{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,21]],"date-time":"2026-05-21T16:52:53Z","timestamp":1779382373490,"version":"3.53.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1011412","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T00:00:00Z","timestamp":1713225600000}}],"reference-count":53,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2024,4,4]],"date-time":"2024-04-04T00:00:00Z","timestamp":1712188800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["EXC 2082\/1-390761711"],"award-info":[{"award-number":["EXC 2082\/1-390761711"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["EXC 2082\/1-390761711"],"award-info":[{"award-number":["EXC 2082\/1-390761711"]}],"id":[{"id":"10.13039\/501100001659","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 shape plays a fundamental role in many biological processes, including adhesion, migration, division and development, but it is not clear which shape model best predicts three-dimensional cell shape in structured environments. Here, we compare different modelling approaches with experimental data. The shapes of single mesenchymal cells cultured in custom-made 3D scaffolds were compared by a Fourier method with surfaces that minimize area under the given adhesion and volume constraints. For the minimized surface model, we found marked differences to the experimentally observed cell shapes, which necessitated the use of more advanced shape models. We used different variants of the cellular Potts model, which effectively includes both surface and bulk contributions. The simulations revealed that the Hamiltonian with linear area energy outperformed the elastic area constraint in accurately modelling the 3D shapes of cells in structured environments. Explicit modelling the nucleus did not improve the accuracy of the simulated cell shapes. Overall, our work identifies effective methods for accurately modelling cellular shapes in complex environments.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1011412","type":"journal-article","created":{"date-parts":[[2024,4,4]],"date-time":"2024-04-04T13:55:31Z","timestamp":1712238931000},"page":"e1011412","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":7,"title":["Modelling cell shape in 3D structured environments: A quantitative comparison with experiments"],"prefix":"10.1371","volume":"20","author":[{"given":"Rabea","family":"Link","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mona","family":"Jaggy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Bastmeyer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1483-640X","authenticated-orcid":true,"given":"Ulrich S.","family":"Schwarz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2024,4,4]]},"reference":[{"key":"pcbi.1011412.ref001","doi-asserted-by":"crossref","first-page":"R790","DOI":"10.1016\/j.cub.2009.07.029","article-title":"Biology and Physics of Cell Shape Changes in Development","volume":"19","author":"E Paluch","year":"2009","journal-title":"Current Biology"},{"key":"pcbi.1011412.ref002","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.ceb.2020.05.008","article-title":"Mechanics of the cellular actin cortex: From signalling to shape change","volume":"66","author":"M Kelkar","year":"2020","journal-title":"Current Opinion in Cell Biology"},{"key":"pcbi.1011412.ref003","doi-asserted-by":"crossref","first-page":"536","DOI":"10.1016\/j.tcb.2012.07.001","article-title":"Actin cortex mechanics and cellular morphogenesis","volume":"22","author":"G Salbreux","year":"2012","journal-title":"Trends in Cell Biology"},{"key":"pcbi.1011412.ref004","doi-asserted-by":"crossref","first-page":"3762","DOI":"10.1529\/biophysj.105.071506","article-title":"Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics","volume":"90","author":"S Kumar","year":"2006","journal-title":"Biophysical Journal"},{"key":"pcbi.1011412.ref005","doi-asserted-by":"crossref","first-page":"1811","DOI":"10.1083\/jcb.123.6.1811","article-title":"Microtubule-dependent control of cell shape and pseudopodial activity is inhibited by the antibody to kinesin motor domain","volume":"123","author":"VI Rodionov","year":"1993","journal-title":"The Journal of Cell Biology"},{"key":"pcbi.1011412.ref006","doi-asserted-by":"crossref","first-page":"17145","DOI":"10.1074\/jbc.R115.640359","article-title":"Intermediate Filaments Play a Pivotal Role in Regulating Cell Architecture and Function","volume":"290","author":"J Lowery","year":"2015","journal-title":"The Journal of Biological