{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T18:22:29Z","timestamp":1777054949467,"version":"3.51.4"},"reference-count":186,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T00:00:00Z","timestamp":1607558400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Mathematical and computational models can assist in gaining an understanding of cell behavior at many levels of organization. Here, we review models in the literature that focus on eukaryotic cell motility at 3 size scales: intracellular signaling that regulates cell shape and movement, single cell motility, and collective cell behavior from a few cells to tissues. We survey recent literature to summarize distinct computational methods (phase-field, polygonal, Cellular Potts, and spherical cells). We discuss models that bridge between levels of organization, and describe levels of detail, both biochemical and geometric, included in the models. We also highlight links between models and experiments. We find that models that span the 3 levels are still in the minority.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1008411","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T19:30:14Z","timestamp":1607628614000},"page":"e1008411","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":84,"title":["Bridging from single to collective cell migration: A review of models and links to experiments"],"prefix":"10.1371","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4943-7591","authenticated-orcid":true,"given":"Andreas","family":"Buttensch\u00f6n","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2233-690X","authenticated-orcid":true,"given":"Leah","family":"Edelstein-Keshet","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2020,12,10]]},"reference":[{"key":"pcbi.1008411.ref001","first-page":"46","volume-title":"Seminars in Cell & Developmental Biology","author":"GB Blanchard","year":"2019"},{"issue":"8","key":"pcbi.1008411.ref002","doi-asserted-by":"crossref","first-page":"3766","DOI":"10.1021\/acsbiomaterials.8b01428","article-title":"Biomechanics of collective cell migration in cancer progression: experimental and computational methods","volume":"5","author":"CP Spatarelu","year":"2019","journal-title":"ACS Biomaterials Science & Engineering"},{"issue":"1","key":"pcbi.1008411.ref003","first-page":"e1365","article-title":"Modeling, signaling and cytoskeleton dynamics: integrated modeling-experimental frameworks in cell migration","volume":"9","author":"M Sun","year":"2017","journal-title":"Wiley Interdisciplinary Reviews: Systems Biology and Medicine"},{"key":"pcbi.1008411.ref004","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1146\/annurev-conmatphys-031218-013516","article-title":"Physical Models of Collective Cell Migration","volume":"11","author":"R Alert","year":"2020","journal-title":"Annual Review of Condensed Matter Physics"},{"issue":"3","key":"pcbi.1008411.ref005","doi-asserted-by":"crossref","first-page":"e1002402","DOI":"10.1371\/journal.pcbi.1002402","article-title":"How cells integrate complex stimuli: the effect of feedback from phosphoinositides and cell shape on cell polarization and motility","volume":"8","author":"AF Mar\u00e9e","year":"2012","journal-title":"PLoS computational biology"},{"key":"pcbi.1008411.ref006","first-page":"189175","article-title":"In silico mechanobiochemical modeling of morphogenesis in cell monolayers","author":"B Marzban","year":"2018","journal-title":"bioRxiv"},{"key":"pcbi.1008411.ref007","doi-asserted-by":"crossref","first-page":"S262","DOI":"10.1016\/j.ydbio.2018.01.013","article-title":"A Rho-GTPase based model explains spontaneous collective migration of neural crest cell clusters","volume":"444","author":"B Merchant","year":"2018","journal-title":"Developmental biology"},{"key":"pcbi.1008411.ref008","first-page":"1","article-title":"Cell\u2013substrate mechanics guide collective cell migration through intercellular adhesion: a dynamic finite element cellular model","author":"J Zhao","year":"2020","journal-title":"Biomechanics and Modeling in Mechanobiology"},{"issue":"1","key":"pcbi.1008411.ref009","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1007\/s10237-019-01204-7","article-title":"A quantitative high-resolution computational mechanics cell model for growing and regenerating tissues","volume":"19","author":"P Van Liedekerke","year":"2020","journal-title":"Biomechanics and Modeling in Mechanobiology"},{"issue":"11","key":"pcbi.1008411.ref010","doi-asserted-by":"crossref","first-page":"2230","DOI":"10.1016\/j.bpj.2018.10.014","article-title":"Dynamics of PAR proteins explain the oscillation and ratcheting mechanisms in dorsal closure","volume":"115","author":"CH Durney","year":"2018","journal-title":"Biophysical journal"},{"issue":"2","key":"pcbi.1008411.ref011","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1093\/bioinformatics\/btv527","article-title":"Computational modeling of development by epithelia, mesenchyme and their interactions: a unified model","volume":"32","author":"M Marin-Riera","year":"2015","journal-title":"Bioinformatics"},{"issue":"3","key":"pcbi.1008411.ref012","doi-asserted-by":"crossref","first-page":"e1006273","DOI":"10.1371\/journal.pcbi.1006273","article-title":"Quantitative agent-based modeling reveals mechanical stress response of growing tumor spheroids is predictable over various growth conditions and cell lines","volume":"15","author":"P Van Liedekerke","year":"2019","journal-title":"PLOS Computational Biology"},{"issue":"3","key":"pcbi.1008411.ref013","doi-asserted-by":"crossref","first-page":"031906","DOI":"10.1063\/1.5023410","article-title":"Epithelial vertex models with active biochemical regulation of contractility can explain organized collective cell motility","volume":"2","author":"S Koride","year":"2018","journal-title":"APL bioengineering"},{"issue":"4","key":"pcbi.1008411.ref014","doi-asserted-by":"crossref","first-page":"e1005451","DOI":"10.1371\/journal.pcbi.1005451","article-title":"Polarization and migration in the zebrafish posterior lateral line system","volume":"13","author":"H Knutsdottir","year":"2017","journal-title":"PLoS computational biology"},{"issue":"77","key":"pcbi.1008411.ref015","doi-asserted-by":"crossref","first-page":"3268","DOI":"10.1098\/rsif.2012.0448","article-title":"Collective cell migration: leadership, invasion and segregation","volume":"9","author":"AJ Kabla","year":"2012","journal-title":"Journal of The Royal Society Interface"},{"issue":"4","key":"pcbi.1008411.ref016","doi-asserted-by":"crossref","first-page":"046004","DOI":"10.1088\/1478-3975\/aab1c0","article-title":"Coupling mechanical tension and GTPase signaling to generate cell and tissue dynamics","volume":"15","author":"C Zmurchok","year":"2018","journal-title":"Physical biology"},{"issue":"9","key":"pcbi.1008411.ref017","doi-asserted-by":"crossref","first-page":"101488","DOI":"10.1016\/j.isci.2020.101488","article-title":"Cell