{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T07:57:10Z","timestamp":1778745430605,"version":"3.51.4"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1005524","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2017,5,18]],"date-time":"2017-05-18T00:00:00Z","timestamp":1495065600000}}],"reference-count":57,"publisher":"Public Library of Science (PLoS)","issue":"5","license":[{"start":{"date-parts":[[2017,5,4]],"date-time":"2017-05-04T00:00:00Z","timestamp":1493856000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["1562078"],"award-info":[{"award-number":["1562078"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Science and Engineering Research Council","award":["41870-12"],"award-info":[{"award-number":["41870-12"]}]},{"DOI":"10.13039\/100000054","name":"National Cancer Institute","doi-asserted-by":"publisher","award":["U54CA209992"],"award-info":[{"award-number":["U54CA209992"]}],"id":[{"id":"10.13039\/100000054","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"DOI":"10.1371\/journal.pcbi.1005524","type":"journal-article","created":{"date-parts":[[2017,5,4]],"date-time":"2017-05-04T13:28:19Z","timestamp":1493904499000},"page":"e1005524","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":59,"title":["A mathematical model coupling polarity signaling to cell adhesion explains diverse cell migration patterns"],"prefix":"10.1371","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6683-4647","authenticated-orcid":true,"given":"William R.","family":"Holmes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JinSeok","family":"Park","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andre","family":"Levchenko","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2233-690X","authenticated-orcid":true,"given":"Leah","family":"Edelstein-Keshet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2017,5,4]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"158102","DOI":"10.1103\/PhysRevLett.111.158102","article-title":"Periodic migration in a physical model of cells on micropatterns","volume":"111","author":"BA Camley","year":"2013","journal-title":"Physical review letters"},{"key":"ref2","doi-asserted-by":"crossref","first-page":"16383","DOI":"10.1073\/pnas.1410533111","article-title":"Microtubules stabilize cell polarity by localizing rear signals","volume":"111","author":"J Zhang","year":"2014","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"ref3","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1038\/ncomms1711","article-title":"Dimensional and temporal controls of three-dimensional cell migration by zyxin and binding partners","volume":"3","author":"SI Fraley","year":"2012","journal-title":"Nature communications"},{"key":"ref4","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1016\/j.cell.2015.01.056","article-title":"Actin flows mediate a universal coupling between cell speed and cell persistence","volume":"161","author":"P Maiuri","year":"2015","journal-title":"Cell"},{"key":"ref5","doi-asserted-by":"crossref","DOI":"10.1038\/nphys3836","article-title":"Deterministic patterns in cell motility","volume":"12","author":"I Lavi","year":"2016","journal-title":"Nat Phys"},{"key":"ref6","doi-asserted-by":"crossref","first-page":"6851","DOI":"10.1073\/pnas.1203252109","article-title":"Coupling actin flow, adhesion, and morphology in a computational cell motility model","volume":"109","author":"D Shao","year":"2012","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"ref7","article-title":"Collagen-rich stroma in aggressive colon tumors induces mesenchymal gene expression and tumor cell invasion","author":"T Vellinga","year":"2016","journal-title":"Oncogene"},{"key":"ref8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1741-7015-4-38","article-title":"Collagen reorganization at the tumor-stromal interface facilitates local invasion","volume":"4","author":"PP Provenzano","year":"2006","journal-title":"BMC medicine"},{"key":"ref9","doi-asserted-by":"crossref","DOI":"10.1038\/srep22580","article-title":"Tumor-induced remote ECM network orientation steers angiogenesis","volume":"6","author":"HE Balcioglu","year":"2016","journal-title":"Scientific reports"},{"key":"ref10","article-title":"Directed migration of cancer cells guided by the graded texture of the underlying matrix","author":"J Park","year":"2016","journal-title":"Nature materials"},{"key":"ref11","doi-asserted-by":"crossref","unstructured":"Park J, Holmes WR, Lee SH, Kim HN, Kim DH, et al. (2017) A mechano-chemical feedback underlies co-existence of qualitatively distinct cell polarity patterns within diverse cell