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Spikes: Exploring the Neural Code (Computational Neuroscience)

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A decade ago, computational neuroscientists and some neurophysiologists were twittering with excitement about information theory. Finally, a tool that could decode the "noise" observed when we record neuronal spike signals!

These days...information theory has become part of the standard toolkit in a few types of experiments. But we're not much closer to understanding the neural code(s) than when this book was written. Nevertheless, Bialek's group of mostly physicists turned neuroscientists continue to develop information theoretic tools. Perhaps they'll come up with one that's not just another hammer.

The authors of Spikes may still turn out to have been ahead of their time (just like Barlow, MacKay and McCulloch, who originally applied information theory to neurons). Or their research program may turn out to have been a detour, a misguided attempt to find a particular physical universal in evolutionarily contingent biological systems.

If you're interested in theoretical neuroscience, I would definitely recommend Dayan and Abbott's textbook. van Hemmen and Sejnowski's "23 Problems in Systems Neuroscience" also has good bits. If you really want to read about information theory, David MacKay's new book is available on the web.

This book asks: How does a nerve convey information about the world toward the brain? It is a crucially important question - one of the most important questions in human history, in fact -- because before one can make realistic theories about how a brain works, one must know what sorts of signals it receives and acts upon.

We were all told, in basic biology, that this question was answered decisively in the 1920s: The nerve encodes and transmits information about the world in the form of frequency modulated pulse trains. The more intense the stimulus, the higher the pulse frequency, and the closer together the pulses in the train. In this system, a single impulse, or "spike", is trivial, in the sense that it is blank. It cannot convey any information alone. It takes at least two pulses to encode sensory meaning. The information that is read by the brain (meaning, say, a level of light, or the intensity of a musical tone) is encoded as the interval between pulses. And so as students we ate this FM story. And answered the inevitable, standardized questions about it on exams.

Now we learn that this familiar, ingrained bedrock idea is not actually true. Somehow, a single spike is - after all -- capable of conveying information to the brain. This news was not revealed in some single egregious experiment but, rather, by a substantial body of experimental results that have filtered into the literature recently. This book gathers and pivots around this unexpected (and probably very unpopular) body of research work, and I suggest that you initially skip all the introductory material and go straight to pages 54-60, where the experimental literature is summarized.

A nice example comes from studying the decision making time of bats. The animal uses echolocation to navigate in flight. An experimental question is this: How many nerve impulses can the creature's brain have decoded before it suddenly decides to swerve? The answer is on the order of one spike. One. Uno.

At this point in the book, the answer is already transparent. The secret of the neural encoding is that there is no code. A single spike conveys information. The information is explicit. No computation is required to extract it.

Ah, but not so fast. On page 4, the authors reiterate the all-or-none law, declaring that: "... incoming stimuli either produce action potentials, which propagate long distances along the cell's axon, or they do not. There are no intermediate signaling mechanisms. This means that a single neuron can provide information to the brain only through the arrival times of the spikes."

Evidently they still want to keep this absolute intact, and so they go on to recreate, in lieu of the familiar FM neural code, another more sophisticated code. This book is their proposal for a new code.

But it seems to me that having driven such wonderfully high piton (their assertion that the FM code isn't one) the authors proceed to rappel down the mountain very fast. Retreating, perhaps, into their alternative code theory.

Instead of following them to lower, safer ground, you might pause to consider this: There might exist, after all, "intermediate signaling mechanisms." The pulse cannot be amplitude modulated (this really is an absolute). But it can surely do many other clever things that would elude detection by the instruments used to study nerve impulses. (Voltage clamps, patch clamps, probes). Like what? It could spin. It could and probably does travel up the axon membrane in one of many discrete longitudinal channels, formed by protein links between adjacent ion channels. In such a nerve the information, or sensory increment level, is inherent in the channel number.

Neurobiology, as an industry, is somewhat at risk to ideas of the type that are let loose in this remarkable book. If one were to follow up on them, one might arrive at a theory of the brain that actually made sense. Well understood structures like the synapse would have to be explained in new ways, etc. There might be uproar.

Also take a look at Findings and Current Opinion in Cognitive Neuroscience, by Squire and Kosslyn. Chapter 25 reviews some the ideas presented in Spikes, and competing explanations offered by other authors in an effort to elucidate the so called "sparse code." One spike. Very sparse indeed. By all means get a copy of Spikes. It would be a shame to miss out on the scientific revolution it so strongly augers.

