{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T10:55:17Z","timestamp":1767178517021,"version":"build-2238731810"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1013305","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T00:00:00Z","timestamp":1754438400000}}],"reference-count":56,"publisher":"Public Library of Science (PLoS)","issue":"7","license":[{"start":{"date-parts":[[2025,7,31]],"date-time":"2025-07-31T00:00:00Z","timestamp":1753920000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"EPSRC Centre for Doctoral Training in Mathematical Modelling, Analysis and Computation","award":["EP\/S023291\/1"],"award-info":[{"award-number":["EP\/S023291\/1"]}]},{"name":"Dr Perry James (Jim) Browne Research Centre on Mathematics and its Applications"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>We derive and simulate a mathematical model for mechanotransduction related to the Rho GTPase signalling pathway. The model addresses the bidirectional coupling between signalling processes and cell mechanics. A numerical method based on bulk-surface finite elements is proposed for the approximation of the coupled system of nonlinear reaction-diffusion equations, defined inside the cell and on the cell membrane, and the equations of elasticity. Our simulation results illustrate novel emergent features such as the strong dependence of the dynamics on cell shape, a threshold-like response to changes in substrate stiffness, and the fact that coupling mechanics and signalling can lead to the robustness of cell deformation to larger changes in substrate stiffness, ensuring mechanical homeostasis in agreement with experiments.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1013305","type":"journal-article","created":{"date-parts":[[2025,7,31]],"date-time":"2025-07-31T17:55:47Z","timestamp":1753984547000},"page":"e1013305","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Mathematical modelling of mechanotransduction via RhoA signalling pathways"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-1068-7558","authenticated-orcid":true,"given":"Sofie","family":"Verhees","sequence":"first","affiliation":[]},{"given":"Chandrasekhar","family":"Venkataraman","sequence":"additional","affiliation":[]},{"given":"Mariya","family":"Ptashnyk","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2025,7,31]]},"reference":[{"issue":"11","key":"pcbi.1013305.ref001","doi-asserted-by":"crossref","first-page":"1852","DOI":"10.1242\/jcs.046870","article-title":"A FAK-p120RasGAP-p190RhoGAP complex regulates polarity in migrating cells","volume":"122","author":"A Tomar","year":"2009","journal-title":"J Cell Sci."},{"key":"pcbi.1013305.ref002","doi-asserted-by":"crossref","first-page":"102066","DOI":"10.1016\/j.ceb.2022.01.011","article-title":"Signalling dynamics, cell decisions, and homeostatic control in health and disease","volume":"75","author":"PO Valls","year":"2022","journal-title":"Curr Opinon Cell Biol."},{"issue":"1","key":"pcbi.1013305.ref003","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1038\/s41580-020-00306-w","article-title":"Crosstalk between mechanotransduction and metabolism","volume":"22","author":"P Romani","year":"2020","journal-title":"Nat Rev Mol Cell Biol."},{"key":"pcbi.1013305.ref004","article-title":"Mechanoregulation of YAP and TAZ in cellular homeostasis and disease progression","volume":"9","author":"X Cai","year":"2021","journal-title":"Front Cell Dev Biol."},{"issue":"12","key":"pcbi.1013305.ref005","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1038\/nrm3896","article-title":"Mechanotransduction and extracellular matrix homeostasis","volume":"15","author":"JD Humphrey","year":"2014","journal-title":"Nat Rev Mol Cell Biol."},{"issue":"7","key":"pcbi.1013305.ref006","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1038\/s41580-023-00583-1","article-title":"Cell\u2013extracellular matrix mechanotransduction in 3D","volume":"24","author":"A Saraswathibhatla","year":"2023","journal-title":"Nat Rev Mol Cell Biol."},{"issue":"1779","key":"pcbi.1013305.ref007","doi-asserted-by":"crossref","first-page":"20180229","DOI":"10.1098\/rstb.2018.0229","article-title":"Mechanotransduction: from the cell surface to the nucleus via RhoA","volume":"374","author":"K Burridge","year":"2019","journal-title":"Phil Trans R Soc B."},{"key":"pcbi.1013305.ref008","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.actbio.2023.01.039","article-title":"Cell response to mechanical microenvironment cues via Rho signaling: from mechanobiology to mechanomedicine","volume":"159","author":"N Xie","year":"2023","journal-title":"Acta Biomaterialia."},{"key":"pcbi.1013305.ref009","doi-asserted-by":"crossref","DOI":"10.3389\/fphys.2018.00824","article-title":"Cellular mechanotransduction: from tension to function","volume":"9","author":"F Martino","year":"2018","journal-title":"Front Physiol."