. We use the DSSP program [40] (CMBI version) to assign relevant structural features (secondary structure and relative solvent accessibility). Cα coordinates, directly available from the PDB, are used to calculate contact density [8]. Sequences for which DSSP does not produce an output due, for instance, to missing entries or format errors are removed. For computational reasons, and to focus on single domains, proteins which have more than 200 amino acids are also removed. After processing by DSSP and the removal of long proteins, the set contains 1602 proteins and 163,379 amino acids. All the tests reported in this paper are run in 5-fold cross validation. The 5 folds are of roughly equal sizes, composed of 318-327 proteins. The datasets are available upon request. Evolutionary information in the form of Multiple sequence alignments have long being shown to improve prediction of protein structural features [20, 33, 37, 41–45]. Multiple sequence alignments for the 1602 proteins are extracted from the NR database as available on March 3 2004 containing over 1.4 million sequences. The database is first redundancy reduced at a 98% threshold, leading to a final 1.05 million sequences. The alignments are 1

http://homepages.fh-giessen.de/˜hg12640/pdbselect


181

˚ binary classes and the four classes in Table 2. Number of residues contained in 12A the Multi class definition. class 0

class 1

˚ 12A

4,062,483

15,755,172

Multi class

1,623,411

3,205,472

class 2

class 3

5,176,584

9,812,188

generated by three runs of PSI-BLAST [46] with parameters b = 3000, e = 10−3 and h = 10−10. Table 2 shows the class distribution of both types of map in the dataset. What is immediately obvious from this table is that the class distribution is more balanced in the 4 class problem and therefore should be easier to learn. 4.5.3. Template Generation For each of the 1602 proteins we search for structural templates in the PDB. We base our search on PDBFINDERII [47] as available on August 22 2005. An obvious problem arising is that all proteins in the set are expected to be in PDB (barring name changes), hence every protein will have a perfect template. To avoid this, we exclude from PDBFINDERII every protein that appears in the set. We also exclude all entries shorter than 10 residues, leading to a final 66,350 chains. Because of the PDBFINDERII origin, only one chain is present in this set for NMR entries. To generate the actual templates for a protein, we run two rounds of PSI-BLAST against the version of the redundancy-reduced NR database described above, with parameters b = 3000 (maximum number of hits), e = 10−3 (expectation of a random hit) and h = 10−10 (expectation of a random hit for sequences used to generate the PSSM). We then run a third round of PSI-BLAST against the PDB using the PSSM generated in the first two rounds. In this third round we deliberately use a high expectation parameter ( e = 10) to include hits that are beyond the usual Comparative Modelling scope ( e < 0.01 at CASP6 [25]). We further remove from each set of hits thus found all those with sequence similarity exceeding 95% over the whole query, to exclude PDB resubmissions of the same structure at different resolution, other chains in N-mers and close homologues. The distribution of sequence similarity of the best template, and average template similarity is plotted in figure 8. Roughly 14% of the proteins have no hits at more than 10% sequence similarity. About 19% of all proteins have at least one very high quality (better than 90% similarity) entry in their template set. Although the distribution is not uniform, all similarity intervals are adequately represented: for about 41% of the proteins no hit is above 30% similarity; for nearly 24% of the proteins the best hit is in the 30-50% similarity interval. The average similarity for all PDB hits for each protein, not surprisingly, is generally low: for roughly 73% of all proteins the average identity is below 30%. It should be noted that template generation is an independent module in the systems. We are currently investigating whether more subtle strategies for template recognition would still benefit contact map predictions, with or without retraining the systems on the new template distributions.

182


Figure 8. Distribution of best-hit (blue) and average (red) sequence similarity in the PSIBLAST templates for the S2171 set. Hits above 95% sequence similarity excluded.

4.5.4. Training/Testing Protocol The predictors of contact maps rely on predictions of secondary structure, solvent accessibility and contact density [8]. True structural information was used for training in both ab initio and template based systems. For testing, we used predictions from our servers: Porter, PaleAle and BrownAle predicting secondary structure, solvent accessibility and contact density respectively. The ab initio models use ab initio secondary structure, solvent accessibility and contact density predictions. The template models use template-based secondary structure and solvent accessibility and ab initio contact density predictions (template-based contact density remains to be investigated). All our experiments are carried out in 5-fold cross validation. The same dataset and multiple alignments are used to train the ab initio and template based secondary structure predictor Porter, solvent accessibility predictor PaleAle and the contact density predictor BrownAle. By design, these were trained using the same 5 fold split as the map predictors, therefore removing a trained fold while testing was a simple procedure and all 1D predictions are by models that were trained on a dataset split independent on the query. The accuracy measure for all classes is calculated in order to compare the ab initio and template based models: C−1 X correctc (9) Accuracy = totalc c=0

where C is the total number of classes. All the accuracy values are calculated as a function of the best hit template found in the PDB to the query sequence. The best hit was determined


183

Table 3. Percentage of classified predicted residue pairs for the ab initio (12AI ) and ˚ predictor (12T E ) as a function of sequence identity to the best template based 12 A template. Template sequence identity 10 means all proteins that have a best hit template in the identity range [0, 10) %, All is the complete set. 10

20

30

40

50

60

70

80

90

≥

All

12AI

85.9

87.5

86.8

85.6

87.2

86.5

86.2

86.1

86.4

87.3

86.8

12T E

85.3

87.8

91.3

93.6

95.7

96.0

95.8

96.4

97.0

97.3

93.2

90

Table 4. Identical to table 2 except only calculated for non template regions of the map. 10

20

30

40

50

60

70

80

90

≥

All

90 12AI

85.8

87.6

88.1

89.9

92.0

90.8

93.1

90.5

94.0

94.0

87.9

12T E

85.3

87.1

88.4

91.4

92.8

92.8

94.0

94.3

94.8

94.4

87.7

by sequence identity between a template sequence and the query sequence.

4.6. Results and Discussion ˚ ab initio and template based predictions ( 12AI Table 3 reports the comparison between 12 A vs. 12T E ) as a function of sequence identity to the best PDB hit. The only decrease in performance is in the [0,10)% identity range, where the accuracy slightly decreases by 0.6%. However, the same results for multi class maps show that there is never a decrease in performance (Table 6). A role in this is played by the quality of predictions in regions not covered by the templates (reported in Tables 4 and 7). In these areas, for a sequence similarity of 20% and greater both 12T E and MT E perform better than, respectively, 12AI and MAI . However, for lower similarity, 12AI outperforms 12T E on areas not covered by templates, while MT E still improves on MAI . This may be either due to more balanced nature of the problem, easier contextual propagation in the multi-class case (the narrower class

Table 5. Percentage of classified predicted residue pairs for 12T E when only considering the residues covered by the best template. Baseline is a predictor that copies the contact assignment from the best hit template.Template sequence identity 10 means all proteins that have a best hit template in the identity range [0, 10) %. 10

20

30

12T E

79.2

86.8

92.0

Baseline

84.0

89.2

92.1

184


Table 6. Percentage of classified predicted residue pairs for the ab initio (MAI ) and template based Multi class predictor (MT E ) as a function of sequence identity to the best template. Template sequence identity 10 means all proteins that have a best hit template in the identity range [0, 10) %, All is the complete set. 10

20

30

40

50

60

70

80

90

≥

All

MAI

59.3

59.4

58.4

57.3

58.3

57.4

58.3

58.5

58.2

59.9

58.8

MT E

60.2

64.2

75.9

82.5

87.8

88.8

88.1

89.7

91.5

92.1

80.8

90

Table 7. Identical to table 5 except only calculated for non template regions of the map. 10

20

30

40

50

60

70

80

90

≥

All

90 MAI

59.0

58.3

61.8

64.8

71.6

69.4

75.0

71.4

75.7

75.5

61.1

MT E

60.3

60.7

65.7

71.2

76.4

75.5

80.3

82.1

80.2

79.4

63.8

Table 8. Percentage of classified predicted residue pairs for MT E when only considering residues covered by the best template. Baseline is a predictor that copies the class assignment from the best hit template. Template sequence identity 10 means all proteins that have a best hit template in the identity range [0, 10) % 10

20

30

MT E

60.2

69.8

78.8

Baseline

54.8

67.1

78.6

ranges impose stricter distance constraints among neighbours), or a combination of both. Ultimately, templates improve multi-class predictions in all regions of sequence similarity (including [0,10)%), both for regions covered and regions not covered by templates. Tables 5 and 8 report the comparison between template based predictions and a baseline ˚ and multi- class respectively. The baseline simply calculates the class for position for 12A (i, j) from the coordinates in the best template. We also tested different baselines in which, instead of just the top template, the top 10 templates and all templates were used to get the class by a majority vote among the templates covering each template. We tested both an unweighed vote and a vote in which each template is weighed by its sequence similarity to the query, cubed. The latter weighing scheme is identical to the one used to present the templates to the neural networks (see equation 7). In all cases the baseline is worse than the best hit baseline, therefore the results are not reported here. We only report the predictions vs. baseline for the [0,30)% templates, since above 30% identity, as expected, the results are essentially the same. In this twilight region, where it is difficult to extract information


185

from templates, MT E outperforms the baseline, however 12T E does not. The multi-class results are clearly encouraging, outperforming the baseline (Table 8), always improving on non-template regions (Table 7) and overall maps (Table 6). Figure 10 and 11 show an example of a map predicted for a low best hit sequence identity of 22.7%.

4.7. Modelling Protein Structures from Predicted Maps In Figure 9, the average RMSD vs sequence length is shown for models for set S258 derived from true 4-class contact maps (stars), from MT E maps (squares) and from MAI maps (Xs), together with the baseline (crosses). The baseline represents a structure collapsed into its center of mass. Note that no templates are allowed that show a sequence identity greater than 90% to the query. Hence, the MT E results are based on a mixture of good, bad and no templates, akin to the distribution one would expect when presented with a protein sequence that is not in the PDB. The distribution of templates for S258 (not reported) resembles closely the one for the training/testing set, reported in Figure 8. It is also important to note that the results are an average of 10 reconstructions. If more reconstructions were run and, especially, if these were ranked, the results would likely improve considerably. The average ˚ and the average TM score 0.51. If the best of the reconstruction RMSD for MT E is 9.46A ˚ and 0.55, respectively. 10 reconstructions is picked, these improve to 8.59 A

Table 9. Reconstruction algorithm results for models derived from multi-class predicted contact maps with (MT E ) and without (MAI ) allowing homology information. Note that, since no templates are allowed that show a sequence identity greater than 90% to the query, the MT E results are based on a mixture of good, bad and no templates (see Figure 8 for a sample distribution of template quality). The reported values are the average over the 10 runs of simulated annealing. Maps MAI MT E

RMSD 14.60 9.46

TM-score 0.27 0.51

Reconstructions based on 4-class maps are significantly better than those from binary maps. Tested on both ab initio and homology-based 4-class maps, results show that homology-based predictions are generally more accurate than ab initio ones even when homology is dubious. For sequence similarity above 30% the predictions’ TM-score is on average slightly above 0.7 indicating high reliability, is approximately 0.45 in the 20-30% interval, and 0.27 in the region below 20%. If reconstruction performances are measured on the S258 set without allowing homology information at any stage (pure ab initio predictions) the average TM-score is 0.27, with 43 of the 258 structures above a TM-score of 0.4.

186


Figure 9. 4-class contact maps: average RMSD vs sequence length is shown for models derived from true contact maps (blue stars), from predicted contact maps using information derived from homologues (MT E ) (purple squares) and from ab initio predicted contact maps (green Xs), together with the baseline (red crosses). Note that, since no templates are allowed that show a sequence identity greater than 90% to the query, the MT E results are based on a mixture of good, bad and no templates (see Figure 8 for a sample distribution of template quality).

5.

Conclusions

In this work we have described a machine learning pipeline for high-throughput prediction of protein structures, and have introduced a number of novel algorithmic ideas. First, based on the observation that protein binary contact maps are somewhat lossy representations of the structure and yield only relatively low-resolution models, we have introduced multi-class maps, and shown that, via a simple simulated annealing protocol, these lead to much more accurate models, with an average RMSD to the native structure of ˚ and a TM score of 0.83. just over 2 A Secondly, extending on ideas we have developed for predictors of secondary structure and solvent accessibility [36] we have presented systems for the prediction of binary and multi-class maps that use structural templates from the PDB to yield far more accurate predictions than their ab initio counterparts. We have also shown that multi-class maps lead to a more balanced prediction problem than binary ones. Although it is unclear whether because of this, or because of the nature of the constraints encoded into them, templatebased systems for the prediction of multi-class maps we tested are capable of exploiting both sequence and structure information even in cases of dubious homology, significantly improving over their ab initio counterpart well into and below the twilight zone of sequence


187

˚ contact maps for ab initio (left) and template-based (right) Figure 10. Protein 1B9LA 12 A predictions. The best template sequence identity is 22.7%. The top right of each map is the true map and the bottom left is predicted. In the predicted half white and red are true negative and positive respectively, blue and green are false negative and positive respectively. The three black lines correspond to |i − j| ≥ 6, 12, 24.

Figure 11. Protein 1B9LA Multi class contact maps for ab initio (left) and template-based (right) predictions. The best template sequence identity is 22.7%. The top right of each map is the true map and the bottom left is predicted. In the predicted half red, blue, green and yellow correspond to class 0, 1, 2 and 3 respectively. The greyscale in the predicted half corresponds to falsely predicted classes. The three black lines correspond to |i − j| ≥ 6, 12, 24.

identity. This turns out to be only partly true, at least in our tests, for binary contact map predictors. Moreover, multi-class map predictions are far more accurate than the maps of the best templates for all the twilight and midnight zone of sequence identity, including the case in which only templates with less than 10% sequence identity to the query are available. Conversely, for binary contact maps, the best template is on average more accurate than the prediction for all the [0%,30%) region of sequence identity. Finally we have shown that template-based predictions of multi-class maps lead to fair to good predictions of protein structures, with an average TM score of 0.7 or higher to the

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native when good templates are available (sequence identity greater than 30%), and of 0.45 in the [20%, 30%) identity region. Ab initio predictions are still, on average, poor, at an average TM score of 0.27. Nevertheless, it is important to note how the component for homology detection in this study is basic (PSI-BLAST), and entirely modular, in that it may be substituted by any other method that finds templates without substantially altering the pipeline. Whether more subtle homology detection or fold recognition components could be substituted to PSI-BLAST, with or without retraining the underlying machine learning systems, is the focus of our current studies. The overall pipeline, including the templatebased component, is available at the URL: http://distill.ucd.ie/distill/. Protein structure predictions are based on multi-class maps, and templates are automatically provided to the pipeline when available.

Acknowledgments This work is supported by Science Foundation Ireland grant 05/RFP/CMS0029, grant RP/2005/219 from the Health Research Board of Ireland and a UCD President’s Award 2004.

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Chapter 7

COARSE-GRAINED STRUCTURAL MODEL OF PROTEIN MOLECULES 1

Kilho Eom1,2 and Sungsoo Na2 Nano-Bio Research Center, Korea Institute of Science and Technology (KIST), Seoul, Republic of Korea 2 Department of Mechanical Engineering, Korea University, Seoul, Republic of Korea

Abstract Understanding the protein mechanics is a priori requisite for gaining insight into protein’s biological functions, since most protein performs its function through the structural deformation renowned as conformational change. Such conformational change has been computationally delineated by atomistic simulations, albeit the mechanics of large protein structure is computationally inaccessible with atomistic simulation such as molecular dynamics simulation. In a recent decade, normal mode analysis with coarse-grained modeling of protein structures has been a computational alternative to atomistic simulations for understanding large protein mechanics. In this review, we delineate the current state-of-art in coarse-grained modeling of proteins for normal mode analysis. Specifically, the pioneered coarse-grained models such as Go model and elastic network model as well as recently developed coarse-grained elastic network model are summarized and discussed for understanding large protein mechanics.

Keywords: protein mechanics, coarse-grained model, normal mode analysis, Go model, elastic network model

Introduction Protein mechanics plays a vital role in the biological function of proteins, since protein performs its biological function through its structural deformation driven by mechanical loading. For instance, motor protein is one of renowned proteins that perform the mechanical function, that is, the transduction of chemical energy into mechanical energy [1]. Specifically,

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the mechanical function of ATPase motor protein is carried out via its structural change upon ATP binding [2-6]. The chaperonin GroEL-GroES complex functions the assistance of protein folding through rotational motion of its domain upon ATP binding [7, 8]. The giant muscle molecule known as titin performs the mechanical function through structural change from folded structure to unfolded (denatured) structure or vice versa upon mechanical loading or unloading [9-13]. Protein mechanics related to protein’s biological function has been computationally studied by atomistic simulations [14] since McCammon et al. [15] studied the dynamic behavior of small protein based on molecular dynamics simulation. The thermal fluctuation behavior of small proteins has been well understood by sampling of trajectories obtained from molecular dynamics simulation [16]. Moreover, the mechanical unfolding of a protein such as titin has been well analyzed by molecular dynamics simulation with consideration of mechanical loading applied to the termini of a protein [17-19]. The basic principle of i = fi , molecular dynamics simulation is to numerically solve the equation of motion, i.e. mi u where mi is the mass of the i-th atom, ui is the displacement field for i-th atom, and fi is the force acting on the i-th atom [14, 20]. The computational difficulty in molecular dynamics simulation resides in computation of the force fi that is a gradient of an anharmonic potential field prescribed to all atoms. Further, the time step for integrating the equation of motion is typically in the order of femto (10-15) seconds, whereas protein performs the function at much larger time scale from at least nano (10-9) seconds to a few seconds. It has been reported that until now the accessible time scale for molecular dynamics is at most in the order of nano seconds [21]. This indicates that molecular dynamics simulation may be computationally inhibited for large protein mechanics, where large spatial and temporal scale is required. In recent decades, normal mode analysis (NMA) has been a computational alternative to atomistic simulation such as molecular dynamics for understanding large protein mechanics [14, 22-24]. The principle of NMA is similar to that typically employed for structural mechanics. Specifically, once the stiffness matrix (Hessian matrix) for a structure is constructed, the modal analysis provides the vibration information of such a structure. The stiffness matrix for a protein structure is usually established based on the computation of second gradients of anharmonic potential field prescribed to all atoms. In general, calculation of stiffness matrix is implemented at equilibrium position, which is obtained by minimization of anharmonic potential. This implies that, for large proteins, the computation of stiffness matrix along the minimization process is a computationally expensive process. Recently, atomistic simulation such as molecular dynamics [15] and NMA [22] with all atoms has been replaced with a coarse-grained model, where degrees of freedom are enormously reduced. Since the dominant motion of a protein structure is represented by that of a carbon backbone chain [14, 16], the coarse-grained models have been suggested such that protein structure is delineated by α-carbon atoms for protein backbone chain. Moreover, the computational inefficiency usually arises from the complicated anharmonic potential field. Consequently, the simplification of such potential field for a protein structure described by αcarbon atoms is the key issue in the coarse-grained modeling of proteins. Go and coworkers [22] introduced the more simplified potential field for α-carbon atoms such that α-carbon atoms are prescribed by potential field consisting of covalent bonds for consecutive α-carbon atoms and non-bonded interaction (i.e. van der Waal’s interaction) for native contacts. The thermal fluctuation behavior of protein structures has been well described by Go model. In a

Coarse-Grained Structural Model of Protein Molecules

195

recent decade, Go model has been taken more attention for gaining insight into protein unfolding mechanics. Cieplak and coworkers [25-28] have showed that molecular simulation with Go potential has allowed them to obtain the force-displacement curve for protein unfolding mechanism, quantitatively comparable to experimental data by single-molecule pulling experiments based on atomic force microscopy (AFM) [9]. This may shed light on Go model such that Go potential may be versatile potential field for understanding protein mechanics with computational efficiency. Inspired by Go model, Tirion suggested the more simple harmonic potential for protein structures [29]. In her model, protein structure is regarded as a harmonic spring network in such a way that α-carbon atoms within the neighborhood is connected by harmonic springs with identical force constant. Tirion’s model has revolutionized the protein modeling for understanding protein dynamics relevant to biological function of proteins [30-37]. Such model has reduced computational expense enormously for estimating low-frequency normal modes related to biological function. Moreover, it is very remarkable that low-frequency normal modes from Tirion’s model are highly correlated with displacement vector representing the conformational change of proteins [38]. Tirion’s model has inspired many researchers for studying protein dynamics and protein mechanics. For example, Wolynes and coworkers [39] studied the energy landscape for protein conformational change based on Tirion’s model. Kim et al [40] introduced the linear interpolation method based on Tirion’s model for describing the conformational change. Brooks and coworkers [41, 42] have studied the conformation change based on iterative method applied to low-frequency normal modes from Tirion’s model with a distance constraint for computing the displacement vector related to incremental conformational change. Micheletti and coworkers [43] employed Tirion’s model for depicting the thermal denaturation (thermal unfolding) of protein’s folded structure. Zheng et al [44] have studied the power-stroke mechanism of motor proteins based on Tirion’s model. The recent studies by Brooks et al [37, 45] and Kim et al [46] have showed that low-frequency normal modes of Tirion’s model is sufficient to provide the functional mode of viral capsid protein. Recently, Thirumalai and coworkers [47] have shown that lowfrequency normal modes are able to describe the allosteric transition of proteins. Bahar and coworkers [48] have provided that allosteric change of protein structure is well delineated by low-frequency normal modes of Tirion’s model. Moreover, they have recently suggested that Tirion’s model with Markov method may enable one to understand the allosteric signal transduction corresponding to conformational change [49, 50]. Although Tirion’s model has greatly succeeded in studying protein dynamics and mechanics with high computational efficiency, the model reduction scheme (coarse-graining) has been taken into account for large protein structures. The model reduction of Tirion’s model is rational since few low-frequency normal modes are necessary for describing the protein dynamics such as conformational change relevant to biological function. Such model reduction has been first attributed to Bahar and coworkers [51] who introduced the coarsegrained structure represented by nodal points whose number is less than total number of αcarbon atoms. In their model, the nodal points within the neighborhood were connected by harmonic spring with identical spring constant. In a recent year, Eom and coworkers [52] have provided the more systematic model reduction method applicable to protein structures. Specifically, they used the model condensation method in a similar spirit to skeletionization method suggested by Rohklin and coworkers [53, 54]. Bahar and coworkers [55] have introduced the Markov method for transformation of original molecular structure into coarse-

196


grained structure. Ma and coworkers [56] have employed the substructure synthesis method, which was broadly used for engineering structural dynamics, for obtaining the low-frequency normal modes relevant to biological function.

Molecular Simulation: Normal Mode Analysis (NMA) All-atom simulation such as molecular dynamics was first provided by Karplus and coworkers [15]. The potential field V prescribed to protein structure was given by [14] V =∑ i

⎛ A B⎞ qi q j 2 2 K C bi − bi0 ) + ∑ (θi − θi0 ) + ∑ D ⎡⎣1 + cos ( nϕi − δ ) ⎤⎦ + ∑ ⎜ 12 − 6 ⎟ + ∑ ( ⎜ rij ⎟⎠ i , j χ rij 2 i 2 i i , j ⎝ rij

(1)

Here, bi, θi, and φi are the i-th covalent bond length, bending angle, and dihedral angle (torsional angle), respectively, rij is the distance between i-th atom and j-th atom, qi is the charge for i-th atom, and a symbol 0 indicates the equilibrim state. The first term in potential energy represents the stretching energy for covalent bonds, the second term indicates the bending energy, the third term shows the torsional energy, and last two terms provides the non-bonded interactions such as van der Waal’s interaction and electrostatic interaction. With the potential energy V given by Eq. 1, molecular dynamics simulation provides the trajectories of position vectors denoted as xi for all atoms. The quantity renowned as crosscorrelation matrix Lij shows the thermal fluctuation behavior comparable to experimental quantity such as Debye-Waller factor [16, 57]. Lij =

(x

i

− xi0 ) ⋅ ( x j − x0j )

(2)

where xi is the position vector for i-th atom, a symbol 0 represents the equilibrium state, and a braket symbol indicates the ensemble average (time average). The diagonal component of cross-correlation matrix, Lii, is the mean-square fluctuation proportional to Debye-Waller factor (B-factor), i.e. Bi = (8π2/3)Lii. Normal mode analysis (NMA) is referred to as quasi-harmonic analysis [58], since the modal analysis is implemented with harmonic approximation to potential energy V for small displacement. V ≈ V0 +

1 ∑ Kij ( xi − xi0 )( x j − x0j ) 2 i, j

(3)

Here, xi is the generalized coordinates for atoms, and Kij is the Hessian matrix (stiffness matrix) for a protein structure given by Kij = ∂2V/∂xi∂xj. Quasi-harmonic analysis (or NMA) is to solve the eigen-value problem such as Kijvj = −ω2mivi, where ω is the natural frequency, vi is the normal mode corresponding to natural frequency ω, and mi is the atomic mass for i-th atom. The cross-correlation matrix representing the thermal fluctuation motion can be computed from equilibrium statistical mechanics theory [57, 59].

Coarse-Grained Structural Model of Protein Molecules L ij =

3N

∑

n=7

k BT (vi ,n ⊗ v j ,n ) m iω n 2

197 (4)

where kB is the Boltzmann’s constant, T is the absolute temperature, and the subscript n for natural frequency and normal mode represents the mode number. It should be noted that summation goes from 7 to 3N, where N is the total number of atoms, since there are six rigid body modes corresponding to zero eigen-modes. Even though there are several different potential fields such as CHARMM and AMBER applicable to protein structures, it was shown that the thermal fluctuation motion and low-frequency normal modes are consistent regardless of details of potential field [58].

Go Model As stated above, the low-frequency normal modes relevant to protein dynamics is insensitive to details of potential field [58]. One may ask which interactions dominate the protein dynamics among various potential fields as mentioned in Eq. 1. Go and coworkers [22] conjectured that short-range interactions may govern the protein dynamics. Moreover, the motion of protein structure is well described by that of backbone chain represented by αcarbon atoms. Go potential is simply represented in the form of [25, 26] V ≈

⎡ k1

∑ ⎢⎣ 2 ( r

− ri 0, i + 1 ) + 2

i , i +1

i

4⎤ k2 ri , i + 1 − ri 0, i +1 ) ⎥ + ∑ 4ε ( 4 ⎦ i, j

⎛ 1 1 ⎜⎜ 6 − 12 r r ij ij ⎝

⎞ ⎟⎟ ⎠

(5)

Here, ri,j is the distance between i-th and j-th α-carbon atoms, and superscript 0 indicates the equilibrium state. The first summation represents the nonlinear elastic energy for covalent bonds, while the last summation shows the non-bonded interaction for native contact. Native contact is defined in such a way that two α-carbon atoms (i-th and j-th α-carbon atoms) are in the native contact if rij is less than the certain distance referred to as cut-off distance, dc, typically given as dc ≈ 10 Å.

Tirion’s Model: Elastic Network Model (ENM) The success of Go model has resulted in the emergence of more simplified model suggested by Tirion [29]. Specifically, Tirion assumed the harmonic approximation to potential field prescribed to α-carbon atoms. Inspired by Go model, she proposed the harmonic potential field only for native contacts and covalent bonds with identical force constant. V ≈∑ i, j

γ 2

(r

ij

− rij0 ) ⋅ H ( rc − rij0 ) 2

(6)

198


where γ is a force constant, rij is the distance between i-th and j-th α-carbon atoms, superscript 0 indicates the equilibrium state, rc is the cut-off distance defining a native contact, and H(x) is the Heaviside unit-step function defined as H(x) = 0 if x < 0; otherwise H(x) = 1. With Tirion’s potential, Bahar and coworkers studied the Gaussian dynamics of proteins, which resulted in the emergence of Gaussian network model (GNM) [30, 32]. GNM assumes the isotropic fluctuation, that is, directionality of fluctuation is not taken into account. Even though the motion of proteins is generally anisotropic, the fluctuation behavior such as Bfactor is well depicted by GNM. The stiffness matrix for GNM, also referred to as Kirchoff matrix, is given by Γij =

N ∂ 2V = −γ (1 − δ ij ) ⋅ H ( rc − rij0 ) − δ ij ∑ Γ ik ∂ri ∂rj k ≠i

(7)

Here, N is the total number of α-carbon atoms, and δij is the Kronecker delta defined as δij = 1 if i = j; otherwise δij = 0. Since isotropic motion is assumed in GNM, GNM is able to only provide the low-frequency normal modes related to mean-square fluctuations. Further, fluctuation information for every residue may provide the insight into the hot spots (residues) which undergo large deformation during the conformational change. In general, Tirion’s model is referred to as elastic network model (ENM) [29, 33] since protein structure is represented by harmonic spring network, which takes into account the anisotropy in thermal fluctuation. For simplicity, let us consider only two α-carbon atoms i and j, which are connected by an entropic spring (Gaussian chain) [33, 60-64]. V ( rij ) =

γ

(r 2

ij

− rij0 )

2

(8)

where rij = [(xi – xj)2 + (yi – yj)2 + (zi – zj)2] with a position vector ri for an α-carbon atom i, given by ri = xiex + yiey + ziez. The stiffness matrix K for a potential given by Eq. 3 can be easily computed such as ⎡ K ij K =⎢ ⎣ − K ij

− K ij ⎤ K ij ⎥⎦

(9)

Here, Kij is the 3×3 block matrix given by K ij = γ

(r

i

− r j ) ⊗ ( ri − r j ) ri − r j

2

(10)

This indicates that the stiffness matrix for an entropic spring is equivalent to the stiffness matrix for an elastic spring (linear elastic truss) with a spring constant γ. Based on 3×3 block matrix Kij, the stiffness matrix corresponding to Tirion’s potential given by Eq. 6 can be easily computed by assembly of such block matrices. The protein structure described by ENM is suggested in Figure 1.


199

Coarse-Grained Elastic Network Model Coarse-graining of protein structures with few degrees of freedom has been attempted, since protein structure is composed of several rigid domains whose motional behavior is like a rigid-body motion such as rotational motion. In recent years, Jernigan and coworkers [65, 66] suggested that protein structure is represented by complex of rigid bodies corresponding to protein domains. That is, they introduced the Hamiltonian for rigid-body motion of a domain as well as interactions between domains. It was remarkably shown that the dynamic behavior such as conformational change of large protein complex (e.g. GroEL-GroES, viral capsid) has been well illustrated by their coarse-grained model [46, 66]. Bahar and coworkers [51] have taken into account the coarse-graining of ENM based on their physical intuition. Their coarse-grained ENM was established in the same manner to ENM except they rescaled the force constant as well as cut-off distance. It is remarkable that their simple coarse-grained model successfully predicts the thermal fluctuations comparable to original structure as well as experimental data. Furthermore, multi-scale model for proteins has been suggested in such a way that the biologically significant substructures such as binding site are described by refined model such as ENM whereas the rest regions of a protein is described by coarse-grained ENM [67].

Figure 1. Model protein, i.e. citrate synthase (pdb: 4cts) described by (a) molecular structure and (b) elastic network model.

The coarse-graining process based on ENM may be systematically implemented by employing the model reduction method typically used in applied mathematics. For instance, Rohklin and coworkers [53, 54] suggested the low-rank approximation to linear algebraic equation, resulting in the reduction of degrees of freedom. They showed that their low-rank approximation, referred to as skeletionization, can be directly applicable to electrostatics [68], hydrodynamics [53], and any other applied mathematics problem represented by linear equation [54]. Inspired by skeletonization scheme, we have employed the model condensation method to reconstruct the coarse-grained structure, i.e. low-resolution structure, from the original structure, i.e. refined structure (See Figure 2) [52, 64]. We define the master residues as the residues which are taken in the coarse-grained structure, while the slave residues are referred to as the residues which are to be eliminated during model condensation. The dynamic motion of a protein structure is governed by harmonic potential V in the form of V=

1 [u M 2

⎡K uS ] ⎢ M ⎣ K SM

K MS ⎤ ⎡u M ⎤ K S ⎥⎦ ⎢⎣ u S ⎥⎦

200


where the subscripts M and S indicate the master residues and slave residues, respectively. KM represents the harmonic interactions between master residues, KS provides the harmonic interactions between slave residues, and KMS shows the harmonic interactions between master and slave residues. With assumption that slave residues are in equilibrium, the effective stiffness matrix Keff for coarse-grained ENM described by master residues is computed as follows. K MS ⎤ ⎡ I 3 M ⎤ ⎡K (12) −K MS K −S1 ⎤⎦ ⎢ M ⎥⎢ ⎥ K ⎣ SM K S ⎦ ⎣ 0 ⎦ Here, ψ is the linear operator that transfroms the original structure described by stiffness matrix K to the coarse-grained structure depicted by effective stiffness matrix Keff, and I3M is the 3NM × 3NM identity matrix, where NM is the total number of master residues. K eff = ψ [ K ] = ⎡⎣I 3 M

Conformational Fluctuation Dynamics In recent decades, the molecular structures of various proteins have been characterized by experiments based on X-ray crystallography and/or nuclear magnetic resonance (NMR) [20]. Until recently, many experimentalists are attempting to characterize the large protein structures based on X-ray crystallography and NMR, and such protein structures realized by experimentalists are deposited in the protein data bank (PDB; http://www.pdb.org). Characterization of protein structure with such experiments is typically given in terms of Debye-Waller factor (B-factor) representing the mean-square fluctuation of residues driven by thermal energy kBT. Consequently, the dynamic behavior of proteins based on theoretical models such as molecular model and/or coarse-grained model is typically compared with Bfactor obtained by experiments. That is, the conformational fluctuation behavior of proteins plays a role in validating the theoretical models for protein structures. As shown in Figure 3, the conformational fluctuation predicted by Tirion’s model (ENM) and/or GNM is quantitatively comparable to that obtained by experiments. It is quite remarkable that simple harmonic oscillator network model delineated by two parameters such as force constant and cut-off distance are able to provide the conformational fluctuation of proteins. This remarkable result indicates that native topology (topology of native contacts) plays a dominant role in the conformational fluctuation. Moreover, the comparison of thermal fluctuations predicted by ENM with that by experiments provides the force constant for an entropic spring connecting the native contacts. For instance, F1-ATPase motor protein (pdb: 1e79) can be represented by GNM with force constant of 0.347 kcal/mol and cut-off distance of 12Å. It should be noted that one has to be cautious in selecting the cut-off distance because the short cut-off distance may generate the unphysical behavior of a structure such as more than six rigid body modes [33]. Further, if one chooses the very large cut-off distance, then the structure is too rigid to fluctuate in the similar pattern to that of real protein. We take into account the coarse-grained elastic network model and its conformational fluctuation behavior. It is shown that, in Figure 3, coarse-grained ENM predicts the thermal fluctuation behavior depicted by B-factor qualitatively comparable to that estimated by experiments and/or original structural model. For a protein composed of N α-carbon atoms, the prediction of B-factor based on ENM requires O(N3) computation, while on the basis of


201

coarse-grained ENM composed of (N/n) α-carbon atoms the calculation of B-factor requires O(N3/n2) computation.

