{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T01:39:39Z","timestamp":1772761179733,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1008213","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T00:00:00Z","timestamp":1616371200000}}],"reference-count":52,"publisher":"Public Library of Science (PLoS)","issue":"3","license":[{"start":{"date-parts":[[2021,3,10]],"date-time":"2021-03-10T00:00:00Z","timestamp":1615334400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000265","name":"Medical Research Council","doi-asserted-by":"publisher","award":["MR\/R009376\/1"],"award-info":[{"award-number":["MR\/R009376\/1"]}],"id":[{"id":"10.13039\/501100000265","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100004440","name":"Wellcome Trust","doi-asserted-by":"publisher","award":["203128\/Z\/16\/Z"],"award-info":[{"award-number":["203128\/Z\/16\/Z"]}],"id":[{"id":"10.13039\/100004440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Cell migration in 3D microenvironments is a complex process which depends on the coordinated activity of leading edge protrusive force and rear retraction in a push-pull mechanism. While the potentiation of protrusions has been widely studied, the precise signalling and mechanical events that lead to retraction of the cell rear are much less well understood, particularly in physiological 3D extra-cellular matrix (ECM). We previously discovered that rear retraction in fast moving cells is a highly dynamic process involving the precise spatiotemporal interplay of mechanosensing by caveolae and signalling through RhoA. To further interrogate the dynamics of rear retraction, we have adopted three distinct mathematical modelling approaches here based on (i) Boolean logic, (ii) deterministic kinetic ordinary differential equations (ODEs) and (iii) stochastic simulations. The aims of this multi-faceted approach are twofold: firstly to derive new biological insight into cell rear dynamics via generation of testable hypotheses and predictions; and secondly to compare and contrast the distinct modelling approaches when used to describe the same, relatively under-studied system. Overall, our modelling approaches complement each other, suggesting that such a multi-faceted approach is more informative than methods based on a single modelling technique to interrogate biological systems. Whilst Boolean logic was not able to fully recapitulate the complexity of rear retraction signalling, an ODE model could make plausible population level predictions. Stochastic simulations added a further level of complexity by accurately mimicking previous experimental findings and acting as a single cell simulator. Our approach highlighted the unanticipated role for CDK1 in rear retraction, a prediction we confirmed experimentally. Moreover, our models led to a novel prediction regarding the potential existence of a \u2018set point\u2019 in local stiffness gradients that promotes polarisation and rapid rear retraction.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1008213","type":"journal-article","created":{"date-parts":[[2021,3,10]],"date-time":"2021-03-10T13:49:23Z","timestamp":1615384163000},"page":"e1008213","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":12,"title":["Combinatorial mathematical modelling approaches to interrogate rear retraction dynamics in 3D cell migration"],"prefix":"10.1371","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1493-351X","authenticated-orcid":true,"given":"Joseph H. R.","family":"Hetmanski","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4723-3277","authenticated-orcid":true,"given":"Matthew C.","family":"Jones","sequence":"additional","affiliation":[]},{"given":"Fatima","family":"Chunara","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6472-0184","authenticated-orcid":true,"given":"Jean-Marc","family":"Schwartz","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2633-2324","authenticated-orcid":true,"given":"Patrick T.","family":"Caswell","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2021,3,10]]},"reference":[{"key":"pcbi.1008213.ref001","article-title":"Molecular Cell Biology","author":"H. Lodish","year":"2003","journal-title":"Perspective"},{"key":"pcbi.1008213.ref002","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":"pcbi.1008213.ref003","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/S0092-8674(00)81280-5","article-title":"Cell migration: A physically integrated process","volume":"84","author":"D Lauffenburger","year":"1996","journal-title":"Cell"},{"key":"pcbi.1008213.ref004","doi-asserted-by":"crossref","first-page":"3030","DOI":"10.1016\/S0006-3495(96)79496-1","article-title":"Cell