Speed modulations in grid cell information geometry

Grid cells, known for their hexagonal spatial firing patterns, are widely regarded as essential to the brain's internal representation of the external space. Maintaining an accurate internal spatial representation is challenging when an animal is running at high speeds, as its self-location constantly changes. Previous studies of speed modulation of grid cells focused on individual or pairs of grid cells, yet neurons represent information via collective population activity. Population noise covariance can have significant impact on information coding that is impossible to infer from individual neuron analysis. To address this issue, we developed a novel Gaussian Process with Kernel Regression (GKR) method that allows study the simultaneously recorded neural population representation from an information geometry framework. We applied GKR to grid cell population activity, and found that running speed increases both grid cell activity toroidal-like manifold size and noise strength. Importantly, the effect of manifold dilation outpaces the effect of noise increasement, as indicated by the overall higher Fisher information at increasing speeds. This result is further supported by improved spatial information decoding accuracy at high speeds. Finally, we showed that the existence of noise covariance is information detrimental because it causes more noise projected onto the manifold surface. In total, our results indicate that grid cell spatial coding improves with increasing running speed. GKR provides a useful tool to understand neural population coding from an intuitive information geometric perspective.