A Comprehensive Study of AFM Stiffness Measurements on Inclined Surfaces: Theoretical, Numerical, and Experimental Evaluation using a Hertz Approach

A Comprehensive Study of AFM Stiffness Measurements on Inclined Surfaces: Theoretical, Numerical, and Experimental Evaluation using a Hertz Approach | 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 A Comprehensive Study of AFM Stiffness Measurements on Inclined Surfaces: Theoretical, Numerical, and Experimental Evaluation using a Hertz Approach Anis Nassim Ahmine, Myriam Bdiri, Sophie Féréol, Redouane Fodil This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4744091/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 28 Oct, 2024 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract In the field of cellular health assessment, the mechanical properties of cells are crucial indicators. Atomic Force Microscopy (AFM) is a prominent nanoscale technique used for its significant benefits in analyzing cell mechanics. Traditional analysis of AFM data often relies on Hertz's law, which assumes a flat surface for the biological sample. However, this assumption does not always hold true due to the diverse geometries of cells. In this study, we present a new theoretical model that includes correction coefficients in Hertz's law to consider cone-like and spherical probes, addressing the local tilt at the probe-sample interface. We validated our model through Finite Element Analysis (FEA) simulations and experimental AFM measurements on tilted polyacrylamide gels. Our findings emphasize the importance of accounting for the local tilt in probe-sample contact to ensure accurate AFM measurements. This marks a significant advancement in our understanding of cell mechanics at the nanoscale. Biological sciences/Biophysics Physical sciences/Engineering AFM Hertz law Local tilt living cells Full Text Additional Declarations No competing interests reported. Supplementary Files AhmineetAl.2024SuplementaryMaterials.docx AnalyzedData.zip Cite Share Download PDF Status: Published Journal Publication published 28 Oct, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 30 Aug, 2024 Reviews received at journal 20 Aug, 2024 Reviews received at journal 15 Aug, 2024 Reviewers agreed at journal 05 Aug, 2024 Reviewers agreed at journal 03 Aug, 2024 Reviewers invited by journal 02 Aug, 2024 Editor assigned by journal 22 Jul, 2024 Editor invited by journal 22 Jul, 2024 Submission checks completed at journal 17 Jul, 2024 First submitted to journal 15 Jul, 2024 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-4744091","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":336167387,"identity":"6c90b460-8583-4914-9a46-4a7bc9d35e2d","order_by":0,"name":"Anis Nassim Ahmine","email":"","orcid":"","institution":"Univ Paris-Est Créteil, INSERM, U955 IMRB, \"Biology of the Neuromuscular System\" Team","correspondingAuthor":false,"prefix":"","firstName":"Anis","middleName":"Nassim","lastName":"Ahmine","suffix":""},{"id":336167388,"identity":"18b65059-ead2-4d29-8f20-5c6261a2b09a","order_by":1,"name":"Myriam Bdiri","email":"","orcid":"","institution":"Univ Paris-Est Créteil, CNRS, UMR 7182, Institut de Chimie et des Matériaux Paris-Est (ICMPE)","correspondingAuthor":false,"prefix":"","firstName":"Myriam","middleName":"","lastName":"Bdiri","suffix":""},{"id":336167389,"identity":"a372a5c0-0f50-4397-a9d3-6367c80eb0c4","order_by":2,"name":"Sophie Féréol","email":"","orcid":"","institution":"Univ Paris-Est Créteil, INSERM, U955 IMRB, \"Biology of the Neuromuscular System\" Team","correspondingAuthor":false,"prefix":"","firstName":"Sophie","middleName":"","lastName":"Féréol","suffix":""},{"id":336167390,"identity":"078f94bf-b786-4910-9806-7b2f4b89ec87","order_by":3,"name":"Redouane Fodil","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA90lEQVRIiWNgGAWjYHACAwjFfIBBIqHABipog1M5kha2BKAWgzSoYBpO5WhaGAwOE9Zi3t688TFPzR05BjbmgzceGJxPbJBuPviBIeEeTi0yZ44VG/Mce2bMwMaWbJFgcDuxQeZYsgRDQjFOLRISOWbSPGyHExvke8wkQFr238gxY2D8kYBbi/wboJZ/h+sb2HhAWs4lNkjkf2NgSMCjRYLHTJq37XACA0TLAaCWHDb8WnjSig3n9h02bIP4JdkY6BdjiQR8WtgPb3zw5ttheX5giN38UWEnCwyxhx8+4NECB2wIU4CYCA0oFpOmfBSMglEwCoY/AAChykqXaBhYCwAAAABJRU5ErkJggg==","orcid":"","institution":"Univ Paris-Est Créteil, INSERM, U955 IMRB, \"Biology of the Neuromuscular System\" Team","correspondingAuthor":true,"prefix":"","firstName":"Redouane","middleName":"","lastName":"Fodil","suffix":""}],"badges":[],"createdAt":"2024-07-15 15:56:05","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4744091/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4744091/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-75958-1","type":"published","date":"2024-10-28T16:13:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":68206513,"identity":"6d0a29c6-9757-4ac0-8be4-f96631260d8c","added_by":"auto","created_at":"2024-11-04 16:32:47","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":966569,"visible":true,"origin":"","legend":"","description":"","filename":"AhmineetAl.2024.