{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T19:54:06Z","timestamp":1773258846524,"version":"3.50.1"},"reference-count":57,"publisher":"Public Library of Science (PLoS)","issue":"4","license":[{"start":{"date-parts":[[2016,4,26]],"date-time":"2016-04-26T00:00:00Z","timestamp":1461628800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1263751"],"award-info":[{"award-number":["DMS-1263751"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["ro1-ca127857"],"award-info":[{"award-number":["ro1-ca127857"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000054","name":"National Cancer Institute","doi-asserted-by":"publisher","award":["CA125123"],"award-info":[{"award-number":["CA125123"]}],"id":[{"id":"10.13039\/100000054","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"DOI":"10.1371\/journal.pcbi.1004839","type":"journal-article","created":{"date-parts":[[2016,4,26]],"date-time":"2016-04-26T17:30:18Z","timestamp":1461691818000},"page":"e1004839","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":53,"title":["A Geometrically-Constrained Mathematical Model of Mammary Gland Ductal Elongation Reveals Novel Cellular Dynamics within the Terminal End Bud"],"prefix":"10.1371","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6603-8448","authenticated-orcid":false,"given":"Ingrid","family":"Paine","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Arnaud","family":"Chauviere","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"John","family":"Landua","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amulya","family":"Sreekumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vittorio","family":"Cristini","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeffrey","family":"Rosen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael T.","family":"Lewis","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2016,4,26]]},"reference":[{"key":"ref1","author":"DAW Thompson","year":"1917"},{"issue":"1\u20132","key":"ref2","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/BF02459572","article-title":"The chemical basis of morphogenesis","volume":"52","author":"AM Turing","year":"1990","journal-title":"Bulletin of mathematical biology"},{"issue":"1","key":"ref3","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/BF02705153","article-title":"Can morphogenesis be understood in terms of physical rules?","volume":"30","author":"R Takaki","year":"2005","journal-title":"Journal of biosciences"},{"issue":"5999","key":"ref4","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.1126\/science.1179047","article-title":"Reaction-diffusion model as a framework for understanding biological pattern formation","volume":"329","author":"S Kondo","year":"2010","journal-title":"Science"},{"issue":"5\u20136","key":"ref5","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1387\/ijdb.072556cc","article-title":"Reptile scale paradigm: Evo-Devo, pattern formation and regeneration","volume":"53","author":"C Chang","year":"2009","journal-title":"The International journal of developmental biology"},{"issue":"8","key":"ref6","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1093\/emboj\/cdg176","article-title":"Modeling the early stages of vascular network assembly","volume":"22","author":"G Serini","year":"2003","journal-title":"The EMBO journal"},{"issue":"10","key":"ref7","doi-asserted-by":"crossref","first-page":"e129","DOI":"10.1371\/journal.pcbi.0020129","article-title":"Simulating properties of in vitro epithelial cell morphogenesis","volume":"2","author":"MR Grant","year":"2006","journal-title":"PLoS computational biology"},{"issue":"5","key":"ref8","doi-asserted-by":"crossref","first-page":"857","DOI":"10.1006\/bulm.1998.0042","article-title":"Continuous and discrete mathematical models of tumor-induced angiogenesis","volume":"60","author":"AR Anderson","year":"1998","journal-title":"Bulletin of mathematical biology"},{"issue":"1","key":"ref9","first-page":"1","article-title":"Tip cell overtaking occurs as a side effect of sprouting in computational models of angiogenesis","volume":"9","author":"SEM Boas","year":"2015","journal-title":"BMC Systems Biology"},{"issue":"2","key":"ref10","doi-asserted-by":"crossref","first-page":"H894","DOI":"10.1152\/ajpheart.00579.2005","article-title":"Scaling laws of vascular trees: of form and function","volume":"290","author":"GS Kassab","year":"2006","journal-title":"American journal of physiology Heart and circulatory physiology"},{"issue":"4","key":"ref11","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1039\/c0ib00092b","article-title":"Phenotypic transition maps of 3D breast acini obtained by imaging-guided agent-based modeling","volume":"3","author":"J Tang","year":"2011","journal-title":"Integrative biology: quantitative biosciences from nano to