Double-ring network model of the head-direction system.

In the head-direction system, the orientation of an animal's head in space is encoded internally by persistent activities of a pool of cells whose firing rates are tuned to the animal's directional heading. To maintain an accurate representation of the heading information when the animal moves, the system integrates horizontal angular head-velocity signals from the vestibular nuclei and updates the representation of directional heading. The integration is a difficult process, given that head velocities can vary over a large range and the neural system is highly nonlinear. Previous models of integration have relied on biologically unrealistic mechanisms, such as instantaneous changes in synaptic strength, or very fast synaptic dynamics. In this paper, we propose a different integration model with two populations of neurons, which performs integration based on the differential input of the vestibular nuclei to these two populations. We mathematically analyze the dynamics of the model and demonstrate that with carefully tuned synaptic connections it can accurately integrate a large range of the vestibular input, with potentially slow synapses.