},{"issue":"4","key":"pcbi.1013305.ref010","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1083\/jcb.201609037","article-title":"Integrin-mediated mechanotransduction","volume":"215","author":"Z Sun","year":"2016","journal-title":"J Cell Biol."},{"key":"pcbi.1013305.ref011","doi-asserted-by":"crossref","first-page":"102208","DOI":"10.1016\/j.ceb.2023.102208","article-title":"Cellular mechanosignaling for sensing and transducing matrix rigidity","volume":"83","author":"KM Young","year":"2023","journal-title":"Curr Opinion Cell Biol."},{"issue":"4","key":"pcbi.1013305.ref012","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1093\/bib\/bbl043","article-title":"Computational methodologies for modelling, analysis and simulation of signalling networks","volume":"7","author":"D Gilbert","year":"2006","journal-title":"Brief Bioinform."},{"key":"pcbi.1013305.ref013","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1007\/s00285-013-0712-4","article-title":"Mathematical modelling and computational study of two-dimensional and three-dimensional dynamics of receptor\u2013ligand interactions in signalling response mechanisms","volume":"69","author":"P Garc\u00eda-Penarrubia","year":"2014","journal-title":"J Math Biol."},{"issue":"2","key":"pcbi.1013305.ref014","doi-asserted-by":"crossref","first-page":"851","DOI":"10.1137\/18M1185661","article-title":"Multiscale analysis and simulation of a signaling process with surface diffusion","volume":"18","author":"M Ptashnyk","year":"2020","journal-title":"Multiscale Model Simul."},{"key":"pcbi.1013305.ref015","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.plrev.2017.06.016","article-title":"Cellular mechanosensing of the biophysical microenvironment: a review of mathematical models of biophysical regulation of cell responses","author":"B Cheng","year":"2017","journal-title":"Physics of Life Reviews."},{"issue":"11","key":"pcbi.1013305.ref016","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1088\/1367-2630\/9\/11\/425","article-title":"Coupling biochemistry and mechanics in cell adhesion: a model for inhomogeneous stress fiber contraction","volume":"9","author":"A Besser","year":"2007","journal-title":"New J Phys."},{"issue":"8","key":"pcbi.1013305.ref017","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1093\/intbio\/zyab012","article-title":"Spatiotemporal model of cellular mechanotransduction via Rho and YAP","volume":"13","author":"JK Novev","year":"2021","journal-title":"Integrat Biol."},{"issue":"20","key":"pcbi.1013305.ref018","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.2021571118","article-title":"A spatial model of YAP\/TAZ signaling reveals how stiffness, dimensionality, and shape contribute to emergent outcomes","volume":"118","author":"KE Scott","year":"2021","journal-title":"Proc Natl Acad Sci USA."},{"issue":"1","key":"pcbi.1013305.ref019","article-title":"Structurally governed cell mechanotransduction through multiscale modeling","volume":"5","author":"J Kang","year":"2015","journal-title":"Sci Rep."},{"issue":"18","key":"pcbi.1013305.ref020","doi-asserted-by":"crossref","first-page":"10140","DOI":"10.1073\/pnas.96.18.10140","article-title":"Pearling in cells: a clue to understanding cell shape","volume":"96","author":"R Bar-Ziv","year":"1999","journal-title":"Proc Natl Acad Sci USA."},{"issue":"12","key":"pcbi.1013305.ref021","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.105.128101","article-title":"Single cells spreading on a protein lattice adopt an energy minimizing shape","volume":"105","author":"B Vianay","year":"2010","journal-title":"Phys Rev Lett."},{"issue":"11","key":"pcbi.1013305.ref022","doi-asserted-by":"crossref","first-page":"2340","DOI":"10.1016\/j.bpj.2014.04.036","article-title":"Dynamics of cell shape and forces on micropatterned substrates predicted by a cellular Potts model","volume":"106","author":"PJ Albert","year":"2014","journal-title":"Biophys J."},{"issue":"11","key":"pcbi.1013305.ref023","doi-asserted-by":"crossref","first-page":"2540","DOI":"10.1016\/j.bpj.2016.04.040","article-title":"A computational Model of YAP\/TAZ Mechanosensing","volume":"110","author":"M Sun","year":"2016","journal-title":"Biophys J."},{"issue":"20","key":"pcbi.1013305.ref024","doi-asserted-by":"crossref","first-page":"4360","DOI":"10.1016\/j.bpj.2021.09.009","article-title":"Exploring the influence of cytosolic and membrane FAK activation on YAP\/TAZ nuclear translocation","volume":"120","author":"KS Eroum\u00e9","year":"2021","journal-title":"Biophys J."},{"key":"pcbi.1013305.ref025","doi-asserted-by":"crossref","unstructured":"Gould PL. Introduction to linear elasticity. New York; Springer; 2013. https:\/\/doi.org\/10.1007\/978-1-4614-4833-4","DOI":"10.1007\/978-1-4614-4833-4"},{"key":"pcbi.1013305.ref026","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1017\/S0962492913000056","article-title":"Finite element methods for surface PDEs","volume":"22","author":"G Dziuk","year":"2013","journal-title":"Acta Numerica."