Computational models of neural networks have proven insufficient to accurately model brain function, mainly as a result of simplifications that ignore the physical reality of neuronal structure in favor of mathematically tractable algorithms and rules. Even the more biologically based "integrate and fire" and "compartmental" styles of modeling suffer from oversimplification in the former case and excessive discretization in the second. This book introduces an integrative approach to modeling neurons and neuronal circuits that retains the integrity of the biological units at all hierarchical levels.
With contributions from more than 40 renowned experts, Modeling in the Neurosciences, Second Edition is essential for those interested in constructing more structured and integrative models with greater biological insight. Focusing on new mathematical and computer models, techniques, and methods, this book represents a cohesive and comprehensive treatment of various aspects of the neurosciences from the molecular to the network level. Many state-of-the-art examples illustrate how mathematical and computer modeling can contribute to the understanding of mechanisms and systems in the neurosciences. Each chapter also includes suggestions of possible refinements for future modeling in this rapidly changing and expanding field.
This book will benefit and inspire the advanced modeler, and will give the beginner sufficient confidence to model a wide selection of neuronal systems at the molecular, cellular, and network levels.
Preface. Contributors. Foreword. Introduction to Modeling in the Neurosciences. Patterns of Genetic Interactions: Analysis of mRNA Levels from cDNA Microarrays. Calcium Signaling in Dendritic Spines. Physiological and Statistical Approaches to Modeling of Synaptic Responses. Natural Variability in the Geometry of Dendritic Branching Patterns. Multicylinder Models for Synaptic and Gap-Junctional Integration. Voltage Transients in Branching Multipolar Neurons with Tapering Dendrites and Sodium Channels. Analytical Solutions of the Frankenhaeuser-Huxley Equations Modified for Dendritic Backpropagation of a Single Sodium Spike. Inverse Problems for Some Cable Models of Dendrites. Equivalent Cables-Analysis and Construction. The Representation of Three-Dimensional Dendritic Structure by a One-Dimensional Model-The Conventional Cable Equation as the First Member of a Hierarchy of Equations. Simulation Analyses of Retinal Cell Responses. Modeling Intracellular Calcium: Diffusion, Dynamics, and Domains. Ephaptic Interactions Between Neurons. Cortical Pyramidal Cells. Semi-Quantitative Theory of Bistable Dendrites with Potential-Dependent Facilitation of Inward Current. Bifurcation Analysis of the Hodgkin-Huxley Equations. Highly Efficient Propagation of Random Impulse Trains Across Unmyelinated Axonal Branch Points: Modifications by Periaxonal K+ and Sodium Channel Kinetics. Dendritic Integration in a Two-Neuron Recurrent Excitatory Network Model. Spike-Train Analysis for Neural Systems. The Poetics of Tremor. Principles and Methods in the Analysis of Brain Networks. The Darwin Brain-Based Automata: Synthetic Neural Models and Real-World Devices. Toward Neural Robotics: From Synthetic Models to Neuromimetic Implementations. Bibliography. Index.