{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T18:28:54Z","timestamp":1786386534451,"version":"build-2736575974"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1014569","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T00:00:00Z","timestamp":1786320000000}}],"reference-count":74,"publisher":"Public Library of Science (PLoS)","issue":"7","license":[{"start":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T00:00:00Z","timestamp":1785369600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-24-CE45-0690"],"award-info":[{"award-number":["ANR-24-CE45-0690"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Excellence Initiative of Aix-Marseille University - A*MIDEX","award":["A-M-AAP-ID-17-66-170301-11.30"],"award-info":[{"award-number":["A-M-AAP-ID-17-66-170301-11.30"]}]},{"name":"INSMI Maths Vives International Research Program"},{"name":"Visiting Professor Campaign, Universit\u00e9 C\u00f4te d'Azur"},{"name":"Canada Research Chairs (Tier 1) in Theoretical and Computational Biology","award":["CRC-2022-00147"],"award-info":[{"award-number":["CRC-2022-00147"]}]},{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Discovery Grants Program","award":["RGPIN-2023-05231"],"award-info":[{"award-number":["RGPIN-2023-05231"]}]},{"DOI":"10.13039\/501100007711","name":"British Columbia Knowledge Development Fund","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007711","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Canada Foundation for Innovation \u2013 John R. Evans Leaders Fund \u2013 Partnerships"},{"name":"British Columbia Foundation for Non Animal Research"},{"name":"French Consortium Approches Quantitatives du Vivant\/Quantitative approaches to living systems"},{"DOI":"10.13039\/100017143","name":"Gruppo Nazionale per la Fisica Matematica","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100017143","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Understanding how cells migrate through confined environments is crucial for elucidating fundamental biological processes, including cancer invasion, immune surveillance, and tissue morphogenesis. The nucleus, as the largest and stiffest cellular organelle, often limits cellular deformability, making it a key factor in migration through narrow pores or highly constrained spaces. In this work, we introduce a geometric surface partial differential equation (GS-PDE) model in which the cell plasma membrane and nuclear envelope are described as evolving energetic closed surfaces governed by force-balance equations. We replicate the results of a biophysical experiment, in which a microfluidic device is used to impose compressive stresses on cells by driving them through narrow microchannels under a controlled pressure gradient. The model is validated by reproducing cell entry into the microchannels. A parametric sensitivity analysis highlights the dominant influence of specific parameters, whose accurate estimation is essential to faithfully capture the experimental setup. We found that surface tension and confinement geometry emerge as key determinants of translocation efficiency. Although tailored to this specific setup for validation purposes, the framework is sufficiently general to be applied to a broad range of cell mechanics scenarios, providing a robust and flexible tool for investigating the interplay between cell mechanics and confinement. It also offers a solid foundation for future extensions integrating more complex biochemical processes such as active confined migration.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1014569","type":"journal-article","created":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T17:52:36Z","timestamp":1785433956000},"page":"e1014569","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["A geometric-surface PDE model for cell-nucleus translocation through confinement"],"prefix":"10.1371","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-6657-2768","authenticated-orcid":true,"given":"Francesca","family":"Ballatore","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9511-8903","authenticated-orcid":true,"given":"Anotida","family":"Madzvamuse","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C\u00e9cile","family":"Jebane","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Emmanu\u00e8le","family":"Helfer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rachele","family":"Allena","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,7,30]]},"reference":[{"issue":"1","key":"pcbi.1014569.ref001","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1038\/nrm1006","article-title":"Border-cell