Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses

Rodrigo Cofre 1, * Bruno Cessac 1
* Corresponding author
1 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : We investigate the effect of electric synapses (gap junctions) on collective neuronal dynamics and spike statistics in a conductance-based Integrate-and-Fire neural network, driven by a Brownian noise, where conductances depend upon spike history. We compute explicitly the time evolution operator and show that, given the spike-history of the network and the membrane potentials at a given time, the further dynamical evolution can be written in a closed form. We show that spike train statistics is described by a Gibbs distribution whose potential can be approximated with an explicit formula, when the noise is weak. This potential form encompasses existing models for spike trains statistics analysis such as maximum entropy models or Generalized Linear Models (GLM). We also discuss the different types of correlations: those induced by a shared stimulus and those induced by neurons interactions.
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Poster communications
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Rodrigo Cofre, Bruno Cessac. Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses. Twenty Second Annual Computational Neuroscience Meeting : CNS 2013, Jul 2013, Paris, France. 14 (Suppl 1), pp.P58, 2013. ⟨hal-00842297⟩

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