Gaussian Process Inference Reveals Non-separability of Position and Velocity Tuning in Grid Cells

Grid cells in medial entorhinal cortex (MEC) support spatial navigation by responding to multiple variables, including position, speed, and head direction. While tuning curves for each of these variables has been examined individually at the level of single-cells, less is known about the conjunctive coding of grid cells for these properties. To investigate this, we analyzed neural recordings of freely foraging rats and constructed four-dimensional (4D) tuning curves across 2D position and 2D velocity. In order to combat the sparse sampling of such a large behavioral space, we applied Gaussian Process (GP) methods to estimate firing rate at un-sampled points. Comparison GP model-derived tuning curves to those predicted by a fully separable model revealed that some cells exhibited significant non-separability of position and velocity tuning, and suggested a data coverage threshold necessary to observe this non-separability. In summary, our use of GPs allowed us to distinguish interactions in position-velocity tuning across a 4D behavioral space that have not been apparent in 2D analyses.