migration: the race is on","volume":"4","author":"DJ Montell","year":"2003","journal-title":"Nat Rev Mol Cell Biol"},{"key":"pcbi.1014569.ref002","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1016\/j.semcdb.2014.05.011","article-title":"Interplay between intercellular signaling and cell movement in development","volume":"35","author":"K Uriu","year":"2014","journal-title":"Semin Cell Dev Biol"},{"issue":"9","key":"pcbi.1014569.ref003","doi-asserted-by":"crossref","first-page":"960","DOI":"10.1038\/ni.f.212","article-title":"Interstitial leukocyte migration and immune function","volume":"9","author":"P Friedl","year":"2008","journal-title":"Nat Immunol"},{"issue":"1","key":"pcbi.1014569.ref004","doi-asserted-by":"crossref","DOI":"10.1002\/wcms.1376","article-title":"Eukaryotic Cell Dynamics from Crawlers to Swimmers","volume":"9","author":"HG Othmer","year":"2019","journal-title":"Wiley Interdiscip Rev Comput Mol Sci"},{"issue":"5","key":"pcbi.1014569.ref005","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1038\/nrc1075","article-title":"Tumour-cell invasion and migration: diversity and escape mechanisms","volume":"3","author":"P Friedl","year":"2003","journal-title":"Nat Rev Cancer"},{"key":"pcbi.1014569.ref006","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.ceb.2018.09.003","article-title":"Control of adhesion and protrusion in cell migration by Rho GTPases","volume":"56","author":"H Warner","year":"2019","journal-title":"Curr Opin Cell Biol"},{"issue":"1","key":"pcbi.1014569.ref007","doi-asserted-by":"crossref","first-page":"4144","DOI":"10.1038\/s41467-018-06641-z","article-title":"Matrix mechanical plasticity regulates cancer cell migration through confining microenvironments","volume":"9","author":"KM Wisdom","year":"2018","journal-title":"Nat Commun"},{"issue":"7","key":"pcbi.1014569.ref008","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1038\/s41580-023-00583-1","article-title":"Cell-extracellular matrix mechanotransduction in 3D","volume":"24","author":"A Saraswathibhatla","year":"2023","journal-title":"Nat Rev Mol Cell Biol"},{"issue":"8","key":"pcbi.1014569.ref009","doi-asserted-by":"crossref","first-page":"893","DOI":"10.1038\/ncb1616","article-title":"Multi-step pericellular proteolysis controls the transition from individual to collective cancer cell invasion","volume":"9","author":"K Wolf","year":"2007","journal-title":"Nat Cell Biol"},{"issue":"1","key":"pcbi.1014569.ref010","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1083\/jcb.200909003","article-title":"Plasticity of cell migration: a multiscale tuning model","volume":"188","author":"P Friedl","year":"2010","journal-title":"J Cell Biol"},{"issue":"9","key":"pcbi.1014569.ref011","doi-asserted-by":"crossref","first-page":"3262","DOI":"10.1182\/blood-2002-12-3791","article-title":"Amoeboid shape change and contact guidance: T-lymphocyte crawling through fibrillar collagen is independent of matrix remodeling by MMPs and other proteases","volume":"102","author":"K Wolf","year":"2003","journal-title":"Blood"},{"issue":"7","key":"pcbi.1014569.ref012","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1083\/jcb.201210152","article-title":"Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force","volume":"201","author":"K Wolf","year":"2013","journal-title":"J Cell Biol"},{"issue":"26","key":"pcbi.1014569.ref013","doi-asserted-by":"crossref","first-page":"10334","DOI":"10.1073\/pnas.1118073109","article-title":"Independent regulation of tumor cell migration by matrix stiffness and confinement","volume":"109","author":"A Pathak","year":"2012","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"6","key":"pcbi.1014569.ref014","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1007\/s12551-024-01244-z","article-title":"Mechanobiology of 3D cell confinement and extracellular crowding","volume":"16","author":"G Da Silva Andr\u00e9","year":"2024","journal-title":"Biophys Rev"},{"issue":"5","key":"pcbi.1014569.ref015","doi-asserted-by":"crossref","first-page":"900","DOI":"10.1016\/j.bpj.2015.07.025","article-title":"Migration in Confined 3D Environments Is Determined by a Combination of Adhesiveness, Nuclear