populations. arXiv:161208948v1.","DOI":"10.1073\/pnas.1700054114"},{"key":"ref12","doi-asserted-by":"crossref","first-page":"e1002793","DOI":"10.1371\/journal.pcbi.1002793","article-title":"A comparison of computational models for eukaryotic cell shape and motility","volume":"8","author":"WR Holmes","year":"2012","journal-title":"PLoS Comput Biol"},{"key":"ref13","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1056\/NEJMra052166","article-title":"Melanoma","volume":"355","author":"AJ Miller","year":"2006","journal-title":"New England Journal of Medicine"},{"key":"ref14","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1111\/j.1600-0749.2005.00235.x","article-title":"Adhesion, migration and communication in melanocytes and melanoma","volume":"18","author":"NK Haass","year":"2005","journal-title":"Pigment cell research"},{"key":"ref15","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1016\/S0962-8924(01)02153-5","article-title":"Rho family proteins: coordinating cell responses","volume":"11","author":"AJ Ridley","year":"2001","journal-title":"Trends in cell biology"},{"key":"ref16","doi-asserted-by":"crossref","first-page":"1704","DOI":"10.1126\/science.1092053","article-title":"Cell migration: Integrating signals from front to back","volume":"302","author":"AJ Ridley","year":"2003","journal-title":"Science"},{"key":"ref17","doi-asserted-by":"crossref","first-page":"a005959","DOI":"10.1101\/cshperspect.a005959","article-title":"Signaling networks that regulate cell migration","volume":"7","author":"P Devreotes","year":"2015","journal-title":"Cold Spring Harbor perspectives in biology"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1016\/j.tcb.2011.08.002","article-title":"Rho protein crosstalk: another social network?","volume":"21","author":"C Guilluy","year":"2011","journal-title":"Trends in cell biology"},{"key":"ref19","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.cels.2016.01.003","article-title":"Bistability in the Rac1, PAK and RhoA signalling network is a feature of cell motility","volume":"2","author":"KM Byrne","year":"2016","journal-title":"Cell Systems"},{"key":"ref20","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1126\/science.285.5429.895","article-title":"Signaling from Rho to the actin cytoskeleton through protein kinases ROCK and LIM-kinase","volume":"285","author":"M Maekawa","year":"1999","journal-title":"Science"},{"key":"ref21","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1186\/1478-811X-8-23","article-title":"Rac and Rho GTPases in cancer cell motility control","volume":"8","author":"M Parri","year":"2010","journal-title":"Cell Commun Signal"},{"key":"ref22","doi-asserted-by":"crossref","first-page":"130132","DOI":"10.1098\/rsob.130132","article-title":"Cross-talk between Rho and Rac GTPases drives deterministic exploration of cellular shape space and morphological heterogeneity","volume":"4","author":"H Sailem","year":"2014","journal-title":"Open biology"},{"key":"ref23","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1186\/gb-2009-10-3-213","article-title":"Rac and Rho driving tumor invasion: who\u2019s at the wheel","volume":"10","author":"M Symons","year":"2009","journal-title":"Genome Biol"},{"key":"ref24","doi-asserted-by":"crossref","first-page":"e1002366","DOI":"10.1371\/journal.pcbi.1002366","article-title":"Modelling cell polarization driven by synthetic spatially graded Rac activation","volume":"8","author":"WR Holmes","year":"2012","journal-title":"PLoS Comput Biol"},{"key":"ref25","first-page":"E3668","article-title":"PNAS","volume":"109","author":"B Lin","year":"2012"},{"key":"ref26","article-title":"The three-way switch operation of Rac1\/RhoA GTPase-based circuit controlling amoeboid-hybrid-mesenchymal transition","volume":"4","author":"B Huang","year":"2014","journal-title":"Scientific reports"},{"key":"ref27","doi-asserted-by":"crossref","first-page":"046001","DOI":"10.1088\/1478-3975\/13\/4\/046001","article-title":"Analysis of a minimal Rho-GTPase circuit regulating cell shape","volume":"13","author":"WR Holmes","year":"2016","journal-title":"Physical Biology"},{"key":"ref28","doi-asserted-by":"crossref","first-page":"e27958","DOI":"10.4161\/sgtp.27958","article-title":"The on-off relationship of Rho and Rac during integrin-mediated adhesion and cell migration","volume":"5","author":"CD Lawson","year":"2014","journal-title":"Small GTPases"},{"key":"ref29","doi-asserted-by":"crossref","first-page":"1169","DOI":"10.1007\/s11538-006-9131-7","article-title":"Polarization and movement of keratocytes: A multiscale modelling approach","volume":"68","author":"AF