What would it mean to understand how a neuron works? Traditionally this questions has been addressed by attempting to solve the encoding problem-that is, given a sample stimulus input, construct a model neuron that predicts the temporal pattern of spikes resulting from observing that stimulus. While much progress has been made on this front (for example, using Weiner-Volterra expansion methods), the remarkable contribution of this book is to turn the question on its head. Instead of asking how a neuron encodes information about the world into discrete spikes, this book instead takes the organism's point of view. Namely, animals do not "observe" the world, but only the spike trains that encode sensory stimuli, and they must be capable of producing successful behavior on the basis of these discrete spikes.

The question for the researcher becomes, given a sample spike train, what do we know about the environmental situation that resulted in this spike train? This question, the decoding problem, is the problem that biological organisms must solve. Perhaps even more remarkably, when posed as a decoding problem, many of the nonlinearities of the neural response disappear, and we are left with a simple linear filtering problem.

`Spikes: Exploring the Neural Code' presents numerous recent results on this front, drawing on behavioral and neurological data as diverse as bat echo location, moth evasion tactics, vertebrate and invertebrate vision, and the incredible French cave beetle capable of reliably detecting temperature changes as small as 1/1000 of a degree. To interpret these results, the authors rely on a variety of mathematical techniques, from probability theory and information theory, to optimal filtering and kernel approaches. This book is very rigorous, and not for math-phobic readers. Understanding all of the ideas presented in this book will take work: about one-third of the book is devoted to a series of appendixes or "Mathematical asides". Finally, one of the most valuable contributions of this book is its extensive list of references for the ideas and results presented in each chapter.

Rieke et al. have written a great book exploring how single neurons and populations of cells code information sensitive spikes and patterns of spikes, i.e. single action potentials, clusters, repetitive bursts, or single bursts. There are quite a few equations in the book, but the authors have written the text so well, that an advanced undergraduate or graduate student in the Neurosciences can understand it. One of my favorate sections discusses the Entropy of information, and the entropy of neural code patterns. This concept will likely shape the future of many neurophysiological investigations.

The point of this review is to evaluate "Spikes: Exploring the Neural Code" from the perspective of an graduate student in computational neurobiology. Overall, this book provides informative and mathematical methods for making sense of spike trains in the brain. While this book may seem appealing to those familiar with the biology of the brain, it is more geared towards the engineer with a strong calculus and statistics background. The concepts should be graspable by the senior undergraduate or graduate student after some time spent computationally evaluating the neuronal models. I would highly recommend this book to any person with an interest in mathematically modeling spike train data of individual neurons.

Synopsis and Opinion:

The goal of this book is to "understand how the nervous system represents signals with realistic time dependencies" (12). Although a lofty and seemingly unattainable goal for a single textbook, Rieke et al. limit most of their evaluation to the spike train data of a single neuron. A single chapter is devoted to the issues associated with a small ensemble of neurons. In order to guide this discussion and properly frame the problem, Rieke appeals to the Bayes' mathematical formalism in the majority of the descriptions of spike train data. If any equations appear within the text without justification, supplementary material is provided in an appendix with formal proofs and discussion.

Chapter 1 is an informative introduction to the problem of neural coding: the ability of an ensemble of neurons to represent any stimulus. The authors set out to frame the problem in a way that is manageable, quantifiable, and justifiable under the limitations of a 300 page book. They appeal to the idea of a homunculus looking at the neuronal spikes, when referring to the task of deciphering the neural code. The question to answer is: how is this homunculus making sense of the data?

Chapter 2 is an extended and detailed look at both the mathematical fundaments of the probabilistic approach to decoding neural spike trains, and the early methods used in quantifying this data. The authors introduce probability theory and use this framework to explain how stimuli might be predicted given a time series of spike data, and also the reverse, how spike data might be predicted from a stimuli. They introduce and quantify the basic neural coding language: spike rates, interspike intervals, and neuronal correlations. Following this introduction, they detail and describe how neurons should perform under natural conditions and seek techniques that can be used to measure the parameters of these models. Many of the issues discussed deal with managing noise that arises in the data and extracting the principle components of the neural code.

Chapter 3 uses Shannon's information theory to try to quantify the amount of information that a neuron can represent. Information theory is presented to the reader and justified as a reasonable approach to solve this problem. This framework is then applied to real world experiments on synaptic vesicles and mammalian ganglion cells.

Chapter 4 seeks to quantify the reliability of the nervous system. This task consists of "comparing the reliability of perception to the reliability of individual neurons" (191). This essentially means predicting the behavior expected from a particular stimulus, and assessing whether the neurons actually fire a response that encodes for this behavior. The remainder of the chapter consists of several case studies that provide quantifiable measures of reliability, and qualify the difficulty of this task.

