Figure 2.

Example simulation of the path integration network for a 14-lap trajectory on a circular track. The input trajectory is actual position-tracking data from a previously published set of cue-rotation experiments (Lee et al., 2004b). Tracking data has been smoothed and interpolated (see Section 4) to be used as simulation input. (A) Position is converted to a track-angle relative to the track’s center (lap crossings, dashed lines) and shown for the duration of the simulation (t = 325 s). (B) The instantaneous velocity vector of the trajectory (x and y components: v_x, top; v_y, bottom) directly modulates the VMO phase vector (Eq. 1). Lap-to-lap (blue/green alternation) variation shows periodicity but also significant differences in traversal. (C) Interference patterns for two example place units with place fields. Inset: single lap with envelope (black lines) and threshold (dashed lines). (D) Firing-rates across time are mapped to position coordinates (left) to reveal distinct place fields. Linearized spatial responses (see Section 4) for each of the 14 completed laps (right) demonstrate the relative stability of VMO-based place fields. Black arrows indicate the running direction of the animal around the track.