Figure 2. Topological representations in the spike order of theta sequences.

A) The MEC-hippocampus loop model for updates to network activity in each region. Information about velocity and salient events are proposed to influence the MEC CAN, which reciprocally interacts with the hippocampus -- though this does not preclude a direct effect of these inputs on the hippocampus as well.

B) Theta sequences in hippocampus and hypothesized theta sequences in MEC. Left: A trajectory through an open arena (black arrow) passes through a sequence of place cells (top) and grid cells from a single module (bottom). Right: Place cells and grid cells both exhibit ordered spiking at the theta timescale that progresses in concert with movement through the maze. Vertical dotted lines mark theta cycle boundaries. Theta disinhibition is out of phase between hippocampus and MEC, allowing communication to alternate across regions.

C-E) MEC grid cells and hippocampal place cells fire as a rodent moves along a linear track (C), runs continuously on a treadmill (D), or progresses through a sequence of discrete sensory events involving odors and tones ¹⁰⁹ (E) (grid cell firing patterns in E are hypothetical). As the animal progresses in position or time, neurons exhibit theta phase precession, shown for hippocampal cells as the transition of spikes from later to earlier theta phases. In each of these experiences, neuronal spikes are ordered within a single theta cycle (red dashed arrow) according to the animal’s past, present, and future. This spike ordering generates a topological graph of the experience, with each node of the topology corresponding to an ordered instance in the experience (bottom panels). When a linear track is stretched ¹⁹³ (C) or when the time of a treadmill run is increased ^87,195 (D), both grid cells and place cells demonstrate the capacity to rescale to span the entire experience. Despite this field stretching, spike ordering is preserved within a theta cycle (bottom panels), preserving the topological representation from the original to the stretched experience by maintaining temporal relationships between neurons. Future work remains to determine the scalability of topological representations for discrete sequences of events. Adapted from ^109,195.