Chapter 5 provides a brief overview of some of the issues of neural coding in a population of neurons. Initially, the methods that can sample many neurons are presented (micro-electrode arrays), followed by a discussion of the statistics of natural scenes. The author later reflects of the models presented: "most progress to date has been made by studying a model world that is a simpler and less structured place than the real world, hoping that the optimal strategies for deal with this simple world will at least give us hints about optimal strategies for the real world" (268).

Style and Structure:

This book is educational and well written, and suitable for the mathematical neurobiologist. Rieke et al. formalize the question they are seeking to ask, develop a model to explore this question, provide the relevant mathematical background for the model, evaluate the model against several scenarios, and provide case studies describing other attempts at answering the question. The logical flow of each chapter is appropriate and thoughtful.

At certain points throughout chapters 3 and 4, the authors digress too far into the case studies without providing enough background for the reader to fully understand the point of the section.

Overall, "Spikes" effectively communicates complex topics for readers with a sufficient mathematical background. They structure of each chapter makes following the authors' arguments very straightforward and relevant to the questions posed in the introduction.

Discussion

The authors' decide to approach neural spike data from a purely mathematical approach. Although this brings a strong theoretical background to problem, much of the biology is lost in the process; the biological justification behind the mathematical simplifications are missing, which may cause the reader to question the relevance of the techniques presented. Dendrites, axons, neurotransmitters, etc. are left out of the models used within the book.

One major complaint is that, for a majority of the book, "Spikes" only looks at an ensemble of spike rates from a single neuron. This process suffers from "grandmother cell-ism" and thus cannot possibly capture the intricacies and extensive dynamics associated with a group of neuron firings. The brain uses populations of thousands of neurons to code for even the simplest of stimuli.

For Potential Readers:

This book will supplement any computational neuroscience course very well, although, be warned that the following prerequisite knowledge is necessary: calculus, physics, some linear algebra, rudimentary neuroscience, signal processing, probability and statistics, time/frequency domain analysis, linear systems. Students will benefit from the author's informative tone, detailed mathematical descriptions, and organized presentation. Professors and researchers could use this book as both a personal reference and teaching tool.

How fast can a bat make up its mind? With its refined sonar system, a speeding bat can detect an obstruction and swerve to avoid it in a split second. Experiments show the bat has time to process only one spike, or nerve impulse, in the available time window. This is remarkable, but it defies explanation in terms of the long established (circa 1926) idea that the nervous system encodes sensory information as a function of time intervals between spikes. It takes two spikes to open and close a time interval. For the hurrying bat, using just one spike to make its decision, there exists no interval to measure.

Somehow, a single spike is conveying information to the brain. This surprising news was revealed not only in bat studies, but also in other results. This book presents them and then asks anew: How does a nerve convey information about the world toward the brain? What's the real neural code?

The authors review several plausible neural codes and offer their own, but one possibility seems evident from inspection: There is no code. If a single spike conveys information, maybe no decipherment is required. The pulse cannot be amplitude modulated (this is absolute). But it can do various other clever things that would elude detection by ordinary lab instruments. The impulse could spin. Or wobble. It could travel up the axon membrane in one of many discrete longitudinal channels formed by linkage between adjacent ion channels. In such a nerve the information, or sensory increment level, would be inherent in the channel number. In any event, Spikes is a mildly written but altogether shocking book. It implies we have been wrong about the nerve since 1926. And we probably have been.

This is one of the best books on brain's neuronal system. Very self-contained, and without a lot of those overstatements you normally find in similar books. The basic points are discussed while many of the classical (but not very useful) points are ignored. The math is clear and the discussion of the real important question always very sharp.

This book appears to be oriented towards neurobiologists with an interest in the mathematical analysis of neural data, and also towards physicists and mathemeticians interested in the information processing by so-called "real" nervous systems. The authors have done a great job in quantifying various neural responses - these include representation of time-dependent signals, calculation of information rate and coding efficiency - and in understanding the reliability of the nervous system to represent answers to its computational problems. The study of neural coding is thus tied to the much broader issue of neural computation. The section on "Mathematical Asides" in the Appendix is particularly helpful in understanding the response of the nervous system. "Spikes" is well-written though somewhat non-inspiring. As a physicist specializing in non-linear processes, I expect the book to be helpful both for neuroscientists and physicists. -- D.K.Bhadra, Advanced Spectral Research.

excellent book, lots of very good examples and figures, everything very clearly explained, clarifies a lot of things in a very logical step by step way.

This is a very interesting look deep into the binary nature of the human brain. It's nice to see the wet science guys taking information theory seriously. And it's also very interesting to see how digital the brain is when you look at interneuronal communication; how every perception you have, is in the end just a string of 1's and 0's.