Electrophysiological Recording Techniques (Neuromethods, 54)

Neuromethods

Series Editor Wolfgang Walz University of Saskatchewan Saskatoon, SK, Canada



For other titles published in this series, go to www.springer.com/series/7657

Electrophysiological Recording Techniques Edited by

Robert P. Vertes Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, FL, USA

Robert W. Stackman Jr. Department of Psychology and Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, FL, USA

Editors Robert P. Vertes, Ph.D. Center for Complex Systems and Brain Sciences Florida Atlantic University 777 Glades Road Boca Raton, Florida 33431-0991 USA [email protected]

Robert W. Stackman, Jr. Ph.D. Department of Psychology and Center for Complex Systems and Brain Sciences Florida Atlantic University 777 Glades Road Boca Raton, Florida 33431-0991 USA [email protected]

ISSN 0893-2336 e-ISSN 1940-6045 ISBN 978-1-60327-201-8 e-ISBN 978-1-60327-202-5 DOI 10.1007/978-1-60327-202-5 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2010938917 © Springer Science+Business Media, LLC 2011 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Humana Press, c/o Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or ­dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. While the advice and information in this book are believed to be true and accurate at the date of going to press, ­neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Humana Press is part of Springer Science+Business Media (www.springer.com)

Preface to the Series Under the guidance of its founders Alan Boulton and Glen Baker, the Neuromethods series by Humana Press has been very successful since the first volume appeared in 1985. In about 17 years, 37 volumes have been published. In 2006, Springer Science + Business Media made a renewed commitment to this series. The new program focuses on methods that are either unique to the nervous system and excitable cells or which need special consideration to be applied to the neurosciences. The program strikes a balance between recent and exciting developments like those concerning new animal models of disease, imaging, in vivo methods, and more established techniques. These include immunocytochemistry and electrophysiological technologies. New trainees in neurosciences still need a sound footing in these older methods in order to apply a critical approach to their results. The careful application of methods is probably the most important step in the process of scientific inquiry. In the past, new methodologies led the way in developing new disciplines in the biological and medical sciences. For example, Physiology emerged out of Anatomy in the 19th century by harnessing new methods based on the newly discovered phenomenon of electricity. Nowadays, the relationships between disciplines and methods are more complex. Methods are now widely shared between disciplines and research areas. New developments in electronic publishing also make it possible for scientists to download chapters or protocols selectively within a very short time of encountering them. This new approach has been taken into account in the design of individual volumes and chapters in this series. Wolfgang Walz

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Preface The application of neurophysiological methods to the study of the brain–behavior relationships represented a major advance to the field of neuroscience when it was in its infancy. Modern neuroscientists now have a great deal more technology available to them than ever before; and consequently the field of neurophysiology has grown considerably. Following a tradition set by the original Neuromethods series, this book presents a current view of the widespread application of electrophysiological methods to the study of the brain and to the problem of brain–behavior relationships. The book has been organized to display the research topics to which modern neurophysiological methods have been applied. Such applications range from recordings of single neurons and ensembles of neurons to recordings of field potentials within discrete brain regions to field potential recordings across multiple brain areas. In the interest of continuity, the present volume begins with a chapter by Stan Leung who contributed to an earlier volume (Volume 15) of the series. The present chapter by Leung describes the basic principles of field potential recording/analysis and current source density (CSD) analysis. Using experimental data as well as model systems of hippocampal pyramidal cells, Leung nicely illustrates the differential patterns of current flow (sources/sinks) along pyramidal cell dendrites and soma to the activation of different segments of the neuron (basal dendrites, soma, proximal or distal regions of apical dendrites), depicting averaged evoked potentials and their derived CSD profiles. Complementing Leung’s chapter, Ding, Schroeder, and colleagues (Chen, Dhamala, Bollimunta, Schroeder, Ding) describe an in vivo procedure for CSD analysis of ongong, non-triggered, neural activity. The method termed ‘phase realigned averaging technique (PRAT)’ extracts generally low amplitude signals from continuous streams of activity. The procedure involves parceling, phase realigning, and averaging ongoing activity at select frequencies to determine spatiotemporal properties, such as peak current flow within defined cortical fields from awake animals. Among other things, the method allows for a determination of the relationship of endogenous activity (e.g., alpha rhythm) to behaviorally relevant events, such as sensory or motor responses to external stimuli. The chapter by Pinault describes a technique that permits the discrete labeling of individual neurons during simultaneous extracellular recording, an important tool for defining the discrete connectivity of neurons whose physiological properties have been identified. Four chapters, those from Fenton, Jeffery and Donnett; Kuang and Tsien; Hampson, Simeral, Berger, Song, Chan and Deadwyler; and Stackman provide details of new strategies that apply to in  vivo single-unit recording from freely moving rodents. Fenton, Jeffery, and Donnett present the challenges that face the design of wireless recording systems. They describe the advantages of their new digital telemetry (DT) system over other analog wireless systems and outline two applications for DT – tetherless recordings from freely moving rodents during truly unrestricted behavioral performance and an epilepsy monitoring system for use in humans. Kuang and Tsien’s chapter addresses two of the exciting challenges emerging in the field, that of how to acquire high-density ensemble neuronal activity from wild type and genetically engineered mice, and second, how to

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analyze these data. The chapter by Stackman addresses the inherent challenges of relating neuronal firing patterns of limbic neurons to distinct behavioral sequences. The chapter focuses on the rodent head direction cell as a model system to delineate the degree to which directional correlates of single-unit activity relate to spatial navigation. In a computational vein, the chapter by Bressler is devoted to event-related potentials (ERPs) while that by Albo and colleagues (Albo, Viana Di Prisco, Vertes) examines spike– field interactions. As Bressler points out, local field potentials (LFPs) recorded with depth electrodes (intracortical) are 1–2  mV in amplitude, whereas those recorded from the scalp (e.g., EEG recordings in humans) are 10–50 mV in amplitude. The latter generally requires special procedures for detection and analysis, particularly if internally or endogenously generated. The chapter by Bressler, then, provides an in-depth description of various procedures for characterizing event related potentials (triggered and nontriggered), with special attention to state of the art time and frequency domain analytical methods that are particularly useful in situations in which standard ensemble averaging techniques may be inappropriate. The chapter by Albo et al. describes current methods for unit-field (and field-field) analysis, or the application of spike-field coherence techniques to the study of unit-field oscillations. The chapter provides a nice overview of the advantages/disadvantages of various approaches to assessing functional interactions among synchronously occurring signals (spike trains and field potentials) across the brain. As a direct application of some of the techniques, they describe their findings showing a three way interaction (coherence) between theta rhythmic units in the anterior thalamus and theta oscillations in the hippocampus and retrosplenial cortex, suggesting that hippocampus may drive the anterior thalamus, which in turn rhythmically paces the retrosplenial cortex, with implications for the role of theta in limbic functions. Recording from ensembles of hippocampal neurons (15-35 cells of CA1/CA3), Deadwyler, Berger, and colleagues (Hampson, Simeral, Berger, Song, Chan, Deadwyler) describe a “closed loop system” which distinguishes among the separate behavioral components of a two choice delayed nonmatch to sample (DNMS) task, and then uses ensemble activity at phases of the task to both predict choice behavior and modify it during task performance. In effect, ensemble activity (or codes) was used to adjust delay times (between sample and choice) during ongoing trials to improve performance on those trials. Specifically, depending on the relative strength (or efficacy) of the ensemble code in the sample phase of the task, the delay between sample and nonmatch task phases could be shortened or lengthened, thereby improving performance. It is well recognized that the septum and hippocampus are strongly interconnected and together serve as a functional unit generating the hippocampal theta rhythm. Theta serves a well-recognized role in mnemonic functions. In a major advance in examining septo-hippocampal interactions, Williams and colleagues (Goutagny, Jackson, Williams) have developed a remarkable in vitro preparation in which the septum and hippocampus are simultaneously dissected (with connections between them intact) and kept viable for at least 8 h. In addition, with a barrier placed between them, the two structures can be independently manipulated to assess the effects of one on the other. Using this preparation, Williams and colleagues have confirmed the pronounced septal influence on the hippocampus in the modulation of theta, and further showed that hippocampal theta activity, in turn, exerts a strong driving influence on the septum. Helen Mayberg is a pioneer in the use of deep brain stimulation (DBS) to treat depression. The chapter by Mayberg and Holtzheimer begins with a review of background material (mainly imaging studies) that led to the use of DBS for major depressive disorders (MDD). In effect, they (and others) found that certain regions of the

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frontal cortex, such as the subcallosal cingulate cortex (SCC) were hyperactive in MDD, whereas other areas such as dorsolateral prefrontal or posterior cingulate cortices were hypoactive in MDD, and that successful antidepressant treatment normalized activity in these regions. This suggested a critical role for the frontal/prefrontal cortex (particularly the SCC) in MDD. Mayberg and Holtzheimer proceed to describe in detail the specific procedures used for DBS of the SCC and summarize the extremely promising results that have been obtained to date with the technique with two groups of patients with treatment resistant depression. DBS is not only a cutting edge procedure for the treatment of depression, but also used in conjunction with other methods and has the potential to define an extended circuitry responsible for MDD. It is daunting to take on the challenge of describing the “current” state of any field of science. This is especially the case for neurophysiological techniques since this area is in a near constant state of improvement. This collection of chapters provides a clear indication of how modern technological advances have influenced the study of the neurophysiological substrates for behavior. As one will find in reviewing this volume, current challenges in electrophysiological techniques will most certainly be conquered by the next generation of improvements in technology and analysis. Robert P. Vertes Robert W. Stackman, Jr.

Contents Preface to the Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii   1 Field Potential Generation and Current Source Density Analysis . . . . . . . . . . . . . L. Stan Leung   2 Current Source Density Analysis of Ongoing Neural Activity: Theory and Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yonghong Chen, Mukesh Dhamala, Anil Bollimunta, Charles E. Schroeder, and Mingzhou Ding   3 The Juxtacellular Recording-Labeling Technique . . . . . . . . . . . . . . . . . . . . . . . . . Didier Pinault   4 Neural Recording Using Digital Telemetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . André A. Fenton, Kathryn J. Jeffery, and James G. Donnett   5 Large-Scale Neural Ensembles in Mice: Methods for Recording and Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hui Kuang and Joe Z. Tsien   6 Behavioral Correlates of Neuronal Activity Recorded as Single-Units: Promises and Pitfalls as Illustrated by the Rodent Head Direction Cell Signal . . . . Robert W. Stackman Jr.   7 Event-Related Potentials of the Cerebral Cortex . . . . . . . . . . . . . . . . . . . . . . . . . Steven L. Bressler   8 Multisite Spike-Field Coherence, Theta Rhythmicity, and Information Flow Within Papez’s Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zimbul Albo, Gonzalo Viana Di Prisco, and Robert P. Vertes   9 Cognitively Relevant Recoding in Hippocampus: Beneficial Feedback of Ensemble Codes in a Closed Loop Paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . Robert E. Hampson, John D. Simeral, Theodore W. Berger, Dong Song, Rosa H.M. Chan, Vasilis Z. Marmarelis, and Sam A. Deadwyler 10 An Intact Septo-Hippocampal Preparation for Investigating the Mechanisms of Hippocampal Oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Romain Goutagny, Jesse Jackson, and Sylvain Williams 11 Targeted Modulation of Neural Circuits: A New Treatment Strategy for Neuropsychiatric Disease . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Helen S. Mayberg and Paul E. Holtzheimer Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Contributors Zimbul Albo  •  Department of Neurology, Baylor College of Medicine, Baylor University, Houston, TX, USA Theodore W. Berger  •  Department of Biomedical Engineering, Viterbi School of Engineering, University of Southern California, Los Angeles, CA, USA Anil Bollimunta  •  J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL, USA Steven L. Bressler  •  Center for Complex Systems and Brain  Sciences, Charles E. Schmidt College of Science, Florida Atlantic University, Boca Raton, FL, USA Rosa H.M. Chan  •  Department of Biomedical Engineering, Viterbi School of Engineering, University of Southern California, Los Angeles, CA, USA Yonghong Chen  •  J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL, USA Sam A. Deadwyler  •  Department of Physiology and Pharmacology, School of Medicine, Wake Forest University, Winston-Salem, NC, USA Mukesh Dhamala  •  Department of Physics and Astronomy, and Georgia State University Neuroscience Institute, Georgia State University, Atlanta, GA, USA Mingzhou Ding  •  J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL, USA James G. Donnett  •  Axona Ltd., St. Albans, UK André A. Fenton  •  Department of Physiology and Pharmacology, The Robert F. Furchgott Center for Neural and Behavioral Science, SUNY Downstate Medical Center, Brooklyn, NY, USA Romain Goutagny  •  Department of Psychiatry, McGill University, Montreal, QC, Canada Robert E. Hampson  •  Department of Physiology and Pharmacology, School of Medicine, Wake Forest University, Winston-Salem, NC, USA Paul E. Holtzheimer  •  Department of Psychiatry, Emory University School of Medicine, Atlanta, GA, USA Jesse Jackson  •  Department of Psychiatry, McGill University, Montreal, QC, Canada Kathryn J. Jeffery  •  Division of Psychology and Language Sciences, Department of Cognitive, Perceptual and Brain Sciences, Institute of Behavioural Neuroscience, University College London, London, UK Hui Kuang  •  The Key Laboratories of MOE and STCSM and College of Life Sciences, Shanghai Institute of Brain Functional Genomics, East China Normal University, Shanghai, China L. Stan Leung  •  Department of Physiology and Pharmacology, The University of Western Ontario, London, ON, Canada Vasilis Z. Marmarelis  •  Department of Biomedical Engineering, University of Southern California, Los Angeles, CA, USA

