Analytically tractable model of synaptic crowding explains emergent small-world structure and network dynamics

• URL: http://arxiv.org/abs/2603.19320v1
• Date: Mon, 16 Mar 2026 21:49:24 GMT
• Title: Analytically tractable model of synaptic crowding explains emergent small-world structure and network dynamics
• Abstract summary: We introduce a minimal wiring rule motivated by synaptic crowding.<n>Mean connectivity grows only logarithmically with network size while variance remains bounded.<n>The model provides testable predictions linking local developmental constraints to macroscopic network organization and dynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural circuits must balance local connectivity constraints against the need for global integration. Here we introduce a minimal wiring rule motivated by synaptic crowding: as a neuron accumulates incoming connections, each additional synapse becomes progressively harder to form. This single-parameter model admits an exact finite-size solution for the induced in-degree distribution and yields simple scaling laws: mean connectivity grows only logarithmically with network size while variance remains bounded -- consistent with homeostatic regulation of synaptic density. When candidates are encountered in order of spatial proximity, the crowding rule produces a broad, approximately power-law distribution of connection lengths without prescribing any explicit distance-dependent wiring law; combined with shortcut rewiring, this yields networks with small-world characteristics. We further show that the induced degree statistics largely determine attractor basin boundaries in threshold network dynamics, while local clustering primarily modulates the prevalence of long-lived non-absorbing outcomes near these boundaries. The model provides testable predictions linking local developmental constraints to macroscopic network organization and dynamics.

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