motility driven by actin polymerization","volume":"71","author":"A Mogilner","year":"1996","journal-title":"Biophys J"},{"key":"pcbi.1008213.ref005","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1016\/0092-8674(87)90233-9","article-title":"Integrins: A family of cell surface receptors","author":"RO Hynes","year":"1987","journal-title":"Cell"},{"key":"pcbi.1008213.ref006","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1038\/nrm1128","article-title":"Rocks: multifunctional kinases in cell behaviour","volume":"4","author":"K Riento","year":"2003","journal-title":"Nat Rev Mol Cell Biol"},{"key":"pcbi.1008213.ref007","author":"GM Cooper","year":"2013"},{"key":"pcbi.1008213.ref008","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1016\/j.devcel.2019.09.006","article-title":"Membrane Tension Orchestrates Rear Retraction in Matrix-Directed Cell Migration","volume":"51","author":"JHR Hetmanski","year":"2019","journal-title":"Dev Cell"},{"key":"pcbi.1008213.ref009","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/0092-8674(92)90163-7","article-title":"The small GTP-binding protein rho regulates the assembly of focal adhesions and actin stress fibers in response to growth factors","volume":"70","author":"AJ Ridley","year":"1992","journal-title":"Cell"},{"key":"pcbi.1008213.ref010","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1038\/nature01148","article-title":"Rho GTPases in cell biology","volume":"420","author":"S Etienne-Manneville","year":"2002","journal-title":"Nature"},{"key":"pcbi.1008213.ref011","doi-asserted-by":"crossref","first-page":"28772","DOI":"10.1074\/jbc.271.46.28772","article-title":"Isolation of a NCK-associated kinase, PRK2, an SH3-binding protein and potential effector of Rho protein signaling","volume":"271","author":"LA Quilliam","year":"1996","journal-title":"J Biol Chem"},{"key":"pcbi.1008213.ref012","doi-asserted-by":"crossref","first-page":"3491","DOI":"10.1242\/jcs.018473","article-title":"Actin stress fibres","volume":"120","author":"S Pellegrin","year":"2007","journal-title":"J Cell Sci"},{"key":"pcbi.1008213.ref013","first-page":"1","article-title":"Dynamic functions of RhoA in tumor cell migration and invasion","volume":"4","author":"K O\u2019Connor","year":"2013","journal-title":"Small GTPases"},{"key":"pcbi.1008213.ref014","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1242\/jcs.107250","article-title":"Formins at a glance","volume":"126","author":"D Breitsprecher","year":"2013","journal-title":"J Cell Sci"},{"key":"pcbi.1008213.ref015","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1038\/nrm3512","article-title":"Caveolae as plasma membrane sensors, protectors and organizers","volume":"14","author":"RG Parton","year":"2013","journal-title":"Nat Rev Mol Cell Biol"},{"key":"pcbi.1008213.ref016","doi-asserted-by":"crossref","first-page":"144","DOI":"10.1016\/S0006-3495(00)76279-5","article-title":"Cell movement is guided by the rigidity of the substrate","volume":"79","author":"CM Lo","year":"2000","journal-title":"Biophys J"},{"key":"pcbi.1008213.ref017","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1093\/jmcb\/mjv017","article-title":"Network-based identification of feedback modules that control RhoA activity and cell migration","volume":"7","author":"TH Kim","year":"2015","journal-title":"J Mol Cell Biol"},{"key":"pcbi.1008213.ref018","doi-asserted-by":"crossref","first-page":"e1004909","DOI":"10.1371\/journal.pcbi.1004909","article-title":"A MAPK-Driven Feedback Loop Suppresses Rac Activity to Promote RhoA-Driven Cancer Cell Invasion","volume":"12","author":"JHR Hetmanski","year":"2016","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1008213.ref019","doi-asserted-by":"crossref","first-page":"2454","DOI":"10.1039\/c3mb70152b","article-title":"Control of the G-protein cascade dynamics by GDP dissociation inhibitors","volume":"9","author":"E Nikonova","year":"2013","journal-title":"Mol Biosyst"},{"key":"pcbi.1008213.ref020","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.cels.2016.01.003","article-title":"Bistability in the Rac1, PAK, and RhoA Signaling Network Drives Actin Cytoskeleton Dynamics and Cell Motility Switches","volume":"2","author":"KM Byrne","year":"2016","journal-title":"Cell Syst"},{"key":"pcbi.1008213.ref021","first-page":"1","article-title":"Rationalizing Rac1 and RhoA GTPase signaling: A mathematical approach","volume":"1248","author":"JHR Hetmanski","year":"2016","journal-title":"Small GTPases"},{"key":"pcbi.1008213.ref022","doi-asserted-by":"crossref","first-page":"1695","DOI":"10.1042\/BST20160184","article-title":"Modelling