Single Neuron Computation In Vivo

This book contains twenty-two original contributions that provide a comprehensive overview of computational approaches to understanding a single neuron structure. The focus on cellular-level processes is twofold. From a computational neuroscience perspective, a thorough understanding of the information processing performed by single neurons leads to an understanding of circuit- and systems-level activity. From the standpoint of artificial neural networks (ANNs), a single real neuron is as complex an operational unit as an entire ANN, and formalizing the complex computations performed by real neurons is essential to the design of enhanced processor elements for use in the next generation of ANNs. The book covers computation in dendrites and spines, computational aspects of ion channels, synapses, patterned discharge and multistate neurons, and stochastic models of neuron dynamics. It is the most up-to-date presentation of biophysical and computational methods.

Neural network research often builds on the fiction that neurons are simple linear threshold units, completely neglecting the highly dynamic and complex nature of synapses, dendrites, and voltage-dependent ionic currents. Biophysics of Computation: Information Processing in Single Neurons challenges this notion, using richly detailed experimental and theoretical findings from cellular biophysics to explain the repertoire of computational functions available to single neurons. The author shows how individual nerve cells can multiply, integrate, or delay synaptic inputs and how information can be encoded in the voltage across the membrane, in the intracellular calcium concentration, or in the timing of individual spikes. Key topics covered include the linear cable equation; cable theory as applied to passive dendritic trees and dendritic spines; chemical and electrical synapses and how to treat them from a computational point of view; nonlinear interactions of synaptic input in passive and active dendritic trees; the Hodgkin-Huxley model of action potential generation and propagation; phase space analysis; linking stochastic ionic channels to membrane-dependent currents; calcium and potassium currents and their role in information processing; the role of diffusion, buffering and binding of calcium, and other messenger systems in information processing and storage; short- and long-term models of synaptic plasticity; simplified models of single cells; stochastic aspects of neuronal firing; the nature of the neuronal code; and unconventional models of sub-cellular computation. Biophysics of Computation: Information Processing in Single Neurons serves as an ideal text for advanced undergraduate and graduate courses in cellular biophysics, computational neuroscience, and neural networks, and will appeal to students and professionals in neuroscience, electrical and computer engineering, and physics.

This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.

Understanding and implementing the brain's computational paradigm is the one true grand challenge facing computer researchers. Not only are the brain's computational capabilities far beyond those of conventional computers, its energy efficiency is truly remarkable. This book, written from the perspective of a computer designer and targeted at computer researchers, is intended to give both background and lay out a course of action for studying the brain's computational paradigm. It contains a mix of concepts and ideas drawn from computational neuroscience, combined with those of the author. As background, relevant biological features are described in terms of their computational and communication properties. The brain's neocortex is constructed of massively interconnected neurons that compute and communicate via voltage spikes, and a strong argument can be made that precise spike timing is an essential element of the paradigm. Drawing from the biological features, a mathematics-based computational paradigm is constructed. The key feature is spiking neurons that perform communication and processing in space-time, with emphasis on time. In these paradigms, time is used as a freely available resource for both communication and computation. Neuron models are first discussed in general, and one is chosen for detailed development. Using the model, single-neuron computation is first explored. Neuron inputs are encoded as spike patterns, and the neuron is trained to identify input pattern similarities. Individual neurons are building blocks for constructing larger ensembles, referred to as "columns". These columns are trained in an unsupervised manner and operate collectively to perform the basic cognitive function of pattern clustering. Similar input patterns are mapped to a much smaller set of similar output patterns, thereby dividing the input patterns into identifiable clusters. Larger cognitive systems are formed by combining columns into a hierarchical architecture. These higher level architectures are the subject of ongoing study, and progress to date is described in detail in later chapters. Simulation plays a major role in model development, and the simulation infrastructure developed by the author is described.

"One hundred years ago, the fundamental building block of the central nervous system, the neuron, was discovered. This study focuses on the existing mathematical models of neurons and their interactions, the simulation of which has been one of the biggest challenges facing modern science." "More than fifty years ago, W. S. McCulloch and W. Pitts devised their model for the neuron, John von Neumann seemed to sense the possibilities for the development of intelligent systems, and Frank Rosenblatt came up with a functioning network of neurons. Despite these advances, the subject had begun to fade as a major research area until John Hopfield arrived on the scene. Drawing an analogy between neural networks and the Ising spin models of ferromagnetism, Hopfield was able to introduce a "computational energy" that would decline toward stable minima under the operation of the system of neurodynamics devised by Roy Glauber." "Like a switch, a neuron is said to be either "on" or "off." The state of the neuron is determined by the states of the other neurons and the connections between them, and the connections are assumed to be reciprocal - that is, neuron number one influences neuron number two exactly as strongly as neuron number two influences neuron number one. According to the Glauber dynamics, the states of the neurons are updated in a random serial way until an equilibrium is reached. An energy function can be associated with each state, and equilibrium corresponds to a minimum of this energy. It follows from Hopfield's assumption of reciprocity that an equilibrium will always be reached." "D. H. Ackley, G. E. Hinton, and T. J. Sejnowski modified the Hopfield network by introducing the simulated annealing algorithm to search out the deepest minima. This is accomplished by - loosely speaking - shaking the machine. The violence of the shaking is controlled by a parameter called temperature, producing the Boltzmann machine - a name designed to emphasize the connection to the statistical physics of Ising spin models." "The Boltzmann machine reduces to the Hopfield model in the special case where the temperature goes to zero. The resulting network, under the Glauber dynamics, produces a homogeneous, irreducible, aperiodic Markov chain as it wanders through state space. The entire theory of Markov chains becomes applicable to the Boltzmann machine." "With ten chapters, five appendices, a list of references, and an index, this study should serve as an introduction to the field of neural networks and its application, and is suitable for an introductory graduate course or an advanced undergraduate course."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

Neuronal dendritic trees are complex structures that endow the cell with powerful computing capabilities and allow for high neural interconnectivity. Studying the function of dendritic structures has a long tradition in theoretical neuroscience, starting with the pioneering work by Wilfrid Rall in the 1950s. Recent advances in experimental techniques allow us to study dendrites with a new perspective and in greater detail. The goal of this volume is to provide a résumé of the state-of-the-art in experimental, computational, and mathematical investigations into the functions of dendrites in a variety of neural systems. The book first looks at morphological properties of dendrites and summarizes the approaches to measure dendrite morphology quantitatively and to actually generate synthetic dendrite morphologies in computer models. This morphological characterization ranges from the study of fractal principles to describe dendrite topologies, to the consequences of optimization principles for dendrite shape. Individual approaches are collected to study the aspects of dendrite shape that relate directly to underlying circuit constraints and computation. The second main theme focuses on how dendrites contribute to the computations that neurons perform. What role do dendritic morphology and the distributions of synapses and membrane properties over the dendritic tree have in determining the output of a neuron in response to its input? A wide range of studies is brought together, with topics ranging from general to system-specific phenomena—some having a strong experimental component, and others being fully theoretical. The studies come from many different neural systems and animal species ranging from invertebrates to mammals. With this broad focus, an overview is given of the diversity of mechanisms that dendrites can employ to shape neural computations.