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Personne# Brice Bathellier

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Modèles du neurone biologique

vignette|390x390px|Fig. 1. Dendrites, soma et axone myélinisé, avec un flux de signal des entrées aux dendrites aux sorties aux bornes des axones. Le signal est une courte impulsion électrique appelée

Brice Bathellier, Wulfram Gerstner, Richard Naud

A complete single-neuron model must correctly reproduce the firing of spikes and bursts. We present a study of a simplified model of deep pyramidal cells of the cortex with active dendrites. We hypothesized that we can model the soma and its apical dendrite with only two compartments, without significant loss in the accuracy of spike-timing predictions. The model is based on experimentally measurable impulse-response functions, which transfer the effect of current injected in one compartment to current reaching the other. Each compartment was modeled with a pair of non-linear differential equations and a small number of parameters that approximate the Hodgkin-and-Huxley equations. The predictive power of this model was tested on electrophysiological experiments where noisy current was injected in both the soma and the apical dendrite simultaneously. We conclude that a simple two-compartment model can predict spike times of pyramidal cells stimulated in the soma and dendrites simultaneously. Our results support that regenerating activity in the apical dendritic is required to properly account for the dynamics of layer 5 pyramidal cells under in-vivo-like conditions.

Brice Bathellier, Wulfram Gerstner, Richard Naud

A complete model for single neurons must reproduce correctly the firing of spikes and bursts. Yet it must remain simple enough to be tractable in large-scale simulations. We present a study of a simplified model of Layer V pyramidal cells of the cortex with active dendrites. We hypothesized that we can model the soma and its apical trunk with only two compartments without significant loss in the accuracy of spike-timing predictions. The model is based on experimentally measurable impulse-response functions [1], which transfer the effect current injected in one compartment to the other. Each compartment was modeled with a pair of non-linear differential equations [2] with a small number of parameters that approximate the Hodgkin-and-Huxley equations. The predictive power of this model was tested on electrophysiological experiments where noisy current was injected in both the soma and the apical dendrite simultaneously

2009Fast oscillations and in particular gamma-band oscillation (20-80 Hz) are commonly observed during brain function and are at the center of several neural processing theories. In many cases, mathematical analysis of fast oscillations in neural networks has been focused on the transition between irregular and oscillatory firing viewed as an instability of the asynchronous activity. But in fact, brain slice experiments as well as detailed simulations of biological neural networks have produced a large corpus of results concerning the properties of fully developed oscillations that are far from this transition point. We propose here a mathematical approach to deal with nonlinear oscillations in a network of heterogeneous or noisy integrate-and-fire neurons connected by strong inhibition. This approach involves limited mathematical complexity and gives a good sense of the oscillation mechanism, making it an interesting tool to understand fast rhythmic activity in simulated or biological neural networks. A surprising result of our approach is that under some conditions, a change of the strength of inhibition only weakly influences the period of the oscillation. This is in contrast to standard theoretical and experimental models of interneuron network gamma oscillations (ING), where frequency tightly depends on inhibition strength, but it is similar to observations made in some in vitro preparations in the hippocampus and the olfactory bulb and in some detailed network models. This result is explained by the phenomenon of suppression that is known to occur in strongly coupled oscillating inhibitory networks but had not yet been related to the behavior of oscillation frequency.