Figure 2. Molecular structure of a model protein (citrate synthase) delineated by (a) elastic network model and (b) coarse-grained elastic network model

Figure 3. B-factor of a motor protein (pdb: 1e79) predicted by elastic network model and coarsegrained elastic network model in comparison with experimental data

Coarse-grained ENM reduces the computational cost for predicting thermal fluctuation of proteins by factor of n2, compared with ENM, whereas the coarse-grained ENM predicts the thermal fluctuation of proteins quantitatively and qualitatively comparable to that predicted by ENM. The success of coarse-grained ENM in depicting the conformational fluctuation of proteins may be attributed to the fact that protein structure is usually represented by combinations of rigid domains that can be described by few degrees of freedom. This feature of protein structure has been taken into account for establishing the coarse-grained models of proteins. For instance, Jernigan and coworkers [66] provide the rigid cluster model such that protein structure is represented by clusters of rigid bodies with soft springs connecting rigid domains. Further, Tama and coworkers [69] suggested block normal mode analysis, where block matrices were used to describe the rigid blocks of proteins, for delineating the conformational fluctuation of proteins. Moreover, as the protein structure is more coarse-grained, the magnitude of conformational fluctuation becomes larger, even though the patterns of conformational fluctuation predicted by coarse-grained structure are qualitatively consistent with original structure. This is rational since our coarse-graining scheme reduces the harmonic springs corresponding to slave residues, resulting in the increase of overall compliance of protein structure. This is consistent with a recent work by Bahar and coworkers [51], where they

202


rescaled the force constant in such a way that the force constant for coarse-grained structure is larger than that for original structure. In order for a coarse-grained ENM to predict the conformational fluctuation quantatively comparable to experimental data or original structural model, the force constant should be rescaled in such a way that the overall stiffness of protein structure described by coarse-grained ENM is comparable to that of protein structure depicted by ENM. Figure 4 shows the thermal fluctuation predicted by coarse-grained ENM with rescaled force constant. It is shown that the conformational fluctuation predicted by coarsegrained ENM is very consistent with experimental data.

Lowest-Frequency Normal Mode Coarse-grained models such as Go model and ENM are computationally acceptable for computational biology communities, since such models are able to capture the low-frequency normal modes relevant to the biological function of proteins. Such coarse-grained models reduce the degrees of freedom enormously as well as simplify the potential field, and they can provide the meaningful low-frequency normal modes comparable to that computed from atomistic model. This indicates that a de novo coarse-grained model for protein structures can be verified based on the comparison of low-frequency normal modes computed from such coarse-grained model with that obtained by conventional models such as atomistic model and/or wellaccepted coarse-grained model such as Go model and Tirion’s model.

Figure 4. Comparison between experimental data and B-factor predicted by coarse-grained elastic network model with rescaled force constant

We have validated our coarse-grained ENM by investigating the low-frequency normal modes predicted by coarse-grained ENM. For instance, we consider the lowest-frequency normal modes predicted by both ENM and coarse-grained ENM. As shown in Figure5, the lowest-frequency normal mode for hemoglobin is well predicted by coarse-grained ENM such that its lowest-frequency normal mode is qualitatively comparable to that obtained from ENM. Specifically, anti-correlated motion between substructure A (residues: 1 ~ 287) and substructure B (residues: 288 ~ 428) can be found in both ENM and coarse-grained ENM.


203

This indicates that coarse-grained ENM may provide the lowest-frequency normal mode, related to the functional motion of protein structure, qualitatively comparable to that computed from original structural model such as Go model and ENM. Further, the rescaling of force constant for coarse-grained ENM may not affect the pattern of lowest-frequency normal mode, since the protein topology is only described by cut-off distance. It can be realized that our coarse-graining allows us to predict the functional lowest-frequency normal mode of proteins with reducing the computational cost by factor of n3.

Collective and Correlated Motion of Proteins The conformational motion of proteins has been well described as collective motion and/or correlated motion. As shown previously in Figure 5, the low-frequency normal modes exhibit the collective motion of a protein domain, and such modes depicts the correlated motion of protein domains. Before we demonstrate the collective and/or correlated motion predicted by ENM and/or coarse-grained ENM, we review the parameters representing the collective motion and/or correlated motion. The collectivity parameter denoted as κi for a given mode index i is defined as [70]

κi =

⎡ Nω 2 2⎤ 1 exp ⎢ −∑ vi , j log vi , j ⎥ Nω ⎣ j =1 ⎦

(13)

where Nω is the total number of normal modes, vi,j represents the j-th component of normal mode vi corresponding to mode index i. The collectivity κi is in the range between 1/Nω and 1, where the value of collectivity close to 1/Nω represents the localized motion while the value of collectivity close to 1 indicates the collective motion.

Figure 5. Lowest-frequency normal mode for a hemoglobin computed from elastic network model and coarse-grained elastic network model.

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The correlated motion between residues i and j is well delineated by correlation matrix Cij defined as [71]

(x

C ij =

i

−x

xi − x

0 i

) ⋅ (x

0 2 i

j

−x

0 j

xj −x

) 0 2 j

3

=

∑L p =1

3( i − 1) + p ,3( j − 1) + p

(14)

⎛ 3 ⎞⎛ 3 ⎞ ⎜ ∑ L 3( i −1) + p ,3 ( i −1) + p ⎟ ⎜ ∑ L 3( j −1) + q ,3( j −1) + q ⎟ ⎝ p =1 ⎠ ⎝ q =1 ⎠

Here, the correlation matrix Cij in terms of cross-correlation matrix Lij, shown in Eq. 14, is based on ENM whose degrees of freedom are 3N. The value of Cij close to –1 shows the anti-correlated motion between residues i and j, whereas the value of Cij close to 1 indicates the correlated motion between these two residues. When the correlation Cij is close to zero, the motion of a residue i is uncorrelated with and/or orthogonal to that of a residue j. For clear understanding of correlated motion described by Cij, let us consider the simple harmonic oscillator embedded in a heat bath with thermal energy kBT. The potential energy for a harmonic oscillator is represented in the form of V = (γ/2)(ui – uj)2, where γ is a force constant (spring constant) and ui is a one-dimensional displacement for a node i (see Figure 6). The Hessian matrix (stiffness matrix) for this system can be given by ⎡γ K=⎢ ⎣ −γ

−γ ⎤ γ ⎥⎦

(15)

which provides the natural frequencies ω0 = 0 and ω1 = (2γ)1/2 and their corresponding normal modes v0 = (1, 1) and v1 = (1, –1). As stated earlier, the zero modes should be excluded for estimating the thermal fluctuation of a system. The non-zero normal mode v1 for a harmonic oscillator enables us to easily know that the thermal energy drives the anti-correlated motion between two nodal points i and j. This is consitent with the quantity of correlation Cij, i.e. Cij = –1, from the definition of correlation Cij such as Cij = Lij/(LiiLjj)1/2, where cross-correlation Lij is given by L=

k BT

ω

2 1

v1 ⊗ v1 =

k BT ⎡ 1 −1⎤ 2γ ⎢⎣ −1 1 ⎥⎦

(16)

Thus, correlation Cij is a physical parameter describing the correlated motion between these two nodal points. As shown in Figure 7, we consider the collectivity parameters κi calculated from both ENM and coarse-grained ENM. It is quite remarkable that coarse-grained ENM is able to reproduce the collectivity parameters corresponding to low-frequency normal mode quantitatively comparable to that estimated from ENM. This indicates that collective motion of proteins can be well depicted by coarse-grained structure represented by few degrees of freedom. This may be attributed to the fact that protein consists of several rigid domains that can be described by few degrees of freedom, and that the collective motion arises from the low-frequency functional modes. However, the coarse-grained ENM cannot predict the collectivity for high-frequency normal modes. Specifically, as shown in Figure 7, the high-


205

frequency normal modes are related to localized motion which cannot be predicted from coarse-grained ENM. This indicates that localized modes (high-frequency modes) of protein can be only estimated from refined molecular model. Figure 8 shows the correlation matrix Cij evaluated from ENM and coarse-grained ENM. It is remarkably found that the collective motion of each domain is well described by both ENM and coarse-grained ENM. Further, coarse-grained ENM provides the correlation between domains, qualitatively comparable to the correlation predicted by ENM. However, coarse-grained ENM overestimates the quantity of correlation between domains. This may be ascribed to our coarse-graining scheme, that is, reduction of harmonic springs corresponding to slave residues, leading to overestimation of overall flexibility and its corresponding correlated motion between domains.

Conformational Transition Conformational change of a protein is quite related to the biological function of a protein. Atomistic simulation such as targeted MD simulation has been employed for understanding conformational change of very small proteins. Remarkably, NMA has been an alternative to MD simulation, since the low-frequency normal modes at equilibrium state are able to well describe the conformational change of proteins. This NMA is referred to as principal component analysis (PCA) that diagonalizes the Hessian matrix (stiffness matrix) [72].

Figure 6. Schematic of a one-dimensional harmonic oscillator that undergoes the thermal fluctuation

Since it was shown that low-frequency normal modes are independent of details of potential field [58] but depend on the topology of protein structures [73], ENM was broadly employed for understanding the conformational change of proteins. Tama and coworkers [37, 38] showed that low-frequency normal modes obtained from ENM are highly correlated with a vector representing the conformational change between two equilibrium states. Bahar and coworkers [74] showed that the conformational change from tense form to relaxed form for hemoglobin is driven by entropic effect described by low-frequency normal modes from ENM. Brooks and coworkers [41, 67] predicted the conformational change depicted by lowfrequency normal modes with a perturbation of Tirion’s potential that incorporates the distance constraint. Kim et al. [40] suggested the linear interpolation between two conformations with constraint that the intermediate conformation distant from the interpolated coordinate is determined by minimization of harmonic potential. Wolynes and coworkers [39]

206


provided the nonlinear elastic energy landscape for conformational change of proteins based on low-frequency normal modes from ENM. Further, Karplus and coworkers [75] employed the same methodology suggested by Wolynes and coworkers for describing the conformational change of a motor protein. Further, Kidera and coworkers [76] used the linear response theory with Tirion’s model for depicting the conformational change of proteins.

Figure 7. Collectivity parameter κi for a hemoglobin (pdb: 1a3n) estimated from elastic network model and coarse-grained elastic network model

Figure 8. Correlation matrix Cij for a motor protein (pdb: 1e79) evaluated by (a) elastic network model and (b) coarse-grained elastic network model

For delineating the correlation between low-frequency normal modes and conformational change, the parameters referred to as overlap Ik and/or cumulative involvement Sk are defined such as


Ik =

(r (r

open

− rclose ) ⋅ v k

open

− rclose )

207

(17.a)

and k

Sk = ∑ I p 2

(17.b)

p =1

Here, ropen and rclose represent the position vectors corresponding to open form and close form, respectively, and vk is the k-th normal mode. Ik indicates the correlation between k-th normal mode and conformational change, and Sk is a quantity representing the contribution from low-frequency normal modes (from first mode to k-th mode) to the conformational change. Figure 9 shows the overlap and cumulative involvement predicted by ENM and coarse-grained ENM. It is remarkable that both models predict that the conformational change is highly correlated with a few low-frequency normal modes. This is consistent with a recent finding that low-frequency normal modes are sufficient to represent the conformational change of a protein.

Figure 9. Overlap Ik and cumulative involvement Sk for citrate synthase computed from elastic network model and coarse-grained elastic network model. Blue color represents the calculation based on elastic network model, whereas red color indicates the computation based on coarse-grained elastic network model. A bar graph shows the square of overlap, and dotted line presents the cumulative involvement.

Conclusion In this article, we review the current state-of-art in coarse-graining of protein molecules for understanding their dynamics relevant to biological functions. The coarse-graining procedure is usually acceptable as long as the protein topology related to its dynamics is sufficiently delineated by such coarse-grained models. We briefly overviewed the broadly accepted coarse-grained models such as Go model and Tirion’s model (ENM), which enables

208


one to gain insight into protein dynamics such as conformational fluctuation and conformational change related to the biological function. Moreover, a recently developed coarse-grained ENM models are taken into account and it is shown that such coarse-grained ENM may allow one to achieve the fast computation on low-frequency normal modes related to biological function. It is provided that the possibility of coarse-graining for a protein structure is attributed to the fact that protein structure is usually composed of several rigid domains that can be described by few degrees of freedom. As previously shown, both ENM and coarse-grained ENM predicts the low-frequency normal modes and the thermal fluctuation quantitatively similar to that obtained by experiments. Further, both ENM and coarse-grained model such as rigid cluster model predict the conformational transitions between two conformations. However, it has to be validated whether coarse-grained ENM is acceptable or not for prediction of conformational change. To our knowledge, this issue has not been well considered except a recent work by Brooks and coworkers [67] who employed mixed ENM for understanding conformational change. As stated above, coarse-grained models have been successful for studying the conformational dynamics of proteins. However, since some proteins such as titin perform the mechanical function, the protein unfolding behavior has to be well understood for insight into the mechanical function. Atomistic simulation is still restricted to small proteins, leading to consideration of coarse-grained models. A recent study by Cieplak and coworkers [28] suggested the molecular model based on Go potential under the mechanical loading. It is very remarkable that their model based on Go potential allows them to predict the forcedisplacement relation under the mechanical loading, comparable to the results of AFM experiments. Moreover, McCammon and coworkers [77] employed Tirion’s potential with mechanical loading applied to the termini of a protein. It was remarkably shown that even Tirion’s model is acceptable for gaining insight into mechanical unfolding of proteins. Recently, Rief and coworker [78] revisited Tirion’s model with bond-breaking model for protein unfolding mechanics. It is remarkably found that their elastic bond network model [78] allowed Rief and coworker to predict the probability distribution of rupture force, quantitatively comparable to AFM experimental data [79]. In summary, the coarse-grained models such as Go model and Tirion model have been reviewed for protein dynamics relevant to biological function. Moreover, such models can be extended for understanding mechanical unfolding of protein structure. In conclusion, coarsegrained models such as Tirion’s model may be versatile for understanding the large protein dynamics and/or large protein unfolding mechanics.

Acknowledgement This work was supported in part by Nano-Bio Research Center at KIST (to K.E.) and LG YONAM FOUNDATION and Basic Research Program of the Korea Science and Engineering Foundation (KOSEF) under grant No. R01-2007-000-10497-0 (to S.N.).


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Chapter 8

DIFFERENTIATING SUPERFICIAL AND ADVANCED UROTHELIAL BLADDER CARCINOMAS BASED ON GENE EXPRESSION PROFILES ANALYZED USING SELF-ORGANIZING MAPS Phei Lang Chang∗, Ke Hung Tsui, Tzu Hao Wang♣, Chien Lun Chen and Sheng Hui Lee Department of Surgery, Division of Urology and Chang Gung Bioinformatics Center, and ♣ Genomic Medicine Research Core Laboratory, Chang Gung Memorial Hospital, Chang Gung University, Taipei, Taiwan

Abstract The aim of this study was to differentiate between superficial and advanced bladder cancers by analyzing the gene expression profiles of these tumors by using the self-organizing maps (SOMs). We also used the GoMiner software for the biological interpretation of 473 interesting genes. Materials and Methods: Between December 2003 and November 2004, 17 patients with urothelial bladder cancers who were admitted to the Chang Gung Memorial Hospital for transurethral resection of the tumor were included in this study. The gene expression data included 7400 cDNAs in 17 arrays. The software, GeneCluster 2.0, was used for analyzing gene expression data by using SOMs. We used a 2-cluster SOM to cluster automatically a set of 17 tissues samples into superficial and advanced bladder cancers based on the gene expression patterns. We also used the GoMiner software for the biological interpretation of top 473 interesting genes. Results: Patients included 11 males and 6 females. Pathological studies confirmed the presence of superficial tumors in 9 patients and advanced tumors in 8 patients. Of the 7400 genes analyzed, 473 genes showed significant changes in their expression. Of these 268 were up-regulated, and 205 were down-regulated. Using the top 473 genes, SOMs were used to differentiate between the gene expression patterns of superficial and advanced bladder cancer ∗

Address correspondence to:Phei Lang Chang, M.D., Chairman, Department of Surgery, Professor; Department of Urology, Chang Gung Memorial Hospital, No. 5, Fu-Shing Street, Kweishan, Taoyuan 333, Taiwan; Tel: 8863-3281200-2137; Fax: 886-3-3274541; E-mail: [email protected]

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Phei Lang Chang, Ke Hung Tsui, Tzu Hao Wang et al. tissue samples. The patient tissue samples were clustered into 2 groups, namely, superficial and advanced bladder cancers, comprising 10 and 7 samples, respectively. Only one patient tissue sample with advanced bladder cancer was clustered into the superficial bladder cancer group. This analysis had a high accuracy rate of 94% (16/17). The top 473 genes also were classified into biologically coherent categories by the GoMiner software. The results revealed that 452, 435, and 452 genes were associated with biological processes, cellular components, and molecular functions, respectively. Conclusion: Based on our results, we believe that superficial and advanced urothelial bladder cancers can be differentiated by their gene expression profiles analyzed by SOMs. The SOM method may be used on microarray data analysis to distinguish tumor stages and predict clinical outcomes. The genes that are uniquely expressed in either stage of bladder cancer can be considered as possible candidates for biomarkers.

Introduction Urothelial carcinoma of the urinary bladder is a common cancer in adult patients and is the second most common cancer of the genitourinary tract.[1] It accounts for 7% and 2% of primary carcinomas in males and females, respectively. Two-thirds of all urothelial carcinoma patients have superficial tumors, and 30% of these tumors become infiltrative.[2] The incidence of primary urinary bladder carcinomas in the United States is approximately 54,000 per year. It is the eighth leading cancer in women and the fourth leading cancer in men.[3] Although the incidence of urinary bladder cancer is lesser than that of other cancers its recurrence rate is the highest.[4] The overall mortality of urinary bladder cancer is approximately 30%.2 The treatment of bladder cancer is based on the clinical stage and the degree of differentiation of the tumor. Generally, superficial bladder tumors are treated by transurethral resection (TUR) with or without intravesical chemotherapy. Radical cystectomy is an effective treatment for patients with advanced muscle-invasive bladder tumors.[5] Although bladder cancer has response to chemotherapy, prognosis is still poor for metastatic tumors.[6] The differential diagnosis of superficial and advanced bladder cancers plays an important role in determining the treatment strategy and in evaluating the prognosis of these cancers. The behavior of bladder cancers varies according to the clinical stage and histological grade of the tumor. The diagnostic modalities that are clinically used for the diagnosis and staging of bladder cancers are urinary cytology, cystourethroscopy, chest x-ray, intravenous urography, intravesical ultrasonography, computed tomography (CT), magnetic resonance imaging (MRI), positron emission tomography, and radionuclide bone scan.[7] Recently, bladder tumor staging and outcome prediction has been carried out based on the genetic alterations and molecular markers of bladder cancer.1 Gene expression profiling by DNA microarray technology enables the identification of the genes responsible for the heterogeneity, recurrence, and progression of bladder cancers. This profiling enables the selection of appropriate treatment strategies and the prediction of disease outcome.[8] The identification of the molecular genetic alterations in bladder cancer has enhanced the diagnosis of bladder cancer. Many molecular genetic alterations have been identified in superficial and advanced bladder cancers. The roles of telomerase, methylation, oncogenes, and tumor suppressor genes in the development and progression of bladder cancer have been studied for many years. The identification of certain genetic alterations have proven to be useful in the diagnosis and treatment of superficial and advanced bladder cancers.[9]

Differentiating Superficial and Advanced Urothelial Bladder Carcinomas…

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Microarray analysis is an effective tool for understanding the progression and metastasis of bladder cancer.[10] However, the data obtained from microarrays is extremely complicated. It is crucial to select an appropriate method to analyze the microarray data. The features of self-organizing maps (SOMs) make them well suited for the clustering of gene expression patterns. They are particularly useful for exploratory data analysis and visualization. They impose a partial structure on the clusters, thereby facilitating the interpretation of the data. SOMs have been tested on a wide variety of problems and were found to be significantly superior in both robustness and accuracy.[11] GeneCluster 2.0 is a software package used for analyzing gene expression data. It offers various methods to evaluate class predictors, visualize marker lists, cluster data, and validate results. It was released in June 1999. It implements the SOMs algorithm popularized by Tamayo et al. as well as various standard preprocessing methodologies used in microarray analysis.[12] Therefore, we selected this software to analyze microarray data.[13] Further, we used the GoMiner software to study the characteristics of noteworthy genes. This program organizes the lists of expressed genes generated from the microarray analysis for biological interpretation within the context of the Gene Ontology (GO) database. It provides quantitative and statistical output files and useful visualizations.[14] We identified the fundamental patterns of top 473 genes inherent in the gene expression data of patients with superficial or advanced bladder cancers. Further, we analyzed and visualized the gene expression data obtained by complementary DNA (cDNA) microarray analysis by using the SOMs method. The aim of this study was to differentiate between superficial and advanced bladder cancers by analyzing the gene expression profiles of these tumors by using the SOMs. We also used the GoMiner software for the biological interpretation of 473 interesting genes.

Materials and Methods Between December 2003 and November 2004, 17 patients with urothelial bladder cancers who were admitted to the Chang Gung Memorial Hospital underwent TUR. These patients were included in this study. Tumor specimens were collected after TUR. The specimens were divided to 2 groups: the fresh tissue and formalin-fixed tissue. Fresh tumor tissue samples obtained during TUR were immediately cut into small pieces, snap-frozen in liquid nitrogen, and stored at –70°C for microarray studies. Formalin-fixed tissues were stained with hematoxylin and eosin (H&E) for pathological examination.

Extraction of RNA from human tissue samples During TUR, samples of cancerous and normal neighboring tissues were obtained from the 17 patients. For RNA isolation, 1 ml of Trizol reagent (Invitrogen, Carlsbad, Calif, USA) was added to every 50–100 mg of pulverized frozen tissue immediately after removal. We used 1 ml of Trizol for (5–10) × 106 cultured cells. We incubated the homogenized tissue at room temperature for 5 min and then added 0.2 ml of chloroform. The mixture was shaken vigorously for 15 s, incubated at room temperature for another 3 min, and centrifuged at 12,000 × g at 4°C for 15 min. The upper colorless aqueous phase was transferred to a new

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microfuge tube. The RNA in this phase was precipitated by adding 0.5 ml isopropanol per ml of Trizol reagent and centrifugation at 12,000 × g at 4°C for 15 min. The RNA pellet was washed with 1 ml of 75% ethanol, vacuum dried briefly, and dissolved in RNase-free water. The RNA quantity and quality were initially evaluated by measuring absorbance at 260/280 nm. We evaluated RNA quality and quantity by using RNA LabChip, a lab-on-a-chip device, and Bioanalyzer 2100 (Agilent, Calif, USA). The Agilent Bioanalyzer provides a common platform for sample handling, separation, detection, and data analysis. With as little as 25-500 ng of RNA input, the Bioanalyzer calculated the ratio of 28S and 18S ribosomal RNA and indicated the concentrations of total RNA.

Microarray Procedures We used 5 to 10 μg total RNAs for labeling and hybridization with 3DNA Submicro Expression Array Detection Kit (Genisphere, Hatfield, PA) according to the protocol of the manufacturers. Indirect labeling of cDNA targets using 3DNA Submicro Expression Array Detection kit (Genisphere) was performed in 2 steps. First, 10 μg total RNA from each experimental (test) and control (control) sample was reverse transcribed to target cDNA using an oligo-d(T) primer tagged with either Cy3- or Cy5-specific 3DNA-capture sequences. Both the synthesized test and control cDNAs were then competitively hybridized to probe cDNAs spotted on the microarray slides for 16 hours (overnight) in 10-slide hybridization chambers (Genetix Ltd, UK). In the second step, synthesized tagged target cDNAs were in situ labeled for 2 hours on the microarray with Cy3-3DNA or Cy5-3DNA based on the sequencecomplementation to the capture sequence. Replications of the experiment with the dyeswapping microarray design, previously described, was used in the experiment to minimize statistical variances of data.[15, 16] After hybridization and washing, the slides were scanned with a ChipReader confocal laser scanner (Virtek, Waterloo, Canada). Spot and background intensities were obtained by using the GenePix Pro 4.1 software (Axon Instruments, Union City, CA). Within-slide normalization based on the local weighted regress (LOWESS) algorithm was then carried out. SOMs were developed by Teuvo Kohonen in 1995 as a method to visualize highdimensional data.[17] It is an excellent tool for data mining and is an unsupervised neural network algorithm. Unsupervised learning involves the aggregation of a diverse collection of data into clusters based on different features in a data set. After preprocessing of the data, the SOMs can cluster the data into biologically meaningful groups. It projects input space on prototypes of a regular grid, which can be utilized to explore the properties of the data. When the number of SOMs units is large, similar units are clustered to facilitate effective analysis of the map and the data.[18] The relationship between the known functional classes of genes are studied by analyzing their distribution on the SOMs. The SOMs presents a non-linear mapping of the data as a 2-dimensional map grid that can be used as a data analysis tool for generating hypotheses on the relationship between the genes. We used the SOMs for visualizing a high-dimensional data set of gene expression patterns on a graphical map display. The similarity relationships within the analyzed data can be interpreted. SOMs were used to differentiate between the gene expression patterns of


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superficial and advanced bladder cancer tissues samples. The details of SOMs analysis methods are shown in Figure 1.

Figure 1. The SOM analysis method. (SOMs: Self-Organizing Maps)

A file containing the gene intensity values for each sample scanned along with the associated annotations was used for entering data in the GeneCluster 2.0 software. Necessary image processing steps such as background subtraction and dye correction were carried out. Once loaded, the experiment file was filtered and normalized using a variety of algorithms. These included: thresholding, scaling, normalizing to a given mean and variance, fold-change analysis, and exclusion of high- and low-scoring features. We also randomized the dataset by bootstrap sampling columns from the dataset with replacement. Unsupervised learning, or clustering, is implemented by the SOMs algorithm to allow us to perform batch runs by varying the number of clusters and cluster geometries. Results were viewed in a visualizer that displays cluster profiles and relevant information about the cluster member.

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GoMiner is a tool for the biological interpretation of genomic and proteomic data, including the data from gene expression microarray.[14] It leverages the GO to identify the biological processes, molecular functions, and cellular components. It takes as input two lists of genes: the total gene set on the microarray and the flagged subset of interesting genes. It displays the genes within the framework of the GO hierarchy, both as a directed acyclic graph and as the equivalent tree structure. The GoMiner software classifies the genes into biological coherent categories and assesses these categories.[14]

Results Between December 2003 and November 2004, cDNA microarray gene expression data were obtained from 17 bladder cancer patients. The patients ranged in age from 47 to 87 years (average age, 64 years). All patients had undergone TUR. Pathological studies confirmed the presence of superficial tumors in 9 patients and advanced tumors in 8 patients. Eight out of the 9 patients with superficial bladder tumors received bladder Bacillus Calmette-Guerin (BCG) instillation after TUR. One of the 9 patients with superficial tumors underwent radical cystectomy and concurrent chemotherapy and radiotherapy due to the presence of local lymph node metastasis. All 8 patients with advanced bladder tumor underwent radical cystectomy after TUR. After radical cystectomy, 2 out of these 8 patients received concurrent chemotherapy and radiotherapy, while 1 of them received only chemotherapy. The gene expression data comprised data from 7400 cDNAs in 17 arrays. Table 1 shows the characteristics of the patient tissue samples. Of the 7400 genes analyzed, 473 genes showed significant changes in their expression. Of these 268 were up-regulated, and 205 were down-regulated. Gene expression data were filtered and normalized after running the GeneCluster program. Using the top 473 interesting genes, the SOM method was applied to a balanced dataset and was used to analyze the gene expression data. The underlying structure of the data was explored by varying the geometry of the SOMs. The SOMs forms a non-linear mapping of the data to a two-dimensional map grid that can be used as an exploratory data analysis tool for generating hypotheses on the relationships of the genes. A 2-cluster SOM was used to automatically cluster a set of 17 tissues samples into superficial and advanced bladder cancer groups based on gene expression patterns. The relationships between the known functional classes of the top 473 genes were investigated by analyzing their distribution on the SOMs. The patient tissue samples were clustered into 2 groups, namely, superficial and advanced bladder cancers, comprising 10 and 7 samples, respectively (Figure 2). One patient tissue sample with advanced bladder cancer was clustered into the superficial bladder cancer group. The top 473 genes were analyzed using SOMs. SOMs were used to differentiate between the gene expression patterns of superficial and advanced bladder cancer tissue samples. This analysis had a high accuracy rate of 94% (16/17).

Differentiating Superficial and Advanced Urothelial Bladder Carcinomas… Table 1. Clinical and pathological parameters of patient tissue samples

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Figure 2. A 2-cluster SOM in GeneCluster analysis

The top 473 genes also were classified into biologically coherent categories by the GoMiner software. The results revealed that 452, 435, and 452 genes were associated with biological processes, cellular components, and molecular functions, respectively. Of the 452 genes annotated as being involved in biological processes, most genes were involved in cellular processes (438 genes), physiological processes (426 genes), and regulation (194 genes) and development (143 genes) of biological processes. Of the 435 genes involved in cellular components, 417 genes were associated with cells and cell


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components; 317 genes, with cell organelles; 158 genes, with organelle components; and 138 genes with protein complexes were classified. Of the 452 genes influencing molecular function, 382 genes were associated with binding; 212, with catalytic activity; and 80, with signal transducer activity. Table 2 shows the results in detail. Table 2. GO analysis of the top 473 genes using GoMiner •

biological_process (452 genes) cellular processes (438 genes) development (143 genes) growth (14 genes) interaction between organisms (8 genes) physiological processes (426 genes) regulation of biological processes (194 genes) reproduction (28 genes) response to stimulus (114 genes) viral life cycle (5 genes)

•

cellular_component (435 genes) cell (417 genes) cell component (417 genes) envelope (23 genes) extracellular matrix (9 genes) extracellular matrix part (1 gene) extracellular region (68 genes) extracellular region component (61 genes) membrane-enclosed lumen (68 genes) organelle (307 genes) organelle part (158 genes) protein complex (138 genes) synapse (2 genes) virion (1 gene) virion part (1 gene)

•

molecular_function (452 genes) antioxidant activity (4 genes) binding (382 genes) catalytic activity (212 genes) enzyme regulator activity (36 genes) motor activity (5 genes) protein tag (1 gene) signal transducer activity (80 genes) structural molecule activity (33 genes) transcription regulator activity (65 genes) translation regulator activity (10 genes) transporter activity (53 genes)

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According to the organizing principles of GO, many important genes are found in cancerrelated biological processes. The cell differentiation-related genes include BMP7, BRD2, CD24, CSF1, DRG1, DZIP1, EFNB2, ELAVL3, FGF1, FZD5, INHA, MDK, NOS3, NTRK2, PMCH, PMP22, SORT1, and TSSK2. The apoptosis-related genes comprise APAF1, APPBP1, BAG1, BCAP31, BIRC5, CDKN2A, ELMO1, IL1B, RAD21, RIPK2, TEGT, TFDP1, UNC5B, VDAC1, and YARS. The genes associated with cell migration include VAV3, WASF2, APBB2, BMP7, PGRMC1, UNC5B, CDH1, HMGCR, IL1B, SPP1, IL8, SYK, ARHGAP8, CDKN1B, and AKAP4. Cell proliferation-related genes include BCAT1, BLZF1, CKS2, CSF1, DYRK2, FGF1, FRAT2, IL1B, KIP2, MCM7, MDK, PIM1, PRDX1, RPS21, SYK, TACSTD2, TFDP1, YY1, and ZFP36L2. Genes related to transcription regulator activity are FALZ, HES1, MEN1, NEO1, NUP62, TBX5, TCF3, and TRIP4. These data are summarized in Table 3. Table 3. Important genes found in cancer-related biological processes Cancer-related biological processes Cell differentiation

Apoptosis

Cell migration

Cell proliferation

Transcription regulator activity

Related genes BMP7, BRD2, CD24, CSF1, DRG1, DZIP1, EFNB2, ELAVL3, FGF1, FZD5, INHA, MDK, NOS3, NTRK2, PMCH, PMP22, SORT1, TSSK2 APAF1, APPBP1, BAG1, BCAP31, BIRC5, CDKN2A, ELMO1, IL1B, RAD21, RIPK2, TEGT, TFDP1, UNC5B, VDAC1, YARS VAV3, WASF2, APBB2, BMP7, PGRMC1, UNC5B, CDH1, HMGCR, IL1B, SPP1, IL8, SYK, ARHGAP8, CDKN1B, AKAP4 BCAT1, BLZF1, CKS2, CSF1, DYRK2, FGF1, FRAT2, IL1B, KIP2, MCM7, MDK, PIM1, PRDX1, RPS21, SYK, TACSTD2, TFDP1, YY1, ZFP36L2 FALZ, HES1, MEN1, NEO1, NUP62, TBX5, TCF3, TRIP4.

Discussion It has been reported that gene profiling provides a genome-based classification method for the diagnosis and prognosis of advanced urothelial bladder carcinoma. It may help identify the patients who require aggressive therapeutic interventions.[19] The gene expression profiling of urothelial bladder cancer may provide insights into the biology of cancer progression and help identify patients with distinct clinical phenotypes.[8] Therefore, in this study, we compared the gene expression profiles of superficial and advanced urothelial bladder cancers and attempted to identify changes in gene expression during the progression of urothelial cancer. We also analyzed the annotation of the significant genes to understand the role of critical genes and pathways during bladder cancer progression. Microarray technology has simplified the monitoring of gene expression patterns during cellular differentiation.[20, 21] Many statistical techniques have been developed for identifying the underlying patterns in complex data. Recently, several clustering techniques


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for gene expression data have been described. They include hierarchical clustering, Bayesian clustering, k-means clustering, and SOMs.[22-24] Hierarchical clustering has proven to be a valuable method of analysis. Bayesian clustering is a structured approach useful when prior data distribution is available. K-means clustering is an unstructured approach, which produces an unorganized collection of clusters. The features of SOMs make them well-suited for clustering and analysis of gene expression patterns and impose partial structure on the clusters.[12] SOMs facilitate easy visualization and interpretation. SOMs are easy to implement, fast, and scalable to large data sets. In this study, the program package GeneCluster V. 2.0 was used to produce and display SOMs of gene expression data. The program was developed by the Center for Genome Research/Massachusetts Institute of Technology and was used to facilitate the interpretation of gene expression data. Transcription studies on a genomic scale using microarray technology have led to major advances in our understanding of the pathogenesis of human diseases. In this study, the gene expression data comprised 7400 cDNAs in 17 arrays. We used the top 473 genes that demonstrated significant changes in expression for the differential diagnosis of superficial and advanced urothelial bladder cancers. Microarray studies have generated controversy due to the probabilistic and inconsistent nature of the results obtained. It is, however, possible to develop simple expression measures that will allow comparisons in the same platforms and studies.[25] A SOM is an unsupervised neural network learning algorithm. It has been successfully used for the analysis and organization of large data files.[26] Therefore, we applied the SOM algorithm for the analysis and visualization of gene expression profiles. A 2-cluster SOM was used to automatically cluster a set of 17 urothelial bladder cancer samples into superficial and advanced bladder cancers based on the expression patterns of 473 genes. The SOM analysis yielded a high accuracy rate of approximately 94%. The clustering algorithm was effective in categorizing the samples into biologically meaningful groups. However, clustering has yielded results that are interpretable in the context of a priori knowledge to know bladder cancer subclasses. In the absence of such knowledge the biological interpretation of clustering results remains a challenge. A gene may be located in some cellular components and influence some biological processes, in which certain molecular functions may be involved. GO addresses the need for consistent descriptions of genes in databases. The GO project has developed 3 structured ontologies that describe gene products in terms of their associated cellular components, biological processes, and molecular functions.[27] The functions of the differentially expressed genes can be assessed by querying the GO database via the GoMiner software. GoMiner is a program package that organizes lists of expressed genes for biological interpretation within the context of the GO database.[14] Therefore, in our study, we used the GoMiner software to query the GO database to analyze the functions of 473 genes. Of the 473 genes, 268 genes were up-regulated and 205 genes were down-regulated. We analyzed these genes and attempted to identify the genes that could function as biomarkers of urothelial bladder cancers. Of these 473 genes, many have been reported to be associated with superficial or advanced bladder cancers. In 2007, it was reported that the overexpression of CD24 is associated with invasiveness in urothelial carcinoma of the bladder. The CD24 gene is related to cell differentiation. It may be a potential serum marker for urothelial bladder carcinoma or a target of antibody-based therapeutics for bladder carcinoma.[28] FGF1 has been observed to behave as a tumorigenic factor in a bladder carcinoma cell model.[29] NOS3

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may play a role in the differentiation of the transitional epithelium in fetal life. It may also be involved in physiological functions of the adult bladder mucosa; this gene is also involved in bladder carcinogenesis.[30] It has been suggested that the expression of the tumor suppressor gene APAF1 is controlled by promoter methylation in the early stages of bladder cancer.[31] The apoptosis-related gene BIRC5 is a useful adjunct marker for the grading of papillary urothelial carcinoma.[32] Decreased CDKN2A expression was found to be correlated with tumor progression in patients with minimally invasive bladder cancer.[33] It was reported that an single nucleotide polymorphism (SNP) in the promoter of the cell migration-related gene CDH1 is a risk factor for bladder cancer.[34] The overexpression of interleukin 8 (IL-8) in transitional cell carcinoma (TCC) results in increased tumorigenicity and metastasis.[35] An analysis of the different patterns of aberrant methylation of the SYK gene in the various types of bladder cancers indicated that SYK may play a role in tumor cell differentiation causing the conversion of TCC into non-urothelial carcinomas and thus increasing the malignant potential of TCC.[36] Analysis of the cell cycle regulators of urothelial bladder cancer indicated that CDKN1B is a potentially useful prognostic biomarker.[37] Real-time PCR assay confirmed that the up-regulation of the CKS2 gene in advanced bladder cancer was significantly higher than that in superficial bladder cancer.[10] The KIP2 gene could be an important target of genetic and epigenetic alterations in bladder cancer affecting the maternal chromosome 11p15.5.[38] The up-regulation of the cell proliferation-related gene YY1 in bladder cancer may account for the efficacy of gefitinib administration in the treatment of this disease.[39] Gene expression profiling of urothelial bladder cancers provides insights into the pathogenesis and prognosis of bladder cancer. Further it enables the identification of the distinct clinical phenotypes of bladder cancer patients. Alterations in specific genes are associated with modifications in various cellular functions such as cell differentiation, signal transduction, transcription, translation, DNA replication, and mitosis. Some studies in the past decade have demonstrated that genetic alterations are responsible for the development and progression of bladder cancer.