Mar\u00e9e","year":"2006","journal-title":"Bull Math Biol"},{"key":"ref30","doi-asserted-by":"crossref","first-page":"1943","DOI":"10.1007\/s11538-007-9200-6","article-title":"Mathematical model for spatial segregation of the Rho-Family GTPases based on inhibitory crosstalk","volume":"69","author":"A Jilkine","year":"2007","journal-title":"Bull Math Biol"},{"key":"ref31","doi-asserted-by":"crossref","first-page":"3684","DOI":"10.1529\/biophysj.107.120824","article-title":"Wave-pinning and cell polarity from a bistable reaction-diffusion system","volume":"94","author":"Y Mori","year":"2008","journal-title":"Biophys J"},{"key":"ref32","doi-asserted-by":"crossref","first-page":"20130003","DOI":"10.1098\/rstb.2013.0003","article-title":"From simple to detailed models for cell polarization","volume":"368","author":"L Edelstein-Keshet","year":"2013","journal-title":"Philosophical Transactions of the Royal Society B: Biological Sciences"},{"key":"ref33","doi-asserted-by":"crossref","first-page":"14467","DOI":"10.1073\/pnas.1105845108","article-title":"Temporary increase in plasma membrane tension coordinates the activation of exocytosis and contraction during cell spreading","volume":"108","author":"NC Gauthier","year":"2011","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"ref34","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1083\/jcb.148.1.127","article-title":"Cell spreading and lamellipodial extension rate is regulated by membrane tension","volume":"148","author":"D Raucher","year":"2000","journal-title":"The Journal of cell biology"},{"key":"ref35","doi-asserted-by":"crossref","first-page":"730","DOI":"10.1039\/c2mb05375f","article-title":"The topology design principles that determine the spatiotemporal dynamics of G-protein cascades","volume":"8","author":"MA Tsyganov","year":"2012","journal-title":"Molecular BioSystems"},{"key":"ref36","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1242\/jcs.037564","article-title":"Spontaneous phosphoinositide 3-kinase signaling dynamics drive spreading and random migration of fibroblasts","volume":"122","author":"MC Weiger","year":"2009","journal-title":"Journal of cell science"},{"key":"ref37","doi-asserted-by":"crossref","first-page":"1753","DOI":"10.1126\/science.1140324","article-title":"Quantitative morphological signatures define local signaling networks regulating cell morphology","volume":"316","author":"C Bakal","year":"2007","journal-title":"science"},{"key":"ref38","doi-asserted-by":"crossref","first-page":"4163","DOI":"10.1091\/mbc.E15-06-0382","article-title":"Apolar and polar transitions drive the conversion between amoeboid and mesenchymal shapes in melanoma cells","volume":"26","author":"S Cooper","year":"2015","journal-title":"Molecular biology of the cell"},{"key":"ref39","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1083\/jcb.200205014","article-title":"The fibronectin-binding integrins <italic>\u03b1<\/italic>5<italic>\u03b2<\/italic>1 and <italic>\u03b1<\/italic>v<italic>\u03b2<\/italic>3 differentially modulate RhoA\u2013GTP loading, organization of cell matrix adhesions, and fibronectin fibrillogenesis","volume":"159","author":"EH Danen","year":"2002","journal-title":"The Journal of cell biology"},{"key":"ref40","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1002\/jcp.22338","article-title":"Involvement of caveolin-1 in fibronectin-induced mouse embryonic stem cell proliferation: Role of FAK, RhoA, PI3K\/Akt, and ERK 1\/2 pathways","volume":"226","author":"JH Park","year":"2011","journal-title":"Journal of cellular physiology"},{"key":"ref41","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1016\/S0960-9822(00)00537-6","article-title":"Integrin engagement suppresses RhoA activity via a c-Src-dependent mechanism","volume":"10","author":"WT Arthur","year":"2000","journal-title":"Current Biology"},{"key":"ref42","doi-asserted-by":"crossref","first-page":"e74659","DOI":"10.1371\/journal.pone.0074659","article-title":"Integrin-specific control of focal adhesion kinase and rhoa regulates membrane protrusion and invasion","volume":"8","author":"P Costa","year":"2013","journal-title":"PLoS One"},{"key":"ref43","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1038\/nrm2530","article-title":"Design principles of biochemical oscillators","volume":"9","author":"B Nov\u00e1k","year":"2008","journal-title":"Nature reviews Molecular cell biology"},{"key":"ref44","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1083\/jcb.200308060","article-title":"Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades","volume":"164","author":"NI Markevich","year":"2004","journal-title":"The Journal of cell biology"},{"key":"ref45","unstructured":"Edelstein-Keshet L (1988) Mathematical models in biology, volume 46 of <italic>Classics in Applied Mathematics<\/italic>. SIAM."