State Space Models for Classifying Grid Cell Spatial Sequences

To navigate accurately, the brain requires an internal map of the external spatial world. The entorhinal cortex (EC) is thought to play an important role in the generation of this internal map, as it contains grid cells that fire periodically in space. However, grid cells are also active at rest, replaying grid cell spike sequences that reflect spatial sequences observed during mobility [1,2,3]. Replay events are thought to play an important role in memory and planning. Little is known, however, on the spatial structure of entorhinal replay, limiting our understanding of how grid cells participate in these higher-order cognitive functions.

A challenge of studying replay is that the animal’s imagined position is not experimentally accessible, and thus relies on statistical methods for inferring the imagined position sequence. The discovery of spatial sequences is therefore sensitive to assumptions about their expected structure–previous methods in EC have assumed linear trajectories or constant velocities [1,2,3]. Recent probabilistic state space models (SSMs) provide a more flexible way of parameterizing and comparing spatial sequences [4,5]. A major challenge lies in applying these models to grid cells. Compared to place cells, where these models have been applied, grid cells have multiple spatial fields, rather than single spatial fields, and are often multimodal (encoding position, speed etc.), not unimodal [6]. Here, we investigate the ability of SSMs to correctly infer the underlying spatial dynamics of grid cell activity. We find that we can classify spatial sequences using grid cell activity over a range of realistic tuning parameters. We quantify the sensitivity of inferences to noisy and multimodal coding, and the ability of models to decode real-life trajectories. Our study provides groundwork for testing hypotheses on entorhinal replay, allowing for better understanding the role of grid cells in higher-order cognition.

[1] Ólafsdóttir, H., et al. Nat Neuroscience (2016). [2] Ólafsdóttir, H., et al. Neuron (2017). [3] O’Neill, J., et al. Science (2017). [4] Krause, E. and Drugowitsch, J. Neuron (2022). [5] Denovellis, E., et al. Elife (2021). [6] Hardcastle, K., et al. Neuron (2017).