Conclusion Based on our results, we believe that superficial and advanced urothelial bladder cancers can be differentiated by their gene expression profiles analyzed by SOMs. The differences between the gene expression profiles of superficial and advanced bladder carcinomas suggest that these cancers may have unique genetic pathways with similar genetic alterations. The genes that are uniquely expressed in either type of bladder cancer can be considered as possible candidates for urinary biomarkers.

References [1] [2]

Konety, BR; Carroll, PR. Smith’s General Urology: Urothelial carcinoma: cancers of the bladder, ureter and renal pelvis. 16th. Columbus, OH: McGraw-Hill; 2008. Flechon, A; Droz, JP. Chemotherapy practices and perspectives in invasive bladder cancer. Expert Rev Anticancer Ther, 2006 Oct 6(10):1473-82.

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[18] Vesanto, J; Alhoniemi, E. Clustering of the self-organizing map. IEEE Trans Neural Netw, 2000;11(3):586-600. [19] Sanchez-Carbayo, M; Socci, ND; Lozano, J; Saint, F; Cordon-Cardo, C. Defining molecular profiles of poor outcome in patients with invasive bladder cancer using oligonucleotide microarrays. J Clin Oncol, 2006 Feb 10;24(5):778-89. [20] Wodicka, L; Dong, H; Mittmann, M; Ho, M; Lockhart, D. Genome-wide expression monitoring in Saccharomyces cerevisiae. Nat. Biotechnol, 1997;15: 1359–67. [21] Chu, S; DeRisi, J; Eisen, M; Mulholland, J; Botstein, D; Brown, PO; Herskowitz, I. The transcriptional program of sporulation in budding yeast. Science, 1998:282, 699– 705. [22] Spellman, PT; Sherlock, G; Zhang, MQ; Iyer, VR; Anders, K; Eisen, MB; Brown, PO; Botstein, D; Futcher, B. Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Mol Biol Cell, 1998;9:3273–97. [23] Eisen, MB; Spellman, PT; Brown, PO; Botstein, D. Cluster analysis and display of genome-wide expression patterns. Proc. Natl. Acad. Sci. USA, 1998;95: 14863–8. [24] Kangas, JA; Kohonen, TK; Laaksonen, JT. Variants of self-organizing maps. IEEE Trans Neural Netw, 1990;1(1):93-9. [25] Garrett-Mayer, E; Parmigiani, G; Zhong, X; Cope, L; Gabrielson, E. Cross-study validation and combined analysis of gene expression microarray data. Biostatistics, 2008 Apr;9(2):333-54. [26] Toronen, P; Kolehmainen, M; Wong, G; Castren, E. Analysis of gene expression data using self-organizing maps. FEBS Letters, 1999;451:142-6. [27] Cimino, JJ; Zhu, X. The practical impact of ontologies on biomedical informatics. Yearb Med Inform, 2006;124-35. [28] Choi, YL; Lee, SH; Kwon, GY; Park, CK; Han, JJ; Choi, JS; Choi, HY; Kim, SH; Shin, YK. Overexpression of CD24: association with invasiveness in urothelial carcinoma of the bladder. Arch Pathol Lab Med, 2007 Feb 131(2):275-81. [29] Jouanneau, J; Plouet, J ; Moens, G; Thiery, JP. FGF-2 and FGF-1 expressed in rat bladder carcinoma cells have similar angiogenic potential but different tumorigenic properties in vivo. Oncogene, 1997 Feb 13;14(6):671-6. [30] Shochina, M; Fellig, Y; Sughayer, M; Pizov, G; Vitner, K; Podeh, D; Hochberg, A; Ariel, I. Nitric oxide synthase immunoreactivity in human bladder carcinoma. Mol Pathol, 2001 Aug 54(4):248-52. [31] Christoph, F; Hinz, S; Kempkensteffen, C; Weikert, S; Krause, H; Schostak, M; Schrader, M; Miller, K. A gene expression profile of tumor suppressor genes commonly methylated in bladder cancer. J Cancer Res Clin Oncol, 2007 Jun 133(6):343-9. [32] Chen, YB; Tu, JJ; Kao, J; Zhou, XK; Chen, YT. Survivin as a useful adjunct marker for the grading of papillary urothelial carcinoma. Arch Pathol Lab Med, 2008 Feb 132(2):224-31. [33] Krüger, S; Mahnken, A; Kausch, I; Feller, AC. P16 immunoreactivity is an independent predictor of tumor progression in minimally invasive urothelial bladder carcinoma. Eur Urol, 2005 Apr 47(4):463-7.


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[34] Kiemeney, LA; van Houwelingen, KP; Bogaerts, M; Witjes, JA; Swinkels, DW; den Heijer, M; Franke, B; Schalken, JA; Verhaegh, GW. Polymorphisms in the E-cadherin (CDH1) gene promoter and the risk of bladder cancer. Eur J Cancer, 2006 Dec 42(18):3219-27. [35] Mian, BM; Dinney, CP; Bermejo, CE; Sweeney, P; Tellez, C; Yang, XD; Gudas, JM; McConkey, DJ; Bar-Eli, M. Fully human anti-interleukin 8 antibody inhibits tumor growth in orthotopic bladder cancer xenografts via down-regulation of matrix metalloproteases and nuclear factor-kappaB. Clin Cancer Res, 2003 Aug 1;9(8):316775. [36] Kunze, E; Wendt, M; Schlott, T. Promoter hypermethylation of the 14-3-3 sigma, SYK and CAGE-1 genes is related to the various phenotypes of urinary bladder carcinomas and associated with progression of transitional cell carcinomas. Int J Mol Med, 2006 Oct 18(4):547-57. [37] Brunner, A; Verdorfer, I; Prelog, M; Mayerl, C; Mikuz, G; Tzankov, A. Large-scale analysis of cell cycle regulators in urothelial bladder cancer identifies p16 and p27 as potentially useful prognostic markers. Pathobiology, 2008;75(1):25-33. [38] Oya, M; Schulz, WA. Decreased expression of p57(KIP2)mRNA in human bladder cancer. Br J Cancer, 2000 Sep 83(5):626-31. [39] Inoue, R; Matsuyama, H; Yano, S; Yamamoto, Y; Iizuka, N; Naito, K. Gefitinibrelated gene signature in bladder cancer cells identified by a cDNA microarray. Anticancer Res, 2006 Nov-Dec 26(6B):4195-202.


ISBN 978-1-60692-0404-4 c 2009 Nova Science Publishers, Inc.

Chapter 9

F ULL S IBLING R ECONSTRUCTION IN W ILD P OPULATIONS F ROM M ICROSATELLITE G ENETIC M ARKERS Mary V. Ashley∗, Tanya Y. Berger-Wolf†, Isabel C. Caballero∗, Wanpracha Chaovalitwongse ‡, Bhaskar DasGupta† and Saad I. Sheikh † ∗ Department of Biological Sciences, University of Illinois at Chicago, Chicago, IL 60607.

I do not believe that the accident of birth makes people sisters and brothers. It makes them siblings. Gives them mutuality of parentage. .

– Maya Angelou

Abstract New technologies for collecting genotypic data from natural populations open the possibilities of investigating many fundamental biological phenomena, including behavior, mating systems, heritabilities of adaptive traits, kin selection, and dispersal patterns. The power and potential of genotypic information often rests in the ability to reconstruct genealogical relationships among individuals. These relationships include parentage, full and half-sibships, and higher order aspects of pedigrees. Some areas of genealogical inference, such as parentage, have been studied extensively. Although methods for pedigree inference and kinship analysis exist, most make assumptions that do not hold for wild populations of animals and plants. In this chapter, we focus on the full sibling relationship and first review existing methods for full sibship reconstructions from microsatellite genetic markers. We then ∗

Email: {ashley,icabal2}@uic.edu Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607. email: {tanyabw,dasgupta,ssheikh}@cs.uic.edu ‡ Department of Industrial Engineering, Rutgers University, Piscataway, NJ 08854. email: [email protected] †

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Mary V. Ashley, Tanya Y. Berger-Wolf, Isabel C. Caballero et al. describe our new combinatorial methods for sibling reconstruction based on simple Mendelian laws and its extension even in the presence of errors in the data. We also describe a generic consensus method for combining sibling reconstruction results from other methods. We present experimental comparison of the best existing approaches on both biological and simulated data. We discuss relative merits and drawbacks of existing methods and suggest a practical approach for reconstructing sibling relationships in wild populations.

1.

Introduction

Kinship analysis of wild populations is often an important and necessary component of understanding an organism’s biology and ecology. Population biologists studying plants and animals in the field want to know how individuals survive, acquire mates, reproduce, and disperse to new populations. Often these parameters are difficult or impossible to infer from observational studies alone, and the establishment of kinship patterns (parentage or sibling relationships, for example) can be extremely useful. The powerful toolbox provided by advances in molecular biology and genome analysis has offered population biologists a growing list of possibilities for inferring kinship. Paternity analysis in wild populations became common upon the arrival of the first DNA-based markers in the mid-1980s, when multi-locus DNA fingerprinting methods became available. Probably the most notable discoveries came from studies of avian mating systems. Multi-locus DNA fingerprinting revealed that many bird species that were behaviorally monogamous were in fact often reproductively promiscuous. Females of such species would furtively engage in extra-pair copulations, apparently unbeknownst to their cuckolded male social partners. In fact, the frequency of extra-pair fertilizations (up to 50% in some species) led avian behavioral ecologist to distinguish between social mating systems and genetic mating systems (reviewed in [55]). The invention of the polymerase chain reaction (PCR) [38] quickly led to the replacement of multi-locus fingerprinting with single-locus PCR-based techniques by the mid 1990s [3, 39]. Microsatellites (also known as SSRs and STRs) were the first and still are the most widespread molecular marker for inferring kinship in wild populations, although their development in each new species studied is often a time-consuming and expensive obstacle. Microsatellite genotypes, which could be obtained from tiny amounts of blood, tissue, or even feces, have been used to infer parentage, particularly paternity, in a large number of wild species. Notable examples include the study of pollination patterns in forest trees [13, 14, 47], identifying fathers of the famed chimpanzees of Gombe [12], and evaluating the success of alternative mating strategies used by male big horn sheep [24]. A breakthrough in paternity assignment came with the release of the software program CERVUS [30] that provided a user-friendly Windows-based program that employed a statistical likelihood method to assign paternity to a candidate father with an estimated level of statistical confidence. There are many cases where field studies can sample cohorts of offspring yet sampling putative parents is problematic. In these cases, sibling relationships (sibship) reconstruction, rather than parentage assignment, is required. For genetic markers showing Mendelian inheritance, such as microsatellites, parentage assignment (maternity or paternity) is computationally much simpler than sibship reconstruction. In diploid organisms, a parent and

Full Sibling Reconstruction in Wild Populations...

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each offspring must share an allele at every genetic locus (barring rare mutations). On the other hand, full siblings will share, on average, half their alleles, but at any one locus, they may share 0,1, or 2 alleles. Sibling reconstruction methods have lagged behind those developed for paternity assignment, but several methods of sibling reconstruction are now available. In this review, we will examine the constraints that Mendelian inheritance dictates for sibling reconstructing, review the use of microsatellite genotyping in wild populations, and evaluate alternative genetic markers. We will then review the various methods for full sibling reconstruction that are currently available and present experimental validation of various methods using both real biological data and simulated data.

1.1.

Microsatellites

While there are several molecular markers used in population genetics, microsatellites are the most commonly used in kinship studies in wild populations. First discovered in the late 1980s when genomic sequencing studies began [48, 54], microsatellites are short (one to six base pairs) simple sequence repeats, such as (CA/GT )n or (AGC/T CG)n that are scattered around eukaryotic genomes. A genomic library for a study species is screened for such repeats and primers for PCR amplification are constructed from the regions flanking the short repeats. Alternatively, microsatellite primers developed for one species may be used for closely related species. For example, microsatellites developed for humans amplify homologous loci in chimpanzees [12]. Figure 1 shows a schematic example of a microsatellite marker with three alleles and the resulting genotypes. Because there is a relatively high rate of mutation for adding or subtracting repeat units, microsatellite loci have high numbers of alleles and high levels of heterozygosity. PCR-based microsatellite analysis provides co-dominant, unlinked markers where alleles and genotypes can be scored precisely by size. These are the characteristics that make them especially useful for estimating kinship and relatedness. There are some technical problems associated with scoring microsatellites, and any method of sibling reconstruction with microsatellites needs to be able to accommodate a low frequency of scoring errors or artifacts, in addition to occasional mutation. Microsatellites have been successfully applied to a wide range of non-model organisms, including vertebrates, invertebrates, plants, and fungi, and are used to infer large-scale population structure as well as individual kinship. For kinship studies, microsatellites have been used more commonly for parentage than for sibship reconstruction, but there are an increasing number of studies that have attempted to reconstruct sibships with partial or no parental sampling. In lemon sharks, cohorts of juvenile sharks were sampled annually from nursery lagoons, and sibship reconstruction was used to infer the mating system and fertility of adults [17]. Sibship reconstruction was used to infer patterns of brood parasitism for individual female cowbirds, who lay their eggs in the nests of other birds [45, 46]. In a study of wood frogs, tadpoles were sampled from ponds and sibgroups reconstructed to study their spatial distribution and the potential for kin selection [22]. Such studies have employed a variety of methods to reconstruct sibling groups from microsatellite data because there was no widely accepted or easily implemented software available. In addition to microsatellites, which assay DNA repeat variation, several PCR-based methods are available to assay variation in DNA sequence. RAPDs (randomly amplified

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Mary V. Ashley, Tanya Y. Berger-Wolf, Isabel C. Caballero et al.

Figure 1. A schematic example of a microsatellite marker. polymorphic DNA), ISSRs (inter-simple sequence repeats), and AFLPs (amplified fragment length polymorphisms) are dominant, multi-locus techniques which are problematic for kinship inference. SNPs (single nucleotide polymorphisms) are single locus markers that focus on a variable single nucleotide position in the genome. While they are numerous in the genome and, once identified, easy to score, they have limitations in the area of kinship reconstruction. The power to identify related individual depends mainly on the number of alleles per locus and their heterozygosity. SNPs are usually biallelic, whereas microsatellites may have 10 or more alleles per locus and typically have high heterozygosities. It appears for at least the next few years, microsatellites will remain the marker of choice for estimating relatedness in wild populations. We thus focus our efforts on developing and comparing methods of sibling reconstruction that are applicable to microsatellites or, more generally, codominant, multiallelic markers.

2.

Sibling Reconstruction Problem

In order to reason about the inherent computational properties of the problem of reconstructing sibling relationships and to compare the accuracy and performance of various computational methods for solving the problem, we must define it formally. The problem of siblings reconstruction was first formally defined in [5] and is restated here. Definition 1. Let U be a population of n diploid individuals of the same generation genotyped at at l microsatellite loci: U = {X1, ...Xn},

where Xi = (hai1, bi1i, ..., hail, bili)


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and aij and bij are the two alleles of the individual i at locus j represented as some identifying string. The goal of the Sibling Reconstruction Problem is to reconstruct the full sibling groups (groups of individuals with the same parents). We assume no knowledge of parental information. Formally, the goal is to find a partition of individuals P1 , ...Pm such that ∀1 ≤ k ≤ m,

∀Xp , Xq ∈ Pk :

P arents(Xp ) = P arents(Xq )

Note, that we have not defined the function P arents(X). This is a biological objective. Computational approaches use the formalization of various biological assumptions and constraints to achieve a good estimate of the biological sibling relationship. We describe the fundamental genetic properties that serve as a basis for most computational approaches in the next section.

3. 3.1.

Genetics of Sibship Mendelian Genetics

Mendelian genetics lay down a very simple rule for gene inheritance in diploid organisms: an offspring inherits one allele from each of its parents for each locus . This introduces two overlapping necessary (but not sufficient) constraints on full sibling groups in absence of genotyping errors or mutations: the 4-allele property and the 2-allele property [5, 10]. 4-Allele Property: The total number of distinct alleles occurring at any locus may not exceed 4. Formally, a set of individuals S ⊆ U has the 4-allele property if [ ∀1 ≤ j ≤ l : {aij , bij } ≤ 4. i∈S

Clearly, the 4-allele property is necessary since a group of siblings can inherit only combinations of the 4 alleles of their common parents. The 4-allele property is effective for identifying sibling groups where the data are mostly heterozygous and the parent individuals share few common alleles. Generally, as in Table 1, a set consisting of any two individuals trivially satisfies the 4-allele property. The set of individuals 1, 3 and 4 from Table 1 satisfies the 4-allele property. However, the set of individuals 2, 3 and 5 fails to satisfy it as there are five alleles occurring at the first locus: {12, 28, 56, 44, 51}. 2-Allele Property: There exists an assignment of individual alleles within a locus to maternal and paternal such that the number of distinct alleles assigned to each parent at this locus does not exceed 2. Formally, a set of individuals S ⊆ U has the 2-allele property if for each individual Xi in each locus there exists an assignment of aij = cij or bij = cij (and the other allele assigned to c¯ij ) such that [ [ cij } ≤ 2 ∀1 ≤ j ≤ l : {cij } ≤ 2 and {¯ i∈S

i∈S

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The 2-allele property is clearly stricter than the 4-allele property. Looking at the Table 1, our previous 4-allele set of individuals 1, 3 and 4 fails to satisfy the 2-allele property since there are more than two alleles on the left side of locus 1: {44, 28, 13}. Moreover, there is no swapping of the left and right sides of alleles that will bring down the number of alleles on each side to two: individuals 1 and 4 with their alleles 44/44 and 13/13 already fill the capacity. Again, any two individuals trivially satisfy the 2-allele property. Table 1. An example of input data for the sibling reconstruction problem. The five individuals have been sampled at two genetic loci. Each allele is represented by a number. Same numbers within a locus represent the same alleles. Individual 1 2 3 4 5

Alleles ha, bi at locus 1 44, 44 12, 56 28, 44 13, 13 28, 51

Alleles ha, bi at locus 2 55, 27 18, 39 55, 18 39, 27 18, 39

Assuming the order of the parental alleles is always the same in the offspring (i.e. the maternal allele is always on the same side), the 2-allele property is equivalent to a biologically consistent full sibling relationship. The parental allele order, however, is not preserved, and an interesting problem arises: given a set of individuals S that satisfies the 4-allele property, does there exist a series of allele reorderings within some loci of individuals in S so that after those reorderings S satisfies the 2-allele property? For example, in Table 1, the individuals 1, 3, and 5 have more than two alleles on the right side of locus 2: {27, 18, 39}. However, switching the alleles 18 and 39 at locus 2 in the individual 5 will bring the number of alleles on either side down to two. Since the number of alleles on either side of locus 1 is also two, the set of individuals 1, 3, and 5 satisfies the 2-allele property. In [10] we show the connection between the two properties that we restate here: Theorem 1. Let a be the number of distinct alleles present in a given locus and R be the number of distinct alleles that either appear with three different alleles in this locus or are homozygous (appear with itself). Then, given a set of individuals with the 4-allele property, there exists a series of allele reorderings within loci resulting in a set that satisfies the 2allele property if and only if for all the loci in the set a + R ≤ 4. In our example of individuals 1, 3, and 5 in locus 1, a = |{44, 28, 51}| = 3 and R = 1 since each allele is paired up only with at most two different alleles but 44 is a homozygote. In locus 2, a = |{55, 27, 18, 39}| = 4 but R = 0 since there are no homozygote alleles and no allele appears with more than two different alleles. Thus, the set of individuals 1, 3, and 5 satisfies a + R ≤ 4 for all loci and, hence, the 2-allele property. The 2-allele property takes into account the fact that the parents can contribute only two alleles each to their offspring. Note, that the 2-allele property is, again, a necessary but not a sufficient constraint for a group of individuals to be siblings (in absence of errors or


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mutations). The full formalization of the Mendelian inheritance constraints in the context of sibling reconstruction is presented in [5, 10].

3.2.

Relatedness Estimators

In the 1980’s several statistical coefficients of relatedness were introduced [31, 33, 36]. All methods use observed allele frequencies to define the probabilistic degree of relatedness between two individuals. In 1999, Queller and Goodnight improved on their approach [37] by defining simple statistical likelihood formulae for different types of relationships and used those to infer sibling relationships. The 1999 paper also defines a method to determine the statistical significance, or “p-value”, of a relationship estimate. This is done by randomly generating two individuals using the observed allele frequencies and the estimated probabilities of inheriting a shared allele as defined in the paper. Such random pairs of individuals are generated a large number of times, then the likelihood ratio that excludes 95% of the individuals is accepted as being at p-value 0.05. Even though this approach was not presented or aimed as a method for sibship reconstruction, it served as a basis for likelihood methods that followed. A number of assumptions are made by all relatedness estimators, including ignoring mutations and genotyping errors. More importantly, the methods assumes that a sample representative of the population has been scored, and there is accurate estimates of allele frequencies for the entire population. If these assumptions do not hold, results will be biased [34]. Finally, any method relying purely on a pairwise genetic distance may lead to inconsistent results, i.e. the transitivity of the sibling relationship may not hold. Moreover, as mentioned before, any pair of individuals can be siblings yet no pairwise distance estimate method cannot exclude that possibility [49].

4.

Methods for Full Sibling Reconstruction

As more microsatellite markers become available for wild species there is a growing interest in the possibility of inferring relatedness among individuals when part or all of the pedigree information is lacking [43]. The majority of the available software requires parental data. However, recently there have been several methods attempting to reconstruct sibship groups from genetic data without parental information [1, 2, 6, 8, 29, 32, 43, 49, 53]. Fernandez and Toro [18] and Butler et al. [9] review many of the methods discussed here. In their survey, Butler et al. [9] classified sibship reconstruction methods into two main groups: (1) methods that generate complete genealogical structures and, thus, require explicit pedigree reconstruction, and (2) pairwise methods that do not imply such pedigree reconstruction. This latter group can be subdivided into methods that estimate pairwise relatedness based on genotypic similarity and likelihood approaches that classify pairs of individuals into different types of relationships based on marker information. In one of the earlier examples of the first type of method, Painter [32] used a Bayesian approach to calculate relationship likelihood and then an exhaustive search to find the most likely sibship in a small population of 9 individuals. He identified the need for using better optimization techniques for larger populations. Among the methods that followed, some use Markov-Chain Monte Carlo (MCMC) techniques to locate a partition of individuals that maximizes the likelihood of the proposed family relationship, such as COLONY [53]

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software and Almudevar’s method [1]. Smith [43] has developed an approach that maximizes a relatedness configuration score derived form the pairwise relatedness likelihood ratio. Almudevar and Field [2] used an exclusion principle that looks for the largest fullsibling families, using partial likelihoods to pick between families of the same size. Another approach is based on Simpson’s index of concentration [9], where groups that conform to Mendelian inheritance rules are formed according to marker information. One of the advantages of these methods is that they avoid the inconsistency problems of pairwise estimators described below. However, the statistical likelihood methods still depend on the knowledge of population allelic data (to calculate likelihoods) which is typically unavailable or inaccurate. Moreover, since most of these methods employ global optimization at their core, they are usually computationally demanding. As described above, a second type of approach, pairwise methods, are widely used for sibship reconstruction. While these methods are typically simple and fast they suffer several disadvantages. First, they can lead to incongruous assignments because only two individuals are considered at a time and transitivity is not preserved. Second, like all statistical methods, they are dependent on the knowledge of allelic frequencies of the population considered. Third, if multiple definite relationships exist, such as full siblings, half siblings, or unrelated, arbitrary thresholds have to be defined to decide the category to which a particular pair is assigned [18]. Here, we consider a different classification of sibling reconstruction methods, based on the computational approach a method employs as the basis for reconstruction. SIBSHIP [49], Pedigree [43], KINGROUP [29], and COLONY [53] rely on statistical estimates of relatedness [37] and reconstruct the maximum likelihood sibling groups. Family Finder [8] and Almudevar [1] mix statistical and combinatorial approaches. Finally, Almudevar and Field [2], 2-allele Minimum Set Cover [5, 6, 10, 41] and Sheikh et al. [40] use only the fundamental Mendelian constraints and combinatorial techniques to reconstruct sibling groups. A common assumption of all but two (Sheikh et al. [40] and COLONY [53]) of the sibship reconstruction methods is that the molecular data is error and mutation free [18]. Data that contain errors test the robustness of these methods and are a major problem of the estimators involving pedigree reconstruction [9]. Following our computationally based classification, we now describe some of the methods in more detail, providing deeper analysis of the two best-performing methods (see Section 5. for experimental comparison), the likelihood based COLONY and the combinatorial 2-allele Minimum Set Cover.

4.1. Statistical Likelihood Methods As Painter’s [32] first likelihood-based sibling reconstruction method exemplified, likelihood maximization methods require sophisticated optimization techniques to find the most likely sibship partition for datasets of size greater than 10 individuals. In 2000, Thomas and Hill [49] introduced a Markov Chain Monte Carlo (MCMC) approach to find the maximum likelihood of a sibship reconstruction. The method compares the likelihood ratio of two individuals being siblings to that of the the pair being unrelated [36]. Starting with a random partition of individuals into potential sibling groups, the


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method uses a “hill-climbing” approach to explore different sibship reconstructions, reassigning individuals into sibling groups to improve the likelihood of all pairs being siblings. The process continues until one of the halting conditions is reached: either the number of iterations exceeds a threshold, or the sibling reconstruction stabilizes, i.e. the likelihood value reaches a fixed point. The algorithm was not computationally efficient and was subsequently improved. Like most likelihood based methods, the main assumption of the approach is that the sample at hand is representative of the entire population in terms of allele frequencies and, thus, the relatedness probabilities. More detrimentally, the method also assumes that the population contains only full siblings and unrelated individuals which typically does not hold for any population. In 2002, Thomas and Hill [50] extended their approach by adding half sibling relationships, thus creating a limited family hierarchy. The algorithm is similar to their previous approach in [49], with the addition that an individual could be assigned to either a half sibling group or a full sibling group at every iteration. Half sibling groups were randomly created every few hundred iterations to ensure that a hierarchical structure existed in the population. In that paper, Thomas and Hill also explored the effects of population size, population structure, and the allelic information available on the performance of their MCMC approach. Typical of the statistical approaches, the accuracy of the reconstruction improved with the increase of available marker information and the nestedness of the full siblings within half sibling groups but decayed with the increase of the population size. In 2001 Smith et al. [43] presented two different MCMC methods for sibship reconstruction. One of the methods is very similar to [50], while the other aims to maximize the joint likelihood of the entire sibship reconstruction rather than pairwise relatedness ratio. The methods performed very well for the Atlantic salmon dataset the authors used in the original publication. The software P EDIGREE is now available for general use as an online service. Smith et al. have also assayed the dependency of the accuracy of reconstruction various data parameters. In general, the methods suffer from typical assumptions of other statistical methods. The accuracy of reconstruction decreases when there is insufficient allelic diversity per locus or the sample is not representative of the population. Konovalov et al. [29] introduced KINGROUP, available as an open source Java TM program. KINGROUP uses the relatedness estimators of [37] with additional algorithms designed for the reconstructions of groups of kin that share a common relationship. Family Finder [8] was introduced in 2003. It is a very efficient method that uses a combination of statistics and graph theory. This approach constructs a graph with individuals as vertices. Edges represent pairwise sibling relationship and are weighted using, again, the likelihood ratio of individuals being siblings to their being unrelated [37]. After constructing this graph “clusters”, or components, corresponding sibling groups are identified by finding light edge cuts. Cuts with the number of edges less than one third of the edges in the graph are chosen. It is a simple and efficient method that can be effective if enough loci are available and allelic diversity is high. While there is some theoretical basis, usage of the likelihood ratio implies the same assumptions as [37]. Furthermore, it assumes that sibling groups are roughly equally sized, which is a dubious assumption and often does not hold, especially for wild population samples.

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4.1.1. COLONY A different likelihood maximization approach was used by Wang [53]. COLONY is a comprehensive statistical approach that uses the simulated annealing heuristic to find a (local) likelihood maximum of a sibship reconstruction. The algorithm starts with known full and half siblings (if any are available) and places the rest into singleton sibling groups, along with the computed likelihood of each group. A proposed alternate solution at every iteration is created by moving a random number of individuals from one full sibling group to another (both groups must not be one of the known full sibling groups). For half siblings, a random number of entire full sibling groups are moved from one half sibling group to another. As before, these must not be the original known half sibling families. After generating a new proposed solution, the likelihood of the old and new configurations of the altered families is calculated. The new configuration is accepted or rejected based on a threshold which depends on the ratio of the new and old likelihoods. COLONY is the first method to fully accommodate sampling bias and genotyping errors, although it relies on many user input parameters to do so. Errors are estimated using the calculated probability of observing the given allele assuming the actual allele is different. The probabilities of allelic dropouts and other typing of errors are based on [19], allelic dropout is considered to be twice as likely as other errors. Simulated annealing relies on random numbers and explores a vast solution space. COLONY can be quite slow, and its performance both in terms of time and accuracy depends drastically on the amount of microsatellite information available. COLONY was designed for both diploid and haplodiploid species. It is perhaps the most comprehensive and sophisticated method currently available for full sibling reconstruction with a strong theoretical basis. However, in addition to other disadvantages common to all statistical sibship reconstruction methods, it also assumes that one of the parents is monogamous which, unfortunately, renders it inappropriate for many species that have promiscuous mating systems.

4.2. Combinatorial Approaches Combinatorial approaches to sibling reconstruction use Mendelian constraints to eliminate sibling groups that are infeasible and to form potential sibling groups that conform to these constraints. Various methods then use different objectives to choose from among these the groups to form the solution. Almudevar and Field [2] were the first to introduce a combinatorial approach. They formulated the Mendelian properties in form of graphs and constructed all maximal feasible sibling groups. They then performed an exhaustive search to select the minimal number of these groups using maximum likelihood of the reconstruction as the guide. Their approach yielded reasonably good results but was computationally very expensive, often resulting in the system running out of memory in our experiments (see Section 5.). Almudevar presented a “hybrid” approach in [1] that used simulated annealing based on MCMC methods to find a locally optimal solution. The method generates putative triplets of parents and children, and then uses simulated annealing to explore the space of different possible pedigrees. The exploration is similar to the approach taken by COLONY described above and uses the likelihood of the sibling group configuration as a guide. Such a heuristic approach is not


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guaranteed to find a globally minimum number of sets. This new version of the method allows for the use of other information in the reconstruction, such as multiple generations of siblings, parental genotypes and sex where available. All the information is translated into constraints that guide the formation of the potential feasible solution. 4.2.1. 2-Allele Minimum Set Cover The 2-Allele Minimum Set cover approach [5, 6, 10, 41], like Almudevar and Field’s, uses Mendelian constraints, specifically the 2-allele property, to form all maximal feasible sibling groups. The goal, then, is to find the smallest number of these that contain all individuals. Unlike Almudevar and Field, this approach finds the true global, rather than local, minimum. We describe the technical details of the approach and the computational complexity of this formulation of the problem below. Recall that we are given a population U of n diploid individuals sampled at l loci U = {X1, ...Xn}, where Xi = (hai1, bi1i, ..., hail, bili) and aij and bij are the two alleles of the individual i at locus j. The goal of the Minimum 2-Allele Set Cover problem is to find the smallest S number of subsets S1 , ..., Sm such that each Si ⊆ U and satisfies the 2-allele constraint and Si = U . We shall denote the Minimum 2-Allele Set Cover on n individuals with l sampled loci as 2-ALLELE n,` . Of all the sibling reconstruction problem formulations, this is the only one for which its computational complexity is known. Computational Complexity The Minimum 2-Allele Set Cover problem is a special case of the M INIMUM S ET C OVER problem, a classical NP-complete problem [28]. M INIMUM S ET C OVER is defined as follows: given a universe U of elements X1, ..., Xn and a collection of subsets S of U , the goal is to find the minimum collection of subsets C ⊆ S whose union is the entire universe U. Recall, that a (1 + ε)-approximate solution (or simply an (1 + ε)-approximation) of a minimization problem is a solution with an objective value no larger than 1 + ε times the value of the optimum, and an algorithm achieving such a solution is said to have an approximation ratio of at most 1 + ε. To say that a problem is r-inapproximable under a certain complexity-theoretic assumption means that the problem does not have a r-approximation unless that complexity-theoretic assumption is false. M INIMUM S ET C OVER cannot be approximated in polynomial time to within a factor of (1 − ) ln n unless N P ⊆ DT IM E(nloglogn) [16]. Johnson introduced a 1 + ln n approximation in 1974 [27]. In the 2-ALLELE n,` the problem the elements are the sampled individuals and the sets S are the groups of individuals that satisfy the 2-allele property. The main difference between M INIMUM S ET C OVER and 2-ALLELE n,` , or more generally k-ALLELE n,` problem for k ∈ {2, 4}, is that the latter add the 2-allele or the 4-allele restriction on

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the structure of the subsets S. We show that this restriction does not make the problem computationally easier and k-ALLELE n,` remains NP-complete. A natural parameter of interest in this class of problems is the maximum size (number of elements) a in any set in S. We denote the corresponding problem of finding the minimum set cover when the size of sibling sets is at most a as a-k-ALLELEn,` in the subsequent discussions. For example, 2-4-ALLELE n,` and 2-2-ALLELE n,` are the problem instances where each subset contains at most two individuals. Recall, that any pair of individuals necessarily satisfies both the 2-allele and the 4-allele properties. Thus, the collection S for 2-k-ALLELE n,` consists of all possible pairs of individuals and the smallest number of subsets that contain all the individuals are any n/2 disjoint pairs. In general, if a is a constant, then a-k-ALLELE n,` can be posed as a minimum set cover problem with the number of subsets polynomial in n and the maximum set size being a. This problem has a natural (1 + ln a)-approximation using the standard approximation algorithms for the minimum set cover problem [51]. For a general a, the same algorithm guarantees a ac + ln c -approximation for any constant c > 0. Recently, Ashley et al. [4] have been able to obtain several non-trivial computational complexity results for these problems which we restate here. For the smallest non-trivial value of a = 3, the 3-k-ALLELE n,n3 problem is 1.0065inapproximable unless RP = N P . This was proved by a reduction from the T RIANGLE PACKING problem [20, p. 192]. A 76 + ε -approximation for any ` > 0 and any constant ε > 0 is easily achieved using the results of Hurkens and Schrijver [25]. For the second smallest value of a = 4 and l = 2, 4-k-ALLELE n,2 is 1.00014inapproximable unless RP 6= N P , proved by a reduction from the M AX -C UT problem on cubic graphs via an intermediate novel mapping of a geometric nature. The 32 + approximation can be achieved for a = 3 by using the result of Berman and Krysta [7]. The n -inapproximability result under the assumption of ZPP 6=NP was proved for all sufficiently large values of a, that is a = nδ , where is any constant strictly less than δ. This result was obtained by reducing a suitable hard instance of the graph coloring problem. In all the reductions above additional loci play an important role of adding complexity to the problem to ensure the inapproximability result. Thus, interestingly and somewhat counterintuitively, while sampling more loci provides more information and typically improves the accuracy of most sibling reconstruction methods, it also adds computational complexity and increases the computational time needed to construct the solution, even beyond the scope of practical computability. The Algorithm In [6] we have presented a fully combinatorial solution for the siblings reconstruction problem based on the 2-Allele Minimum Cover formulation. We briefly describe the 2-A LLELE C OVER algorithm here. The algorithm works by first generating all maximal sibling groups that obey the 2-allele property and then finds the optimal minimum number of sibling groups necessary to explain the data. The algorithm maintains a complete enumeration of canonical possible sibling groups, called the possibilities table, shown in Table 2. Each potential sibling group is mapped to a set of possible canonical representations. Genetic feasibility of membership of each new individual in a sibling group is checked using this


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mapping. The intricate process of generating the maximal feasible 2-allele sets is described in detail in [6]. The 2-allele property reduces the possible combinations of alleles at a locus in a group of siblings down to a few canonical options, assuming that the alleles in the group are renumbered 1 through 4. Table 2 lists all different types of sibling groups possible with the 2-allele property using such a numbering. We do this by listing all possible pairs of parents whose alleles are among 1,2,3, and 4 and all the genetically different offspring they can produce. However, in any sibling group with a given set of parents only a subset of the offspring possibilities from the table may be present. Table 2. Canonical possible combinations of parent alleles and all resulting offspring allele combinations Parents

8*(1, 2) and (3, 4)

7*(1, 2) and (1, 3)

4*(1, 2) and (1, 2)

Offspring allele a allele b 1 1 2 2 3 4 3 4

3 4 3 4 1 1 2 2

1 1 2 2 3 1 3

1 3 1 3 1 2 2

1 1 2 2

1 2 1 2

Parents

Offspring allele a allele b

(1, 1) and (1, 1)

1

1

3*(1, 1) and (1, 2)

1 1 2

1 2 1

4*(1, 1) and (2, 3)

1 1 2 3

2 3 1 1

2*(1, 1) and (2, 2)

1 2

2 1

The maximal feasible 2-allele sets are generated using the canonical possibilities in Table 2 in a way which provably produces all maximal such sets and does it in provably fewest number of queries per individual. After that, the minimum set cover is constructed

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as the solution to the sibling reconstruction problem. Note, that since 2-allele minimum cover and Minimum Set Cover are both NP-complete problems, the solution time is not guaranteed to be polynomial. We use the commercial mixed integer linear program solver CPLEX1 to solve the problem to optimality. On datasets with several hundreds individuals it may take several hours to days to obtain a solution. Subsequently, Chaovalitwongse et al. [10] have presented a full mathematical optimization formulation for the Minimum 2-allele Cover problem. We shall briefly describe the 2- ALLELE OPTIMIZATION MODEL (2AOM) here. The formulation directly models the objective of finding the minimum number of 2-allele sets that contain all individuals, rather than using the intermediate steps of generating all maximal 2-allele sets and finding the minimum set cover of those.

