Analyzing Co-expression Networks with Network Skeleton Extraction

Analyzing Co-expression Networks with Network Skeleton Extraction | 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 Analyzing Co-expression Networks with Network Skeleton Extraction Eliza Duvall, Rosemary Braun This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8989183/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract Background : A central question in systems biology is to infer how genes work together to perform a specific function. While publicly available gene regulatory networks are commonly used to analyze experimental data, these networks may contain inaccuracies or inconsistencies across databases, especially for less well-studied organisms or systems where regulatory networks change over time. Data-driven network reconstruction from co-expression data is an appealing alternative, but requires sparsification to yield biologically representative networks. Threshold-based sparsification can lead to an excessively fragmented network, masking the relationship between genes and neglecting the ''strength of weak ties'', wherein a critical but weak relationship may serve as a vital link between two subnetworks. Results : Here we present Network Skeleton Extraction (NSE), a co-expression network generation method using spectral sparsification to sparsify co-expression statistics into minimal co-expression graphs. Spectral sparsification has the advantage of maintaining connections among genes in a manner that preserves the coarse-grained structure of the input graph. In our method, the degree of sparsification is optimized by predicting each gene's expression as a function of its connected genes at each sparsification level. This yields networks that are maximally sparse while still being predictive of gene expression. A probabilistic model also provides a null distribution of networks with similar spectral properties against which inferred networks can be compared. We illustrate the method by applying it to Xenopus transcriptome data from four cell types and six developmental stages to obtain networks specific to the organism, cell type, and developmental stage. Conclusions : By applying NSE to pre-defined gene sets in a phenotype-conditional manner, we can identify pathways whose coordination differs significantly across cell types and developmental stages. co-expression spectral sparsification network biology Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 11 Apr, 2026 Reviewers agreed at journal 20 Mar, 2026 Reviewers invited by journal 20 Mar, 2026 Editor assigned by journal 06 Mar, 2026 Editor invited by journal 06 Mar, 2026 Submission checks completed at journal 05 Mar, 2026 First submitted to journal 05 Mar, 2026 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-8989183","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":610146825,"identity":"6fb77442-785d-48b2-bc07-d2444d46f932","order_by":0,"name":"Eliza Duvall","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+0lEQVRIiWNgGAWjYFCCBCAusJADMZmRhJmxKkZoMZAwBpKMzSA+D7FaEhuI1sLPnmMm8cNAIn07e+/zx4VtNvb27L3PHjBUWIMMwQoke96YSfYYSOTu7Dlu2DyzLS2xh+e4uQHDmXScWgxu5Bgb8AC1bLiRxtjMu+1wAo9EGpsEY9thnFrsgVoM/wAdZgDR8t+eR/4ZUMs/3FoMJHIMHwNtSYBqOcDYI8EG1NKAW4vEmWeFj2UMJAw3nDnGOJv3X3JizxmgwxKOpRvj0sLfnrzh4JsKG3mD420Mn3nO2Nmztx9jk/hQYy2LSwsOkECa8lEwCkbBKBgFaAAAUkpR/NHnngIAAAAASUVORK5CYII=","orcid":"","institution":"Northwestern University","correspondingAuthor":true,"prefix":"","firstName":"Eliza","middleName":"","lastName":"Duvall","suffix":""},{"id":610146826,"identity":"18108ef5-0706-408f-9b5f-cbc84b3d56b0","order_by":1,"name":"Rosemary Braun","email":"","orcid":"","institution":"Northwestern University","correspondingAuthor":false,"prefix":"","firstName":"Rosemary","middleName":"","lastName":"Braun","suffix":""}],"badges":[],"createdAt":"2026-02-27 14:38:23","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8989183/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8989183/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105343895,"identity":"c51a3697-9f70-4f9c-bed8-d5dc3e793293","added_by":"auto","created_at":"2026-03-25 03:25:47","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1769752,"visible":true,"origin":"","legend":"","description":"","filename":"DuvallBraunAnalyzingCoexpressionNetworksNSE.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8989183/v1_covered_30ddf189-6f42-4b84-a8bd-352de6d6a0a8.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Analyzing Co-expression Networks with Network Skeleton Extraction","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"bmc-bioinformatics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"binf","sideBox":"Learn more about [BMC Bioinformatics](http://bmcbioinformatics.biomedcentral.com/)","snPcode":"","submissionUrl":"https://www.editorialmanager.com/binf","title":"BMC Bioinformatics","twitterHandle":"@BMC_Bioinformatics","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"em","reportingPortfolio":"BMC Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"co-expression, spectral sparsification, network biology","lastPublishedDoi":"10.21203/rs.3.rs-8989183/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8989183/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003eBackground\u003c/strong\u003e: A central question in systems biology is to infer how genes work together to perform a specific function. While publicly available gene regulatory networks are commonly used to analyze experimental data, these networks may contain inaccuracies or inconsistencies across databases, especially for less well-studied organisms or systems where regulatory networks change over time. Data-driven network reconstruction from co-expression data is an appealing alternative, but requires sparsification to yield biologically representative networks. Threshold-based sparsification can lead to an excessively fragmented network, masking the relationship between genes and neglecting the ''strength of weak ties'', wherein a critical but weak relationship may serve as a vital link between two subnetworks.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults\u003c/strong\u003e: Here we present Network Skeleton Extraction (NSE), a co-expression network generation method using spectral sparsification to sparsify co-expression statistics into minimal co-expression graphs. 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