Uncovering 2-D toroidal representations in grid cell ensemble activity during 1-D behavior

Abstract Neuroscience is pushing toward studying the brain during naturalistic behaviors with open-ended tasks. Grid cells are a classic example, where free behavior was key to observing their characteristic spatial representations in two-dimensional environments. In contrast, it has been difficult to identify grid cells and study their computations in more restrictive experiments, such as head-fixed wheel running. Here, we challenge this view by showing that shifting the focus from single neurons to the population level changes the minimal experimental complexity required to study grid cell representations. Specifically, we combine the manifold approximation in UMAP with persistent homology to study the topology of the population activity. With these methods, we show that the population activity of grid cells covers a similar two-dimensional toroidal state space during wheel running as in open field foraging, with and without a virtual reality setup. Trajectories on the torus correspond to single trial runs in virtual reality and changes in experimental conditions are reflected in the internal representation, while the toroidal representation undergoes occasional shifts in its alignment to the environment. These findings show that our method can uncover latent topologies that go beyond the complexity of the task, allowing us to investigate internal dynamics in simple experimental settings in which the analysis of grid cells has so far remained elusive.