Individual 1 2 3 4 5 .. .

Locus 1 alleles ha, bi

Locus 2 alleles ha, bi

44, 44 12, 56 28, 44 13, 13 28, 51

55, 27 18, 39 55, 18 39, 27 18, 39

...

Figure 2. A multidimensional matrix representation of a dataset of microsatellite samples. Recall, that U is the set of individuals, S is a set of sibling groups, and C ∈ S is the reconstructed set of sibling groups which is returned as the solution. Let K be the set of possible observed alleles and L be the set of sampled loci. As the input, we are given |U | = n individuals sampled at |L| = l loci. We represent the data as a multidimensional 0-1 matrix M shown in Figure 2. The matrix entry M (i, k, l) = 1 if the individual i ∈ U has the allele k ∈ K in locus l ∈ L. From the input matrix, alik is defined as an indicator variable and equals to 1 if the first allele at locus l of individual i is k. Similarly, blik is an indicator variable for the second l = max{al + bl } is an indicator of whether k allele at locus l of individual i is k. fik ik ik l . Finally hlik = alik · blik is an appears at locus l of individual i, that is, M (i, k, l) = fik indicator of whether the individual i is homozygous (allele k appears twice) at locus l. The following decision variables are then used: • zs ∈ {0, 1}: indicates whether any individual is selected to be a member of sibling group s; • xis ∈ {0, 1}: indicates whether the individual i is selected to be a member of sibling group s; 1

CPLEX is a registered trademark of ILOG


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l • ysk ∈ {0, 1}: indicates whether any member of sibling group s has the allele k at locus l; l ∈ {0, 1}: indicates whether there is at least one homozygous individual in sibling • wsk group s with the allele k appearing twice at locus l; l 0 • vskk 0 ∈ {0, 1}: indicates whether the allele k appears with allele k in sibling group s at locus l.

With these variable, the mathematical representation of the objective function and the constraints of the 2AOM problem are as follows. Objective function: The overall objective function is to minimize the total number of sibling groups: X zs min ∀s∈S

The minimization objective is subject to three types of constraints stated below. Cover and logical constraints: Ensure that every individual is assigned to at least one sibling group: X xis ≥ 1, ∀i ∈ U ∀s∈S

The binary sibling group variable s is activated for the assignment of any individual i to the sibling group s: xis ≤ zs ,

∀i ∈ U, ∀s ∈ S

l with the assign2-allele constraints: Activate the binary indicator variable for alleles ysk ment of any individual i to the sibling set s. Here C1 is a large constant which can be defined as C1 = 2|U | + 1: X l l fik xis ≤ C1 ysk , ∀s ∈ S, ∀k ∈ K, ∀l ∈ L ∀i∈U

Activate the binary indicator variables for homozygous individuals with allele k appearing twice at locus l in sibling group s. Here C2 is a large constant which can be defined as C2 = |U | + 1: X l hlik xis ≤ C2 wsk , ∀s ∈ S, ∀k ∈ K, ∀l ∈ L ∀i∈U l Activate the binary indicator variable for allele pair vskk 0 for any assignment to the 0 sibling group s of the individual i with alleles hk, k i at locus l. Here C3 is a large constant and can be defined as C3 = |U | + 1: X l l l fik hik xis ≤ C3 vskk ∀s ∈ S, ∀k 6= k0 ∈ K, ∀l ∈ L 0, ∀i∈U

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Mary V. Ashley, Tanya Y. Berger-Wolf, Isabel C. Caballero et al. Ensures that the number of distinct alleles plus the number of homozygous alleles does not exceed 4, conforming to Theorem 1: X

l l ysk + wsk ≤ 4,

∀s ∈ S, ∀l ∈ L

∀k∈K

Every allele in the set should not appear with more than two other alleles (excluding itself), also conforming to Theorem 1: X

l vskk 0 ≤ 2,

∀s ∈ S, ∀k ∈ K, ∀l ∈ L

∀k 0 ∈K\k

Binary and nonnegativity constraints: l l , wsk ∈ {0, 1}, zs , xis, ysk

∀i ∈ U, ∀s ∈ S, ∀k ∈ K, ∀l ∈ L

The total number of discrete variables in the 2AOM is O(|U ||K||S|) and so is the total number of constraints. Thus, the 2AOM formulation of the 2-allele minimum cover problem is a very large-scale mixed integer program problem and may not be easy to solve in large instances. The main justification for a formal mathematical model of the problem is that it allows for the theoretical investigation of its computational properties and guides approximation approaches.

4.3. Consensus-based Approach Among all the methods for sibling reconstruction, only COLONY [53] is designed to tolerate genotyping errors or mutation. Yet, both errors and mutations cannot be avoided in practice and identifying these errors without any prior kinship information is a challenging task. A new approach for reconstructing sibling relationships from microsatellite data designed explicitly to tolerate genotyping errors and mutations in data based on the idea of a consensus of several partial solutions was proposed by Sheikh et al. in [40, 42] Consider an individual Xi which has some genotyping error(s). Any error that is affecting sibling reconstruction must be preventing Xi ’s sibling relationship with at least one other individual Xj , who in reality is its sibling. It is unlikely that an error would cause two unrelated individuals to be paired up as siblings, unless all error-free loci do not contain enough information. Thus, we can discard one locus at a time, assuming it to be erroneous, and obtain a sibling reconstruction solution based on the remaining loci. If all such solutions put the individuals Xi and Xj in the same sibling group (i.e., there is a consensus among those solutions), we consider them to be siblings. The core of the consensus-based error-tolerant approach is concerned with pairs of individuals that do not consistently end up in the same sibling group during this process, that is, there is no consensus about their sibling relationship. Definition 2. A consensus method for the sibling reconstruction problem is a computable function f that takes k solutions S = {S1, ..., Sk} as input and computes one final solution.


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The strict consensus places two individuals into a sibling groups only if they are together in all input solutions. While it always results in a consistent solution, it also produces many singleton sibling groups. In [40, 42] a distance based consensus for sibling reconstruction was introduced. Starting with a strict consensus of the input solutions, distance based consensus iteratively merges two sets until the quality of the solution cannot be improved. The computational complexity and the algorithms change depending on the cost of the merging operations and the function that defines the quality of the solution. The approach taken in [40, 42] uses the number of the sibling groups in the resulting solution as the measure of the quality of the solution, that is, it seeks to minimize the number of groups. The cost of the merging operation is based on the size of the groups being merged and errors that need to be corrected for the 2-allele property to be preserved in the combined group. Any method or a mix of methods for sibling reconstruction can be used as the base to produce the input solution for the consensus method. The running time of the consensus method depends on the running times of the base methods. In our experiments (see Section 5.) consensus based on 2-allele minimum cover algorithm typically achieved over 95% accuracy.

5.

Experimental Validation

To assess and compare the accuracy of various sibling reconstruction methods we used datasets with known genetics and genealogy. Since most sibling reconstruction methods do not tolerate errors in data, we first used error free datasets. However, biological datasets containing no errors are rare. Thus, in addition to biological datasets, we created simulated sets using a large number of parameters over a wide range of values. We compare the performance of five sibling reconstruction methods, spanning the variety of computational techniques: Almudevar and Field [2], Family Finder [8], KINGROUP [29], COLONY [53], and 2-allele Minimum Cover [6]. In addition, we used the same datasets with introduced errors to assess the performance of COLONY and the distance-based consensus of the 2-allele Minimum Cover when errors are present. We measure the error by comparing the known sibling sets with those generated by various sibling reconstruction methods, and calculating the minimum partition distance [21]. The error is the percentage of individuals that would need to be removed to make the reconstructed sibling sets equal to the true sibling sets. Note, we are computing the error in terms of individuals, not in terms of the number of sibling groups reconstructed incorrectly. Thus, the accuracy is the percent of individuals correctly assigned to sibling groups. The experiments were run on a combination of a cluster of 64 mixed AMD and Intel Xeon nodes of 2.8 GHz and 3.0GHz processors and a single Intel Xeon Quad Core 3.2 GHz Intel processor with 24 GB RAM memory.

5.1.

Biological Datasets

For validation of our methods, both the 2-allele and the consensus extension, we used biological datasets of offspring that resulted from one generation of controlled crosses, thus

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the identity of the parents and their microsatellite genotypes were known. Radishes. The wild radish Raphanus raphanistrum dataset is a subsample of [11]. It consists of samples from 64 radishes from two families with 11 sampled loci. Close to 53% of allele entries are missing. Salmon. The Atlantic salmon Salmo salar dataset comes from the genetic improvement program of the Atlantic Salmon Federation [23]. We use a truncated sample of 351 individuals from 6 families and 4 loci. There are no missing alleles at any locus. This dataset is a subset of one of the samples of genotyped individuals used by [2] to illustrate their technique. Shrimp. The tiger shrimp Penaeus monodon dataset [26] consists of 59 individuals from 13 families with 7 loci. There are 16 missing allele entries (3.87% of all allele entries). Flies. Scaptodrosophila hibisci dataset [56] consists of 190 same generation individuals (flies) from 6 families sampled at various number of loci with up to 8 alleles per locus. All individuals shared at least 2 sampled loci which were chosen for our study. 25% of allele entries were missing. Table 3 summarizes the results of the four algorithms on the biological datasets. Table 3. Accuracy (percent) of the 2-allele algorithm and the three reference algorithms on biological datasets. Here l is the number of loci in a dataset and “Inds” column gives the number of individuals in the dataset. The three reference algorithms are [2] (A&F), Family Finder by [8] (B&M), and the KINGROUP by [29] (KG). Dataset Shrimp Salmon Radishes Flies

l 7 4 5 2

Inds 59 351 64 190

Ours 77.97 98.30 75.90 100.00

A&F 67.80 Out of memory Out of memory

31.05

B&M 77.97 99.71 53.30 27.89

KG 77.97 96.02 29.95 54.73

Almudevar and Field’s algorithm ran out of 4GB memory on the salmon and radish datasets.

5.2.

Synthetic Datasets

To test and compare sibling reconstruction approaches, we also use random simulations to produce synthetic datasets. We first create random diploid parents and then generate complete genetic data for offspring varying the number of males, females, alleles, loci, number of families and number of offspring per family. We then use the 2-allele algorithm described above to reconstruct the sibling groups. We compare our results to the actual known sibling groups in the data to assess accuracy. We measure the error rates of algorithm using the Gusfield Partition Distance [21]. In addition, we compare the accuracy of our 2allele algorithm to the two reference sibling reconstruction methods, [8] and [29], described


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above. We repeat the entire process for each fixed combination of parameter values 1000 times. We omit the comparison of the results to the algorithm of [2] since the current version of the provided software requires user interaction and therefore it is infeasible to use it in the automated simulation pipeline of 1000 iterations of over a hundred combinations of parameter values. First, we generate the parent generation of M males and F females with parents with l loci and a specified number of alleles per locus a. We create populations with uniform as well as non-uniform allele distributions. After the parents are created, their offsprings are generated by selecting f pairs of parents. A male and a female are chosen independently, uniformly at random from the parent population. For these parents a specified number of offsprings o is generated. Here, too, we create populations with a uniform as well as a skewed family size distribution. Each offspring randomly receives one allele each from its mother and father at each locus. This is a rather simplistic approach, however, it’s consistent with the genetics of known parents and provides a baseline for the accuracy of the algorithm since biological data are generally not random and uniform. The parameter ranges for the study are as follows: • The number of adult females F and the number of adult males M were equal and set to 5, 10 or 15. • The number of loci sampled l = 2, 4, 6 • The number of alleles per locus (for the uniform allele frequency distribution) a = 5, 10, 15. • Non-uniform allele frequency distribution (for 4 alleles): 12 - 4 - 1 - 1, as in [1]. • The number of families in the population f = 2, 5, 10. • The number of offspring per mating pair (for the uniform family size distribution) o = 2, 5, 10. • Non-uniform family size distribution (for 5 families): 25 - 10 - 10 - 4 - 1, as in [1] All datasets were generated on the 64-node cluster running RedHat Linux 9.0. The 2allele algorithm is used on this generated population to find the smallest number of 2-allele sets necessary to explain this offspring population. We use the commercial MIP solver CPLEX 9.0 for Windows XP on a single processor machine to solve the minimum set cover problem to optimality. The reference algorithms were run on a single processor machine running Windows XP 2 . We measure the reconstruction accuracy of various methods as the function of the number of alleles per each locus, family size (number of offspring), number of families (and polygamy), and the variation in allele frequency and family size distributions. Figure 3 shows representative results for the accuracy of our 2-allele algorithm, the Greedy Consensus algorithm and the two reference algorithms on uniform allele frequency and family sizes distributions. 2

The difference in platforms and operating systems is dictated by the available software licenses and provided binary code

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Figure 3. Accuracy of the sibling group reconstruction methods on randomly generated data. The y-axis shows the accuracy of reconstruction as a function of various simulation parameters. The accuracy of our 2-allele algorithm and Greedy Consensus approach is shown, as well as that of the two reference algorithms: [8] and [53] (COLONY). The title shows the value of the fixed parameters: the number of adult males/females, number of families, the number of offspring per family, the number of loci, and the number of alleles per locus.


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The results of COLONY, our 2-allele Minimum Cover and the consensus based approach on simulated datasets with introduced errors are shown in Figure 4.

Figure 4. Results on simulated datasets with errors. Only 50 iterations were used for the COLONY algorithm due to its computational inefficiency and time constraints.

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Overall, we have compared our 2-allele algorithm as well as the robust consensus approach to the best existing sibling reconstruction methods on biological and synthetic data over a wide range of parameters. We have identified the strengths and weaknesses of various approaches to sibling reconstruction and pinpointed the data parameters under which those are manifested.

6.

Conclusion

Full utilization of new genetic tools provided by advances in DNA and genome analysis will only be realized if computational approaches to exploit the genetic information keep pace. Pedigree reconstruction in wild populations is an emerging field, made possible by the development of markers, particularly DNA microsatellites, that can be used to genotype any organism, including free-living populations sampled in the field. Rules of Mendelian inheritance and principles of population genetics can be applied to microsatellite genotyping data to infer familial relationships such as parentage and sibship, and thus reconstruct wild pedigrees. Such pedigrees, in turn, can be used to learn about a species’ evolutionary potential, their mating systems and reproductive patterns, dispersal and inbreeding (reviewed in [35]). The findings of pedigree reconstruction have been especially notable in the area of paternity assignment, where dozens of examples of previously undocumented multiple paternity have now been reported (e.g. [15, 17, 44, 52]). Our focus has been on a more challenging computational problem than paternity (or parentage) assignment, that of sibling reconstruction. Sibling reconstruction is needed when wild samples consist primarily of offspring cohorts, in cases where it is logistically difficult or impossible to sample the parental generation. We first develop a formal definition of the sibling reconstruction problem and formalize the genetics of sibship. Sibling reconstruction methods can be divided into three categories depending on their approach, methods that rely only statistical estimates of relatedness [29, 32, 43, 49, 50, 53], those that combine statistical and combinatorial approaches [8], and those that use only Mendelian constraints and combinatorial techniques [1, 2, 5, 6, 10, 41]. Statistical methods rely on estimates of pairwise relatedness and typically reconstruct maximum likelihood sibling groups. The performance of statistical methods depends upon an accurate estimate of underlying allele frequencies within the sampled populations , rather than the observed sample. Furthermore, they are often computationally demanding. Combinatorial approaches offer the advantage that sibling groupings are based only on Mendelian constraints without needing information on population allele frequencies. A new method we describe here, the 2-allele minimum set cover, generates all sibling groups that obey the 2-allele property and then finds the optimal minimum number of sibling groups needed to explain the data. To accommodate genotyping errors and mutations, we also describe a new consensus-based approach applied here to the 2-allele minimum cover algorithm. We tested the performance of various sibling reconstruction methods using both real biological data and synthetic data sets. For real data, the actual pedigree and sibgroups were known from controlled crosses, and we tested the accuracy of five different methods in recovering the known sibgroups. We found that our 2-allele distance-based consensus method performed very well, recovering over 95% of the known sibgroups. We also produced synthetic datasets which simulated a variety of mating systems, family structures,


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and genetic data. Again, our method produced very good results. Of the other methods tested, COLONY [53], a statistical approach, also performed very well when the assumptions of monogamy held and there were a sufficient number of loci and accurate estimates of allele frequencies. There is no one method that is guaranteed to provide the correct answer, since samples of different populations suffer from different sampling biases and all methods make assumptions that may not hold for a specific dataset. We favor the 2-allele method for this very reason: it makes the fewest assumptions. Also, the 2-allele algorithm overall performs well over a wide range of data parameters, thus making it a good general method, especially when few loci are sampled or the allelic variation is low. Our current recommendation is to use the proposed consensus approach on the 2-allele method in combination with other available methods, keeping in mind aspects of the study organism’s biology or sampling biases, as a way to achieve confidence in sibling reconstruction. Another consideration is presentation and implementation of the methods. Most molecular ecologists do not have a background in computer science, and will opt for a method that is easily accessible, user-friendly, and produces results that can be readily interpreted, regardless of the underlying mathematical or computational elegance. COLONY is available as a Windows executable. However, it is computationally intensive and as such, is impractical to run on a personal computer. Our method does not require installation on a user’s computer but provides a web-based service. It only requires an Internet connection to send the dataset for analysis using a web interface 3 . Our software accepts any file formatting using Excel software which is widely used by biologists. Sibling reconstruction is among the first kinship reconstruction problems that have generated a variety of computational methods. However, more complicated pedigrees and genealogical relationships await computational solutions. Computationally, kinship reconstruction in wild populations is not only a rich source of interesting problems, but one that poses a particular challenge of testing the accuracy of devised solutions. Real biological data must be used to conduct comparisons of feasibility and accuracy of different methods. More benchmark data is needed to ground truth algorithms and software. Finally, novel approaches must be developed to assess accuracy of the resulting solutions and confidence in the answers provided.

Acknowledgments This research is supported by the following grants: NSF IIS-0612044 and IIS-0611998 (Berger-Wolf, Ashley, Chaovalitwongse, DasGupta), Fulbright Scholarship (Sheikh), NSF CCF-0546574 (Chaovalitwongse). We are grateful to the people who have shared their data with us: Jeff Connor, Atlantic Salmon Federation, Dean Jerry, and Stuart Barker. We would also like to thank Anthony Almudevar, Bernie May, and Dmitry Konovalov for sharing their software. 3

See http://compbio.cs.uic.edu for more details

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Chapter 10

RECENT ISSUES AND COMPUTATIONAL APPROACHES FOR DEVELOPING PROGNOSTIC GENE SIGNATURES FROM GENE EXPRESSION DATA Seon-Young Kim1,∗ and Hyun Ju Kim2,† 1

Functional Genomics Research Center, KRIBB, 111 Gwahangno, Yuseong-gu, Daejeon, 305-806, Korea 2 Department of Food and Nutrition, Daejeon Health Sciences College, 77-3 Gayang 2-dong, Dong-gu, Daejeon, 300-711 Korea

Abstract Microarray gene expression profiling, which monitors the expression of tens of thousands of genes simultaneously, is a promising tool for developing prognostic markers for cancer patients. Many researchers have applied microarray gene expression profiling in order to develop better prognostic markers, and have demonstrated promising results in many types of cancer. Unfortunately, there are concerns regarding the premature clinical use of newlydeveloped prognostic gene signatures, as problems associated with their application remain unresolved, diminishing the reliability of their intended results. This review first discusses these presently unsolved problems in the development of prognostic gene signatures. Recent computational approaches to circumventing these problems are then presented, and therein we discuss these approaches in the categorized framework of mechanism-derived bottom-up approaches, meta-analytic approaches, integrative approaches that combine genomics and clinical data, and sub-type-specific analysis approaches. We believe that recent bioinformatics approaches, which integrate rapidly accumulating genomics, clinical, and other forms of data, will help overcome current problems, and will help realize the successful application of prognostic gene signatures in personalized medicine.

∗ Correspondence: Seon-Young Kim ([email protected]); Tel.: 82-42-879-8116; Fax: 82-42-879-8119 † E-mail:[email protected]

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1. Introduction The accurate prognosis of cancer patients is important for avoiding over- or under-treatment, and is a means to improve a patient’s survivability and quality of life. For example, many early-stage, node-negative breast cancer patients currently receive hormonal therapy and/or adjuvant chemotherapy to prevent distant metastases, while it is estimated that approximately 70 to 80% of these patients would have survived without these treatments [1]. The situation is similar with other types of cancer. For example, while adjuvant chemotherapy is clearly beneficial for stage III colon cancer patients, its benefit for stage II colon cancer patients is not clearly defined [2]. Improved prognostic markers that can discern high-risk from low-risk patients will save 75% of colon cancer patients, who are ordinarily treated by surgery only, from the unnecessary suffering that results from chemotherapy [2, 3]. The recent developments of several high-throughput technologies, including microarray gene expression profiling, proteomics, metabolomics, and genome-wide genotyping, have provided researchers with an unprecedented opportunity to develop effective biomarkers for cancer diagnosis, prognosis, and treatment. Among these technologies, microarray gene expression profiling has been the most ubiquitously used, as it readily provides information concerning the expression of tens of thousands of genes. The use of gene expression profiling for prognostic marker development has steadily increased in recent years. For example, when we queried the number of articles in PubMed following a search with the keywords ‘microarray cancer prognosis,’ the returned results increased from five in 1999 to 365 in 2007 (Figure 1). Indeed, many researchers have applied gene expression profiling to develop better prognostic markers, and have demonstrated that gene expression signatures can more effectively predict patient outcomes compared to conventional clinical criteria for many types of cancer, including bladder [4, 5], breast [1, 3, 6], colon [3, 7, 8], gliomas [9, 10], head and neck [5, 11], kidney [12, 13], leukemia [14, 15], liver [16], lung [17, 18], lymphoma [19, 20], prostate [21], and stomach [22] cancers. There are already several commercial products specifically targeted to breast cancer, including MammaPrint from Agendia (http://www.agendia.com) or Oncotype DX from Genomic Health (http://www. genomichealth.com), and are used to select breast cancer patients for adjuvant chemotherapy. Additionally, several large-scale clinical trials are presently being investigated to prove the clinical utility of gene expression-based prognostic tests [23-27]. Unfortunately, there are also some concerns regarding the usefulness of gene expressionbased prognostic markers, as several issues remain unresolved [28-30], and many promising results that have been presented in the literature suffer from one or more flaws [31-33]. These unresolved issues include the small overlap between independently-developed gene signatures [30], the instability of many published gene signatures [28], and the poor performance of a gene signature when applied to other data sets [34]. In this review, we first discuss the current challenges to the development of prognostic gene signatures. We then describe recent computational approaches to overcome these problems, with the intent to develop improved prognostic gene signatures.

Recent Issues and Computational Approaches for Developing PGS…

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Year Figure 1. Exponential growth of the number of publications studying the development of prognostic gene signatures for predicting cancer patient outcomes. We searched PubMed using the keywords ‘microarray cancer prognosis’ from 1999 to 2007 and summarized the number of published articles in each year.

2. Current issues in the development of prognostic gene signatures 2. 1. Small overlap and instability of gene expression signatures The first challenge to prognostic gene signature development is that there is only a small overlap between independently-identified prognostic gene signatures, which can affect their reliability when used. This problem can be illustrated by two examples, consisting of three breast cancer prognostic signatures and three colon cancer prognostic signatures (Figure 2). In the breast cancer example, the pair-wise overlap between three well-known prognostic gene signatures is only three genes between the Amsterdam-70 [1] and Veridix-76 [3] signatures, one gene between the Amsterdam-70 and Sweden-64 signatures [35], and no genes between the Veridix-76 and Sweden-64 signatures (Figure 2A). The situation is similar in the colon cancer example. When three prognostic gene signatures were compared as a basis for discerning good from poor prognostic patients, there was only one gene overlap between the Wang-23 [3]and Eschlich-121 [7] gene signatures, and no gene overlap between the Barrier30 [8] and either the Wang-23 or Eschlich-121 gene signatures (Figure 2B). In fact, since many gene expression studies have observed such small overlaps between gene signatures, it has become a subject of great interest.


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Figure 2. The small overlap between independently developed prognostic gene signatures. Two examples derived from breast and colon cancer studies are shown. We retrieved the reported prognostic gene signatures from each study and counted the number of overlapped genes between different gene signatures. A. Breast cancer; Amsterdam-70 [1, 6], Veridix-76 [3], and Sweden-64 [35]. B. Colon cancer; Wang-23 [3], Eschlich-121 [7], and Barrier-30 [8].

The small overlap between gene signatures, as observed in several studies from the literature, was originally ascribed to many factors, including differences in the microarray platforms used, patient cohorts, and statistical analyses; however, Ein-Dor et al.’s work demonstrated that even with a single data set, wherein many of the above-mentioned variables were controlled, it is possible to create many non-overlapping prognostic gene signatures [30]. Similarly, when Michiels et al. re-analyzed seven published microarray studies using a multiple random sampling strategy, they found that many of the originally reported prognostic gene signatures were not identified, thus casting doubt on the stability of the prognostic gene signatures [28]. Moreover, they found that five out of the seven re-analyzed studies did not classify patients better than random chance, and concluded that the prognostic value of many overly optimistic studies need to be cautiously evaluated. Ein-Dor et al. further studied this instability problem, developed a mathematical method to better understand the relationship between gene list overlap and sample size, and concluded that thousands of samples are needed to generate a gene list with more than a half overlap [34]. Clearly, one of the causes for the small overlap and instability of prognostic gene signatures is the small sample size [34, 36]; however, researchers are now realizing that the complexity and scale of genomic data is a more fundamental cause for the small overlap and instability problems [67, 68]. Current gene expression data contain information consisting of over tens of thousands of genes, whose respective expressions are correlated and co-regulated in a complex way. Due to the complexity and correlation structure of the gene expression data, many equally prognostic, but related gene signatures, can be identified from the same data [62, 67]. For example, although Ein-Dor et al. were able to identify at least eight equally prognostic gene signatures from a single data set, the eight gene signatures were not completely independent of one another, but represented similar biological processes when analyzed at the gene set level [62, 69, 70]. Fan et al. applied five gene expression signatures


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on a single data set to compare the predictions derived from distinct gene signatures, and found that four of the five gene signatures agreed well with the predicted outcome, despite a poor overlap between them [70]. Thus, in terms of the predicted outcome, which should be the final criterion for measuring classifier performance, recent gene expression-based prognostic classifiers agree well with one another [68, 70]. In this regard, thousands of samples may not be needed for developing prognostic gene signatures, so long as a reliable predicted outcome, rather than a high-degree of overlap between gene lists, is the primary criterion for a marker’s performance [68].

2.2. Poor inter-study performance The second challenge to prognostic gene signature development is poor inter-study performance, wherein the performance of a developed and validated prognostic gene signature in one data set is not reproduced in another data set [34]. The causes of poor interstudy performance may include differences in microarray platforms, patient cohorts, and data analysis. For example, many important prognostic genes selected in one microarray platform cannot be evaluated in other data sets produced using another microarray platform, simply because those genes are not represented in the second platform. As a result of a reduced number of prognostic genes, the overall performance of a gene signature is likely to be reduced. Poor inter-study performance is also closely related to the problem of small overlap and the instability of prognostic gene signatures. According to Michiels et al., the performance of many promising gene signatures was not reproduced even in their own data sets when seven data sets were reanalyzed using a multiple random sample method [28]. The predicted outcome performance was observed to strongly depend on the selected patients in the training sets [28]. Another important cause of poor inter-study performance is the preponderance of flaws in the statistical analyses of many gene expression studies, which is the subject of the next section.

2. 3. Flaws in statistical analyses in many published microarray studies The third challenge to prognostic gene signature development involves the preponderance of flaws in many inadequately reported microarray gene expression studies. Microarray gene expression studies deal with data consisting of features that number in the tens of thousands, while samples typically number in the tens to hundreds, creating a situation that can be simultaneously described as both a curse of dimensionality and a curse of dataset sparsity [36]. This peculiar nature of microarray data is a significant challenge to statistical analyses, and is also a source of the flaws inherent to many reported studies [31-33, 36-39]. Dupuy et al. reviewed many published microarray studies investigating cancer patient outcomes, found various flaws, and summarized them in three categories, corresponding to either an inadequate control of false-discovery rate in outcome-related gene findings, a spurious claim of outcome-related class discovery using genes selected for their correlation with outcome, or a biased estimation of the prediction accuracy of outcomes in supervised class prediction [33].

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Among these, we discuss in greater detail a few flaws commonly found in supervised class prediction. The first flaw is the reporting of overly optimistic results coming from the inadequate validation of identified prognostic gene signatures. Due to samples being limited in most gene expression studies, sample training-testing splits or n-fold cross-validations are commonly used. Herein, the critical point to mention is that the entire model building process should be repeated in each cross-validation step [33, 38]. A partial validation is likely to produce overly optimistic results [33, 38]. For example, van’t Veer et al.’s work is criticized for including the same patients in the validation step, leading to much lower error rates [1, 6, 38]. Reporting an odds ratio, a hazard ratio, or a p-value from a log-rank test to assess the performance of a prognostic classifier is another flaw found in many studies [33, 40, 41]. The odds or hazard ratio is simply a measure of association, not of prediction accuracy [33, 40]. The performance of a prognostic marker should be assessed by how it successfully classifies patients into different prognostic groups; therefore, the prediction error rate, specificity, and sensitivity should be the ultimate results for reporting [40]. In addition, the value of new markers should be judged by their ability to improve an already optimized predictive model [42, 43].

3. Current computational approaches for developing prognostic gene signatures We now describe recent computational approaches to developing prognostic gene signatures. Many researchers have suggested interesting ideas for the integration of genomics, clinical, and many other forms of data to develop more efficient prognostic gene signatures, and to enhance our understanding of the carcinogenic processes underlying different clinical outcomes. Herein, we have grouped these ideas into the categories of bottom-up approaches, meta-analyses, integrative analyses, and subtype-specific analyses.

3. 1. Bottom-up approach Most gene expression studies with the purpose of developing prognostic gene signatures begin with complete gene expression data, and then derive a prognostic model by selecting a number of genes (usually in the tens) by the degree of association between individual genes and clinical parameters. This approach is referred to as top-down, as it is not based on any mechanistic assumptions of the prognostic model. Recently, an opposite approach, referred to as the bottom-up approach, has been successfully applied to the development of prognostic gene signatures for several types of cancer [44, 45]. In the bottom-up approach, the first step is the derivation of mechanism-based gene model(s) based on experimental data or a priori knowledge of pathways or gene ontology information. The prognostic value of the gene model is then validated in clinical sample gene expression data. In addition to the potential of developing effective prognostic gene signatures, the bottom-up approach has the added advantage of providing specific testable ideas of mechanisms behind the disease [45]. In the bottom-up approach, mechanism-based gene models are derived from diverse sources (Figure 3). In vitro-derived cellular processes, comparative genomics approaches using transgenic or


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knockout mouse models, and a priori knowledge, such as pathways and gene ontology information, are examples of data sources used in gene model construction. Prognostic gene signatures

Evaluate the signature(s) with gene expression data of clinical samples

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In vivo animal model

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Figure 3. Bottom-up approaches for developing prognostic gene signatures. In vitro cellular model, comparative genomics approach using in vivo animal models, and the gene sets approach using predefined gene sets are three examples of mechanism-derived bottom-up approaches for gene expression signature identification.

