The combined effects of inhibitory and electrical synapses in synchrony.

Recent experimental results have shown that GABAergic interneurons in the central nervous system are frequently connected via electrical synapses. Hence, depending on the area or the subpopulation, interneurons interact via inhibitory synapses or electrical synapses alone or via both types of interactions. The theoretical work presented here addresses the significance of these different modes of interactions for the interneuron networks dynamics. We consider the simplest system in which this issue can be investigated in models or in experiments: a pair of neurons, interacting via electrical synapses, inhibitory synapses, or both, and activated by the injection of a noisy external current. Assuming that the couplings and the noise are weak, we derive an analytical expression relating the cross-correlation (CC) of the activity of the two neurons to the phase response function of the neurons. When electrical and inhibitory interactions are not too strong, they combine their effect in a linear manner. In this regime, the effect of electrical and inhibitory interactions when combined can be deduced knowing the effects of each of the interactions separately. As a consequence, depending on intrinsic neuronal properties, electrical and inhibitory synapses may cooperate, both promoting synchrony, or may compete, with one promoting synchrony while the other impedes it. In contrast, for sufficiently strong couplings, the two types of synapses combine in a nonlinear fashion. Remarkably, we find that in this regime, combining electrical synapses with inhibition amplifies synchrony, whereas electrical synapses alone would desynchronize the activity of the neurons. We apply our theory to predict how the shape of the CC of two neurons changes as a function of ionic channel conductances, focusing on the effect of persistent sodium conductance, of the firing rate of the neurons and the nature and the strength of their interactions. These predictions may be tested using dynamic clamp techniques