Dynamics of Neurons connected by Inhibitory Synapses and Electrical Coupling

Networks of inhibitory neurons are thought to play crucial roles in generating and coordinating electrical activity in the brain. For this reason, there has been much interest in trying to understand the mechanisms underlying the behavior that these networks display. Recent findings show that cells in many inhibitory networks are not only connected by pulsatile inhibitory connections but are also connected by electrical (diffusive) coupling. However, it is unclear how these two modes of intercellular communication and the intrinsic properties of cells interact to determine the dynamics of the networks.

To obtain insight into this issue, we construct a theoretical framework for the phase-locking dynamics in pairs of intrinsically oscillating neurons connected by weak electrical and inhibitory coupling. An integrate-and-fire model, consisting of a set of simple ordinary differential equations, is used to describe the activity of coupled cells. We employ the method of averaging (Kuramoto 1984) to reduce the integrate-and-fire model to a single differential equation describing the evolution of the phase difference between the cells. We then study the bifurcation structure of the reduced system, examining how the coupling kinetics and intrinsic properties of the cells influence the phase-locking in the coupled cells. Finally, theoretical results are compared with preliminary experimental findings from the laboratory of Dr. Barry Connors (Brown University).