Theoretical estimation of transcript complexity via the condition number of a random matrix

Theoretical estimation of transcript complexity via the condition number of a random matrix | 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 Method Article Theoretical estimation of transcript complexity via the condition number of a random matrix Bo Zhang, Yaohui Guo, Guoping Liu, Meng Zou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6026688/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 Transcript quantification varies substantially across classical tools like Cufflinks, StringTie, featureCounts, and RSEM, undermining reliability and reproducibility. To address this, we propose a systematic framework for evaluating transcript complexity by calculating the condition number of a gene-specific random matrix, which bounds quantification error and reflects tool discrepancies. Specifically, genes with low condition numbers consistently show high correlations (PCC > 0.8) across tools, whereas genes with high condition numbers exhibit poorer correlations, reflecting tool-specific biases. Longer reads reduce complexity, and as reads lengthen, the condition number approaches 1. Additionally, hybrid-seq reduces quantification error for genes with high condition numbers in short-read data and low condition numbers in long-read data. Notably, unique mapping strategies introduce quantification errors exceeding those of multiple mapping approaches by over 10-fold, even for low-complexity genes, but this discrepancy disappears with sufficiently long read lengths. Integrating transcript complexity metrics with sequencing strategies is essential for improving RNA-seq quantification accuracy. Transcript complexity Condition number Random matrix hybrid-seq unique mapping Full Text Additional Declarations No competing interests reported. Supplementary Files Supplementarynotes.pdf 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. 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-6026688","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Method Article","associatedPublications":[],"authors":[{"id":415786142,"identity":"46fd9107-6abf-4e85-b00d-f393159a1a7b","order_by":0,"name":"Bo Zhang","email":"","orcid":"","institution":"Huazhong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Bo","middleName":"","lastName":"Zhang","suffix":""},{"id":415786143,"identity":"7b303387-292c-45fb-acce-fb1fea107673","order_by":1,"name":"Yaohui Guo","email":"","orcid":"","institution":"Huazhong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Yaohui","middleName":"","lastName":"Guo","suffix":""},{"id":415786144,"identity":"1c6ba206-523a-4d92-9de5-603ae4c8df0d","order_by":2,"name":"Guoping Liu","email":"","orcid":"","institution":"Huazhong University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Guoping","middleName":"","lastName":"Liu","suffix":""},{"id":415786145,"identity":"417a4d1d-f6f5-45e5-97c2-e3f8eb0de226","order_by":3,"name":"Meng Zou","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA10lEQVRIiWNgGAWjYBADOQMIzUy8FmOgFsYGkrQkbiBai3x7j+mGjztq07dLpD9/wFBhndjAfvYAXi2MPWfMbs48czx354wcwwaGM+mJDTx5CXi1MEvkmN3mbTuWu+FGDmMDY9vhxAYJHgO8WthAWv62HUs3uJH+sIHxHxFaeEBaGNtqEgxuJBg2MDYQoUWC51jZzd62A4YbzrwxnJFwLN24jScHvxb59uZtN3621ckbHE9/8OFDjbVsP/sZ/Fqg4DCESgD5jhj1QFBHpLpRMApGwSgYkQAAKyVJSK/XUfoAAAAASUVORK5CYII=","orcid":"","institution":"Huazhong University of Science and Technology","correspondingAuthor":true,"prefix":"","firstName":"Meng","middleName":"","lastName":"Zou","suffix":""}],"badges":[],"createdAt":"2025-02-14 02:38:08","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6026688/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6026688/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":77152858,"identity":"934188d0-e267-49a9-aba9-ac2ed107c774","added_by":"auto","created_at":"2025-02-25 15:31:48","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1602551,"visible":true,"origin":"","legend":"","description":"","filename":"TCCN.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6026688/v1_covered_e1a9a78b-4a09-41d5-b22c-56df33c20900.pdf"},{"id":76444397,"identity":"8b88da89-e59f-4104-9e39-b87fb8f6cd34","added_by":"auto","created_at":"2025-02-17 08:46:33","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":1327986,"visible":true,"origin":"","legend":"","description":"","filename":"Supplementarynotes.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6026688/v1/0a77210e3acca3cee3215b48.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Theoretical estimation of transcript complexity via the condition number of a random matrix","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":"Transcript complexity, Condition number, Random matrix, hybrid-seq, unique mapping","lastPublishedDoi":"10.21203/rs.3.rs-6026688/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6026688/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Transcript quantification varies substantially across classical tools like Cufflinks, StringTie, featureCounts, and RSEM, undermining reliability and reproducibility. 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