Shape and Durotaxis Explained from Cell-Extracellular Matrix Forces and Focal Adhesion Dynamics","volume":"23","author":"EG Rens","year":"2020","journal-title":"Iscience"},{"issue":"1","key":"pcbi.1008411.ref018","doi-asserted-by":"crossref","first-page":"012401","DOI":"10.1103\/PhysRevE.95.012401","article-title":"Crawling and turning in a minimal reaction-diffusion cell motility model: coupling cell shape and biochemistry","volume":"95","author":"BA Camley","year":"2017","journal-title":"Physical Review E"},{"issue":"11","key":"pcbi.1008411.ref019","doi-asserted-by":"crossref","first-page":"2291","DOI":"10.1016\/j.bpj.2013.11.4498","article-title":"Vertex models of epithelial morphogenesis","volume":"106","author":"AG Fletcher","year":"2014","journal-title":"Biophysical journal"},{"issue":"51","key":"pcbi.1008411.ref020","doi-asserted-by":"crossref","first-page":"14621","DOI":"10.1073\/pnas.1521151113","article-title":"Emergent structures and dynamics of cell colonies by contact inhibition of locomotion","volume":"113","author":"B Smeets","year":"2016","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"13","key":"pcbi.1008411.ref021","doi-asserted-by":"crossref","first-page":"2013","DOI":"10.1103\/PhysRevLett.69.2013","article-title":"Simulation of biological cell sorting using a two-dimensional extended Potts model","volume":"69","author":"F Graner","year":"1992","journal-title":"Physical review letters"},{"key":"pcbi.1008411.ref022","doi-asserted-by":"crossref","first-page":"9172","DOI":"10.1038\/srep09172","article-title":"Collisions of deformable cells lead to collective migration","volume":"5","author":"J L\u00f6ber","year":"2015","journal-title":"Scientific reports"},{"key":"pcbi.1008411.ref023","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1007\/978-3-7643-8123-3_13","volume-title":"Single-cell-based models in biology and medicine","author":"KA Rejniak","year":"2007"},{"issue":"4","key":"pcbi.1008411.ref024","doi-asserted-by":"crossref","first-page":"e33501","DOI":"10.1371\/journal.pone.0033501","article-title":"Study on multicellular systems using a phase field model","volume":"7","author":"M Nonomura","year":"2012","journal-title":"PloS one"},{"issue":"1","key":"pcbi.1008411.ref025","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-017-10069-8","article-title":"Connecting individual to collective cell migration","volume":"7","author":"M George","year":"2017","journal-title":"Scientific reports"},{"issue":"10","key":"pcbi.1008411.ref026","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1004280","article-title":"Crawling and gliding: a computational model for shape-driven cell migration","volume":"11","author":"I Niculescu","year":"2015","journal-title":"PLoS computational biology"},{"issue":"3","key":"pcbi.1008411.ref027","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1088\/1478-3975\/2\/3\/001","article-title":"A single-cell-based model of tumor growth in vitro: monolayers and spheroids","volume":"2","author":"D Drasdo","year":"2005","journal-title":"Physical biology"},{"issue":"2","key":"pcbi.1008411.ref028","doi-asserted-by":"crossref","first-page":"e1004412","DOI":"10.1371\/journal.pcbi.1004412","article-title":"Inferring growth control mechanisms in growing multi-cellular spheroids of NSCLC cells from spatial-temporal image data","volume":"12","author":"N Jagiella","year":"2016","journal-title":"PLoS computational biology"},{"key":"pcbi.1008411.ref029","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.jtbi.2018.02.022","article-title":"Adhesion and volume constraints via nonlocal interactions determine cell organisation and migration profiles","volume":"445","author":"JA Carrillo","year":"2018","journal-title":"Journal of theoretical biology"},{"key":"pcbi.1008411.ref030","volume-title":"Cellular automaton modeling of biological pattern formation","author":"A Deutsch","year":"2005"},{"key":"pcbi.1008411.ref031","first-page":"601781","article-title":"From Energy to Cellular Force in the Cellular Potts Model","author":"EG Rens","year":"2019","journal-title":"bioRxiv"},{"issue":"1","key":"pcbi.1008411.ref032","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1242\/jcs.114.1.3","article-title":"Actin dynamics","volume":"114","author":"TD Pollard","year":"2001","journal-title":"Journal of cell science"},{"issue":"3","key":"pcbi.1008411.ref033","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1016\/S0006-3495(02)73897-6","article-title":"Regulation of actin dynamics in rapidly moving cells: a quantitative analysis","volume":"83","author":"A Mogilner","year":"2002","journal-title":"Biophysical journal"},{"issue":"6","key":"pcbi.1008411.ref034","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":"Biophysical journal"},{"issue":"6","key":"pcbi.1008411.ref035","doi-asserted-by":"crossref","first-page":"563","DOI":"10.1007\/s00249-003-0300-4","article-title":"Analysis of actin dynamics at the leading edge of crawling cells: implications for the shape of keratocyte lamellipodia","volume":"32","author":"H Grimm","year":"2003","journal-title":"European Biophysics Journal"},{"issue":"9","key":"pcbi.1008411.ref036","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pbio.0050233","article-title":"Emergence of large-scale cell morphology and movement from local actin filament growth dynamics","volume":"5","author":"CI Lacayo","year":"2007","journal-title":"PLoS biology"},{"issue":"7194","key":"pcbi.1008411.ref037","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.1008411.ref038","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1146\/annurev-cellbio-101512-122308","article-title":"Mathematical modeling of eukaryotic cell migration: insights beyond experiments","volume":"29","author":"G Danuser","year":"2013","journal-title":"Annual review of cell and developmental biology"},{"issue":"10","key":"pcbi.1008411.ref039","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1039\/c5ib00043b","article-title":"Multiscale mechanobiology: computational models for integrating molecules to multicellular systems","volume":"7","author":"M Mak","year":"2015","journal-title":"Integrative Biology"},{"issue":"9","key":"pcbi.1008411.ref040","doi-asserted-by":"crossref","first-page":"3529","DOI":"10.1016\/j.bpj.2009.01.037","article-title":"An open model of actin dendritic nucleation","volume":"96","author":"JA Ditlev","year":"2009","journal-title":"Biophysical journal"},{"key":"pcbi.1008411.ref041","first-page":"143","volume-title":"Seminars in cell & developmental biology","author":"A Mogilner","year":"2020"},{"issue":"8","key":"pcbi.1008411.ref042","doi-asserted-by":"crossref","first-page":"1589","DOI":"10.1016\/j.bpj.2016.08.044","article-title":"Theory from the Oster Laboratory leaps ahead of experiment in understanding actin-based cellular motility","volume":"111","author":"TD