3.1.1. In vitro-derived prognostic models In vitro-derived prognostic models begin from the identification of differentially expressed genes in specific cellular processes. For example, Chang et al. identified a common serum response signature by selecting differentially expressed genes in fibroblasts by serum treatment, and defined a core serum response signature by removing a set of proliferationrelated genes [46]. They then observed that the defined core serum-response signature was consistently expressed in diverse human cancers, including breast, lung, gastric, prostate, and hepatocellular carcinomas, and was prognostic of metastasis and patient survival in those cancers [45, 46]. Bild et al. identified gene expression patterns of several oncogenic pathways by infecting human mammary epithelial cells with adenovirus expressing either c-Myc, activated H-Ras, c-Src, E2F3 or activated β-catenin [47]. They then demonstrated that tumors can be classified into prognostically different groups by the patterns of pathway deregulation. Moreover, they demonstrated that the patterns of pathway deregulation in breast cancer cell lines could predict the sensitivity of the cells to therapeutic drugs that target the pathways, thus paving the way for individualized treatments [48]. Oh et al. treated the ER+ MCF-7 breast cancer cell line with 17β-estradiol to identify estrogen-related genes, observed their natural pattern of expression in primary tumors in order to divide primary tumors into two

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groups, identified a gene signature by supervised analysis of the two groups of tumors, and finally validated their outcome predictor in three independent data sets [49].

3.1.2. Comparative genomics approach The comparative genomics approach using in vivo transgenic or knockout mouse models has also been useful for understanding tumor progression processes and developing prognostic gene signatures. Lee et al. developed seven different mouse models, including Myc, MycTgfa, Myc-E2f1, E2F1, Acox1-/-, diethylnitrosamine (DENA), and ciprofibrate-induced mouse hepatocellular carcinoma (HCC) models, and compared the patterns of gene expression in the seven mouse models to the patterns from 91 human HCCs [50]. They found that gene expression patterns of Myc, E2f1, and Myc-E2f1 transgenic mice were most similar to human HCC patients with good prognoses, while gene expression patterns of Myc-Tgfa mice and DENA-induced mice were most similar to those of human HCC patients with poor prognoses. Their work demonstrated that appropriate mouse models can be effectively used to understand human cancers [50]. Lee et al. later integrated gene expression data from rat fetal fibroblasts and adult hepatocytes with HCCs from human and mouse models, and demonstrated that a fetal fibroblast-like gene expression pattern was indicative of poor prognoses among human HCC patients [51]. Sweet-Cordero et al. generated mouse lung cancers using the latent mutated Kras2 allele, developed a gene expression signature from the Kra2-mediated mouse lung cancer model, and applied gene set enrichment analysis to compare the gene expression patterns of mouse models and human lung cancers [52]. They then identified a gene expression signature for the KRAS2 mutation in human lung cancer by integrating mouse and human data, and validated their gene expression signature by gene expression analysis of the KRAS2 knockdown human lung cancer cell line [52]. 3.1.3. Gene sets approach The gene sets approach is a recently introduced bottom-up approach that uses predefined gene sets prepared from diverse biological knowledge, including pathways, chromosomal locations, protein domains, protein-protein interactions, and gene ontology information [5355]. As a result of genes in the same pathways or biological processes often being coregulated, observing gene expression changes at the gene set level enables the understanding of moderate, but coordinate changes that are often missed by individual gene analysis [55, 56]. Moreover, concordance between two independent studies is greatly improved by gene set level comparison [53, 57]; thus, a gene set approach is a potential solution to the problem of the small overlap between independent studies pursuing similar biological questions. Pang et al. described a pathway-based classification and regression method using a random forests algorithm in the analysis of gene expression data [58]. They prepared a total of 441 pathways, derived from KEGG and BioCarta pathway databases, and applied random forest classification to analyze a categorical phenotype and random forest regression to analyze continuous clinical outcome. They demonstrated that the pathway-based method may be more useful for identifying and developing good classifiers and predictors compared to single gene-based methods [58]. Chuang et al. described a network-based classification of metastasis by combining the analysis of protein-protein interaction and gene expression data [59]. Their approach circumvents the weakness of microarray gene expression analysis in identifying genes that contribute to metastasis by gene mutation (i.e., TP53, BRACA1, and ERBB2 in breast cancer)


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rather than by changes in gene expression. By focusing on sub-networks of interconnected genes instead of individual genes, their method facilitated the identification of mutated, but not differentially expressed, genes that interconnect many differentially expressed genes. In addition, they showed that sub-network markers are more reproducible between different studies than markers developed without network information, and that sub-network markers achieve a higher accuracy of outcome prediction [59]. Kim et al. described a gene sets approach for identifying prognostic gene signatures for outcome prediction by simultaneously applying a gene set-based classification on multiple data sets [56]. They collected 12 publicly available breast cancer data sets comprising 1,756 tissues, and prepared a total of 2,411 gene sets from diverse sources, including gene ontology, pathways, protein domains, and chromosomal locations. By exhaustively searching all gene sets against all data sets, they found many gene sets to be prognostic in most of the analyzed data sets. Many gene sets related to biological processes, such as cell cycle and proliferation, were found to have prognostic power in differentiating metastatic from non-metastatic breast cancer patients. As more data sets become available, their approach will be useful in developing stable prognostic gene signatures and understanding the underlying biology for different patient outcomes [56].

3.2. Meta-analysis Meta-analysis is the quantitative synthesis of information from several studies [60], and is applicable to variable study designs in genetics, from family-based linkage studies and population-based association studies, to genome-wide association studies [61]. By combining the relevant evidence from many studies, one can reach more precise estimates of effect. In the area of cancer prognosis, the integrated analysis of multiple data sets can provide a broader insight into the genetic regulation of specific biological pathways under a variety of conditions. Moreover, increasing sample size by meta-analysis increases the possibility of developing more robust prognostic gene signatures. Using the integrated analysis of two independent microarray data of breast cancer prognosis, Zhang et al. confirmed that the gene expression profile generated by an integrated analysis of multiple data sets achieves better prediction of breast cancer recurrence [62]. Choi et al. adopted the classical meta-analysis framework in microarray analysis, and used a t-like statistic, defined as effect size, as the summary statistic [63]. Using a hierarchical modeling approach to assess both intra- and inter-study variations across multiple data sets, they estimated an overall effect size as the measurement of the magnitude of differential expression for a gene through parameter estimation. They then presented advantages of the effect size approach applied to microarray data, that is, it provides a standardized index that allows a direct comparison between results from different measures, is based on a wellestablished statistical framework for combining different results to integrate multiple microarray data efficiently, and by using appropriate modeling of inter-study variation, it has the capacity to accommodate variability between multiple studies. As a result of the explosion in microarray technology-based data by different investigators working on similar experiments, it is challenging to combine results across multiple studies using different platforms. Shen et al. proposed a Bayesian mixture modelbased transformation of DNA microarray data, and applied it to develop a signature of breast

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cancer recurrence across multiple microarray experiments produced using different platforms [64]. They combined multiple studies on a common probability scale, and developed a 90 gene meta-signature that strongly associated with survival in breast cancer patients. The metasignature accommodated the heterogeneity of diverse study settings, and achieved better prognostic performance compared to the individual signatures. A key feature of the model is the use of latent variables that represent quantities, which can be combined across diverse platforms [65]. Warnat et al. used mean rank scores and quantile discretization to derive numerically comparable measures of gene expression data produced from different platforms, and achieved higher classification accuracies from the combined data set than individual data sets [66]. Recently, Hong et al. compared three meta-analysis methods for detecting differentially expressed genes in microarray experiments [67]. They compared three methods, including tbased hierarchical modeling, rank products, and Fisher’s Inverse χ2-test with P-values, and using both simulated and real datasets, demonstrated that, in general, the non-parametric rank product method had a higher sensitivity and specificity than the parametric t-based method [67]. They also demonstrated that meta-analysis, either parametric or non-parametric, always identified more genes at the same P-value, suggesting an increased power and a potentially low false negative rate.

3.3. Integrated analysis of genomic and clinical data Cancer is an enormously heterogeneous disease that is represented by complex biological phenotypes that reflect multiple genetic changes. As a result of complexity and heterogeneity, individual cancer patients have distinct tumor phenotypes, disease outcomes, and responses to therapies [68]. For these reasons, integrated analysis of both genomics and clinical information is necessary to understand the full spectrum of diverse carcinogenesis processes, and to develop individualized prognostic and predictive regimens [68]. The integrated use of both genomic and clinical data was introduced by Pittman et al., who suggested an integrated clinocogenomic modeling framework based on statistical classification tree models [69]. They first summarized gene expression data in terms of metagenes, a dominant common expression pattern within a cluster of genes, and achieved an improved accuracy of predicting a recurrence of individual breast cancer patients by combining metagenes with traditional clinical risk factors [69]. Gevaert et al. proposed a strategy based on Bayesian networks to integrate both clinical and microarray data in their construction of prognostic models to classify cancer patients into poor or good prognosis groups [70, 71]. The probabilistic model has an advantage of flexibility in model building by allowing the integration of data sources in several ways [70]. The integrative analysis of genomics and clinical data was also successfully applied to predict the outcome of patients with diffuse large B-cell lymphoma after chemotherapy [72]. Sun et al. applied a new feature selection algorithm, referred to as IRELIEF, to derive a hybrid prognostic signature from both gene expression and clinical data, and demonstrated that the hybrid prognostic signature performed better than either conventional clinical markers or markers developed from gene expression data only [73].


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3.4. Subtype-specific analysis As previously mentioned, cancer is a vastly heterogeneous disease. For example, molecular profiling studies have established that breast cancer consists of at least three to six different heterogeneous subtypes [74-76]. The status of estrogen receptor (ER) expression is one of the most important molecular characteristics in distinguishing breast cancer patients and guiding their hormonal therapy [74, 75, 77]. Another study demonstrated that different breast cancer molecular subtypes respond differently to preoperative chemotherapy, which emphasizes the importance of identifying molecular sub-types within each cancer [78]. The subtype-specific development of prognostic gene signatures is another promising approach, considering the enormous molecular heterogeneity of many cancers. For example, for breast cancer, wherein several ER+-specific and a few ER--specific prognostic gene signatures have been reported, it was found that ER+ and ER- prognostic gene signatures are fundamentally different from one another in terms of biological processes or pathways [3, 49, 79, 80]. While most ER+ gene signatures are primarily composed of genes related to cell proliferation and growth, an immune response gene expression module was representative of an ER- prognostic gene signature, clearly demonstrating the importance of developing separate prognostic gene signatures for ER+ and ER- breast cancers [49, 79, 80].

4. Conclusion Microarray gene expression profiling has dramatically increased our understanding of cancer biology, and has revealed a new opportunity for developing effective prognostic markers for cancer patients. Many gene expression studies have presented promising results in developing prognostic markers, while there are also concerns for the premature clinical use of gene expression-based prognostic markers due to several unresolved issues. Clearly, the complexity and enormous amount of information in gene expression data is one source of these problems. Recently, many promising computational approaches, including the bottomup approach, meta-analytic approach, integrative approach, and subtype-specific analyses, have contributed to an improved use of complex genomics data, and will lead to the development of more effective prognostic gene signatures.

Acknowledgements This work was supported by a grant from NTC700711 from the Korea Research Council for Fundamental Science & Technology and KRIBB Research Initiative Grant (to SYK).

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Chapter 11

COMPARISON OF Φ-VALUES AND FOLDING TIME PREDICTIONS BY USING MONTE-CARLO AND DYNAMIC PROGRAMMING APPROACHES Oxana V. Galzitskaya∗ and Sergiy O. Garbuzynskiy Institute of Protein Research, Russian Academy of Sciences, Pushchino, Moscow Region, Russian Federation, 142290

Abstract We calculate time of folding and explore the transition state ensembles for ten proteins with known experimental data at the point of thermodynamic equilibrium between unfolded and native state using a Monte Carlo Gō model and Dynamic Programming where each residue is considered to be either folded as in the native state or completely disordered. The order of events in folding simulations has been explored in detail for each of the proteins. The times of folding for ten proteins which reach the native state within a limit of 108 Monte Carlo steps are in a good correlation with experimentally measured folding time at mid-transition point (the correlation coefficient is 0.71). A lower correlation was obtained if to use Dynamic Programming approach (the correlation coefficient is 0.53). Moreover, Φ-values calculated from the Monte Carlo simulations for ten proteins correlate with experimental data (the correlation coefficient is 0.41) practically at the same level as Φ-values calculated from Dynamic Programming approach (the correlation coefficient is 0.48). The model provides good prediction of folding nuclei for proteins whose 3D structures have been determined by X-ray, and exhibits a more limited success for proteins whose structures have been determined by NMR.

Introduction Folding nucleus from experiment and theory A progress in the understanding of protein folding achieved in 1990s (Fersht 1995; Dobson and Karplus, 1999) has been achieved by investigation of “simple” proteins: without accumulation of any intermediates at the folding pathways, without cis-trans proline ∗

To whom correspondence should be addressed. E-mail: [email protected]

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Oxana V. Galzitskaya and Sergiy O. Garbuzynskiy

isomerization, and without S-S bond formation. The folding (and the unfolding) kinetics looks very simple in this case: all the properties of the native (or denatured) protein are restored synchronically, following the single-exponential kinetics (Kragelund et al., 1995). For some proteins, this simplicity is observed in a wide range of conditions, including the denaturant-free water ("biological" conditions in Fig. 1), the zone of the reversible thermodynamic transition between two phases (the native and the denatured state) and the unfolding zone; these proteins obtained a name of "two-state proteins". For the other, "multistate" proteins, the two-state folding occurs only in the transition zone, if any, while the unfolding demonstrates a "two-state" manner. Usually, the complicated folding demonstrates three phases, and the corresponding proteins obtained a name of "three-state proteins" (Fersht, 1995; Dobson and Karplus, 1999; Kragelund et al., 1995). Thus, the most universal features of folding (and unfolding) can be observed just in and around the transition zone, while the moving of this zone towards the "biological" conditions reveals individualities of various proteins (which are the "unnecessary complications", when we try to understand the basics of protein folding).

Figure 1. Folding nucleus identification using site-directed mutations (a scheme). (a) Mutation of a residue, having its native environment and conformation (i.e., its native interactions) already in the transition state TS, changes the mutant’s folding rate rather than its unfolding rate. (b) Mutation of residue, which remains denatured in the TS, has the opposite effect. “Wild type” means non-mutated protein. kapp = kf + ku, where kf is the folding rate and ku is the unfolding rate: thus, kapp ≈ kf in the folding zone (where kf » ku), kapp ≈ ku in the unfolding zone (where kf « ku) and kf ≈ ku ≈ kapp/2 at the midtransition (Matouschek et al., 1990). Extrapolations which are necessary for Φ-value analysis are drawn by dotted lines to the zero denaturant concentration.

The transition state corresponds to the free energy maximum on the folding/unfolding pathway, − or, it is better to say, to the free energy saddle point on the network of these pathways (see Fig. 3 below). The folded part of the transition state is called the "folding nucleus", and the folding pathway via formation of a nucleus (which usually consists of amino acid residues remote in protein chain (Abkevich et al., 1994a; Itzhaki et al., 1995) obtained a name of "nucleation-condensation" mechanism of folding. Folding nucleus, being the folded part of transition state, plays a key role in protein folding: its instability determines the folding and unfolding rates. It should be stressed that the folding nucleus corresponds to the free energy maximum. It has been shown that the nucleus looks like some part of 3D structure of the native protein

Comparison of Φ-Values and Folding Time Predictions by Using Monte-Carlo…

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(Matouschek et al., 1989; Matouschek et al., 1990) which is often surrounded by some unstructured, probably molten globule-like drop. So far, there is only one (unfortunately, only one and very laborious) experimental method to identify folding nuclei in proteins: to find residues whose mutations affect the folding rate by changing the TS stability as strongly as that of the native protein (Fig. 1). For the basics of this method and pioneer works see (Matouschek et al., 1989; Fersht et al., 1992; Leffler and Grunwald, 1963; Matthews, 1987; Goldenberg et al., 1989). The participation of a residue in the folding nucleus is expressed by the residue's Φ value. For a given residue, its Φ is defined as Φ =Δlnkf/ΔlnK,

(1)

where kf is the folding rate constant, K = kf /ku is the folding-unfolding equilibrium constant, and Δ means the shift of the corresponding value induced by mutation of this residue. According to the model of a native-like folding nucleus (Matouschek et al., 1989; Matouschek et al., 1990), Φ = 1 means that the residue has its native conformation and environment already in the transition state (i.e., that this residue is in the folding nucleus), while Φ = 0 means that the residue remains unfolded in the TS. The values Φ ≈ 0.5 are ambiguous: either the residue is at the surface of the nucleus, or it is in one of the alternative nuclei, belonging to different folding pathways. It is noteworthy that the values Φ < 0 and Φ > 1 (which would be inconsistent with the model of a native-like folding nucleus) are extremely rare and never concern a residue with a reliable measured ΔlnK. To estimate Φ, the rates kf and ku have to be measured at (or extrapolated to) the same conditions. Usually, being interested in the "biologically-relevant" nucleus, one extrapolates them to the zero denaturant concentration. However, it should be noted that the nucleus corresponding to the protein’s mid-transition is outlined more reliably: here the extrapolation is shorter and therefore more robust, especially when the branches of the chevron are curved; the latter suggests a change of the nucleus with the folding conditions (Otzen et al., 1999). The major assumptions, underlying the Φ-analysis of the folding nucleus by point mutations (Matouschek et al., 1989), are that the mutations do not change substantially either the folding pathway, or the nucleus, or the structure of the folded state, or the unfolded state ensemble. Experimentally, this is proved to be usually correct when the mutated residue is not larger than the initial one, and when the mutation is not connected with introduction of charges inside the globule; the proof is done by double mutations (Fersht et al., 1992). However, some strong mutations can significantly affect the distribution of structures in the TS ensemble (Burton et al., 1997). Several other observations have been done: (1) The TS-stabilizing contacts are very diverse. In some proteins the nucleus is stabilized by hydrophobic interactions (Itzhaki et al., 1995; Fulton et al., 1999; Kragelund et al., 1999), in some it includes hydrogen bonds and salt bridges (Lopez-Hernandez E and Serrano, 1996; Grantcharova et al., 1998). (2) The position of nucleus relatively to the whole protein structure is very diverse. In some it is situated in the centre, in the hydrophobic core (Itzhaki et al., 1995; Kragelund et al., 1999; Chiti et al., 1999), in some it is on the boundary of the

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Oxana V. Galzitskaya and Sergiy O. Garbuzynskiy globule (Kragelund et al., 1999; Lopez-Hernandez and Serrano, 1996; Grantcharova et al., 1998). (3) The accessible surface areas of the nuclei are also rather different (Jackson, 1998). (4) Proteins with different amino acid sequences but with similar three-dimensional structures have similar folding nuclei as a rule (Martinez and Serrano, 1999; Riddle et al., 1999; Perl et al., 1998). However, there are several examples which show that this is not always so (Galzitskaya, 2002, see the examples below, Fig.2).

Summing up the experimental data, Grantcharova et al. (2001) conclude that mutations, both artificial and natural, can radically change folding pathways (create and destroy folding intermediates, transforming two- into multi-state folding proteins and vice versa, shift the folding nuclei at the opposite side of the molecule, etc.) — without any considerable variation of three-dimensional structures of native proteins (Grantcharova et al., 2001). This means that the native structure is a subject of much more severe natural selection than that of the folding nucleus and than of folding pathways, – at least when we speak about relatively small proteins, which usually fold anyway much faster than they are synthesized by a ribosome. As regards the theoretical search for folding/unfolding nuclei in proteins, several different approaches have been suggested. The most direct approach to theoretical search of the nucleus is to generate a plausible transition state for unfolding (which must coincide with that for folding closely to midtransition) using the all-atom molecular dynamic simulations of protein unfolding (Li and Daggett, 1996; Caflisch and Karplus, 1995; Brooks et al., 1998). According to these simulations, held for few very small proteins at highly denaturing conditions (otherwise, the calculation takes too long), the unfolding is hierarchic (Lazaridis and Karplus, 1997; Tsai et al., 1999; Daggett and Fersht, 2003) (at least when it occurs far from the equilibrium): tertiary interactions break early, whereas secondary structures remain for a longer time. The repeated trajectories show a statistical distribution around the experimentally found transition states and demonstrate a broad ensemble of the transition state (TS) structures. However, these simulations usually need extremely denaturing conditions (500 K, etc.) to be completed. Therefore, the transition states found for such an extreme unfolding can be, in principle, rather different from those existing for folding (Finkelstein, 1997). Recently, however, some molecular dynamic simulations of unfolding of very small proteins (Mayor et al., 2000; Ferguson et al., 2001; Mayor et al., 2003) have been performed at more realistic, although also highly denaturating conditions. They have been performed at temperatures, accessible for "wet" experiments (350oK), as well as for simulations at current supercomputers. They gave TS structures, which are consistent with experiment (Mayor et al., 2003); however, these simulations take enormous time and can be performed for very small proteins only.


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Figure 2. (a) Profiles of experimental Φ-values obtained for B1 domains of protein G (filled circles) and of protein L (open circles). Schemes of three-dimensional structures of these domains colored according to the Φ-values of the amino-acid residues, from white (Φ = 0) to black (Φ = 1). The experimentally studied residues are shown as beads against the background of the native chain fold. Φvalues are given for them only. Adapted from (Galzitskaya, 2002). Although sequence identity of B1 domains of G and L proteins is as low as 15 % (McCalliter et al., 2000), RMSD between Cα atoms of these two structures after their superposition is 1.35Å indicating that 3D structures of these domains are similar. Nevertheless, their folding nuclei have different location. (b) Profiles of Φ-values obtained from the experiments for SH3-domains. Investigated residues are shown by filled circles for α-spectrin, by open circles for src-kinase and by filled triangles for Sso7d -protein. Schemes of three-dimensional structures of these proteins drawn according to the Φ-values of the amino-acid residues, from white (Φ = 0) to black (Φ = 1). Triangles on the structure correspond to residues with Φ < 0 and Φ > 1.

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Further progress is due to the analysis of multidimensional networks of the protein folding-unfolding trajectories done by various algorithms (Galzitskaya and Finkelstein, 1999; Alm and Baker, 1999). All these approaches (Galzitskaya and Finkelstein, 1999; Alm and Baker, 1999; Muñoz and Eaton, 1999) use different approximations and algorithms, consider only the attractive native interactions (the “Gō model”, Taketomi et al., 1975) to reduce the energy frustrations and heterogeneity of interactions, and model the trade-off between the formation of attractive interactions and the loss of conformational entropy during protein folding. These works also simulate unfolding of known 3D protein structures rather than their folding, but the unfolding is considered close to the mid-transition point, where folding and unfolding pathways coincide according to the detailed balance principle. Under these "nearequilibrium" conditions, all single-domain proteins demonstrate two-state (i.e., “all-or-none”) transitions both in thermodynamics (Privalov, 1979) and kinetics (Fersht, 1995; 1997). This means that at the mid-transition all semi-folded and misfolded globules are unstable relative to both native and unfolded states of protein chain, and this allows us to take into account only the pathways going from the native to the unfolded state and to neglect those leading to misfolded globules, stabilized by non-native interactions. These works allowed the authors to outline the folding nuclei. Despite the relative simplicity of these models, they give a promising (~50%) correlation with experimental Φvalues (Baker, 2000; Takada, 1999; Alm et al., 2002; Garbuzynskiy et al., 2004). This suggests that the chain’s folding pattern and the size of the protein, taken into account by these models, play more important role in folding than the high resolution details of protein structure (Alm and Baker, 1999; Finkelstein and Badretdinov, 1997; Clementi et al., 2000). Some progress has been made using experimental constraints to obtain the folding nucleus at atomic resolution (or rather, to visualize a possible shape for the folding nucleus that is consistent with the available, but sparse experimental data). Vendruscolo and coauthors reconstructed the putative transition state ensemble for acylphosphatase using experimental Φ-values as constraints in high-temperature unfolding simulations (Vendruscolo et al., 2001; Paci et al., 2002). However, they did not test whether the proposed conformations represent the set of conformations for which the transmission coefficient to the folded state is equal 0.5 (Galzitskaya and Finkelstein, 1998).

Sensitivity of folding pathway to the details of amino-acid sequence One of the important questions in molecular biology is what determines folding pathways: native structure or protein sequence. There are many proteins that have similar structure but very different sequences, and relevant question is whether such proteins have similar or different folding mechanisms. Comparison of proteins having similar native topologies is an important approach for elucidating fundamental aspects of the protein folding process. Experimental evidence regarding folding nucleus structure shows that proteins similar in three-dimensional (3D) structure have, as a rule, similar folding nuclei (Martinez and Serrano, 1999; Riddle et al., 1999; Perl et al., 1998). However there are several exceptions, indicating that folding pathways are sensitive to some features of the amino acid sequence (Martinez and Serrano, 1999; Riddle et al., 1999).


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Proteins with ferredoxin-like fold One of the possibilities to study the influence of details of the sequence on the folding process is to consider two nearest proteins with similar topology from the same family. Thus the transition states for four proteins with ferredoxin-like fold have been characterized and experimentally studied: AcP, Ada2h, U1A, and S6 (two helices are packed on the β-sheet with five or four strands). These proteins have a symmetrical position of secondary structure elements which is destroyed by connection of these elements in the chain. The TS of proteins Ada2h (human activation domain of procarboxypeptidase A2) and AcP (acylphosphatase) are similar in structure despite the low sequence similarity (13%) and different length of the secondary structure elements (Taddei et al., 2000; Chiti et al., 1999). For both proteins the second α-helix and the inside strands are more structured than the rest part of the protein structure. An alternative nucleus which includes the first α-helix has been found for protein U1A and other nucleus with both α-helices – for protein S6 (Ternstrom et al., 1999). At the same time the folding rates of Ada2h and AcP differ by three orders of magnitude. The authors explain such a result by the difference in the relative contact order for these proteins (Chiti et al., 1999). A strong correlation is observed between the relative order and the logarithm of folding rate for some proteins with similar topology (HPr and MerP) (Oliveberg et al., 2001). Immunoglobulin-binding domains of proteins L and G Immunoglobulin-binding domains of proteins L and G are structural homologs (see Fig.2a), but have little sequence similarity. The α-helix is packed across a four-stranded sheet in these proteins. Of interest is the experimental fact that the symmetry of the given topology is fully broken under folding of these proteins. So, the first (N-terminal) β-hairpin belongs to the folding nucleus of protein L and the second (C-terminal) one to that of protein G (McCallister et al., 2000; Kim et al., 2000). Such a result can be explained by the existence of more favorable contacts in the second β-hairpin of protein G. Indeed, the isolated fragment corresponding to the second β-hairpin is stable in water solution (Blanco et al., 1994). Therefore, the region of protein which has high probability to form local structures in the unfolded state can play an important role in the stabilization of the ensemble of TS. Experimental data for other proteins (Yi et al., 2000; Kortemme et al., 2000; Gillespie and Shortle; 1997; Cordier-Ochsenbein et al., 1998) also show that local characteristics of the sequence probably can be important for choosing the specific pathway of folding. Proteins with the SH3 domain fold The folding of small proteins with the SH3 domain fold (with simple topology, see Fig. 2b) has been studied. Protein-engineering and kinetic analysis of the src SH3-domain has been done by the group of Baker (Grantcharova et al., 1998), who give a detailed picture of TS in which the distal hairpin and the short turn 310-helix are highly ordered at the ensemble of TS. Simultaneously Martinez and Serrano (Martinez and Serrano, 1999) described TS for the αspectrin SH3 domain, making the mutations in the same structural positions. A remarkable similarity between TS of these proteins has been observed despite of 27% sequence identity. Stabilizing mutations (Martinez et al., 1998) and changes in pH (Martinez and Serrano, 1999) do not change the structure of TS of the α-spectrin SH3-domain. In the case of the src SH3-domain, stabilization of local structure by introduction of S-S-bonds and global stabilization by sodium sulfate does not change the position of TS along the reaction coordinate (Grantcharova and Baker, 2001). Seemingly, as the authors believe, the structure

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of the SH3-domain allows for a large variation in the sequence and experimental conditions without changing TS. Probably, the reason is that there are no alternative structural elements that can be sufficiently stabilized upon folding to become the folding nucleus. On the other hand, modifying the topology by circular permutation for the α–spectrin SH3-domain (Viguera et al., 1996) and circularization of the src SH3-domain (Grantcharova and Baker, 2001) can significantly change the distribution of structures in the ensemble of TS in favor of alternative folding. Thus, the shift in the structure of transition states can be done by at least two methods: when distant elements are covalently linked to reduce the entropic cost upon their interaction or upon introducing mutations that strongly destabilize (or stabilize) the energy of interactions in the protein. The characterization of SH3 structural analogs has shown that the TS structure is not always conserved in proteins with similar topologies. So, the DNA-binding protein Sso7d has different TS than that of the src and α-spectrin SH3-domains, the n-src-loop and the Cterminus (which is an α-helix in the Sso7d-protein instead of β–strand) are structured in TS. At the same time, the distal hairpin is weakly ordered (Guerois and Serrano, 2000). The authors concluded that for prediction of the structure of TS for the given protein it is necessary to take into account not only the protein topology but also the characteristics of the sequence which have not been taken into account in the theoretical methods for prediction of the structure of TS. From these works, one can conclude that the TS structure is conserved within the SH3 sequence superfamily rather than among SH3 analogs. If to consider that the SH3 fold allows several alternative folding pathways, then domination of one pathway over the others depends on the detailed structure. The authors think that this may be due to the fact that functional restriction results in the appearance of conservative regions inside one superfamily but not between them. Namely such characteristics can partly determine which folding pathway will be preferred for the given topology. It should be mentioned that the kinetic analysis for the other SH3 domains, Fyn and PI3kinase, gives correlation between the folding rate and the stability of the native state similar to that pointed out by Clarke et al. (1999) for immunoglobulin domains.

Prediction of protein folding rates There is an enormous diversity in the protein folding behavior from small proteins that usually fold with simple two-state kinetics to large proteins that usually fold with multi-state kinetics. Some general trends and correlations are beginning to emerge between the structural, thermodynamic and kinetic properties of proteins (Jackson, 1998; Plaxco et al., 1998; Shakhnovich, 1998; Galzitskaya et al., 2003; Kuznetsov and Rackovsky, 2004; Ivankov and Finkelstein, 2004). Until now, the differences in folding rates have been investigated much better than the differences in folding behavior, though these two aspects are closely related. The first comparison of a parameter with observed experimentally folding rates has been done when it has been shown that topology may be a critical determinant of two-state folding kinetics (Plaxco et al., 1998). But the topology itself cannot explain the differences in the refolding rates for some proteins sharing the same fold (SH3 domains, cold shock proteins, fibronectin


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domains, proteins of the ferredoxin fold) (Guijarro et al., 1998; Plaxco et al., 1998; Perl et al., 1998; van Nuland et al., 1998; Zerovnik et al., 1998). On the other hand, a number of basic correlations between the protein size and folding rate have been suggested (Thirumalai et al., 1995; Gutin et al., 1996; Finkelstein and Badretdinov, 1997). All of them point out that, as might be expected, the folding rate decreases with protein size, but suggest different scaling laws for this decrease. However, the current statistical analysis of protein folding data shows that all the suggested scalings, from log(L) to -L1/2 and -L2/3, correlate with the observed folding rates nearly equally: the correlation between folding rates and protein sizes is not as large, 60% (Gutin et al., 1996; Galzitskaya et al., 2001; Finkelstein and Galzitskaya, 2004). It has been shown, though, that the protein size by itself determines folding rates of only three-state folding proteins and fails to predict those for two-state folders (Galzitskaya et al., 2003). However, sequence length, being the major determinant of the type of folding behavior, is not sufficient to determine the folding type of a protein since large proteins do not necessarily exhibit multi-state kinetics (for example Variable surface antigen VlsE, which is 348 residues long, is nevertheless a twostate protein). These first attempts to explain the differences in folding rates of various proteins were a new stimulus for further efforts to find new parameters and a simple model for describing protein folding processes. It has been found that proteins with two-state and multi-state kinetics have different ratedetermining amino acids: proteins with two-state kinetics are rich in F and G while proteins with multi-state kinetics are rich in C, H, L, and R (Ma et al., 2007). Although the amino acid composition may be one of the determinant factors for protein folding behavior, it gives no further explanation on why the difference in intrinsic properties leads to the different folding type. As the authors noted in the paper, the amino acid sequence composition as an indicator of protein folding type may be unable to account for the effect of a single amino acid mutation that can switch the folding type of a protein. On the contrary, in the other work it has been demonstrated using a simple model that folding rates depend only on the topology of the native state but not on the sequence composition (Voelz and Dill, 2007). One more parameter, the number of native contacts (Makarov et al., 2002) which can be predicted from primary structure, was suggested for prediction of the folding rates of small single-domain proteins that fold through simple two-state kinetics (Punta and Rost, 2005). The above mentioned somewhat conflicting results demonstrate that the theory of protein folding rate requires further development. Therefore, the search for the factors affecting the protein folding process continues. The capillarity model (Finkelstein and Badretdinov, 1997) gave rise to the hypothesis that protein folding rates are determined by the average "entropy capacity" (the entropy capacity of an amino acid residue is defined as the number of contacts divided by the number of degrees of freedom; thus, this value is, in a sense, reciprocal to the expected melting temperature) (Galzitskaya et al., 2000). It has been shown (Galzitskaya and Garbuzynskiy, 2006) that entropy capacity correlates with folding rates for alpha-helical proteins (correlation coefficient is 0.79) and proteins with mixed (α/β) secondary structure (correlation coefficient is 0.84). Consideration of the compactness specifically addresses the issue of why some proteins fold more rapidly than others. Statistical analysis demonstrates that four main structural

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classes (Murzin et al., 1995) of proteins (all-α, all-β, α/β, α+β) differ from one another in a statistically significant manner with respect to the number of rotatable angles φ, ψ and χ and the average number of contacts per residue (Galzitskaya and Garbuzynskiy, 2006). On the whole, it has been shown that among proteins of the same size α/β proteins have, on average, a greater number of contacts per residue due to their more compact (more “spherical,” since a sphere is the most compact geometrical body: a sphere has the minimal accessible surface area in comparison with other geometrical bodies of equal volumes) structure, rather than to tighter packing (Galzitskaya et al., 2008). From previous works, it is possible to suggest a relationship between the number of contacts and folding rates. For 75 proteins for which both folding rates and tertiary structures are known, α-helical proteins have on average the fastest folding kinetics and the smallest number of contacts per residue (they are less compact than others), whereas α/β proteins have on average the slowest folding kinetics and the largest number of contacts (they are more compact than others) (Galzitskaya et al., 2008). An explanation is that the expected surface of the boundary between folded and unfolded phases in the transition state (Galzitskaya et al., 2001) for a more spherical protein is larger than for a non-spherical protein. Thus, the fact that α/β proteins are more spherical explains both the more average number of contacts per residue (Galzitskaya et al., 2008) and the slower folding kinetics. In this work, we predict folding time and structure of folding nuclei for proteins with known experimental data on both, and compare the predicted things with experimental ones. The predicted order of events in the course of folding is also analyzed. We model the folding process by means of a relatively simple theoretical approach, and use two methods (MonteCarlo simulations and Dynamic Programming) to investigate free-energy landscapes of protein folding. It is noteworthy that the correlation between predicted and experimental Φ-values is considerably worse than those typical for prediction of protein folding rates. The first obvious reason is that the observed Φ-values being predicted are restricted to the narrow region of 0 – 1 with an experimental error of ~±0.1, while the observed folding rates (determined with a relatively small experimental error) are in the wide range of 107 s-1 – 10-4 s-1. A more important reason is that the folding nucleus is not as stable to the action of mutations (and thus, to the unavoidable errors in energy estimates used to outline them) as a 3D protein structure, and it would be strange to obtain a perfect prediction of the folding nuclei with the same force fields which are still not able to predict the mutation-stable 3D native structure of a protein (Shakhnovich, 2006; Krieger et al., 2004).

Results Monte-Carlo simulations of protein folding To construct a theoretical pathway of protein folding, we did Monte Carlo simulations for 17 proteins (Garbuzynskiy et al., 2004). We performed travelling from the unfolded state to the native 3D structure without misfolding to other compact states. In our model, the folding pathways are treated as sequential insertion of residues from the unfolded state to their native


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positions according to the 3D native structure or removal of residues from the native position to the coil, respectively (Fig. 3).

