Theoretical Neuroscience Computational and Mathematical Modeling of Neural Systems - Peter Dayan, L. F. Abbott.pdf

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Preface
Theoretical analysis and computational modeling are important tools for
characterizing what nervous systems do, determining how they function,
and understanding why they operate in particular ways. Neuroscience
encompasses approaches ranging from molecular and cellular studies to
human psychophysics and psychology. Theoretical neuroscience encour-
ages cross-talk among these sub-disciplines by constructing compact rep-
resentations of what has been learned, building bridges between different
levels of description, and identifying unifying concepts and principles. In
this book, we present the basic methods used for these purposes and dis-
cuss examples in which theoretical approaches have yielded insight into
nervous system function.
The questions what, how, and why are addressed by descriptive, mecha-
nistic, and interpretive models, each of which we discuss in the following
chapters. Descriptive models summarize large amounts of experimental descriptive models
data compactly yet accurately, thereby characterizing what neurons and
neural circuits do. These models may be based loosely on biophysical,
anatomical, and physiological findings, but their primary purpose is to de-
scribe phenomena not to explain them. Mechanistic models, on the other mechanistic models
hand, address the question of how nervous systems operate on the ba-
sis of known anatomy, physiology, and circuitry. Such models often form
a bridge between descriptive models couched at different levels. Inter-
pretive models use computational and information-theoretic principles to interpretive models
explore the behavioral and cognitive significance of various aspects of ner-
vous system function, addressing the question of why nervous system op-
erate as they do.
It is often difficul to identify the appropriate level of modeling for a partic-
ular problem. A frequent mistake is to assume that a more detailed model
is necessarily superior. Because models act as bridges between levels of
understanding, they must be detailed enough to make contact with the
lower level yet simple enough to yield clear results at the higher level.
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Theoretical Neuroscience
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Organization and Approach
This book is organized into three parts on the basis of general themes.
Part I (chapters 1-4) is devoted to the coding of information by action
potentials and the represention of information by populations of neurons
with selective responses. Modeling of neurons and neural circuits on the
basis of cellular and synaptic biophysics is presented in part II (chapters
5-7). The role of plasticity in development and learning is discussed in
Part III (chapters 8-10). With the exception of chapters 5 and 6, which
jointly cover neuronal modeling, the chapters are largely independent and
can be selected and ordered in a variety of ways for a one- or two-semester
course at either the undergraduate or graduate level.
Although we provide some background material, readers without previ-
ous exposure to neuroscience should refer to a neuroscience textbook such
as Kandel, Schwartz & Jessell (2000); Nicholls, Martin & Wallace (1992);
Bear, Connors & Paradiso (1996); Shepherd (1997); Zigmond, Bloom, Lan-
dis & Squire (1998); Purves et al (2000).
Theoretical neuroscience is based on the belief that methods of mathemat-
ics, physics, and computer science can elucidate nervous system function.
Unfortunately, mathematics can sometimes seem more of an obstacle than
an aid to understanding. We have not hesitated to employ the level of
analysis needed to be precise and rigorous. At times, this may stretch the
tolerance of some of our readers. We encourage such readers to consult
the mathematical appendix, which provides a brief review of most of the
mathematical methods used in the text, but also to persevere and attempt
to understand the implications and consequences of a difficult derivation
even if its steps are unclear.
Theoretical neuroscience, like any skill, can only be mastered with prac-
tice. We have provided exercises for this purpose on the web site for this
book and urge the reader to do them. In addition, it will be highly in-
structive for the reader to construct the models discussed in the text and
explore their properties beyond what we have been able to do in the avail-
able space.
Referencing
In order to maintain the flow of the text, we have kept citations within
the chapters to a minimum. Each chapter ends with an annotated bib-
liography containing suggestions for further reading (which are denoted
by a bold font), information about work cited within the chapter, and ref-
erences to related studies. We concentrate on introducing the basic tools
of computational neuroscience and discussing applications that we think
best help the reader to understand and appreciate them. This means that
a number of systems where computational approaches have been applied
Peter Dayan and L.F. Abbott
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3
with significant success are not discussed. References given in the anno-
tated bibliographies lead the reader toward such applications. In most
of the areas we cover, many people have provided critical insights. The
books and review articles in the further reading category provide more
comprehensive references to work that we apologetically have failed to
cite.