},{"key":"pcbi.1013305.ref027","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.semcdb.2016.09.004","article-title":"Cellular adaptation to biomechanical stress across length scales in tissue homeostasis and disease","volume":"67","author":"PM Gilbert","year":"2017","journal-title":"Sem1in Cell Develop Biol."},{"issue":"1","key":"pcbi.1013305.ref028","doi-asserted-by":"crossref","first-page":"18374","DOI":"10.1038\/s41598-023-44835-8","article-title":"Environmental stiffness restores mechanical homeostasis in vimentin-depleted cells","volume":"13","author":"J Grolleman","year":"2023","journal-title":"Sci Rep."},{"key":"pcbi.1013305.ref029","doi-asserted-by":"crossref","first-page":"111965","DOI":"10.1016\/j.jtbi.2024.111965","article-title":"A theoretical model for focal adhesion and cytoskeleton formation in non-motile cells","volume":"596","author":"GR McNicol","year":"2025","journal-title":"J Theor Biol."},{"key":"pcbi.1013305.ref030","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1038\/s41392-023-01501-9","article-title":"Cellular mechanotransduction in health and diseases: from molecular mechanism to therapeutic targets","volume":"8","author":"X Di","year":"2023","journal-title":"Sig Transduct Target Ther."},{"issue":"1","key":"pcbi.1013305.ref031","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.ceb.2006.12.002","article-title":"The cell as a material","volume":"19","author":"KE Kasza","year":"2007","journal-title":"Curr Opin Cell Biol."},{"issue":"3","key":"pcbi.1013305.ref032","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1038\/nmat3517","article-title":"The cytoplasm of living cells behaves as a poroelastic material","volume":"12","author":"E Moeendarbary","year":"2013","journal-title":"Nat Mater."},{"issue":"3","key":"pcbi.1013305.ref033","doi-asserted-by":"crossref","first-page":"035015","DOI":"10.1088\/1367-2630\/15\/3\/035015","article-title":"Controlling cell\u2013matrix traction forces by extracellular geometry","volume":"15","author":"S Banerjee","year":"2013","journal-title":"New J Phys."},{"issue":"4","key":"pcbi.1013305.ref034","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1016\/j.bpj.2014.06.045","article-title":"Geometry regulates traction stresses in adherent cells","volume":"107","author":"PW Oakes","year":"2014","journal-title":"Biophys J."},{"issue":"10","key":"pcbi.1013305.ref035","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1140\/epje\/i2020-11988-1","article-title":"Reversible elastic phase field approach and application to cell monolayers","volume":"43","author":"R Chojowski","year":"2020","journal-title":"Eur Phys J E."},{"issue":"1","key":"pcbi.1013305.ref036","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/j.bpj.2022.11.2943","article-title":"Predicting YAP\/TAZ nuclear translocation in response to ECM mechanosensing","volume":"122","author":"B Cheng","year":"2023","journal-title":"Biophys J."},{"key":"pcbi.1013305.ref037","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.ceb.2016.03.006","article-title":"Mechanotransduction and nuclear function","volume":"40","author":"DM Graham","year":"2016","journal-title":"Curr Opinion Cell Biol."},{"issue":"5675","key":"pcbi.1013305.ref038","doi-asserted-by":"crossref","first-page":"1301","DOI":"10.1126\/science.1095087","article-title":"Elastic behavior of cross-linked and bundled actin networks","volume":"304","author":"ML Gardel","year":"2004","journal-title":"Science."},{"issue":"1","key":"pcbi.1013305.ref039","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.yexcr.2015.10.029","article-title":"Focal adhesions, stress fibers and mechanical tension","volume":"343","author":"K Burridge","year":"2016","journal-title":"Exp Cell Res."},{"issue":"1","key":"pcbi.1013305.ref040","doi-asserted-by":"crossref","first-page":"8720","DOI":"10.1038\/ncomms9720","article-title":"Local 3D matrix microenvironment regulates cell migration through spatiotemporal dynamics of contractility-dependent adhesions","volume":"6","author":"AD Doyle","year":"2015","journal-title":"Nat Commun."},{"issue":"10","key":"pcbi.1013305.ref041","doi-asserted-by":"crossref","first-page":"1801","DOI":"10.1242\/jcs.001586","article-title":"Force activates smooth muscle \u03b1-actin promoter activity through the Rho signaling pathway","volume":"120","author":"X-H Zhao","year":"2007","journal-title":"J Cell Sci."},{"issue":"8","key":"pcbi.1013305.ref042","doi-asserted-by":"crossref","first-page":"1968","DOI":"10.1016\/j.bpj.2020.03.002","article-title":"The poisson ratio of the cellular actin cortex is frequency dependent","volume":"118","author":"M Mokbel","year":"2020","journal-title":"Biophys J."