},{"key":"ref46","doi-asserted-by":"crossref","first-page":"046005","DOI":"10.1088\/1478-3975\/9\/4\/046005","article-title":"Regimes of wave type patterning driven by refractory actin feedback: transition from static polarization to dynamic wave behaviour","volume":"9","author":"W Holmes","year":"2012","journal-title":"Physical biology"},{"key":"ref47","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/j.jtbi.2013.06.020","article-title":"A model for intracellular actin waves explored by nonlinear local perturbation analysis","volume":"334","author":"MA Mata","year":"2013","journal-title":"Journal of theoretical biology"},{"key":"ref48","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/s11538-013-9914-6","article-title":"An efficient, nonlinear stability analysis for detecting pattern formation in reaction diffusion systems","volume":"76","author":"WR Holmes","year":"2014","journal-title":"Bulletin of mathematical biology"},{"key":"ref49","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1016\/j.bpj.2014.11.3457","article-title":"Local perturbation analysis: A computational tool for biophysical reaction-diffusion models","volume":"108","author":"WR Holmes","year":"2015","journal-title":"Biophysical journal"},{"key":"ref50","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1038\/35002131","article-title":"Construction of a genetic toggle switch in Escherichia coli","volume":"403","author":"TS Gardner","year":"2000","journal-title":"Nature"},{"key":"ref51","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1038\/sj.embor.7400051","article-title":"Chemotaxis: signalling modules join hands at front and tail","volume":"5","author":"M Postma","year":"2004","journal-title":"EMBO reports"},{"key":"ref52","doi-asserted-by":"crossref","first-page":"e1002474","DOI":"10.1371\/journal.pbio.1002474","article-title":"Membrane tension acts through PLD2 and mTORC2 to limit actin network assembly during neutrophil migration","volume":"14","author":"A Diz-Mu\u00f1oz","year":"2016","journal-title":"PLoS Biol"},{"key":"ref53","doi-asserted-by":"crossref","first-page":"2147","DOI":"10.1091\/mbc.E07-12-1269","article-title":"GEF-H1 couples nocodazole-induced microtubule disassembly to cell contractility via RhoA","volume":"19","author":"YC Chang","year":"2008","journal-title":"Molecular biology of the cell"},{"key":"ref54","doi-asserted-by":"crossref","first-page":"1401","DOI":"10.1137\/10079118X","article-title":"Asymptotic and bifurcation analysis of wave-pinning in a reaction-diffusion model for cell polarization","volume":"71","author":"Y Mori","year":"2011","journal-title":"SIAM J Applied Math"},{"key":"ref55","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/j.bpj.2009.09.051","article-title":"Directional persistence of cell migration coincides with stability of asymmetric intracellular signaling","volume":"98","author":"MC Weiger","year":"2010","journal-title":"Biophysical journal"},{"key":"ref56","doi-asserted-by":"crossref","first-page":"122001","DOI":"10.1088\/1367-2630\/18\/12\/122001","article-title":"Nonlinear self-adapting wave patterns","volume":"18","author":"DA Kessler","year":"2016","journal-title":"New Journal of Physics"},{"key":"ref57","doi-asserted-by":"crossref","first-page":"e0115857","DOI":"10.1371\/journal.pone.0115857","article-title":"Dynamics of actin waves on patterned substrates: a quantitative analysis of circular dorsal ruffles","volume":"10","author":"E Bernitt","year":"2015","journal-title":"PloS one"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1005524","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2017,5,18]],"date-time":"2017-05-18T00:00:00Z","timestamp":1495065600000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/dx.plos.org\/10.1371\/journal.pcbi.1005524","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,23]],"date-time":"2019-09-23T04:56:30Z","timestamp":1569214590000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1005524"}},"subtitle":[],"editor":[{"given":"Qing","family":"Nie","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2017,5,4]]},"references-count":57,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2017,5,4]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1005524","relation":{"new_version":[{"id-type":"doi","id":"10.1371\/journal.pcbi.1005524","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,5,4]]}}}