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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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Related in: MedlinePlus

Couplings between and within modules.Both couplings between and within modules have a mean value very close to zero. The probability of the absolute value of the couplings for the model with constant (A) and full (B) fields are shown here. For the between module couplings (blue bars) there is a bigger peak at zero compared to the within module couplings (green bars), and the green histogram has bigger mass at larger values.
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pcbi.1004052.g006: Couplings between and within modules.Both couplings between and within modules have a mean value very close to zero. The probability of the absolute value of the couplings for the model with constant (A) and full (B) fields are shown here. For the between module couplings (blue bars) there is a bigger peak at zero compared to the within module couplings (green bars), and the green histogram has bigger mass at larger values.

Mentions: One would expect, based on the experimental indications of modules operating independently, that grid cells of the same module are more likely to participate in the same functional network than neurons from different modules. We found that the couplings within and between modules in data set 1 both had means close to zero (within modules (mean±std): −0.01±0.13, between modules: −0.01±0.09). However, the within module couplings had a greater variance (, P<0.001)), i.e. there was a higher proportion of couplings with high absolute values within modules than between, as can be seen in Fig. 6. This result was found to be stable with respect to data limitations, as shown in the next section.


Correlations and functional connections in a population of grid cells.

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

Couplings between and within modules.Both couplings between and within modules have a mean value very close to zero. The probability of the absolute value of the couplings for the model with constant (A) and full (B) fields are shown here. For the between module couplings (blue bars) there is a bigger peak at zero compared to the within module couplings (green bars), and the green histogram has bigger mass at larger values.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004052.g006: Couplings between and within modules.Both couplings between and within modules have a mean value very close to zero. The probability of the absolute value of the couplings for the model with constant (A) and full (B) fields are shown here. For the between module couplings (blue bars) there is a bigger peak at zero compared to the within module couplings (green bars), and the green histogram has bigger mass at larger values.
Mentions: One would expect, based on the experimental indications of modules operating independently, that grid cells of the same module are more likely to participate in the same functional network than neurons from different modules. We found that the couplings within and between modules in data set 1 both had means close to zero (within modules (mean±std): −0.01±0.13, between modules: −0.01±0.09). However, the within module couplings had a greater variance (, P<0.001)), i.e. there was a higher proportion of couplings with high absolute values within modules than between, as can be seen in Fig. 6. This result was found to be stable with respect to data limitations, as shown in the next section.

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