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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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Noise correlations versus phase distance.(A) shows all three modules of data set 1 combined, while (B) shows the one module of data set 2. For the smaller modules of data set 1 (C, D) the noise correlations are positive for small phase differences while they approach zero for larger phase separations. No significant pattern can be observed for the cells from the largest module of data set 1 (E). The distance in phase was normalized by the average spacing of the spatial fields in each module. In each plot, the circles represent the inferred values using the full data length. The noise correlations were calculated by binning the environment into 7.5 × 7.5 cm spatial bins. The black lines show the average values of the correlations calculated from 20 random partitions (see Material and Methods) of the data. The error bars are the standard deviation of the mean values over these 20 random partitions. Note that the normalized maximal phase distance occurs at the minimum overlap between the two commonly oriented hexagonal patterns and is 0.5/cos(30) ≈ 0.6.
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pcbi.1004052.g001: Noise correlations versus phase distance.(A) shows all three modules of data set 1 combined, while (B) shows the one module of data set 2. For the smaller modules of data set 1 (C, D) the noise correlations are positive for small phase differences while they approach zero for larger phase separations. No significant pattern can be observed for the cells from the largest module of data set 1 (E). The distance in phase was normalized by the average spacing of the spatial fields in each module. In each plot, the circles represent the inferred values using the full data length. The noise correlations were calculated by binning the environment into 7.5 × 7.5 cm spatial bins. The black lines show the average values of the correlations calculated from 20 random partitions (see Material and Methods) of the data. The error bars are the standard deviation of the mean values over these 20 random partitions. Note that the normalized maximal phase distance occurs at the minimum overlap between the two commonly oriented hexagonal patterns and is 0.5/cos(30) ≈ 0.6.

Mentions: To calculate correlations between pairs of grid cells, beyond what is expected from spatial rate covariations, we binned the spike data into 1 ms intervals and smoothed the firing rates with a 20 ms Gaussian filter. The trajectory of the animal was then binned spatially by dividing the environment into a number of N × N square boxes, using different values of N = 2, 3, 4, 5, 10, 15, 20, 40, 75. Noise correlations, Cij, between cells i and j were then determined as the mean of the Pearson correlation coefficients, ρ, calculated over the trajectories through each spatial bin (see Material and Methods). As shown in Fig. 1, in the case of dividing the environment into 20 × 20 spatial bins, we found noise correlation values close to zero, or slightly negative, for cells with non-overlapping spatial fields. On the other hand, cell pairs close in phase distance showed positive noise correlation values that increased for cells closer to each other in phase; see Fig. 1A and B. The slope () and intercept () of a linear regression line (not shown) are and for data set 1, and and for data set 2, all significantly different from 0 (t-test, P < 0.001).


Correlations and functional connections in a population of grid cells.

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

Noise correlations versus phase distance.(A) shows all three modules of data set 1 combined, while (B) shows the one module of data set 2. For the smaller modules of data set 1 (C, D) the noise correlations are positive for small phase differences while they approach zero for larger phase separations. No significant pattern can be observed for the cells from the largest module of data set 1 (E). The distance in phase was normalized by the average spacing of the spatial fields in each module. In each plot, the circles represent the inferred values using the full data length. The noise correlations were calculated by binning the environment into 7.5 × 7.5 cm spatial bins. The black lines show the average values of the correlations calculated from 20 random partitions (see Material and Methods) of the data. The error bars are the standard deviation of the mean values over these 20 random partitions. Note that the normalized maximal phase distance occurs at the minimum overlap between the two commonly oriented hexagonal patterns and is 0.5/cos(30) ≈ 0.6.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004052.g001: Noise correlations versus phase distance.(A) shows all three modules of data set 1 combined, while (B) shows the one module of data set 2. For the smaller modules of data set 1 (C, D) the noise correlations are positive for small phase differences while they approach zero for larger phase separations. No significant pattern can be observed for the cells from the largest module of data set 1 (E). The distance in phase was normalized by the average spacing of the spatial fields in each module. In each plot, the circles represent the inferred values using the full data length. The noise correlations were calculated by binning the environment into 7.5 × 7.5 cm spatial bins. The black lines show the average values of the correlations calculated from 20 random partitions (see Material and Methods) of the data. The error bars are the standard deviation of the mean values over these 20 random partitions. Note that the normalized maximal phase distance occurs at the minimum overlap between the two commonly oriented hexagonal patterns and is 0.5/cos(30) ≈ 0.6.
Mentions: To calculate correlations between pairs of grid cells, beyond what is expected from spatial rate covariations, we binned the spike data into 1 ms intervals and smoothed the firing rates with a 20 ms Gaussian filter. The trajectory of the animal was then binned spatially by dividing the environment into a number of N × N square boxes, using different values of N = 2, 3, 4, 5, 10, 15, 20, 40, 75. Noise correlations, Cij, between cells i and j were then determined as the mean of the Pearson correlation coefficients, ρ, calculated over the trajectories through each spatial bin (see Material and Methods). As shown in Fig. 1, in the case of dividing the environment into 20 × 20 spatial bins, we found noise correlation values close to zero, or slightly negative, for cells with non-overlapping spatial fields. On the other hand, cell pairs close in phase distance showed positive noise correlation values that increased for cells closer to each other in phase; see Fig. 1A and B. The slope () and intercept () of a linear regression line (not shown) are and for data set 1, and and for data set 2, all significantly different from 0 (t-test, P < 0.001).

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