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Helen S. Mayberg  •  Departments of Psychiatry and Neurology, Emory University School of Medicine, Atlanta, GA, USA Didier Pinault  •  Faculté de Médecine, INSERM U666, Physiopathologie Clinique et Expérimentale de la Schizophrénie, Université Louis Pasteur, Université de Strasbourg, Strasbourg, France Charles E. Schroeder  •  Nathan Kline Institute for Psychiatric Research, Orangeburg, NY, USA; Columbia University College of Physicians and Surgeons, New York, NY, USA John D. Simeral  •  Division of Biology and Medicine, Department of Neuroscience, Brown University, Providence, RI, USA Dong Song  •  Department of Biomedical Engineering, Viterbi School of Engineering, University of Southern California, Los Angeles, CA, USA Robert W. Stackman, Jr.  •  Department of Psychology, and Center for Complex Systems and Brain Sciences, Charles E. Schmidt College of Science, Florida Atlantic University, Boca Raton, FL, USA Joe Z. Tsien  •  Brain and Behavior Discovery Institute, School of Medicine, Medical College of Georgia, Augusta, GA, USA; Department of Neurology, School of Medicine, Medical College of Georgia, Augusta, GA, USA Robert P. Vertes  •  Center for Complex Systems and Brain Sciences, Charles E. Schmidt College of Science, Florida Atlantic University, Boca Raton, FL, USA Gonzalo Viana Di Prisco  •  Department of Neurology, Baylor College of Medicine, Baylor University, Houston, TX, USA Sylvain Williams  •  Department of Psychiatry, McGill University, Montreal, QC, Canada

Chapter 1 Field Potential Generation and Current Source Density Analysis L. Stan Leung Abstract The basic principles underlying field potential generation and the application of current source density (CSD) analysis are outlined in this chapter. Currents in the brain are mainly derived from synaptic or action currents flowing in a closed loop, traversing both intracellular and extracellular media. Extracellular currents generate the field potentials, with a spatial organization of an open or a closed field that may be standing or traveling. CSD analysis is the method used to derive the macroscopic sources and sinks that generate a potential field. Assuming that the medium is homogeneous and resistive, CSD can be approximated by a second-order derivative of the field potential. When the activation is spatially extensive, the current may essentially flow in one or two dimensions, and the CSD may be approximated using one- or two-dimensional mapping. The field potentials should first be mapped regularly at an adequate interval, over an appropriate spatial extent. A multichannel electrode array offers accurate sampling intervals, and the field potentials can be sampled simultaneously in one or two dimensions. Examples of potential fields and CSDs in a layered cortical structure (hippocampal CA1 area) are illustrated, with different fields generated by basal or apical dendritic excitation, proximal and distal dendritic excitation, proximal inhibition, and synchronous action potentials (population spikes). Generation of field potentials from sinks and sources of neuronal cables, arranged in a particular geometry, may be used to predict the CSD profiles. Successful application of CSD analysis would facilitate the understanding of neuronal dynamics, synaptic transmission, and plasticity in cortical structures. Key words: Current source density, Field potential, Dendritic excitation, Population spike, Inhibitory field, Silicon probe, Cable theory, Electroencephalogram, Field mapping

1. Introduction As indicated by its name, field potential is a measure not localized to a small volume. Instead, it is spatially distributed in a conductive medium, so called a volume conductor. For neural activity, the volume conductor includes the brain, blood vessels and meninges, skull, scalp, and the body. The types of field potentials Robert P. Vertes and Robert W. Stackman Jr. (eds.), Electrophysiological Recording Techniques, Neuromethods, vol. 54, DOI 10.1007/978-1-60327-202-5_1, © Springer Science+Business Media, LLC 2011

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include spontaneous, induced, or evoked electrical activities that are recorded on the scalp, on the surface of the brain, or inside a particular brain structure. An electroencephalogram (EEG) is a spontaneous electric activity conventionally recorded on the scalp of humans. Local field potentials are extracellular recordings in a particular brain structure. Changes in currents or electric field also give rise to a magnetic field that is recorded as a magnetoencephalogram (MEG). With the advent of recordings of single cells and patches of dendrites (1), it may be asked whether field potentials have a role to play in modern neuroscience. The answer is affirmative. Human EEG continues to have a major importance in diagnosis of neurological disease and epilepsy, in particular. Evoked potentials also have diagnostic value for disorders of the sensory or motor pathways. Animal and human EEG/MEG and local field potentials have played a major role in revealing network oscillations and synchrony. There are many highlights in field potential research. Hans Berger’s discovery of the alpha rhythm in the 1920s was followed by Edgar Adrian’s confirmation. Adrian subsequently reported an induced rhythm of 30–90Hz (now called the gamma rhythm) in the olfactory bulb. The gamma rhythm has been recognized as a means of synchronizing distributed neurons within and across brain structures. Oscillatory field potentials and synchrony have been intensively studied since the landmark reports of gamma in the visual cortex (2) and thalamus (3), following pioneering studies in the olfactory system (4). The theory of field potentials is not covered in introductory or advanced neurophysiology textbooks, with the exception of Johnston and Wu (5) and a section written by Brinley (6). A basic coverage of field potentials was given by Hubbard et al. (7), a more specialized treatment was given by Freeman (4) and Niedermeyer and Lopes da Silva (8), and a decidedly more biophysical coverage was given by Plonsey (9) and Nunez (10). A major neurophysiological problem is to find the sources and sinks of the currents that generate the field potential. The current source per volume is defined as the current source density (CSD). In general, the inverse problem of finding the CSDs from the potential field has no definitive solution. However, with the knowledge of the anatomy, geometry, and the possible neural sources and sinks, it is possible to postulate a likely solution. Direct recording of field potentials from the brain regions that generate the potentials is important for refining the solution. CSD analysis can be readily applied to reveal the sites and time courses of the dendritic or somatic synaptic activation or action currents in a population of synchronously activated neurons. CSD analysis has been the subject of previous reviews (11, 12). In recent

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years, advances in computer and electrode fabrication ­technology have made potential mapping and CSD analysis more precise, and with an increasing capability to address more research questions than ever before. Multichannel field potential recording and CSD analysis will be the focus of the present review.

2. Field Potential Theory 2.1. Current Flow in a Cable



A common example used to illustrate the relationship among intra and extracellular potentials and membrane currents is an axon. An axon is modeled by a cable, which is an engineering terminology for a long metallic wire that carries voltage across long distances. Below the threshold of an action potential, an axon can be considered as an electric cable that conducts passively or electrotonically. Dendrites and dendritic trees can also be represented as cables. The passive flow of current down an axon (cable) is illustrated in Fig. 1a. Assume currents are injected at x = 0, the currents flow down the long axis of the axon in both positive and negative directions. We also assume that extracellular currents can only flow along a thin layer of extracellular fluid, such as along the long axis of a moistened axon suspended in air. For each unit length, the extracellular resistance is small in comparison to intracellular resistance, and the currents are mainly determined by the intracellular resistance/length assumed to be ri [ohm/cm]. For the locations 0, 1, and 2 inside the axon, the intracellular (longitudinal) current between two points is determined by Ohm’s Law (voltage = current × resistance), such that I 0 = −(V1 − V0 )/(ri ∆x ),

(1)

where ri Dx is the resistance across a small segment of axon of length Dx, and the first negative sign on the right side indicates a positive direction of current flow when V0 is greater than V1, as shown in Fig. 1a. Similarly,

I 1 = −(V 2 − V1 )/(ri ∆x ).

(2)

To conserve charges (per time), the membrane current is J1 = I 0 − I 1 ,



= −(V1 − V0 )/(ri ∆x ) + (V2 − V1 )/(ri ∆x ),



(3)

= (V0 + V2 − 2V1 )/(ri ∆x ).

Equation (3) determines the membrane current per length from the spatial distribution of the intracellular potential.

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Fig. 1. Current flow in an axon suspended in air or in a volume conductor. (a) Injection of current into the axon suspended in air sets up local current loops. Injected current at the origin (x = 0) moves to the right and left, and a decrease in longitudinal intracellular currents (I ) gives a membrane current (J ). At steady-state following constant current injection, the voltage decays exponentially with distance (x) in an infinite cable model of the axon. (b) Schematic extracellular potential field during an action potential in an axon suspended in a conductive medium (after (13)). The maximal current sink (inward Na+ current) is at the origin, and the current sources (current outflow) surround the sink, giving rise to a spatial sequence of positive–negative–positive fields. The extracellular (field) currents are perpendicular to the potential contours, and only one major current loop is drawn for simplicity.

If the differential form of the above (Equations 1–3) is used, i.e., when Dx → 0, then

I = −(1/ri )



J =−

∂V ∂x

∂ ∂ 2V I = (1/ri ) 2 . ∂x ∂x

(4)

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Adding the relation that the membrane current J = cm



∂V V + , ∂t rm

where rm is the membrane resistance per length and cm is the membrane capacitance per length, then

cm

∂V V 1 ∂ 2V + = . ∂t rm ri ∂x 2

∂ 2V ∂V . + (ri /rm )V = c m ∂x 2 ∂t

(5)

When the steady-state condition is considered, that is, at a long time after continuous injection of current at x = 0 (when membrane capacitance currents can be ignored), then

∂ 2V + (ri /rm )V = 0 ∂x 2 and for an infinite cable with current injection at x = 0, the solution for x > 0 is



V = V0 e − x /λ ,

(6)

where V0 = intracellular voltage at x = 0 and l = (rm/ri)0.5. Equation (6) gives the familiar steady-state solution to an infinite cable equation, which is an exponential decay with space constant l. 2.2. Theory of Extracellular (Field) Potentials

Field potential generation is instantaneous or quasi-stationary, that is, it depends on the extracellular current ( J ) distribution, or the current field, at one instant of time. In other words, it is a snapshot of the changing world, independent of the future or the past. The reason for an instantaneous generation of potential field is because extracellular currents are mainly resistive, and capacitance and inductive currents that would impose time shifts do not make a significant contribution. In addition, currents flow in a closed loop, and there is no gain or loss of currents around the loop (when capacitance currents are included). For solving the intracellular potentials, the extracellular potential (or resistance) is ignored as a first approximation (Sect. 2.1). Similarly, extracellular potentials are assumed to be generated from a set of membrane currents impressing on the extracellular medium, without explicit reference to the intracellular potentials (9). Since the general case is a three-dimensional medium, we define the CSD, or Iv, as the sum of the net membrane currents in a local volume. Thus, current source is the net outward membrane current within a volume, while current sink is the net inward membrane current within a volume.

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In the generation of field potentials, we may assume that the extracellular medium contains sources and sinks (CSDs) that give rise to the extracellular current vector ( J ), electric field vector ( E ), and scalar potential field (f). The fields are described by three standard electric field equations (12, 14) as follows. E = −∇�



(7)

J = σE = −σ∇� f

(8)

∇·J = −I v

(9)

and

where s = conductivity tensor  ∂ ˆ ∂ ˆ ∂ ˆ  ∇ = ∂x i + ∂y j + ∂z k  gradient operator

and

 ∂ ∂ ∂ ˆ k divergence operator ∇ =  ˆi + ˆj + ∂y ∂z   ∂x Combining the equations above gives the Poisson’s equation ∇·(s∇ � f) = − I v



(10)

and assumption of s that is homogeneous and isotropic gives

∂ 2f � ∂ 2f � ∂ 2f � I v + + =− , ∂x 2 ∂y 2 ∂z 2 s

(11)

which gives a solution of

f (r ) =

Io 4psr

(12)

when a single current source of Io is placed at the origin at distance r from where the potential is measured. The generation of the potential field by CSDs is mathematically identical to the generation of the potential field by electrostatic charges, since a common equation, the Poisson’s equation, describes both generation processes. 2.3. Qualitative Aspects of Potential Fields Generated by Action and Synaptic Currents 2.3.1. Action Currents in Single Cells

The analysis of an injected current in a cable (Fig. 1a) is similar to that of an action potential with an inward current at the origin (x = 0). If the axon is inside a volume conductor (e.g. in a large bath of saline or in the brain), the potential will spread through the volume and result in “volume conduction” (13). The site of the current flow from the extracellular into the intracellular medium corresponds to a current sink, i.e., where the current disappears from the extracellular medium. A current sink ­generates

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a local negative potential. An outward membrane current is a ­current source for the extracellular medium and it generates a local positive potential. As indicated by Fig. 1b, the current sources are located at sites (left and right) away from the origin (sink), where the current flows out of the membrane; only the main current loops are drawn in Fig. 1b. The spatial sequence of CSD is source–sink–source, corresponding to positive–negative–positive potential field. Extracellular potential field lines are of decreasing magnitude away from the axon. Zero isopotential lines separate regions of positive and negative potentials. Since the one sink is relatively more intense than each of the two sources, the extracellular medium is occupied more by negative potentials. 2.3.2. Synaptic Currents in Single Cells

Synaptic excitation is assumed to occur at the distal apical dendrite of a pyramidal cell in the cerebral cortex (Fig. 2a). The distal apical dendrites are depolarized by an excitatory postsynaptic potential (EPSP) that has an inward current (sink) at the synaptic site. Since the distal apical dendrite is more depolarized (or more positive in potential) than the rest of the cell, longitudinal current flows away from the apical dendrite toward the cell body. For long apical dendrites, most currents would flow out of the more proximal location dendrites and then extracellularly to complete current loops. The outflow at the more proximal apical dendrites is a current source, and it is passive (without an electromotive force). Distal excitation generates a dipole field, with negative potential at the distal apical dendrite, positive potential at the proximal apical dendrite, and a zero isopotential in between (Fig. 2a).

Fig. 2. Qualitative potential fields in a pyramidal cell (population assumed to line up in parallel) following excitation at different levels and somatic inhibition. The pyramidal cell schematic includes two basal dendrites (top) and a single apical dendrite (bottom). (a) Excitation of the distal apical dendrites gives a distal dipole (positive–negative) field separated by a zero isopotential (horizontal dotted line). (b) Proximal apical excitation generates a proximal dipole field. (c) Basal dendritic excitation makes the basal dendritic layers negative and the soma layer positive. (d) Somatic inhibition sets up a field that is positive at the soma and possibly negative at the apical dendrites; inhibitory currents and potentials have a slow time course.

