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How Smart is a Neuron?
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Alwyn Scott
How Smart is a Neuron?
A Review of Christof Koch’s ‘Biophysics of Computation’
In the United States, automatic numerical computation stems from the Second World
War, where the need to calculate artillery trajectories led to the development of the
world’s first general purpose electronic computer, called the ENIAC (for electronic
numerical integrator and calculator). Switched on in the summer of 1945, this
machine employed 17,468 vacuum tubes connected by half a million solder joints and
a tangle of plug-in cables, looking much like an enormous telephone switchboard.
Although the subsequent development of modern digital computers seems
straightforward in retrospect, the path into the future was not so easy for some to
appreciate at the time. As a student of physics in the early 1950s, I recall seeing an
announcement of the newly invented
transistor that included a photograph showing a
small object looking like a dried pea with three wires sticking out. This spidery gob of
plastic, I asked, is going to revolutionize electronics? How could such a tiny device
replace the glowing output tubes of my ham radio transmitter?
A few years later, I found myself working for a semiconductor electronics com-
pany that was making transistor circuits for the computers of the ballistic missile
early warning system, a giant machine designed to gather inputs from arctic radar
sites and process the information to decide whether (or not) to incinerate the Soviet
Union. On an idle afternoon, one of the guys speculated that it might be possible to
put up to 100 transistors on a single slice of semiconductor crystal, which seemed to
me a crazy idea. How could one ever check that all of the circuits were working? But
the onboard computational demands of intercontinental atomic warfare (for reduced
size and power consumption) soon led to the forced development of
integrated cir-
cuits, in which thousands, then tens of thousands, then hundreds of thousands, and
millions of transistor circuits can be reliably interconnected on a single slice of
semiconductor crystal. (Intel’s Pentium III chip, for example, has 28 million
Journal of Consciousness Studies, 7, No. 5, 2000, pp. 70–5
* Christof Koch,
Biophysics of Computation: Information Processing in Single Neurons (New York:
Oxford University Press, 1999, xxiii + 562 pp., $62.95, ISBN 0 19 510491 9 (hbk.)).
Alwyn Scott, Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA

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transistors, corresponding to the hardware of about 1600 ENIACs, running at much
higher reliability and much faster rates of data transfer.)
Going back to 1943 — when ENIAC was under secret development — an event of
major significance for neuroscience occurred, and this was unrelated to the war effort
(McCulloch and Pitts, 1943). Warren McCulloch, then a professor of psychiatry, and
Walter Pitts, a young mathematician, published a seminal paper in which the operat-
ing principles of a digital computer were independently invented (!) and applied as a
mathematical theory for the functioning of a human brain. In response to the enthusi-
astic promotion of this paper by physicist John Neumann in the early 1950s, research-
ers throughout the world began to study models of the nervous system that were based
on the ‘McCulloch–Pitts neuron’.
Inevitably, popular articles by science journalists about ‘giant brains’ began to
appear in the Sunday supplements. In one sense this lurid description was literally
true — for the 30 ton ENIAC filled a large room — but those starry-eyed writers
intended more. In a widely circulated joke from those days, a group of engineers
assemble the most powerful computer that had ever been conceived and ask it the ulti-
mate question: ‘Is there a God?’ After several tense minutes of clicking and clacking
and flashing of lights, a card pops out which reads: ‘There is
As is well known, McCulloch and Pitts modelled the neuron as a single switch that
would fire (or not) according to whether (or not) the total input was above (or below)
some threshold level. The total input was then taken to be a weighted linear sum of all
of the synaptic (input) signals. Since the human brain comprises some 10 to 100 billion
(thousand million) neurons, each with 1000 to 100,000 synapses, a full
McCulloch–Pitts model of the brain is an enormously complex dynamic system, but
is it intricate enough to model a real brain? This is the fundamental question raised by
Christof Koch in his
Biophysics of Computation.
