This document provides background information on a book titled "Coherent Behavior in Neuronal Networks". It begins with a preface written by the book's four editors - Kresimir Josic, Jonathan Rubin, Manuel A. Matias, and Ranulfo Romo. The preface describes the motivation and goals for the book, which is to provide a sampling of recent research on coherent neuronal network behavior from an interdisciplinary perspective, with contributions from both experimentalists and theorists. It then provides a brief overview of the book's scientific content, which covers topics such as ongoing cortical activity, small neuronal network interactions, spatiotemporal neuronal activity patterns, and coherence in encoding and decoding across different systems.

2. Springer Series in Computational Neuroscience
Volume 3
Series Editors
Alain Destexhe
Unite´ de Neurosciences Integratives´ et Computationnelles (UNIC)
CNRS Gif-
sur-Yvette
France
Romain Brette
Equipe Audition (ENS/CNRS)´
´
Departement d’Etudes Cognitives´
´
Ecole Normale
Superieure Paris
France
For other titles published in this series, go to
http://www.springer.com/series/8164

3. Kresimirˇ Josic´ •
Jonathan Rubin
Manuel A. Mat´ıas •
Ranulfo Romo
Editors
Coherent Behavior
in Neuronal Networks
123

4. Editors
Kresimirˇ Josic´ Manuel A. Mat´ıas
Dept. Mathematics IFISC
University of Houston CSIC-UIB
651 Phillip G. Hoffman Hall 07122 Palma de Mallorca
Houston TX 77204-3008 Spain
USA manuel@ifisc.uib-csic.es
josic@math.uh.edu
Jonathan Rubin Ranulfo Romo
Dept. Mathematics Universidad Nacional
University of Pittsburgh Autonoma´ de Mexico´
301 Thackeray Hall Instituto de Fisiolog´ıa Celular
Pittsburgh PA 15260 04510 Mexico, D.F.
USA Mexico
rubin@math.pitt.edu rromo@ifc.unam.mx
Cover illustration: Neuronal Composition. Image by Treina Tai McAlister.
ISBN 978-1-4419-0388-4 e-ISBN 978-1-4419-0389-1 DOI
10.1007/978-1-4419-0389-1
Springer Dordrecht Heidelberg London New York
Library of Congress Control Number: 2009926178
c Springer Science+Business Media, LLC 2009
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher (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
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subject to proprietary rights.
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)

5. Preface
New developments in experimental methods are leading to an increasingly detailed
description of how networks of interacting neurons process information. These
findings strongly suggest that dynamic network behaviors underlie information pro-
cessing, and that these activity patterns cannot be fully explained by simple concepts
such as synchrony and phase locking. These new results raise significant challenges,
and at the same time offer exciting opportunities, for experimental and theoretical
neuroscientists. Moreover, advances in understanding in this area will require inter-
disciplinary efforts aimed at developing improved quantitative models that provide
new insight into the emergence and function of experimentally observed behaviors and
lead to predictions that can guide future experimental investigations.
We have undertaken two major projects to promote the translation of these new
developments into scientific progress. First, we organized the workshop Coher-ent
behavior in neuronal networks, which took place on October 17–20, 2007, in
Mallorca, Spain, funded by the US National Science Foundation, the Spanish Min-
isterio de Educaci on´ y Ciencia, Govern de les Illes Balears, the Office of Naval
Research Global, Universitat de les Illes Balears, the Consejo Superior de Investi-
gaciones Cient´ıficas, the University of Houston, the University of Pittsburgh, and the
Ajuntament de Palma de Mallorca. This unique workshop brought together a highly
interdisciplinary and international mixture of 95 researchers with interests in the
functional relevance of, and the mechanisms underlying, coherent behavior in neuronal
networks. Reflecting the belief that understanding coherent behavior in neuronal
networks requires interdisciplinary approaches, a key component of the meeting was
the inclusion of linked back-to-back talks by experimental and theo-retical
collaborators, on their joint research endeavors. Scientifically, the meeting was
structured around multiple themes, including the possible roles of globally co-herent
rhythms in the coordination of distributed processing, the possible roles of coherence
in stimulus encoding and decoding, the interplay of coherence of neu-ronal network
activity with Hebbian plasticity, and the mechanisms and functional implications of
repeated spiking sequences. Participants responded quite positively to the workshop,
expressing a strong desire for further activities to encourage the exchange of ideas and
establishment of collaborative efforts in this field.
To address this need, and to reach a wider audience with interests in the broad area
of coherent behavior in neuronal networks, our second project has been editing
v

