TY - JOUR
T1 - Where can a place cell put its fields? Let us count the ways
JF - bioRxiv
DO - 10.1101/2019.12.19.881458
SP - 2019.12.19.881458
AU - Yim, Man Yi
AU - Sadun, Lorenzo A
AU - Fiete, Ila R
AU - Taillefumier, Thibaud
Y1 - 2019/01/01
UR - http://biorxiv.org/content/early/2019/12/19/2019.12.19.881458.abstract
N2 - 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 characterize and count which field arrangements a place cell can realize with such structured inputs. The number of realizable place-field arrangements across the unique grid-like coding states is much larger than with one-hot coded inputs of the same input dimension, though the realizable place-field arrangements make up a vanishing fraction of potential arrangements. We show that the “separating capacity” or spatial range over which all field arrangements are realizable is given by the rank of the grid-like input matrix, and this rank equals the sum of distinct grid periods, a small fraction of the unique coding range of the input, which scales as the product of periods. Compared to random inputs over the same range, grid-structured inputs generate larger margins, conferring stability to place fields. Finally, the realizable arrangements are determined by the input geometry, thus the model predicts that place fields should lie in constrained arrangements within and across environments, and in relation to their grid inputs.Significance statement Place 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 and relatively low-dimensional place scaffold.
ER -