Pollard","year":"2016","journal-title":"Biophysical journal"},{"issue":"5","key":"pcbi.1008411.ref043","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1083\/jcb.200210140","article-title":"Fluorescence resonance energy transfer (FRET) microscopy imaging of live cell protein localizations","volume":"160","author":"RB Sekar","year":"2003","journal-title":"The Journal of cell biology"},{"issue":"5350","key":"pcbi.1008411.ref044","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.279.5350.509","article-title":"Rho GTPases and the actin cytoskeleton","volume":"279","author":"A Hall","year":"1998","journal-title":"Science"},{"issue":"1399","key":"pcbi.1008411.ref045","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1098\/rstb.2000.0632","article-title":"Rho GTPases: molecular switches that control the organization and dynamics of the actin cytoskeleton","volume":"355","author":"A Hall","year":"2000","journal-title":"Philosophical Transactions of the Royal Society of London Series B: Biological Sciences"},{"issue":"15","key":"pcbi.1008411.ref046","doi-asserted-by":"crossref","first-page":"2713","DOI":"10.1242\/jcs.114.15.2713","article-title":"Rho GTPases and cell migration","volume":"114","author":"AJ Ridley","year":"2001","journal-title":"Journal of cell science"},{"key":"pcbi.1008411.ref047","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-1-4939-8612-5_1","volume-title":"Rho GTPases","author":"S Khatibi","year":"2018"},{"issue":"3","key":"pcbi.1008411.ref048","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1038\/nrm1838","article-title":"Cell-signalling dynamics in time and space","volume":"7","author":"BN Kholodenko","year":"2006","journal-title":"Nature reviews Molecular cell biology"},{"issue":"2","key":"pcbi.1008411.ref049","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/S0955-0674(03)00017-6","article-title":"Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell","volume":"15","author":"JJ Tyson","year":"2003","journal-title":"Current opinion in cell biology"},{"issue":"1","key":"pcbi.1008411.ref050","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"},{"issue":"1","key":"pcbi.1008411.ref051","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 systems"},{"issue":"5","key":"pcbi.1008411.ref052","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":"Bulletin of mathematical biology"},{"key":"pcbi.1008411.ref053","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1146\/annurev-cellbio-100616-060739","article-title":"Excitable signal transduction networks in directed cell migration","volume":"33","author":"PN Devreotes","year":"2017","journal-title":"Annual review of cell and developmental biology"},{"issue":"6","key":"pcbi.1008411.ref054","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.0030108","article-title":"A mass conserved reaction\u2013diffusion system captures properties of cell polarity","volume":"3","author":"M Otsuji","year":"2007","journal-title":"PLoS computational biology"},{"issue":"6","key":"pcbi.1008411.ref055","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":"Bulletin of mathematical biology"},{"issue":"2","key":"pcbi.1008411.ref056","doi-asserted-by":"crossref","first-page":"812","DOI":"10.1529\/biophysj.104.055624","article-title":"A molecular model for axon guidance based on cross talk between rho GTPases","volume":"89","author":"Y Sakumura","year":"2005","journal-title":"Biophysical journal"},{"issue":"1","key":"pcbi.1008411.ref057","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1002831","article-title":"Computational analysis of Rho GTPase cycling","volume":"9","author":"CV Falkenberg","year":"2013","journal-title":"PLoS computational biology"},{"issue":"5","key":"pcbi.1008411.ref058","doi-asserted-by":"crossref","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":"JH Hetmanski","year":"2016","journal-title":"PLoS computational biology"},{"issue":"7","key":"pcbi.1008411.ref059","doi-asserted-by":"crossref","first-page":"1188","DOI":"10.1093\/bioinformatics\/bty766","article-title":"PhysiBoSS: a multi-scale agent-based modelling framework integrating physical dimension and cell signalling","volume":"35","author":"G Letort","year":"2018","journal-title":"Bioinformatics"},{"issue":"4","key":"pcbi.1008411.ref060","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"},{"issue":"9","key":"pcbi.1008411.ref061","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":"Biophysical journal"},{"issue":"4","key":"pcbi.1008411.ref062","doi-asserted-by":"crossref","first-page":"1420","DOI":"10.1137\/100815335","article-title":"A computational model of cell polarization and motility coupling mechanics and biochemistry","volume":"9","author":"B Vanderlei","year":"2011","journal-title":"Multiscale Modeling & Simulation"},{"key":"pcbi.1008411.ref063","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":"Journal of theoretical biology"},{"issue":"28","key":"pcbi.1008411.ref064","doi-asserted-by":"crossref","first-page":"E5750","DOI":"10.1073\/pnas.1700054114","article-title":"Mechanochemical feedback underlies coexistence of qualitatively distinct cell polarity patterns within diverse cell populations","volume":"114","author":"J Park","year":"2017","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"5","key":"pcbi.1008411.ref065","doi-asserted-by":"crossref","first-page":"e1005524","DOI":"10.1371\/journal.pcbi.1005524","article-title":"A mathematical model coupling polarity signaling to cell adhesion explains diverse cell migration patterns","volume":"13","author":"WR Holmes","year":"2017","journal-title":"PLoS computational biology"},{"issue":"4","key":"pcbi.1008411.ref066","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 journal on applied mathematics"},{"key":"pcbi.1008411.ref067","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":"Journal of theoretical biology"},{"issue":"11","key":"pcbi.1008411.ref068","doi-asserted-by":"crossref","first-page":"2235","DOI":"10.1016\/j.bpj.2015.10.032","article-title":"Modeling the mechanosensitivity of neutrophils passing through a narrow channel","volume":"109","author":"T Wu","year":"2015","journal-title":"Biophysical journal"},{"issue":"1","key":"pcbi.1008411.ref069","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.bpj.2018.05.033","article-title":"Spherical caps in cell polarization","volume":"115","author":"R Diegmiller","year":"2018","journal-title":"Biophysical journal"},{"issue":"52","key":"pcbi.1008411.ref070","doi-asserted-by":"crossref","first-page":"E3668","DOI":"10.1073\/pnas.1210295109","article-title":"Synthetic spatially graded Rac activation drives cell polarization and movement","volume":"109","author":"B Lin","year":"2012","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"15","key":"pcbi.1008411.ref071","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":"pcbi.1008411.ref072","doi-asserted-by":"crossref","first-page":"110386","DOI":"10.1016\/j.jtbi.2020.110386","article-title":"A