Also appearing in the early 1950s was another classic paper by neurophysiologists
Alan Hodgkin and Andrew Huxley, in which the dynamics of nerve impulse conduc-
tion along the giant axon (or outgoing fibre) of the common Atlantic squid was well
described (Hodgkin and Huxley, 1952). Based upon independent measurements of
parameters characterizing an isolated patch of active membrane, they developed a
theory that accurately predicts both the speed and the shape of a nerve impulse, along
with several other curious aspects of neural behaviour. In the context of the Hodgkin–
Huxley theory, each patch of active membrane on a neuron may function like a
switch, thus permitting far more intricate behaviour than is allowed to the
McCulloch–Pitts model neuron.
Throughout the 1960s and early 1970s there was an uneasy truce between these two
lines of research. As computers became more and more powerful, network models
based on the McCulloch–Pitts neuron grew increasingly sophisticated, and corre-
sponding engineering systems (with ‘synaptic’ input weights adjusted through appro-
priate learning routines) were employed for automatic recognition of patterns in such
diverse areas as character recognition, aerial photograph analysis and cytology,
among several others. During the same period, waxing computer power made it pos-
sible to analyse versions of the Hodgkin–Huxley membrane equations with ever more
interesting geometries, taking account of local enlargements (or varicosities) of the
fibres, branching structures in axonal (outgoing) and dendritic (incoming) trees,

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periodically active (myelinated) axons, and so on. Thus theoretical representations of
neurons became ever more intricate.
By the early 1970s advances in electron micrography and electrophysiology made
it evident to some neuroscientists that the dynamics of real neurons were far more
complex than the McCulloch–Pitts model implied. Thus in 1972 neurologist Steven
Waxman proposed the concept of a ‘multiplex neuron’ in which patches of membrane
near the branching regions of incoming (axonal) and outgoing (dendritic) processes
of the neuron are viewed as localities of low safety factor, where active nerve
impulses can become extinguished (Waxman, 1972).
In other words, an individual neuron might be able to perform logical computations
at its branching regions, making it more like an integrated circuit chip than a single
switch. As reasonable as it seemed to some of us at the time (Scott, 1975), this
expanded view of the neuron’s computational power was far from being universally
accepted. Jerry Lettvin, a noted electrophysiologist at MIT, told me in the spring of
1978 that when he and his colleagues reported blockages of nerve impulses in the
optic nerves of cats and speculated on the possibilities of this phenomenon for visual
information processing (Chung
et al., 1970), his NIH funding was cut off. ‘When you are
ready to start doing science again,’ he was told, ‘we are ready to resume supporting you.’
Why were such seemingly reasonable suggestions so widely ignored in the 1970s?
Although one can only speculate, four possibilities come to mind. (1) Admitting to
increased computational power of the individual neuron would tend to undercut the
validity of the extensive neural network studies that were based on the
McCulloch–Pitts model. (2) Many of the studies in this area were being done in the
Soviet Union (Khodorov, 1974), and Western scientists (particularly in the US) tended
to ignore or disparage Soviet science. (3) The reputations of some senior scientists
were invested in simpler models of the neuron. (4) There was a widespread and
uncritical belief in the concept of ‘all-or-nothing’ propagation of a nerve impulse,
which left no room for the concept of impulse failure at branching regions of the
axonal or dendritic trees.
One of the encouraging aspects of science, however, is that the truth does out in
time. Like old soldiers, the old guard withers away as evidence for the new paradigm
accumulates, until what was once considered flagrant speculation becomes widely
accepted as established knowledge. So it was with our collective perceptions of the
neuron. Towards the end of the 1980s, as the extensive list of references in
of Computation shows, the experimental, theoretical and numerical evidence for
impressive computational power of an individual neuron was compelling. Former
heresy has become common sense.
