Selection for folding stability predicts observed covariation between protein positions in the PDB

Selection for folding stability predicts observed covariation between protein positions in the PDB | 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 Selection for folding stability predicts observed covariation between protein positions in the PDB Fatemeh Saebi, Jonas Minning, Ugo Bastolla This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9486392/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 We present the Stability constrained model of protein evolution (SCPE) in the pairwise approximation. This model enforces protein folding stability, both against unfolding and against misfolding, which we predict with a statistical physics model based on contact interactions. We assume that the multivariate distribution of the protein family is described by the Potts model,whose pairwise couplings extend our previous model that only considered single-site terms, and predict the corresponding parameters as in our previous work, by requiring that the amino acid distribution has minimal Kullback-Leibler divergence with respect to the global, not site-specific distribution, while constraining protein folding stability. Adopting the zero mean condition to fix the couplings, we can compute the amino acid distributions at any pairs of sites by inverting the rescaled coupling matrix, allowing explicit computations in affordable time. We then solve the SCPE pairwise model in the small coupling approximation (SCA), which neglects the indirect couplings through other sites. Despite being inaccurate, the SCA provides an explicit formula for the pairwise couplings that gives insight on selective forces. For pairs of sites in contact, the predicted couplings are inversely related with the zero mean of the contact energies of the amino acid pairs, while for pairs not in contact this relation is positive, i.e. destabilizing pairs of amino acids are favoured by negative design at short-range pairs that can form wrong contacts with high probability. We test these predictions on a representative set of the Protein Data Bank, assessing the influence of sites in the core versus the surface of the protein and of protein size and hydrophobicity, which increase the importance of negative design. Our results suggest that a large number of couplings are influenced by negative design, but the strongest couplings correspond to native contacts. Finally, we determine the global, not site-specific couplings, which are not influenced by selection for protein folding stability. We interpret them as the result of variations of global (not site-specific) mutational or selective forces across the lineages where the proteins evolve. Consistently, the strongest global couplings are self-couplings between equal amino acids, which are influenced by identical mutational and selective forces. Cys-Cys, which form disulfide bridges, shows the strongest global coupling, followed by pairs of metabolically costly amino acids (Trp-Trp, Tyr-Tyr, Trp-Tyr) and by positively charged amino acids that tend to interact with nucleic acids (Lys-Lys, Arg-Arg). Ser, Thr, Asn and Gln form a cluster of globally correlated polar amino acids. 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. 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-9486392","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":631101858,"identity":"6ae0a75f-05a1-46d2-b9ed-5e7bcdc60df4","order_by":0,"name":"Fatemeh Saebi","email":"","orcid":"","institution":"Spanish National Research Council","correspondingAuthor":false,"prefix":"","firstName":"Fatemeh","middleName":"","lastName":"Saebi","suffix":""},{"id":631101859,"identity":"710638bc-a4df-4f7b-944c-b324ad80361e","order_by":1,"name":"Jonas Minning","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Jonas","middleName":"","lastName":"Minning","suffix":""},{"id":631101866,"identity":"6cb1c3d0-4a0b-4d87-9127-58af95cc2d2a","order_by":2,"name":"Ugo Bastolla","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIie2PMQrCMBRAfxHSJdT1S8VeoSKog9irVARdMkvHQqGewXN4gYigSw4QqYsWnCsuutlkFIm6OeQNnwz/kfcBLJZ/BPUctsFNiX6SrxQOSIHynxWMPy9rwiIrb1WCtLkqL2cJ48hzuXO6m5Tjro9cIMViNugxmE5yGjd61KTIuA+bvA4rGPEZ8JggEN8YJue3SinBQWglqhX3YQyTLESlhJJqxcnrX8AU1jqKBYr6lq5Qt4TqlknmmxSvWK6rJBl1OvvtpWTJOAqW283VFPbaqYaTfi9YLBaL5S1PTR5F7OlC88YAAAAASUVORK5CYII=","orcid":"","institution":"Spanish National Research Council","correspondingAuthor":true,"prefix":"","firstName":"Ugo","middleName":"","lastName":"Bastolla","suffix":""}],"badges":[],"createdAt":"2026-04-21 15:23:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9486392/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9486392/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108182614,"identity":"10efac1b-6912-457d-bff6-e6cc2193ef44","added_by":"auto","created_at":"2026-04-30 08:59:27","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":658608,"visible":true,"origin":"","legend":"","description":"","filename":"PaperCorrelatedselection.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9486392/v1_covered_871b407a-607e-419c-a584-a0a3593d0880.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Selection for folding stability predicts observed covariation between protein positions in the PDB","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-9486392/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9486392/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe present the Stability constrained model of protein evolution (SCPE) in the pairwise approximation. This model enforces protein folding stability, both against unfolding and against misfolding, which we predict with a statistical physics model based on contact interactions.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe assume that the multivariate distribution of the protein family is described by the Potts model,whose pairwise couplings extend our previous model that only considered single-site terms, and predict the corresponding parameters as in our previous work, by requiring that the amino acid distribution has minimal Kullback-Leibler divergence with respect to the global, not site-specific distribution, while constraining protein folding stability. Adopting the zero mean condition to fix the couplings, we can compute the amino acid distributions at any pairs of sites by inverting the rescaled coupling matrix, allowing explicit computations in affordable time.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe then solve the SCPE pairwise model in the small coupling approximation (SCA), which neglects the indirect couplings through other sites. Despite being inaccurate, the SCA provides an explicit formula for the pairwise couplings that gives insight on selective forces. For pairs of sites in contact, the predicted couplings are inversely related with the zero mean of the contact energies of the amino acid pairs, while for pairs not in contact this relation is positive, i.e. destabilizing pairs of amino acids are favoured by negative design at short-range pairs that can form wrong contacts with high probability.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe test these predictions on a representative set of the Protein Data Bank, assessing the influence of sites in the core versus the surface of the protein and of protein size and hydrophobicity, which increase the importance of negative design. Our results suggest that a large number of couplings are influenced by negative design, but the strongest couplings correspond to native contacts.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFinally, we determine the global, not site-specific couplings, which are not influenced by selection for protein folding stability. We interpret them as the result of variations of global (not site-specific) mutational or selective forces across the lineages where the proteins evolve. Consistently, the strongest global couplings are self-couplings between equal amino acids, which are influenced by identical mutational and selective forces. Cys-Cys, which form disulfide bridges, shows the strongest global coupling, followed by pairs of metabolically costly amino acids (Trp-Trp, Tyr-Tyr, Trp-Tyr) and by positively charged amino acids that tend to interact with nucleic acids (Lys-Lys, Arg-Arg). 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