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Athens University of Economics and Business
Wulfram Gerstner and Werner Kistler
Spiking neuron models: single neurons, populations, plasticity
Cambridge University Press, New York, NY, 2002
Not often does nowadays one find in a learned book expressions such as "not known", "can not be easily answered", and "poorly understood". Yet, this is the state of the art in many areas of neuroscience that Gerstner and Kistler tackle in their book Spiking Neuron Models. Their work examines how single neurons and groups of them behave and change their behavior in the context of living organisms. In this detailed and fascinating advanced textbook the two authors employ the power of mathematical analysis together with results from biochemistry, physics, and information theory to map the functioning of neural systems. These systems are orders of magnitude more complex than anything artificial we humans can build and, possibly, understand. A single neuron in a vertebrate cortex often connects to more than 10,000 postsynaptic neurons, by comparison a TTL logic gate can typically drive no more than 20 similar gates; the mammalian brain contains more than 1010 neurons, the Pentium 4 CPU contains "only" 55*106 transistors. We therefore have to resort on experimental data and a phenomenological neuron model to study neuronal dynamics.
A typical neuron consists of the dendrites where input signals arrive, the soma that processes those inputs in a non-linear fashion, and the axon where the output signal is generated, in the form of a short electrical spike, and transferred to other neurons. These spikes can be recorded by means of intracellular electrodes and used as a basis for building a theory of neuronal dynamics. The book is divided into three parts. The first part examines neurons in isolation. After building a detailed neuron model, the four-dimensional differential equations are reduced into a two-dimensional model that leads itself to phase analysis. The formal study of spiking and of spike trains brings forward the fascinating question of noise in neural systems: how do neural systems deal with environmental noise, and is what we experimentally observe as noise in the neural firing characteristics really noise, or signaling that we are unable to comprehend? In many areas of the brain, neurons are organized in populations of units with similar properties. These are analyzed in the book's second part by treating them as population models. These models allow us to study phenomena such as signal transmission, neuronal coding, oscillations, and synchrony. Moreover, the essentially flat structure of the unfolded human cerebral cortex allows us to study it as a continuous two-dimensional sheet of neurons and derive the corresponding stationary and dynamic patters of neuronal activity. Finally the book's third part deals with models of synaptic plasticity arising from Hebb's remarkably prescient postulate: that axons that repeatedly cause a cell to fire, will increase their efficiency over time. This result has been experimentally confirmed and is thought to be the neuronal correlate of learning and memory.
The treatment of the material is formal and rigorous; the mathematically inclined reader will surely marvel at how the intricate phenomena occurring within our brain are modeled by the equations presented in the text. In addition, numerous clear illustrations of waveforms, patterns, connection models, and equivalent electrical circuits will help the reader understand the necessarily dense textual descriptions. Researchers will also appreciate the more than 450 references lend authority to the treatment, especially since many of the references point to very recent research results. The book can be used in computational neuroscience, theoretical biology, neural modeling, biophysics, and neural network courses. Of particular pedagogical importance in an educational setting is the large number of examples that accompany the presented theory. Most sections that introduce a new concept are followed by one or more concrete examples where the theory is applied. Thus, the discussion of stochastic spike arrival is accompanied by two examples detailing membrane potential fluctuations, and balanced excitation and inhibition. Unfortunately, although all chapters end with a survey and a brief literature review, no exercises are given to help students test their understanding.
Given the number of questions that neuroscientists are still struggling with, Spiking Neuron Models is clearly an important book: hopefully it will lead future researchers to give us the answers on how we think.