mechanochemical model for rho GTPase mediated cell polarization","volume":"504","author":"KH Kopfer","year":"2020","journal-title":"Journal of Theoretical Biology"},{"issue":"2","key":"pcbi.1008411.ref073","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.tcb.2015.09.003","article-title":"Taking aim at moving targets in computational cell migration","volume":"26","author":"P Masuzzo","year":"2016","journal-title":"Trends in cell biology"},{"key":"pcbi.1008411.ref074","doi-asserted-by":"crossref","first-page":"6619","DOI":"10.1038\/ncomms7619","article-title":"Interplay between chemotaxis and contact inhibition of locomotion determines exploratory cell migration","volume":"6","author":"B Lin","year":"2015","journal-title":"Nature communications"},{"issue":"9","key":"pcbi.1008411.ref075","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1039\/c4ib00099d","article-title":"Simultaneous and independent tuning of RhoA and Rac1 activity with orthogonally inducible promoters","volume":"6","author":"JL MacKay","year":"2014","journal-title":"Integrative Biology"},{"key":"pcbi.1008411.ref076","doi-asserted-by":"crossref","first-page":"1438","DOI":"10.1016\/j.bpj.2020.01.035","article-title":"Simple Rho GTPase Dynamics Generate a Complex Regulatory Landscape Associated with Cell Shape","volume":"118","author":"C Zmurchok","year":"2020","journal-title":"Biophysical Journal"},{"issue":"9","key":"pcbi.1008411.ref077","doi-asserted-by":"crossref","first-page":"1692","DOI":"10.1016\/j.bpj.2019.09.024","article-title":"Extent of cell confinement in microtracks affects speed and results in differential matrix strains","volume":"117","author":"JA Mosier","year":"2019","journal-title":"Biophysical Journal"},{"issue":"1-2","key":"pcbi.1008411.ref078","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.cell.2011.10.050","article-title":"Membrane tension maintains cell polarity by confining signals to the leading edge during neutrophil migration","volume":"148","author":"AR Houk","year":"2012","journal-title":"Cell"},{"issue":"3","key":"pcbi.1008411.ref079","first-page":"245","article-title":"Roles of the cytoskeleton, cell adhesion and rho signalling in mechanosensing and mechanotransduction","volume":"161","author":"K Ohashi","year":"2017","journal-title":"The Journal of Biochemistry"},{"key":"pcbi.1008411.ref080","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":"Current opinion in cell biology"},{"issue":"7","key":"pcbi.1008411.ref081","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1039\/C7IB00019G","article-title":"Cellular orientation is guided by strain gradients","volume":"9","author":"S Chagnon-Lessard","year":"2017","journal-title":"Integrative Biology"},{"issue":"5","key":"pcbi.1008411.ref082","doi-asserted-by":"crossref","first-page":"e0126383","DOI":"10.1371\/journal.pone.0126383","article-title":"Topological data analysis of biological aggregation models","volume":"10","author":"CM Topaz","year":"2015","journal-title":"PloS one"},{"issue":"3","key":"pcbi.1008411.ref083","doi-asserted-by":"crossref","first-page":"e0213679","DOI":"10.1371\/journal.pone.0213679","article-title":"A topological approach to selecting models of biological experiments","volume":"14","author":"M Ulmer","year":"2019","journal-title":"PloS one"},{"issue":"12","key":"pcbi.1008411.ref084","doi-asserted-by":"crossref","first-page":"123125","DOI":"10.1063\/1.5125493","article-title":"Analyzing collective motion with machine learning and topology","volume":"29","author":"D Bhaskar","year":"2019","journal-title":"Chaos: An Interdisciplinary Journal of Nonlinear Science"},{"issue":"10","key":"pcbi.1008411.ref085","doi-asserted-by":"crossref","first-page":"5113","DOI":"10.1073\/pnas.1917763117","article-title":"Topological data analysis of zebrafish patterns","volume":"117","author":"MR McGuirl","year":"2020","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"14","key":"pcbi.1008411.ref086","doi-asserted-by":"crossref","first-page":"1833","DOI":"10.1091\/mbc.e17-03-0134","article-title":"Single and collective cell migration: the mechanics of adhesions","volume":"28","author":"C De Pascalis","year":"2017","journal-title":"Molecular biology of the cell"},{"issue":"6","key":"pcbi.1008411.ref087","doi-asserted-by":"crossref","first-page":"160056","DOI":"10.1098\/rsob.160056","article-title":"Multidisciplinary approaches to understanding collective cell migration in developmental biology","volume":"6","author":"LJ Schumacher","year":"2016","journal-title":"Open biology"},{"issue":"12","key":"pcbi.1008411.ref088","doi-asserted-by":"crossref","first-page":"e1005239","DOI":"10.1371\/journal.pcbi.1005239","article-title":"Modeling contact inhibition of locomotion of colliding cells migrating on micropatterned substrates","volume":"12","author":"DA Kulawiak","year":"2016","journal-title":"PLoS computational biology"},{"issue":"16","key":"pcbi.1008411.ref089","doi-asserted-by":"crossref","first-page":"2935","DOI":"10.1242\/dev.081471","article-title":"Multiscale mechanisms of cell migration during development: theory and experiment","volume":"139","author":"R McLennan","year":"2012","journal-title":"Development"},{"issue":"11","key":"pcbi.1008411.ref090","doi-asserted-by":"crossref","first-page":"2014","DOI":"10.1242\/dev.117507","article-title":"Neural crest migration is driven by a few trailblazer cells with a unique molecular signature narrowly confined to the invasive front","volume":"142","author":"R McLennan","year":"2015","journal-title":"Development"},{"issue":"41","key":"pcbi.1008411.ref091","doi-asserted-by":"crossref","first-page":"14770","DOI":"10.1073\/pnas.1414498111","article-title":"Polarity mechanisms such as contact inhibition of locomotion regulate persistent rotational motion of mammalian cells on micropatterns","volume":"111","author":"BA Camley","year":"2014","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"2","key":"pcbi.1008411.ref092","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1016\/j.ydbio.2010.04.010","article-title":"Cranial neural crest migration: new rules for an old road","volume":"344","author":"PM Kulesa","year":"2010","journal-title":"Developmental biology"},{"issue":"9","key":"pcbi.1008411.ref093","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0104969","article-title":"Directional collective cell migration emerges as a property of cell interactions","volume":"9","author":"ML Woods","year":"2014","journal-title":"PLoS One"},{"issue":"9","key":"pcbi.1008411.ref094","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1039\/C4IB00115J","article-title":"Collective motion of cells: from experiments to models","volume":"6","author":"E M\u00e9hes","year":"2014","journal-title":"Integrative