Synaptic crowding as an exactly solvable wiring rule: degree statistics, emergent small-world wiring, and threshold-network basins

Analytically tractable model of synaptic crowding explains emergent small-world structure and network dynamics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Analytically tractable model of synaptic crowding explains emergent small-world structure and network dynamics Makoto Fukushima This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8509424/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions 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 yields exact, closed-form predictions for network connectivity statistics at any system size for synchronous threshold dynamics. We show that mean connectivity grows only logarithmically with network size while variance remains bounded consistent with homeostatic regulation of synaptic density. When combined with spatially local wiring, the crowding rule produces small-world networks with broad, multi-scale connection-length distributions, without requiring an explicit distance-dependent wiring law. We further demonstrate that the induced connectivity statistics largely determine attractor basin boundaries in threshold network dynamics, while local clustering primarily modulates the prevalence of additional dynamical states near these boundaries. The model provides falsifiable predictions linking local developmental constraints to macroscopic network organization and dynamics, offering a minimal baseline for interpreting connectomic data and designing sparse artificial networks. Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Complex networks Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Statistical physics Full Text Additional Declarations The authors declare no competing interests. Supplementary Files SupplementarySoftware1generatefigures.zip Supplementary Software Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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