macro"},{"issue":"7","key":"ref12","doi-asserted-by":"crossref","first-page":"1347","DOI":"10.1016\/j.bpj.2015.08.003","article-title":"A Mechanistic Collective Cell Model for Epithelial Colony Growth and Contact Inhibition","volume":"109","author":"S Aland","year":"2015","journal-title":"Biophysical journal"},{"issue":"1\u20132","key":"ref13","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1007\/s00285-008-0172-4","article-title":"From single cells to tissue architecture-a bottom-up approach to modelling the spatio-temporal organisation of complex multi-cellular systems","volume":"58","author":"J Galle","year":"2009","journal-title":"Journal of mathematical biology"},{"key":"ref14","author":"V Cristini","year":"2010"},{"key":"ref15","first-page":"913","article-title":"Encyclopedia of Complexity and Systems Science","author":"H Hatzikirou","year":"2009"},{"issue":"4\u20135","key":"ref16","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1007\/s00285-008-0218-7","article-title":"Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications","volume":"58","author":"L Preziosi","year":"2009","journal-title":"Journal of mathematical biology"},{"issue":"5","key":"ref17","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1111\/j.1365-2184.2009.00627.x","article-title":"An integrative computational model for intestinal tissue renewal","volume":"42","author":"IM van Leeuwen","year":"2009","journal-title":"Cell proliferation"},{"key":"ref18","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1186\/1752-0509-6-93","article-title":"A reaction-diffusion mechanism influences cell lineage progression as a basis for formation, regeneration, and stability of intestinal crypts","volume":"6","author":"L Zhang","year":"2012","journal-title":"BMC Syst Biol"},{"issue":"23","key":"ref19","doi-asserted-by":"crossref","first-page":"10371","DOI":"10.1073\/pnas.0909374107","article-title":"Prediction and validation of cell alignment along microvessels as order principle to restore tissue architecture in liver regeneration","volume":"107","author":"S Hoehme","year":"2010","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"key":"ref20","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.jtbi.2012.02.002","article-title":"Patient-calibrated agent-based modelling of ductal carcinoma in situ (DCIS): from microscopic measurements to macroscopic predictions of clinical progression","volume":"301","author":"P Macklin","year":"2012","journal-title":"Journal of theoretical biology"},{"issue":"3","key":"ref21","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1002\/stem.1533","article-title":"Irradiation of juvenile, but not adult, mammary gland increases stem cell self-renewal and estrogen receptor negative tumors","volume":"32","author":"J Tang","year":"2014","journal-title":"Stem cells"},{"issue":"9","key":"ref22","doi-asserted-by":"crossref","first-page":"130088","DOI":"10.1098\/rsob.130088","article-title":"The control of branching morphogenesis","volume":"3","author":"D Iber","year":"2013","journal-title":"Open biology"},{"issue":"2","key":"ref23","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1093\/imammb\/dql029","article-title":"Mathematical analysis of a free-boundary model for lung branching morphogenesis","volume":"24","author":"D Hartmann","year":"2007","journal-title":"Mathematical medicine and biology: a journal of the IMA"},{"key":"ref24","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.jtbi.2015.04.015","article-title":"A spatially-averaged mathematical model of kidney branching morphogenesis","volume":"379","author":"VS Zubkov","year":"2015","journal-title":"Journal of theoretical biology"},{"issue":"3","key":"ref25","doi-asserted-by":"crossref","first-page":"868","DOI":"10.1007\/s11538-007-9282-1","article-title":"Modeling of branching patterns in plants","volume":"70","author":"N Bessonov","year":"2008","journal-title":"Bulletin of mathematical biology"},{"issue":"2","key":"ref26","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1042\/BST0380645","article-title":"The role of chemical dynamics in plant morphogenesis(1)","volume":"38","author":"DM Holloway","year":"2010","journal-title":"Biochemical Society transactions"},{"key":"ref27","first-page":"679","article-title":"Modeling mammary gland morphogenesis as a reaction-diffusion process","volume":"1","author":"MR Grant","year":"2004","journal-title":"Conference proceedings: Annual International Conference of the IEEE Engineering in Medicine and Biology Society IEEE Engineering in Medicine and Biology Society Conference"},{"issue":"3","key":"ref28","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1109\/TMI.2011.2175401","article-title":"Three-dimensional in silico breast phantoms for multimodal image simulations","volume":"31","author":"DM Mahr","year":"2012","journal-title":"IEEE transactions on