Volume, Contractility, and Cell Stiffness","volume":"109","author":"LA Lautscham","year":"2015","journal-title":"Biophys J"},{"issue":"9","key":"pcbi.1014569.ref016","doi-asserted-by":"crossref","first-page":"2039","DOI":"10.1016\/j.bpj.2016.09.034","article-title":"Measuring Cell Viscoelastic Properties Using a Microfluidic Extensional Flow Device","volume":"111","author":"L Guillou","year":"2016","journal-title":"Biophys J"},{"issue":"13","key":"pcbi.1014569.ref017","doi-asserted-by":"crossref","first-page":"2343","DOI":"10.1039\/D0LC00092B","article-title":"Cell elasticity measurement using a microfluidic device with real-time pressure feedback","volume":"20","author":"Z Chen","year":"2020","journal-title":"Lab Chip"},{"key":"pcbi.1014569.ref018","doi-asserted-by":"crossref","first-page":"107714","DOI":"10.1016\/j.isci.2023.107714","article-title":"Enhanced cell viscosity: A new phenotype associated with lamin A\/C alterations","volume":"26","author":"C Jebane","year":"2023","journal-title":"iScience"},{"key":"pcbi.1014569.ref019","doi-asserted-by":"crossref","first-page":"108979","DOI":"10.1016\/j.ijmecsci.2024.108979","article-title":"Single-cell mechanical characterization in constriction-based cytometry","volume":"268","author":"A Abarca-Ortega","year":"2024","journal-title":"Int J Mech Sci"},{"issue":"12","key":"pcbi.1014569.ref020","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1008411","article-title":"Bridging from single to collective cell migration: A review of models and links to experiments","volume":"16","author":"A Buttensch\u00f6n","year":"2020","journal-title":"PLoS Comput Biol"},{"issue":"3","key":"pcbi.1014569.ref021","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/s10237-013-0510-3","article-title":"Influence of nucleus deformability on cell entry into cylindrical structures","volume":"13","author":"C Giverso","year":"2014","journal-title":"Biomech Model Mechanobiol"},{"issue":"13","key":"pcbi.1014569.ref022","doi-asserted-by":"crossref","first-page":"1599","DOI":"10.1091\/mbc.E17-05-0313","article-title":"Multicompartment cell-based modeling of confined migration: regulation by cell intrinsic and extrinsic factors","volume":"29","author":"S Kumar","year":"2018","journal-title":"Mol Biol Cell"},{"key":"pcbi.1014569.ref023","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1016\/j.jtbi.2012.11.003","article-title":"Modeling the influence of nucleus elasticity on cell invasion in fiber networks and microchannels","volume":"317","author":"M Scianna","year":"2013","journal-title":"J Theor Biol"},{"issue":"1","key":"pcbi.1014569.ref024","doi-asserted-by":"crossref","first-page":"14886","DOI":"10.1038\/s41598-019-51494-1","article-title":"Modeling Living Cells Within Microfluidic Systems Using Cellular Automata Models","volume":"9","author":"J Ballesteros Hernando","year":"2019","journal-title":"Sci Rep"},{"key":"pcbi.1014569.ref025","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1007\/s10237-010-0271-1","article-title":"Modeling cell entry into a micro-channel","volume":"10","author":"F Leong","year":"2010","journal-title":"Biomech Model Mechanobiol"},{"key":"pcbi.1014569.ref026","doi-asserted-by":"crossref","first-page":"106317","DOI":"10.1016\/j.compfluid.2024.106317","article-title":"A coupled VOF\/embedded boundary method to model two-phase flows on arbitrary solid surfaces","volume":"278","author":"M Tavares","year":"2024","journal-title":"Comput Fluids"},{"key":"pcbi.1014569.ref027","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.jcp.2014.10.004","article-title":"A poroelastic immersed boundary method with applications to cell biology","volume":"282","author":"W Strychalski","year":"2015","journal-title":"J Computat Phys"},{"issue":"4","key":"pcbi.1014569.ref028","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1109\/TVCG.2008.37","article-title":"Two-way coupled SPH and particle level set fluid simulation","volume":"14","author":"F Losasso","year":"2008","journal-title":"IEEE Trans Vis Comput Graph"},{"issue":"7","key":"pcbi.1014569.ref029","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1038\/ncb2775","article-title":"Matrix geometry determines optimal cancer cell migration strategy and modulates response to interventions","volume":"15","author":"M Tozluo\u011flu","year":"2013","journal-title":"Nat Cell