GTPase dynamics to understand RhoA-driven cancer cell invasion","volume":"44","author":"JHR Hetmanski","year":"2016","journal-title":"Biochem Soc Trans"},{"key":"pcbi.1008213.ref023","doi-asserted-by":"crossref","first-page":"i495","DOI":"10.1093\/bioinformatics\/bts410","article-title":"Boolean approach to signalling pathway modelling in HGF-induced keratinocyte migration","volume":"28","author":"A Singh","year":"2012","journal-title":"Bioinformatics"},{"key":"pcbi.1008213.ref024","doi-asserted-by":"crossref","first-page":"e1000438","DOI":"10.1371\/journal.pcbi.1000438","article-title":"The logic of EGFR\/ErbB signaling: theoretical properties and analysis of high-throughput data","volume":"5","author":"R Samaga","year":"2009","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1008213.ref025","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":"Mol Biosyst"},{"key":"pcbi.1008213.ref026","doi-asserted-by":"crossref","first-page":"55001","DOI":"10.1088\/1478-3975\/9\/5\/055001","article-title":"Boolean modeling in systems biology: an overview of methodology and applications","volume":"9","author":"R-S Wang","year":"2012","journal-title":"Phys Biol"},{"key":"pcbi.1008213.ref027","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.ymeth.2006.08.003","article-title":"Mathematical modeling as a tool for investigating cell cycle control networks","volume":"41","author":"JC Sible","year":"2007","journal-title":"Methods"},{"key":"pcbi.1008213.ref028","doi-asserted-by":"crossref","first-page":"3067","DOI":"10.1093\/bioinformatics\/btl485","article-title":"COPASI\u2014A COmplex PAthway SImulator","volume":"22","author":"S Hoops","year":"2006","journal-title":"Bioinformatics"},{"key":"pcbi.1008213.ref029","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1242\/jcs.99.2.419","article-title":"Migration of individual microvessel endothelial cells: stochastic model and parameter measurement","volume":"99","author":"CL Stokes","year":"1991","journal-title":"J Cell Sci"},{"key":"pcbi.1008213.ref030","doi-asserted-by":"crossref","first-page":"1811","DOI":"10.1016\/j.bpj.2009.05.064","article-title":"Stochastic collective movement of cells and fingering morphology: No maverick cells","volume":"97","author":"GY Ouaknin","year":"2009","journal-title":"Biophys J"},{"key":"pcbi.1008213.ref031","doi-asserted-by":"crossref","first-page":"e1002404","DOI":"10.1371\/journal.pbio.1002404","article-title":"Self-Generated Chemoattractant Gradients: Attractant Depletion Extends the Range and Robustness of Chemotaxis","volume":"14","author":"L Tweedy","year":"2016","journal-title":"PLoS Biol"},{"key":"pcbi.1008213.ref032","doi-asserted-by":"crossref","first-page":"15313","DOI":"10.1038\/ncomms15313","article-title":"Shifting the optimal stiffness for cell migration","volume":"8","author":"BL Bangasser","year":"2017","journal-title":"Nat Commun"},{"key":"pcbi.1008213.ref033","doi-asserted-by":"crossref","first-page":"2090","DOI":"10.1091\/mbc.E15-11-0756","article-title":"Src-dependent phosphorylation of caveolin-1 Tyr-14 promotes swelling and release of caveolae","volume":"27","author":"AM Zimnicka","year":"2016","journal-title":"Mol Biol Cell"},{"key":"pcbi.1008213.ref034","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1016\/j.ejcb.2008.02.001","article-title":"Caveolin-1 in cell polarization and directional migration","author":"A Grande-Garc\u00eda","year":"2008","journal-title":"European Journal of Cell Biology"},{"key":"pcbi.1008213.ref035","doi-asserted-by":"crossref","first-page":"1125","DOI":"10.1016\/j.chembiol.2009.11.001","article-title":"Inhibitors Target Actin Nucleators","author":"L Blanchoin","year":"2009","journal-title":"Chemistry and Biology"},{"key":"pcbi.1008213.ref036","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1038\/sj.onc.1209124","article-title":"Phosphorylation of the cytokinesis regulator ECT2 at G2\/M phase stimulates association of the mitotic kinase Plk1 and accumulation of GTP-bound RhoA","volume":"25","author":"F Niiya","year":"2006","journal-title":"Oncogene"},{"key":"pcbi.1008213.ref037","first-page":"565","volume-title":"CAK-Cyclin-Dependent Activating Kinase: A key kinase in cell cycle control and a target for Drugs? Cell Cycle","author":"G Lolli","year":"2005"},{"key":"pcbi.1008213.ref038","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1083\/jcb.201508080","article-title":"Modulation of FAK and Src adhesion signaling occurs independently of adhesion complex composition","volume":"212","author":"ER Horton","year":"2016","journal-title":"J Cell