Chemistry"},{"key":"pcbi.1011412.ref007","doi-asserted-by":"crossref","first-page":"031304","DOI":"10.1063\/5.0099405","article-title":"Multiscale architecture: Mechanics of composite cytoskeletal networks","volume":"3","author":"C Lorenz","year":"2022","journal-title":"Biophysics Reviews"},{"issue":"5","key":"pcbi.1011412.ref008","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1016\/j.devcel.2020.02.013","article-title":"Of cell shapes and motion: the physical basis of animal cell migration","volume":"52","author":"DL Bodor","year":"2020","journal-title":"Developmental Cell"},{"key":"pcbi.1011412.ref009","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1016\/j.ceb.2006.10.001","article-title":"Cell shape and cell division","volume":"18","author":"M Thery","year":"2006","journal-title":"Current Opinion in Cell Biology"},{"issue":"6208","key":"pcbi.1011412.ref010","doi-asserted-by":"crossref","first-page":"1257998","DOI":"10.1126\/science.1257998","article-title":"Lattice light-sheet microscopy: imaging molecules to embryos at high spatiotemporal resolution","volume":"346","author":"BC Chen","year":"2014","journal-title":"Science"},{"key":"pcbi.1011412.ref011","doi-asserted-by":"crossref","first-page":"e26990","DOI":"10.7554\/eLife.26990","article-title":"Actin-based protrusions of migrating neutrophils are intrinsically lamellar and facilitate direction changes","volume":"6","author":"LK Fritz-Laylin","year":"2017","journal-title":"Elife"},{"key":"pcbi.1011412.ref012","article-title":"Myosin II controls cellular branching morphogenesis and migration in three dimensions by minimizing cell-surface curvature","author":"H Elliott","year":"2015","journal-title":"Nature Cell Biology"},{"issue":"2","key":"pcbi.1011412.ref013","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1111\/j.1365-2818.2007.01799.x","article-title":"Comparison of quantitative methods for cell-shape analysis","volume":"227","author":"Z Pincus","year":"2007","journal-title":"Journal of Microscopy"},{"issue":"7","key":"pcbi.1011412.ref014","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1177\/1087057110370894","article-title":"Automated Image Analysis for High-Content Screening and Analysis","volume":"15","author":"A Shariff","year":"2010","journal-title":"Journal of Biomolecular Screening"},{"issue":"7","key":"pcbi.1011412.ref015","doi-asserted-by":"crossref","first-page":"697","DOI":"10.1038\/nmeth.2084","article-title":"Biological imaging software tools","volume":"9","author":"KW Eliceiri","year":"2012","journal-title":"Nature Methods"},{"key":"pcbi.1011412.ref016","doi-asserted-by":"crossref","first-page":"2302145","DOI":"10.1002\/adfm.202302145","article-title":"Cell Shape and Forces in Elastic and Structured Environments: From Single Cells to Organoids","author":"R Link","year":"2023","journal-title":"Advanced Functional Materials"},{"issue":"4","key":"pcbi.1011412.ref017","doi-asserted-by":"crossref","first-page":"048101","DOI":"10.1103\/PhysRevLett.103.048101","article-title":"Effect of Adhesion Geometry and Rigidity on Cellular Force Distributions","volume":"103","author":"IB Bischofs","year":"2009","journal-title":"Physical Review Letters"},{"key":"pcbi.1011412.ref018","doi-asserted-by":"crossref","first-page":"2340","DOI":"10.1016\/j.bpj.2014.04.036","article-title":"Dynamics of cell shape and forces on micropatterned substrates predicted by a cellular Potts model","volume":"106","author":"PJ Albert","year":"2014","journal-title":"Biophysical Journal"},{"issue":"6","key":"pcbi.1011412.ref019","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1038\/ncb3525","article-title":"Actin cortex architecture regulates cell surface tension","volume":"19","author":"P Chugh","year":"2017","journal-title":"Nat Cell Biol"},{"issue":"7","key":"pcbi.1011412.ref020","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1016\/j.tcb.2020.03.005","article-title":"Actin Cell Cortex: Structure and Molecular Organization","volume":"30","author":"TM Svitkina","year":"2020","journal-title":"Trends in Cell Biology"},{"issue":"11","key":"pcbi.1011412.ref021","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":"1720","key":"pcbi.1011412.ref022","doi-asserted-by":"crossref","first-page":"20150520","DOI":"10.1098\/rstb.2015.0520","article-title":"Vertex models: from cell mechanics to tissue morphogenesis","volume":"372","author":"S Alt","year":"2017","journal-title":"Philosophical Transactions of the Royal Society B: Biological Sciences"},{"key":"pcbi.1011412.ref023","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1007\/978-3-030-30645-8_61","article-title":"On