Figure 3. A sketch of the network of pathways of sequential unfolding (and folding) of native 3D protein structure (I0). IL is the coil where all L links of the protein chain are disordered. In each of the many intermediates of the type Iν, ν chain links (shown in the dashed line) are unfolded, while the other L-ν links keep their native positions and conformations (they are shown as the solid line against the background of a dotted cloud denoting the globular part of the intermediate). The central structure in the lower line exemplifies a microstate with ν unfolded links forming one closed unfolded loop and one unfolded tail; the central structure in the central line exemplifies a microstate where ν unfolded links form two closed unfolded loops. The networks used in computations are much larger than the one shown in the sketch: they include millions of semi-folded microstates.

The removed (inserted) residues are assumed to loose (gain) all the non-bonded interactions and gain (loose) the coil entropy except that spent to close the disordered loops protruding from the remaining globule (Galzitskaya and Finkelstein, 1999). The general assumption of this model is that the residues remaining in the globule keep their native position and that the unfolded regions do not fold to another, non-native globule. Thus, we neglect non-native interactions that make our model similar to that of Gō (Taketomi et al., 1975).

Estimation of free energy Our model considers the native structure I0, the unfolded state IL and an ensemble of intermediate microstates Iν consisting of a native-like part and of ν unfolded chain links (ν=0 for I0, ν=L for IL, L being the total number of the chain links, and ν=1, …, L-1 for the semifolded intermediates with ν disordered links). The model uses a simple free energy estimate (Galzitskaya & Finkelstein, 1999) of each microstate I:

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F ( I ) = ε × nInb − T [η I × σ +

∑S

loops ∈ I

loop

].

(2)

nInb is the number of native atom-atom contacts in the native-like part of I ( nInb does not include contacts of neighbor residues, also existing in the coil); ε is the energy of one contact;

η I is the number of residues in the unfolded part of I; T is the temperature; σ is the entropy difference between the coil and the native state of a residue (we take σ =2.3R according to Privalov (Privalov, 1979), R being the gas constant). The sum Σ is taken over all closed unfolded loops (see legend to Fig.3) protruding from the native-like part of I. At the point of equilibrium between the native state I0 and the coil IL, we have F(I0)=F(IL), i.e., the contact energy ε (which is influenced by the solvent) and the temperature T are connected (at the mid-transition) by equation

ε = −TNσ / n0nb ,

(3)

nb

where n0 is the number of contacts in the native structure and N is the total number of the protein chain residues. It follows from equations (2) and (3) that the F(I)/T values (which only determine the transition state, see equation (5) below) do not depend on temperature, provided that the solvent composition corresponds to the mid-transition at this temperature. The entropy spent to close a disordered loop between the still fixed residues k and l is estimated (Finkelstein and Badretdinov, 1997) as Sloop = -5/2R ln|k - l|-3/2R (r2kl - a2) / (2Aa|k - l|);

(4)

here rkl is the distance between the Cα atoms of residues k and l, a = 3.8Å is the distance between the neighbor Cα atoms in the chain, and A is the persistence length for a polypeptide (according to Flory (Flory, 1969), we take A = 20Å). The term -5/2R ln|k - l| is the main in equation (4); the coefficient -5/2 (rather than Flory's value -3/2) follows from the condition that a loop cannot penetrate inside the globule (Finkelstein and Badretdinov, 1997). We consider our model as an approximation of the protein folding process, rather than a detailed description of the chain motions. Thereby our model of folding is a trade-off between the configurational entropy loss and the gain of attractive interactions. The model takes into account the topology of the native state.

Investigation of folding kinetics We calculated how long a given protein chain folds to its known native structure, starting from unfolded chain by Monte-Carlo (MC) simulation using the Metropolis scheme (Metropolis et al., 1953) at point of mid-transition. The kinematic scheme of elementary movements includes removal of a residue from the native position to the coil or insertion of a residue from the coil to the native position (Galzitskaya and Finkelstein, 1998). Thus, we did


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a travelling from the unfolded state to the native 3D structure without misfolding to other compact states. An elementary MC step was done as follows. We randomly chose a residue (namely, we generated a random number between 1 and L, where L being here the total number of residues; thus, a link was one residue-long). If the chosen residue had been already fixed in the native position, we tried to unfold it. If the chosen residue was in the coil, we tried to fix it according to its native position. Then we computed the free energy difference, ΔF, between new and previous intermediate structures. The MC step leads to the new structure with a probability w, which is equal to exp(-ΔF/RT), if ΔF>0, or to 1, if ΔF≤0. Thus, if ΔF≤0, the MC step always leads to the new structure. If ΔF>0, w is compared with a random number ξ (0TAT or Term -->Tyr, has been described in the pathogenesis of Hb Pakse [26]. Computer-based protein structure modeling was used in a bioinformatics analysis of the tertiary structure of these elongated amino acid sequences. The elongated part of Hb Pakse showed additional helices, which may cause the main alteration in Hb Pakse [26]. Abnormalities in the fold structure of globin in Hb Pakse were identified, and helices additional to the normal alpha globin chains were shown in the elongated part of Hb Pakse [26].

Computational Medicine Research in Hematology Wiwanitkit [27]

411

A functional analysis was performed on 4 important beta hemoglobinopathies (hemoglobin C, D, E, and S) using PolyPhen, a novel bioinformatic tool. The mutations Hb C (beta 6, Glu --> Lys), Hb D (beta 121, Glu --> Gln), Hb E (beta 26, Glu --> Lys), and Hb S (beta 6, Glu --> Val) were selected for further study [27]. According to the in silico mutation study, the functional change in the studied hemoglobinopathies was variable [27]. The position-specific independent counts (PSIC) difference score ranged from 1.362 (Hb D) to 2.986 (Hb S) [27]. Regarding the degree of damage, all had probable damage [27]. This analysis demonstrated that the functional aberration in the hemoglobinopathy was based on complex pathogenesis [27]. Identifying only the structural aberration in a hemoglobinopathy is not sufficient; additional functional analysis is recommended [27]. The functional analysis presented here may be a good model for further research [27].

Pharmacogenomics study on congenital hemoglobin disorder is also of interest [28 – 30]. Genetic association studies, which attempt to link polymorphisms with certain disease phenotypes and drug response, are taking the first steps in helping individualized therapy in sickle cell patients in order to enhance efficacy and decrease the toxicity [28]. Finally, the newest “omic” science, interactomics, is also proposed for usage in hematology. Red blood cell interactome can lead to considerable insight into disorder diagnosis, severity, and drug or gene therapy response [20]. C. Examples • A study on structure aberration in Hb Siam Hb Siam is an example of hemoglobinopathy that was first identified in India. Hb Siam is caused by the mutation [alpha15(A13)Gly-->Arg (alpha1) (GGT-->CGT)] in the alpha globin gene [31 - 33]. Similar to other hemoglobinopathies, Hb Siam is a protein disorder. At present, the molecular structure of Hb Siam is not welldocumented. Basically, the study on the tertiary structure is warranted for complete knowledge on the structural change in any protein disorder. The study on the secondary and tertiary structures, which can assist explain the pathogenesis of the Hb Siam disorder, is needed. The main objective of this study is to find the secondary and tertiary structures of Hb Siam by bioinformatic method. In this study, the author performed a bioinformatic analysis to assess the effect of sequence change in the Hb Siam disorder on the secondary and tertiary structures of the alpha globin chain. A computer-based study for amino acid sequence comparison and protein structure modeling was done. The database ExPASY [34] was applied for searching for the amino acid sequence of normal human alpha globin chain. Then the mutation alpha 15 Gly-->Arg was experimentally performed. Concerning secondary structure modeling, the author performed protein secondary structure predictions of alpha globins in both normal and hemoglobin Siam disorder from its primary sequence using NNPREDICT server [35]. The calculated secondary structures were presented and compared. In addition, the calculated tertiary structures were also presented and compared. All programs used in this study are standard programs used in bioinformatic study. From searching the database ExPASY, the sequence of the alpha globin chain was derived, as presented in Table 2. The experimentally mutated alpha globin chain in hemoglobin Siam disorder is derived as presented in Table 2. Using NNPREDICT server, the calculation for secondary structure of alpha globin chains of normal and Hb Siam disorder was performed.

412

Viroj Wiwanitkit Table 2. Alpha globin chains according to the database ExPASY and the derived mutated alpha globin chains of hemoglobin Siam disorder. Protein

Primary structure

Normal alpha globin chain (Entry name: Q9NYR7, gene name: HBA2, AC number: Q9NYR7)

MVLSPADKTNVKAAWGKVGAHAGEY GAEALEKMFLSFPTTKTYFPHFDLSHG SAQVKGHGKKVADALTNAVAHVDD MPNALSALSDLHAHKLRVDPVNFKLL SHCLLVTLAAHLPAEFTPAVHASLDKF LASVSTVLTSKYR

2. Derived alpha globin chain of hemoglobin Siam disorder

MVLSPADKTNVKAAWAKVGAHAGEY GAEALEKMFLSFPTTKTYFPHFDLSHG SAQVKGHGKKVADALTNAVAHVDD MPNALSALSDLHAHKLRVDPVNFKLL SHCLLVTLAAHLPAEFTPAVHASLDKF LASVSTVLTSKYR

Considering the derived secondary structures, there are 73 helix and 4 strands in the normal alpha globin chain and there are 72 helix and 4 strands in the alpha globin chain of Hb Siam. According to this study, the secondary structures of human alpha globin chains of normal and hemoglobin Siam disorder are calculated and presented. Based on this information, the main difference between the predicted alpha globin secondary structures of alpha globin chains between normal and hemoglobin Siam is the deletion of a helix in the Hb Siam. The results from this study can be good data for further study on hemoglobin Siam disorder, which can bring to the further understanding on this hemoglobinopathy. A. alpha globin chain in normal --------H--HHHHHHH---H-HHHHHHHHHHH--------------------HEH---HHHHHHHHHHH------HHHHHHHHHHH---------HHHHHHHHHHHHHH-------H HHHHHHHHHHHHHHEEE----B. alpha globin chain in hemoglobin Siam * --------H—HHH-HHH---H-HHHHHHHHHHH--------------------HEH---HHHHHHHHHHH------HHHHHHHHHHH---------HHHHHHHHHHHHHH-------H HHHHHHHHHHHHHHEEE----Figure 1. Calculated secondary structures of alpha globin chains of normal and Hb Siam disorder (Secondary structure prediction: H = helix, E = strand, - = no prediction) * The difference is presented as red highlight.

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• A study on structure aberration in Hb Siriraj Of several types of hemoglobinopathy, hemoglobin (Hb) Siriraj disorder is a beta chain variant in which beta 7 Glu is replaced by a lysine [36 – 38]. This disorder was firstly found in Bangkok, Thailand [36 - 38]. An individual with Hb Siriraj usually presents with mild or asymptomatic manifestation [36 - 37]. However, an individual with concomitant sickle cell anemia is more severe and manifests anemic symptoms [36]. The molecular structure of Hb Siriraj is not well understood. Considering the primary structure of Hb Siriraj, a specific mutation is seen for a long time and can be easily detected by isolation of beta-chain by ion-exchange chromatography of total globin on CM-cellulose [36 - 38]. However, there is a lack on the knowledge of the secondary structure of this hemoglobinopathy. Further study, which can explain more in the pathogenesis of the Hb Siriraj, is needed. Here, the author performs a bioinformatic analysis to study the effect of sequence change in the Hb Siriraj on the secondary structure of beta globin chain. A computer-based study for amino acid sequence comparison and protein structure modeling is used. A similar procedure as presented in Hb Siam was performed and the main difference between the globin chains of normal and Hb Siriraj is an additional helix in the structure. Indeed, an additional helix in the structure within the globin is reported to be an important factor leading to the instability of Hb [39]. In addition, a similar additional helix within the molecule of Hb C as well as Hb S is reported [40], and this might be a clue for a mild sickle cell syndrome resulted from Hb Siriraj.

Computational Medicine Research on Prothrombin Disorder A. Basic knowledge on prothrombin disorder Prothrombin is an important protein in thrombohaemostasis. There have been extensive studies on the structure and function of prothrombin, a protein critical for the coagulation of blood. The biological functions of prothrombin and its activated form, thrombin are discussed, as well as the structure and functional domains of the protein [41]. Prothrombin deficiencies represent a group of thrombohaemostatic disorders that can be detected and seen in both acquired and congenital forms. Congenital Prothrombin deficiency is a rare bleeding disorder which is inherited as an autosomal recessive trait [42]. Some cases are lethal but most are of mild severity [42]. Several prothrombin deficiency disorders are reported. B. Some interesting computational medicine researches on prothrombin disorder Similar to hemoglobin, there are many recent interesting computational medicine researches on prothrombin disorders. Genomics can be successfully used to study the congenital prothrombin disorder. Considering proteomics, the analysis of prothrombin complex concentrates can be used as a model to assess to what extent these technologies can detect differences in blood-derived treatments beyond that of standard quality control [43]. Proteomic technologies allow the identification of potentially modified proteins in clotting factor concentrates, showing that they could become a useful tool for transfusion medicine to assess the impact of processing on the integrity of blood-derived therapeutics [43]. A proteomic analysis of changes in

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Viroj Wiwanitkit prothrombin and plasma proteins associated with the G20210A mutation was recently studied by Gelfi et al. [44]. This study, based on proteomic investigation by two-dimensional gel electrophoresis and electrospray ionization tandem mass spectrometry protein identification, indicated that the G20210A mutation was associated with increased glycosylation of prothrombin, which implies greater stability to the protein [44]. In addition, there are many recent studies on the structures of prothrombin disorders. For example, Wiwanitkit recently reported the structural aberration in prothrombin Shanghai [45]. The main structural aberration in prothrombin Shanghai disorder is the loss of two helices [45]. Wiwanitkit noted that the disorder in this region as detected in this study could be a good explanation of pathogenesis [45]. C. Examples • A study on functional aberration in some prothrombin disorders Congenital prothrombin deficiency is a rare bleeding disorder inherited as an autosomal recessive trait [46]. Some cases are lethal but most are mild [46]. Several prothrombin deficiency disorders are reported. Until present, there have been many prothrombin deficiency variants documented in the literature. Every variant has its highly specific underlying genetic defect and therefore has its specific property and manifestation. The single substitution in the amino acid chain is the commoner form of prothrombin deficiency variant. Usually, a prothrombin deficiency variant due to a single amino acid substitution presents only one aberration in the secondary structure. However, the functional aberrations according to the structural aberration are well documented. Although many prothrombin deficiency variants present similar structural abnormal points, their functions sometimes are discordant. Here, the author performed a functional analysis on some prothrombin deficiency variants using a novel bioinformatic tool. The database ExPASY (Expert Protein Analysis System) was used for the data mining of the amino acid sequence for human prothrombin. The mutations of three well-known prothrombin deficiency variants, Shanghai (29 Glu-->Gly) [47], Carora (44 TyrÆ Cys) [48] and Barcelona (273 Arg-->Cys) [49] were selected for further investigation. All these three selected prothrombin deficiencies have as underlying pathogenesis a single amino acid substitution. A novel bioinformatic simulation tool, PolyPhen [50], was applied for mutation study. Briefly, we studied the effect of each mutation on prothrombin structure and function. Briefly, PolyPhen is an automatic tool for prediction of possible impact of an amino acid substitution on the structure and function of a specific human protein. This prediction is based on classical rules, which are applied to the sequence, phylogenetic and structural information characterizing the substitution. Concerning the input, PolyPhen works with human proteins and identifies them by the amino acid sequence itself. Amino acid replacement is indicated by position number and substitution. For a given amino acid substitution in a human protein, PolyPhen performs several steps: a) sequence-based characterisation of the substitution site, b) calculation of the degree of functional change, PSIC scores, c) calculation of structural parameters and contacts and d) specific prediction.


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Table 3. Functional change in the studied prothrombin deficiency variants. Studied prothrombin deficiency variants

PSIC difference score*

Degree of damaging

Shanghai Carora Barcelona

2.6 2.4 0.4

Probably damaging Probably damaging Benign

* PSIC difference score is the score showing the degree of functional change **There are four degrees of damaging: a) probably damaging, high confidence supposed to affect protein function or structure, b) possibly damaging, supposed to affect protein function or structure, c) benign, most likely lacking any phenotypic effect and d) unknown, in some rare cases, the lack of data do not allow PolyPhen to make a prediction.

According to the in silico mutation study, the functional change in the studied prothrombin variants is shown in Table 3. PSIC difference score varies from 0.4 to 2.6. Concerning the degree of damaging, benign is detected in the Barcelona variant while probably damaging is detected in the Carora and Shanghai variants (Table 1). Here, the author studied the functional changes in some common prothrombin deficiency variants. The three selected prothrombin deficiencies variants are those with a single institution and have a single structural aberration. According to this study, the functional aberration increases from Barcelona, Carora and Shanghai orderly. This finding is concordant with the reported clinical features in these variants [4 - 6]. It also shows the trend that the mutation in earlier order of amino acid tends to have a more severe presentation. Here, it can be demonstrated that the functional aberration in a prothrombin deficiency variant is based on complex pathogenesis. The identification of only the structural aberration in prothrombin deficiency variants is not sufficient and it should be supplemented with a further functional analysis for a better insight on this specific topic on prothrombin.

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Thomas SM. Genomics: the implications for ethics and education. Br Med Bull. 1999;55(2):429-45. Leach AR, Hann MM. The in silico world of virtual libraries. Drug Discov Today. 2000 Aug;5(8):326-336. Marshall T, Williams KM. Proteomics and its impact upon biomedical science. Br J Biomed Sci. 2002;59(1):47-64. Goh SH, Lee YT, Bouffard GG, Miller JL. Hembase: browser and genome portal for hematology and erythroid biology. Nucleic Acids Res. 2004 Jan 1;32(Database issue):D572-4. Waenlor W. Analysis of hemoglobin disorders by application of computational tools for nanohematology. Nanomedicine. 2005 Sep;1(3):219. Walker J, Flower D, Rigley K. Microarrays in hematology. Curr Opin Hematol. 2002 Jan;9(1):23-9. Thomas PD, Mi H, Lewis S. Ontology annotation: mapping genomic regions to biological function. Curr Opin Chem Biol. 2007 Feb;11(1):4-11.

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INDEX A AAA, 327 AAC, 326, 327, 328 aberrant methylation, 226 academic, 12, 16, 390, 409 ACC, 327 accessibility, 157, 161, 166, 179, 180, 182, 186, 190, 191, 325 accounting, 62, 75, 142 accuracy, 13, 14, 15, 76, 90, 92, 133, 134, 135, 136, 145, 166, 177, 182, 183, 216, 217, 220, 225, 234, 239, 240, 242, 247, 248, 249, 250, 252, 253, 263, 264, 267, 268, 291, 315, 317, 318, 320, 325, 327, 328, 330, 331, 333, 335, 336, 337, 375, 377, 382 acetylation, 93, 96 ACF, 326, 329 Ach, 97 achievement, 307 acid, 13, 15, 16, 17, 41, 134, 146, 162, 165, 168, 169, 171, 174, 177, 279, 280, 281, 282, 285, 295, 296, 303, 304, 310, 311, 313, 317, 320, 321, 323, 324, 325, 326, 327, 328, 329, 330, 331, 332, 333, 334, 335, 337, 338, 339, 340, 352, 358, 359, 376, 378, 379, 380, 381, 382, 383, 384, 385, 400, 410, 411, 413, 414, 415 acidic, 14 ACM, 254, 255 actin, 23, 362, 372 activation, 17, 93, 97, 178, 283, 376 activators, 362 active site, 45 acute, 62, 84, 271 acute leukemia, 84 acute myeloid leukemia (AML), 271 acyl transferase, 14 Adams, 188

adaptation, 20, 24, 25, 355, 398 adaptive control, 67, 80 adenine, 3 adenocarcinoma, 227, 271 adenoviral vectors, 91 adenovirus, 265 adenoviruses, 91 adenylate kinase, 352, 359 adjustment, 76, 77, 85, 127 administration, 226 adult, 216, 226, 249, 250, 266, 271 adults, 233 Africa, 20 African American, 25 Ag, 386 AGC, 233 age, 50, 53, 145, 220 agent, 100, 101, 102, 104, 105, 107, 109, 110, 112, 116, 386 agents, 9, 11, 12, 99, 100, 101, 102, 103, 104, 109, 110, 113, 114, 115, 116, 119, 126, 227, 352 aggregation, 218 aid, 364, 369, 373, 402 air, 246 Airlines, 99 alanine, 392 albinism, 20 allele, 3, 7, 8, 21, 22, 23, 24, 25, 232, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 252, 253, 266 alleles, 9, 3, 19, 20, 21, 22, 23, 24, 25, 233, 234, 235, 236, 241, 243, 244, 245, 246, 248, 249, 250, 380 allosteric, 195, 212, 352 alpha, 143, 145, 155, 285, 313, 408, 410, 411, 412, 417 alternative, 9, 12, 1, 8, 62, 63, 65, 67, 69, 72, 73, 74, 75, 77, 78, 109, 132, 138, 139, 141, 149, 170,

420

Index

171, 175, 193, 194, 205, 232, 233, 279, 283, 284, 312, 346, 387, 402 alternative hypothesis, 63, 65, 73, 74, 78 alternatives, 76, 77, 101, 137, 171, 179 American Airlines, 99 amino acid side chains, 381 amino acids, 15, 43, 133, 136, 167, 168, 169, 170, 172, 174, 175, 178, 179, 180, 285, 317, 318, 320, 321, 323, 325, 327, 328, 331, 352, 360, 375, 376, 377, 378, 379, 380, 382, 383, 384, 387, 410 ammonia, 13 amphibia, 255 amplitude, 211, 213 Amsterdam, 127, 261, 262, 358 analog, 31, 296 anatomy, 6, 7 anemia, 409 angiogenesis, 10, 47, 48 angiogenic, 228 animal models, 10, 59, 265 animals, 13, 60, 61, 66, 79, 231, 232 anisotropy, 198, 211 ANN, 382 annealing, 173, 175, 185, 186, 188, 240, 253 annexin I, 309 annotation, 41, 42, 44, 90, 143, 146, 224, 368, 385, 405, 408, 416 antibacterial, 17 antibody, 9, 6, 11, 15, 16, 17, 18, 225, 229, 364 antigen, 15, 16, 285, 377, 386, 387 antioxidant, 223 API, 394, 395, 396, 397, 402, 403, 404 apoptosis, 10, 47, 48, 93, 96, 97, 224, 226 apoptotic, 97 application, 10, 13, 14, 15, 16, 7, 39, 41, 42, 43, 62, 65, 66, 67, 73, 75, 79, 82, 83, 100, 102, 128, 130, 142, 158, 166, 212, 259, 272, 315, 318, 322, 334, 338, 344, 353, 356, 361, 371, 389, 390, 391, 394, 398, 402, 403, 404, 415 applied mathematics, 200 aqueous solution, 308 ARB, 55 archetype, 353, 354 arginine, 13, 14, 17, 418 argument, 348, 397, 398 Ariel, 228 Aristotelian, 342, 343, 348, 350, 351 Aristotle, 342, 347, 357 arithmetic, 21, 134, 352, 356 arrest, 97 arthropods, 141 Asia, 416 Asian, 416

assessment, 43, 65, 77, 79, 80, 85, 190, 366, 407, 408, 418 assignment, 11, 21, 99, 100, 102, 103, 104, 106, 109, 113, 116, 123, 126, 127, 128, 183, 184, 232, 233, 235, 245, 246, 252, 254, 319, 392, 400 assumptions, 10, 13, 30, 32, 33, 34, 59, 60, 63, 66, 77, 78, 79, 231, 235, 237, 239, 253, 264, 279, 291, 347 asymptomatic, 54, 413 asymptotics, 82 ATF, 365 Atlantic, 239, 248, 253 atomic force, 195 atomic force microscopy (AFM), 195, 209 atoms, 148, 149, 167, 168, 170, 173, 174, 176, 194, 195, 196, 197, 198, 201, 281, 288, 294, 295 ATP, 159, 194, 210 ATPase, 194, 201, 209, 210 autocorrelation, 334 autoimmune, 386, 387 autoimmune diseases, 386 automata, 15, 341 autosomal recessive, 413, 414 availability, 3, 41, 70, 130, 135, 140, 363, 364 averaging, 126, 294, 299 avoidance, 347 Azobenzene, 210

B B cell, 62 Bacillus, 220 Bacillus Calmette-Guerin (BCG), 220 back, 177, 178, 327, 330, 352 bacterial, 145, 385 Banach spaces, 37 barrier, 157, 289, 290, 291, 292, 293, 294, 296, 298, 299, 301, 302, 303, 307 base pair, 91, 162, 233 Bayesian, 85, 133, 134, 136, 144, 145, 178, 225, 237, 267, 268, 275, 317, 321, 330, 335, 340 Bayesian analysis, 134 B-cell, 268, 271, 275 B-cell lymphoma, 268, 271, 275 beads-on-a-string, 150 behavior, 13, 106, 194, 195, 196, 198, 199, 200, 201, 209, 216, 284, 285, 304, 346, 392 benchmark, 12, 136, 143, 144, 165, 166, 253, 334, 336 benchmarking, 172 bending, 155, 157, 160, 196 benefits, 4, 20, 48, 55, 396, 401 benign, 6, 415 bias, 68, 178, 240

Index biliary tract, 62, 81 binary decision, 102 binding, 14, 15, 16, 17, 43, 90, 91, 92, 93, 94, 95, 97, 149, 159, 160, 161, 194, 199, 212, 213, 223, 283, 284, 298, 311, 352, 362, 364, 365, 369, 370, 380, 381, 387, 388 binomial distribution, 76 biochemistry, 12 biogenesis, 93, 95 bioinformatics, 9, 14, 15, 16, 3, 4, 11, 12, 13, 14, 15, 16, 43, 45, 90, 92, 93, 130, 135, 188, 254, 259, 274, 371, 372, 375, 390, 407, 408, 410 biological processes, 12, 13, 43, 60, 147, 216, 220, 222, 223, 224, 225, 262, 266, 267, 269 biological rhythms, 93 biological systems, 346, 347, 351, 356 biomarker, 226 biomarkers, 13, 1, 4, 216, 225, 226, 260, 273 biometric, 377, 388 biomolecular, 210, 212 biomolecular systems, 212 biomolecules, 213 biopolymers, 158, 160, 161, 191, 309, 337 biosciences, 1, 391 biosemiotic, 347 birds, 233, 257 birth, 231 bladder, 10, 12, 13, 47, 54, 215, 216, 217, 219, 220, 224, 225, 226, 227, 228, 229, 260, 270 bladder cancer, 12, 13, 54, 215, 216, 217, 219, 220, 224, 225, 226, 227, 228, 229 bladder carcinogenesis, 226 bleeding, 413, 414 blocks, 14, 77, 136, 144, 145, 202 blood, 232, 376, 382, 409, 411, 413, 416 Bohr, 190 bonds, 196, 283, 342, 343 bone scan, 216 Boolean algebras, 344 bootstrap, 134, 137, 141, 142, 173, 219, 333 Boston, 358, 372, 405 bottlenecks, 166 bottom-up, 14, 259, 264, 265, 266, 269 bounds, 101, 102, 103, 106, 112, 126 brain, 62 branching, 11, 100, 106, 109, 110, 111, 112, 113, 119, 120, 121, 126 breakdown, 311 breast cancer, 7, 62, 81, 86, 260, 261, 265, 266, 267, 268, 269, 270, 272, 273, 274, 275, 276 breast carcinoma, 275 British Columbia, 10, 47, 50, 52 brothers, 231

421

browser, 404, 405, 408, 415 browsing, 402 budding, 228

C C++, 390, 391, 399, 402, 403, 404, 405, 406 cadherin, 228 calculus, 344 calf, 358 calibration, 82 Canada, 47, 48, 49, 50, 55, 218, 341 cancer, 9, 10, 13, 1, 2, 3, 4, 5, 6, 7, 8, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 62, 79, 80, 84, 96, 97, 215, 216, 217, 219, 220, 224, 225, 226, 227, 228, 229, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276 cancer cells, 1, 7, 79, 97, 229 cancer progression, 224, 273 cancerous cells, 93 candidates, 13, 15, 1, 6, 131, 216, 226, 364, 375, 377 carbon, 194, 195, 196, 197, 198, 201 carbon atoms, 194, 195, 196, 197, 198, 201 carboxyl, 14 carcinogen, 60, 77 carcinogenesis, 90, 94, 226, 268 carcinogenic, 264 carcinoma, 62, 91, 216, 224, 225, 226, 227, 228, 265, 266, 270, 271, 274 carcinomas, 85, 216, 226, 229, 265, 270, 275 case study, 96 casting, 262 catabolic, 17 catabolism, 17 catalysis, 14, 209 catalytic activity, 223 categorization, 353 category a, 347 Catholic, 405 cation, 27 Caucasians, 25 causality, 348, 349 causation, 15, 341, 342, 346, 350, 351, 355, 356 cave, 146 CD8+, 386, 388 cDNA, 1, 2, 3, 4, 6, 59, 62, 74, 80, 81, 82, 83, 91, 217, 218, 220, 227, 229 CDR, 15, 16CE, 229 cell, 11, 15, 1, 2, 4, 6, 48, 49, 79, 80, 89, 90, 92, 93, 94, 95, 96, 97, 148, 163, 222, 223, 224, 225, 226, 228, 229, 265, 266, 267, 268, 269, 270, 271, 272, 275, 319, 352, 359, 360, 365, 372, 375, 376, 377, 378, 381, 386, 387, 388, 409, 411, 413, 416 cell culture, 92

422

Index

cell cycle, 90, 92, 93, 94, 95, 97, 226, 228, 229, 267, 365, 372 cell differentiation, 224, 225, 226 cell fate, 11, 89 cell growth, 96 cell line, 6, 265, 266 cell organelles, 223 cell organization, 352 cell surface, 319 cellular automaton, 355 cellular regulation, 157 cellulose, 413 central nervous system, 270 centromeric, 158 cerebrospinal fluid, 376 cervix, 49, 51, 227 CGT, 411, 417 chemical energy, 194 chemical properties, 14, 315, 321 chemotherapeutic agent, 227 chemotherapy, 216, 220, 226, 260, 268, 269, 271, 276 chest, 216 children, 416 chiral, 157, 158 chirality, 149, 160 chloroform, 217 chromatin, vi, 12, 91, 92, 96, 97, 147, 148, 149, 151, 152, 153, 155, 156, 157, 158, 159, 160, 161, 162, 163, 362, 364, 371, 373 chromatography, 413 chromosome, 22, 23, 24, 93, 152, 155, 157, 159, 160, 161, 226 chromosomes, 12, 3, 147, 148, 150, 151, 155, 156, 158, 161 chymotrypsin, 311, 387 circadian, 93, 96 circadian clock, 93 circadian rhythm, 93, 96 circadian timing, 96 cis, 278, 362, 364, 365, 368, 369, 372 classes, 11, 99, 116, 117, 119, 167, 171, 172, 175, 178, 179, 181, 182, 187, 191, 218, 220, 270, 286, 316, 318, 319, 325, 326, 328, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339, 382 classical, 11, 63, 100, 129, 130, 241, 267, 343, 346, 360, 414 classical logic, 343 classification, 14, 4, 17, 18, 41, 42, 47, 63, 79, 80, 82, 84, 178, 224, 238, 266, 267, 268, 270, 271, 273, 274, 312, 315, 317, 318, 319, 320, 321, 329, 330, 332, 333, 334, 335, 336, 337, 368, 370, 382 clinical oncology, 273

clinical trials, 10, 59, 260 clinics, 48 clone, 2, 377, 378, 382, 383, 386, 388 cloning, 407 closure, 15, 341, 347, 348, 350, 355, 356, 359, 404 cluster analysis, 21 cluster model, 202, 208, 213 clustering, 12, 21, 80, 134, 217, 219, 224, 225, 255, 317, 321, 330, 332, 338, 368 clusters, 6, 137, 167, 202, 217, 218, 219, 225, 239, 330, 365, 416 CMC, 213 c-Myc, 90, 94, 96, 265 CNS, 386, 387 coagulation, 413 codes, 15, 16, 43, 48, 49, 317, 341, 350, 389, 403 coding, 4, 43, 90, 92, 373, 385 codominant, 234 codon, 410 coefficient of variation, 71 coenzyme, 311 coherence, 345, 346, 358 coil, 161, 175, 287, 288, 289, 291, 292, 309, 320, 321, 325 colon, 60, 61, 66, 68, 70, 80, 97, 260, 261, 262, 270 colon cancer, 61, 66, 68, 70, 97, 260, 261, 262, 270 colorectal cancer, 7, 270 Columbia, 10, 47, 50, 52, 360 Columbia University, 360 communication, 254, 402 communities, 202 community, 44, 257, 272, 402 compaction, 149, 151, 155, 157, 158 compiler, 390, 392, 396 complement, 408 complementarity, 15, 43, 352 complementary DNA, 85, 217 complex interactions, 377 complex systems, 353 complexity, 10, 72, 89, 90, 94, 144, 147, 148, 177, 178, 241, 242, 247, 262, 268, 269, 275, 321, 329, 338, 354, 358, 376 compliance, 202 complications, 278 components, 13, 15, 12, 22, 43, 70, 121, 132, 166, 179, 188, 216, 220, 222, 225, 239, 324, 325, 326, 329, 331, 341, 350, 351, 352, 353, 355, 379, 384, 389, 390, 402, 403 composition, 14, 17, 159, 285, 288, 315, 317, 320, 321, 323, 324, 325, 326, 327, 328, 329, 330, 331, 333, 334, 335, 336, 337, 338, 339, 353, 355, 358, 409 compounds, 12, 13, 14, 15, 16, 17

Index computation, 15, 40, 134, 194, 201, 208, 341, 345, 352, 356, 359 computational performance, 404 computed tomography, 216 computer science, 253, 402 computer simulations, 160, 162 computerization, 130 computing, 64, 130, 135, 136, 137, 195, 248, 358, 392, 403, 404 concentrates, 41, 413, 418 concentration, 158, 238, 278, 279, 376, 378, 379, 380 concordance, 266 concrete, 344, 351, 354 condensation, 93, 158, 161, 196, 200, 279, 311 confidence, 48, 50, 126, 232, 253, 256, 415 confidence interval, 48, 50 confidence intervals, 48 configuration, 16, 135, 173, 238, 240, 351, 389, 390, 400 congruence, 141, 142 consciousness, 354, 355, 358 consensus, 13, 138, 190, 232, 246, 247, 248, 250, 252, 253, 276, 325, 363, 369 consent, 20 conservation, 14, 133, 312, 313, 364, 369, 370 constraints, 11, 15, 29, 99, 100, 101, 102, 103, 104, 105, 106, 108, 110, 112, 152, 155, 157, 158, 166, 167, 169, 170, 172, 173, 175, 184, 186, 211, 233, 235, 237, 238, 240, 241, 245, 246, 251, 252, 282, 341, 346, 349 construction, 12, 106, 134, 137, 138, 145, 265, 268, 328, 333, 343, 348, 349, 353, 354, 390, 391, 399, 403 consulting, 368 consumption, 11, 100, 101, 102, 123, 351 control, 12, 2, 26, 62, 63, 67, 68, 69, 70, 72, 73, 74, 75, 77, 79, 80, 82, 85, 86, 90, 92, 95, 96, 128, 147, 160, 218, 263, 346, 355, 359, 360, 361, 362, 364, 373, 392, 394, 403, 409, 416 convergence, 11, 99, 100, 106, 126 conversion, 226 convex, 37, 116 COP, 331 copolymers, 312 copper, 152 corn, 60 correlation, 10, 14, 22, 47, 51, 54, 55, 61, 70, 71, 76, 78, 79, 196, 197, 204, 205, 207, 262, 263, 277, 282, 283, 284, 285, 286, 294, 296, 300, 301, 302, 304, 305, 306, 307, 320, 323, 326, 327, 329, 331, 334, 341, 366, 370, 381, 410, 416

