Effects of inhibitory neurons on the quorum percolation model and dynamical extension with the Brette-Gerstner model

Tanguy Fardet (1, 2) , Samuel Bottani (1) , Stéphane Métens (1) , Pascal Monceau (1)

1 MSC - Matière et Systèmes Complexes
2 UPD7 - Université Paris Diderot - Paris 7

The Quorum Percolation model (QP) has been designed in the context of neuro-biology to describe the initiation of activity bursts occurring in neuronal cultures from the point of view of statistical physics rather than from a dynamical synchronization approach. This paper aims at investigating an extension of the original QP model by taking into account the presence of inhibitory neurons in the cultures (IQP model). The first part of this paper is focused on an equivalence between the presence of inhibitory neurons and a reduction of the network connectivity. By relying on a simple topological argument, we show that the mean activation behavior of networks containing a fraction η of inhibitory neu-rons can be mapped onto purely excitatory networks with an appropriately modified wiring, provided that η remains in the range usually observed in neu-ronal cultures, namely η 20%. As a striking result, we show that such a mapping enables to predict the evolution of the critical point of the IQP model with the fraction of inhibitory neurons. In a second part, we bridge the gap between the description of bursts in the framework of percolation and the temporal description of neural networks activity by showing how dynamical simulations of bursts with an adaptive exponential integrate-and-fire model lead to a mean description of bursts activation which is captured by Quorum Percolation.

Mots clés: Quorum percolation; Inhibitory neurons; Neuronal cultures; Dynamical model

Domaines: Adaptation et Systèmes auto-organisés [nlin.AO]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]; Biophysique [physics.bio-ph]; Neurosciences

Tanguy Fardet, Samuel Bottani, Stéphane Métens, Pascal Monceau. Effects of inhibitory neurons on the quorum percolation model and dynamical extension with the Brette-Gerstner model. Physica A: Statistical Mechanics and its Applications, 2018, ⟨10.1016/j.physa.2018.02.002⟩. ⟨hal-01713016⟩