biology"},{"issue":"11","key":"pcbi.1008411.ref095","doi-asserted-by":"crossref","first-page":"113002","DOI":"10.1088\/1361-6463\/aa56fe","article-title":"Physical models of collective cell motility: from cell to tissue","volume":"50","author":"BA Camley","year":"2017","journal-title":"Journal of physics D: Applied physics"},{"issue":"88","key":"pcbi.1008411.ref096","doi-asserted-by":"crossref","first-page":"20130717","DOI":"10.1098\/rsif.2013.0717","article-title":"Contact inhibition of locomotion probabilities drive solitary versus collective cell migration","volume":"10","author":"RA Desai","year":"2013","journal-title":"Journal of The Royal Society Interface"},{"issue":"20","key":"pcbi.1008411.ref097","doi-asserted-by":"crossref","first-page":"2641","DOI":"10.1093\/bioinformatics\/btq437","article-title":"A cell-based simulation software for multi-cellular systems","volume":"26","author":"S Hoehme","year":"2010","journal-title":"Bioinformatics"},{"issue":"6","key":"pcbi.1008411.ref098","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1007\/s002850050158","article-title":"A non-local model for a swarm","volume":"38","author":"A Mogilner","year":"1999","journal-title":"Journal of mathematical biology"},{"issue":"112","key":"pcbi.1008411.ref099","doi-asserted-by":"crossref","first-page":"20150812","DOI":"10.1098\/rsif.2015.0812","article-title":"Modelling stripe formation in zebrafish: an agent-based approach","volume":"12","author":"A Volkening","year":"2015","journal-title":"Journal of the Royal Society Interface"},{"issue":"15","key":"pcbi.1008411.ref100","doi-asserted-by":"crossref","first-page":"E2134","DOI":"10.1073\/pnas.1522656113","article-title":"Modeling and analysis of collective cell migration in an in vivo three-dimensional environment","volume":"113","author":"D Cai","year":"2016","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"4","key":"pcbi.1008411.ref101","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0122799","article-title":"A mathematical model of collective cell migration in a three-dimensional, heterogeneous environment","volume":"10","author":"DP Stonko","year":"2015","journal-title":"PloS one"},{"issue":"10","key":"pcbi.1008411.ref102","doi-asserted-by":"crossref","first-page":"108104","DOI":"10.1103\/PhysRevLett.105.108104","article-title":"Computational model for cell morphodynamics","volume":"105","author":"D Shao","year":"2010","journal-title":"Physical review letters"},{"issue":"22","key":"pcbi.1008411.ref103","first-page":"223001","article-title":"Collective gradient sensing and chemotaxis: modeling and recent developments","volume":"30","author":"BA Camley","year":"2018","journal-title":"Journal of Physics: Condensed Matter"},{"issue":"3","key":"pcbi.1008411.ref104","doi-asserted-by":"crossref","first-page":"036002","DOI":"10.1088\/1478-3975\/ab71f1","article-title":"A Rho-GTPase based model explains group advantage in collective chemotaxis of neural crest cells","volume":"17","author":"B Merchant","year":"2020","journal-title":"Physical Biology"},{"key":"pcbi.1008411.ref105","first-page":"1","article-title":"The role of single-cell mechanical behaviour and polarity in driving collective cell migration","author":"S Jain","year":"2020","journal-title":"Nature Physics"},{"issue":"1","key":"pcbi.1008411.ref106","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":"Biophysical journal"},{"issue":"6","key":"pcbi.1008411.ref107","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1016\/j.bpj.2012.07.048","article-title":"Computational modeling of single-cell migration: the leading role of extracellular matrix fibers","volume":"103","author":"DK Schl\u00fcter","year":"2012","journal-title":"Biophysical journal"},{"issue":"7224","key":"pcbi.1008411.ref108","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1038\/nature07441","article-title":"Contact inhibition of locomotion in vivo controls neural crest directional migration","volume":"456","author":"C Carmona-Fontaine","year":"2008","journal-title":"Nature"},{"issue":"12","key":"pcbi.1008411.ref109","doi-asserted-by":"crossref","first-page":"1194","DOI":"10.1038\/ncb2122","article-title":"Competition amongst Eph receptors regulates contact inhibition of locomotion and invasiveness in prostate cancer cells","volume":"12","author":"JW Astin","year":"2010","journal-title":"Nature cell biology"},{"issue":"7","key":"pcbi.1008411.ref110","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/j.tcb.2015.05.001","article-title":"Forcing contact inhibition of locomotion","volume":"25","author":"A Roycroft","year":"2015","journal-title":"Trends in cell biology"},{"issue":"2","key":"pcbi.1008411.ref111","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.cell.2015.02.015","article-title":"Inter-cellular forces orchestrate contact inhibition of locomotion","volume":"161","author":"JR Davis","year":"2015","journal-title":"Cell"},{"issue":"38","key":"pcbi.1008411.ref112","doi-asserted-by":"crossref","first-page":"7420","DOI":"10.1021\/bi300758e","article-title":"From mechanical force to RhoA activation","volume":"51","author":"EC Lessey","year":"2012","journal-title":"Biochemistry"},{"key":"pcbi.1008411.ref113","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/ncomms11288","article-title":"Repulsive cues combined with physical barriers and cell-cell adhesion determine progenitor cell positioning during organogenesis","volume":"7","author":"A Paksa","year":"2016","journal-title":"Nature communications"},{"issue":"7","key":"pcbi.1008411.ref114","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1038\/ncb2772","article-title":"Chase-and-run between adjacent cell populations promotes directional collective migration","volume":"15","author":"E Theveneau","year":"2013","journal-title":"Nature cell biology"},{"key":"pcbi.1008411.ref115","doi-asserted-by":"crossref","first-page":"e06656","DOI":"10.7554\/eLife.06656","article-title":"Correction: Mapping the dynamics of force transduction at cell\u2013cell junctions of epithelial clusters","volume":"4","author":"MR Ng","year":"2015","journal-title":"eLife"},{"key":"pcbi.1008411.ref116","doi-asserted-by":"crossref","first-page":"e58945","DOI":"10.7554\/eLife.58945","article-title":"Size-dependent patterns of cell proliferation and migration in freely-expanding epithelia","volume":"9","author":"MA Heinrich","year":"2020","journal-title":"eLife"},{"key":"pcbi.1008411.ref117","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/j.ceb.2019.10.001","article-title":"Multicellular scale front-to-rear polarity in collective migration","volume":"62","author":"L Capuana","year":"2020","journal-title":"Current opinion in cell biology"},{"issue":"6","key":"pcbi.1008411.ref118","doi-asserted-by":"crossref","first-page":"e1006208","DOI":"10.1371\/journal.pcbi.1006208","article-title":"Mechanical positioning of multiple nuclei in muscle cells","volume":"14","author":"A Manhart","year":"2018","journal-title":"PLoS