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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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Stability of the inferred couplings.Stability of the phase-dependent trend in inferred couplings filtered for cell pairs where at least one cell is phase precessing (A), as well as for couplings filtered for cells on the same tetrode (B). The phase dependence of the coupling can be seen to be similar to when all pairs were included. Couplings inferred using one random half of the data plotted against those inferred from the other half, assuming constant external field (C) or Gaussian spatial fields (D). The within module couplings (green triangles) consistently show more stability across partitions of the data than the between module couplings (blue circles), but not as much as the self-couplings (red triangles). A: PCC, within modules = 0.88, PCC, between modules = 0.73, PCC, SC = 0.99. B: PCC, within modules = 0.73, PPC, between modules = 0.51, PCC, SC = 0.94. (E) The effect on between grid cells-couplings from including non-grid cells in the inference for the biggest data set (data set 1, 65 cells) is small.
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pcbi.1004052.g007: Stability of the inferred couplings.Stability of the phase-dependent trend in inferred couplings filtered for cell pairs where at least one cell is phase precessing (A), as well as for couplings filtered for cells on the same tetrode (B). The phase dependence of the coupling can be seen to be similar to when all pairs were included. Couplings inferred using one random half of the data plotted against those inferred from the other half, assuming constant external field (C) or Gaussian spatial fields (D). The within module couplings (green triangles) consistently show more stability across partitions of the data than the between module couplings (blue circles), but not as much as the self-couplings (red triangles). A: PCC, within modules = 0.88, PCC, between modules = 0.73, PCC, SC = 0.99. B: PCC, within modules = 0.73, PPC, between modules = 0.51, PCC, SC = 0.94. (E) The effect on between grid cells-couplings from including non-grid cells in the inference for the biggest data set (data set 1, 65 cells) is small.

Mentions: It is known that some grid cells show phase precession. This could be an additional source of correlation, so we tried to address how phase precession can influence the couplings. We first investigated whether or not any of the cells in our data phase precess, focusing on data set 1. In general, quantifying phase precession in two-dimensions is a difficult task due to the changes in the animals movement direction within the field. To classify cells as phase precessing or not, we thus used a novel approach described in [24], correlating the distance to the field peak projected onto the current running direction with the phase of theta at the time of spikes. Our analysis revealed that 13 of the 27 grid cells showed significant phase precession (5 of 8 in module 1, 6 of 7 in module 2, and 2 of 7 in module 3). We then excluded the couplings between phase precessing cells from the analysis for the two smaller modules and found that this did not remove the trend reported in Fig. 4 between the spatial phase difference and the inferred couplings. As can be seen in Fig. 7A, there was still a significant negative relationship between coupling value and spatial phase distance for cell pairs in which at least one of the cells do not show significant phase precession (both the slope () and intercept () of the linear regression line are 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)

Stability of the inferred couplings.Stability of the phase-dependent trend in inferred couplings filtered for cell pairs where at least one cell is phase precessing (A), as well as for couplings filtered for cells on the same tetrode (B). The phase dependence of the coupling can be seen to be similar to when all pairs were included. Couplings inferred using one random half of the data plotted against those inferred from the other half, assuming constant external field (C) or Gaussian spatial fields (D). The within module couplings (green triangles) consistently show more stability across partitions of the data than the between module couplings (blue circles), but not as much as the self-couplings (red triangles). A: PCC, within modules = 0.88, PCC, between modules = 0.73, PCC, SC = 0.99. B: PCC, within modules = 0.73, PPC, between modules = 0.51, PCC, SC = 0.94. (E) The effect on between grid cells-couplings from including non-grid cells in the inference for the biggest data set (data set 1, 65 cells) is small.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004052.g007: Stability of the inferred couplings.Stability of the phase-dependent trend in inferred couplings filtered for cell pairs where at least one cell is phase precessing (A), as well as for couplings filtered for cells on the same tetrode (B). The phase dependence of the coupling can be seen to be similar to when all pairs were included. Couplings inferred using one random half of the data plotted against those inferred from the other half, assuming constant external field (C) or Gaussian spatial fields (D). The within module couplings (green triangles) consistently show more stability across partitions of the data than the between module couplings (blue circles), but not as much as the self-couplings (red triangles). A: PCC, within modules = 0.88, PCC, between modules = 0.73, PCC, SC = 0.99. B: PCC, within modules = 0.73, PPC, between modules = 0.51, PCC, SC = 0.94. (E) The effect on between grid cells-couplings from including non-grid cells in the inference for the biggest data set (data set 1, 65 cells) is small.
Mentions: It is known that some grid cells show phase precession. This could be an additional source of correlation, so we tried to address how phase precession can influence the couplings. We first investigated whether or not any of the cells in our data phase precess, focusing on data set 1. In general, quantifying phase precession in two-dimensions is a difficult task due to the changes in the animals movement direction within the field. To classify cells as phase precessing or not, we thus used a novel approach described in [24], correlating the distance to the field peak projected onto the current running direction with the phase of theta at the time of spikes. Our analysis revealed that 13 of the 27 grid cells showed significant phase precession (5 of 8 in module 1, 6 of 7 in module 2, and 2 of 7 in module 3). We then excluded the couplings between phase precessing cells from the analysis for the two smaller modules and found that this did not remove the trend reported in Fig. 4 between the spatial phase difference and the inferred couplings. As can be seen in Fig. 7A, there was still a significant negative relationship between coupling value and spatial phase distance for cell pairs in which at least one of the cells do not show significant phase precession (both the slope () and intercept () of the linear regression line are 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