Where can a place cell put its fields? Let us count the ways

Abstract

A hippocampal place cell exhibits multiple firing fields within and across environments. What factors determine the configuration of these fields, and could they be set down in arbitrary locations? We conceptualize place cells as performing evidence combination across many inputs and selecting a threshold to fire. Thus, mathematically they are perceptrons, except that they act on geometrically organized inputs in the form of multiscale periodic grid-cell drive, and external cues. We analytically count which field arrangements a place cell can realize with structured grid inputs, to show that many more place-field arrangements are realizable with grid-like than one-hot coded inputs. However, the arrangements have a rigid structure, defining an underlying response scaffold. We show that the "separating capacity" or spatial range over which all potential field arrangements are realizable equals the rank of the grid-like input matrix, which in turn equals the sum of distinct grid periods, a small fraction of the unique grid-cell coding range. Learning different grid-to-place weights beyond this small range will alter previous arrangements, which could explain the volatility of the place code. However, compared to random inputs over the same range, grid-structured inputs generate larger margins, conferring relative robustness to place fields when grid input weights are fixed. Significance statementPlace cells encode cognitive maps of the world by combining external cues with an internal coordinate scaffold, but our ability to predict basic properties of the code, including where a place cell will exhibit fields without external cues (the scaffold), remains weak. Here we geometrically characterize the place cell scaffold, assuming it is derived from multiperiodic modular grid cell inputs, and provide exact combinatorial results on the space of permitted field arrangements. We show that the modular inputs permit a large number of place field arrangements, with robust fields, but also strongly constrain their geometry and thus predict a structured place scaffold.

A theory of joint attractor dynamics in the hippocampus and the entorhinal cortex accounts for artificial remapping and grid cell field-to-field variability

“…Under independent remapping in grid cells and place cells, the capacity of the joint representation is limited by the grid-to-place connections (Appendix 1). This result is in line with recent analysis ( Yim et al, 2019 ), which indicates that once grid phases are set, realizable patterns of place fields by a binary perceptron (involving a linear weighting of grid cell inputs) are limited. As an alternative to independent remapping in place cells and grid cells, it has been proposed that place cell firing locations may be determined in a new environment by grid cell inputs ( Fyhn et al, 2007 ; Monaco et al, 2011 ).…”