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If excitatory synapses are activated at the proximal dendrites (Fig. 2b), the inward current at the dendrite causes main current to flow proximally toward the soma (thick arrow) and a smaller current flowing distally (thin arrow). The latter assumes that the somatic loop has a lower resistance than a distal current loop. The zero isopotential is expected to be somewhere along the path of the major current loop, i.e., between the proximal dendritic synaptic site and the soma. When the basal dendrites are synaptically excited (Fig. 2c), the current flows to the soma and exit there to complete an extracellular loop. The sink is at the basal dendrites and the main source will be at the soma. The dipole field (negative at the basal dendrites, positive at the soma) will have a zero isopotential between the activated synapses and the soma. If an inhibitory postsynaptic potential (IPSP) occurs at the soma, it may be Cl− entering through GABA-A receptors, or K+ exiting through GABA-B receptors. In either case, the inhibitory postsynaptic current is an outward current and constitutes a current source at the soma. The current source drives currents extracellularly to passive sinks on either side of the soma. The reversal of the extracellular potential field depends on the magnitude of the basal and apical dendritic sources. In Fig. 2d, it is assumed that the apical dendritic current loop is the major current loop, and the isopotential line is at the proximal apical dendritic layer (15). A field generated by inhibitory synaptic currents is generally smaller than the one generated by excitatory synaptic currents for several reasons. The main reason is that inhibitory synaptic currents are normally smaller than the excitatory synaptic currents because of the following: (1) at rest (~ −60 mV), the electromotive force of an inhibitory current (reversal potential ~ −72 mV) is smaller than that of an excitatory current (reversal potential ~0 mV); (2) capacitative currents are larger for excitation than inhibition, since excitatory currents rises 5–10 times faster than inhibitory currents. The above does not suggest that synaptic inhibition is less effective than excitation, since inhibition can occur with shunting (conductance change without voltage change). In general, excitatory and inhibitory fields could not be distinguished without additional neurophysiological data. For example, the somatic inhibitory field (Fig. 2d) may not be readily distinguished from a proximal dendritic excitatory field (Fig. 2b). Thus, intracellular recording or unit recording is necessary to confirm whether the dominant event is excitation or inhibition. 2.3.3. Geometrical and Temporal Considerations: Open and Closed Field, Standing and Traveling Wave

Individual pyramidal cells are lined up in palisades (parallel) in the cerebral cortex (Fig. 3a). When the cells are synchronously activated during an evoked potential or a spontaneous EEG, the potential field of individual cells will sum to give a large signal. The large signal results from summation of extracellular currents, or potentials (Equation 12), from individual neurons.

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Fig. 3. Open and closed fields, and volume for CSD measurement. (a) Schematic open field generated by distal dendritic excitation of palisades of pyramidal cells in a cerebral cortex. The potential field has positive and negative poles, and potential field lines are crossed by current flows with arrows. (b1) Schematic closed potential field with a single polarity at the center, generated by (b2) a single cell with distal excitation indicated by arrows at the periphery of the cell, or by (b3) a radially symmetric cluster of cells each excited at the distal dendrite (indicated by arrows). (c) Volume element of dimension Dx, Dy, and Dz used for CSD estimate. Current (J ) outflow subtracting the inflow in each dimension gives the current source (or sink) for that dimension. An increase in current in the z direction is depicted, indicating a net source for the volume shown.

Figures 2 and 3a illustrate open fields. An open field is the one that is not contained in space, and its effect can be detected at large distances away from the source. Because of the volume conductor, the potential can be observed far from the current sources and sinks that generate the potential (Fig. 3a1). This is why the EEG can be recorded on the scalp, where there are no neuronal sources and sinks. Theoretically, a single source gives potentials that decrease ultimately with 1/r (r = distance away from the source; 12). Given that currents flow in a closed loop in the brain, a source is always accompanied by a sink and a source-sink pair (dipole) is the minimal unit of extracellular potential generation. Dipole potentials decrease ultimately with 1/r 2. Concatenation of two dipoles, a “+ − − +” sequence (or effectively a “+ − +” sequence)

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generates a field that decays ultimately with 1/r 3. The latter ­configuration resembles the source–sink–source structure of an action potential (Fig. 1b), and explains, in part, the faster decay of an action potential with distance, when compared with a dipole field (e.g. distal excitatory synaptic potential). Although the potential field (and the accompanying current flow field) ultimately decreases with distance, it is still present at large distances. Indeed, potentials recorded on the scalp are caused by volume conduction. A closed field is a potential field that can only be detected within the structure itself. A single cell may have a symmetrical spherical geometry such that uniform activation of its dendrites (or cell bodies) will only generate radial currents (Fig. 3b2). Distal sinks (excitation) are balanced by proximal passive sources. Radially symmetric source–sink gives a potential field only within the spatial domain of the sinks and sources (Fig. 3b1). Other than a single cell, activation of a structure of many cells may result in radially symmetric sources and sinks that generate a closed field (Fig. 3b3). If the spatial potential field is recorded at different times, the field associated with a propagating action potential (or compound action potential from a population of axons) will move with time. The shifting of the field with time gives a traveling (propagating) potential field. For synaptic excitation, there is also some delay in charging of the membrane capacitance. However, for most general purposes, the potential field associated with synaptic currents can be considered as standing since the shift in field polarity is small in space and relatively rapid in time (within 10 ms).

3. General Application of CSD Analysis 3.1. Single vs. Multichannel Electrode Mapping 3.1.1. Pros and Cons of Single vs. Array Electrode Mapping

Typically, the potential field is sampled (mapped) at discrete locations, in a Cartesian (rectangular) coordinate system, before the application of CSD analysis. There are two main methods for mapping – by a single electrode sequentially or by an array of electrodes simultaneously. Practically, there are advantages and disadvantages of each method (Table 1). Since the silicon probe is the most frequently used multichannel probe that is commercially available, acquisition is focused on using the silicon probe. There are many advantages of using an electrode array for simultaneous registration of potentials in the brain (Table 1). Linear arrays of 8–64 electrodes, of various inter-electrode distances, are now commercially available (see Appendix). Mapping an instantaneous potential field by simultaneous recordings in an array is theoretically rigorous. Some events in the brain occur only once,

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Table 1 Advantages of sequential single-electrode mapping vs. simultaneous ­multichannel mapping by a silicon probe Single electrode recording

Multichannel probe recording

Area of coverage

Flexible

Limited

Depth sampling interval

Flexible

Fixed but accurate

Technical requirements

Few

Many

Disruption of the brain

Small

Moderate

Duration of mapping

Slow

Fast

Nonstationary events

No

Yes

Overall signal to noise

Adequate

Superior

for example, seizures, epileptiform, and other transients, and simultaneous recordings are needed to capture these events. A rapid acquisition of the potential profile (and CSDs) will allow studies in which the responses change with time, such as experiments on synaptic plasticity and pharmacological responses. A practical disadvantage in using multichannel probes is the necessity to maintain viability and calibration of multiple recording channels. Special hardware (e.g. multiple analog-to-digital converters and sample-and-hold circuits) and software are needed to achieve simultaneous recordings for multiple channels (Sect. 3.1.2). The area of mapping is limited by the availability of multichannel probes. As described in Sect. 4.1, the spatial sampling interval depends on the spatial frequency of the potential field. The most useful probes are those with electrodes lined up in a single dimension in depth. It is impractical to sample potentials by many depth probes for several reasons. First, if each probe maps the z direction, multiple probes have to protrude from a surface grid in the x–y plane, and these types of multishank probes are costly. Second, neighboring probes cannot be too close to each other, otherwise serious distortion and lesion of the brain tissue would occur. Mapping by a single electrode is flexible in terms of mapping intervals, in x, y, and z-dimensions. Considering a glass microelectrode, serious disruption of the brain occurs at the widest part of the micropipette (typically 1–1.5 mm outer diameter) and less so at the tapering end of ~1-mm diameter. A single microelectrode track inflicts little detectable damage to the tissue, and multiple tracks of different spatial intervals are possible. Averaging of the event enhances the signal-to-noise ratio. Equipment requirements for single-electrode mapping are relatively simple, and only

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an amplifier and an analog-to-digital converter are needed. However, an accurate micromanipulator is important (Sect. 3.2.2). A major assumption of single-electrode mapping is that an event, usually an evoked potential, is stationary, such that the event recorded at one location and time is the same as that recorded at another location and time. Whether the event is stationary or not should be confirmed. One way is to record the same event from a nonmoving (fixed) electrode to show that the event is stable in time. Another way is to return the mapping electrode to the same location, and repeat the recording at different times. In general, single-electrode mapping is counter-indicated for nonstationary events, such as seizure and one-time transients (e.g. interictal spikes). Single-electrode mapping can be automated for speed and accuracy. In one particular implementation (16, 17), a programmable microdrive pulled up a microelectrode (in a z-axis), paused for a time delay (for brain tissue to settle), and then acquired an average-evoked potential (AEP) before the cycle repeated itself. With additional x and y-axis controls of a micromanipulator, the electrode can be placed at any Cartesian coordinates (x, y, and z), and mapping over a volume can be achieved. Single track or one-dimensional mapping may make use of recordings acquired by surface arrays of electrodes, such as those used to map the surface distribution of potentials on a cortical surface (4, 15). A surface array may have electrodes separated by 200–300 mm, and its recordings may be used to justify singledimensional mapping or to provide an estimate of the lateral current spread. Surface arrays can be applied to determine potential and CSD profiles on the surface of a brain slice in vitro. It is possible to apply a mixed strategy of moving the silicon probe in order to map a larger extent of the brain. A small movement (25–100 mm) of a silicon probe was found to not significantly disrupt the brain tissue, such that in the regions that overlapped before and after movements, the CSDs remained essentially the same (18). 3.1.2. Specifics of Multichannel Recording

A silicon probe consists of an array of electrodes made by thinfilm technology on a silicon micro-machined substrate and insulated by dielectric (silicon dioxide/nitride) deposits. The commercially available probes were originally developed at the University of Michigan (19). Commercial availability depends on reliable batch processing. A typical recording area (electrode site) is made of iridium, rectangular or square in shape, of 5–20 mm dimension. Adjacent electrodes can be separated by 30–200 mm. Fabrication dimensional accuracy is 10 mm. Multiple-shank probes are also available.

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Impedance of each electrode in the silicon probe is about 2 MW at 1 kHz. Electrode impedance should be matched by preamplifiers of high input resistance impedance (>0.2 GW). The preamplification, main amplification, filtering, and analog-to-digital conversion should be identical for all the electrodes in the array. Identical signal processing for each channel is important for CSD analysis, since a small distortion at a single channel will be magnified. Gain calibration of the complete multichannel system can be made by placing a silicon probe in a large saline bath and passing square stimulating current pulses across a pair of long silver wires placed at a large distance (>2 cm) away from the recording electrode. The goal is to achieve recordings of the same waveform and identical magnitude at all electrodes. Recording from chronically implanted animals provides an important application of silicon probes. In one application, a silicon probe is connected by means of a flexible ribbon cable to a small connector embedded in dental cement to the skull (20). Bragin et al. (21, 22) used a microdrive to drive a single probe slowly through the brain. Single neuron activity can be recorded from a silicon probe. The single unit signals from electrodes well within the shank (~200-mm wide) were reported to be lower than those from electrodes near the tip (22). This occurs likely because of tissue disruption that was more severe at the shank than the tip of the probe. Even when an electrode is placed in a cell-free conductive medium (such as a saline bath), the electrode would inevitably distort the potential and the current flow field. The distortion is typically larger for the larger silicon probe than a single microelectrode. Drake et  al. (19) documented the distortion of the field of an action potential by a silicon probe. They reported up to 60% increase of the potential (compared with a theoretical condition with no recording probe) on the recording face of the probe, and up to 100% attenuation of the potential on the nonrecording side of the probe. The field distortion is considered acceptable when the dimension of the probe is smaller than the inter-electrode interval. We confirmed a possible distortion of the field potentials recorded by a silicon probe (16 electrodes at 50 mm intervals) in the hippocampus. The latter probe has a nonconducting flat shank of 15-mm thickness and it tapers from the main shank of 200 mm thickness to 33 mm at the tip. We (Wu and Leung, unpublished data) found that the maximal orthodromic population spike amplitude recorded by a silicon probe was smaller than that recorded by a single glass micropipette. The probe-recorded potential may be small because extracellular currents flowing from one side (the “blind” side) of the silicon probe cannot reach the recording electrode. Accentuation of the field on the recording side, an effect of a nonconductive boundary condition, apparently did not fully compensate for the loss of signal from the “blind” side.

