A systems model of alternating theta sweeps via firing rate adaptation

Place and grid cells provide a neural system for self-location and tend to fire in sequences within each cycle of the hippocampal theta rhythm when rodents run on a linear track. These sequences correspond to the decoded location of the animal sweeping forward from its current location ("theta sweeps"). However, recent findings in open-field environments show alternating left-right theta sweeps and propose a circuit for their generation. Here, we present a computational model of this circuit, comprising theta-modulated head-direction cells, conjunctive grid × direction cells, and pure grid cells, based on continuous attractor dynamics, firing rate adaptation, and modulation by the medial-septal theta rhythm. Due to firing rate adaptation, the head-direction ring attractor exhibits left-right sweeps coding for internal direction, providing an input to the grid cell attractor network shifted along the internal direction, via an intermediate layer of conjunctive grid × direction cells, producing left-right sweeps of position by grid cells. Our model explains the empirical findings, including the alignment of internal position and direction sweeps and the dependence of sweep length on grid spacing. It makes predictions for theta-modulated head-direction cells, including relationships between theta phase precession during turning, theta skipping, anticipatory firing, and directional tuning width, several of which we verify in experimental data from anteroventral thalamus. The model also predicts relationships between position and direction sweeps, running speed, and dorsal-ventral location within the entorhinal cortex. Overall, a simple intrinsic mechanism explains the complex theta dynamics of an internal direction signal within the hippocampal formation, with testable predictions.