6. vi Preface
this volume. The chapters collected here include work from some workshop par-
ticipants as well as some nonparticipants. The goal of the book is not to provide a
summary of workshop activities but rather to provide a representative sampling of the
diverse recent research activities and perspectives on coherent behavior in neu-ronal
networks, and to serve as a resource to the research community. Nonetheless, we have
made sure that the interdisciplinary flavor of the workshop has extended to this
volume. Indeed, many of the chapters are coauthored by collaborating theo-rists and
experimentalists. We hope that these chapters will provide useful examples of how
theoretical abstractions can be derived from experimental data and used to attain
general, mechanistic insights, and how theoretical insights can guide ex-periments in
turn. Several chapters also include reviews or examples of novel methodologies, some
experimental and some theoretical, that may be useful in ana-lyzing coherent behavior
in neuronal networks.
Scientifically, the book starts with a focus on ongoing or persistent cortical activ-
ity, as a baseline upon which sensory processing and faster oscillations must occur. In
particular, the first chapters consider spatiotemporal patterning of synaptic inputs
during such states, as well as the more abstract question of identifying repeating motifs
within these inputs. From there, the book moves to small networks and small-scale
interactions, including input-dominated cultured networks, which are particularly well
suited for the study of how network dynamics interact with plastic-ity in an ongoing
feedback cycle. Next, we return to larger scale but abstract issues, but with a shift in
focus to the spatiotemporal relationships observed in the activity patterns of different
cells, such as synchrony or causality. Subsequent chapters offer a broad survey of
coherence in encoding and decoding, such as in stimulus discrim-ination and
perception across systems such as motor, olfactory, and visual, with a particular
emphasis on the role of noise.
We believe this book is suitable for special topics courses for graduate students,
particularly in interdisciplinary neuroscience training programs, and for interdis-
ciplinary journal club discussions. More broadly, we hope this volume will be a
valuable resource for the many researchers, across a wide variety of disciplines, who
are working on problems relating to neuronal activity patterns. We look forward to
following and participating in future developments in the field, as interdisciplinary
collaborations become increasingly widespread and continue to generate exciting
advances in our understanding of coherent behavior in neuronal networks.
Houston, TX KresimirM Josi´c
Pittsburgh, PA Jonathan Rubin
Palma de Mallorca, Spain Manuel A. Mat´ıas
Mexico, D.F. Ranulfo Romo

7. Contents
On the Dynamics of Synaptic Inputs During Ongoing Activity
in the Cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Michael Okun, Alik Mokeichev, Yonatan Katz, and Ilan Lampl
Timing Excitation and Inhibition in the Cortical Network . . . . . . . . . . . . . . . . . . . . 17
Albert Compte, Ramon Reig, and Maria V. Sanchez-Vives
Finding Repeating Synaptic Inputs in a Single Neocortical
Neuron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Gloster Aaron
Reverberatory Activity in Neuronal Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Pak-Ming Lau and Guo-Qiang Bi
Gap Junctions and Emergent Rhythms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
S. Coombes and M. Zachariou
The Feed-Forward Chain as a Filter-Amplifier Motif . . . . . . . . . . . . . . . . . . . . . . . . . 95
Martin Golubitsky, LieJune Shiau, Claire Postlethwaite,
and Yanyan Zhang
Gain Modulation as a Mechanism for Switching Reference
Frames, Tasks, and Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .121
Emilio Salinas and Nicholas M. Bentley
Far in Space and Yet in Synchrony: Neuronal Mechanisms
for Zero-Lag Long-Range Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .143
Raul Vicente, Leonardo L. Gollo, Claudio R. Mirasso,
Ingo Fischer, and Gordon Pipa
Characterizing Oscillatory Cortical Networks with Granger
Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169
Anil Bollimunta, Yonghong Chen, Charles E. Schroeder,
and Mingzhou Ding
vii

