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Grid cells in the entorhinal cortex encode the position of an animal in itsenvironment using spatially periodic tuning curves of varying periodicity.Recent experiments established that these cells are functionally organized indiscrete modules with uniform grid spacing. Here we develop a theory forefficient coding of position, which takes into account the temporal statisticsof the animal's motion. The theory predicts a sharp decrease of modulepopulation sizes with grid spacing, in agreement with the trends seen in theexperimental data. We identify a simple scheme for readout of the grid cellcode by neural circuitry, that can match in accuracy the optimal Bayesiandecoder of the spikes. This readout scheme requires persistence over varyingtimescales, ranging from ~1ms to ~1s, depending on the grid cell module. Ourresults suggest that the brain employs an efficient representation of positionwhich takes advantage of the spatiotemporal statistics of the encoded variable,in similarity to the principles that govern early sensory coding.

An Efficient Coding Theory for a Dynamic Trajectory Predicts non-Uniform Allocation of Grid Cells to Modules in the Entorhinal Cortex