Biol"},{"key":"pcbi.1014569.ref030","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.finel.2015.09.002","article-title":"The bulk-surface finite element method for reaction\u2013diffusion systems on stationary volumes","volume":"108","author":"A Madzvamuse","year":"2016","journal-title":"Finite Elem Anal Des"},{"key":"pcbi.1014569.ref031","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/j.jtbi.2018.09.008","article-title":"A coupled bulk-surface model for cell polarisation","volume":"481","author":"D Cusseddu","year":"2019","journal-title":"J Theor Biol"},{"key":"pcbi.1014569.ref032","doi-asserted-by":"crossref","first-page":"111966","DOI":"10.1016\/j.jtbi.2024.111966","article-title":"A bulk-surface mechanobiochemical modelling approach for single cell migration in two-space dimensions","volume":"595","author":"D Hernandez-Aristizabal","year":"2024","journal-title":"J Theor Biol"},{"issue":"1","key":"pcbi.1014569.ref033","doi-asserted-by":"crossref","DOI":"10.1137\/19M1298585","article-title":"A Conservative Finite Element ALE Scheme for Mass-Conservative Reaction-Diffusion Equations on Evolving Two-Dimensional Domains","volume":"43","author":"J Mackenzie","year":"2021","journal-title":"SIAM J Sci Comput"},{"issue":"1","key":"pcbi.1014569.ref034","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1016\/j.jocit.2018.09.007","article-title":"The discriminant role of mechanics during cell migration","volume":"4","author":"R Allena","year":"2018","journal-title":"J Cell Immunother"},{"issue":"1","key":"pcbi.1014569.ref035","article-title":"Potential theramechanics for cancer invasion: an in silico study","volume":"1","author":"R Allena","year":"2024","journal-title":"Math Med Life Sci"},{"issue":"3","key":"pcbi.1014569.ref036","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1137\/100788938","article-title":"Modeling Cell Movement and Chemotaxis Using Pseudopod-Based Feedback","volume":"33","author":"MP Neilson","year":"2011","journal-title":"SIAM J Sci Comput"},{"issue":"76","key":"pcbi.1014569.ref037","doi-asserted-by":"crossref","first-page":"3027","DOI":"10.1098\/rsif.2012.0276","article-title":"Modelling cell motility and chemotaxis with evolving surface finite elements","volume":"9","author":"CM Elliott","year":"2012","journal-title":"J R Soc Interface"},{"issue":"7778","key":"pcbi.1014569.ref038","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1038\/s41586-019-1637-x","article-title":"A sensor kinase controls turgor-driven plant infection by the rice blast fungus","volume":"574","author":"LS Ryder","year":"2019","journal-title":"Nature"},{"issue":"10","key":"pcbi.1014569.ref039","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1007\/s11538-023-01187-8","article-title":"The Influence of Nucleus Mechanics in Modelling Adhesion-independent Cell Migration in Structured and Confined Environments","volume":"85","author":"C Giverso","year":"2023","journal-title":"Bull Math Biol"},{"key":"pcbi.1014569.ref040","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.ijnonlinmec.2014.01.012","article-title":"Crawling on directional surfaces","volume":"61","author":"P Gidoni","year":"2014","journal-title":"Int J Non-Linear Mech"},{"issue":"09","key":"pcbi.1014569.ref041","doi-asserted-by":"crossref","first-page":"1901","DOI":"10.1142\/S0218202511005593","article-title":"A multiphase model of tumor and tissue growth including cell adhesion and plastic reorganization","volume":"21","author":"L Preziosi","year":"2011","journal-title":"Math Models Methods Appl Sci"},{"issue":"6","key":"pcbi.1014569.ref042","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1007\/s00285-011-0401-0","article-title":"The surface finite element method for pattern formation on evolving biological surfaces","volume":"63","author":"R Barreira","year":"2011","journal-title":"J Math Biol"},{"issue":"7194","key":"pcbi.1014569.ref043","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1038\/nature06952","article-title":"Mechanism of shape determination in motile cells","volume":"453","author":"K Keren","year":"2008","journal-title":"Nature"},{"key":"pcbi.1014569.ref044","doi-asserted-by":"crossref","first-page":"2318","DOI":"10.1242\/jcs.007732","article-title":"Possible roles of the endocytic cycle in cell motility","volume":"120","author":"D Traynor","year":"2007","journal-title":"J Cell Sci"},{"key":"pcbi.1014569.ref045","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.jcp.2015.12.038","article-title":"A