Quantitative modeling of the emergence of macroscopic grid-like representations

Grid cells are neurons in the entorhinal cortex that are thought to perform neural computations in support of spatial navigation. When subjects navigate through spatial environments, grid cells exhibit firing fields that are arranged in a triangular grid pattern. As direct recordings of grid cells from the human brain are only rarely possible, functional magnetic resonance imaging (fMRI) studies proposed and described an indirect measure of entorhinal grid-cell activity, which is quantified as a hexadirectional modulation of fMRI activity as a function of the subjects movement direction. However, it still remains unclear how the activity of a population of grid cells may exhibit hexadirectional modulation and thus provides the basis for the hexadirectional modulation of entorhinal cortex activity measured with fMRI. Here, we thus performed numerical simulations and analytical calculations to better understand how the aggregated activity of many grid cells may be hexadirectionally modulated. Our simulations implemented three different hypotheses proposing that the hexadirectional modulation occurs because grid cells show head-direction tuning aligned with the grid axes; are subjected to repetition suppression; or exhibit a bias towards a particular grid phase offset. Our simulations suggest that hexadirectional modulation is best explained by the conjunctive grid by head-direction cell hypothesis, which can produce the strongest and most robust hexasymmetry. In contrast, our simulations including previously observed biological properties of grid cells do not provide clear support for the structure-function mapping hypothesis. Our observations on hexadirectional modulation generated by grid-cell adaptation effects and the available data on adaptation properties of grid cells are insufficient to substantiate or refute the repetition suppression hypothesis. Furthermore, we found that the magnitude of the hexadirectional modulation depends considerably on the subjects navigation pattern. Our results thus indicate that future fMRI studies could be designed to test which of the three hypotheses most likely accounts for the fMRI measure of grid cells. These findings also underline the importance of quantifying the biological properties of single grid cells in humans to further elucidate how hexadirectional modulations of fMRI activity may emerge.