Synchronization in Networks of Excitatory and Inhibitory Neurons with Sparse, Random Connectivity

Abstract

In model networks of E-cells and I-cells (excitatory and inhibitory neurons, respectively), synchronous rhythmic spiking often comes about from the interplay between the two cell groups: the E-cells synchronize the I-cells and vice versa. Under ideal conditions-homogeneity in relevant network parameters and all-to-all connectivity, for instance-this mechanism can yield perfect synchronization. We find that approximate, imperfect synchronization is possible even with very sparse, random connectivity. The crucial quantity is the expected number of inputs per cell. As long as it is large enough (more precisely, as long as the variance of the total number of synaptic inputs per cell is small enough), tight synchronization is possible. The desynchronizing effect of random connectivity can be reduced by strengthening the E --> I synapses. More surprising, it cannot be reduced by strengthening the I --> E synapses. However, the decay time constant of inhibition plays an important role. Faster decay yields tighter synchrony. In particular, in models in which the inhibitory synapses are assumed to be instantaneous, the effects of sparse, random connectivity cannot be seen.

Modeling Gaba Alterations in Schizophrenia: A Link Between Impaired Inhibition and Altered Gamma and Beta Range Auditory Entrainment

“…There is some debate about the biophysically relevant decay times for GABA A in cortex with both fairly short (3.71 ms) and extremely long (33.2 ms) decay times reported (Galaretta and Hestrin 1997;Hefti and Smith 2002) although there is agreement that GABA A decay is generally longer than AMPA type excitatory currents. We choose 8 ms as the mean decay time both because it is an intermediate value in the range of reported values and because decay times in the 6-to 10-ms range are traditionally used in the modeling literature (Börgers et al 2005;Börgers and Kopell 2003;Cunningham et al 2004;Whittington et al 1995). We believe that what is of primary importance for the dynamic mechanisms presented here is that inhibitory decay be longer than excitatory decay in the control for which there is some experimental agreement.…”

The Dynamics of a Periodically Forced Cortical Microcircuit, With an Application to Schizophrenia

“…Such attracting trajectories have been studied previously in systems of ODEs and are referred to as rivers [9,10]. A similar river has been previously described specifically in the context of the "theta" model [5]. In the system considered here, the river exists because the time scale for the inhibitory variable g I is significantly slower than that for the g E or θ variables.…”

“…There is some debate about the biophysically relevant decay times for GABA A in cortex, with both fairly short (3.71 ms) and extremely long (33.2 ms) decay times reported [15,19], though there is agreement that GABA A decay is generally longer than AMPA-type excitatory currents. We choose 8 ms decay both because it is an intermediate value in the range of reported values and because decay times in the 6 to 10 ms range are traditionally used in the modeling literature [4,5,8,29]. We believe that what is of primary importance for the dynamic mechanisms presented here is that inhibitory decay be longer than excitatory decay in the control, for which there is experimental agreement.…”

“…As in previous computational studies of gamma/betarange behavior in reduced cortical networks [4,5], we implement our cortical microcircuit using the "theta" model, in which a spiking cell is represented by a point traveling around a circle with varying speed. Time is considered on the scale of milliseconds, as this is the relevant timescale for consideration of neuronal spiking.…”

“…Progress has been made in understanding the role of inhibition in maintaining synchrony [1,25], and in understanding the mechanisms and functional importance of gamma rhythms in networks that contain both excitation and inhibition [3,5,6,7,11,23]. Though this work is motivated by a specific neuroscience application, the associated method has far wider relevance.…”