Rich-club connectivity, diverse population coupling, and dynamical activity patterns emerging from local cortical circuits
Fig 1
Connectivity properties synthesized by the generative model.
(A) The generated (dots) and theoretical (solid lines) in-degree distributions with different hybrid parameters q; q = 0 and q = 1 correspond to the pure Poisson and log-normal distributions, respectively. (B) The generated (dots) connection probabilities as a function of inter-neuron distance with different decay constants τD. The decay constants of fitted exponential curves (solid lines) are 5.57 ± 0.05, 11.17 ± 0.04, 19.25 ± 0.15 (95% confidence), respectively. (C) The generated (dots) connection probabilities as a function of shared pre-synaptic common neighbors with different common neighbor coefficients aΓ; the error bars show one SEM of 65 trials. The solid colored lines are the linear fit to the data. For each trial, the results are calculated from 2000 samples; each sample consists of 12 neurons randomly selected from a circular region in the network containing 2000 excitatory neurons to approximate the sampling methods used in [3]. The results are not sensitive to the diameter of the sampling area. The solid black line is the expected curve from the E-R random networks. (D) The mean clustering coefficient (CC) of the network (colored and black dots) increases as the common neighbor coefficient aΓ increases. The solid line is the fitted exponential function (0.22 − 0.089e−aΓ/7.04; R2 = 0.996). The convergence of mean CC for 4 example aΓ values (colored dots) after iterations of the algorithm is shown in the inset. (E) The generated (dots) and theoretical (solid line; log-normal) distributions of unitary EPSP magnitudes. (F) The average incoming connection strength and the in-degree of individual excitatory neurons (dots) follow the inverse square root scaling (solid line fitted; R2 = 0.917); note the plot is on a log-log scale. All the empirical data sets or points in (A-B) and (D-F) show the results of individual realizations of the generative model with default parameter values (unless otherwise stated).