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

TL;DR

This paper introduces a simple model based on synaptic crowding that explains how neural networks develop small-world properties and specific dynamic behaviors, linking local constraints to global network features.

Contribution

The authors present an analytically solvable model of synaptic wiring that predicts network structure and dynamics from local synaptic constraints, a novel approach in neural network modeling.

Findings

Mean connectivity grows logarithmically with network size.

Networks exhibit small-world features without explicit distance rules.

Degree distribution influences attractor basin boundaries.

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.