},{"issue":"6","key":"pcbi.1013305.ref043","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.1083\/jcb.133.6.1403","article-title":"Rho-stimulated contractility drives the formation of stress fibers and focal adhesions.","volume":"133","author":"M Chrzanowska-Wodnicka","year":"1996","journal-title":"J Cell Biol."},{"issue":"7","key":"pcbi.1013305.ref044","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0181085","article-title":"Engineered extracellular matrices with controlled mechanics modulate renal proximal tubular cell epithelialization","volume":"12","author":"JA Beamish","year":"2017","journal-title":"PLoS ONE."},{"issue":"2","key":"pcbi.1013305.ref045","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/S0006-291X(03)01165-3","article-title":"Cell shape provides global control of focal adhesion assembly","volume":"307","author":"CS Chen","year":"2003","journal-title":"Biochem Biophys Res Commun."},{"issue":"4","key":"pcbi.1013305.ref046","doi-asserted-by":"crossref","first-page":"483","DOI":"10.1016\/S1534-5807(04)00075-9","article-title":"Cell shape, cytoskeletal tension, and RhoA regulate stem cell lineage commitment","volume":"6","author":"R McBeath","year":"2004","journal-title":"Developm Cell."},{"key":"pcbi.1013305.ref047","doi-asserted-by":"crossref","unstructured":"Kassab GS. Biomechanical homeostasis. Coronary circulation. Springer; 2024. p. 1\u201343. https:\/\/doi.org\/10.1007\/978-3-031-62652-4_1","DOI":"10.1007\/978-3-031-62652-4_1"},{"issue":"4","key":"pcbi.1013305.ref048","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1016\/j.bpj.2023.01.011","article-title":"Cell size and actin architecture determine force generation in optogenetically activated cells","volume":"122","author":"T Andersen","year":"2023","journal-title":"Biophys J."},{"key":"pcbi.1013305.ref049","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/j.semcdb.2016.09.004","article-title":"Cellular adaptation to biomechanical stress across length scales in tissue homeostasis and disease","volume":"67","author":"PM Gilbert","year":"2017","journal-title":"Seminars Cell Develop Biol."},{"issue":"34","key":"pcbi.1013305.ref050","doi-asserted-by":"crossref","DOI":"10.1126\/sciadv.adi6286","article-title":"Cellular stiffness sensing through talin 1 in tissue mechanical homeostasis","volume":"10","author":"M Chanduri","year":"2024","journal-title":"Sci Adv."},{"issue":"4","key":"pcbi.1013305.ref051","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1089\/ten.teb.2021.0151","article-title":"Characterizing and engineering biomimetic materials for viscoelastic mechanotransduction studies","volume":"28","author":"L Cacopardo","year":"2022","journal-title":"Tissue Eng Part B: Rev."},{"issue":"8","key":"pcbi.1013305.ref052","doi-asserted-by":"crossref","first-page":"1114","DOI":"10.1016\/j.jbiomech.2009.02.012","article-title":"Endothelial actin and cell stiffness is modulated by substrate stiffness in 2D and 3D","volume":"42","author":"FJ Byfield","year":"2009","journal-title":"J Biomech."},{"issue":"1","key":"pcbi.1013305.ref053","doi-asserted-by":"crossref","DOI":"10.1038\/ncomms7365","article-title":"Substrate stress relaxation regulates cell spreading","volume":"6","author":"O Chaudhuri","year":"2015","journal-title":"Nat Commun."},{"issue":"9","key":"pcbi.1013305.ref054","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1038\/s41563-022-01294-2","article-title":"Directed cell migration towards softer environments","volume":"21","author":"A Isomursu","year":"2022","journal-title":"Nat Mater."},{"issue":"3","key":"pcbi.1013305.ref055","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1002\/smll.201100934","article-title":"Physical aspects of cell culture substrates: topography, roughness, and elasticity","volume":"8","author":"AM Ross","year":"2011","journal-title":"Small."},{"issue":"1","key":"pcbi.1013305.ref056","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41540-024-00414-9","article-title":"Insights gained from computational modeling of YAP\/TAZ signaling for cellular mechanotransduction","volume":"10","author":"H Jafarinia","year":"2024","journal-title":"npj Syst Biol Appl."}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1013305","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T00:00:00Z","timestamp":1754438400000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1013305","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T17:46:42Z","timestamp":1754502402000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1013305"}},"subtitle":[],"editor":[{"given":"Jochen","family":"Hub","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2025,7,31]]},"references-count":56,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7,31]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1013305","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,7,31]]}}}