Stochastic dynamics and synchronization in motif-based neuronal networks

Abstract: Neuronal networks exhibit complex dynamics shaped by connectivity and stochastic input. Empirical studies show that neuronal networks contain recurring subgraphs, or motifs, but the collective influence of different motif types after embedding in large stochastic networks remains less well understood. We construct a spiking network composed of six representative structural classes and examine how intrinsic noise, coupling strength, inter-motif connectivity, network size, and neuronal heterogeneity shape synchronization. Both motif- and network-level coherence peak at intermediate noise intensities, consistent with coherence resonance. Bidirectionally coupled pairs (M2) and the type-2 recurrent feed-forward loop (M3c) consistently exhibit high motif-level coherence. Rewiring these motifs while preserving local synapse number and strength produces some of the largest reductions in network coherence, showing that connection arrangement contributes beyond strong local coupling alone. M2 and M3c also exhibit frequent spike doublets, linking short inter-spike intervals with elevated coherence. Relative to a degree- and weight-matched random control, the motif-structured network reaches greater coherence at weaker noise. Increasing network size enhances coherence until the response begins to saturate, whereas applied-current heterogeneity lowers peak coherence and shifts the optimum toward stronger noise without erasing the relative differences among motif classes. These results show that local connection arrangement remains dynamically consequential after embedding and can shape noise-driven coherence at the population level.