8. viii Contents
Neurophysiology of Interceptive Behavior in the Primate:
Encoding and Decoding Target Parameters
in the Parietofrontal System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .191
Hugo Merchant and Oswaldo P´erez
Noise Correlations and Information Encoding and Decoding . . . . . . . . . . . . . . . .207
Bruno B. Averbeck
Stochastic Synchrony in the Olfactory Bulb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .229
Bard Ermentrout, Nathaniel Urban, and Roberto F. Gal´an
Stochastic Neural Dynamics as a Principle of Perception . . . . . . . . . . . . . . . . . .
. . .247 Gustavo Deco and Ranulfo Romo
Large-Scale Computational Modeling of the Primary Visual
Cortex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .263
Aaditya V. Rangan, Louis Tao, Gregor Kovaˇciˇc, and David Cai
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .297

9. Contributors
Gloster Aaron Department of Biology, Wesleyan University,
Middletown, CT 06459, USA, gaaron@wesleyan.edu
Bruno B. Averbeck Sobell Department of Motor Neuroscience
and Movement Disorders, Institute of Neurology, UCL, London WC1N 3BG,
UK, b.averbeck@ion.ucl.ac.uk
Nicholas M. Bentley Department of Neurobiology and Anatomy, Wake Forest
University School of Medicine, Winston-Salem, NC 27157, USA,
nbentley@wfubmc.edu
Guo-Qiang Bi Department of Neurobiology, University of Pittsburgh School
of Medicine, Pittsburgh, PA 15261, USA, gqbi@pitt.edu
Anil Bollimunta J. Crayton Pruitt Family Department of Biomedical Engineering,
University of Florida, Gainesville, FL 32611, USA, banil@ufl.edu
David Cai Courant Institute of Mathematical Sciences, New York University,
251 Mercer Street, New York, NY 10012, USA, cai@cims.nyu.edu
Yonghong Chen J. Crayton Pruitt Family Department of Biomedical Engineering,
University of Florida, Gainesville, FL 32611, USA, ychen@bme.ufl.edu
Albert Compte Institut d’Investigacions Biom`ediques August Pi i Sunyer
(IDIBAPS), 08036 Barcelona, Spain, acompte@clinic.ub.es
Stephen Coombes School of Mathematical Sciences, University of Nottingham,
Nottingham NG7 2RD, UK, stephen.coombes@nottingham.ac.uk
Gustavo Deco Institucio´ Catalana de Recerca i Estudis Avanc¸ats (ICREA),
Universitat Pompeu Fabra, Passeig de Circumvallacio,´ 8, 08003 Barcelona,
Spain, gustavo.deco@upf.edu
Mingzhou Ding J. Crayton Pruitt Family Department of Biomedical Engineering,
University of Florida, Gainesville, FL 32611, USA, mding@bme.ufl.edu
Bard Ermentrout Department of Mathematics, University of Pittsburgh,
Pittsburgh, PA 15260, USA, bard@math.pitt.edu
ix

10. x Contributors
Ingo Fischer School of Engineering and Physical Science, Heriot-Watt
University, Edinburgh EH14 4AS, UK, I.Fischer@hw.ac.uk
Roberto F. Galan´ Department of Neurosciences, Case Western Reserve Univer-sity
School of Medicine, Cleveland, OH 44106-4975, USA, rfgalan@case.edu
Leonardo L. Gollo Instituto de F´ısica Interdisciplinar y Sistemas Complejos
(IFISC), Universitat de les Illes Balears-CSIC, Crta. de Valldemossa km 7.5,
07122 Palma de Mallorca, Spain, leonardo@ifisc.uib-csic.es
Martin Golubitsky Mathematical Biosciences Institute, Ohio State University,
1735 Neil Avenue, Columbus, OH 43210, USA, mg@mbi.ohio-state.edu
Yonatan Katz Department of Neurobiology, Weizmann Institute of Science,
Rehovot 76100, Israel, yonatan.katz@weizmann.ac.il
Gregor Kovaciˇcˇ Mathematical Sciences Department, Rensselaer
Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA, kovacg@rpi.edu
Ilan Lampl Department of Neurobiology, Weizmann Institute of Science,
Rehovot 76100, Israel, ilan.lampl@weizmann.ac.il
Pak-Ming Lau Department of Neurobiology, University of Pittsburgh School
of Medicine, Pittsburgh, PA 15261, USA
Hugo Merchant Instituto de Neurobiolog´ıa, UNAM, Campus Juriquilla,
Quer´etaro Qro. 76230, M´exico, merchant@inb.unam.mx
Claudio R. Mirasso Instituto de F´ısica Interdisciplinar y Sistemas Complejos
(IFISC), Universitat de les Illes Balears-CSIC, Crta. de Valldemossa km 7.5,
07122 Palma de Mallorca, Spain, claudio@ifisc.uib-csic.es
Alik Mokeichev Department of Neurobiology, Weizmann Institute of Science,
Rehovot 76100, Israel, alik.mokeichev@weizmann.ac.il
Michael Okun Department of Neurobiology, Weizmann Institute of Science,
Rehovot 76100, Israel, michael.okun@weizmann.ac.il
Oswaldo Perez´ Instituto de Neurobiolog´ıa, UNAM, Campus Juriquilla, Quer
´etaro Qro. 76230, M´exico
Gordon Pipa Department of Neurophysiology, Max-Planck Institute for
Brain Research, Deutschordenstrasse 46, 60528 Frankfurt, Germany,
pipa@mpih-frankfurt.mpg.de
Claire Postlethwaite Department of Mathematics, University of Auckland, Private
Bag 92019, Auckland, New Zealand, c.postlethwaite@math.auckland.ac.nz
Aaditya V. Rangan Courant Institute of Mathematical Sciences, New York
University, 251 Mercer Street, New York, NY 10012, USA, rangan@cims.nyu.edu