Biol"},{"key":"pcbi.1008213.ref039","doi-asserted-by":"crossref","first-page":"3203","DOI":"10.1083\/jcb.201802088","article-title":"Cell adhesion is regulated by CDK1 during the cell cycle","volume":"217","author":"MC Jones","year":"2018","journal-title":"J Cell Biol"},{"key":"pcbi.1008213.ref040","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.1083\/jcb.201502040","article-title":"\u03b15\u03b21 integrin recycling promotes Arp2\/3-independent cancer cell invasion via the formin FHOD3","volume":"210","author":"NR Paul","year":"2015","journal-title":"J Cell Biol"},{"key":"pcbi.1008213.ref041","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1016\/j.jtbi.2004.09.004","article-title":"Model of coupled transient changes of Rac, Rho, adhesions and stress fibers alignment in endothelial cells responding to shear stress","volume":"232","author":"G Civelekoglu-Scholey","year":"2005","journal-title":"J Theor Biol"},{"key":"pcbi.1008213.ref042","article-title":"A mathematical model of the coupled mechanisms of cell adhesion, contraction and spreading","author":"FJ Vernerey","year":"2013","journal-title":"Journal of mathematical biology"},{"key":"pcbi.1008213.ref043","doi-asserted-by":"crossref","first-page":"811","DOI":"10.1038\/nature06046","article-title":"Cdk1 is sufficient to drive the mammalian cell cycle","volume":"448","author":"D Santamar\u00eda","year":"2007","journal-title":"Nature"},{"key":"pcbi.1008213.ref044","first-page":"130","volume-title":"Nature Reviews Drug Discovery","author":"U Asghar","year":"2015"},{"key":"pcbi.1008213.ref045","doi-asserted-by":"crossref","first-page":"1282","DOI":"10.1038\/ncb3239","article-title":"Feedback regulation through myosin II confers robustness on RhoA signalling at E-cadherin junctions","volume":"17","author":"R Priya","year":"2015","journal-title":"Nat Cell Biol"},{"key":"pcbi.1008213.ref046","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1006\/bbrc.2000.3225","article-title":"Phosphorylation of CPI-17, an Inhibitor of Myosin Phosphatase, by Protein Kinase N","volume":"274","author":"T Hamaguchi","year":"2000","journal-title":"Biochem Biophys Res Commun"},{"key":"pcbi.1008213.ref047","doi-asserted-by":"crossref","first-page":"3577","DOI":"10.1074\/jbc.275.5.3577","article-title":"Rho-associated kinase ROCK activates LIM-kinase 1 by phosphorylation at threonine 508 within the activation loop","volume":"275","author":"K Ohashi","year":"2000","journal-title":"J Biol Chem"},{"key":"pcbi.1008213.ref048","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1038\/31735","article-title":"Cofilin phosphorylation by LIM-kinase 1 and its role in Rac-mediated actin reorganization","volume":"393","author":"N Yang","year":"1998","journal-title":"Nature"},{"key":"pcbi.1008213.ref049","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/978-1-4939-8612-5_3","article-title":"Modeling Rho GTPase dynamics using boolean logic","author":"JHR Hetmanski","year":"2018","journal-title":"Methods in Molecular Biology. Humana Press Inc."},{"key":"pcbi.1008213.ref050","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1186\/1752-0509-1-2","article-title":"Structural and functional analysis of cellular networks with CellNetAnalyzer","volume":"1","author":"S Klamt","year":"2007","journal-title":"BMC Syst Biol"},{"key":"pcbi.1008213.ref051","doi-asserted-by":"crossref","first-page":"1708","DOI":"10.1126\/science.1064829","article-title":"Taking Cell-Matrix Adhesions to the Third Dimension","volume":"294","author":"E Cukierman","year":"2001","journal-title":"Science (80-)"},{"key":"pcbi.1008213.ref052","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1083\/jcb.200212049","article-title":"Activity of Rho-family GTPases during cell division as visualized with FRET-based probes","volume":"162","author":"H Yoshizaki","year":"2003","journal-title":"J Cell Biol"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1008213","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2021,3,22]],"date-time":"2021-03-22T00:00:00Z","timestamp":1616371200000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008213","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,28]],"date-time":"2021-04-28T16:37:51Z","timestamp":1619627871000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008213"}},"subtitle":[],"editor":[{"given":"David","family":"Umulis","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,3,10]]},"references-count":52,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2021,3,10]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1008213","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2020.08.03.234021","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,10]]}}}