Place-cell capacity and volatility with grid-like inputs

Abstract

What factors constrain the arrangement of the multiple 1elds of a place cell? By modeling place cells as perceptrons that act on multiscale periodic grid-cell inputs, we analytically enumerate a place cell’s repertoire - how many 1eld arrangements it can realize without external cues while its grid inputs are unique; and derive its capacity - the spatial range over which it can achieve any 1eld arrangement. We show that the repertoire is very large and relatively noise-robust. However, the repertoire is a vanishing fraction of all arrangements, while capacity scales only as the sum of the grid periods so 1eld arrangements are constrained over larger distances. Thus, grid-driven place 1eld arrangements de1ne a large response scaffold that is strongly constrained by its structured inputs. Finally, we show that altering grid-place weights to generate an arbitrary new place 1eld strongly affects existing arrangements, which could explain the volatility of the place code.