11. Contributors xi
Ramon Reig Institut d’Investigacions Biom`ediques August Pi i Sunyer
(IDIBAPS), 08036 Barcelona, Spain, rreig@clinic.ub.es
Ranulfo Romo Instituto de Fisiolog´ıa Celular, Universidad Nacional
Autonoma´ de M´exico, 04510 M´exico, D.F., M´exico, rromo@ifc.unam.mx
Emilio Salinas Department of Neurobiology and Anatomy, Wake Forest
University School of Medicine, Winston-Salem, NC 27157, USA,
esalinas@wfubmc.edu
Maria V. Sanchez-Vives Institut d’Investigacions Biom`ediques August Pi i
Sunyer (IDIBAPS), 08036 Barcelona, Spain
Institucio´ Catalana de Recerca i Estudis Avanc¸ats (ICREA), 08010
Barcelona, Spain, msanche3@clinic.ub.es
Charles E. Schroeder Nathan Kline Institute for Psychiatric Research,
Orangeburg, NY 10962, USA
Columbia University College of Physicians and Surgeons, New York, NY
10027, USA, schrod@nki.rfmh.org
LieJune Shiau Department of Mathematics, University of Houston, Clear Lake,
Houston, TX 77058, USA, shiau@uhcl.edu
Louis Tao Center for Bioinformatics, National Laboratory of Protein Engineering
and Plant Genetics Engineering, College of Life Sciences, Peking University,
Beijing 100871, People’s Republic of China, taolt@mail.cbi.pku.edu.cn
Nathaniel Urban Department of Biology, Carnegie Mellon University,
Pittsburgh, PA, USA, nurban@cmu.edu
Raul Vicente Department of Neurophysiology, Max-Planck Institute for Brain
Research, Deutschordenstrasse 46, 60528 Frankfurt, Germany,
raulvicente@mpih-frankfurt.mpg.de
Margarita Zachariou School of Mathematical Sciences, University of Nottingham,
Nottingham NG7 2RD, UK, margarita.zachariou@nottingham.ac.uk
Yanyan Zhang Department of Mathematics, Ohio State University, Columbus,
OH 43210, USA, yzhang@math.ohio-state.edu

