High-order Michaelis-Menten equations allow inference of hidden kinetic parameters in enzyme catalysis

High-order Michaelis-Menten equations allow inference of hidden kinetic parameters in enzyme catalysis | 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 Article High-order Michaelis-Menten equations allow inference of hidden kinetic parameters in enzyme catalysis Shlomi Reuveni, Divya Singh, Tal Robin, Michael Urbakh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4569854/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 20 Mar, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Single-molecule measurements provide a platform for investigating the dynamical properties of enzymatic reactions. To this end, the single-molecule Michaelis-Menten equation was instrumental as it asserts that the first moment of the enzymatic turnover time depends linearly on the reciprocal of the substrate concentration. This, in turn, provides robust and convenient means to determine the maximal turnover rate and the Michaelis-Menten constant. Yet, the information provided by these parameters is incomplete and does not allow full characterization of enzyme kinetics at the single molecule level. Here we show that the missing kinetic information can be accessed via a set of high-order Michaelis-Menten equations that we derive. These equations capture universal linear relations between the reciprocal of the substrate concentration and distinguished combinations of turnover time moments, essentially generalizing the Michaelis-Menten equation to moments of any order. We demonstrate how key observables such as the lifetime of the enzyme-substrate complex, the rate of substrate-enzyme binding, and the probability of successful product formation, can all be inferred using these high-order Michaelis-Menten equations. Physical sciences/Physics/Chemical physics Physical sciences/Chemistry/Theoretical chemistry Full Text Additional Declarations There is NO Competing Interest. Supplementary Files SMHighorderMichaelisMentenequationsNC.pdf Cite Share Download PDF Status: Published Journal Publication published 20 Mar, 2025 Read the published version in Nature Communications → 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. 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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-4569854","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":318873354,"identity":"382f8181-8328-4a0f-aa5e-54fd0aefce05","order_by":0,"name":"Shlomi Reuveni","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIiWNgGAWjYDACCeYGBgYDBgZ+dHEZ3FoYIVok26B8mDgPfi1AYHAMVQsDTi3ysxsbH90ouCdnfL/5mcTHNoY6/hkJjB9+MFjg1GJw52CzcY5BsbHZMTYzyRlnGCQkbiQwS/bgcZiBRGKbdI5BQuK2Ywxm0jwVQIfdSGCQxucX+RkQLfWb29i/Sf8xYJCQB9ryG6/3b0C0JBiw8ZhJMwBtMbiRwIbXFoMbiSC/JBjOOJZTbNlzRkJy45mHbZY9Bvgclnzwcc6fBHn+5uMbb/xss+GXO558+MaPijo5nA5DA6BogUbuKBgFo2AUjALyAQDNpUnSfhsISgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-2292-8005","institution":"Tel Aviv University","correspondingAuthor":true,"prefix":"","firstName":"Shlomi","middleName":"","lastName":"Reuveni","suffix":""},{"id":318873355,"identity":"5c68116c-8454-40d0-a622-42d13a853a39","order_by":1,"name":"Divya Singh","email":"","orcid":"","institution":"Tel Aviv University","correspondingAuthor":false,"prefix":"","firstName":"Divya","middleName":"","lastName":"Singh","suffix":""},{"id":318873356,"identity":"f5a79e78-b7d5-431f-a1c9-bc4872884e3b","order_by":2,"name":"Tal Robin","email":"","orcid":"","institution":"Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York, NY, USA.","correspondingAuthor":false,"prefix":"","firstName":"Tal","middleName":"","lastName":"Robin","suffix":""},{"id":318873357,"identity":"0a8f6abd-1167-4966-8bd8-51e8992138ba","order_by":3,"name":"Michael Urbakh","email":"","orcid":"https://orcid.org/0000-0002-3959-5414","institution":"Tel Aviv University","correspondingAuthor":false,"prefix":"","firstName":"Michael","middleName":"","lastName":"Urbakh","suffix":""}],"badges":[],"createdAt":"2024-06-12 11:26:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4569854/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4569854/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41467-025-57327-2","type":"published","date":"2025-03-20T04:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":78942232,"identity":"6eebb202-85c2-4368-b415-a8c032ef0ec5","added_by":"auto","created_at":"2025-03-21 07:06:17","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1291995,"visible":true,"origin":"","legend":"","description":"","filename":"HighorderMichaelisMentenequationsNC.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4569854/v1_covered_696eeee2-743f-4bec-8f6c-2949768e4733.pdf"},{"id":59071009,"identity":"68b7c661-42bc-49a7-8518-08fd207d677c","added_by":"auto","created_at":"2024-06-26 04:38:45","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":895129,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"SMHighorderMichaelisMentenequationsNC.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4569854/v1/240faf8bd43af59bffbe0029.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"High-order Michaelis-Menten equations allow inference of hidden kinetic parameters in enzyme catalysis","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4569854/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4569854/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Single-molecule measurements provide a platform for investigating the dynamical properties of enzymatic reactions. 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