Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model.

Christoforos A Papasavvas,Andrew J Trevelyan,Marcus Kaiser,Yujiang Wang

doi:10.1103/physreve.92.032723

Christoforos A Papasavvas, Andrew J Trevelyan + Show 2 more

Open Access

https://doi.org/10.1103/physreve.92.032723

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Abstract

Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics.

Highlights

Neurons can be understood as information processing units that transform synaptic input into a spike train output
Dendrite-targeting interneurons provide the subtractive inhibition, whereas divisive inhibition is provided by somatargeting interneurons [2,4]
The role of divisive inhibition in the transition from order to chaos through a period-doubling cascade is examined

Summary

Introduction

Neurons can be understood as information processing units that transform synaptic input into a spike train output. This transformation is often described by an input-output function, which can be experimentally measured. Recent experiments have demonstrated that different inhibitory mechanisms can modulate this function [1,2]. These inhibitory mechanisms can be considered to be either subtractive or divisive based on the modulation that is applied on the postsynaptic neurons. Recent studies demonstrated that the two types of modulations are applied on the cortical pyramidal neurons by two distinct inhibitory populations. The connectivity patterns between these populations were revealed in recent anatomical study in neocortex, where it was shown that the dendrite-targeting interneurons inhibit the soma targeting but not the other way around [5]

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