generative modeling of cell shape using 3D GANs","volume":"11752 LNCS","author":"D Wiesner","year":"2019","journal-title":"Lecture Notes in Computer Science"},{"issue":"22","key":"pcbi.1011412.ref024","doi-asserted-by":"crossref","first-page":"4046","DOI":"10.1091\/mbc.E15-06-0370","article-title":"Joint modeling of cell and nuclear shape variation","volume":"26","author":"GR Johnson","year":"2015","journal-title":"Molecular Biology of the Cell"},{"key":"pcbi.1011412.ref025","doi-asserted-by":"crossref","first-page":"1","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"},{"issue":"26","key":"pcbi.1011412.ref026","doi-asserted-by":"crossref","first-page":"1808110","DOI":"10.1002\/adma.201808110","article-title":"3D scaffolds to study basic cell biology","volume":"31","author":"M Hippler","year":"2019","journal-title":"Advanced Materials"},{"issue":"6","key":"pcbi.1011412.ref027","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1002\/cm.20126","article-title":"Cell distribution of stress fibres in response to the geometry of the adhesive environment","volume":"63","author":"M Thery","year":"2006","journal-title":"Cell Motility and the Cytoskeleton"},{"issue":"6","key":"pcbi.1011412.ref028","doi-asserted-by":"crossref","first-page":"1206","DOI":"10.1016\/j.cub.2021.01.002","article-title":"Acto-myosin network geometry defines centrosome position","volume":"31","author":"AJ Jimenez","year":"2021","journal-title":"Current Biology"},{"key":"pcbi.1011412.ref029","doi-asserted-by":"crossref","first-page":"2444","DOI":"10.1039\/C3SM52424H","article-title":"Cytoskeletal transition in patterned cells correlates with interfacial energy model","volume":"10","author":"A M\u00fcller","year":"2014","journal-title":"Soft Matter"},{"key":"pcbi.1011412.ref030","doi-asserted-by":"crossref","unstructured":"Kenmotsu K. Surfaces with constant mean curvature. 221. American Mathematical Soc.; 2003.","DOI":"10.1090\/mmono\/221"},{"issue":"2","key":"pcbi.1011412.ref031","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1080\/10586458.1992.10504253","article-title":"The Surface Evolver","volume":"1","author":"KA Brakke","year":"1992","journal-title":"Experimental Mathematics"},{"key":"pcbi.1011412.ref032","doi-asserted-by":"crossref","unstructured":"Garland M, Heckbert PS. Surface simplification using quadric error metrics. Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1997. 1997; p. 209\u2013216.","DOI":"10.1145\/258734.258849"},{"issue":"13","key":"pcbi.1011412.ref033","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.1011412.ref034","doi-asserted-by":"crossref","first-page":"2128","DOI":"10.1103\/PhysRevE.47.2128","article-title":"Simulation of the differential adhesion driven rearrangement of biological cells","volume":"47","author":"F Graner","year":"1993","journal-title":"Physical Review E"},{"key":"pcbi.1011412.ref035","doi-asserted-by":"crossref","first-page":"e7190","DOI":"10.1371\/journal.pone.0007190","article-title":"3D Multi-Cell Simulation of Tumor Growth and Angiogenesis","volume":"4","author":"A Shirinifard","year":"2009","journal-title":"PLoS ONE"},{"key":"pcbi.1011412.ref036","doi-asserted-by":"crossref","first-page":"e1004863","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"},{"key":"pcbi.1011412.ref037","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.46842","article-title":"Bridging the gap between single-cell migration and collective dynamics","volume":"8","author":"F Th\u00fcroff","year":"2019","journal-title":"eLife"},{"key":"pcbi.1011412.ref038","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":"AFM Mar\u00e9e","year":"2006","journal-title":"Bulletin of Mathematical Biology"},{"key":"pcbi.1011412.ref039","doi-asserted-by":"crossref","first-page":"128101","DOI":"10.1103\/PhysRevLett.105.128101","article-title":"Single Cells Spreading on a Protein Lattice Adopt an Energy Minimizing Shape","volume":"105","author":"B Vianay","year":"2010","journal-title":"Phys Rev Lett"},{"key":"pcbi.1011412.ref040","doi-asserted-by":"crossref","first-page":"2609","DOI":"10.1016\/j.bpj.2021.04.036","article-title":"Local actin dynamics couple speed and persistence in a Cellular Potts Model of cell migration","volume":"120","author":"IMN Wortel","year":"2021","journal-title":"Biophysical Journal"},{"issue":"1","key":"pcbi.1011412.ref041","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/npjcompumats.2016.19","article-title":"Computational approaches to substrate-based