Grid cells are not a parsimonious source of the hexadirectional signal

Hexadirectional modulation is widely treated as a proxy for population-level grid-cell activity in humans. Conventional analyses test the sixth harmonic of the mean directional response, whereas we show grid-cell firing predicts a dominant sixfold modulation of cell-level variance, rather than population-level mean. Using analytical derivations, simulations and recordings from 23,453 rodent medial entorhinal neurons, we show that grid cell tuning alone cannot account for the measured mean signal. Analysis of 1,349 conjunctive grid-head-direction cells revealed insufficient grid-axis alignment and directional tuning specificity to account for population-level hexadirectionality. A hypothetical additional nonlinearity mechanism near the cell level can produce a a small sixfold population-level mean modulation, ≤ 2%, under favorable circumstances. Moreover, the current methodology does not adequately differentiate genuinely symmetric activity and stable directional peaks, nor contextualize a harmonic measurement in a solid spectral framework. These findings show that mean hexadirectional modulation neither follows directly from grid-cell firing nor uniquely identifies grid-cell activity. We provide an improved framework for testing a link between the two in future studies.