medical imaging"},{"issue":"10","key":"ref29","doi-asserted-by":"crossref","first-page":"2146","DOI":"10.1109\/TMI.2015.2424854","article-title":"Description and Characterization of a Novel Method for Partial Volume Simulation in Software Breast Phantoms","volume":"34","author":"F Chen","year":"2015","journal-title":"IEEE transactions on medical imaging"},{"issue":"5","key":"ref30","doi-asserted-by":"crossref","first-page":"1450","DOI":"10.1007\/s11538-008-9308-3","article-title":"A computational study of the development of epithelial acini: II. Necessary conditions for structure and lumen stability","volume":"70","author":"KA Rejniak","year":"2008","journal-title":"Bulletin of mathematical biology"},{"issue":"5797","key":"ref31","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1126\/science.1131000","article-title":"Tissue geometry determines sites of mammary branching morphogenesis in organotypic cultures","volume":"314","author":"CM Nelson","year":"2006","journal-title":"Science"},{"issue":"1","key":"ref32","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.ydbio.2008.02.014","article-title":"Terminal end bud maintenance in mammary gland is dependent upon FGFR2b signaling","volume":"317","author":"S Parsa","year":"2008","journal-title":"Developmental biology"},{"issue":"2","key":"ref33","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1016\/0012-1606(83)90086-6","article-title":"Mammary ductal elongation: differentiation of myoepithelium and basal lamina during branching morphogenesis","volume":"97","author":"JM Williams","year":"1983","journal-title":"Developmental biology"},{"issue":"3","key":"ref34","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1002\/ijc.2910260315","article-title":"The effect of age on the histopathogenesis of 7,12-dimethylbenz(a)-anthracene-induced mammary tumors in the Lewis rat","volume":"26","author":"SZ Haslam","year":"1980","journal-title":"International journal of cancer Journal international du cancer"},{"issue":"9","key":"ref35","doi-asserted-by":"crossref","first-page":"4020","DOI":"10.1073\/pnas.74.9.4020","article-title":"Histopathogenesis of 7,12-diemthylbenz(a)anthracene-induced rat mammary tumors","volume":"74","author":"SZ Haslam","year":"1977","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"issue":"7372","key":"ref36","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1038\/nature10573","article-title":"Distinct stem cells contribute to mammary gland development and maintenance","volume":"479","author":"A Van Keymeulen","year":"2011","journal-title":"Nature"},{"issue":"7488","key":"ref37","doi-asserted-by":"crossref","first-page":"322","DOI":"10.1038\/nature12948","article-title":"In situ identification of bipotent stem cells in the mammary gland","volume":"506","author":"AC Rios","year":"2014","journal-title":"Nature"},{"issue":"17","key":"ref38","doi-asserted-by":"crossref","first-page":"1882","DOI":"10.1101\/gad.1932810","article-title":"s-SHIP promoter expression marks activated stem cells in developing mouse mammary tissue","volume":"24","author":"L Bai","year":"2010","journal-title":"Genes & development"},{"issue":"2","key":"ref39","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1002\/1097-0029(20010115)52:2<155::AID-JEMT1001>3.0.CO;2-P","article-title":"Postnatal mammary gland morphogenesis","volume":"52","author":"GB Silberstein","year":"2001","journal-title":"Microscopy research and technique"},{"issue":"12","key":"ref40","doi-asserted-by":"crossref","first-page":"4013","DOI":"10.1242\/dev.122.12.4013","article-title":"Apoptosis in the terminal endbud of the murine mammary gland: a mechanism of ductal morphogenesis","volume":"122","author":"RC Humphreys","year":"1996","journal-title":"Development"},{"issue":"Pt 3","key":"ref41","first-page":"381","article-title":"Myoepithelial cell differentiation in rat mammary glands","volume":"111","author":"CJ Radnor","year":"1972","journal-title":"Journal of anatomy"},{"issue":"11","key":"ref42","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1101\/gad.242511.114","article-title":"Mammary stem cells and the differentiation hierarchy: current status and perspectives","volume":"28","author":"JE Visvader","year":"2014","journal-title":"Genes & development"},{"key":"ref43","first-page":"155","article-title":"Methods in Mammary Gland Biology and Breast Cancer Research","author":"CWDaGB Silberstein","year":"2001"},{"issue":"2","key":"ref44","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.devcel.2006.12.003","article-title":"BIM regulates apoptosis during mammary ductal morphogenesis, and its absence reveals alternative cell death mechanisms","volume":"12","author":"AA Mailleux","year":"2007","journal-title":"Developmental cell"},{"issue":"1","key":"ref45","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.ydbio.2008.06.005","article-title":"Genetic