computational biology"},{"issue":"2","key":"pcbi.1008411.ref119","doi-asserted-by":"crossref","first-page":"446","DOI":"10.1016\/0012-1606(81)90276-1","article-title":"The mechanical basis of morphogenesis: I. Epithelial folding and invagination","volume":"85","author":"GM Odell","year":"1981","journal-title":"Developmental biology"},{"issue":"2","key":"pcbi.1008411.ref120","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1083\/jcb.201508047","article-title":"Collective cell migration in development","volume":"212","author":"E Scarpa","year":"2016","journal-title":"Journal of Cell Biology"},{"issue":"7","key":"pcbi.1008411.ref121","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1038\/nrm2720","article-title":"Collective cell migration in morphogenesis, regeneration and cancer","volume":"10","author":"P Friedl","year":"2009","journal-title":"Nature reviews Molecular cell biology"},{"issue":"9","key":"pcbi.1008411.ref122","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1016\/j.tcb.2015.06.003","article-title":"Collective cell migration: guidance principles and hierarchies","volume":"25","author":"A Haeger","year":"2015","journal-title":"Trends in cell biology"},{"issue":"7260","key":"pcbi.1008411.ref123","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1038\/nature08241","article-title":"A genetically encoded photoactivatable Rac controls the motility of living cells","volume":"461","author":"YI Wu","year":"2009","journal-title":"Nature"},{"issue":"9","key":"pcbi.1008411.ref124","doi-asserted-by":"crossref","first-page":"1442","DOI":"10.1091\/mbc.E15-12-0832","article-title":"Subcellular optogenetic activation of Cdc42 controls local and distal signaling to drive immune cell migration","volume":"27","author":"PR O\u2019Neill","year":"2016","journal-title":"Molecular biology of the cell"},{"issue":"1","key":"pcbi.1008411.ref125","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.devcel.2018.05.029","article-title":"Membrane flow drives an adhesion-independent amoeboid cell migration mode","volume":"46","author":"PR O\u2019Neill","year":"2018","journal-title":"Developmental cell"},{"issue":"28","key":"pcbi.1008411.ref126","doi-asserted-by":"crossref","first-page":"11417","DOI":"10.1073\/pnas.1014853108","article-title":"Chemotactic cell trapping in controlled alternating gradient fields","volume":"108","author":"B Meier","year":"2011","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"6","key":"pcbi.1008411.ref127","doi-asserted-by":"crossref","first-page":"471","DOI":"10.1002\/cyto.a.22600","article-title":"Image based validation of dynamical models for cell reorientation","volume":"87","author":"R Lockley","year":"2015","journal-title":"Cytometry Part A"},{"issue":"8","key":"pcbi.1008411.ref128","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1038\/nrm882","article-title":"ERM proteins and merlin: integrators at the cell cortex","volume":"3","author":"A Bretscher","year":"2002","journal-title":"Nature reviews Molecular cell biology"},{"issue":"3","key":"pcbi.1008411.ref129","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1038\/ncb3115","article-title":"A molecular mechanotransduction pathway regulates collective migration of epithelial cells","volume":"17","author":"T Das","year":"2015","journal-title":"Nature cell biology"},{"issue":"5","key":"pcbi.1008411.ref130","doi-asserted-by":"crossref","first-page":"1807","DOI":"10.1073\/pnas.1321852111","article-title":"Nonautonomous contact guidance signaling during collective cell migration","volume":"111","author":"C Londono","year":"2014","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"3","key":"pcbi.1008411.ref131","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1038\/ncb2917","article-title":"Interplay of RhoA and mechanical forces in collective cell migration driven by leader cells","volume":"16","author":"M Reffay","year":"2014","journal-title":"Nature cell biology"},{"issue":"32","key":"pcbi.1008411.ref132","doi-asserted-by":"crossref","first-page":"12974","DOI":"10.1073\/pnas.1119313109","article-title":"Emerging modes of collective cell migration induced by geometrical constraints","volume":"109","author":"SRK Vedula","year":"2012","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"3","key":"pcbi.1008411.ref133","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1016\/j.bpj.2019.06.013","article-title":"Sustained oscillations of epithelial cell sheets","volume":"117","author":"G Peyret","year":"2019","journal-title":"Biophysical journal"},{"issue":"12","key":"pcbi.1008411.ref134","doi-asserted-by":"crossref","first-page":"2492","DOI":"10.1016\/j.bpj.2015.11.001","article-title":"Seeds of locally aligned motion and stress coordinate a collective cell migration","volume":"109","author":"A Zaritsky","year":"2015","journal-title":"Biophysical journal"},{"issue":"6","key":"pcbi.1008411.ref135","doi-asserted-by":"crossref","first-page":"1543","DOI":"10.1083\/jcb.201609095","article-title":"Diverse roles of guanine nucleotide exchange factors in regulating collective cell migration","volume":"216","author":"A Zaritsky","year":"2017","journal-title":"J Cell Biol"},{"issue":"7","key":"pcbi.1008411.ref136","doi-asserted-by":"crossref","first-page":"1769","DOI":"10.1016\/j.cell.2018.09.054","article-title":"Cell membranes resist flow","volume":"175","author":"Z Shi","year":"2018","journal-title":"Cell"},{"key":"pcbi.1008411.ref137","doi-asserted-by":"crossref","first-page":"8281","DOI":"10.1038\/ncomms9281","article-title":"TrkB\/BDNF signalling patterns the sympathetic nervous system","volume":"6","author":"JC Kasemeier-Kulesa","year":"2015","journal-title":"Nature communications"},{"issue":"4","key":"pcbi.1008411.ref138","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s40571-015-0082-3","article-title":"Simulating tissue mechanics with agent-based models: concepts, perspectives and some novel results","volume":"2","author":"P Van Liedekerke","year":"2015","journal-title":"Computational particle mechanics"},{"key":"pcbi.1008411.ref139","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/B978-0-12-811718-7.00014-9","volume-title":"Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes","author":"P Van Liedekerke","year":"2018"},{"key":"pcbi.1008411.ref140","first-page":"1","volume-title":"Cell Migrations: Causes and Functions","author":"Y Yang","year":"2019"},{"issue":"2","key":"pcbi.1008411.ref141","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/j.pbiomolbio.2013.09.003","article-title":"Implementing vertex dynamics models of cell populations in biology within a consistent computational framework","volume":"113","author":"AG Fletcher","year":"2013","journal-title":"Progress in biophysics and molecular biology"},{"key":"pcbi.1008411.ref142","article-title":"Multiscale model of colorectal cancer using the cellular Potts framework","volume":"14","author":"JM