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Dynamics and spike trains statistics in conductance-based integrate-and-fire neural networks with chemical and electric synapses

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  • Cofré, Rodrigo
  • Cessac, Bruno

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 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.

Suggested Citation

  • Cofré, Rodrigo & Cessac, Bruno, 2013. "Dynamics and spike trains statistics in conductance-based integrate-and-fire neural networks with chemical and electric synapses," Chaos, Solitons & Fractals, Elsevier, vol. 50(C), pages 13-31.
    • Handle: RePEc:eee:chsofr:v:50:y:2013:i:c:p:13-31
    DOI: 10.1016/j.chaos.2012.12.006
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    References listed on IDEAS

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    1. Daniele Linaro & Marco Storace & Michele Giugliano, 2011. "Accurate and Fast Simulation of Channel Noise in Conductance-Based Model Neurons by Diffusion Approximation," PLOS Computational Biology, Public Library of Science, vol. 7(3), pages 1-17, March.
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    5. Yasser Roudi & Sheila Nirenberg & Peter E Latham, 2009. "Pairwise Maximum Entropy Models for Studying Large Biological Systems: When They Can Work and When They Can't," PLOS Computational Biology, Public Library of Science, vol. 5(5), pages 1-18, May.
    6. Ifije E. Ohiorhenuan & Ferenc Mechler & Keith P. Purpura & Anita M. Schmid & Qin Hu & Jonathan D. Victor, 2010. "Sparse coding and high-order correlations in fine-scale cortical networks," Nature, Nature, vol. 466(7306), pages 617-621, July.
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    Cited by:

    1. D’Onofrio, Giuseppe & Lansky, Petr & Tamborrino, Massimiliano, 2019. "Inhibition enhances the coherence in the Jacobi neuronal model," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 108-113.
    2. Ma, Xiaowen & Xu, Ying, 2022. "Taming the hybrid synapse under energy balance between neurons," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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