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Methods In Neuronal Modeling: From Ions To Netw...
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This work is the standard handbook of computational and numerical methods and techniques for modeling nervous systems at various levels of resolution, from individual channels to single neurons, from small groups of neurons to neural networks. The second edition is completely updated from the first edition (originally published in 1989), with 7 new chapters and 7 completely revised chapters. The book was published in summer of 1998. For more information (and to order the book) please contact The MIT Press . You can also order it directly (at a discount) via www.amazon.com . We here provide a list of further computational resources, tutorials for the various computer simulators, software packages and data referred to in the handbook.
Much research focuses on the question of how information is processed in nervous systems, from the level of individual ionic channels to large-scale neuronal networks, and from \"simple\" animals such as sea slugs and flies to cats and primates. New interdisciplinary methodologies combine a bottom-up experimental methodology with the more top-down-driven computational and modeling approach. This book serves as a handbook of computational methods and techniques for modeling the functional properties of single and groups of nerve cells. The contributors highlight several key trends: (1) the tightening link between analytical/numerical models and the associated experimental data, (2) the broadening of modeling methods, at both the subcellular level and the level of large neuronal networks that incorporate real biophysical properties of neurons as well as the statistical properties of spike trains, and (3) the organization of the data gained by physical emulation of the nervous system components through the use of very large scale circuit integration (VLSI) technology. The field of neuroscience has grown dramatically since the first edition of this book was published nine years ago. Half of the chapters of the second edition are completely new; the remaining ones have all been thoroughly revised. Many chapters provide an opportunity for interactive tutorials and simulation programs. They can be accessed via Christof Koch's Website.
Biological neuron models, also known as a spiking neuron models,[1] are mathematical descriptions of the properties of certain cells in the nervous system that generate sharp electrical potentials across their cell membrane, roughly one millisecond in duration, called action potentials or spikes (Fig. 2). Since spikes are transmitted along the axon and synapses from the sending neuron to many other neurons, spiking neurons are considered to be a major information processing unit of the nervous system. Spiking neuron models can be divided into different categories: the most detailed mathematical models are biophysical neuron models (also called Hodgkin-Huxley models) that describe the membrane voltage as a function of the input current and the activation of ion channels. Mathematically simpler are integrate-and-fire models that describe the membrane voltage as a function of the input current and predict the spike times without a description of the biophysical processes that shape the time course of an action potential. Even more abstract models only predict output spikes (but not membrane voltage) as a function of the stimulation where the stimulation can occur through sensory input or pharmacologically. This article provides a short overview of different spiking neuron models and links, whenever possible to experimental phenomena. It includes deterministic and probabilistic models.
Although it is not unusual in science and engineering to have several descriptive models for different abstraction/detail levels, the number of different, sometimes contradicting, biological neuron models is exceptionally high. This situation is partly the result of the many different experimental settings, and the difficulty to separate the intrinsic properties of a single neuron from measurements effects and interactions of many cells (network effects). To accelerate the convergence to a unified theory, we list several models in each category, and where applicable, also references to supporting experiments.
Ultimately, biological neuron models aim to explain the mechanisms underlying the operation of the nervous system. However several approaches can be distinguished from more realistic models (e.g., mechanistic models) to more pragmatic models (e.g., phenomenological models).[2] Modeling helps to analyze experimental data and address questions such as: How are the spikes of a neuron related to sensory stimulation or motor activity such as arm movements What is the neural code used by the nervous system Models are also important in the context of restoring lost brain functionality through neuroprosthetic devices.
A shortcoming of this model is that it describes neither adaptation nor leakage. If the model receives a below-threshold short current pulse at some time, it will retain that voltage boost forever - until another input later makes it fire. This characteristic is clearly not in line with observed neuronal behavior. The following extensions make the integrate-and-fire model more plausible from a biological point of view.