For young scientists who are interested in understanding the dynamics of the
human brain this change in collective attitude is of profound significance, to which
Koch’s book provides an ideal introduction. Written in a precise yet easy style, the 21
chapters of
Biophysics of Computation begin at the beginning, introducing the reader
to elementary electrical properties of membrane patches, linear cable theory and the
properties of passive dendritic trees. These introductory chapters are followed by two
on the properties of synapses and the various ways that synapses can interact to per-
form logic on passive dendritic trees. Then the Hodgkin–Huxley formulation for
impulse propagation on a single fibre is discussed in detail, and various simplifying
models are presented. As a basis for the Hodgkin–Huxley description the present

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understanding of ionic channels is reviewed, emphasizing the importance of calcium
currents. Further chapters discuss linearization of the H–H equations for small ampli-
tude behaviour; present a careful examination of ionic diffusion processes; and
describe electrochemical properties of dendritic spines, synaptic plasticity, simple
neural models, stochastic neural models and the properties of bursting cells. Do you
get the picture? Just about every facet of currently available neural knowledge is
touched upon, with appropriate references to a carefully selected bibliography that
will help the diligent novice delve deeply into whatever aspect of neural information
processing he or she chooses.
All of the above comprises an extended introduction to Chapters 17 to 19, which:
‘synthesize the previously learned lessons into a complete account of the events
occurring in realistic dendritic trees with all of their attendant nonlinearities’. ‘We
will see’, the author writes, ‘that dendrites can indeed be very powerful, nontradi-
tional computational devices, implementing a number of continuous operations.’
Biophysics of Computation offers a definitive statement for the direction in
which the neural research of the new century should go. Chapter 20, the penultimate,
discusses several speculations for non-neural computation in the brain, ranging from
molecular computing below the level of a single neuron to the effects of chemical
diffusants (nitric oxide, calcium ions, carbon monoxide, etc.) on large numbers of
neurons. Although this entire area has been neglected by most of the neuroscience
community, Koch points out that there are no good reasons for doing so. As we enter
the new century, neuroscientists should keep their minds open.
Finally, in the summary of Chapter 21, seven problems for future research projects
are listed, emphasizing that the investigation of information processing in single neu-
rons is very much a work in progress. It is of interest to examine these ‘strategic ques-
tions’ as they reveal the author’s intuitions about possible directions of future
developments. (Note that these are not direct quotes, as I have taken the liberty of
summarizing Koch’s questions.)
(1) How can the operation of multiplication be implemented at the level of a single
(2) What are the sources of noise in a neural system and how does this noise influ-
ence the logical operation of a single neuron?
(3) How is the style of neural computation influenced by metabolic considerations?
(4) What is the function of the apical dendrite, which is a typical cortical structure?
(5) How and where does learning actually take place in a neural system?
(6) What are the functions of the dendritic trees, the forms of which vary so widely
from neuron to neuron?
(7) How can we construct neural models that are sufficiently realistic to capture the
essential functions of real neurons yet simple enough to allow large-scale compu-
tations of brain dynamics?
As these questions indicate, Koch is not merely concerned with understanding
what unusual behaviours the neuron does or might exhibit. His broad aim is to com-
prehend the relation between this behavioural ability and the computational tasks that
the neuron is called upon to perform. In his words:
Thinking about brain style computation requires a certain frame of mind, related to but
distinctly different from that of the biophysicist. For instance, how should we think of a

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chemical synapse? In terms of complicated pre- and post-synaptic elements? Ionic chan-
nels? Calcium binding proteins? Or as a non-reciprocal and stochastic switching device
that transmits a binary signal rapidly between two neurons and remembers its history of
usage? The answer is that we must be concerned with both aspects, with biophysics as
well as computation.
This excellent book is evidently a labour of love, stemming from the author’s 1982
doctoral thesis on information processing in dendritic trees. As far as I can tell all rel-
evant aspects of neural processing are considered, with what seem to me to be just the
proper amounts of emphasis. The writing style is precise and rigorous without being
stuffy, and the many references to a fifty-page bibliography will be of enormous value
to young researchers starting out in this field.