mosaic analysis reveals FGF receptor 2 function in terminal end buds during mammary gland branching morphogenesis","volume":"321","author":"P Lu","year":"2008","journal-title":"Developmental biology"},{"issue":"4","key":"ref46","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1016\/j.devcel.2008.03.003","article-title":"Collective epithelial migration and cell rearrangements drive mammary branching morphogenesis","volume":"14","author":"AJ Ewald","year":"2008","journal-title":"Developmental cell"},{"issue":"1","key":"ref47","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/S0092-8674(02)01001-2","article-title":"The role of apoptosis in creating and maintaining luminal space within normal and oncogene-expressing mammary acini","volume":"111","author":"J Debnath","year":"2002","journal-title":"Cell"},{"issue":"10","key":"ref48","doi-asserted-by":"crossref","first-page":"3438","DOI":"10.1073\/pnas.0400443101","article-title":"Tumor necrosis factor-related apoptosis-inducing ligand (TRAIL) is required for induction of autophagy during lumen formation in vitro","volume":"101","author":"KR Mills","year":"2004","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"},{"issue":"3","key":"ref49","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/S1534-5807(03)00054-6","article-title":"Netrin-1\/neogenin interaction stabilizes multipotent progenitor cap cells during mammary gland morphogenesis","volume":"4","author":"K Srinivasan","year":"2003","journal-title":"Developmental cell"},{"issue":"7","key":"ref50","doi-asserted-by":"crossref","first-page":"1562","DOI":"10.1242\/dev.108258","article-title":"Plk2 regulates mitotic spindle orientation and mammary gland development","volume":"141","author":"E Villegas","year":"2014","journal-title":"Development"},{"issue":"11","key":"ref51","doi-asserted-by":"crossref","first-page":"4336","DOI":"10.1210\/en.2011-1100","article-title":"Repressor of estrogen receptor activity (REA) is essential for mammary gland morphogenesis and functional activities: studies in conditional knockout mice","volume":"152","author":"S Park","year":"2011","journal-title":"Endocrinology"},{"issue":"6","key":"ref52","doi-asserted-by":"crossref","first-page":"R96","DOI":"10.1186\/bcr2198","article-title":"ErbB3 is required for ductal morphogenesis in the mouse mammary gland. Breast cancer research","volume":"10","author":"AJ Jackson-Fisher","year":"2008","journal-title":"BCR"},{"issue":"11","key":"ref53","doi-asserted-by":"crossref","first-page":"4937","DOI":"10.1210\/endo.142.11.8500","article-title":"Targeted disruption of the IGF-I receptor gene decreases cellular proliferation in mammary terminal end buds","volume":"142","author":"SG Bonnette","year":"2001","journal-title":"Endocrinology"},{"issue":"4","key":"ref54","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1083\/jcb.200107119","article-title":"Inducible dimerization of FGFR1: development of a mouse model to analyze progressive transformation of the mammary gland","volume":"157","author":"BE Welm","year":"2002","journal-title":"The Journal of cell biology"},{"issue":"1\u20132","key":"ref55","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s00335-014-9551-x","article-title":"In-silico QTL mapping of postpubertal mammary ductal development in the mouse uncovers potential human breast cancer risk loci","volume":"26","author":"DL Hadsell","year":"2015","journal-title":"Mammalian genome: official journal of the International Mammalian Genome Society"},{"issue":"4","key":"ref56","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1007\/s10911-009-9155-3","article-title":"Methods for preparing fluorescent and neutral red-stained whole mounts of mouse mammary glands","volume":"14","author":"JD Landua","year":"2009","journal-title":"Journal of mammary gland biology and neoplasia"},{"issue":"7","key":"ref57","doi-asserted-by":"crossref","first-page":"2415","DOI":"10.1073\/pnas.0712168105","article-title":"A chemical method for fast and sensitive detection of DNA synthesis in vivo","volume":"105","author":"A Salic","year":"2008","journal-title":"Proceedings of the National Academy of Sciences of the United States of America"}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/dx.plos.org\/10.1371\/journal.pcbi.1004839","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,18]],"date-time":"2022-06-18T19:21:19Z","timestamp":1655580079000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1004839"}},"subtitle":[],"editor":[{"given":"Alexandre V","family":"Morozov","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2016,4,26]]},"references-count":57,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2016,4,26]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1004839","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4,26]]}}}