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How Structure Determines Correlations in Neuronal Networks

Figure 6

Correlation distributions depend on range of inhibition in ring networks.

A: Distance dependent connectivity in a ring. Nodes are connected with a fixed weight to neurons with a probability depending on their mutual distance. Average interaction is the product of connection probability and weight averaged over populations. The connectivity profile may be different for excitatory neurons (red, positive weight) and inhibitory ones (green, negative weight). Average interaction on a randomly picked neuron at a distance corresponds to the sum (blue). B: Typical spectrum for a connectivity matrix with local inhibition. Parameters: , others as in Figure 2. C,D: Examples for average interaction profiles used in E and F. C: Global inhibition () and local excitation, for small (dashed) and large (dotted) , hat profile. D: Local inhibition and global excitation, inverted hat profile. Other parameters as in B. E,F: Top: Correlation distributions for fixed and increasing (E) and fixed and increasing (F), logarithmic colour scale. Values between (random network) and (connectivity in boxcar 0.5). Overall connectivity remains constant. Average correlation (dashed blue: numerical, red: analytical) does not change. Bottom: real parts of eigenvalues for corresponding connectivity matrices. Rings with local excitation tend to be less stable.

doi: https://doi.org/10.1371/journal.pcbi.1002059.g006