423

correlation coefficient, 14, 22, 277, 286, 296, 300, 301, 302, 304, 305, 306, 307, 381 correlation function, 320, 326, 327, 331 correlations, 50, 150, 157, 162, 284, 285, 305, 311, 321, 331 costs, 11, 100, 101, 103, 109, 110, 137, 382 coupling, 97, 317, 321, 324, 325, 326 covalent, 17, 195, 196, 197, 198, 352 covalent bond, 195, 196, 197, 198 covering, 55, 184, 254 CpG islands, 368, 370 CPU, 119, 135, 178 CRC, 87, 211 creativity, 354 CREB, 365 critical points, 166 critical value, 30, 31, 73, 77 criticism, 138 cross-linking, 151 cross-validation, 264, 320, 335, 336 crystal structure, 13, 14, 16, 151, 398 crystal structures, 16 crystalline, 161 crystallization, 188 crystals, 157 CSF, 376 C-terminal, 148, 283, 291, 296, 298, 299, 301, 302, 410 C-terminus, 284, 302, 303 Cuba, 44 culture, 92, 355 cumulative distribution function, 74 cyanobacteria, 93, 96 Cybernetics, 359 cycles, 135, 177 cycling, 363 cystectomy, 216, 220 cysteine, 376, 418 cystourethroscopy, 216 cytology, 216 cytomegalovirus, 92 cytosine, 3

D data analysis, 13, 15, 82, 216, 217, 218, 220, 263, 375, 377, 403 data collection, 40 data distribution, 225 data generation, 70 data mining, 12, 40, 218, 332, 409, 414 data processing, 391, 403

424

Index

data set, 70, 71, 72, 79, 145, 175, 218, 225, 252, 260, 262, 263, 266, 267, 268, 275, 328, 329, 331, 381, 382, 383 data structure, 396, 404 database, 10, 11, 15, 16, 1, 6, 7, 8, 12, 21, 39, 40, 41, 42, 43, 44, 49, 89, 91, 93, 94, 132, 140, 143, 144, 146, 175, 180, 181, 190, 191, 217, 225, 305, 312, 326, 327, 330, 331, 335, 337, 372, 373, 375, 377, 383, 384, 385, 389, 398, 399, 400, 408, 409, 411, 412, 414, 416 de novo, 166, 202 death, 94, 96 decay, 175, 178, 342, 345 decision making, 272 decision trees, 335 decisions, 94, 106, 116 decomposition, 101, 126, 128, 321, 338 deconvolution, 15, 375 defects, 23, 154, 159, 408 deficiency, 413, 414, 415, 418 definition, 9, 19, 20, 22, 31, 40, 69, 95, 139, 171, 177, 178, 181, 205, 252, 289, 316, 318, 321, 342, 347, 348, 349, 350, 354, 369, 399, 403 deformation, 12, 149, 157, 193, 194, 198, 213 degenerate, 377, 386, 388 degradation, 17 degrees of freedom, 68, 73, 74, 168, 194, 199, 200, 202, 204, 205, 208, 285 denaturation, 195, 308 dendrites, 23 density, 26, 59, 83, 151, 177, 179, 180, 182, 398 deoxyribonucleic acid, 358 deoxyribose, 162 deregulation, 265 dermatologist, 48 detection, 11, 6, 7, 15, 42, 79, 80, 81, 129, 188, 218, 345, 363, 364, 365, 366, 369, 371 determinism, 346, 354, 355 developing countries, 416 developmental process, 364 deviation, 71, 175 diabetic nephropathy, 85 diagnostic markers, 227 diet, 61, 66 dietary, 60, 61 dietary fat, 61 diets, 68 differential diagnosis, 216, 225 differentiation, 21, 90, 93, 95, 96, 216, 224, 225, 226, 227, 370, 386 diffusion, 62, 80, 85 diffusion tensor imaging (DTI), 62 digestion, 148, 150, 151, 159

dimensionality, 10, 59, 60, 263, 333, 382 dimer, 160 dimeric, 342, 345 dimerization, 16 dipeptides, 327, 328 diploid, 7, 232, 234, 235, 240, 241, 248 direct measure, 366 directionality, 198 discipline, 60 Discovery, 8, 11, 16, 81, 373 discrete variable, 246 discretization, 268 discriminant analysis, 323, 327 discrimination, 15, 21, 328, 417 discriminatory, 82 disease gene, 9, 19, 22, 407 diseases, 12 disequilibrium, 9, 19, 20, 22, 27, 371 disorder, 408, 409, 410, 411, 412, 413, 414, 416, 417, 418 displacement, 194, 195, 196, 204, 209 dissociation, 15 distribution, 15, 22, 23, 61, 64, 65, 70, 71, 73, 74, 75, 76, 77, 78, 82, 116, 121, 134, 138, 142, 172, 181, 185, 186, 209, 218, 220, 225, 233, 249, 255, 279, 280, 284, 289, 307, 325, 328, 361, 365, 366, 367, 368, 370, 371, 373, 384, 385, 394, 400, 404 distribution function, 73 divergence, 142 diversification, 24 diversity, 14, 15, 17, 18, 25, 60, 141, 146, 239, 284, 312 division, 331 DNA, 12, 1, 3, 4, 20, 21, 42, 43, 59, 60, 61, 62, 78, 81, 82, 83, 84, 85, 90, 91, 92, 93, 95, 96, 97, 142, 147, 148, 149, 150, 151, 152, 155, 156, 157, 158, 159, 160, 161, 162, 163, 216, 226, 232, 233, 252, 254, 255, 256, 257, 267, 273, 284, 352, 362, 364, 371, 372, 373, 407, 409 DNA damage, 93, 97 DNA polymerase, 256 DNA repair, 93, 97 DNA sequencing, 407 doctors, 41, 44 donor, 386 dosage, 15 down-regulation, 90, 229 draft, 173 dropouts, 240 Drosophila, 15, 158, 361 drug action, 15 drug design, 17, 45 drug discovery, 9, 11, 12, 13, 14, 16, 39

Index drug targets, 13, 14, 15 drugs, 9, 10, 11, 12, 15, 16, 43, 47, 55, 265, 417 dualism, 346 duplication, 139, 140, 145, 146 duration, 360 duties, 346

E E-cadherin, 228 ecological, 55 ecologists, 253 ecology, 232 Eden, 273 elasticity, 157, 210, 211, 212 electric charge, 155 electron, 148, 150, 151, 155, 398, 405 electron density, 398 electron microscopy, 148, 150, 155, 405 electrophoresis, 62, 81, 85, 86, 410, 414 elongation, 410 email, 231, 385 emission, 216 encoding, 20, 93, 169, 173, 179, 180, 350, 356, 382 endocrine, 272 endothelium, 2 energy, 149, 166, 167, 168, 169, 172, 173, 175, 194, 195, 196, 197, 204, 206, 211, 278, 282, 284, 286, 288, 290, 291, 292, 293, 294, 303, 304, 308, 311, 314, 327, 334, 339, 345, 348, 350, 351, 352 energy consumption, 351 energy parameters, 175 England, 272, 273, 274, 275 entropy, 177, 212, 282, 285, 287, 288, 291, 366, 367 environment, 17, 20, 278, 279, 293, 345, 349, 354, 355, 389, 391, 394, 395 environmental factors, 20 enzymatic, 13, 256 enzymatic activity, 13 enzymes, 15, 13, 14, 17, 341, 352 Epi, 93 epidemiology, 273 epigenetic, 148, 226 epigenetic alterations, 226 epigenetic code, 148 epithelial cell, 265, 275 epithelial cells, 265, 275 epithelial ovarian cancer, 95 epithelium, 226 epitopes, 15, 375, 376, 381, 383, 384, 386, 387, 388 equality, 30, 32 equilibrium, 22, 194, 196, 197, 198, 200, 205, 206, 212, 279, 280, 282, 288, 347, 350, 351, 352, 357, 359

425

equilibrium state, 196, 197, 198, 205, 206, 347, 350, 352, 357 erythrocyte, 409, 416 erythroid, 408, 415 Escherichia coli, 17, 209, 312 ESI, 409 ESN, 158 esophageal cancer, 51, 54 esophagus, 51 EST, 9, 1, 2, 3, 4, 5, 6, 7 estimating, 67, 77, 78, 83, 195, 205, 234 estimator, 68, 69, 74 estimators, 237, 238, 239, 340 estradiol, 265 estrogen, 265, 269, 273, 276 ethanol, 218 ethics, 415 ethnic groups, 25 etiology, 48, 376 eukaryote, 93, 146, 160, 371 eukaryotes, 96, 141, 371, 373 eukaryotic cell, 12, 147 evolution, 11, 15, 20, 22, 25, 129, 130, 132, 134, 138, 140, 142, 143, 144, 145, 146, 158, 256, 313, 341, 347, 353, 355, 357 evolutionary process, 354, 356 examinations, 54 exclusion, 219, 238, 369 execution, 392, 403 exercise, 357 experimental condition, 60, 66, 284 experimental design, 60, 62, 80, 83, 84 expertise, 403, 409 exposure, 20, 52, 54, 325, 386 expressed sequence tag, 5, 6, 7 external influences, 345 extracellular matrix, 210, 223 extraction, 15, 42, 361, 362, 364, 365, 368, 369, 370, 416 extrapolation, 279

F factorial, 60, 62 failure, 173, 348, 350, 351, 357, 359 false negative, 78, 187, 268 false positive, 67, 75, 174, 364 familial, 54, 252 family, 10, 14, 55, 59, 63, 67, 70, 71, 75, 76, 77, 97, 137, 166, 176, 190, 237, 239, 248, 249, 250, 252, 255, 267, 283, 311, 315, 317, 318, 364 family members, 55, 97 family structure, 252 fats, 61

426

Index

feature selection, 268, 333, 334, 340 feature subset selection, 340 feces, 232 feedback, 93, 96, 97 feeding, 352 females, 13, 51, 52, 53, 215, 216, 248, 249, 250 fertility, 233 fetal, 226, 266 FGF-2, 228 fiber, 12, 62, 147, 148, 149, 150, 151, 152, 155, 156, 157, 158, 159, 160, 161, 162 fibers, 151, 152, 155, 156, 157, 158, 160, 162, 163 fibroblast, 266, 273 fibroblasts, 93, 265, 266 fibronectin, 285, 301, 302, 305, 309 field theory, 62 filament, 159 filters, 42 fingerprinting, 232 fish, 60 fish oil, 60 fixation, 25, 355 flank, 233 flexibility, 16, 42, 155, 160, 161, 162, 205, 211, 268, 343, 386, 389, 404 floating, 394, 396, 397 flow, 12, 254, 354, 392 fluctuations, 157, 198, 199, 201, 212, 313, 366 fluid, 376 fluorescence, 62, 85, 410 focusing, 133, 267, 390 folding, 14, 148, 151, 153, 155, 156, 157, 158, 161, 162, 163, 175, 188, 189, 194, 211, 212, 277, 278, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 291, 293, 294, 296, 298, 299, 302, 303, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 325, 326, 331, 337, 338, 353 folding intermediates, 280, 312 forests, 266, 274, 340 Fort Worth, 99 fossil, 142 France, 1, 127, 147 free energy, 149, 278, 279, 288, 289, 290, 291, 292, 293, 294, 303, 304, 306, 307, 351 freedom, 68, 73, 74, 155, 159, 168, 173, 194, 199, 200, 202, 204, 205, 208, 285 frequency distribution, 249, 353, 371 Freud, 354, 358 function values, 116, 117, 119 functional analysis, 8, 410, 414, 415 functional changes, 415 fungal, 141, 142, 146 fungi, 141, 233

Fur, 167 fusion, 3, 361

G garbage, 392, 393, 394, 395, 396 gas, 288 gastric, 2, 7, 265, 272 gastroenterologist, 48 gauge, 116 Gaussian, 198, 211, 322, 367 gel, 62, 81, 85, 86, 92, 410, 414 gels, 21 GenBank, 385 gender, 55 gene expression, 9, 10, 11, 12, 13, 1, 2, 6, 7, 59, 60, 64, 65, 66, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 89, 90, 95, 97, 147, 215, 216, 217, 218, 220, 224, 225, 226, 227, 228, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 371, 373, 407, 408 gene promoter, 11, 89, 92, 229 gene silencing, 90 gene therapy, 411 gene transfer, 138 genealogy, 247 generalization, 40, 320, 335, 380, 381, 382 generation, 11, 6, 12, 15, 40, 70, 99, 100, 101, 106, 107, 108, 109, 119, 123, 126, 127, 128, 144, 175, 181, 191, 234, 248, 249, 252, 254, 345, 349, 355, 357, 398, 403 genetic alteration, 216, 226 genetic code, 148, 350, 352, 356, 358, 360 genetic defect, 409, 414 genetic disorders, 56 genetic factors, 48, 409 genetic information, 51, 147, 252, 352 genetic marker, 13, 231, 232, 233, 255, 256, 275 genetics, 25, 26, 143, 227, 233, 235, 247, 249, 252, 257, 267, 270, 274, 416, 417 Geneva, 410, 417 genitourinary tract, 216 genome, 9, 11, 15, 16, 1, 3, 4, 5, 6, 7, 19, 20, 22, 27, 42, 60, 89, 90, 93, 94, 97, 129, 130, 131, 137, 138, 140, 141, 142, 143, 145, 146, 148, 150, 162, 166, 224, 227, 228, 232, 234, 252, 260, 267, 274, 317, 341, 346, 361, 362, 364, 365, 366, 369, 371, 372, 373, 407, 408, 409, 415 genome sequences, 9, 1, 130, 141, 364 genome sequencing, 10, 89 genomes, 11, 44, 69, 129, 130, 138, 140, 141, 142, 143, 150, 233, 364, 366, 369, 371

Index genomic, 9, 12, 19, 20, 21, 42, 92, 130, 145, 147, 157, 162, 167, 178, 220, 225, 227, 233, 262, 268, 275, 351, 368, 373, 377, 409, 416 genomic regions, 416 genomics, 10, 14, 16, 4, 59, 62, 63, 65, 67, 70, 74, 79, 144, 146, 165, 188, 259, 264, 265, 266, 268, 269, 274, 352, 364, 365, 372, 373, 407, 408, 409, 416, 417 genotype, 21, 24, 252, 346 genotypes, 22, 232, 233, 241, 248 GGT, 411, 417 Gibbs, 363, 369, 372 GlaxoSmithKline, 43 gliomas, 260, 270 glycine, 295, 401 glycoproteins, 62 glycosylation, 414 God, 357 grading, 226, 228 grants, 5, 79, 253 graph, 171, 177, 188, 208, 220, 239, 242, 254 gravity, 401 grid environment, 403 GroEL, 194, 199, 210, 212 group variance, 65 grouping, 141 groups, 13, 1, 2, 4, 13, 17, 22, 23, 24, 25, 40, 41, 52, 60, 61, 66, 70, 71, 72, 73, 78, 130, 134, 137, 138, 139, 140, 141, 150, 155, 216, 217, 218, 220, 225, 233, 234, 235, 237, 238, 239, 240, 241, 242, 243, 244, 245, 247, 248, 252, 254, 256, 264, 265, 268, 294, 321, 325, 329, 334, 368, 370, 372 growth, 10, 2, 3, 47, 48, 95, 96, 97, 223, 229, 255, 261, 269, 342, 360 growth inhibition, 95 guanine, 3 guidance, 332 guidelines, 272

H H1, 15, 148, 153, 155, 159, 161, 162, 163 H2, 15 haemoglobin, 416, 417 Haifa, 29 Hamiltonian, 199 handling, 218, 390, 400 haplotype, 9, 19, 22, 23, 24, 26, 27 haplotypes, 9, 19, 23, 24 HapMap, 25 health, 20, 41, 409, 416 healthcare, 48 heart, 43, 151 heat, 204

427

height, 366, 367 Heisenberg, 348 Helicobacter pylori, 13 helix, 151, 161, 173, 283, 284, 296, 298, 299, 302, 309, 311, 318, 319, 320, 321, 325, 336, 338, 410, 412, 413 hemagglutinin, 386, 387 hematological, 408, 409 hematology, 16, 407, 408, 411, 415, 416 hematopoietic, 227 heme, 320, 408 hemoglobin, 16, 203, 204, 206, 207, 320, 407, 408, 409, 410, 411, 412, 413, 415, 416, 417 Hemoglobin, vii, 213, 407, 408, 416, 417 hemoglobin (Hb), 413 hemoglobinopathies, 409, 410, 411, 417 hemoglobinopathy, 408, 410, 411, 412, 413, 417 hemostasis, 417 hepatitis, 82 hepatitis C, 82 hepatocellular, 265, 266, 271, 274 hepatocellular carcinoma, 265, 266, 271, 274 hepatocytes, 266 Hessian matrix, 194, 197, 204, 205 heterochromatin, 152, 157, 159 heterogeneity, 216, 268, 269, 282 heterogeneous, 268, 269, 333, 368 heteropolymers, 310 heterozygosity, 233, 234 heuristic, 101, 128, 133, 240 high resolution, 282 high-frequency, 205 high-level, 390 high-risk, 260 Hilbert, 37 Hilbert space, 37 histogram, 61 histological, 216, 270 histology, 48, 49 histone, 92, 93, 95, 96, 148, 149, 150, 153, 155, 157, 158, 159, 160, 161, 162, 163 HIV, 211, 386, 388 HIV-1, 211, 386, 388 HLA, 387, 388 Holland, 127, 358 homogenized, 217 homolog, 96 homologous chromosomes, 3 homologous proteins, 331 homology, 12, 13, 15, 17, 132, 133, 150, 165, 167, 170, 175, 176, 185, 186, 188, 337, 339, 354, 363 homozygote, 236 Hong Kong, 310

428

Index

horizontal gene transfer, 138 hormonal therapy, 260, 269 hormone, 52, 273, 351, 364 hormones, 364 host, 146, 386, 390, 394 hot spots, 198 House, 39, 407 HPC, 145 human, 9, 10, 15, 1, 2, 3, 4, 5, 6, 7, 8, 14, 17, 19, 20, 21, 24, 25, 26, 27, 42, 45, 49, 54, 55, 56, 59, 85, 89, 90, 91, 92, 93, 94, 95, 96, 97, 140, 146, 217, 225, 227, 228, 229, 257, 265, 266, 272, 273, 274, 275, 283, 314, 355, 361, 362, 365, 370, 371, 372, 373, 385, 386, 388, 408, 409, 410, 411, 412, 414, 416 human ES, 2, 3, 5 human genome, 9, 10, 3, 4, 5, 7, 19, 27, 89, 90, 93, 94, 140, 146, 371 humans, 20, 25, 27, 62, 79, 233, 355 Hungarian, 417 hybrid, 240, 268, 335, 339 hybridization, 66, 91, 92, 96, 218, 228, 364 hydrodynamics, 200 hydrogen, 14, 146, 191, 280, 295, 310 hydrogen atoms, 295 hydrogen bonds, 14, 280, 310 hydrolysis, 17, 210 hydrophobic, 280, 308, 311, 312, 321, 325, 330, 333, 334 hydrophobic interactions, 280 hydrophobicity, 320, 321, 325, 331, 333, 334, 337 hypercycle, 347 hypermethylation, 229 hypothesis, 13, 54, 55, 59, 61, 63, 64, 65, 66, 67, 70, 73, 74, 77, 78, 81, 135, 143, 146, 152, 285, 326, 384 hypothesis test, 59, 61, 63, 65, 66, 70, 73, 81 hypoxia, 95

I id, 179, 290, 357 identification, 14, 6, 7, 17, 25, 26, 43, 48, 61, 91, 132, 216, 226, 228, 265, 267, 278, 315, 362, 372, 373, 386, 387, 388, 407, 413, 415 identity, 14, 175, 176, 179, 180, 181, 183, 184, 185, 186, 187, 188, 200, 248, 281, 283, 299, 315, 333, 335, 336 IL-1, 291, 292 IL-2, 291, 292 IL-8, 226 Illinois, 231 image analysis, 405 images, 80, 150, 155

imaging, 62, 67, 216 imaging modalities, 62 immune response, 269, 276, 386 immunoglobulin, 17, 210, 284, 309 immunological, 387 immunology, 408 immunoprecipitation, 91, 92, 96, 97, 364 immunoreactivity, 228 implementation, 40, 101, 108, 130, 133, 134, 136, 137, 139, 140, 253, 357, 390, 391, 392, 394, 400, 403 in situ, 162, 171, 218 in transition, 226 in vitro, 10, 15, 39, 40, 62, 96, 151, 156, 380, 381, 387 in vivo, 10, 15, 17, 39, 40, 148, 149, 151, 155, 156, 157, 159, 228, 265, 266, 364, 371, 409 inactive, 161 inbreeding, 252 incidence, 50, 52, 53, 55, 216 inclusion, 136 independence, 22, 66, 70, 72, 73, 74, 79, 381 independent variable, 351 indexing, 35, 378, 392 India, 339, 410, 411, 417 Indian, 417 indication, 151 indices, 333, 382, 396 indigenous, 20 individual development, 355 Indochina, 410 induction, 340 industrial, 12, 16, 390 industrial application, 390 inefficiency, 16, 195, 251 inequality, 30, 32, 67, 116, 117 infancy, 418 infection, 91 infectious, 376, 386 infinite, 346, 348, 353, 356 influenza, 386, 387 information exchange, 94 information technology, 12, 39, 41, 44 informed consent, 20 infrastructure, 12, 346, 390, 394 inheritance, 232, 233, 235, 237, 238 inherited, 143, 408, 410, 413, 414 inherited disorder, 408 inhibition, 95, 381 inhibitor, 311 inhibitors, 17, 387 initiation, 66, 80, 361, 362, 365, 370, 371, 387 injection, 60, 61

Index innovation, 11 inorganic, 346 insertion, 3, 287, 289 insight, 12, 17, 48, 108, 142, 193, 195, 198, 208, 209, 267, 326, 411, 415 inspection, 319, 372 Inspection, 137 instability, 260, 261, 262, 263, 279, 291, 410, 413 insulin, 320 integration, 4, 16, 42, 74, 264, 268, 273 integrity, 395, 414 Intel, 248 interaction, 9, 12, 19, 20, 26, 42, 43, 93, 148, 149, 160, 195, 196, 197, 223, 249, 266, 284, 326, 342, 343, 362, 376, 387, 398 interactions, 9, 14, 19, 20, 22, 43, 96, 150, 155, 157, 159, 160, 161, 168, 169, 171, 172, 196, 197, 199, 200, 213, 266, 278, 280, 282, 284, 287, 288, 291, 309, 310, 313, 371, 377, 381, 388 interdisciplinary, 41 interface, 16, 12, 139, 141, 162, 253, 384, 385, 389, 390, 394, 395, 398, 402, 404 interferon, 62, 82 interleukin, 226, 229, 309 interleukin-1, 309 internal clock, 351 internal constraints, 346 internal time, 348, 350, 351, 357 internalization, 354, 355 internalizing, 355 International Classification of Diseases, 49, 55 internet, 404 Internet, 26, 253 interphase, 150, 151 interrelations, 354 interval, 50, 67, 68, 171, 181, 185, 293, 294, 295, 299 intervention, 166 intracranial, 418 intravenous, 216 intravesical chemotherapy, 216 intrinsic, 156, 212, 285, 311, 352 intron, 362, 370 intuition, 199 invasive, 216, 226, 227, 228 invertebrates, 233 ionization, 414 ionizing radiation, 86, 151 Ireland, 165, 188 irradiation, 20, 77 ISCO, 163 island, 97, 370 isolation, 6, 217, 413

429

isomerization, 278 isomers, 148 isotropic, 198 Israel, 29 Italy, 315, 340, 416 iteration, 15, 102, 108, 239, 240, 341, 345

J jackknife, 319, 320, 321, 326, 327, 328, 329, 330, 331, 332, 333, 335, 336 Japan, 11, 20, 89, 94, 361, 389, 405 Japanese, 26 Java, 15, 239, 375, 383, 385, 404 JAVA, 42, 116 jobs, 11, 99, 100, 101, 102, 103, 104, 109, 116, 119, 126, 403 joining, 134, 144, 155 Jun, 227, 228 Jung, 73, 74, 75, 77, 82 justification, 25, 246

K kelp, 257 kernel, 322, 382 kidney, 10, 47, 54, 86, 260, 271 kin selection, 13, 231, 233 kinase, 213, 281, 284, 311, 352, 359 kinetics, 213, 278, 282, 284, 285, 286, 289, 290, 308, 310, 311, 312, 313, 314 kinship analysis, 13, 231 knockout, 265, 266 Korea, 193, 209, 259, 269

L L1, 15, 285, 354 L2, 15, 285, 354 labeling, 218 labor, 355 lactoglobulin, 150, 159 Lagrangian, 100, 101 landscapes, 211, 286, 308, 314 language, 16, 343, 354, 355, 357, 389, 390, 391, 392, 394, 395, 396, 397, 398, 399, 400, 401, 402, 403, 404, 405 large-scale, 11, 129, 130, 131, 133, 135, 136, 140, 142, 144, 260, 365, 391 larvae, 255 laser, 218 lattice, 308, 325 law, 151, 345, 353, 354, 355, 358, 360 laws, 13, 166, 232, 285, 354

430

Index

learning, 41, 169, 172, 177, 178, 188, 218, 219, 225, 321, 330, 331, 335, 340, 382 left-handed, 148, 151, 162 leukemia, 62, 84, 260, 271 licenses, 250 life cycle, 223 life sciences, 39 life span, 351 ligand, 15, 17, 43, 213 ligands, 14, 15, 43, 45, 377, 387, 388 likelihood, 134, 137, 140, 144, 145, 232, 237, 238, 239, 240, 252, 253, 255, 256, 332 limitation, 138, 156, 345, 346, 362, 364, 369 limitations, 4, 135, 140, 159, 171, 210, 234 linear, 11, 61, 70, 74, 99, 101, 116, 126, 127, 128, 151, 155, 158, 159, 166, 175, 195, 199, 200, 206, 218, 220, 244, 308, 320, 321, 331, 335, 336, 340, 344, 352, 380, 382 linear function, 166 linear model, 74 linear programming, 11, 99, 101, 127 linear regression, 70, 320, 321 linkage, 20, 26, 27, 267 links, 95, 148, 287, 288, 291, 295, 306 Linux, 116, 136, 249, 383 liquid crystals, 157 liquid nitrogen, 217 liver, 48, 260 liver cancer, 48 loading, 194, 209 localization, 366, 367 location, 92, 94, 97, 100, 102, 110, 127, 150, 162, 281 locus, 21, 22, 25, 26, 232, 233, 234, 235, 236, 239, 241, 243, 244, 245, 246, 247, 248, 249, 250, 409, 416 lognormal, 71, 82 London, 146, 310, 359 long distance, 369 long period, 296 losses, 139 luciferase, 92 Luciferase, 92 lumen, 223 luminescence, 92 lung, 10, 47, 54, 91, 260, 265, 266, 271, 275 lung cancer, 54, 266 lymph, 220, 270, 382 lymph node, 220, 382 lymphocyte, 388 lymphocytes, 387 lymphoma, 55, 80, 260, 268, 271, 275 lymphomas, 50

lysine, 93, 96, 150, 413

M M.O., 211 machine learning, 15, 166, 176, 186, 188, 189, 331, 332, 340, 375, 377 machinery, 356, 362 machines, 167, 176, 178, 189, 211, 213, 335, 339, 388, 391 macromolecules, 158, 213, 391, 399 Madison, 92 magnetic, 62, 152, 160, 200, 216 magnetic resonance, 62, 216 magnetic resonance imaging (MRI), 62, 79, 80, 216 Maine, 44 maintenance, 12, 346, 351 major histocompatibility complex, 376, 387 males, 13, 51, 52, 53, 215, 216, 248, 249, 250 malignant, 5, 226, 270 mammal, 370 Mammalian, 14 mammalian cell, 90, 93, 371 mammalian cells, 90, 93, 371 mammals, 370, 371, 373 management, 177, 227, 385, 390, 391, 393, 394, 402, 403 manipulation, 10, 39, 43, 152, 155, 157, 344 mapping, 9, 19, 22, 26, 43, 96, 143, 176, 218, 220, 242, 243, 347, 349, 353, 355, 368, 373, 416 Markov, 134, 145, 195, 196, 212, 237, 238 Markov chain, 145 masking, 42 mass spectrometry, 62, 87, 409, 414, 416 Massachusetts, 225 Massachusetts Institute of Technology, 225 maternal, 226, 236 mathematical logic, 343 mathematics, 200, 342, 357 matrix, 15, 22, 62, 73, 74, 78, 91, 134, 138, 144, 169, 170, 171, 172, 174, 176, 177, 179, 194, 196, 197, 198, 199, 200, 204, 205, 207, 210, 223, 229, 244, 294, 295, 299, 324, 363, 375, 380, 383, 384, 394, 398, 401 matrix library, 91 matrix protein, 210 maturation, 15, 17, 86, 212 Maximum Likelihood, 133, 134, 136 Maya, 231 Mb, 369 measurement, 10, 59, 62, 71, 72, 85, 152, 267, 329, 341, 344, 345, 346, 366, 367, 381 measures, 22, 25, 26, 48, 74, 149, 173, 175, 225, 267, 268, 323, 382

Index mechanical energy, 194 mechanical properties, 155, 161, 212, 358 media, 213 medicine, 10, 14, 16, 39, 40, 41, 42, 43, 259, 270, 271, 273, 274, 275, 407, 408, 409, 413, 417, 418 melanin, 20, 23 melanoma, 10, 47, 48, 52, 54, 382 melanosomes, 23 melting, 285 melting temperature, 285 membership, 178, 242, 330 membranes, 351 memory, 116, 130, 135, 136, 240, 248, 249, 352, 391, 393, 394, 395, 396, 404 men, 54, 216 Mendeleev, 352 mental development, 355 mercury, 21 mesoscopic, 157 messenger RNA, 6 meta-analysis, 267, 268, 274, 275 metabolic, 13, 143, 346, 349, 350, 352, 354, 358, 359 metabolism, 12, 93, 95, 143, 145, 146, 147, 156, 157, 346, 347, 348, 349, 351, 352, 359 metabolomics, 62, 260 metaphase, 155 metastases, 260 metastasis, 217, 220, 226, 265, 266, 270, 274 metastatic, 6, 216, 267, 270, 271, 272 metastatic disease, 272 methylation, 93, 96, 216, 226 metric, 9, 29, 30, 32, 37 metric spaces, 9, 29, 37 Mg2+, 359 MHC, 376, 377, 380, 387, 388 mice, 266, 409, 416 microarray, 13, 15, 12, 59, 60, 66, 67, 69, 70, 73, 77, 78, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 94, 95, 96, 97, 216, 217, 218, 220, 225, 227, 228, 229, 259, 260, 261, 262, 263, 266, 267, 268, 270, 272, 273, 274, 275, 361, 362, 364, 365, 368, 408 microarray technology, 92, 216, 225, 267, 362 Microarrays, 81, 83, 87, 272, 416 microorganisms, 13 microRNAs, 90, 96, 98 microRNAs (miRNAs), 90 microsatellites, 232, 233, 234, 252, 254 microscope, 150 microscopy, 148, 150, 155, 195, 210, 405 migration, 224, 226 mimicry, 387

431

mining, 9, 10, 1, 3, 7, 12, 40, 47, 48, 49, 51, 54, 55, 94, 218, 332, 409, 414 Ministry of Education, 94 MIP, 250 miRNAs, 91 mirror, 406 misfolded, 282 misfolding, 287, 289 MIT, 189, 358, 360, 372 mitochondria, 143, 145 mitochondrial, 93, 95, 143, 145, 146 mitosis, 226 mitotic, 93, 96, 151 modalities, 62, 216 model reduction, 195, 200 modeling, 12, 17, 18, 43, 96, 148, 150, 158, 160, 162, 163, 193, 195, 210, 213, 267, 268, 274, 275, 307, 355, 377, 381, 404, 409, 410, 411, 413 modulation, 97 modules, 4, 210, 344, 358, 371, 394, 400 MOE, 403 molecular biology, 232, 282, 352, 405, 409 molecular dynamics, 12, 16, 18, 149, 150, 160, 168, 193, 194, 196, 210, 308, 311, 403 molecular markers, 216, 233, 256 molecular mechanisms, 4, 25 molecular structure, 16, 43, 196, 199, 200, 389, 390, 391, 399, 401, 404, 405, 411, 413 molecular weight, 21, 320, 334 molecules, 15, 43, 62, 130, 150, 208, 213, 305, 306, 307, 352, 398 Monte Carlo, 14, 65, 134, 145, 150, 166, 237, 238, 277, 287, 296, 305, 307, 313 Monte Carlo method, 134, 296 Monte-Carlo, vi, 153, 154, 155, 277, 286, 287, 289, 290, 294, 295, 296, 298, 299, 301, 302, 303, 306, 307 Monte-Carlo simulation, 153, 155, 286, 287, 296, 299, 307 morphological, 130, 133, 353 mortality, 216 Moscow, 277, 310, 357 moths, 130 motion, 194, 197, 198, 199, 200, 203, 204, 205, 210, 351 motivation, 103 motor activity, 223 mouse, 15, 265, 266, 274, 361, 365, 370 mouse model, 265, 266, 274 movement, 149 MPI, 403 mRNA, 2, 5, 229, 373 mucosa, 226

432

Index

multidimensional, 244, 282 multiple sclerosis (MS), 382, 386, 387 multiplicity, 62, 91 multiplier, 37, 127 muscle, 194, 216, 227, 314 mutagenesis, 4, 313 mutant, 43, 132, 278, 294 mutation, 62, 233, 238, 246, 266, 279, 285, 286, 294, 295, 409, 410, 411, 413, 414, 415, 417, 418 mutations, 1, 5, 23, 64, 179, 189, 232, 235, 237, 246, 252, 278, 279, 280, 283, 286, 294, 295, 312, 347, 409, 410, 414, 416 mutuality, 231 myelin, 386 myeloid, 62, 271 myosin, 21

N NA, 12, 20, 93, 147, 150, 157, 417 nanomachines, 212 nanometer, 162 nanostructures, 417 National Academy of Sciences, 83, 86, 271, 272, 273, 274, 275 National Institute of Neurological Disorders and Stroke, 386 National Institutes of Health, 40, 375 National Science Foundation, 126 natural, 13, 34, 35, 36, 68, 108, 157, 197, 205, 231, 242, 256, 265, 280, 347, 353, 376, 377, 378, 380 natural selection, 280, 347 neck, 260, 270 neglect, 282, 287, 291 nematodes, 141 neoplastic, 56, 376 neoplastic diseases, 376 nervous system, 386 network, 12, 14, 15, 12, 90, 177, 178, 189, 191, 193, 195, 198, 199, 201, 203, 204, 207, 208, 209, 211, 212, 213, 218, 225, 266, 278, 287, 291, 306, 314, 315, 317, 321, 325, 330, 332, 333, 335, 337, 338, 341, 349, 352, 356, 359, 360 networking, 100 neural network, 12, 14, 165, 167, 176, 177, 178, 184, 189, 190, 191, 218, 225, 315, 317, 320, 321, 325, 330, 331, 332, 333, 335, 337, 338 neural networks, 12, 165, 167, 176, 177, 178, 184, 189, 190, 191, 320, 331, 333, 335, 338 neuroblastoma, 275 neuroimaging, 81 New England, 81, 270, 271 New Jersey, 21, 310, 371