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Several techniques are used to confirm the location of a ­ articular electrode on a silicon probe. Recording of field potenp tials evoked by stimulation of known afferents will provide information on line. Some of these responses in CA1 area of the hippocampus are described later (Sect. 4). Bragin et al. (21, 22) sectioned the brain with the implanted probe in place. Using a special electronic circuit that allows for both recording and passing current, lesion can be made at a specific electrode of the probe and then verified histologically (18). 3.2. Experimental CSD Analysis 3.2.1. Second-Order Differencing

On the basis of (Equation 11), CSDs (Iv) in a homogeneous medium are derived from a second-order derivative of the potential field (Ø) in three dimensions. Since it is necessary to map the potential field at discrete locations, the second-order differentiation is replaced by second-order differencing. In other words,



∂ 2f ≈ [f (x +∆x , y , z, t ) + f (x − ∆x , y , z, t ) − 2f (x , y , z, t )]/(∆x )2 ∂x 2



∂ 2f ≈ [f (x , y + ∆y , z, t ) + f (x , y − ∆y , z, t ) − 2f (x , y , z, t )]/(∆y )2 ∂y 2



∂ 2f ≈ [f (x , y , z + ∆z, t ) + f (x , y , z − ∆z, t ) − 2f (x , y , z, t )]/(∆z)2 ∂z 2 and



I v ≈ s {[2f (x , y , z , t ) − f (x + ∆x , y , z , t ) − f (x − ∆x , y , z , t )]/(∆x )2 +[2f (x , y , z , t ) − f (x , y + ∆y , z , t ) − f (x , y − ∆y , z , t )]/(∆y )2 +[2f (x , y , z , t ) − f (x , y , z + ∆z , t ) − f (x , y , z − ∆z , t )]/(∆z)2} (13)

A general consideration before attempting CSD analysis for a new structure is to decide on the extent of mapping, the mapping interval, and the electrodes to be used for mapping. Although many CSD studies used one-dimensional mapping, the underlying assumption should be experimentally tested. For an unknown structure and input, the extent of the potential field should be mapped by multiple tracks or by means of cortical surface arrays. Even if three-dimensional CSD analysis may not be practical, the three-dimensional potential field gives an estimate of the error of using one-dimensional CSDs. In general, whether the conductivity is homogeneous or isotropic will affect the results. However, accurate measurement of conductivity for a particular preparation is difficult, and theoretical and experimental studies have determined that small (even several folds) differences in isotropicity or layer conductivity did not significantly affect the locations of the CSDs. A nonisotropic medium was found in the cerebellum (23) and a lower conductivity (inhomogeneity) was reported in the pyramidal cell layer than other dendritic layers in CA1 (24).

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With the assumption that there is negligible change in ­currents in the x and y directions, I v ≈ s [2f (z, t ) − f (z + ∆z, t ) − f (z − ∆z, t )]/(∆z)2



≈ s /(∆z)2 {[(f (x , y , z, t ) − f (x , y , z + ∆z , t )] −[ f (x , y , z − ∆z, t ) − ( f (x , y , z, t )]} I v ≈ {Jz + ∆z / 2 − Jz − ∆z / 2} / (∆z)

(14) (15)

The equation above indicates that the CSD Iv is the difference of the Jz leaving (at z + Dz/2) and entering (at z − Dz/2) a particular volume, as illustrated in Fig. 3c, with Jz ≈ −s (∆f / ∆z) . When outflow is larger than inflow, Iv is positive or there is a source. When outflow is smaller than inflow, Iv is negative or there is a sink. 3.2.2. Accuracy of the CSD Estimates



The spatial interval used for deriving CSD is a parameter that needs to be experimentally determined. Sampling of a signal requires a rate that is at least double that of the frequency of the signal, as required by the sampling theorem. A higher sampling rate will give better accuracy. Thus, the spatial sampling interval should be at least double that of the main spatial frequency of the potential function in each dimension. In field mapping of the cerebellum and hippocampus, 20–50 mm was determined to be an adequate spatial sampling interval (18, 25, 26). Since the CSD estimate is based on differencing, it will amplify or increase the noise of a single channel. This suggests that if different amplifiers and analog-to-digital converters are involved in sampling of potentials at different depths, the calibration of different channels must be accurate. In addition, (Equation 14) indicates that a major error may come from the inaccuracy of the interval Dz (on account of the square of Dz). An accurate micromanipulator, calibrated to 1 mm or less, is important for accuracy. Spatial smoothing of the CSDs has been extensively discussed by Freeman and Nicholson (23). A simple smoothing formula uses a spatial interval of N = 2 instead of N = 1 in the following equation (an extension of Equation 14): I v ≈ s [2f (z, t ) − f (z + N ∆z, t ) − f (z − N ∆z, t )]/(N ∆z)2 . (16) The two-step differencing formula is equivalent to doing a running spatial average of three consecutive depth potentials f ′i = (¼fi−1 + ½fi + ¼fi+1); [fi−1, fi and fi+1 are the raw data at Dz intervals] and then applying (Equation 14) (N = 1 differencing) to f′i (23). Polynomial fit to the potential profile was also used. Smoothing reduces the noise (that is unrelated to the signal) and improves the reliability of the CSDs. The down side of smoothing is that accuracy is degraded.

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4. CSD Analysis of Hippocampal Field Potentials

4.1. Synaptic Excitation and Inhibition in CA1

The following gives examples of CSD analysis applied to hippocampal CA1 area. Similar analysis applied to the dentate gyrus has been reported by Golarai and Sutula (26), Canning and Leung (27), and Canning et al. (28). CSD analysis had also been done in the visual cortex (11) and olfactory cortex (29). The layered structure of the afferent excitation of hippocampal CA1 area is readily revealed by potential mapping and CSD analysis. The following results were obtained by mapping of the potentials evoked in CA1 in the rat under urethane (1.5 mg/kg i.p.) anesthesia. Stimulation of the medial perforant path that synapses on the distal apical dendrites of CA1 gave a maximally negative potential at the distal apical dendrites (Fig. 4a1, (16)). However, because of volume conduction from the dentate gyrus (DG), there was no positive potential as predicted in Fig. 2a. CSD analysis (Fig. 4a2) gives a pattern of sinks and sources that is consistent with the current flows in Fig. 2a. The sink was located at the distal apical dendrites, accompanied by distributed proximal sources that gradually diminished in amplitude toward the soma. Smoothing by the two-step differencing (N = 2 in (Equation 16)) smoothed out the dendritic source distribution and decreased the magnitude of the maximal sink. Volume conduction from the DG to CA1 is illustrated by the AEPs following medial perforant path stimulation (Fig. 5a). The initial field potential (:

< y (z, t * ) > =

1 M

M

∑y

m =1

m

(z, t − qm / 2pf ),

(4)

where t* is the adjusted time as the shifting operation disrupts the original physiological time. 5. Compute CSD profiles at frequency f as the negative of the second spatial derivative of < y > :

I ∝ − < y > ′′ = −

∂2 < y > . ∂z 2

(5)

The second derivative can be approximated by the finite difference formula in (3). This method will be henceforth referred to as the PRAT. The resulting LFP and CSD profile will be referred to PRAT-LFP and PRAT-CSD, respectively. By scanning across the frequency spectrum of interest, one can analyze the current sources at different frequencies. See Csicsvari et al. (11) for a similar method based on band-pass filtering.

4. Simulations Mathematical models are used to generate spontaneous spatiotemporal signals similar to that recorded in physiological experiments. The PRAT algorithm is then used to perform CSD analysis. By comparing the PRAT-CSD pattern with the corresponding mathematical functions, we are able to assess the validity of our method. Obviously, such a direct cross-validation is not possible in the analysis of real physiological data where the answer is not known a priori. 4.1. The Model

Experimentally, the data to be analyzed come from a cortical column. Here a cortical column is represented by the unit interval.

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The transmembrane current is assumed to have a sinusoidal profile containing a source and a sink: az cos(2pf z z + q z ), where az, fz, qz (=−p/2) are amplitude, frequency, and phase. This term is referred to as the spatial dynamics term. Solving the differential equation ∂ 2j = az cos(2pf z z + q z ), ∂z 2

we obtain

f (z) = C1z + C 2 − az cos(2pf z z + q z ) / (2pf z )2 , where C1 and C2 are constants. The temporal dynamics Y(t) is modeled in two different ways: (1) a 10 Hz sinusoidal function at sin(2pf t t + qt ) and (2) a second-order autoregressive process [AR(2)]: Y (t ) = aY (t − 1) + bY (t − 2) + x (t ) , with a = 0.6, b = −0.9, and x(t) being a white Gaussian noise. Like the 10-Hz sinusoid, the AR(2) process chosen this way also has a spectral peak at 10 Hz. Multiplying the space- and time-dependent functions and adding noise, we generate spatiotemporal LFP signals y(z, t):



y (z, t ) = j (z)ψ (t ) + h(z, t ),

(6)

where h(z, t) is a stochastic process with long-range power law (power a 1/frequency) correlation in all channels as well as random amplitude Gaussian noise in different channels (12). This choice is motivated by the observation that 1/f spectra are commonly observed in EEG and LFP recordings from the mammalian cortex (13–15). 4.2. CSD Analyses with PRAT

The above models were simulated and these data were assumed to be acquired by a multi-electrode with 14 equally spaced contacts. Figures 1 and 2 show the results for the two different temporal functions, 10-Hz sinusoid and AR(2), respectively. In both figures, panel (a) gives the color-coded power spectra at different contacts or channels (vertical axis) where oscillation at 10 Hz is clearly seen; panel (b) displays the superposition of 500 trials with random initial phases at the reference contact denoted by zk; panel (c) shows the same 500 trials after phase realignment; panel (d) is the PRAT-LFP. The time label is from −100 to 0 ms. This label is motivated by the fact that, in the next section, experimental data from the prestimulus time period will be considered where the stimulus onset is defined as 0 ms. It is evident that the PRATLFPs in Figs. 1d and 2d are not able to reveal the underlying current/source pattern in the mathematical model, suggesting that LFPs have limited ability to precisely localize generators of transmembrane current flow. The PRAT-CSD profiles obtained by taking the second spatial derivative on the PRAT-LFPs are

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Fig. 1. Simulation example where the temporal dynamics is defined by a 10 Hz sinusoid. (a) Power spectra (5–80 Hz) as a function of electrode contact. (b) Trials from the reference contact before phase realignment. (c) The same trials after phase alignment. (d) The PRAT-LFP profile. (e) The PRAT-CSD profile. (f) The spectrum of the total transmembrane current flow. The horizontal axis is frequency (Hz) in (a) and (f). It is time otherwise in the unit of millisecond.

shown in Figs. 1e and 2e. The source and the sink pairs in the CSD profiles are clearly seen at around electrode contact 4 and 11. Temporally, the source-sink pair oscillates at a frequency of 10 Hz. Thus, the PRAT method recovers the dynamics built into the mathematical model. The above analysis can be carried out for each frequency from 5 to 80 Hz. Integrating the rectified PRAT-CSD profile over space and a given time interval yields the amount of transmembrane current at frequency f. The results are plotted in panel (f) and are called the CSD spectra. From the CSD spectrum, the greatest amount of transmembrane current is seen to occur at10 Hz. This again is in agreement with the conditions implemented in the mathematical model.

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Fig. 2. Simulation example where the temporal dynamics is defined by an AR(2) process; the conventions are otherwise the same as in Fig. 1.

5. Application to Experimental Data Field potential oscillations are ubiquitous in the nervous system. Depending on the signal rhythmicity, these oscillations are classified according to the following approximate nomenclature: delta (1–3 Hz), theta (4–7 Hz), alpha (8–12 Hz), beta (13–25 Hz), and gamma (25–90 Hz). The alpha rhythm is a prominent oscillatory activity in the 8–12 Hz band in EEG recordings over the occipital and parietal areas during wakefulness (16, 17). Nearly 80 years after its discovery (18), its genesis, cellular mechanisms, and functions remain unclear. Early work emphasized the ­pacemaking

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role of the thalamus (19). More recent evidence suggests that it might be of a cortical origin (20). This problem is considered in this chapter by recording LFP and multiunit activity (MUA) from the inferotemporal cortex of a behaving macaque monkey. The PRAT method, in conjunction with other methods such as CSDMUA coherence, is applied to address two problems: (1) laminar location of alpha current generators and (2) effect of prestimulus alpha oscillation on stimulus-evoked processing. 5.1. Experimental Paradigm

The data considered here is part of a previously published study (21, 22). A male macaque monkey was trained to discriminate stimuli in both visual and auditory domains. There are two conditions. In Condition 1, the monkey was presented with a mixed stream of auditory and visual stimuli. In each sensory modality, a standard stimulus occurred 86% of the time and an oddball stimulus 14% of the time. Selective attention was manipulated by instructing the monkey to respond to the oddball stimulus in the attended modality only. Task difficulty was balanced between the modalities. In Condition 2, the monkey performed the oddball detection task in the auditory domain in the absence of visual stimulation. The reason for analyzing activity in visual cortices during auditory discrimination was that the discrimination kept the monkey verifiably alert without using visual stimuli, so that we could study spontaneous ongoing neural activity.

