The role of oscillations in grid cells' toroidal topology

TL;DR

This study demonstrates that neural oscillations are crucial for the toroidal topology of grid cell activity, with oscillatory modulation influencing the robustness of this topological structure in the brain.

Contribution

It reveals that oscillations at theta and eta bands are essential for the emergence and stability of the toroidal topology in grid cell activity, supported by both data analysis and a simple model.

Findings

Oscillations at theta and eta bands influence grid cell topology.

Jittering spike times by 100-500 ms disrupts toroidal topology.

Oscillatory modulation enhances the similarity between model and real data.

Abstract

Persistent homology applied to the activity of grid cells in the Medial Entorhinal Cortex suggests that this activity lies on a toroidal manifold. By analyzing real data and a simple model, we show that neural oscillations play a key role in the appearance of this toroidal topology. To quantitatively monitor how changes in spike trains influence the topology of the data, we first define a robust measure for the degree of toroidality of a dataset. Using this measure, we find that small perturbations ($\sim$ 100 ms) of spike times have little influence on both the toroidality and the hexagonality of the ratemaps. Jittering spikes by $\sim$ 100-500 ms, however, destroys the toroidal topology, while still having little impact on grid scores. These critical jittering time scales fall in the range of the periods of oscillations between the theta and eta bands. We thus hypothesized that these oscillatory modulations of neuronal spiking play a key role in the appearance and robustness of toroidal topology and the hexagonal spatial selectivity is not sufficient. We confirmed this hypothesis using a simple model for the activity of grid cells, consisting of an ensemble of independent rate-modulated Poisson processes. When these rates were modulated by oscillations, the network behaved similarly to the real data in exhibiting toroidal topology, even when the position of the fields were perturbed. In the absence of oscillations, this similarity was substantially lower. Furthermore, we find that the experimentally recorded spike trains indeed exhibit temporal modulations at the eta and theta bands, and that the ratio of the power in the eta band to that of the theta band, $A_{\eta}/A_{\theta}$, correlates with the critical jittering time at which the toroidal topology disappears.