Scale-Invariant Geometry of Neural Dynamics Across Biological Timescales

Scale-Invariant Geometry of Neural Dynamics Across Biological Timescales | 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 Research Article Scale-Invariant Geometry of Neural Dynamics Across Biological Timescales Prateek Vadde This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8032654/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Neural systems operate across temporal scales spanning microseconds to seconds, yet whether geometric principles unify dynamics across these scales remains unknown. We measured neural trajectory curvature —quantified via condition number of population activity—across biophysical ion channel models, spiking neural networks, rate-based recurrent networks, and human EEG (n=42). Curvature follows a power law 𝜅 ∝ 𝜏𝛼 across four orders of magnitude (𝛼 = −1.51 ± 0.08, 95% CI [−1.65, −1.40], 𝑅2 = 0.97, permutation p=0.018). This scaling replicates in an independent task dataset (n=14, Go/No-Go; 𝛼 = −1.86 ± 0.15, no significant task difference: Δ𝛼 = −0.29 ± 0.17, p=0.094) and generalizes cross-species (mouse single-unit recordings: 𝛼 = −0.64 ± 0.08, 𝑅2 = 0.935) and cross-modality (MEG: 𝛼 = −0.48). Theorydata calibration across seven manipulations shows strong correlation (Spearman 𝜌 = 0.929, p=0.0025). Trial-level curvature predicts reaction time (r=0.132, 𝑝 < 0.001, 𝑅2 = 1.7%). Computational modeling links scaling to dimensionality reduction in recurrent dynamics. As a biological validation, schizophrenia patients (n=27) show reduced curvature versus controls (n=56; Cohen’s d=-0.77, p=0.0014), correlating with symptom severity (r=0.48, p=0.021). These data demonstrate a scale-invariant geometric principle governing neural dynamics from ion channels to cognition, with quantifiable disruption in psychiatric illness. Computational Neuroscience scale invariance power laws neural dynamics trajectory geometry computational neuroscience Full Text Additional Declarations The authors declare no competing interests. Supplementary Files SupplementaryDataS1.csv Supplementary Datasheet S1 SupplementaryTableS2.csv Supplementary Table S2 SupplementaryTableS1.csv Supplementary table S1 SupplementaryFiguresAll.pdf All Supplementary Figures Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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We measured neural trajectory curvature —quantified via condition number of population activity—across biophysical ion channel models, spiking neural networks, rate-based recurrent networks, and human EEG (n=42). Curvature follows a power law 𝜅 ∝ 𝜏𝛼 across four orders of magnitude (𝛼 = −1.51 ± 0.08, 95% CI [−1.65, −1.40], 𝑅2 = 0.97, permutation p=0.018). This scaling replicates in an independent task dataset (n=14, Go/No-Go; 𝛼 = −1.86 ± 0.15, no significant task difference: Δ𝛼 = −0.29 ± 0.17, p=0.094) and generalizes cross-species (mouse single-unit recordings: 𝛼 = −0.64 ± 0.08, 𝑅2 = 0.935) and cross-modality (MEG: 𝛼 = −0.48). Theorydata calibration across seven manipulations shows strong correlation (Spearman 𝜌 = 0.929, p=0.0025). Trial-level curvature predicts reaction time (r=0.132, 𝑝 \u0026lt; 0.001, 𝑅2 = 1.7%). Computational modeling links scaling to dimensionality reduction in recurrent dynamics. As a biological validation, schizophrenia patients (n=27) show reduced curvature versus controls (n=56; Cohen’s d=-0.77, p=0.0014), correlating with symptom severity (r=0.48, p=0.021). 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