A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin-Huxley models

M. Carlu, O. Chehab, L. Dalla Porta, D. Depannemaecker, C. Héricé, M. Jedynak, E. Köksal Ersöz, P. Muratore, S. Souihel, C. Capone, Y. Zerlaut, A. Destexhe, M. di Volo

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Abstract

We present a mean-field formalism able to predict the collective dynamics of large networks of conductance-based interacting spiking neurons. We apply this formalism to several neuronal models, from the simplest Adaptive Exponential Integrate-and-Fire model to the more complex Hodgkin-Huxley and Morris-Lecar models. We show that the resulting mean-field models are capable of predicting the correct spontaneous activity of both excitatory and inhibitory neurons in asynchronous irregular regimes, typical of cortical dynamics. Moreover, it is possible to quantitatively predict the population response to external stimuli in the form of external spike trains. This mean-field formalism therefore provides a paradigm to bridge the scale between population dynamics and the microscopic complexity of the individual cells physiology.NEW & NOTEWORTHY Population models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin-Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.

Original languageEnglish
Pages (from-to)1042-1051
Number of pages10
JournalJournal of Neurophysiology
Volume123
Issue number3
Early online date18 Dec 2019
DOIs
Publication statusPublished - 1 Mar 2020

Keywords

  • asynchronous irregular
  • cortical dynamics
  • mean field
  • population models
  • spiking networks

Cite this

Carlu, M., Chehab, O., Dalla Porta, L., Depannemaecker, D., Héricé, C., Jedynak, M., Köksal Ersöz, E., Muratore, P., Souihel, S., Capone, C., Zerlaut, Y., Destexhe, A., & di Volo, M. (2020). A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin-Huxley models. Journal of Neurophysiology, 123(3), 1042-1051. https://doi.org/10.1152/jn.00399.2019