5.2. Recordings

LFP and MUA were sampled with a linear array electrode with 14 contacts spanning all six cortical layers in the inferotemporal cortex. Data from one penetration, collected during periods of adequate task performance (i.e. >80% target detection), were analyzed to demonstrate the method presented above. Problem 1: Laminar generators of ongoing alpha oscillation. Data from Condition 2 were analyzed. The length of a contiguous segment of spontaneous ongoing activity was on average 30 s long and there were five such segments for the penetration. After highpass filtering (3 Hz, zero phase-shift) and down-sampling to 200 Hz, the LFP data were further divided into epochs of 200 ms in duration, which were considered trials or realizations of an underlying stochastic process. The power spectrum of each recording contact was estimated and the contact showing the highest power spectral density at 10 Hz was chosen as the reference channel. The PRAT method was used to obtain PRAT-LFP and PRAT-CSD. Figure 3a shows the results where the reference contact is channel 6. The PRAT-LFPs (solid lines) exhibit clear oscillation at 10 Hz. The PRAT-CSD (color coded) revealed an alpha current generator in the supra-granular layers (around contacts 5–7) with an underlying source/sink/source configuration. The alpha current generator in the infra-granular layers (around contact 10) was relatively weak. No alpha current ­generator was seen in the ­granular layer. The generator around contact three is believed to reflect

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Fig. 3. Analysis of spontaneous alpha activity in inferotemporal cortex. (a) PRAT-CSD profile displayed as a color-coded plot, which is the second spatial derivative of the PRAT-LFPs (solid traces). A single epoch of MUA from two contacts is superimposed. (b) Laminar distribution of the peak (10 Hz) LFP power across recording contacts. (c) CSD-MUA coherence spectra at different contacts.

dendritic backpropagation. In Fig. 3b, the alpha band power is plotted as a function of the recording contact. The highest power occurs around channels 5 and 6, suggesting that the alpha current generator in the supra-granular layers may play an important role in the overall organization of alpha activity in the column. The respective roles of the alpha current generators can be further delineated by examining the concomitant MUA data. In Fig. 3a, an epoch of MUAs at channels 6 and 10 are overlain on the CSD profile. The MUA near the supra-granular layer alpha generator varies rhythmically with the underlying current, while the MUA near the infra-granular alpha generator is not modulated by the current. This suggests that the alpha current generator in the supra-granular layers is possibly the pacemaker of the alpha rhythm in the column. We confirmed this impression by calculating the CSD-MUA coherence. The MUA data were epoched the same way as the LFP data and down-sampled from 2 kHz by taking a temporal average in nonoverlapping windows of 5 ms duration to achieve effectively the same sampling resolution of 200 Hz as the down-sampled LFPs. The coherence between single-trial CSDs around alpha current generators identified by the PRAT-CSD method and the corresponding mean-centered single-trial MUAs was calculated by the multivariate autoregressive

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(MVAR) spectral analysis method (23). Figure 3c gives the CSDMUA coherence at channels 5, 6, 7, and 10 where relatively high transmembrane current flows were found. In the supra-granular layers, the CSD-MUA coherence is relatively strong, reaching values close to 0.16, while in the infra-granular layers, the CSDMUA coherence is close to zero. This supra-granular bias is consistent with the single epoch data in Fig. 3a. The above results demonstrate that the inferotemporal cortex contains an alpha pacemaker in the supra-granular layers, in agreement with the suggestion that the alpha rhythm might be of a cortical origin. A more thorough analysis of this problem has been carried out by Bollimunta et al. (24). The alpha pacemaker in the supra-granular layers has a source/sink/source configuration. In light of the substantially enlarged basal dendritic arbor reaching the size of 400 mm in IT (25), this alpha generator most likely reflects the activity of superficial pyramidal neurons. The CSD-MUA coherence further suggests basal dendritic excitation. It is worth noting that Lukach et al. (26), in an in vitro slice study, have shown that the supra-granular layers contain the pacemaker of alpha range oscillations in the entorhinal cortex in rats. Problem 2: Effect of prestimulus alpha oscillation on stimulus evoked response. The data recorded under Condition 1 were considered. The continuous LFP recordings were divided into 600 ms (−200, 400 ms) epochs based on the standard visual stimulus triggers. The prestimulus interval was defined to be from −200 to 0 ms, where 0 ms denotes stimulus onset. After data preprocessing, approximately 2,000 trials during which the monkey paid attention to the visual stimulus were made available for further analysis. The stimulus-evoked CSD from contact 5 in the supragranular layers was computed using the conventional method and shown in Fig. 4. From this figure, an early stimulus processing

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period (50–100 ms) and a late processing period (100–200 ms) were defined. Figure 5a shows the CSD profile of the ongoing prestimulus alpha oscillation determined by the PRAT method. Note the similarity between the CSD profile in Fig. 5a and that in Fig. 3a. Although obtained under different experimental conditions, these transmembrane current flow patterns are likely to reflect the same physiological generating mechanisms. To examine the relation between prestimulus alpha oscillation and stimulus-evoked response, the magnitude of the prestimulus oscillation at 10 Hz was estimated on a trial-by-trial basis. A template matching method was used for this purpose. For single-trial LFP data, the second spatial derivative see (3) was ­calculated to yield single-trial CSD profiles. The PRAT-CSD in Fig. 5a was used as a template and moved along a given ­single-trial a

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CSD profile to find the best pattern match defined in terms of cross correlation. The correlation coefficient at the best match location was retained as an index of the magnitude of the prestimulus alpha activity in that trial. The procedure was repeated for all trials. Figure 5b shows a single-trial CSD profile with a high matching index value; the similarity between the transmembrane current flow pattern that is between the two vertical lines and the PRAT-CSD in Fig. 5a is noticeable. All the trials were sorted into groups of 500 trials, according to the values of the template matching index, each group having 90% of the trials overlapped with the previous one, starting from the lower matching index value to the highest. For the 500 trials in each group, a PRAT procedure was performed to yield a group PRAT-CSD profile. The total transmembrane current flow (TTCF) was computed by integrating the rectified ongoing laminar CSD over time (100 ms) and space (depth). For the same group of trials, the stimulus-evoked CSD profile, shown in Fig. 5c, was calculated in the conventional way. The TTCF during the early (50–100 ms) and the late (100–200 ms) poststimulus time period were obtained and plotted against the prestimulus alpha TTCF in Fig. 5(d) (blue for early and red for late). All quantities were normalized to a maximum value of 1. The solid straight lines represent least squares fits. The correlation coefficient between prestimulus alpha activity and the early evoked response is 0.1, while the correlation coefficient between prestimulus alpha activity and the late component is 0.9. The above results demonstrate that the magnitude of the prestimulus alpha oscillation can affect stimulus processing. In particular, the prestimulus alpha oscillation is shown to be more strongly correlated with the late evoked component than the early evoked component. This observation appears to contradict intuitive expectations and thus calls for a possible explanation. In the cortex, excitatory neuronal information transmission is mediated by the release of the neurotransmitter glutamate. There are two major classes of glutamate receptors: AMPA and NMDA. On the one hand, experimental evidence suggests that the early evoked component reflects the fast response to stimulus input and is mainly mediated by AMPA receptors (27, 28). On the other hand, the late evoked component is apparently related to neuronal responses to feedback input from higher order areas and is thought to engage the NMDA receptors (28, 29). Spontaneous field potential oscillations in the theta and alpha range before the onset of stimulus reflect the cyclical variation in the excitability of neuronal ensembles (30–33). They involve the potentiation of NMDA receptors (34–36). The NMDA-mediated increase in excitability is an essential ingredient in recent theories of attention and memory (29, 37). This differential involvement of glutamate receptors with distinct stages of information processing

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and prestimulus facilitation of NMDA receptors may underlie the correlation pattern observed between prestimulus ongoing alpha activity and stimulus evoked response.

Acknowledgment This work was supported by NIH grants MH070948, MH079388, and MH060358. References 1. Mitzdorf U (1985) Current source density method and application in cat cerebral cortex: investigation of evoked potentials and EEG phenomenon. Physiol Rev 65:37–100. 2. Nakagawa H, Matsumoto N (2000) Current source density analysis of ON/OFF channels in the frog optic tectum. Prog Neurobiol 61:1–44. 3. Nicholson C, Freeman JA (1975) Theory of current source-density analysis and determination of conductivity tensor for anuran cerebellum. J Neurophysiol 38:356–368. 4. Schroeder CE, Steinschneider M, Javitt DC, Tenke CE, Givre SJ, Mehta AD, Simpson GV, Arezzo JC, Vaughan HG (1995) Localization of ERP generators and identification of underlying neural processes. Electroencephalogr Clin Neurophysiol Suppl 44:55–75. 5. Liang H, Bressler SL, Ding M, Truccolo WA, Nakamura R (2002) Synchronized activity in prefrontal cortex during anticipation of visuomotor processing. Neuroreport 13:2011–2015. 6. Zhang Y, Wang X, Bressler SL, Chen Y, Ding M (2008) Prestimulus cortical activity is correlated with speed of visuomotor processing. J Cogn Neurosci 20(10):1915–1925. 7. Pitts W (1952) Investigations on synaptic transmission. In: Cybernetics: transactions of the ninth conference. von Foerster H (Ed), Josiah Macy Jr. Foundation, New York, pp 159–166. 8. Howland B, Lettvin JY, McCulloch WS, Pitts W, Wall PD (1955) Reflex inhibition by dorsal root interaction. J Neurophysiol 18:1–17. 9. Freeman JA, Nicholson C (1975) Experimental optimization of current source-density technique for anuran cerebellum. J Neurophysiol 38:369–382. 10. Hämälainen M, Hari R, Ilmoniemi RJ, Knuutila J, Lounasmaa OV (1993) Magnetoen­ cephalography – theory, instrumentation, and

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applications to noninvasive studies of the working human brain. Rev Modern Phys 65:413–497. Csicsvari J, Jamieson B, Wise K, Buzsaki G (2003) Mechanisms of gamma oscillations in the hippocampus of the behaving rat. Neuron 37:311–322. Rangarajan G, Ding M (2000) Integrated approach to the assessment of long range correlation in time series data. Phys Rev E 61:4991–5001. Buzsaki G, Draguhn A (2004) Neuronal oscillations in cortical networks. Science 304: 1926–1929. Freeman WJ, Rogers LJ, Holmes MD, Silbergeld DL (2000) Spatial spectral analysis of human electrocorticograms including the alpha and gamma bands. J Neurosci Methods 95:111–121. O’Connor SC, Robinson PA (2004) Unifying and interpreting the spectral wavenumber content of EEGs, ECoGs, and ERPs. J Theor Biol 231:397–412. Shaw JC (2003) Brain’s alpha rhythm and the mind. Elsevier, Amsterdam Niedermeyer E (2005) The normal EEG of the waking adult. In: Electroencephalography: basic principles, clinical applications and related fields. Niedermeyer E (Ed), Williams and Wilkins, Baltimore, pp 149–173. Berger H (1929) Über das elektroencephalogramm des menschen (On the electroencephalogram of man). Arch Psychiatr Nervenkr 87:527–570. Andersen P, Andersson SA (1968) Physiological basis of the alpha rhythm. Appleton-CenturyCrofts, New York Lopes da Silva FH, Vos JE, Mooibroek J, Van Rotterdam A (1980) Relative contributions of intracortical and thalamo-cortical processes in the generation of alpha rhythms, revealed by

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Chen et al. partial coherence analysis. Electroencephalogr Clin Neurophysiol 50:449–456. Mehta AD, Ulbert I, Schroeder CE (2000a) Intermodal selective attention in monkeys. I. Distribution and timing of effects across visual areas. Cereb Cortex 10:343–358. Mehta AD, Ulbert I, Schroeder CE (2000b) Intermodal selective attention in monkeys. II. Physiological mechanisms of modulation. Cereb Cortex 10:359–370. Ding M, Bressler SL, Yang W, Liang H (2000). Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment. Biol Cybern 83:35–45. Bollimunta A, Chen Y, Schroeder CE, Ding M (2008) Neuronal mechanisms of cortical alpha oscillations in awake-behaving macaques. J Neurosci 28(40):9976–9988. Elston GN, Tweedale R, Rosa MGP (1999) Cortical integration in the visual system of the macaque monkey: large-scale morphological differences in the pyramidal neurons in the occipital, parietal and temporal lobes. Proc R Soc Lond 266:1367–1374. Lukatch HS, MacIver MB (1997) Physiology, pharmacology, and topography of cholinergic neocortical oscillations in vitro. J Neurophysiol 77:2427–2445. Hackley SA (1993) An evaluation of the automaticity of sensory processing using eventrelated potentials and brain-stem reflexes. Psychophysiology 30:415–428. Roelfsema PR, Ooyen A (2005) Ation-gated reinforcement learning of internal representa-

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Chapter 3 The Juxtacellular Recording-Labeling Technique Didier Pinault Abstract The single-cell juxtacellular recording–labeling technique makes it possible to label the neuron recorded extracellularly. It is a very useful tool for achieving single-cell structure–function correlation studies in living, intact neural networks and for determining their phenotype and genotype. It can reveal the overall picture of the smallest neurons, including interneurons. It can be combined with other electrophysiological techniques (e.g. electro-encephalographic recordings and intracerebral electrical stimulation), electron microscope, immunohistochemical, molecular and/or genetic techniques. Its principle consists in iontophoresing tracer molecules into the membrane of the neuron being recorded. This is done under continuous electrophysiological monitoring, allowing the retrieval of the neuron labeled in more than 85% of attempts. Continuous DC recordings suggest that the juxtacellular filling “or tickling” procedure produces a transient micro-electroporation, which allows the internalization of the tracer into the intracellular space. Since this procedure allows single neurons to be recorded for long periods, many electrophysiological features can be collected, and the finest and remotest axonal ramifications can be marked. In spite of some limitations and pitfalls, the juxtacellular technique remains the high standard for investigating the genetic, molecular, physiological, and architectural bases of cell–cell communication. It is also a very versatile and useful tool when it comes to decipher, for instance, the molecular, cellular, and network mechanisms of brain state, physiological, and pathological oscillations. Key words: Neuronal tract tracing, Iontophoresis, Biocytin, Neurobiotin, Single-cell labeling, Extracellular, Structure-function, Neural network, Ultrastructure

1. Overview and Scope of this Chapter

The purpose of this chapter is to gather practical information and advice for acquiring expertise in employing the single-cell juxtacellular recording/marking procedure devised and developed in whole animal preparations (1, 2). Some of our results obtained with this single-cell recording/labeling technique are illustrated. Its advantages and limitations are presented with reference to other approaches employing recording glass micropipettes.

Robert P. Vertes and Robert W. Stackman Jr. (eds.), Electrophysiological Recording Techniques, Neuromethods, vol. 54, DOI 10.1007/978-1-60327-202-5_3, © Springer Science+Business Media, LLC 2011

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Also, this chapter provides insight into the kinds of questions that can be addressed using the juxtacellular technique considering future trends.

2. Historical Considerations 2.1. The Golgi Impregnation Method

To understand how the brain works, modern neuroscientists seek to correlate the dendritic and axonal architectures of single nerve cells with their biophysical, molecular, synaptic, and genetic properties, which are specifically associated with a brain operation or a neurobiological disorder. For a long period, physiological and morphological data of single nerve cells have been obtained separately. It all started with the silver impregnation method discovered by Camillo Golgi in 1873, which had laid the foundations of the connectionist view of neural organization (3, 72, 73). The Golgi method, however, generally failed to impregnate myelinated axons in adult brains (4). In addition, not all axons that were impregnated could be followed to either their sites of termination or cells of origin. Therefore, the limitations and capriciousness of the Golgi method represent serious drawbacks. Furthermore, it cannot be combined with immunocytochemical procedures. Thus, the postmortem Golgi technique is used less and less nowadays.

