Riemannian Tensor Analysis Identifies a Bifurcation state in the Single-Cell Transcriptomic Landscape of Parkinson's Disease

Riemannian Tensor Analysis Identifies a Bifurcation state in the Single-Cell Transcriptomic Landscape of Parkinson's Disease | 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 Riemannian Tensor Analysis Identifies a Bifurcation state in the Single-Cell Transcriptomic Landscape of Parkinson's Disease Jino Choi, Moonseok Choi, Kyusung Kim, Sarah Bauermeister, Do-Geun Kim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9698660/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 The transition from healthy aging to Parkinson's disease (PD) involves highly volatile transcriptomic rewiring that remains invisible to conventional mean-based analyses. To decode this critical tipping point, we integrated single-cell RNA-sequencing with a novel Log-Euclidean Riemannian tensor framework. By conceptualizing distinct transcriptomic states as symmetric positive definite (SPD) covariance tensors, we bypassed Euclidean geometric artifacts to accurately map the macroscopic network architecture of the human prefrontal cortex. Our analysis identified a highly unstable, intermediate bifurcation (BIF) state. Thermodynamic and topological validation demonstrated that this BIF state operates as a definitive geometric saddle point, characterized by maximal von Neumann entropy and positioned perfectly equidistant between the healthy (HC) and pathological (PD) Fréchet means on the non-Euclidean manifold. Furthermore, spectral deconstruction of differential covariance networks ( ) isolated the exact topological drivers of this transition—revealing the catastrophic structural collapse of core synaptic and electrophysiological hubs prior to overt pathological commitment. Ultimately, this ab initio geometric framework fundamentally redefines PD progression, providing a quantitative blueprint to intercept neurodegenerative trajectories during their final reversible window. Computational Biology Epidemiology Riemannian tensor analysis Bifurcation state Single-cell transcriptomics Gene covariance manifold Parkinson’s disease Full Text Additional Declarations The authors declare no competing interests. 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. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9698660","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":639418660,"identity":"11d2bf13-0229-44c2-8574-df50856b104f","order_by":0,"name":"Jino Choi","email":"","orcid":"","institution":"Korea Brain Research Institute","correspondingAuthor":false,"prefix":"","firstName":"Jino","middleName":"","lastName":"Choi","suffix":""},{"id":639420565,"identity":"0a471547-534b-47df-8257-e38ca63494a4","order_by":1,"name":"Moonseok Choi","email":"","orcid":"","institution":"Korea Brain Research 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