Rich-club connectivity, diverse population coupling, and dynamical activity patterns emerging from local cortical circuits
Fig 9
Rich-club connectivity is related to the heterogeneous population coupling.
(A) An example of the rich-club connectivity among high total degree (k > 600) excitatory neurons (red dots). Only a 10% random subset of the synaptic connections are plotted (lines) for visualization purpose, with a probability of 1/Φ(k = 600) colored in blue and otherwise in yellow to illustrate the proportion between the number of connections expected from their total degrees alone (blue) and the number of extra connections due to the rich-club connectivity (green). The circle shows the range within which both the rich-club and stPR coefficients are calculated as used in Figs 2B and 8. (B) The rich-club neurons have high stPR coefficients. Left y-axis (blue): the blue dashed line shows the stPR coefficient z scores for the neurons with a total degree > k averaged over 10 trials and the shaded area shows one SEM. Within each trial, 10 random 66-neuron samples (as in Fig 8) are collected to calculate the k-dependent stPR coefficient z scores. Right y-axis (red): the red dashed line shows the normalized rich-club coefficient curve from Fig 2B and the shaded area shows one SEM. Inset: normalized rich-club coefficient Φ(k) (y-axis) versus k-dependent stPR coefficient z score (x-axis) from 10 realizations of the network (shown with 10 different colors). (C) Distributions of stPR coefficients pooled from 10 trials before (black) and after (red) spike shuffling from the local cortical circuits with different common neighbour factors aΓ. For comparison, the total count (area under curve) and bin size are the same for each distribution. (D) stPR coefficients before shuffling, normalized by the SD of stPR coefficients after shuffling (i.e., coefficients of control case) and plotted in the same k-dependent manner as in (B). Each curve shows the average of 10 trials.