computational method for the coupled solution of reaction-diffusion equations on evolving domains and manifolds: Application to a model of cell migration and chemotaxis","volume":"309","author":"G MacDonald","year":"2016","journal-title":"J Comput Phys"},{"key":"pcbi.1014569.ref046","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1017\/S0962492904000224","article-title":"Computation of geometric partial differential equations and mean curvature flow","volume":"14","author":"K Deckelnick","year":"2005","journal-title":"Acta Numerica"},{"key":"pcbi.1014569.ref047","doi-asserted-by":"crossref","unstructured":"Helfrich W. Elastic properties of lipid bilayers: Theory and possible experiments. Zeitschrift f\u00fcr Naturforschung C. 2014;28. doi: 10.1515\/znc-1973-11-1209","DOI":"10.1515\/znc-1973-11-1209"},{"key":"pcbi.1014569.ref048","doi-asserted-by":"crossref","unstructured":"Kolley-K\u00f6chel F, Sischka J, Voigt A, Fischer-Friedrich E, Aland S. A numerical approach for the dynamics of active viscoelastic surfaces. arXiv preprint. 2025. doi: 10.48550\/arXiv.2509.13777","DOI":"10.4171\/ifb\/576"},{"key":"pcbi.1014569.ref049","volume-title":"The Earth: Its Origin, History and Physical Constitution","author":"H Jeffreys","year":"1929","edition":"1"},{"key":"pcbi.1014569.ref050","doi-asserted-by":"crossref","first-page":"031915","DOI":"10.1103\/PhysRevE.79.031915","article-title":"Relaxation dynamics of fluid membranes","volume":"79","author":"M Arroyo","year":"2009","journal-title":"Phys Rev E Stat Nonlin Soft Matter Phys"},{"issue":"10","key":"pcbi.1014569.ref051","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/j.tcb.2012.07.001","article-title":"Actin cortex mechanics and cellular morphogenesis","volume":"22","author":"G Salbreux","year":"2012","journal-title":"Trends Cell Biol"},{"issue":"2","key":"pcbi.1014569.ref052","doi-asserted-by":"crossref","first-page":"94","DOI":"10.2976\/1.3054712","article-title":"Active gels as a description of the actin-myosin cytoskeleton","volume":"3","author":"J-F Joanny","year":"2009","journal-title":"HFSP J"},{"issue":"14","key":"pcbi.1014569.ref053","doi-asserted-by":"crossref","first-page":"1984","DOI":"10.1091\/mbc.e16-09-0653","article-title":"Chromatin and lamin A determine two different mechanical response regimes of the cell nucleus","volume":"28","author":"AD Stephens","year":"2017","journal-title":"Mol Biol Cell"},{"issue":"2","key":"pcbi.1014569.ref054","doi-asserted-by":"crossref","first-page":"220","DOI":"10.1091\/mbc.E17-06-0410","article-title":"Chromatin histone modifications and rigidity affect nuclear morphology independent of lamins","volume":"29","author":"AD Stephens","year":"2018","journal-title":"Mol Biol Cell"},{"issue":"2","key":"pcbi.1014569.ref055","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1002\/j.2040-4603.2011.tb00343.x","article-title":"Mechanics of the nucleus","volume":"1","author":"J Lammerding","year":"2011","journal-title":"Compr Physiol"},{"key":"pcbi.1014569.ref056","unstructured":"The FEniCS computing platform. 2026. Available from: https:\/\/fenicsproject.org\/"},{"key":"pcbi.1014569.ref057","volume-title":"Differential geometry of curves and surfaces","author":"MP Do Carmo","year":"1976"},{"key":"pcbi.1014569.ref058","doi-asserted-by":"crossref","first-page":"4281","DOI":"10.1016\/j.jcp.2007.11.023","article-title":"On the parametric finite element approximation of evolving hypersurfaces in R3","volume":"227","author":"J Barrett","year":"2008","journal-title":"J Computat Phys"},{"key":"pcbi.1014569.ref059","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"},{"issue":"1","key":"pcbi.1014569.ref060","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.jcp.2005.09.012","article-title":"Time-stepping schemes for moving grid finite elements applied to reaction\u2013diffusion systems on fixed and growing domains","volume":"214","author":"A Madzvamuse","year":"2006","journal-title":"J Computat Phys"},{"key":"pcbi.1014569.ref061","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.amc.2014.07.004","article-title":"Fully implicit time-stepping schemes and non-linear solvers for systems of reaction\u2013diffusion equations","volume":"244","author":"A Madzvamuse","year":"2014","journal-title":"Appl Math