Journal ArticleDOI
Rate models for conductance-based cortical neuronal networks
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This work shows that conductance-based models of large cortical neuronal networks can be described by simplified rate models, provided that the network state does not possess a high degree of synchrony.Abstract:
Population rate models provide powerful tools for investigating the principles that underlie the cooperative function of large neuronal systems. However, biophysical interpretations of these models have been ambiguous. Hence, their applicability to real neuronal systems and their experimental validation have been severely limited. In this work, we show that conductance-based models of large cortical neuronal networks can be described by simplified rate models, provided that the network state does not possess a high degree of synchrony. We first derive a precise mapping between the parameters of the rate equations and those of the conductance-based network models for time-independent inputs. This mapping is based on the assumption that the effect of increasing the cell's input conductance on its f-I curve is mainly subtractive. This assumption is confirmed by a single compartment Hodgkin-Huxley type model with a transient potassium A-current. This approach is applied to the study of a network model of a hypercolumn in primary visual cortex. We also explore extensions of the rate model to the dynamic domain by studying the firing-rate response of our conductance-based neuron to time-dependent noisy inputs. We show that the dynamics of this response can be approximated by a time-dependent second-order differential equation. This phenomenological single-cell rate model is used to calculate the response of a conductance-based network to time-dependent inputs.read more
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References
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Journal ArticleDOI
A quantitative description of membrane current and its application to conduction and excitation in nerve
A. L. Hodgkin,A. F. Huxley +1 more
TL;DR: This article concludes a series of papers concerned with the flow of electric current through the surface membrane of a giant nerve fibre by putting them into mathematical form and showing that they will account for conduction and excitation in quantitative terms.
Book
Numerical Recipes in C: The Art of Scientific Computing
TL;DR: Numerical Recipes: The Art of Scientific Computing as discussed by the authors is a complete text and reference book on scientific computing with over 100 new routines (now well over 300 in all), plus upgraded versions of many of the original routines, with many new topics presented at the same accessible level.
Journal ArticleDOI
Numerical Recipes in C: The Art of Scientific Computing
Mary C. Seiler,Fritz A. Seiler +1 more
Book
Ionic channels of excitable membranes
TL;DR: The Ionic Channel of Excitable Membranes (ICOMB) as discussed by the authors is an extended version of ICOMB with new chapters on fast chemical synapses, modulation through G protein coupled receptors and second messenger systems, molecules cloning, site directed mutagenesis, and cell biology.
Journal ArticleDOI
Neurons with graded response have collective computational properties like those of two-state neurons.
TL;DR: A model for a large network of "neurons" with a graded response (or sigmoid input-output relation) is studied and collective properties in very close correspondence with the earlier stochastic model based on McCulloch - Pitts neurons are studied.
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