Multi-Stability and Pattern-Selection in Oscillatory Networks with Fast Inhibition and Electrical Synapses

Tiaza Bem,Pascal Branchereau,John Hallam,Pierre Meyrand,Olaf Sporns

doi:10.1371/journal.pone.0003830

Abstract

A model or hybrid network consisting of oscillatory cells interconnected by inhibitory and electrical synapses may express different stable activity patterns without any change of network topology or parameters, and switching between the patterns can be induced by specific transient signals. However, little is known of properties of such signals. In the present study, we employ numerical simulations of neural networks of different size composed of relaxation oscillators, to investigate switching between in-phase (IP) and anti-phase (AP) activity patterns. We show that the time windows of susceptibility to switching between the patterns are similar in 2-, 4- and 6-cell fully-connected networks. Moreover, in a network (N = 4, 6) expressing a given AP pattern, a stimulus with a given profile consisting of depolarizing and hyperpolarizing signals sent to different subpopulations of cells can evoke switching to another AP pattern. Interestingly, the resulting pattern encodes the profile of the switching stimulus. These results can be extended to different network architectures. Indeed, relaxation oscillators are not only models of cellular pacemakers, bursting or spiking, but are also analogous to firing-rate models of neural activity. We show that rules of switching similar to those found for relaxation oscillators apply to oscillating circuits of excitatory cells interconnected by electrical synapses and cross-inhibition. Our results suggest that incoming information, arriving in a proper time window, may be stored in an oscillatory network in the form of a specific spatio-temporal activity pattern which is expressed until new pertinent information arrives.

Highlights

Multi-stability of a dynamic system consists of the ability to express, for a given set of parameters, multiple stable states and to switch between these states in response to some external transient input
We demonstrate that a firing-rate model network consisting of two oscillatory populations of excitatory cells interconnected by cross-inhibition and electrical coupling expresses switching between patterns according to rules similar to those found for two relaxation oscillators
Bi-stability of a 2-cell inhibitory network is a robust phenomenon. It has been demonstrated in modeling studies either for the slow inhibitory synapses alone [13] or for fast inhibition combined with electrical coupling [14,15,16] and, can be found in hybrid networks in which biological cells from snail ganglion [15] or cortical slices [17] are interconnected by a dynamic clamp system

Summary

Introduction

Multi-stability of a dynamic system consists of the ability to express, for a given set of parameters, multiple stable states and to switch between these states in response to some external transient input. Studies in computational processes in nonoscillatory networks gave rise to the concept of a binary memory switch, where transient inputs can turn a plateau like activity on or off in a sub-set of cells within the network [6,7,8,9,10,11,12]. Bi-stability of in-phase (IP) and antiphase (AP) solutions was first found in a half-center network model consisting of two inhibitory neurons with slow synaptic kinetics [13]. Such bi-stability does not necessarily require slow synaptic transmission and, it was found when fast synaptic inhibition was combined with electrical coupling in similar network models [14,15,16]. Bi-stable behavior of a 2-cell inhibitory network has been confirmed in dynamic clamp experiments on hybrid networks consisting of biological neurons of different intrinsic properties [15,17]

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