{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:22:27Z","timestamp":1772173347231,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1011835","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T00:00:00Z","timestamp":1710288000000}}],"reference-count":48,"publisher":"Public Library of Science (PLoS)","issue":"3","license":[{"start":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T00:00:00Z","timestamp":1709251200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000288","name":"Royal Society","doi-asserted-by":"publisher","award":["IEC\\R3\\193090"],"award-info":[{"award-number":["IEC\\R3\\193090"]}],"id":[{"id":"10.13039\/501100000288","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000646","name":"Japan Society for the Promotion of Science London","doi-asserted-by":"publisher","award":["JSPSBP120205703"],"award-info":[{"award-number":["JSPSBP120205703"]}],"id":[{"id":"10.13039\/501100000646","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000646","name":"Japan Society for the Promotion of Science London","doi-asserted-by":"publisher","award":["JP21H04434"],"award-info":[{"award-number":["JP21H04434"]}],"id":[{"id":"10.13039\/501100000646","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    From mathematical models of growth to computer simulations of pigmentation, the study of shell formation has given rise to an abundant number of models, working at various scales. Yet, attempts to combine those models have remained sparse, due to the challenge of combining categorically different approaches. In this paper, we propose a framework to streamline the process of combining the molecular and tissue scales of shell formation. We choose these levels as a proxy to link the genotype level, which is better described by molecular models, and the phenotype level, which is better described by tissue-level mechanics. We also show how to connect observations on shell populations to the approach, resulting in collections of molecular parameters that may be associated with different populations of real shell specimens. The approach is as follows: we use a Quality-Diversity algorithm, a type of black-box optimization algorithm, to explore the range of concentration profiles emerging as solutions of a molecular model, and that define growth patterns for the mechanical model. At the same time, the mechanical model is simulated over a wide range of growth patterns, resulting in a variety of spine shapes. While time-consuming, these steps only need to be performed once and then function as look-up tables. Actual pictures of shell spines can then be matched against the list of existing spine shapes, yielding a potential growth pattern which, in turn, gives us matching molecular parameters. The framework is modular, such that models can be easily swapped without changing the overall working of the method. As a demonstration of the approach, we solve specific molecular and mechanical models, adapted from available theoretical studies on molluscan shells, and apply the multiscale framework to evaluate the characteristics of spines from three distinct populations of\n                    <jats:italic>Turbo sazae<\/jats:italic>\n                    .\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1011835","type":"journal-article","created":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T13:44:03Z","timestamp":1709300643000},"page":"e1011835","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["A multiscale computational framework for the development of spines in molluscan shells"],"prefix":"10.1371","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3597-7973","authenticated-orcid":true,"given":"Derek E.","family":"Moulton","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9100-1855","authenticated-orcid":true,"given":"Nathana\u00ebl","family":"Aubert-Kato","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9173-8278","authenticated-orcid":true,"given":"Axel A.","family":"Almet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Atsuko","family":"Sato","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2024,3,1]]},"reference":[{"issue":"1-3","key":"pcbi.1011835.ref001","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.pbiomolbio.2007.07.019","article-title":"Multi-scale computational modelling in biology and physiology","volume":"96","author":"James Southern","year":"2008","journal-title":"Progress in biophysics and molecular biology"},{"key":"pcbi.1011835.ref002","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-87710-5","volume-title":"The mathematics and mechanics of biological growth","author":"Alain Goriely","year":"2017"},{"key":"pcbi.1011835.ref003","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1200\/CCI.18.00069","article-title":"A review of cell-based computational modeling in cancer biology","volume":"2","author":"John Metzcar","year":"2019","journal-title":"JCO clinical cancer informatics"},{"issue":"2","key":"pcbi.1011835.ref004","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1038\/s41569-018-0104-y","article-title":"Computational models in cardiology","volume":"16","author":"Steven A Niederer","year":"2019","journal-title":"Nature Reviews Cardiology"},{"issue":"1902","key":"pcbi.1011835.ref005","doi-asserted-by":"crossref","first-page":"3525","DOI":"10.1098\/rsta.2009.0095","article-title":"Multi-scale models of cell and tissue dynamics","volume":"367","author":"Magdalena A Stolarska","year":"2009","journal-title":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"key":"pcbi.1011835.ref006","doi-asserted-by":"crossref","DOI":"10.1201\/9781351115667","volume-title":"Biology and Evolution of the Mollusca","author":"Winston Frank Ponder","year":"2019"},{"issue":"5","key":"pcbi.1011835.ref007","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1086\/285962","article-title":"The evolution of ideas: a phylogeny of shell models","volume":"148","author":"JR Stone","year":"1996","journal-title":"The American Naturalist"},{"key":"pcbi.1011835.ref008","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/978-1-4757-9153-2_8","article-title":"Theoretical modeling of ammonoid morphology","author":"Takashi Okamoto","year":"1996","journal-title":"Ammonoid paleobiology"},{"key":"pcbi.1011835.ref009","doi-asserted-by":"crossref","unstructured":"Henry Moseley. 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