Emergent Computation: Emphasizing Bioinformatics (Biological and Medical Physics, Biomedical Engineering)

BIOLOGICAL AND MEDICAL PHYSICS BIOMEDICAL ENGINEERING

BIOLOGICAL AND MEDICAL PHYSICS BIOMEDICAL ENGINEERING The fields of biological and medical physics and biomedical engineering are broad, multidisciplinary and dynamic. They lie at the crossroads of frontier research in physics, biology, chemistry, and medicine. The Biological & Medical Physics/ Biomedical Engineering Series is intended to be comprehensive, covering a broad range of topics important to the study of the physical, chemical and biological sciences. Its goal is to provide scientists and engineers with textbooks, monographs, and reference works to address the growing need for information.

Editor-in-Chief: Elias Greenbaum, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA

Editorial Board: Masuo Aizawa, Department of Bioengineering, Tokyo Institute of Technology, Yokohama, Japan Olaf S. Andersen, Department of Physiology, Biophysics and Molecular Medicine, Cornell University, New York, USA Robert H. Austin, Department of Physics, Princeton University, Princeton, New Jersey, USA James Barber, Department of Biochemistry, Imperial College of Science, Technology and Medicine, London, England Howard C. Berg, Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts, USA Victor Bloomfield, Department of Biochemistry, University of Minnesota, St. Paul, Minnesota, USA Robert Callender, Department of Biochemistry, Albert Einstein College of Medicine, Bronx, New York, USA Britton Chance, Department of Biochemistry and Biophysics, University of Pennsylvania, Philadelphia, USA Steven Chu, Department of Physics, Stanford University, Stanford, California, USA Louis J. DeFelice, Department of Pharmacology, Vanderbilt University, Nashville, Tennessee, USA Johann Deisenhofer, Howard Hughes Medical Institute, The University of Texas, Dallas, Texas, USA George Feher, Department of Physics, University of California, San Diego, La Jolla, California, USA Continued after Index

Matthew Simon

Emergent Computation Emphasizing Bioinformatics With 274 Illustrations



-}-

[ML

KB]

FML 4 ] ML3

+

L

->

L

—*

then:

] = kx[M ][L ]

[ML

[ML2] = k2[ML J L [ML3] = k3[ML2][L ] = k 3 k 2 k 1 [M [ML4] = k4[ML3][L ] = k 4 k 3 k 2 k![M J L Thus we conclude that V

=

I

iJ

=

V V VV

6 Emergent Computation

Equilibrium Constant Also, if we consider the following reaction: i

A

+

B
S +

C C T A G G 3

Note

1

5

1

DNA segments 31

5' G G A T C C 2


cdJI 65 13 74 10 77 13 74 127 128 63 13 116

_

^

g

_

_

_

8 8 Emergent Computation

The Beginning: Numbers It is important, from the point of view of computation, to know and have a clear understanding of the numbers involved in understanding the subject under study. The numbers are as follows: two pairs of Watson-Crick complementary bases: ( A/T, C/G for DNA; A/U, C/G for RNA ). These four DNA bases support a maximum of 43 = 64 possible codon triplets, which allow (with mRNA and tRNA) the construction of polypeptide chains or proteins, composed of 20 amino acids. These are the numbers we must deal with-or are they? The following discussion, interesting per se, will challenge these numbers. This chapter refers to more biochemistry than most of the rest of the book, but the main ideas should be easy to follow.

Error Detection: Parity DNA and RNA are complicated molecules. The replication of such molecules, as with any complex process, is subject to error. Errors occur in nature, and of course apply to the replication of DNA and RNA and explain some genetic diseases, as well as innovations that are useful during evolution. The following discussion is quite interesting, in that errors that may take place can be detected using a simple parity check [11], [99], [171]. It is first necessary to examine not only the four nucleotide bases, but other nucleotide bases that might also have been possible candidates in the genetic code. These bases will be viewed from the point of view of hydrogen bonding: donors and acceptors. In addition, we must consider steric "stacking," the pairing of purine with pyrimidine. Using the classification by Mac Donaill, an acceptor will be signified by "0", and a donor will be signified by a "1". In addition, a purine derivative will be signified by "R" (from puRine) where R is equivalent to "0", and a pyrimidine derivative will be signified by "Y" (from pYrimidine) where Y is equivalent to "1". This information may be encoded in binary as four bits, the first three bits representing the donor/acceptor bonding sites of a nucleotide and the last bit encodes for purine or pyrimidine. We will find, for example: C = (l00, l) while G = (011, 0) These are complements, or distance is dc®G\

C®G = (111, 1) = /000, 0 ) , and the Hamming

= o((\ 11, lYJ = ^ 0 0 0 , 0 ^ = 0.

Note that Mac Donaill

uses C® G , not C®G, encoding the idea of Watson-Crick complements. We find the following.

The Beginning Numbers 89

C= Figure 3.1 Parity: C and G pairs

Figure 3.2 Parity: T and A pairs

9 0 Emergent Computation

Figure 3.3 Parity: U and A pairs

isoC = (00\, l)

isoG = (llO, 0)

Figure 3.4 Parity: iso C and iso G pairs

The Beginning Numbers 91

Figure 3.5 Parity: Kand

Xpairs

* = (O1O, 0) Figure 3.6 Parity: ^and npairs

The base TC is discussed in [11, pp. 33-37].

9 2 Emergent Computation

Figure 3.7 Parity: or and T pairs

Figure 3.8 Parity: J3and £ pairs If we collect the above information, we find that the rightmost bit acts as a parity check and thus the following.

The Beginning Numbers 93

f

C = (lOO, l )

naturally J

occurring

TT i T

/A I A I \

iso C = (001, l)

A = (101, 0)

even parity

wo G = (llO, 0)

nr = (101, l)

r = (ooi, o)

HoM

>

odd parity