Computat"},{"issue":"9","key":"pcbi.1014569.ref062","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1145\/361002.361007","article-title":"Multidimensional binary search trees used for associative searching","volume":"18","author":"JL Bentley","year":"1975","journal-title":"Commun ACM"},{"key":"pcbi.1014569.ref063","doi-asserted-by":"crossref","first-page":"6213","DOI":"10.1038\/srep06213","article-title":"Quantification of surface tension and internal pressure generated by single mitotic cells","volume":"4","author":"E Fischer-Friedrich","year":"2014","journal-title":"Sci Rep"},{"issue":"44","key":"pcbi.1014569.ref064","doi-asserted-by":"crossref","first-page":"18581","DOI":"10.1073\/pnas.0903353106","article-title":"Role of cortical tension in bleb growth","volume":"106","author":"J-Y Tinevez","year":"2009","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"8","key":"pcbi.1014569.ref065","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0269619","article-title":"The bending rigidity of the red blood cell cytoplasmic membrane","volume":"17","author":"S Himbert","year":"2022","journal-title":"PLoS One"},{"issue":"1","key":"pcbi.1014569.ref066","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.physa.2006.05.008","article-title":"Transport of a 1D viscoelastic actin\u2013myosin strip of gel as a model of a crawling cell","volume":"372","author":"K Larripa","year":"2006","journal-title":"Phys A: Stat Mech Appl"},{"issue":"4","key":"pcbi.1014569.ref067","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/0014-4827(50)90002-4","article-title":"The physical properties of cytoplasm. A study by means of the magnetic particle method. Part II. Theoretical treatment","volume":"1","author":"FHC Crick","year":"1950","journal-title":"Exp Cell Res"},{"issue":"7","key":"pcbi.1014569.ref068","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.1016\/j.bpj.2016.08.011","article-title":"A Chemomechanical Model for Nuclear Morphology and Stresses during Cell Transendothelial Migration","volume":"111","author":"X Cao","year":"2016","journal-title":"Biophys J"},{"key":"pcbi.1014569.ref069","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.ceb.2016.01.011","article-title":"Squish and squeeze-the nucleus as a physical barrier during migration in confined environments","volume":"40","author":"AL McGregor","year":"2016","journal-title":"Curr Opin Cell Biol"},{"issue":"3","key":"pcbi.1014569.ref070","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1006\/bbrc.2000.2360","article-title":"Viscoelastic properties of the cell nucleus","volume":"269","author":"F Guilak","year":"2000","journal-title":"Biochem Biophys Res Commun"},{"issue":"7","key":"pcbi.1014569.ref071","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1016\/j.jbiomech.2009.01.024","article-title":"In situ mechanical properties of the chondrocyte cytoplasm and nucleus","volume":"42","author":"G Ofek","year":"2009","journal-title":"J Biomech"},{"issue":"2","key":"pcbi.1014569.ref072","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1007\/s00211-025-01457-8","article-title":"A fully discrete evolving surface finite element method for the Cahn\u2013Hilliard equation with a regular potential","volume":"157","author":"CM Elliott","year":"2025","journal-title":"Numer Math"},{"key":"pcbi.1014569.ref073","unstructured":"Elliott C, Mavrakis A. A Fully Discrete Surface Finite Element Method for the Navier\u2013Stokes Equations on Evolving Surfaces with Prescribed Normal Velocity. arXiv preprint. 2025;12. doi: 10.48550\/arXiv.2512.11737"},{"key":"pcbi.1014569.ref074","article-title":"Navier\u2013Stokes equations in a curved thin domain, Part III: thin-film limit","volume":"25","author":"T-H Miura","year":"2020","journal-title":"Adv Diff Eq"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1014569","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T00:00:00Z","timestamp":1786320000000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1014569","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T17:46:34Z","timestamp":1786383994000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1014569"}},"subtitle":[],"editor":[{"given":"Philip K","family":"Maini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2026,7,30]]},"references-count":74,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,7,30]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1014569","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,30]]}}}