Limits...
Correlations and functional connections in a population of grid cells.

Dunn B, Mørreaunet M, Roudi Y - PLoS Comput. Biol. (2015)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Kavli Institute for Systems Neuroscience and Centre for Neural Computation, NTNU, Trondheim, Norway.

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.

Show MeSH

Related in: MedlinePlus

Couplings versus phase distance.Inferred couplings are positive for small phase differences while they become negative for larger phase separations, both for data set 1 (A) and data set 2 (B). When we break the population to the three contributing modules of data set 1, this pattern persists for the smaller modules (C,D) while for the largest module (E) the excitatory part is absent. In each plot, the circles represent the inferred values using the full data length. The black lines show the average values of the couplings calculated from 20 random partitions of the data.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4340907&req=5

pcbi.1004052.g004: Couplings versus phase distance.Inferred couplings are positive for small phase differences while they become negative for larger phase separations, both for data set 1 (A) and data set 2 (B). When we break the population to the three contributing modules of data set 1, this pattern persists for the smaller modules (C,D) while for the largest module (E) the excitatory part is absent. In each plot, the circles represent the inferred values using the full data length. The black lines show the average values of the couplings calculated from 20 random partitions of the data.

Mentions: Interestingly, no matter which of the various external fields we used, when neurons i and j both belong to one of the two smaller modules of data set 1, or the one module of data set 2, the inferred couplings, Jij, showed a consistent dependence on the spatial phase difference, with nearby phases showing positive Jij while those further away more negative values. This is shown in Fig. 4 for both data sets for the case of the Gaussian fields. The slopes and intercepts of linear regression lines were all significantly different from zero, both for the full data and the 20 sets of random halves (t-test, P<0.02) for all figures except for Fig. 4E, where the slope and intercept of linear regression were not significantly different from 0 (t-test, P>0.7). We remind that with the Gaussian fields, the correlations between two cells due to overlapping fields are explained away.


Correlations and functional connections in a population of grid cells.

Dunn B, Mørreaunet M, Roudi Y - PLoS Comput. Biol. (2015)

Couplings versus phase distance.Inferred couplings are positive for small phase differences while they become negative for larger phase separations, both for data set 1 (A) and data set 2 (B). When we break the population to the three contributing modules of data set 1, this pattern persists for the smaller modules (C,D) while for the largest module (E) the excitatory part is absent. In each plot, the circles represent the inferred values using the full data length. The black lines show the average values of the couplings calculated from 20 random partitions of the data.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4340907&req=5

pcbi.1004052.g004: Couplings versus phase distance.Inferred couplings are positive for small phase differences while they become negative for larger phase separations, both for data set 1 (A) and data set 2 (B). When we break the population to the three contributing modules of data set 1, this pattern persists for the smaller modules (C,D) while for the largest module (E) the excitatory part is absent. In each plot, the circles represent the inferred values using the full data length. The black lines show the average values of the couplings calculated from 20 random partitions of the data.
Mentions: Interestingly, no matter which of the various external fields we used, when neurons i and j both belong to one of the two smaller modules of data set 1, or the one module of data set 2, the inferred couplings, Jij, showed a consistent dependence on the spatial phase difference, with nearby phases showing positive Jij while those further away more negative values. This is shown in Fig. 4 for both data sets for the case of the Gaussian fields. The slopes and intercepts of linear regression lines were all significantly different from zero, both for the full data and the 20 sets of random halves (t-test, P<0.02) for all figures except for Fig. 4E, where the slope and intercept of linear regression were not significantly different from 0 (t-test, P>0.7). We remind that with the Gaussian fields, the correlations between two cells due to overlapping fields are explained away.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Kavli Institute for Systems Neuroscience and Centre for Neural Computation, NTNU, Trondheim, Norway.

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.

Show MeSH
Related in: MedlinePlus