Acknowledgments
We are extremely grateful to a large number of students at Brandeis,
the Gatsby Computational Neuroscience Unit and MIT, and colleagues
at many institutions, who have painstakingly read, commented on, and
criticized, numerous versions of all the chapters. We particularly thank
Bard Ermentrout, Mark Kvale, Mark Goldman, John Hertz, Zhaoping
Li, Eve Marder, and Read Montague for providing extensive discussion
and advice on the whole book. A number of people read significant
portions of the text and provided valuable comments, criticism, and in-
sight: Bill Bialek, Pat Churchland, Nathanial Daw, Dawei Dong, Peter
F oldiak, Fabrizio Gabbiani, Zoubin Ghahramani, Geoff Goodhill, David
Heeger, Geoff Hinton, Ken Miller, Tony Movshon, Phil Nelson, Sacha Nel-
son, Bruno Olshausen, Mark Plumbley, Alex Pouget, Fred Rieke, John
Rinzel, Emilio Salinas, Sebastian Seung, Mike Shadlen, Satinder Singh,
Rich Sutton, Nick Swindale, Carl Van Vreeswijk, Chris Williams, David
Willshaw, Charlie Wilson, Angela Yu, and Rich Zemel. We have received
significant additional assistance and advice from: Greg DeAngelis, Matt
Beal, Sue Becker, Tony Bell, Paul Bressloff, Emery Brown, Matteo Caran-
dini, Frances Chance, Yang Dan, Kenji Doya, Ed Erwin, John Fitzpatrick,
David Foster, Marcus Frean, Ralph Freeman, Enrique Garibay, Frederico
Girosi, Charlie Gross, Mike Jordan, Sham Kakade, Szabolcs Kali, Christof
Koch, Simon Laughin, John Lisman, Shawn Lockery, Guy Mayraz, Quaid
Morris, Randy O’Reilly, Max Riesenhuber, Sam Roweis, Simon Osindero,
Tomaso Poggio, Clay Reid, Dario Ringach, Horacio Rotstein, Lana Ruther-
ford, Ken Sagino, Maneesh Sahani, Alexei Samsonovich, Idan Segev, Terry
Sejnowski, Haim Sompolinksy, Fiona Stevens, David Tank, Alessandro
Treves, Gina Turrigiano, David Van Essen, Martin Wainwright, Xiao-Jing
Wang, Max Welling, Matt Wilson, Danny Young, and Ketchen Zhang. We
apologise to anyone we may have inadvertently omitted from these lists.
Karen Abbott provided valuable help with the figures. From MIT Press,
we thank Michael Rutter for his patience and consistent commitment, and
Sara Meirowitz and Larry Cohen for picking up where Michael left off.
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Chapter 1
Neural Encoding I: Firing
Rates and Spike Statistics
1.1 Introduction
Neurons are remarkable among the cells of the body in their ability to
propagate signals rapidly over large distances. They do this by generat-
ing characteristic electrical pulses called action potentials, or more simply
spikes, that can travel down nerve fibers. Neurons represent and transmit
information by firing sequences of spikes in various temporal patterns.
The study of neural coding, which is the subject of the first four chapters of
this book, involves measuring and characterizing how stimulus attributes,
such as light or sound intensity, or motor actions, such as the direction of
an arm movement, are represented by action potentials.
The link between stimulus and response can be studied from two opposite
points of view. Neural encoding, the subject of chapters 1 and 2, refers to
the map from stimulus to response. For example, we can catalogue how
neurons respond to a wide variety of stimuli, and then construct models
that attempt to predict responses to other stimuli. Neural decoding refers
to the reverse map, from response to stimulus, and the challenge is to re-
construct a stimulus, or certain aspects of that stimulus, from the spike
sequences it evokes. Neural decoding is discussed in chapter 3. In chapter
4, we consider how the amount of information encoded by sequences of
action potentials can be quantified and maximized. Before embarking on
this tour of neural coding, we briefly review how neurons generate their
responses and discuss how neural activity is recorded. The biophysical
mechanisms underlying neural responses and action potential generation
are treated in greater detail in chapters 5 and 6.
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Theoretical Neuroscience

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