Synchrony in Excitatory Neural Networks

Abstract

Synchronization properties of fully connected networks of identical oscillatory neurons are studied, assuming purely excitatory interactions. We analyze their dependence on the time course of the synaptic interaction and on the response of the neurons to small depolarizations. Two types of responses are distinguished. In the first type, neurons always respond to small depolarization by advancing the next spike. In the second type, an excitatory postsynaptic potential (EPSP) received after the refractory period delays the firing of the next spike, while an EPSP received at a later time advances the firing. For these two types of responses we derive general conditions under which excitation destabilizes in-phase synchrony. We show that excitation is generally desynchronizing for neurons with a response of type I but can be synchronizing for responses of type II when the synaptic interactions are fast. These results are illustrated on three models of neurons: the Lapicque integrate-and-fire model, the model of Connor et al., and the Hodgkin-Huxley model. The latter exhibits a type II response, at variance with the first two models, that have type I responses. We then examine the consequences of these results for large networks, focusing on the states of partial coherence that emerge. Finally, we study the Lapicque model and the model of Connor et al. at large coupling and show that excitation can be desynchronizing even beyond the weak coupling regime.

A Model of the Effects of Applied Electric Fields on Neuronal Synchronization

“…As we have seen in our simplified phase model (Fig. 8) previously, identical neurons (Δg c = 0%) with excitatory coupling typically phase lock in the anti-phase state (Hansel, 1995). For E = 200 mV/cm and g c (1,2) = 2.1 mS/ cm 2 , Δω is zero and Δf is given in Fig.…”

“…6 The coupling functions f 1,2 (E , φ j − φ i ) in the reduced phase model can be rigorously calculated using the averaging technique described in Refs. (Ermentrout and Kopell, 1984;Hansel et al, 1995;Ermentrout, 1996). In brief, suppose a pair of neurons is described by the following dynamical equations:…”

Phase response properties of half-center oscillators

“…PRCs measure the phase shift of an oscillator in response to a brief perturbation as a function of the timing of the input. PRCs in conjunction with coupled oscillators theory have been widely used in neuroscience to understand how changes in a neuron's intrinsic properties affect its frequency (Schwemmer and Lewis 2011;Ly and Ermentrout 2011), how neuronal oscillators phase-lock to external input (Brumberg and Gutkin 2007;Gouwens et al 2010), and how networks of neurons synchronize (e.g., Ermentrout 1984;Hansel 1995;Mancilla 2007). In almost all cases, the oscillatory units have been taken to be the individual neurons.…”

The effects of cholinergic neuromodulation on neuronal phase-response curves of modeled cortical neurons

“…(Although the PRC can be constructed for both excitatory and inhibitory perturbations, the standard convention is to report results for depolarizing inputs.) In the case of a saddle-node bifurcation, the PRC is purely positive, or type I (except possibly for an arbitrarily small region near the origin Hansel and Mato 1995), with a phase advance in response to perturbations at all phases (Ermentrout 1996). In the case of a Hopf-Andronov bifurcation, the PRC is biphasic, or type II, with a phase delay in response to perturbations early in the period and a phase advance in response to perturbations late in the period (Hansel and Mato 1995;Ermentrout 1996;Moehlis et al 2006).…”