2.2. Iontophoretic Application of Neuronal Tracers

Meanwhile, numerous neuroanatomical tract-tracing methods have been contrived and developed (5–7). Most of the purely anatomical techniques currently available employ a tracer-filled microsyringe or coarse glass pipette to expel by pressure, or by iontophoresis, a large amount of tracer into the brain tissue. Once captured by and internalized in the neuronal elements, the neuronal tracer is transported anterogradely and/or retrogradely to the dendritic and axonal ramifications. An appropriate histological procedure allows the tracer molecules that are internalized into the neuronal elements to be revealed. These tracing methods can be combined with immunocytochemical and electron microscopic techniques. Thereby, anatomical and synaptic relationships between brain regions have been assessed. However, the overall picture of a given dye-filled neuron is usually precluded. In addition, these tracing methods do not allow precise connectional studies of local neural networks and of direct correlation with physiology.

2.3. Combining Electrophysiological Recording with Neuronal Tracing

Some of the drawbacks of the pure histological and anatomical methods have been overcome by electrophysiological techniques that employ injectable dyes. It all started in 1949 when (71) manufactured the first electric recording glass micropipette, which contained a suitable electrolyte. This major breakthrough has been

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generating the great, still increasing population of electrophysiologists, who study the physiological properties of single neurons at both extracellular and intracellular levels (8). The electrophysiological data obtained so far have tentatively been correlated with the architecture of the Golgi-impregnated neurons. This deductive reasoning lasted till the advent of injectable tracers (9, 74, 75). Dissolved in an electrolyte, such a substance, once intracellularly injected into the recorded neuron, is made visible after processing the nervous tissue histologically. During the last quarter of the twentieth century, neuroscientists wishing to examine the functional architecture of single nerve cells had been succeeding in studying intrinsic and synaptic membrane properties of single neurons in combination with direct intracellular injection of tracer. The outcome of this technical breakthrough has thus deepened our understanding of the structure of physiologically identified neurons. 2.4. Limitations of Direct Intracellular Application of Tracers

The use of tracer-filled intracellular micropipettes remains a powerful means for structure–function correlation studies. In spite of its unique advantages, direct intracellular iontophoresis of markers may damage or kill the neuron under study, yielding a relatively low rate of success. Indeed, having injected the recorded neuron, the experimenter rapidly withdraws the micropipette that is being sealed with the recorded neuron’s membrane without controlling its electrical behavior. These conditions would not allow us to know whether the injected neuron is still viable at this stage. Maintaining the intracellularly injected neurons alive in an in vivo preparation remains a difficult task as long as they cannot be visually or electrophysiologically watched over after the staining procedure. Therefore, it is important to have a reliable control not only before but also and especially at the end of the filling procedure. Furthermore, because of the complications in getting stable penetrations, marking neurons with intracellular micropipettes remains difficult to apply for labeling small cells and exploring deep brain regions especially in whole animal preparations. In addition, unless applying intra-axonal dye injection (10), it often precludes the whole picture of the axonal arbor of the recorded neurons (11), particularly those forming long-range connections. Therefore, the intracellular approach, which remains irreplaceable for studying membrane events that are responsible for the firing patterns, may be discouraging when it comes to unraveling the wiring of cells and the set of connections in in vivo preparations. Single-cell labeling has also been attempted using extracellular, marker-filled, recording micropipettes with some success, but it is impossible to ensure that the labeled neuron is the one that was being recorded (2, 12, 13). These pipettes have a tip diameter of a few micrometers and the intensity of the current pulses, which are delivered in a blind manner by a high compliance

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iontophoresis device, ranges from 50 to 2,000 nA. With such intensity, the current pulses usually produce damage at the recording site, and the surrounding neuronal elements can subsequently take up the applied marker (2). The main advantage of this extracellular technique is to identify one cell or more on the basis of electrophysiological criteria and afterwards to stain a few (rarely one) neurons at the recording site. As a corollary, some (or all) of the tracer-filled cells including their entire axonal projection can be traced individually, allowing one to elaborate some fundamental principles of anatomical organization (14–18). However, great care must be taken when analyzing the histochemical material as passing fibers can also be stained at the application site (19). Therefore, blind extracellular iontophoresis of marker molecules with recording pipettes may be reliable for tracing neuronal pathways, but it is not quite suitable for structure–function correlation studies, since it is still a challenge to ascertain that a tracer-filled neuron was the recorded unit, simply because the application procedure is made without electrophysiological monitoring. The so-called extracellular technique is neither more nor less than the multiunit juxtacellular labeling technique (2).

3. Principle of the Juxtacellular Technique 3.1. Overview

The extracellular technique has been refined such as to stain the recorded neuron at will under direct electrophysiological control (1, 2). Thereby, the powerful and versatile single-cell juxtacellular recording-labeling technique, which requires the use of a tracerfilled sharp micropipette (tip diameter: 0.5–1.5 mm; Fig. 1a), has been devised to stain long-axon projection neurons as well as interneurons (Fig. 2). The micropipette tip must physically and electrically be brought in juxtaposition with the membrane of the neuron being recorded (Fig. 1b, c2). This is achieved under continuous electrophysiological control (Fig. 1c1–c4). The principle of the single-cell juxtacellular filling procedure rests on the electrical stimulation of the recorded neuron’s membrane with iontophoretic positive rectangular nanocurrent pulses (0.5–8 nA; 200 ms duty cycle; Fig. 1c2), which are delivered through the bridge circuitry of an intracellular preamplifier (Fig. 1b) still under continuous electrophysiological monitoring of the electrode tip-cell

Fig. 1. (continued) It is achieved with a tracer/saline filled micropipette under continuous electrophysiological monitoring. (c1) Extracellular recording. (c2) Physical approach and juxtacellular recording and tracer iontophoresis with square pulses of nanocurrents (0.5–8 nA, 200 ms on, 200 ms off). Note that the current pulses drive the firing of the recorded neuron. (c3) Back to the extracellular recording. (c4) Gentle physical withdrawal of the micropipette from the recorded neuron. Note that the withdrawal is correlated with a progressive diminution of the action potential amplitude. See text for more details. (a) Is adapted from Pinault (25).

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Fig. 1. Experimental design and principle of the juxtacellular technique. (a) Photomicrographs showing the main physical features of a typical sharp-tip glass micropipette for juxtacellular or intracellular recording. The micropipette’s tip is shown below at a higher magnification. (b) Schematic diagram of a conventional intracellular preamplifier. It is used to record either intracellular, extracellular, or juxtacellular voltage signals (V) and to inject nanocurrent (I) through the tip of the glass micropipette while recording. The Wheatstone bridge is used to determine the resistance of the micropipette by adjusting a known resistance (Rb) so that the measure current is zero. A resistance in series (Rs ³ 100 megohms) must be quite larger (×10–100) than the micropipette resistance (Rm < 100 megohms) to measure the full signal at the micropipette tip and draw negligible current from the signal source. The low pass filtering properties of the micropipette and its amplifier are due to inevitable capacitances between the micropipette and the preparation (ground). That is why a feedback circuit (Rc) is required to compensate the capacitance effects (Cp). (c1–c4) The four steps of the juxtacellular filling procedure.

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Fig. 2. Juxtacellular labeling with biocytin of projection (a) and local-circuit (b) neurons. (a) Dendritic and axonal ramifications of a thalamic reticular nucleus (TRN) cell projecting to the thalamus. This photomicrograph shows parts of its somatodendritic and axonal arborizations within the same horizontal 100-micrometers thick horizontal section. The right inset shows dense axon terminations at higher magnification. (b) A basket cell of the cerebellar cortex that had its main axonal and dendritic projections within the same saggital 100-mm thick section. Its axon gave off seven basket-like arborizations, each known to enclose the perikaryon of a Purkinje cell.

membrane interaction. The intensity of the delivered current must be high enough to entrain the firing of the recorded neuron (Fig. 1c2) but not too high so as to injure or damage the neuron. These conditions allow the internalization of the tracer molecules into the neuron being recorded. The intensity of the juxtacellular current pulses is 10–100 times lower than that usually applied with the extracellular technique. The single-cell juxtacellular recording–labeling technique well circumvents the specific problems encountered with the intracellular and extracellular methods. Although relatively simple, the juxtacellular recording–labeling technique requires intracellular equipment and conditions, and a good deal of electrophysiological experience. We will see that this single-cell labeling technique makes investigating the physiological and structural bases of cell–cell communication very reliable for structure– function correlation studies, provided care is taken to avoid the possible drawbacks and pitfalls that are described later.

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From an electrochemical point of view, the tracer molecules that are internalized during juxtacellular iontophoresis with positive current pulses are, theoretically, those that are positively charged and/or those that are cotransported with the ions of the saline solution. As the clearest possible evidence, the internalization of the tracer molecules is firing-dependent since negative current pulses, which inhibit cellular firing, remain ineffective in labeling the recorded neuron (1, 2). 3.2. Internalization of the Tracer into the Recorded Neuron

The following properties of the juxtacellular technique provide the experimenter with convincing evidence that the recorded neuron is labeled: 1. The fact that the juxtacellular current pulses systematically increase firing frequency unambiguously indicates that the tracer injection is targeted to the neuron being recorded (Fig. 3a1–a3). Iontophoresing marker molecules onto the target neuron’s membrane under continuous display of its electrical behavior require constant adjustment of the ejecting current, which must entrain its firing without provoking injurious discharges. Controlling the electrical behavior of the target neuron for the duration of the filling procedure allows the experimenter to keep the recorded neuron alive until the complete withdrawal of the micropipette tip from the recorded neuron, which is not possible (or extremely difficult) with the intracellular method, and the retrieval of the neuron’s histological silhouette in more than 85% of filling attempts. 2. When expelling the neuronal tracer only in the immediate extracellular space of the recorded neuron, namely with currents subthreshold to those that modulate its firing, the ejected tracer fails to be internalized into neuronal elements (2). Therefore, to have the label internalized into the recorded cell, the juxtacellular iontophoretic current must be of threshold or suprathreshold intensity to “tickle,” but subthreshold to injure, the target neuron. 3. An excess of tracer deposit can be seen against the membrane of the labeled neuron, especially after long-lasting juxtacellular application (>5 min) and after a relatively short survival time (Fig. 3a4). 4. As a control experiment, following a voluntary electrical killing of the neuron that had just been recorded and entrained juxtacellularly with a tracer-filled micropipette (Fig. 3b1), the histochemical reaction product usually discloses a badly damaged neuron (Fig. 3b2). 5. The micropipette often causes hemorrhage along its descent into the brain tissue. So, after the histochemical process, the track left by the micropipette can often be seen just above the tracer-filled neuron’s cell body (2, 20) (Fig. 3a4).

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Fig. 3. The juxtacellular technique labels the neuron being recorded. (a1) Extracellular recording of a typical thalamic reticular nucleus (TRN) cell that exhibits a short-latency high-frequency burst in response to an electrical stimulation of the internal capsule (IC stim). (a2) Juxtacellular recording/labeling of the same TRN cell with a Neurobiotin-filled micropipette. The intensity of the rectangular current pulses (200 ms on/200 ms off; lower trace: current monitor) is ~8 nA. The asterisk indicates the moment when the background noise starts to increase (about 50 s after the beginning of pulse application), meaning that the current passing through the micropipette tip starts to excite the cell membrane; moreover, the same current pulses suddenly and strongly entrain the firing of the recorded neuron (arrow). (a3) Spontaneous activity recorded extracellularly after juxtacellular tracer application. (a4) After an application of 10 min and a postinjection survival period of 1 h, one TRN perikaryon with long dendritic profiles and fine protrusions is found at the intended stereotaxic aim in the TRN (horizontal section photographed from a dorsal view). Arrows indicate portions of its axon trunk.

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6. A reversible electrically-induced microporation is the most likely mechanism responsible for the internalization of the tracer molecules during the juxtacellular filling procedure. Indeed, during this procedure, a hyperpolarizing DC shift of a few millivolts of the membrane potential can be recorded, and a microlesion of the tracer-filled neuron’s membrane can be observed after a relatively short survival time (2). 3.3. Required Equipment

The material requirements for successful application of the juxtacellular recording–labeling technique are the same as for intracellular recordings: (1) A heavy stereotaxic frame that must be well isolated from any source of mechanical vibration; (2) an intracellular preamplifier, a signal conditioner (gain and bandpass), an oscilloscope, and an analog-to-digital converter to store voltage and current signals on a computer disk for on-line and off-line analyses; (3) a reliable stepping micromanipulator whereby the micropipette can be advanced in a well-controlled mode with steps ranging from 1 to 3 micrometers; (4) a stereotaxic brain atlas (1) for the accurate insertion of the recording/labeling micropipette and (2) to follow the trajectory of its tip during the descent, allowing to the first approximate identification of the spatial location of the recorded neurons. Conventional intracellular amplifiers provide the source of iontophoretic nanocurrent passing through the micropipette tip, while the electric activity (voltage signals) of the neuron is being recorded. The major elements constituting such an amplifier are illustrated in a schematic diagram (Fig. 1b). For greater details, the reader may refer to the literature (21). In brief, a microelectrode amplifier requires a main control unit with: (1) a bridge balance, (2) a capacitance neutralizer, and (3) a current pump. Injecting constant current requires a very large resistance (Rs ³ 100 megohms) in series with the micropipette whose resistance must be much lower (Rme < 100 megohms). The voltage output (e.g. ×10) of the intracellular preamplifier is then connected to a signal conditioner, which allows the observation of the recorded extracellular/juxtacellular activity in satisfactory conditions (e.g. total gain: ×500; bandpass: 100 Hz–6 kHz). Cutting the high-pass

Fig. 3. (continued) The two inset photomicrographs are the surface (left) and depth (right) of the same horizontal 80-mm thick section containing the perikaryon that shows the marks (indicated by two arrowheads) left by the final position of the micropipette tip. Note the presence of tracer deposit close the cell membrane. (a5) Composite two-dimensional reconstruction of this tracer-filled TRN cell from superimposed camera lucida drawings (under oil immersion at 100×) from serial sections to show its patterns of dendritic and axonal ramifications. (b1) Recording of the electrically induced death of an identified TRN neuron just after having applied the juxtacellular filling procedure. (b2) Afterwards, the histochemical reaction product reveals a cell body with absent or damaged dendritic profiles. It has been observed at the expected stereotaxic locus and looks like a dead or badly injured cell. Abbreviations: A anterior; L lateral; P posterior; M median; VL ventrolateral nucleus of the thalamus; Po posterior complex of the thalamus. Adapted from Pinault (1).