New York, 26, 56, 80, 84, 85, 86, 212, 309, 311, 312, 337, 339, 359, 360, 371 New Zealand, 340 next generation, 13 Nielsen, 27 NIH, 40, 79, 386, 390 nitric oxide, 17 nitric oxide synthase, 17 nitrogen, 217 NMR, 14, 62, 80, 84, 170, 179, 181, 189, 200, 277, 289, 305, 310, 311, 314, 403 nodes, 101, 106, 109, 110, 112, 117, 119, 120, 121, 122, 124, 125, 139, 141, 142, 171, 248 noise, 70, 71, 136, 170, 171, 177, 272, 332 non-Hodgkin lymphoma, 55 non-human, 55 non-native, 282, 287, 309 non-native interactions, 282, 287 normal, 9, 12, 3, 5, 6, 7, 8, 19, 20, 25, 27, 62, 64, 65, 70, 75, 76, 77, 79, 80, 83, 93, 97, 193, 194, 195, 197, 198, 202, 203, 204, 205, 206, 207, 208, 210, 211, 212, 213, 217, 331, 385, 408, 410, 411, 412, 413 normal distribution, 64, 65, 70, 76, 83, 331, 385 normalization, 218 norms, 325 North America, 338 NOS3, 224, 225 N-terminal, 162, 283, 296, 298, 299, 301, 302, 303 nuclear, 93, 145, 159, 200, 229, 255 nuclear magnetic resonance, 200 nuclease, 148, 150, 310 nucleation, 279, 311 nuclei, 14, 155, 277, 279, 280, 281, 282, 286, 300, 305, 307, 310 nucleic acid, 43, 144, 162, 210, 352 nucleoprotein, 12, 147, 148 nucleosome, 148, 149, 150, 151, 153, 155, 156, 157, 158, 159, 160, 161, 162, 163, 372, 373 nucleosomes, 148, 149, 150, 151, 155, 156, 157, 158, 159, 161, 163, 362 nucleotides, 133, 352 nucleus, 148, 156, 157, 278, 279, 280, 282, 283, 284, 286, 291, 293, 294, 302, 308, 309, 312, 313 null hypothesis, 63, 64, 65, 73, 74, 77, 78, 384 nutrition, 342

O observations, 48, 55, 63, 151, 279, 382 odds ratio, 264, 273 Oedipus, 354, 355 Oedipus complex, 354, 355 Ohio, 20

Index oil, 60 oligomers, 160 oligonucleotide arrays, 59, 80, 83 olive, 60 olive oil, 60 oncogene, 5, 90, 96, 97, 98, 216, 228, 270 Oncogenesis, 1 oncology, 273 Oncology, 48, 49, 55 online, 10, 41, 47, 146, 239 on-line, 132, 143 online information, 10, 47 operating system, 250, 383, 391, 394 operator, 200, 324, 328, 344, 348, 349 opioid, 387 optical, 152, 158, 311 optical tweezers, 152, 158 optimization, 12, 14, 29, 37, 100, 127, 158, 163, 237, 238, 325, 338, 340 organ, 217, 225 organelle, 146, 223 organelles, 143 organic, 311 organism, 14, 43, 60, 94, 142, 232, 252, 253, 351, 355, 359, 386, 407 orientation, 14, 103, 168, 171, 173 oscillation, 106 oscillator, 201, 204, 205, 206 osteomalacia, 20 outliers, 332 ovarian cancer, 6, 275 ovary, 2, 52, 151 oxidative, 410 oxidative stress, 410 oxide, 17, 228 oxygen, 410 oyster, 155 ozone, 20

P p53, 94 Pacific, 310, 405 packaging, 150 pairing, 359 pancreas, 6 paradox, 159, 309, 357 parallel implementation, 137 parallelism, 140 parallelization, 135 paramagnetic, 310 parameter, 15, 64, 68, 71, 73, 82, 134, 181, 203, 205, 207, 211, 242, 248, 249, 267, 285, 341, 345, 348, 349, 350, 351, 356, 382, 391, 396

433

parameter estimation, 267 parasite, 17 parentage, 13, 231, 232, 233, 252, 254, 255 parents, 232, 234, 235, 236, 240, 243, 248, 249 Paris, 147, 358, 359 Parkinson, 44 particles, 150, 153, 344 partition, 109, 235, 237, 238, 247, 254, 256, 293 paternal, 235 paternity, 232, 233, 252, 254, 256, 257 pathogenesis, 225, 226, 376, 409, 410, 411, 413, 414, 415 pathogenic, 13, 14 pathogens, 386, 388 pathology, 408, 409 pathways, 4, 95, 97, 211, 224, 226, 264, 265, 266, 267, 269, 273, 278, 279, 280, 282, 284, 287, 291, 292, 296, 298, 299, 306, 307, 308, 309, 311, 364 patient care, 41 patients, 10, 12, 13, 47, 48, 50, 52, 55, 82, 215, 216, 217, 220, 224, 226, 227, 228, 259, 260, 261, 262, 263, 264, 266, 267, 268, 269, 270, 271, 272, 273, 275, 386, 410, 411 PCA, 205 PCR, 4, 21, 60, 92, 226, 232, 233 pediatric, 271 pedigree, 13, 231, 237, 238, 252, 253, 255, 256 pelvis, 226 penalties, 17, 102, 103, 133, 144 penalty, 9, 11, 29, 30, 37, 99, 100, 101, 103 Pennsylvania, 59 peptide, 15, 42, 308, 327, 375, 376, 377, 378, 380, 381, 382, 383, 384, 385, 386, 387, 388 peptides, 15, 13, 18, 43, 319, 321, 323, 327, 372, 375, 376, 377, 378, 380, 381, 382, 383, 385, 386, 387, 388 periodic, 352, 400 periodic table, 400 periodicity, 93 peripheral blood, 376, 382 permit, 388 personal communication, 254 perturbation, 106, 206 pH, 283, 314 pharmaceutical, 16 pharmaceutical companies, 16 pharmacogenomics, 16 pharmacology, 408 phenotype, 3, 15, 266, 346 phenotypes, 9, 19, 20, 224, 226, 229, 268, 411 phenotypic, 25, 95, 354, 415 Philadelphia, 254 philosophy, 342

434

Index

phosphorylation, 93, 96 photoreceptor, 27 phylogenetic, 11, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 145, 146, 414 phylogenetic tree, 11, 129, 130, 133, 134, 136, 138, 139, 143, 144, 145, 146 phylogeny, 130, 133, 134, 137, 139, 140, 143, 144, 145 physical properties, 161, 382, 387 physical world, 14, 341, 342, 345, 357 physicists, 155 physicochemical, 333, 335, 336 physico-chemical properties, 14, 315, 321, 333, 335, 336 physics, 160, 308, 313, 342, 344 physiological, 12, 25, 80, 133, 150, 151, 152, 222, 223, 226, 351, 376 physiological factors, 376 pilot study, 41 pipelines, 11, 129, 136, 165 planning, 10, 59, 60, 61, 65, 69, 70, 79, 81, 84, 135 plants, 13, 231, 232, 233, 370, 371, 373 plaque, 91 plasma, 414, 418 plasma proteins, 414, 418 plasmid, 92 plastic, 152, 213 plasticity, 157, 210 platforms, 4, 225, 250, 262, 263, 267 Plato, 342, 350, 353, 357 play, 9, 19, 20, 29, 226, 242, 282, 283, 326, 332, 333, 351, 377 Pleistocene, 146 PLO, 406 plug-in, 399, 405 PLUS, 84, 383, 384 point mutation, 279, 312 polarity, 401 pollination, 232 polydactyly, 372 polygamy, 250 polygenic, 25 polymer, 147, 212, 213 polymer chains, 212, 213 polymerase, 159, 160, 232, 257, 373 polymerase chain reaction, 232, 257 polymerization, 352 polymorphism, 9, 6, 19, 25, 149, 156, 160, 162, 226, 353 polymorphisms, 9, 1, 4, 5, 6, 7, 20, 234, 257, 411 polynomial, 178, 241, 242, 244, 382 polypeptide, 14, 288, 315, 317, 321, 337, 398

polypeptides, 328 polyploid, 7 polyunsaturated fat, 80 polyunsaturated fatty acid, 80 polyunsaturated fatty acids, 80 pools, 352 poor, 4, 78, 134, 188, 216, 228, 260, 261, 263, 266, 268 poor performance, 260 population, 24, 25, 55, 232, 233, 234, 237, 238, 239, 241, 249, 250, 252, 254, 257, 267, 273, 363, 409, 416, 417 population size, 239 portability, 392 positive correlation, 53 positron, 216 positron emission tomography, 216 post-translational, 93, 96, 148, 157 post-translational modifications, 148, 157 power, 10, 13, 59, 60, 61, 62, 63, 64, 65, 67, 69, 70, 71, 72, 75, 76, 77, 78, 79, 81, 84, 86, 137, 177, 178, 195, 231, 234, 267, 268, 273, 332, 382 pragmatic, 355 pRb, 90 pRB, 97 predictability, 274 predictive accuracy, 273, 327, 328 predictive model, 264, 346, 382 predictive models, 346 predictors, 12, 165, 167, 175, 176, 182, 186, 187, 217, 266, 332, 382 pre-existing, 4 preference, 370 preprocessing, 217, 218 press, 87 prevention, 48, 409 preventive, 80 prices, 105 primary data, 40 primary tumor, 265, 271 primates, 141 primitives, 398 principal component analysis, 205 prior knowledge, 371 private, 41, 44 probability, 50, 64, 65, 67, 73, 74, 75, 76, 101, 103, 134, 173, 176, 178, 190, 209, 240, 268, 283, 289, 293, 294, 295, 321, 324, 382 probability density function, 190 probability distribution, 134, 209 probe, 218 production, 20, 140, 188, 408 progenitor cells, 274

Index prognosis, 216, 224, 226, 260, 261, 267, 268, 270, 271, 272, 273, 275, 276 prognostic marker, 13, 229, 259, 260, 264, 269 prognostic value, 262, 264 program, 11, 16, 6, 22, 41, 50, 99, 101, 106, 110, 117, 131, 134, 144, 160, 180, 217, 220, 225, 228, 232, 244, 246, 248, 255, 295, 335, 389, 390, 391, 392, 393, 394, 395, 398, 399, 400, 402, 403, 404 programming, 14, 16, 29, 37, 100, 128, 292, 306, 383, 389, 390, 391, 392, 394, 395, 398, 402, 403, 404, 405 proliferation, 62, 96, 224, 226, 265, 267, 269 promoter, 11, 15, 89, 90, 91, 92, 93, 95, 96, 149, 226, 229, 361, 362, 363, 364, 365, 366, 368, 369, 370, 371, 372, 373 promoter region, 11, 15, 89, 90, 361, 362, 364, 365, 368, 370 propagation, 177, 178, 183, 189, 191, 212, 330 property, iv, 9, 29, 30, 34, 43, 101, 104, 148, 170, 235, 236, 241, 242, 243, 247, 252, 321, 334, 344, 347, 348, 349, 351, 353, 399, 400, 414 prophase, 152 proposition, 30, 31, 104, 105 prostate, 2, 5, 6, 51, 52, 54, 260, 265, 272 prostate cancer, 51, 54, 272 protection, 20 protein arrays, 62 protein binding, 212 protein conformations, 167 protein engineering, 210, 309, 311, 312, 313 protein family, 143, 317 protein folding, 188, 194, 278, 279, 282, 284, 285, 286, 287, 288, 306, 307, 308, 309, 310, 311, 312, 313, 314, 325, 331, 338, 353 protein function, 316, 336, 415 protein secondary structure, 190, 191, 211, 321, 337, 338, 411 protein sequence, 12, 41, 42, 136, 145, 165, 185, 282, 316, 329, 334, 335, 337, 352, 371, 385 protein structure, 12, 166, 167, 168, 169, 170, 171, 175, 186, 187, 188, 189, 190, 191, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203, 206, 208, 209, 212, 213, 280, 282, 283, 286, 287, 294, 307, 310, 317, 318, 330, 334, 337, 339, 358, 410, 411, 413 protein structure analysis, 191 protein synthesis, 146, 352 protein-coding sequences, 385 protein-protein interactions, 266 proteobacteria, 145 proteolysis, 97 proteome, 16, 85, 142, 143, 146, 407, 408, 410, 416 proteomes, 130, 144, 146

435

proteomics, 10, 59, 62, 260, 273, 408, 409, 413, 416, 417 prothrombin, 16, 407, 408, 413, 414, 415, 418 prothrombin complex concentrates, 413, 418 prothrombin deficiency, 413, 414, 415, 418 protocol, 20, 91, 166, 167, 173, 175, 186, 218 prototyping, 403, 404 proxy, 397 pruning, 139 PSD, 42 pseudo, 166, 172, 173, 317, 321, 329, 331, 338, 339 PSI, 144, 167, 181, 182, 188 psychology, 354 public, 11, 6, 7, 41, 42, 69, 89, 91, 132 Puerto Rican, 26 PUFA, 60, 61, 66, 68 PUFAs, 60, 66 P-value, 268 PVC, 358

Q QSAR, 17 quadrupole, 21 quality control, 413 quality of life, 260 quantization, 330 quantum, 15, 341, 344, 345, 346, 348, 357, 359, 360 quantum computers, 359 quantum mechanics, 15, 341, 345 quantum state, 345, 346 quantum theory, 344, 357 Quebec, 51 Quercus, 257 query, 10, 7, 39, 41, 132, 179, 180, 181, 182, 183, 184, 185, 186, 187, 225, 326, 327, 329

R R&D, 43 race, 22 racial differences, 21, 22, 23, 24, 25 racial groups, 22, 23 radiation, 20, 25, 26, 54, 86, 140, 151 radical cystectomy, 220 radiotherapy, 220 radius, 400 radius of gyration, 400 random, 11, 22, 50, 62, 64, 70, 74, 78, 99, 100, 101, 102, 103, 116, 120, 123, 169, 173, 181, 237, 238, 240, 248, 249, 262, 263, 266, 272, 274, 289, 291, 310, 321, 322, 333, 335, 347, 363, 384 random numbers, 120, 240 random walk, 173

436

Index

randomness, 122 range, 11, 15, 70, 79, 129, 138, 150, 157, 162, 167, 176, 177, 183, 184, 190, 197, 204, 233, 247, 251, 253, 278, 286, 310, 361, 369, 371, 372, 408 rat, 60, 66, 80, 86, 227, 228, 266 RBF, 322, 335 reactant, 351 reaction rate, 293 reactivity, 386, 387 reading, 52, 312, 392, 397, 400 reagent, 217, 409 reality, 51, 247, 342, 344, 345, 353, 354, 355 reasoning, 332, 392 receptor sites, 43 receptor-positive, 273 receptors, 27, 377 recognition, 13, 14, 16, 17, 181, 188, 326, 338, 357, 372, 376, 377, 381, 386, 388 recombination, 43, 93, 356 reconciliation, 139 reconstruction, 13, 130, 132, 136, 137, 138, 142, 143, 144, 145, 146, 167, 170, 172, 173, 175, 178, 185, 189, 231, 232, 233, 234, 236, 237, 238, 239, 240, 241, 242, 244, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 257, 363 recurrence, 216, 267, 268 recursion, 292 red blood cell, 409, 416 reductionism, 353, 358 redundancy, 132, 180, 181, 329 refining, 168 reflection, 342, 345, 355 reflectivity, 358 regeneration, 350 regional, 50, 52 Registry, 50 regression, 14, 69, 70, 266, 274, 315, 317, 320, 321, 322, 332, 334, 335, 336, 337, 340, 346, 382, 387 regression analysis, 387 regression method, 266, 320 regular, 41, 54, 151, 178, 218 regulation, 12, 15, 65, 74, 90, 92, 93, 95, 96, 97, 98, 147, 149, 150, 157, 222, 223, 226, 229, 267, 361, 362, 371, 373 regulators, 90, 92, 93, 226, 229, 372 rejection, 63, 69, 73, 74 relational database, 15, 375, 409 relationship, 13, 12, 54, 55, 91, 104, 132, 169, 218, 231, 235, 236, 237, 239, 246, 247, 255, 256, 262, 286, 330, 365, 380 relationships, 11, 13, 129, 130, 132, 137, 138, 139, 140, 141, 142, 169, 218, 220, 231, 232, 234, 237, 238, 246, 252, 253, 254, 256, 320, 331, 339, 353

relaxation, 11, 99, 100, 101, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 119, 126, 127, 128, 159, 310 reliability, 14, 40, 185, 259, 261, 366, 369 remodeling, 149, 159, 160, 362 renal, 226, 271 renal cell carcinoma, 271 repair, 93, 97, 150, 346, 349, 353, 359, 410 repair system, 359 replacement rate, 146 replication, 83, 92, 93, 95, 96, 97, 150, 226, 353 repression, 94 reproduction, 10, 47, 48, 223, 255, 352 reputation, 102 resection, 13, 215, 216 residues, 12, 13, 14, 132, 150, 165, 167, 170, 171, 173, 176, 181, 183, 184, 198, 200, 202, 203, 204, 205, 279, 281, 285, 287, 288, 289, 290, 291, 295, 296, 297, 298, 299, 300, 301, 302, 303, 304, 309, 311, 313, 314, 326, 327, 328, 334, 410 resolution, 62, 135, 146, 148, 159, 167, 170, 172, 179, 181, 186, 200, 282, 313, 319, 353 resources, 3, 4, 97, 101, 130, 132, 135, 140, 143, 402 respiratory, 93 retinoblastoma, 90 returns, 110, 111, 344 reverse transcriptase, 211 Reynolds, 372 Rho, 7 rhythms, 93, 96 ribosomal, 211, 218 ribosomal RNA, 211, 218 ribosome, 280 rice, 15, 361, 365, 369, 370 rickets, 20 rigidity, 155 risk, 12, 50, 54, 226, 229, 255, 260, 268 risk factors, 268 risks, 12, 54 RNA, 3, 42, 90, 97, 159, 160, 212, 217, 218, 310, 352, 361, 373 robustness, 94, 211, 217, 238 rodents, 141 room temperature, 217 Root Mean Square Deviation, 167 routines, 392 routing, 100, 102, 127 Russia, 309 Russian, 277, 307, 359, 360 Russian Academy of Sciences, 277

S S phase, 93

Index Saccharomyces cerevisiae, 142, 228, 372 saline, 60 salmon, 239, 248, 249, 255 salt, 150, 151, 153, 155, 158, 162, 280 sample, 10, 13, 21, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 86, 102, 185, 186, 216, 218, 219, 220, 232, 237, 239, 248, 252, 262, 263, 264, 267, 320, 332, 382, 392, 398, 400 sample mean, 64 sampling, 16, 18, 64, 73, 137, 138, 142, 194, 219, 232, 233, 240, 242, 253, 262, 372 sampling distribution, 64, 73 saturated fat, 60 saturated fatty acids, 60 savings, 4, 119 scalability, 273, 403 scalable, 146, 225 scaling, 130, 219, 285, 311 scaling law, 285 scatter, 381 scheduling, 102, 126, 127 Schmid, 44, 227, 274, 313 scientific computing, 389, 390, 391, 395, 402, 403, 404 scores, 78, 133, 268, 318, 319, 380, 383, 384, 385, 415 scripts, 389, 392, 401, 404 sea urchin, 163 seals, 148 search, 11, 15, 18, 25, 40, 42, 50, 77, 91, 92, 99, 101, 103, 106, 109, 110, 111, 112, 119, 120, 121, 130, 132, 134, 135, 139, 141, 143, 144, 145, 158, 166, 167, 168, 172, 173, 175, 181, 191, 237, 240, 260, 280, 285, 291, 310, 334, 357, 361, 363, 369, 375, 383, 384, 385 search engine, 42 searches, 41, 132, 134, 135, 155, 166, 167, 377, 385 searching, 11, 15, 40, 41, 42, 60, 89, 91, 166, 172, 267, 291, 306, 375, 411 seed, 131, 254, 363 segregation, 93 selecting, 70, 110, 136, 137, 201, 249, 264, 265 selectivity, 14 self, 213, 215, 219, 227, 333, 358 self-consistency, 319, 320, 321, 326, 330, 331, 332 self-organization, 330, 360 self-organizing, 12, 176, 215, 217, 227, 228 Self-Organizing Maps, vi, 215, 219, 227 semantic, 15, 341, 348 semantics, 130, 390, 392, 404 semiotics, 15, 341, 343, 347, 355 senescence, 97, 359

437

sensitivity, 14, 76, 78, 79, 84, 132, 144, 264, 265, 268, 328, 332, 369, 370, 382 separation, 218, 382 sequencing, 10, 3, 4, 89, 130, 142, 146, 233, 317, 364 series, 3, 42, 60, 236, 321, 354, 360 serum, 225, 265, 273 services, 95, 416 set theory, 332 severity, 409, 411, 413 sex, 241, 369 Shanghai, 414, 415, 418 shape, 43, 156, 159, 211, 213, 282, 357 shares, 16, 166, 391, 407, 408 sharing, 12, 16, 44, 145, 253, 285, 403, 416 sheep, 232, 255 shock, 285, 313 short period, 10, 39 short-range, 197 shrimp, 248, 255 SIB, 238 sibling, 13, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 250, 251, 252, 253, 254, 256, 257 siblings, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 247, 257 sickle cell, 409, 411, 413, 416, 417 sickle cell anemia, 409, 413 side effects, 13, 14 sign, 342, 343, 344, 345, 348 signal transduction, 195, 226 signaling, 10, 20, 25, 26, 47, 48, 210 signals, 10, 47, 48, 97, 177, 312, 371, 372, 373 signal-to-noise ratio, 136 significance level, 22, 63, 75, 385 signs, 15, 341, 343, 345, 355 silica, 21 silico methods, 150, 336 similarity, 12, 14, 13, 14, 132, 133, 135, 165, 166, 167, 176, 179, 180, 181, 182, 183, 184, 185, 218, 237, 283, 315, 317, 318, 319, 321, 328, 331, 333, 334, 335, 336, 382 simulation, 12, 16, 18, 43, 59, 63, 64, 65, 69, 70, 71, 72, 78, 84, 94, 144, 149, 150, 153, 160, 162, 193, 194, 196, 205, 209, 210, 211, 249, 250, 289, 299, 306, 312, 313, 414 simulations, 12, 14, 64, 72, 150, 155, 158, 160, 167, 168, 175, 180, 193, 194, 210, 248, 277, 280, 282, 286, 287, 293, 296, 299, 302, 305, 307, 308, 311, 314 Singapore, 310, 360 single nucleotide polymorphism, 6, 7, 20, 226, 234 single test, 75

438

Index

single-nucleotide polymorphism, 5, 6 siRNA, 90 sites, 10, 8, 15, 17, 22, 43, 45, 47, 48, 51, 52, 91, 93, 94, 95, 97, 134, 135, 137, 146, 157, 159, 362, 365, 369, 370, 371, 373 skeleton, 150, 410 skills, 39, 163, 409 skin, 9, 19, 20, 21, 23, 24, 25, 26, 48 skin cancer, 48 sleep, 96 Sm, 241 smiles, 392 SNP, v, 9, 3, 6, 7, 19, 20, 21, 22, 24, 25, 26, 27, 226 SNPs, 3, 4, 5, 6, 7, 8, 20, 21, 22, 23, 24, 27, 234, 418 social group, 256 sodium, 284 software, 12, 13, 12, 13, 22, 42, 44, 50, 54, 143, 145, 215, 216, 217, 218, 219, 220, 222, 225, 232, 233, 237, 238, 239, 249, 250, 253, 256, 346, 367, 370, 371, 389, 390, 391, 394, 400, 402, 403, 404, 405 solid tumors, 6 solvation, 43 solvent, 150, 166, 179, 180, 182, 186, 190, 191, 288, 325 somatic mutations, 5 soot, 54 sorting, 368, 403 South Africa, 83 Southeast Asia, 416 spacers, 362 Spain, 129 spatial, 93, 194, 233, 309, 354 spatiotemporal, 357 speciation, 139, 140, 145 species, 11, 15, 7, 41, 42, 129, 130, 131, 137, 138, 139, 140, 141, 142, 143, 146, 232, 233, 237, 240, 252, 274, 351, 354, 360, 361, 369, 370, 372 specificity, 15, 66, 91, 95, 264, 268, 328, 366, 369, 375, 386, 387 spectroscopy, 62, 210, 273, 311 spectrum, 10, 15, 47, 94, 268, 333, 375, 377, 409 speed, 11, 99, 100, 135, 136, 404 sperm, 163 spin, 344 spindle, 93 springs, 195, 202, 205 squamous cell, 270 squamous cell carcinoma, 270 stability, 108, 149, 157, 211, 262, 279, 284, 291, 308, 309, 312, 346, 351, 358, 403, 414 stabilization, 11, 82, 99, 100, 102, 108, 112, 119, 120, 121, 122, 126, 127, 283, 308 stabilize, 103, 284, 309

stages, 13, 2, 12, 61, 140, 166, 178, 216, 226, 295, 355 standard deviation, 70, 71, 320, 378 standard model, 102 standards, 95 staphylococcal, 310 stars, 185, 186 statistical analysis, 15, 272, 285, 375 statistical mechanics, 197, 212 statistics, 9, 19, 20, 64, 67, 69, 72, 73, 76, 78, 80, 227, 239, 339 steady state, 346 stiffness, 155, 194, 197, 198, 199, 200, 202, 204, 205 stimuli, 94 stimulus, 223, 285 stochastic, vi, 11, 99, 100, 101, 102, 103, 107, 108, 109, 111, 113, 115, 116, 117, 123, 124, 125, 126, 127, 128, 170 stochastic model, 116 stock, 102, 127 stoichiometry, 163 stomach, 13, 48, 51, 52, 260 strategies, 9, 10, 1, 4, 47, 48, 54, 90, 109, 119, 120, 121, 135, 137, 181, 216, 232, 257, 386 strategy use, 54 strength, 149, 366, 367 stress, 152, 158, 410 stretching, 155, 158, 160, 161, 196, 211 stroke, 195 STRs, 232 structuring, 296, 301 students, 39 subgroups, 370 substitution, 17, 134, 332, 364, 414, 418 substrates, 14 subtraction, 2, 219 success rate, 329, 331, 332 suffering, 260, 386 sulfate, 284 Sun, 155, 162, 268, 271, 274, 275, 338, 417, 418 supercomputers, 140, 280 superficial bladder cancer, 13, 216, 220, 226 superiority, 334 superposition, 14, 281, 345 suppression, 408 suppressor, 216, 226, 228 suppressors, 90, 96, 98 supramolecular, 12, 147 surface area, 280, 286 surgery, 215, 260 surveillance, 10, 47, 48, 54, 55 survivability, 260 survival, 265, 268, 270, 271, 273

Index Survivin, 228 Sweden, 261, 262 switching, 236, 352 symbols, 177 symmetry, 78, 283, 311 symptoms, 413 synapse, 223 syndrome, 54, 413, 417 synergistic, 12 synergistic effect, 12 syntax, 390, 391, 392, 404 synthesis, 10, 20, 23, 59, 60, 146, 196, 212, 267, 274, 352, 387, 410 systemic biology, 43 systems, 13, 15, 4, 12, 16, 47, 94, 95, 135, 166, 167, 169, 178, 180, 181, 182, 186, 188, 212, 231, 232, 252, 255, 341, 345, 347, 349, 350, 351, 352, 353, 355, 356, 357, 358, 359, 360, 386, 388, 391, 405, 408 systomics, 43

T T cell, 376, 377, 381, 382, 383, 386, 387, 388 T lymphocytes, 387 Taiwan, 215 tandem mass spectrometry, 409, 414, 416 tanks, 255 Tanning, 26 targets, 13, 14, 15, 16, 81, 90, 92, 93, 95, 97, 166, 218, 227, 386 taxa, 134, 139, 145, 353, 354 taxonomy, 144, 353 TCC, 226, 376, 382, 386 T-cell, 15, 375, 376, 377, 378, 381, 386, 387, 388 T-cell receptor, 377 TCR, 15, 375, 376, 377, 380, 386, 388 technology, 15, 26, 41, 80, 81, 224, 375, 377, 390, 402, 408, 410, 416 telomerase, 216 telomeres, 157 TEM, 151 temperature, 173, 175, 197, 217, 282, 288 temporal, 194, 256, 342, 354, 357 tenascin, 210 tension, 152, 160 termination codon, 410 test procedure, 334, 336, 337 test statistic, 64, 65, 67, 69, 72, 73, 74, 76 Texas, 99 Thai, 417 Thailand, 39, 407, 410, 413 thalassemia, 408, 409, 410, 416 Thalassemia, 416

439

theoretical assumptions, 151 theoretical biology, 12, 350, 351 therapeutic agents, 9, 11, 12 therapeutic approaches, 4, 376 therapeutic interventions, 224 therapeutics, 97, 225, 414, 418 therapy, 6, 48, 227, 260, 269, 272, 273, 411, 416 thermal denaturation, 195, 308 thermal energy, 200, 204, 205 thermodynamic, 14, 149, 157, 277, 278, 284, 309, 349, 352 thermodynamic equilibrium, 14, 277, 309 thermodynamic stability, 157 thermodynamics, 282, 313 threat, 273 three-dimensional, 280, 281, 282, 310, 312, 331, 345, 350, 357 three-dimensional space, 345 threshold, 69, 73, 170, 171, 176, 180, 239, 240, 255, 318, 363, 384, 385 threshold level, 384 thresholds, 132, 171, 172, 175, 238 thrombin, 413 thymine, 3 thymus, 358 tiger, 248, 255 time constraints, 251 time periods, 294 timing, 96, 361, 362 tissue, 10, 13, 1, 2, 3, 4, 6, 47, 48, 94, 216, 217, 220, 221, 232 title, 250, 392, 394 tobacco, 54 Tokyo, 20 tolerance, 106, 116 top-down, 264 topological, 12, 138, 139, 140, 141, 146, 147, 149, 152, 157, 158 topology, 48, 134, 135, 138, 141, 142, 143, 145, 157, 163, 175, 201, 203, 206, 208, 283, 284, 285, 288, 307, 308, 309, 313, 318 toxicity, 12, 15, 16, 411 toxicological, 80 toxicology, 408 TP53, 266 trade, 170, 282, 288, 382 trade-off, 282, 288, 382 training, 39, 172, 176, 177, 178, 182, 185, 263, 264, 320, 327, 330, 331, 332, 382, 391, 402 traits, 9, 13, 19, 20, 25, 49, 54, 55, 231, 353, 354 trajectory, 290, 294, 303, 304 trans, 278, 362 transcriptase, 211

440

Index

transcription, 11, 21, 89, 90, 91, 92, 93, 95, 96, 97, 149, 150, 160, 223, 224, 226, 356, 361, 362, 369, 371, 372 transcription factor, 11, 21, 89, 90, 91, 92, 93, 95, 96, 97, 370, 72 transcription factors, 91, 92, 93, 97 transcriptional, 11, 15, 70, 89, 90, 91, 93, 94, 95, 96, 98, 228, 272, 361, 362, 370, 371, 372, 373 transcriptomics, 3 transcripts, 2, 3, 4 transducer, 223 transduction, 194 transfection, 92 transfer, 13, 138, 166, 178, 345 transformation, 65, 84, 97, 157, 196, 267, 344, 348, 349, 353, 354, 398 transformations, 354, 358 transfusion, 414, 418 transgene, 409 transgenic, 264, 266, 409, 416 transgenic mice, 266, 416 transition, 14, 95, 130, 157, 158, 195, 213, 277, 278, 279, 280, 282, 283, 284, 286, 288, 289, 291, 293, 294, 296, 298, 305, 306, 307, 308, 309, 310, 311, 312, 313, 314, 325, 355 transitional cell carcinoma, 227, 229 transitions, 208, 211, 212, 213, 282, 292 translation, 90, 223, 226, 317, 343, 356, 371, 372 translational, 93, 96, 148, 157, 365 transmission, 282 transparency, 272, 335 transparent, 336 transport, 23 transportation, 126 transposon, 369 transposons, 369 transurethral resection, 13, 215, 216 traps, 308 trees, 130, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 145, 146, 232, 335 trial, 272 trust, 108 tumor, 9, 13, 1, 2, 5, 7, 61, 79, 80, 85, 90, 96, 97, 98, 215, 216, 217, 220, 226, 227, 228, 229, 266, 268, 270, 271, 275, 382, 386, 387, 388 tumor cells, 3, 97 tumor growth, 229 tumor progression, 226, 228, 266 tumorigenesis, 270 tumorigenic, 225, 228 tumors, 12, 13, 6, 215, 216, 217, 220, 265, 273 tumour, 2, 5, 6, 7, 270 tumours, 3, 4, 275

turnover, 352 two-dimensional, 220, 410, 414 Type I error, 63, 64, 75 typology, 359 tyrosine, 23

U ultrasonography, 216, 227 ultraviolet (UV), 20, 24, 25, 26 uncertainty, 4, 100, 102, 128, 170, 348 unfolded, 14, 167, 169, 194, 277, 279, 282, 283, 286, 287, 288, 289, 291, 293, 294, 295, 296, 301, 302, 304, 307 unification, 344 uniform, 116, 121, 181, 249, 250, 289 United States, 216, 271, 272, 273, 274, 275 universal genetic code, 360 universal law, 355 universe, 241, 356, 360 untranslated regions, 3, 5 ureter, 226 urinary, 216, 226, 229 urinary bladder, 216, 229 urinary bladder cancer, 216 urine, 85 user-defined, 42, 91 Utah, 254 UV exposure, 20 UV irradiation, 20 UV radiation, 20

V vaccine, 386 vacuum, 218 Valencia, 91, 129, 188, 189, 190 validation, 1, 12, 60, 86, 178, 180, 182, 228, 233, 248, 264, 272, 319, 320, 325, 328, 333, 337, 382 validity, 34, 273, 345, 367 variability, 24, 25, 61, 70, 71, 73, 76, 122, 163, 267 variables, 22, 60, 101, 102, 103, 105, 106, 108, 109, 110, 111, 112, 113, 114, 115, 123, 126, 245, 246, 262, 268, 328, 335, 351, 382, 392, 394 variance, 61, 64, 68, 70, 74, 77, 82, 84, 101, 219, 384, 385 variation, 9, 3, 4, 7, 19, 20, 23, 25, 26, 27, 233, 250, 253, 255, 256, 267, 274, 280, 284, 354, 360, 408, 416 vector, 70, 74, 91, 92, 102, 103, 104, 173, 176, 189, 190, 195, 196, 198, 206, 317, 321, 322, 323, 325, 326, 330, 331, 333, 334, 335, 337, 338, 339, 382, 388, 401, 403 vertebrates, 140, 233, 373

Index vesicle, 23 vibration, 194 virulence, 13 virus, 91, 386, 387 virus infection, 91 visible, 350, 353 vision, 358 visualization, 26, 217, 225, 401, 403 vitamin D, 20 vocabulary, 42 voting, 325, 333 Vygotsky, 355, 360

W water, 62, 218, 278, 283, 320 water-soluble, 320 wavelet, 150 weakness, 266 wealth, 156 web, 15, 3, 7, 42, 44, 45, 141, 143, 162, 253, 373, 375, 377, 383, 388, 404, 408 web browser, 404 web-based, 7, 44, 377, 383, 388, 408 websites, 3 Weinberg, 10, 22, 47, 48, 55, 56 wells, 378 western blot, 4

441

wild type, 21, 43 wild-type allele, 21 windows, 126, 127 wisdom, 357 women, 26, 216 wood, 233 workflow, 17 World Health Organization, 55 writing, 397

X xenografts, 229 X-ray crystallography, 13, 14, 200, 403 X-ray diffraction, 150

Y YAC, 409, 416 yang, 96 yeast, 15, 90, 95, 145, 146, 150, 161, 228, 361, 362, 372, 373 yield, 12, 113, 114, 115, 167, 186, 326, 331 yin, 96

Z zebrafish, 27 zinc, 369, 372

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