Theoretical Framework for Prion Aggregation Kinetics: From Nucleation to Spatial Propagation

Theoretical Framework for Prion Aggregation Kinetics: From Nucleation to Spatial Propagation | 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 Theoretical Framework for Prion Aggregation Kinetics: From Nucleation to Spatial Propagation Abdsalam Bitar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8835911/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 Prion diseases are characterized by the templated conversion of native proteins into misfolded amyloid aggregates exhibiting sigmoidal growth kinetics with distinct lag and growth phases. We present a unified theoretical framework integrating four mathematical models: the Nucleated Polymerization Model (NPM) using moment equations, the Smoluchowski coagulation equation with size-resolved kinetics, the heterodimer reaction-diffusion system for spatial propagation, and the Fisher-Kolmogorov equation for traveling wave analysis. Theoretical analysis of the NPM reveals a lag phase of $39\pm5$ hours followed by exponential growth and monomer depletion to steady state. Size-resolved analysis predicts bimodal aggregate distributions with mean size increasing from 5 to 31 monomers while maintaining mass conservation. Spatial propagation analysis yields a propagation speed of $0.051$ mm/hr, consistent with the analytical prediction $v=2\sqrt{Dk}$ within 14% error. Stochastic analysis demonstrates significant heterogeneity in lag times (CV=0.35). Parameter sensitivity analysis identifies the critical nucleus size $n_0$ as the dominant control of aggregation onset, with larger nuclei dramatically increasing lag times due to combinatorial penalties. The theoretical framework reproduces experimental observations including concentration-dependent scaling ($\tau \propto c^{-0.15}$) and seeding effects. This theoretical synthesis provides a mathematical foundation for quantitative analysis of protein aggregation mechanisms, validating classical theoretical predictions while generating new insights into kinetic control points for therapeutic intervention. Full Text Additional Declarations No competing interests reported. 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-8835911","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":590064204,"identity":"5f452ea4-f9e2-49ca-8f41-c9c610325a4e","order_by":0,"name":"Abdsalam Bitar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+0lEQVRIiWNgGAWjYDACCQYDBoYCBgYDZhCvAoiZmRuI0AJCzCA9Z0BaGInVwgDUwtgGEiKghX928+YPPwzsos3Z+Q9+rpxXG83fDtTyo2IbbkvuHCuT7DFIzt3ZzMwseXbb8dwZhxkbGHvO3MZtzY0cMwYeA+bcDYeZGSQbtx3LbQBqYWZsw61F/kaO8cc/BvUgLcw/G+ccy51PSIvBjRwDaR6DwyAtbJKNDTVABgEthkC/SMsYHAf5xcyy4diB3I1ALQfx+UXudvPmj28qqnO38x98fLOhpi533vnDBx/8qMDjfTRwGEweIFo9ENSRongUjIJRMApGCAAAy+pc5bfprAMAAAAASUVORK5CYII=","orcid":"","institution":"Independent Research","correspondingAuthor":true,"prefix":"","firstName":"Abdsalam","middleName":"","lastName":"Bitar","suffix":""}],"badges":[],"createdAt":"2026-02-10 03:38:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8835911/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8835911/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104270141,"identity":"835ac097-4615-42c7-aec9-020b76db4157","added_by":"auto","created_at":"2026-03-09 21:54:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":809518,"visible":true,"origin":"","legend":"","description":"","filename":"CC.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8835911/v1_covered_efe2fbce-01c9-46d3-a9f6-bd2786eaae71.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Theoretical Framework for Prion Aggregation Kinetics: From Nucleation to Spatial Propagation","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8835911/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8835911/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Prion diseases are characterized by the templated conversion of native proteins into misfolded amyloid aggregates exhibiting sigmoidal growth kinetics with distinct lag and growth phases. We present a unified theoretical framework integrating four mathematical models: the Nucleated Polymerization Model (NPM) using moment equations, the Smoluchowski coagulation equation with size-resolved kinetics, the heterodimer reaction-diffusion system for spatial propagation, and the Fisher-Kolmogorov equation for traveling wave analysis. Theoretical analysis of the NPM reveals a lag phase of $39\\pm5$ hours followed by exponential growth and monomer depletion to steady state. Size-resolved analysis predicts bimodal aggregate distributions with mean size increasing from 5 to 31 monomers while maintaining mass conservation. Spatial propagation analysis yields a propagation speed of $0.051$ mm/hr, consistent with the analytical prediction $v=2\\sqrt{Dk}$ within 14\\% error. Stochastic analysis demonstrates significant heterogeneity in lag times (CV=0.35). Parameter sensitivity analysis identifies the critical nucleus size $n_0$ as the dominant control of aggregation onset, with larger nuclei dramatically increasing lag times due to combinatorial penalties. The theoretical framework reproduces experimental observations including concentration-dependent scaling ($\\tau \\propto c^{-0.15}$) and seeding effects. 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