cell motility","volume":"2","author":"F Ziebert","year":"2016","journal-title":"npj Computational Materials"},{"key":"pcbi.1011412.ref042","doi-asserted-by":"crossref","unstructured":"Anderson ARA, editor. Single cell based models in biology and medicine. Mathematics and biosciences in interaction. Basel; Berlin [u.a.]: Birkh\u00e4user; 2007.","DOI":"10.1007\/978-3-7643-8123-3"},{"key":"pcbi.1011412.ref043","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/B978-0-12-388403-9.00013-8","article-title":"Multi-Scale Modeling of Tissues Using CompuCell3D","volume":"110","author":"MH Swat","year":"2012","journal-title":"Methods in Cell Biology"},{"issue":"2","key":"pcbi.1011412.ref044","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/s12195-008-0019-5","article-title":"Shapes of Red Blood Cells: Comparison of 3D Confocal Images with the Bilayer-Couple Model","volume":"1","author":"K Khairy","year":"2008","journal-title":"Cellular and Molecular Bioengineering"},{"key":"pcbi.1011412.ref045","doi-asserted-by":"crossref","unstructured":"Ducroz C, Olivo-Marin JC, Dufour A. Characterization of cell shape and deformation in 3D using Spherical Harmonics. Proceedings\u2014International Symposium on Biomedical Imaging. 2012; p. 848\u2013851.","DOI":"10.1109\/ISBI.2012.6235681"},{"issue":"1","key":"pcbi.1011412.ref046","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1109\/MSP.2014.2359131","article-title":"Signal processing challenges in quantitative 3-D cell morphology: More than meets the eye","volume":"32","author":"A Dufour","year":"2015","journal-title":"IEEE Signal Processing Magazine"},{"key":"pcbi.1011412.ref047","first-page":"1","article-title":"Dynamic spherical harmonics approach for shape classification of migrating cells","volume":"10","author":"A Medyukhina","year":"2020","journal-title":"Scientific Reports 2020 10:1"},{"issue":"6","key":"pcbi.1011412.ref048","doi-asserted-by":"crossref","first-page":"btad383","DOI":"10.1093\/bioinformatics\/btad383","article-title":"Cell shape characterization, alignment, and comparison using FlowShape","volume":"39","author":"C van Bavel","year":"2023","journal-title":"Bioinformatics"},{"key":"pcbi.1011412.ref049","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1006\/aama.1994.1008","article-title":"Computing fourier transforms and convolutions on the 2-sphere","volume":"15","author":"JR Driscoll","year":"1994","journal-title":"Advances in Applied Mathematics"},{"issue":"8","key":"pcbi.1011412.ref050","doi-asserted-by":"crossref","first-page":"2574","DOI":"10.1029\/2018GC007529","article-title":"SHTools: Tools for Working with Spherical Harmonics","volume":"19","author":"MA Wieczorek","year":"2018","journal-title":"Geochemistry, Geophysics, Geosystems"},{"key":"pcbi.1011412.ref051","doi-asserted-by":"crossref","first-page":"770","DOI":"10.1016\/j.bpj.2017.06.058","article-title":"Tension and Elasticity Contribute to Fibroblast Cell Shape in Three Dimensions","volume":"113","author":"CA Brand","year":"2017","journal-title":"Biophysical Journal"},{"issue":"12","key":"pcbi.1011412.ref052","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1038\/nrm.2017.109","article-title":"Mechanobiology by the numbers: a close relationship between biology and physics","volume":"18","author":"US Schwarz","year":"2017","journal-title":"Nature Reviews Molecular Cell Biology"},{"key":"pcbi.1011412.ref053","doi-asserted-by":"crossref","unstructured":"Belousov R, Savino S, Moghe P, Hiiragi T, Rondoni L, Erzberger A. When time matters: Poissonian cellular Potts models reveal nonequilibrium kinetics of cell sorting. arXiv preprint arXiv:230604443. 2023;.","DOI":"10.1103\/PhysRevLett.132.248401"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1011412","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2024,4,16]],"date-time":"2024-04-16T00:00:00Z","timestamp":1713225600000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1011412","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,15]],"date-time":"2024-11-15T13:25:16Z","timestamp":1731677116000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1011412"}},"subtitle":[],"editor":[{"given":"Padmini","family":"Rangamani","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2024,4,4]]},"references-count":53,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,4,4]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1011412","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2023.08.07.552225","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,4]]}}}