Osborne","year":"2015","journal-title":"Cancer informatics"},{"issue":"2","key":"pcbi.1008411.ref143","doi-asserted-by":"crossref","first-page":"e1005387","DOI":"10.1371\/journal.pcbi.1005387","article-title":"Comparing individual-based approaches to modelling the self-organization of multicellular tissues","volume":"13","author":"JM Osborne","year":"2017","journal-title":"PLoS computational biology"},{"key":"pcbi.1008411.ref144","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/B978-0-12-388403-9.00013-8","volume-title":"Methods in cell biology","author":"MH Swat","year":"2012"},{"issue":"9","key":"pcbi.1008411.ref145","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1093\/bioinformatics\/btt772","article-title":"Morpheus: a user-friendly modeling environment for multiscale and multicellular systems biology","volume":"30","author":"J Starru\u00df","year":"2014","journal-title":"Bioinformatics"},{"key":"pcbi.1008411.ref146","article-title":"Self-organized multicellular structures from simple cell signaling: a computational model","author":"N Mulberry","year":"2020","journal-title":"Physical Biology"},{"issue":"1","key":"pcbi.1008411.ref147","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.bpj.2019.05.020","article-title":"Mechanochemical coupling and junctional forces during collective cell migration","volume":"117","author":"J Bui","year":"2019","journal-title":"Biophysical journal"},{"issue":"8","key":"pcbi.1008411.ref148","doi-asserted-by":"crossref","first-page":"e12097","DOI":"10.1371\/journal.pone.0012097","article-title":"A sub-cellular viscoelastic model for cell population mechanics","volume":"5","author":"Y Jamali","year":"2010","journal-title":"PLoS One"},{"issue":"4","key":"pcbi.1008411.ref149","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1016\/j.devcel.2013.01.017","article-title":"Three-dimensional epithelial morphogenesis in the developing Drosophila egg","volume":"24","author":"M Osterfield","year":"2013","journal-title":"Developmental cell"},{"issue":"1","key":"pcbi.1008411.ref150","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.jtbi.2005.07.011","article-title":"Regulatory network for cell shape changes during Drosophila ventral furrow formation","volume":"239","author":"J Aracena","year":"2006","journal-title":"Journal of Theoretical Biology"},{"issue":"3","key":"pcbi.1008411.ref151","doi-asserted-by":"crossref","first-page":"035001","DOI":"10.1088\/1478-3975\/aa6591","article-title":"Modeling collective cell migration in geometric confinement","volume":"14","author":"V Tarle","year":"2017","journal-title":"Physical biology"},{"issue":"4","key":"pcbi.1008411.ref152","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1004863","article-title":"Dynamics of cell ensembles on adhesive micropatterns: bridging the gap between single cell spreading and collective cell migration","volume":"12","author":"PJ Albert","year":"2016","journal-title":"PLoS computational biology"},{"issue":"1","key":"pcbi.1008411.ref153","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-017-05321-0","article-title":"Collective motion of cells crawling on a substrate: roles of cell shape and contact inhibition","volume":"7","author":"SK Schnyder","year":"2017","journal-title":"Scientific reports"},{"issue":"6","key":"pcbi.1008411.ref154","doi-asserted-by":"crossref","first-page":"6635","DOI":"10.1103\/PhysRevE.52.6635","article-title":"Monte Carlo approach to tissue-cell populations","volume":"52","author":"D Drasdo","year":"1995","journal-title":"Physical review E"},{"issue":"19","key":"pcbi.1008411.ref155","doi-asserted-by":"crossref","first-page":"10448","DOI":"10.1073\/pnas.97.19.10448","article-title":"A model for individual and collective cell movement in Dictyostelium discoideum","volume":"97","author":"E Palsson","year":"2000","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"1","key":"pcbi.1008411.ref156","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jtbi.2008.05.004","article-title":"A 3-D model used to explore how cell adhesion and stiffness affect cell sorting and movement in multicellular systems","volume":"254","author":"E Palsson","year":"2008","journal-title":"Journal of Theoretical Biology"},{"issue":"3","key":"pcbi.1008411.ref157","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0059249","article-title":"A computational model for collective cellular motion in three dimensions: general framework and case study for cell pair dynamics","volume":"8","author":"F Frascoli","year":"2013","journal-title":"PloS one"},{"issue":"9","key":"pcbi.1008411.ref158","doi-asserted-by":"crossref","first-page":"1826","DOI":"10.1016\/j.bpj.2018.09.010","article-title":"Dynamic migration modes of collective cells","volume":"115","author":"SZ Lin","year":"2018","journal-title":"Biophysical journal"},{"issue":"156","key":"pcbi.1008411.ref159","doi-asserted-by":"crossref","first-page":"20190258","DOI":"10.1098\/rsif.2019.0258","article-title":"Dynamic instability and migration modes of collective cells in channels","volume":"16","author":"SZ Lin","year":"2019","journal-title":"Journal of the Royal Society Interface"},{"issue":"8","key":"pcbi.1008411.ref160","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1039\/c3ib40054a","article-title":"Guidance of collective cell migration by substrate geometry","volume":"5","author":"K Doxzen","year":"2013","journal-title":"Integrative biology"},{"issue":"1","key":"pcbi.1008411.ref161","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s42005-019-0185-x","article-title":"Confinement and substrate topography control cell migration in a 3D computational model","volume":"2","author":"B Winkler","year":"2019","journal-title":"Communications Physics"},{"issue":"1","key":"pcbi.1008411.ref162","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1073\/pnas.1312076111","article-title":"Theory of epithelial sheet morphology in three dimensions","volume":"111","author":"E Hannezo","year":"2014","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"pcbi.1008411.ref163","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/978-3-030-17593-1_4","volume-title":"Cell Migrations: Causes and Functions","author":"S Banerjee","year":"2019"},{"issue":"3","key":"pcbi.1008411.ref164","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1016\/j.bpj.2010.11.083","article-title":"Continuum model of collective cell migration in wound healing and colony expansion","volume":"100","author":"JC Arciero","year":"2011","journal-title":"Biophysical journal"},{"issue":"4","key":"pcbi.1008411.ref165","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1007\/s10237-018-1010-2","article-title":"A hybrid computational model for collective cell durotaxis","volume":"17","author":"J Escribano","year":"2018","journal-title":"Biomechanics and modeling in mechanobiology"},{"issue":"09","key":"pcbi.1008411.ref166","doi-asserted-by":"crossref","first-page":"1737","DOI":"10.1142\/S0218202518400043","article-title":"An age-structured continuum model for myxobacteria","volume":"28","author":"P Degond","year":"2018","journal-title":"Mathematical Models and Methods in Applied Sciences"},{"key":"pcbi.1008411.ref167","doi-asserted-by":"crossref","unstructured":"Aceves-Sanchez P, Degond P, Keaveny EE, Manhart A, Merino-Aceituno S, Peurichard D. Large-scale dynamics of self-propelled particles moving through obstacles: model derivation and pattern formation. arXiv preprint arXiv:200412638. 