Correlations and functional connections in a population of grid cells

TL;DR

This study analyzes the correlations and inferred functional connections among grid cells in rats, revealing phase-dependent connectivity patterns that support attractor dynamics in grid pattern generation.

Contribution

It provides the first detailed analysis of pairwise correlations and functional connectivity in grid cells, accounting for various covariates and revealing phase-dependent network structure.

Findings

Correlations decay with phase difference between cells.

Functional connections are positive for nearby phases, negative or zero for distant phases.

Connections within the same module tend to be stronger and support attractor network models.

Abstract

We study the statistics of spike trains of simultaneously recorded grid cells in freely behaving rats. We evaluate pairwise correlations between these cells and, using a generalized linear model (kinetic Ising model), study their functional connectivity. Even when we account for the covariations in firing rates due to overlapping fields, both the pairwise correlations and functional connections decay as a function of the shortest distance between the vertices of the spatial firing pattern of pairs of grid cells, i.e. their phase difference. The functional connectivity takes positive values between cells with nearby phases and approaches zero or negative values for larger phase differences. We also find similar results when, in addition to correlations due to overlapping fields, we account for correlations due to theta oscillations and head directional inputs. The inferred connections between neurons can be both negative and positive regardless of whether the cells share common spatial firing characteristics, that is, whether they belong to the same modules, or not. The mean strength of these inferred connections is close to zero, but the strongest inferred connections are found between cells of the same module. Taken together, our results suggest that grid cells in the same module do indeed form a local network of interconnected neurons with a functional connectivity that supports a role for attractor dynamics in the generation of the grid pattern.