Correlations and Functional Connections in a Population of Grid Cells

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 maximum entropy kinetic pairwise 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. They take positive values between cells with nearby phases and approach zero or negative values for larger phase differences. We find similar results also 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 in the same module and those from different modules can be both negative and positive, with a mean close to zero, but with the strongest inferred connections 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 grid pattern.

Grid cells correlation structure suggests organized feedforward projections into superficial layers of the medial entorhinal cortex

“…A recent analysis of grid cells along a linear track, also found strong temporal correlations between grid cells with overlapping rate-maps, although they did not separate their data into same vs. different module pairs as they were analyzing linear-track data (Mathis et al, 2013). In another study, Dunn et al (2015) describe correlations between conjunctive cells in the deep layers arising probably from synaptic origin, which complements our work, which describes correlations between pure grid cells in superficial layers, which arise most likely from a common-input source.…”

Spatial representation in the hippocampal formation: a history

“…The strongest prediction of the attractor models, however, is perhaps that grid cells with similar grid phases have enhanced connectivity. Statistical analysis of firing patterns in simultaneously recorded grid cells confirm this prediction 245,246 , but direct measurements of connections between functionally verified cell types are still missing. Attractor models do not provide the only possible explanation of how grid patterns might be created.…”

Grid cells and cortical representation

“…Mathis et al 120 analyzed data from grid cells on a one-dimensional track showing that noise correlation amongst these cells decays as the phase difference increases. In another study 121 , a kinetic Ising model 122 was used to infer effective connections in a population of 27 grid cells recorded simultaneously in an open field. Inferred connections between pairs of grid cells decayed with increasing phase difference, starting as positive for neurons with nearly identical phases and turning to negative at larger phase differences.…”