Self-regulated emergence of heavy-tailed weight distributions in evolving complex network architectures

Abstract

The nervous system continuously adjusts connection strengths and reorganizes its structure to form and maintain complex connectivity patterns with heavy-tailed weight distributions. We propose a parsimonious model in which structural and synaptic plasticity are driven by common diffusion dynamics. Synaptic plasticity alone generates heavy-tailed weight distributions, but only when activity spreading remains predominantly local. However, when combined with structural plasticity through adaptive rewiring, the model also generates these distributions with more extensive activity flow. Furthermore, adaptive rewiring produces complex network structures with convergent-divergent circuits. These circuits contain motifs that are pervasive in nervous systems and are responsible for context-sensitive signal propagation and enhanced signal to noise ratios. Our model robustly reproduces these results across diverse dynamical regimes while capturing key connectivity features of both C. elegans and mouse brain networks. These findings suggest that the underlying principles are shared across species of varying complexity.