Structure and function of model inhibition change with sparsity.

(A) An illustration visualizing changing weight distributions from the perspective of an inhibitory interneuron. As sparsity (λ) increases, the proportion of stronger (solid lines) I→E projections increases and the number of weaker (dashed lines) I→E projections dwindles. (B) Estimated probability density functions for the inhibitory to excitatory connection weights in the optimal computational models at different sparsity levels reveal an increasing fraction of inhibitory synapses are stronger as sparsity increases. (C) Estimated kurtosis vs. sparsity quantifies the changes visible in the distributions, demonstrating that inhibition is more targeted and less global at lower sparsity levels with smaller E:I ratios. (D) With increasing sparsity (corresponding to higher optimal E:I ratios), the inhibitory subpopulation’s mean activity level declines (p < 10⁻⁸, significant after accounting for multiple comparisons; except for λ = 0.1 and λ = 0.2) and becomes less diverse exhibiting a lower standard deviation (p < 10⁻⁸, significant after accounting for multiple comparisons). (E) Despite the changes in inhibitory structure and function due to changes in sparsity level (and optimal E:I cell type ratio), the changes to inhibitory synaptic distributions and firing rates counteract each other so that the total inhibitory influence in the network remains constant and the circuit maintains balance between the recurrent excitatory and inhibitory activity.