Figure 5. Heterogeneity of timescales in E-I spiking networks.

(a) Top: Schematic of a spiking network with excitatory (black) and inhibitory populations (red) arranged in assemblies with heterogeneous distribution of sizes. Bottom: In a representative trial, neural assemblies activate and deactivate at random times generating metastable activity (one representative E neuron per assembly; larger assemblies on top; representative network of ${\displaystyle N=10,000}$ neurons), where larger assemblies tend to activate for longer intervals. (b) The average activation times <T> of individual assemblies (blue dots; the average was calculated across 100s simulation and across all neurons within the same assembly for all assemblies in 20 different network realizations; self-coupling units are in [mV], see Methods section). Fit of ${\displaystyle \log (T)=a_2{s}_E^2+a_1{s}_E+a_0}$ with ${\displaystyle a_2=0.14,a_1=1.97,a_0=5.51}$ (pink curve). Inset: cross-validated model selection for polynomial fit. As the assembly strength (i.e. the product of its size and average recurrent coupling) increases, <T> increases, leading to a large distribution of timescales ranging from 20 ms to 100s. (c) Eigenvalue distribution of the full weight matrix ${\displaystyle J}$ (brown) and the mean-field-reduced weight matrix ${\displaystyle {\displaystyle J^{MF}}}$ (pink). (d) The Schur eigenvectors of the weight matrix ${\displaystyle {\displaystyle J^{MF}}}$ show that the slow (gapped) Schur eigenvalues (top) are associated with eigenvectors corresponding to E/I cluster pairs (bottom). See Appendix (e) Spiking network model for more details and for the scaling to larger networks.