An efficient coding theory for a dynamic trajectory predicts non-uniform allocation of entorhinal grid cells to modules

Grid cells in the entorhinal cortex encode the position of an animal in its environment with spatially periodic tuning curves with different periodicities. Recent experiments established that these cells are functionally organized in discrete modules with uniform grid spacing. Here we develop a theory for efficient coding of position, which takes into account the temporal statistics of the animal’s motion. The theory predicts a sharp decrease of module population sizes with grid spacing, in agreement with the trend seen in the experimental data. We identify a simple scheme for readout of the grid cell code by neural circuitry, that can match in accuracy the optimal Bayesian decoder. This readout scheme requires persistence over different timescales, depending on the grid cell module. Thus, we propose that the brain may employ an efficient representation of position which takes advantage of the spatiotemporal statistics of the encoded variable, in similarity to the principles that govern early sensory processing.Author summary: Grid cells encode a mammal’s estimate of position by firing in multiple locations. These locations are arranged on the vertices of a triangular lattice. Lattices vary in spacing and therefore represent position over different spatial scales. We suggest that grid cells encode position while taking into account the spatiotemporal statistics of an animal’s movement trajectory. Based on this hypothesis, we develop a theory for efficient encoding of trajectories in the brain. One of the main predictions of our theory is that different numbers of grid cells should be allocated to each spatial scale.