12. On the Dynamics of Synaptic Inputs
During Ongoing Activity in the Cortex
Michael Okun
1
, Alik Mokeichev
1
, Yonatan Katz, and Ilan Lampl
Abstract In this chapter, we provide an overview of the dynamical properties of
spontaneous activity in the cortex, as represented by the subthreshold membrane
potential fluctuations of the cortical neurons. First, we discuss the main findings from
various intracellular recording studies performed in anesthetized animals as well as
from a handful of studies in awake animals. Then, we focus on two specific questions
pertaining to random and deterministic properties of cortical spontaneous activity. One
of the questions is the relationship between excitation and inhibition, which is shown
to posses a well-defined structure, owing to the spatio-temporal or-ganization of the
spontaneous activity in local cortical circuits at the millisecond scale. The other
question regards the spontaneous activity at a scale of seconds and minutes. Here,
examination of repeating patterns in subthreshold voltage fluctua-tions failed to reveal
any evidence for deterministic structures.
Introduction
Even in the absence of sensory stimuli, cortical activity is highly prominent. At the
single-cell level, spontaneous activity in the cortex is observed using extracellular,
intracellular, and calcium imaging recordings, whereas populations of cells can be seen
using voltage sensitive dyes. At a larger scale, spontaneous activity can be observed in
EEG, MEG, and fMRI recordings. In this chapter, we focus on the on-going cortical
activity as expressed by the dynamics of the subthreshold membrane potential of single
neurons. Since synaptic inputs are the main cause of membrane potential fluctuations
in cortical neurons [51], this technique is one of the most powerful tools to probe the
network activity. The intracellular recording technique
I. Lampl ( )
Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100,
Israel e-mail: ilan.lampl@weizmann.ac.il
1
Equal contribution.
K. Josi´c et al. (eds.), Coherent Behavior in Neuronal Networks, Springer Series 1
in Computational Neuroscience 3, DOI 10.1007/978-1-4419-0389-1
1, c Springer Science+Business Media, LLC 2009

13. 2 M. Okun et al.
provides the most accurate data in terms of spatial and temporal precision, which
comes at the expense of low yield of recorded cells and limited recording duration,
because of the mechanical sensitivity of the technique. Nevertheless, an increasing
number of studies have used this method to unveil the dynamics of spontaneous
activity in the cortex.
A particularly distinctive feature of the subthreshold dynamics in cortical neurons is
the appearance of Up-Down states of membrane potential, originally described in
anesthetized cats [52] and rats [17]. The Up-Down dynamics is characterized by large
(10–20 mV) depolarizations relative to the baseline potential, lasting for several
hundreds of milliseconds (the Up state), resulting in bimodal membrane po-tential
distribution (Fig. 1a). This activity pattern was also observed in other species,
including mice [42] and ferrets [23, 25]. Indirect EEG evidence for the presence of Up-
Down states is also available for monkeys [39] and humans [4,52]. In a series of
studies in drug-free cats, it was found that Up-Down dynamics occurs during slow
wave sleep (SWS) [53,54]. Similar behavior during SWS and periods of drowsiness
was observed in rats and mice as well [33, 42]. On the other end of scale, Up-Down
dynamics was also reproduced in slices [49].
While Up-Down dynamics is readily observed under some conditions of anes-
thesia (urethane, ketamine-xylazine), quite a different activity pattern,
characterized by rather short (10–50 ms) depolarizations and membrane potential
distribution that is not bimodal, emerges with other anesthetics (most distinctively
the inhaled ones, such as isoflurane and halothane). This kind of activity appears
to be a manifesta-tion of lighter anesthesia when compared with the Up-Down
dynamics, since the bimodal distribution of the membrane potential tends to
appear when the concentra-tion of the inhaled anesthetic is increased (unpublished
results). Furthermore, under light gas anesthesia membrane dynamics is more
similar to the activity observed in awake animals (see below).
Since it is plausible that the spontaneous dynamics in awake animals differs
substantially from the anesthetized condition, intracellular recordings of cortical
neurons in awake animals have been performed as well. Rather unfortunately
these data are also most experimentally demanding to obtain, since intracellular
record-ings are extremely sensitive to mechanical instabilities, which are almost
inevitable in awake, drug-free animals. At present time only a handful of such
studies were performed, mostly in head fixed animals: monkeys [14, 35], cats [8,
53, 54], rats [12, 20, 22, 34, 40], mice [18, 43], and bats [16]. A methodology for
whole-cell recording in behaving rodents is being developed as well [32].
Perhaps somewhat surprisingly, there exist large discrepancies between these
studies. Two recent investigations reported diametrically opposing results: one group
recorded neurons from the primary auditory cortex (A1) of rats [20, 27] and the other
recorded from the parietal association cortex in cats [46]. According to Zador and his
colleagues, the spontaneous subthreshold activity in the rat A1 is char-acterized by
infrequent large positive excursions (“bumps”), resulting in membrane potential
distribution with sharp peak and heavy tail at its positive side (average kurtosis of 15),
quite distinct from the Gaussian distribution. On the contrary, in [46] the membrane
potential exhibits activity resembling a continuous Up state,

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