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

Mallory Carlu (1) , Omar Chehab (2) , Leonardo Dalla Porta (3) , Damien Depannemaecker (1) , Charlotte Héricé (4) , Maciej Jedynak (5) , Elif Köksal Ersöz (6, 7) , Paolo Muratore (8) , Selma Souihel (9) , Cristiano Capone (10, 1) , Yan Zerlaut (1) , Alain Destexhe (1) , Matteo Di Volo (1)

1 NeuroPSI - Institut des Neurosciences Paris-Saclay
2 ENS Paris Saclay - Ecole Normale Supérieure Paris-Saclay
3 IDIBAPS - Institut d'Investigacions Biomèdiques August Pi i Sunyer
4 University of Strathclyde [Glasgow]
5 GIN - [GIN] Grenoble Institut des Neurosciences
6 LTSI - Laboratoire Traitement du Signal et de l'Image
7 MATHNEURO - Mathématiques pour les Neurosciences
8 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
9 BIOVISION - Biologically plausible Integrative mOdels of the Visual system : towards synergIstic Solutions for visually-Impaired people and artificial visiON
10 INFN - Istituto Nazionale di Fisica Nucleare [Sezione di Roma 1]

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 populations 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.

Mots clés: asynchronous irregular; cortical dynamics; mean field; population models; spiking networks

Domaines: Neurobiologie; Bio-informatique [q-bio.QM]; Physique mathématique [math-ph]

Mallory Carlu, Omar Chehab, Leonardo Dalla Porta, Damien Depannemaecker, Charlotte Héricé, et al.. A mean-field approach to the dynamics of networks of complex neurons, from nonlinear Integrate-and-Fire to Hodgkin-Huxley models. Journal of Neurophysiology, 2020, 123 (3), pp.1042-1051. ⟨10.1152/jn.00399.2019⟩. ⟨hal-02414751⟩