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filter at ³100 Hz is a useful strategy to follow the state of the target neuron without balancing the bridge. Two approaches are available to establish the settings of the juxtacellular 200 ms current pulses: (1) In our laboratory, the settings are those that are produced directly by the preamplifier’s dye injection system, which is very easy to use because of the manual potentiometer for current intensity adjustment in the front panel of the preamplifier. (2) The other approach is to use a stimulator that is connected to the current-command on the rear panel, similar to those used during any intracellular recording experiment. This later approach offers the advantage that the experimenter can change both the duration and the frequency of the current pulse. 3.4. Anesthesia and Surgery

Juxtacellular labeling can be achieved either under nonanesthetized conditions (22, 23) or, most often, under anesthesia. The type of anesthesia may be important especially for labeling axons. For instance, from our own experience with Neurobiotin, the labeling of thalamic axons was better in quality and in quantity under urethane anesthesia than under neuroleptic analgesia (>50% vs. 90%)? In our laboratory, we first inject a small column (~1 mm) of pure water at the top of the capillary. Thanks to the microfilament and because of the lack of viscosity, the water quickly runs into the tip and the thin shank in less than 10–15 min. Then, it is easy to backfill the micropipette with the tracer-containing saline solution, using micropipette filler. It is important to note that these micropipettes are usable at least 4–5 h after the filling of the micropipette, the time that is required for the ions and tracer molecules to diffuse up to the micropipette tip.

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Fig. 4. Stabilizing micro-cranioduratomy for single-cell anatomo-electrophysiological exploration of living intact brain networks. In this experiment, the target is the thalamic reticular nucleus (TRN). (a) Dorsal view of the craniotomy made on the right side of the cranium, above the dorsal thalamus. The white circle indicates the minute hole (or micro-craniotomy; diameter 10 Hz

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Fig. 1. Schematic showing extraction of neural codes by canonical discriminant analysis (CDA) and application to DNMS trials. Middle Left: Diagram of recording array shows electrode arrangement along longitudinal axis of hippocampus and location of recording tips in CA3 and CA1 cell layers. Upper Left: Neural firing patterns recorded from hippocampal ensembles consist of 3 s duration perievent histograms (±1.5 s) as color contour plot featuring neurons on vertical axis and time on horizontal axis surrounding behavioral events (0 s) within DNMS trial (Left Sample shown). Middle: Data Matrices used in CDA. Firing rate (X) across neurons (n) is binned in 0.25 s increments (t) to yield data matrices Xn,t for each behavioral event (Event 1, 2, etc.). The data matrices are converted to population vectors by condensing neurons × time (n × t) to a single dimension (p) for further computation. The covariance matrix is then constructed from all data matrices and represents the total variance in ensemble firing across all neurons, time bins and behavioral events in the task (see Methods). Eigenvector deconvolution and orthogonal rotation of the covariance matrix yields eigenvalues (Ee1, E2, etc.) and eigenvectors (weighting coefficients, W 1,p, W 2,p, etc.) representing the different Discriminant Functions (DFs) as described in Methods. Lower Right: Relation between event-related discriminant functions (DFs 1–5) portrayed with respect to proportion of variance in ensemble firing (indicated level in pyramid) in terms of hierarchy of trial-relevant DFs extracted by the CDA. LP lever press events (i.e. Sample or Nonmatch); Non-LP non-lever press events (i.e. Nosepoke and ITI); SmR Sample Response; NR Nonmatch Response; ITI Intertrial Interval; L Left (position of lever press); R Right (position of lever press). Lower Middle: Perievent histogram of DF-adjusted neuron firing rates for same ensemble as in upper left display showing firing specific to Left Sample (SmR) event. Mean firing rate over trials (XL.SmR,p) was multiplied by the respective coefficient (W5,p) for DF5 for each neuron and time bin (p) to reveal the trial-unique firing pattern for Left SmR code trials shown in diagram at lower left. DNMS Trial Diagram: ITI intertrial interval; SmR Sample response; Delay Delay interval; LNP last nosepoke during Delay; DR Decision response; Re Reinforcement.

where Xi,p is the matrix of ensemble firing rates per 0.25 s time bin, with dimensions: i = total number of behavioral events in the dataset, and p = the neuron × time dimension of the population vector. Wj,p is the matrix of eigenvector coefficients, with dimensions:

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p (from the population vectors) and j (representing the unique eigenvectors or discriminant functions extracted by the CDA). Di,j is the matrix of discriminant scores, with dimensions: i (behavioral events) and j (discriminant functions). Finally, ei,p is the matrix of residual error, with dimensions i and p identical to the data matrix X. The symbol · indicates the matrix “dot-product” multiplication operation summed over dimension j, for every possible value of i and p. In the final step of the CDA, the eigenvectors were orthogonally rotated to distribute the resulting scores with mean = 0 and standard deviation = 1, while maximizing the Mahalonobis distances between event classifications. The variance contributions for each eigenvector produced an additional matrix of eigenvalues (Ej), one for each row (j) of the eigenvector coefficient matrix Wj,p (Fig. 1). The sum of all eigenvalues represents the total variance extracted from the dataset by the CDA (excluding the residual error, e, see (1)). The ratio of any given eigenvalue i to the sum of all eigenvalues represents the proportion of total variance accounted for by that eigenvector (proportion of variance = Ei/ ∑ E) in the CDA (50). For the data shown in Fig. 1 (upper left), the first five eigenvectors accounted for >85% of the total variance and were significantly different from all other eigenvectors as well as the residual error in the covariance matrix. The most important aspect of the analysis with respect to deriving ensemble encoding of task-related events is the fact that each eigenvector provides a Discriminant Function (DF) that identifies a single source of variance in firing calculated across all neurons in the ensemble (50). In Fig. 1, each row (E1, E2, etc.) of the matrix of eigenvectors (W1,p, W2,p, etc.) represents a set of DF coefficients with the same dimensions i and p as the perievent histograms, which can be applied to raw firing rates of single neurons to determine the degree of firing across all neurons in the ensemble associated with a particular behavioral event (see below). 3.6. Derivation of DF-Associated Ensemble Firing Patterns



Using the above parameters, it is possible to examine the associated ensemble firing pattern for all behavioral events by adjusting neuron firing rates using coefficients for a particular DF (Figs. 1 and 2). Since each DF extracted by the CDA represents a trialunique behavioral event (Fig. 1, lower right), multiplying the mean firing rates of each neuron (per 0.25 s bin) in the ensemble, summed within each trial, by the respective DF coefficients provides the adjusted ensemble “code” for that event. The example in Fig. 1 (lower middle, Adjusted Firing Rates) shows this relationship is: Ap = X (Left SmR),p × W(DF5),p

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Fig. 2. Illustration of DF5-adjusted ensemble firing patterns for Sample response (SmR) from three different animals (Rats 1, 2, 3) with hippocampal ensembles of 15, 20, and 25 neurons, respectively. Each color contour pattern was generated as shown in Fig. 1 via by multiplying mean neuron firing rates by the respective DF5 coefficients for Left and Right SmRs. The DF5 ensemble patterns illustrate firing specific to successful SmRs on different trials (Correct Left, top row; Correct Right, bottom row). This can be contrasted with the firing for the same ensembles for Left or Right SmRs associated with error trials (second and third rows).

firing rates (as in (1)), X(Left SmR),p is the mean ensemble firing rate over all Left SmR events, and W(DF5),p is the set of coefficients for DF5. 3.7. Identification of Ensemble Codes for Behavioral Events

The individual CDA-extracted DFs account for sources of variance of ensemble neural firing patterns for specific behavioral events as depicted in the perievent histograms. The DFs are ranked in terms of proportion of variance relative to the overall ensemble firing rate, contributed across all neurons, time points, and events. Successively ranked DFs identify firing of different hippocampal cell types (FCTs) that encode less (higher proportion of overall variance) or more (less percentage) complex

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circumstances within the DNMS task. This is shown in Fig. 1 (lower right), where the largest source of variance is accounted for by DF1 which discriminates very general factors like ensemble firing associated with any lever press (e.g. SmRs “and” NRs) as distinct from all other DNMS trial events (i.e. nosepokes (delays), reward delivery, ITI, etc). In contrast, DF2 the next largest source of variance typically discriminates SmRs vs. NRs, and DF3 (the third highest percentage of variance) usually distinguishes firing during the ITI from all other within-trial events (i.e. SmRs, LNP, DRs). While it is clear that these three eigenvectors (DFs 1–3) satisfy a classification scheme which distinguishes task-related events from other more general factors within the testing environment, they do not discriminate events or conditions specific to performance on individual trials. However, once this larger source of variance extracted by DFs 1–3 is identified, smaller but more trial-unique sources of variance in ensemble firing are determined as shown by the blue line distinguishing Task (DFs 1–3) vs. Trial (DFs 4–5) in DF “Pyramid” in Fig. 1 (lower right). DF4 and DF5 were consistently identified with SmR and NR, respectively, as significant sources of variance by the CDA. Since DF4 and DF5 can also be classified with respect to association with behavioral success or failure (i.e. correct vs. error) in terms of magnitude of mean score (or “strength”) across trials, each reflects performance of the task. Finally, we have determined that only DF5 which reflects the ensemble code of the Sample lever press (SmRs) covaries with trial performance in terms of success or failure on the same trial (45, 47, 51, 52). DF4 (NR) covaries with trial outcome but is more influenced by the prior trials (52). However, because the SmR occurs before either the Delay or Nonmatch decision phases of the task, the magnitude of the DF5 score can “predict” performance on the same trial since it reflects the “strength” of encoding of the Sample information that must be used to make the Nonmatch decision after the variable duration of the interposed delay interval. 3.8. Computation of Ensemble Single-Trial DF Scores



It is also possible to derive an ensemble “code” (i.e. DF score) corresponding to each DF and associated DNMS event(s) on a single trial (49, 50). To calculate DF scores with dimensions i and j corresponding to DF and events, respectively, it is first necessary to transpose the eigenvector matrix Wj,p, by exchanging the rows for the columns, producing matrix W′p,j. Individual trial DF scores (D) are then computed using the formula: X i , p ·W ′ p , j = Di , j ,

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where X is the raw data matrix as in (9.1), W′ is the transpose of the eigenvector matrix from (9.1), D is the resulting matrix of discriminant scores, and dimensions i, p, and j are the same as in

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(9.1 and 9.2). Since each DF score Di,j has only the dimensions i and j for behavioral event and DF, it incorporates all of the adjusted neuron firing rates of all time bins and neurons within the ensemble. 3.9. Online Detection of Neural Codes

The next step in the implementation of ensemble codes to control behavior was to detect the code during the trial and utilize that information to change the parameters of the same trial in accordance with the “strength” of the detected code. DF5 scores were calculated online within 3 s following the SmR on each trial. The coefficients identified from prior sessions were entered into a customized MATLAB (The Mathworks, Natick, MA) program which computed DF scores “online” using the “live” ensemble firing recorded during the trial (47). DF5 adjusted ensemble firing rates were monitored continuously along with DF5 scores ­calculated every 0.25 s (see “waterfall” and stripchart displays in Fig. 2a). The following two exceptions from prior descriptions occur in online calculations: (1) DF5 coefficients (W) for each ensemble are derived from analysis of ≥5 previous DNMS sessions, but the neural firing dataset (X) is obtained online from the current “real-time” ensemble activity on individual trials and (2) online DF5 scores are computed continuously (with (9.3) above) using a revolving 3 s buffer on real-time activity from the same neurons and time bins as in prior constructed perievent histograms (see “Computation” above). Mean DF5 scores for Left vs. Right SmR events on correct vs. error trials computed from previous DNMS sessions are used as criteria to determine “weak” and/or “strong” SmR codes online. Weak SmR codes are designated as DF5 scores £1.0 standard deviation below the mean for Left or Right SmRs on correct trials for a given ensemble (Fig. 3a). Strong SmR codes include only DF5 scores >1.0 standard deviations above the mean of all prior Left and Right SmR correct trials for the ensemble (Fig. 3a).