2020;.","DOI":"10.1007\/s11538-020-00805-z"},{"issue":"4","key":"pcbi.1008411.ref168","doi-asserted-by":"crossref","first-page":"046003","DOI":"10.1088\/1478-3975\/ab907e","article-title":"Leader-cell-driven epithelial sheet fingering","volume":"17","author":"Y Yang","year":"2020","journal-title":"Physical Biology"},{"issue":"9","key":"pcbi.1008411.ref169","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1101\/gad.978802","article-title":"Role of Rho family GTPases in epithelial morphogenesis","volume":"16","author":"L Van Aelst","year":"2002","journal-title":"Genes & development"},{"issue":"3","key":"pcbi.1008411.ref170","doi-asserted-by":"crossref","first-page":"e983869","DOI":"10.4161\/sgtp.28997","article-title":"Rho GTPases in collective cell migration","volume":"5","author":"MM Zegers","year":"2014","journal-title":"Small GTPases"},{"issue":"1","key":"pcbi.1008411.ref171","doi-asserted-by":"crossref","first-page":"3469","DOI":"10.1038\/s41467-018-05927-6","article-title":"Mechanical interactions among followers determine the emergence of leaders in migrating epithelial cell collectives","volume":"9","author":"M Vishwakarma","year":"2018","journal-title":"Nature communications"},{"issue":"11","key":"pcbi.1008411.ref172","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1038\/nmat4062","article-title":"Collective and individual migration following the epithelial\u2013mesenchymal transition","volume":"13","author":"IY Wong","year":"2014","journal-title":"Nature materials"},{"issue":"1","key":"pcbi.1008411.ref173","first-page":"1","article-title":"Switch-like enhancement of epithelial-mesenchymal transition by YAP through feedback regulation of WT1 and Rho-family GTPases","volume":"10","author":"J Park","year":"2019","journal-title":"Nature communications"},{"issue":"5","key":"pcbi.1008411.ref174","doi-asserted-by":"crossref","first-page":"20160042","DOI":"10.1098\/rsfs.2016.0042","article-title":"Prediction of traction forces of motile cells","volume":"6","author":"C Roux","year":"2016","journal-title":"Interface focus"},{"key":"pcbi.1008411.ref175","doi-asserted-by":"crossref","unstructured":"Marzban B. A multiphysics computational framework for understanding cell and microtissue morphogenesis [PhD Thesis]. University of Rhode Island; 2018. Available from: https:\/\/doi.org\/10.23860\/diss-marzban-bahador-2018.","DOI":"10.23860\/diss-marzban-bahador-2018"},{"issue":"9","key":"pcbi.1008411.ref176","doi-asserted-by":"crossref","first-page":"3671","DOI":"10.1529\/biophysj.107.117002","article-title":"Exploring the control circuit of cell migration by mathematical modeling","volume":"94","author":"J Satulovsky","year":"2008","journal-title":"Biophysical journal"},{"issue":"3","key":"pcbi.1008411.ref177","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1006\/jtbi.1996.0237","article-title":"Modelling morphogenesis: from single cells to crawling slugs","volume":"184","author":"NJ Savill","year":"1997","journal-title":"Journal of theoretical biology"},{"issue":"7","key":"pcbi.1008411.ref178","doi-asserted-by":"crossref","first-page":"3879","DOI":"10.1073\/pnas.061535198","article-title":"How amoeboids self-organize into a fruiting body: multicellular coordination in Dictyostelium discoideum","volume":"98","author":"AF Mar\u00e9e","year":"2001","journal-title":"Proceedings of the National Academy of Sciences"},{"key":"pcbi.1008411.ref179","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1006\/jtbi.2000.1087","article-title":"Evolving Mechanisms of Morphogenesis: on the Interplay between Differential Adhesionand Cell Differentiation","volume":"203","author":"P Hogeweg","year":"2000","journal-title":"J theor Biol"},{"issue":"2","key":"pcbi.1008411.ref180","doi-asserted-by":"crossref","first-page":"e1004092","DOI":"10.1371\/journal.pcbi.1004092","article-title":"Segment-specific adhesion as a driver of convergent extension","volume":"11","author":"RM Vroomans","year":"2015","journal-title":"PLoS computational biology"},{"key":"pcbi.1008411.ref181","article-title":"Cognac: a chaste plugin for the multiscale simulation of gene regulatory networks driving the spatial dynamics of tissues and cancer","volume":"14","author":"S Rubinacci","year":"2015","journal-title":"Cancer informatics"},{"issue":"6398","key":"pcbi.1008411.ref182","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1126\/science.aat0271","article-title":"Programming self-organizing multicellular structures with synthetic cell-cell signaling","volume":"361","author":"S Toda","year":"2018","journal-title":"Science"},{"key":"pcbi.1008411.ref183","first-page":"784496","article-title":"A Modular Computational Framework for the Design of Multicellular Genetic Circuits of Morphogenesis","author":"C Lam","year":"2020","journal-title":"bioRxiv"},{"issue":"45","key":"pcbi.1008411.ref184","doi-asserted-by":"crossref","first-page":"18289","DOI":"10.1073\/pnas.1108993108","article-title":"Balanced Rac1 and RhoA activities regulate cell shape and drive invagination morphogenesis in epithelia","volume":"108","author":"BK Chauhan","year":"2011","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"1","key":"pcbi.1008411.ref185","first-page":"115","article-title":"Hybrid models of tumor growth","volume":"3","author":"KA Rejniak","year":"2011","journal-title":"Wiley Interdisciplinary Reviews: Systems Biology and Medicine"},{"issue":"1","key":"pcbi.1008411.ref186","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1186\/s13628-015-0022-x","article-title":"The biophysical nature of cells: potential cell behaviours revealed by analytical and computational studies of cell surface mechanics","volume":"8","author":"R Magno","year":"2015","journal-title":"BMC biophysics"}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008411","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,14]],"date-time":"2023-10-14T23:19:29Z","timestamp":1697325569000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008411"}},"subtitle":[],"editor":[{"given":"Alex","family":"Mogilner","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2020,12,10]]},"references-count":186,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2020,12,10]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1008411","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,10]]}}}