The models in this category are generalized integrate-and-fire models that include a certain level of stochasticity. Cortical neurons in experiments are found to respond reliably to time-dependent input, albeit with a small degree of variations between one trial and the next if the same stimulus is repeated.[31][32] Stochasticity in neurons has two important sources. First, even in a very controlled experiment where input current is injected directly into the soma, ion channels open and close stochastically[33] and this channel noise leads to a small amount of variability in the exact value of the membrane potential and the exact timing of output spikes. Second, for a neuron embedded in a cortical network, it is hard to control the exact input because most inputs come from unobserved neurons somewhere else in the brain.[22]
The time course of the filters η , κ , θ 1 {\\displaystyle \\eta ,\\kappa ,\\theta _{1}} that characterize the spike response model can be directly extracted from experimental data.[18] With optimized parameters the SRM describes the time course of the subthreshold membrane voltage for time-dependent input with a precision of 2mV and can predict the timing of most output spikes with a precision of 4ms.[17][18] The SRM is closely related to linear-nonlinear-Poisson cascade models (also called Generalized Linear Model).[43] The estimation of parameters of probabilistic neuron models such as the SRM using methods developed for Generalized Linear Models[48] is discussed in Chapter 10 of the textbook Neuronal Dynamics.[22]
The models in this category were derived following experiments involving natural stimulation such as light, sound, touch, or odor. In these experiments, the spike pattern resulting from each stimulus presentation varies from trial to trial, but the averaged response from several trials often converges to a clear pattern. Consequently, the models in this category generate a probabilistic relationship between the input stimulus to spike occurrences. Importantly, the recorded neurons are often located several processing steps after the sensory neurons, so that these models summarize the effects of the sequence of processing steps in a compact form
Spiking Neuron Models are used in a variety of applications that need encoding into or decoding from neuronal spike trains in the context of neuroprosthesis and brain-computer interfaces such as retinal prosthesis:[7][88][89][90] or artificial limb control and sensation.[91][92][93] Applications are not part of this article; for more information on this topic please refer to the main article.
Figure 4. Simulating weak PING rhythms using a model specification structure. (A) The conceptual object-based architecture of a biophysically-detailed network of excitatory (blue) and inhibitory (red) cells. (B) Mapping the object-based architecture onto a DynaSim specification structure that contains all the high-level information necessary to construct the complete system of equations for the full model using objects from a library of pre-existing ionic mechanisms.
Figure 5. Searching parameter space using the DynaSim toolbox. (A) MATLAB code using the DynaSim dsSimulate function with the vary option to specify a set of 9 simulations varying two parameters (Iapp in population E and tauD of the connection from I to E). (B) Raster plots produced by dsPlot with the plot_type option given an array of DynaSim data structures containing results for all 9 simulations. (C) Plots produced by dsPlotFR showing how mean firing rates for E and I populations change as a function of the two varied parameters.
This chapter gives a brief summary of techniques for modeling neural tissue as a complex biosystem at the cellular, synaptic, and network levels. A sampling of the most often studied neuronal models with some of their salient characteristics is presented, ranging from the abstract rate-coded cell through the integrate-and-fire point neuron to the multicompartment neuron with a full range of ionic conductances. An indication is given of how the choice of a particular model will be determined by the interplay of prior knowledge about the system in question, the hypotheses being tested, and purely practical computational constraints. While interest centers on the more mature art of modeling functional aspects of neuronal systems as anatomically static, but functionally plastic adult structures, in a concluding section we look to near-future developments that may in principle allow network models to reflect the influence of mechanical, metabolic, and extrasynaptic signaling properties of both neurons and glia as the nervous system develops, matures, and perhaps suffers from disease processes. These comments will serve as an introduction to techniques for modeling tumor growth and other abnormal aspects of nervous system function that are covered in later chapters of this book (Part III, 6). Through the use of complex-systems modeling techniques, bringing together information that often in the past has been studied in isolation within particular subdisciplines of neuro- and developmental biology, one can hope to gain new insight into the interplay of genetic programs and the multitude of environmental factors that together control neural systems development and function. 59ce067264
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