3.10. Use of Hippocampal Ensemble Codes for “Closed Loop” Control of DNMS Performance

The utility of the single trial ensemble codes derived above is that they can be employed in a “Closed Loop” feedback paradigm in which the duration of the DNMS delay interval (in seconds) is altered on the basis of the strength of the SmR code (magnitude of DF5 score) on the same trial. This procedure is unique because it requires extracting in real-time, indications of how precisely the information presented (i.e. lever position) is encoded by the neural ensemble at the time of the SmR. The Closed Loop paradigm tests this directly by altering on the same trial a task parameter (the duration of the delay interval) that is dependent on the strength of such encoding. In the Closed Loop procedure, the delay interval is shortened to 10 s for weak SmR codes because most trained animals perform this type of trial correctly on ≥95% of ­occurrences (Fig. 4). However, when a strong SmR code is

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Fig. 4. Implementation of Closed Loop paradigm to control DNMS performance. (a) Presentation shows real-time computer monitoring of hippocampal ensemble activity utilized during implementation of CDA for online extraction of single trial SmR codes utilized in Closed Loop paradigm (b). Downward scrolling “waterfall” display (Real-Time Neural Activity) provides updated moving columnar, color-coded graphic representation of neuron firing rate (red >10 Hz, blue 30 s provided a behavioral measure of code strength related directly to retention of trial specific information under conditions never before experienced by the animal. 3.11. Specificity of Closed Loop Control

It is important to employ direct control measures to verify the dependence of the altered DNMS performance on ensemble activity detected within the Closed Loop paradigm. Two procedures were employed for this purpose, the first controlled for strength of SmR code by merely reversing the Closed Loop contingency such that delays were extended when a weak SmR code was detected, and shortened when a strong SmR code occurred (“Reversed” condition), while the second tested the specificity of the ensemble firing pattern by utilizing a randomized set of DF5 coefficients to adjust neuron firing rates (“Randomized” condition). The latter procedure controls for the possibility that the strong and weak SmR codes merely reflect synchronous changes in firing

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rates across all neurons in the ensemble rather than specifically different patterns of firing to the same behavioral event (SmR).

4. Demonstration of Closed Loop Model

4.1. Multivariate Analyses of Ensemble Firing

The following section provides a demonstration of the application of the closed loop DNMS model in each of 15 male LongEvans rats implanted with array electrodes to record bilaterally from ensembles of 15–30 CA3 and CA1 pyramidal cells and trained to criterion in the two-lever DNMS task with 1–30 s delays (40, 44). Experiments were conducted in which neural ensemble activity was recorded for a minimum of five consecutive daily sessions in each animal then subjected to multivariate CDA analysis to extract sources of variance, i.e. DFs, in ensemble neural firing associated with the encoding of specific DNMS events (see above). The sources of ensemble firing associated with Left or Right SmRs was determined and correlated with correct and error performance on individual DNMS trials to define the “SmR code,” the strength of which “predicted” behavioral outcome across trials (Fig. 4). Animals were then tested in a “Closed Loop” version of the DNMS task in which the delay interval was either extended when strong SmR codes occurred or shortened on weak SmR code trials (Fig. 5). Perievent histograms (±1.5 s in 0.25 s time bins) were constructed as synchronized to the SmR, NR, LNP, and ITI events in the task. The four events were further classified into left vs. right lever presses and correct vs. error trials, making a total of 16 possible behavioral event classifications. CDA analyses of hippocampal ensemble firing patterns were applied to firing rates of all neurons within an ensemble, and a covariance matrix was used to compute total variance in firing rate across all neurons and time bins in ensemble-based perievent histograms (Fig. 1). Eigenvector decomposition of the covariance matrix extracted five significant (F(1,1978) > 7.14, p < 0.01) sources of variance, or discriminant functions (DFs), each of which represented a proportion of the total variance associated with a specified behavioral event or event classification (Fig. 1). The coefficients of the DFs were used to “weight” single neuronal firing rates which revealed specific “adjusted” firing patterns across each ensemble (animal) for a particular source of variance in the covariance matrix (e.g. Left Sample DF5 histogram in Fig. 1). The sum of the weighted firing rates across all neurons provided a single DF score or “ensemble code,” the value of which could be used to quickly evaluate the level of ensemble activity, or code strength, for a given event. As indicated previously, DF4 and DF5 were the only sources of

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The SmR code was next examined for accuracy of “prediction” of trial outcome by the use of a “reclassification” scheme comparing DF5 score with trial outcome applied to the original dataset (49). Utilizing this scheme, correct identification occurred on 95.8 ± 2.1% of the occasions for all error trials, indicating SmR codes (DF5 scores) extracted online could provide similar predictability via their strength (i.e. magnitude). The CDA computed online SmR code strengths (magnitude of DF5 score) during at least four 100-trial sessions for each of the 15 animals effectively identified 89.2 ± 2.7% of all error trials in those sessions. Since the online computation of DF5 scores after the occurrence of the SmR required only 5 s (Fig. 4a), SmR code strength was used to determine the duration of the delay on the same trial, constituting a “Closed Loop” feedback procedure (Fig. 4b).

4.5. Closed Loop Feedback Control of DNMS Behavior

In the “Closed Loop” procedure, SmR codes (DF5 scores) were classified as: (1) weak SmR codes if ≤1.0 standard deviation below the mean of DF5 scores on all correct trials in the five prior sessions and (2) strong SmR codes if ≥1.0 standard deviations above the mean for correct trials in same prior sessions. Implementation of the Closed Loop required that delays on weak SmR code trials be shortened to 10 s and for strong SmR code trials extended to one of the three (randomly selected) intervals: 40, 50, or 60 s; beyond the maximum 30 s delay duration the animals were trained under (Fig. 3b). Figure 4a illustrates the real-time display of all digitized neural activity in the ensemble and the DF scores (stripcharts) computed online used to implement the Closed Loop paradigm (Fig. 4b). In order to prevent detection of the Closed Loop contingency, no more than 25 trials (50% strong or weak SmR code trials) were “adjusted” by the procedure within any one session. The number of Closed Loop sessions conducted per animal (n = 15 animals) ranged from 12 to 49. Figure 5 shows the results of applying the Closed Loop ­procedure on performance during the session. In Fig. 5a, the triangles show performance on trials identified online as weak SmR code within Closed Loop sessions but without shortening of delay duration. In marked contrast, however, when weak SmR

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code trials within the same sessions were identified and shortened to 10 s via the Closed Loop paradigm, performance for short delays (1–10 s) did not change but performance was significantly enhanced (squares) on trials with delays >15 s (F(1,401) = 8.14, p < 0.01) because of the elimination of trials that were “at risk” for error with delays >10 s (triangles) because of weak SmR codes which produced an elevation in overall performance at all delays because of weak SmR codes (squares). Figure 5b illustrates performance in sessions where both strong SmR and weak SmR codes trials were manipulated by the Closed Loop paradigm. The circles show performance on non-Closed Loop trials over the same delay intervals. For delays of 1–30 s performance on strong SmR code trials was well above Normal levels (F(1,401) = 18.39, p < 0.001), as shown also in Fig.  3b. The Closed Loop contingency was employed to extend delays to 40, 50, or 60 s in duration on strong SmR code trials. For comparison, a similar number of trials on which SmR codes were not detected were randomly extended to the same delays in the same sessions. When strong SmR codes were identified and the delay extended by the Closed Loop procedure, performance was significantly higher at all three increased delays (dashed curve, Fig. 5b) than on trials where SmR codes were not monitored to set delay duration (delay = 40 s: F(1,401) = 24.33, p < 0.001; delay = 50 s: F(1,401) = 16.23, p < 0.001; delay = 60 s: F(1,401) = 6.51, p < 0.02). The triangles in Fig. 5b show mean performance on all other trials in the session, which are elevated above normal session performance (circles) due to elimination of trials with weak SmR codes as in Fig. 5a. Figure 5b demonstrates the capacity of strong SmR codes to sustain behavioral performance well beyond the delay intervals to which animals had been previously trained (1–30 s). However, similar to normal (1–30 s) delay conditions, performance on strong SmR code trials exhibited a significant delay-dependent decline (F(5,401) = 11.75, p < 0.001) across those same Closed Loop trials with extended delays (Fig. 5b, red curve) documenting continued vulnerability to the capacity to retain trial-specific information over time. Figure 5c shows results of both types of Closed Loop manipulations from a single animal to verify that the procedure: (1) eliminated “at-risk” weak SmR code trials and (2) revealed enhanced performance on strong SmR code trials, in the same animal. 4.6. Validation of Closed Loop Control of Performance

To validate the relationship between single trial SmR code strength and Closed Loop facilitation of DNMS performance, the two tests mentioned above were employed in the same set of animals. The first test involved reversing the contingency of the Closed Loop procedure such that trials with weak SmR codes were extended to 40–60 s and strong SmR code trials shortened to 10 s (“Reverse” test). In the second test, individual neuron DF5 coefficients derived from the CDA were randomly rearranged, or

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“shuffled,” between neurons in the ensemble and the Closed Loop operated as before (“Shuffle” test). The results of the two control tests are shown in Fig. 5d in terms of mean performance over all trials, compared with the results of Normal (black bars) and facilitated Closed Loop sessions (white bars). Performance on extended trials in the “Reversed” condition (Fig. 5d, light gray bars) did not differ significantly from performance on Normal trials (F(1,1752) = 0.5, N.S.), because extending weak SmR code trials to ≥40 s delays significantly (F(1,1752) = 5.32, p < 0.02) reduced performance relative to Normal trials (Fig. 5b), and was not different from chance levels at 50 and 60 s delays (F(1,1752) = 2.41, N.S.). However, strong SmR codes, significantly improved performance relative to non-Closed Loop conditions (F(1,1752) = 7.49, p < 0.01) when the trial was shortened to 10 s, presumably because under Normal conditions some weak SmR code trials are at-risk for error even at 10 s delays (Fig. 3). In the second control procedure (Shuffle test), calculations of online SmR code strength were made with the coefficients of the CDA “Randomized” between neurons in the ensemble and Fig. 5d (dark gray bars) shows that the Closed Loop procedure did not change performance on extended trials (F(1,1752) = 0.7, N.S.; n = 15 animals, 500 trials each), which was at chance levels for both “Shuffle” and Normal conditions. The two results (Fig. 5d) clearly establish: (1) the validity of the calculated SmR code strengths on single trials and (2) dependence of DNMS performance on specific patterns of firing (DF5) within hippocampal neural ensembles. 4.7. Reliability of the Closed Loop Paradigm Across Animals

Figure 6 shows the results of implementing the Closed Loop paradigm in 15 different animals over an average of 29.6 ± 3.1 (range 12–49) sessions per animal, each with hippocampal ensembles consisting of 15–30 neurons (mean 21.0 ± 1.3 neurons per animal). Overall, the mean number of strong SmR code trials was 13.3 ± 2.4 and weak SmR code trials was 21.6 ± 2.7 per 100-trial session (n = 15 animals). The mean (± S.E.M.) strong SmR code values (DF5 scores) across animals were: Left 2.3 ± 0.2, range 2.1–2.8; Right -2.5 ± 0.3, range -2.0 to -2.7; and for weak SmR codes: Left 0.4 ± 0.3, range 0–0.8; Right -0.5 ± 0.3, range 0 to -0.9. Figure 6 shows that performance on Closed Loop trials was significantly improved in each animal relative to the mean for Normal trials (dotted red line) at extended delays on strong SmR code trials (40 s: 90.4 ± 3.3%; 50 s: 78.1 ± 4.6%; 60 s: 61.2 ± 2.4%; all F(1,1752) > 11.6, p < 0.001). Performance across all animals on weak SmR code trials was also significantly elevated when the delay was shortened by the Closed Loop paradigm (mean 94.3 ± 1.6%), comp a r e d t o Normal trials (dotted red line, 63.7 ± 2.1%, F(1,1752) > 16.6, p < 0.001).

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Delay (sec) Fig. 6. Reliability of Closed Loop improvement of performance across individual animals. DNMS mean % correct performance (± S.E.M.) shown separately for each of 15 animals (colored bars) summed over at least ten Closed Loop sessions on with Extended (strong SmR code) and Shortened (weak SmR code) delays. Individual means are shown for all 15 animals and compared to the overall mean % correct (dashed red lines) computed across the same animals in Normal (non-Closed Loop) control sessions with trials of the same delay. There were no significant differences across animals for performance within any of the extended or shortened trial delays.

4.8. Application of Nonlinear Ensemble Analyses to the Closed Loop

We have recently shown that hippocampal CA1 neural firing can be predicted from CA3 firing by means of a nonlinear, multiinput/multi-output (MIMO) model (53–56) utilizing the same hippocampal ensemble activity reported above. The nonlinear MIMO model is adapted from a Laguerre-Volterra network (57), whereby the fine temporal relationship between one or more input series (spike trains) and a single output series (MISO) can be described by a combination of first, second and third-order Volterra kernels (56). The resulting Volterra models with multiple inputs and a single output (MISO, Fig. 7a) are coupled with other MISO models using the same inputs to produce the MIMO model. Figure 7a shows the coupling of MISO models into a single MIMO model and also shows the decomposition of a MISO model into Volterra kernels. The MIMO model thus uses nonlinear, nonparametric estimation to predict the probability of CA1 neuron firing in terms of output trains of spike occurrences (i.e. spike trains) based on CA3 spike trains as input, which is logically consistent with the strong synaptic connection of the CA3-CA1 Shaffer collateral projections (58). Online implementation of the MIMO model allowed prediction of CA1 output

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Fig. 7. Nonlinear MIMO model applied to the Closed Loop paradigm. (a) Multi-input, single-output (MISO) model shows nonlinear estimation (K) consisting of first-, second-, and third-order Volterra kernels (k0 - k2) predicting the probability of CA1 spike firing (u) from the temporal relationships between input spikes (x) recorded from multiple CA3 neurons (see Electrode Array in Fig. 1). Single CA1 spike train (y) over time is predicted by a stochastic model using threshold (q), feedback kernel (h), and noise (s) terms. (b) Expanded multi-input, multi-output (MIMO) nonlinear model is a concatenation of MISO models that produces the same inputs to all elements, but independent spike train outputs so that CA1 output spikes trains (yi), are continuously predicted from CA3 input spike trains (xi). (c) Validity of ensemble CA1 spike train estimation by MIMO model illustrated by color stripchart comparisons of predicted vs. actual CA1 firing probabilities (red = maximum probability, >10 Hz firing; blue = minimum firing, 85% match to the “Correct” CA1 pattern are extended, while trials with 20 s) delay trials. This MIMO-derived output probability was then used as a template for identifying both correct and incorrect codes for DNMS trials. The MIMO model was computed online during the Sample phase of DNMS trials and the derived CA1 spike trains compared to the template for correct encoding on long delay trials. Trials with >85% match to the correct trial template were extended during the delay, while trials with