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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.

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Effect of theta on the couplings.(A) Adding theta to the Gaussian model has little effect on the couplings (data set 1) with PCC, All = 0.95, PCC, SC = 0.97, PCC, NonSC = 0.94. (B) Mean of couplings from the two theta clusters in the Gaussian model with and without theta included. Black: couplings between cells with similar theta phase preference. Blue: couplings between cells with opposite theta phase preference. Error bars show the standard error of the mean. Without theta taken into account, the connections between cells that fire in the opposite theta phase are on average negative, while they are positive for those that tend to fire in the same theta phase. This difference is suppressed when theta is taken into account.
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pcbi.1004052.g005: Effect of theta on the couplings.(A) Adding theta to the Gaussian model has little effect on the couplings (data set 1) with PCC, All = 0.95, PCC, SC = 0.97, PCC, NonSC = 0.94. (B) Mean of couplings from the two theta clusters in the Gaussian model with and without theta included. Black: couplings between cells with similar theta phase preference. Blue: couplings between cells with opposite theta phase preference. Error bars show the standard error of the mean. Without theta taken into account, the connections between cells that fire in the opposite theta phase are on average negative, while they are positive for those that tend to fire in the same theta phase. This difference is suppressed when theta is taken into account.

Mentions: Since many cells in our data had some theta phase and head directional preferences, we also considered a model in which each cell was coupled to the head direction of the animal and the LFP theta oscillation through coupling constants that were inferred from the data; see Material and Methods. In general, there were only small differences between the couplings when theta and head direction were added. This can be seen in Fig. 5A, which shows the couplings in the model with Gaussian fields with and without theta included. In this case, we observed a small but selective change, depending on the phase preference of the neurons. The cells could be clustered into two groups according to their theta phase preference (see Material and Methods): one with connections between cells of similar theta phase preference, and the other with connections between cells with opposite preference.


Correlations and functional connections in a population of grid cells.

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

Effect of theta on the couplings.(A) Adding theta to the Gaussian model has little effect on the couplings (data set 1) with PCC, All = 0.95, PCC, SC = 0.97, PCC, NonSC = 0.94. (B) Mean of couplings from the two theta clusters in the Gaussian model with and without theta included. Black: couplings between cells with similar theta phase preference. Blue: couplings between cells with opposite theta phase preference. Error bars show the standard error of the mean. Without theta taken into account, the connections between cells that fire in the opposite theta phase are on average negative, while they are positive for those that tend to fire in the same theta phase. This difference is suppressed when theta is taken into account.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004052.g005: Effect of theta on the couplings.(A) Adding theta to the Gaussian model has little effect on the couplings (data set 1) with PCC, All = 0.95, PCC, SC = 0.97, PCC, NonSC = 0.94. (B) Mean of couplings from the two theta clusters in the Gaussian model with and without theta included. Black: couplings between cells with similar theta phase preference. Blue: couplings between cells with opposite theta phase preference. Error bars show the standard error of the mean. Without theta taken into account, the connections between cells that fire in the opposite theta phase are on average negative, while they are positive for those that tend to fire in the same theta phase. This difference is suppressed when theta is taken into account.
Mentions: Since many cells in our data had some theta phase and head directional preferences, we also considered a model in which each cell was coupled to the head direction of the animal and the LFP theta oscillation through coupling constants that were inferred from the data; see Material and Methods. In general, there were only small differences between the couplings when theta and head direction were added. This can be seen in Fig. 5A, which shows the couplings in the model with Gaussian fields with and without theta included. In this case, we observed a small but selective change, depending on the phase preference of the neurons. The cells could be clustered into two groups according to their theta phase preference (see Material and Methods): one with connections between cells of similar theta phase preference, and the other with connections between cells with opposite preference.

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