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4744091/v1_covered_115b6ccd-80b1-4381-90c2-95706d470401.pdf"},{"id":62265555,"identity":"5a7b7a84-8985-4121-90de-61c51b644443","added_by":"auto","created_at":"2024-08-12 09:17:49","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":300782,"visible":true,"origin":"","legend":"","description":"","filename":"AhmineetAl.2024SuplementaryMaterials.docx","url":"https://assets-eu.researchsquare.com/files/rs-4744091/v1/00fdbe23275549895c17e7a1.docx"},{"id":62265554,"identity":"120c3a4b-bc04-4fd8-9bab-a0a7cfa79606","added_by":"auto","created_at":"2024-08-12 09:17:49","extension":"zip","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":62644,"visible":true,"origin":"","legend":"","description":"","filename":"AnalyzedData.zip","url":"https://assets-eu.researchsquare.com/files/rs-4744091/v1/6ec29fe72e3ed401a0f11f27.zip"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Comprehensive Study of AFM Stiffness Measurements on Inclined Surfaces: Theoretical, Numerical, and Experimental Evaluation using a Hertz Approach","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"AFM, Hertz law, Local tilt, living cells","lastPublishedDoi":"10.21203/rs.3.rs-4744091/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4744091/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn the field of cellular health assessment, the mechanical properties of cells are crucial indicators. Atomic Force Microscopy (AFM) is a prominent nanoscale technique used for its significant benefits in analyzing cell mechanics. Traditional analysis of AFM data often relies on Hertz's law, which assumes a flat surface for the biological sample. However, this assumption does not always hold true due to the diverse geometries of cells. In this study, we present a new theoretical model that includes correction coefficients in Hertz's law to consider cone-like and spherical probes, addressing the local tilt at the probe-sample interface. We validated our model through Finite Element Analysis (FEA) simulations and experimental AFM measurements on tilted polyacrylamide gels. Our findings emphasize the importance of accounting for the local tilt in probe-sample contact to ensure accurate AFM measurements. This marks a significant advancement in our understanding of cell mechanics at the nanoscale.\u003c/p\u003e","manuscriptTitle":"A Comprehensive Study of AFM Stiffness Measurements on Inclined Surfaces: Theoretical, Numerical, and Experimental Evaluation using a Hertz Approach","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-12 09:17:44","doi":"10.21203/rs.3.rs-4744091/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-08-30T18:50:37+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-08-20T18:52:29+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-08-15T17:43:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"34331311598219247077533595265624220674","date":"2024-08-05T12:56:13+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"178762088640422320695898335748540813137","date":"2024-08-03T14:38:40+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-08-02T14:45:51+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-07-22T16:08:41+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-07-22T15:41:49+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-17T23:15:46+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-07-15T15:54:29+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"36342781-247e-426b-b1b2-5dbbf6a51038","owner":[],"postedDate":"August 12th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":35603447,"name":"Biological sciences/Biophysics"},{"id":35603448,"name":"Physical sciences/Engineering"}],"tags":[],"updatedAt":"2024-11-04T16:22:37+00:00","versionOfRecord":{"articleIdentity":"rs-4744091","link":"https://doi.org/10.1038/s41598-024-75958-1","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-10-28 16:13:00","publishedOnDateReadable":"October 28th, 2024"},"versionCreatedAt":"2024-08-12 09:17:44","video":"","vorDoi":"10.1038/s41598-024-75958-1","vorDoiUrl":"https://doi.org/10.1038/s41598-024-75958-1","workflowStages":[]},"version":"v1","identity":"rs-4744091","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4744091","identity":"rs-4744091","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}