In addition to its obvious value for those engaged in experimental, theoretical or
numerical studies of neuronal behaviour
Biophysics of Computation would also work
well as the text for an introductory course in neural dynamics, perhaps as part of a
neuroscience programme. Considering the rate at which new experimental informa-
tion is accumulating in this area (from the ongoing efforts of myriad electro-
physiologists and electron microscopists), and taking account of the ever increasing
availability of computational power, it seems inevitable that computational biophys-
ics will become established as a major research area within the next few years. Those
who would enter this exciting arena must make themselves familiar with the contents
of Koch’s book.
As is often the case, the writer of this positive review feels compelled to offer a few
reservations, if for no other reason than to demonstrate that he is unbiased and has
read the entire book. Indeed Koch invites such comments for consideration in future
editions. Mine are twofold.
First, I was disappointed to find no mention of Steve Waxman’s 1972 paper in
which the concept of the multiplex neuron was introduced (Waxman, 1972).
Although largely ignored by the neuroscience community of the early 1970s, this
publication proposes the same broad view of neural intricacy as does
Biophysics of
Computation. Certainly Koch’s list of references needs to be carefully selected, and
he has done so, but Waxman’s seminal work deserves a mention.
Second, there are very few references to the many significant publications of
Soviet scientists on the dynamics of individual neurons, especially those appearing
during the 1970s (Khodorov, 1974). This is an unfortunate oversight that could be
rectified in a future edition by asking for suggestions from some of the leading Rus-
sian neuroscientists.
Having established that
Biophysics of Computation is an important addition to the
literature of neuronal information processing, one question remains: Why should
readers of
the Journal of Consciousness Studies find it interesting?
To answer this question, consider the enormous influence that the McCulloch–Pitts
paper has had on the cognitive science community since its discovery and promotion
by Neumann in the late 1940s. This subtle influence is not, I believe, unrelated to the
subsequent journalistic anthropomorphizing of ENIAC and her increasingly sophisti-
cated offspring. From this early perspective each neuron is regarded as a single
switch, and the human brain is likened to a digital computer, as we currently under-
stand the meaning of that term. This limited model of the brain has been widely dis-
seminated throughout the realms of science, leading many to conclude that the human

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is essentially a digital computer. Others suggest that mysterious physical phe-
nomena—such as quantum theory—must be brought in to neuroscience to square
what we know about the nature of mind with the facts of neurology.
From the perspective of Christof Koch’s
Biophysics of Computation the situation is
quite different. A neuron can no longer be viewed as a single switch; it is more or less
analogous to an integrated circuit chip. I write ‘more or less’ because much of a neu-
ron’s behaviour remains under a shroud, making it difficult to discern what a system
of 10 to 100 billion real neurons, as described in this book, might or might not be able
to do. Cognitive scientists should give priority to accepting and appreciating these
emerging vistas and offering re-evaluations of the brain’s abilities for the benefit of
those psychologists, philosophers and physicists who are engaged in consciousness
Chung, S.H., Raymond, S.A. and Lettvin, J.Y. (1970), ‘Multiple meaning in single visual units’,
Behavior, Evol., 3, pp. 72–101.
Hodgkin, A.L. and Huxley, A.F. (1952), ‘A quantitative description of membrane current and its applica-
tion to conduction and excitation in nerve’,
J. Physiol., 117, pp. 500–44.
Khodorov, B.I. (1974),
The Problem of Excitability (New York: Plenum Press).
McCulloch, W.S. and Pitts, W.H. (1943), ‘A logical calculus of the ideas immanent in nervous activity’,
Bull. Math. Biophys., 5, pp. 115–33.
Scott, A.C. (1975), ‘The electrophysics of a nerve fiber’,
Rev. Mod. Phys., 47, pp. 487–533.
Waxman, S.G. (1972), ‘Regional differentiation of the axon: A review with special reference to the con-
cept of the multiplex neuron’,
Brain Res., 47, pp. 269–88.