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window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":14593532,"created_at":"2015-08-02T16:50:45.837-07:00","from_world_paper_id":140350846,"updated_at":"2025-02-03T03:42:50.936-08:00","_data":{"ai_title_tag":"Turing Space in Limb Skeletal Pattern Formation","grobid_abstract":"been derived in an analytically rigorous fashion from a substantially more complex system involving multiple morphogens, extracellular matrix deposition, haptotaxis, and cell translocation. We identify regions in the parameter space of the reduced system where Turing-type pattern formation is possible, which we refer to as its \"Turing space.\" Obtained values of the parameters are used in numerical simulations of the reduced system, using a new Galerkin finite element method, in tissue domains with nonstandard geometry. The reduced system exhibits patterns of spots and stripes like those seen in developing limbs, indicating its potential utility in hybrid continuum-discrete stochastic modeling of limb development. Lastly, we discuss the possible role in limb evolution of selection for increasingly morphostatic developmental mechanisms.","publication_date":"2008,,","publication_name":"Bulletin of Mathematical Biology","grobid_abstract_attachment_id":"44049637"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"The Morphostatic Limit for a Model of Skeletal Pattern Formation in the Vertebrate Limb","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [33732628,33545496,33728423]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon'; window.userInChina = "false";</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":44049637,"attachmentType":"pdf"}"><img alt="First page of “The Morphostatic Limit for a Model of Skeletal Pattern Formation in the Vertebrate Limb”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/44049637/mini_magick20190215-15342-d49kb.png?1550228948" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">The Morphostatic Limit for a Model of Skeletal Pattern Formation in the Vertebrate Limb</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="33732628" href="https://independent.academia.edu/MarkAlber"><img alt="Profile image of Mark Alber" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Mark Alber</a><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="33545496" href="https://nd.academia.edu/YongTaoZhang"><img alt="Profile image of Yong-Tao Zhang" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Yong-Tao Zhang</a><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="33728423" href="https://pan-pl.academia.edu/BogdanKazmierczak"><img alt="Profile image of Bogdan Kazmierczak" class="ds-work-card--author-avatar" src="//a.academia-assets.com/images/s65_no_pic.png" />Bogdan Kazmierczak</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2008, Bulletin of Mathematical Biology</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">24 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 14593532; 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if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">been derived in an analytically rigorous fashion from a substantially more complex system involving multiple morphogens, extracellular matrix deposition, haptotaxis, and cell translocation. We identify regions in the parameter space of the reduced system where Turing-type pattern formation is possible, which we refer to as its "Turing space." Obtained values of the parameters are used in numerical simulations of the reduced system, using a new Galerkin finite element method, in tissue domains with nonstandard geometry. The reduced system exhibits patterns of spots and stripes like those seen in developing limbs, indicating its potential utility in hybrid continuum-discrete stochastic modeling of limb development. Lastly, we discuss the possible role in limb evolution of selection for increasingly morphostatic developmental mechanisms.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":44049637,"attachmentType":"pdf","workUrl":"https://www.academia.edu/14593532/The_Morphostatic_Limit_for_a_Model_of_Skeletal_Pattern_Formation_in_the_Vertebrate_Limb"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":44049637,"attachmentType":"pdf","workUrl":"https://www.academia.edu/14593532/The_Morphostatic_Limit_for_a_Model_of_Skeletal_Pattern_Formation_in_the_Vertebrate_Limb"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div><div class="ds-signup-banner-trigger-container"><div class="ds-signup-banner-trigger ds-signup-banner-trigger-control"></div></div><div class="ds-signup-banner ds-signup-banner-control"><div id="ds-signup-banner-close-button"><button class="ds2-5-button ds2-5-button--secondary ds2-5-button--inverse"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">close</span></button></div><div class="ds-signup-banner-ctas"><img src="//a.academia-assets.com/images/academia-logo-capital-white.svg" /><h4 class="ds2-5-heading-serif-sm">Sign up for access to the world's latest research</h4><button class="ds2-5-button ds2-5-button--inverse ds2-5-button--full-width js-swp-download-button" data-signup-modal="{"location":"signup-banner"}">Sign up for free<span class="material-symbols-outlined" style="font-size: 20px" translate="no">arrow_forward</span></button></div><div class="ds-signup-banner-divider"></div><div class="ds-signup-banner-reasons"><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Get notified about relevant papers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Save papers to use in your research</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Join the discussion with peers</span></div><div class="ds-signup-banner-reasons-item"><span class="material-symbols-outlined" style="font-size: 24px" translate="no">check</span><span>Track your impact</span></div></div></div><script>(() => { // Set up signup banner show/hide behavior: // 1. 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The main aspects of limb development have been modeled, including outgrowth and shaping of the limb bud, establishment of molecular gradients within the bud, and formation of the skeleton. These processes occur interdependently during development, although (as described in this review), there are various interpretations of the biological relationships among them. A wide range of mathematical and computational methods have been used to study these processes, including ordinary and partial differential equation systems, cellular automata and discrete, stochastic models, finite difference methods, finite element methods, the immersed boundary method, and various combinations of the above. Multiscale mathematical modeling and associated computational simulation have become integrated into the study of limb morphogenesis and pattern formation to an extent with few parallels in the field of developmental biology. These methods have contributed to the design and analysis of experiments employing microsurgical and genetic manipulations, evaluation of alternative hypotheses for limb bud outgrowth, interpretation of the effects of natural mutations, and the formulation of scenarios for the origination and evolution of the limb skeleton. Highlights  We review major mathematical and computational models of vertebrate limb development.  Models cover limb bud outgrowth and shaping, gradient formation, and skeletogenesis.  Models help explain microsurgical experiments, mutations, and evolution of the limb.  Multiscale mathematical modeling is now central to the study of limb morphogenesis.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Mathematical modeling of vertebrate limb development","attachmentId":86468876,"attachmentType":"pdf","work_url":"https://www.academia.edu/79913015/Mathematical_modeling_of_vertebrate_limb_development","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/79913015/Mathematical_modeling_of_vertebrate_limb_development"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="14593551" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/14593551/Multiscale_Models_for_Vertebrate_Limb_Development">Multiscale Models for Vertebrate Limb Development</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33732628" href="https://independent.academia.edu/MarkAlber">Mark Alber</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33728423" href="https://pan-pl.academia.edu/BogdanKazmierczak">Bogdan Kazmierczak</a><span>, </span><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33545496" href="https://nd.academia.edu/YongTaoZhang">Yong-Tao Zhang</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Current Topics in Developmental Biology, 2008</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Multiscale Models for Vertebrate Limb Development","attachmentId":44049642,"attachmentType":"pdf","work_url":"https://www.academia.edu/14593551/Multiscale_Models_for_Vertebrate_Limb_Development","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/14593551/Multiscale_Models_for_Vertebrate_Limb_Development"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="14767357" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/14767357/A_Hybrid_Discrete_Continuum_Model_for_3_D_Skeletogenesis_of_the_Vertebrate_Limb">A Hybrid Discrete-Continuum Model for 3-D Skeletogenesis of the Vertebrate Limb</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33732628" href="https://independent.academia.edu/MarkAlber">Mark Alber</a></div><p class="ds-related-work--metadata ds2-5-body-xs">International Conference on Cellular Automata for Research and Industry, 2004</p><p class="ds-related-work--abstract ds2-5-body-sm">We present a dynamic, three-dimensional, composite model framework for vertebrate development. Our integrated model combines submodels that address length-scales from subcellular to tissues and organs in a unified framework. Interacting submodels include a discrete model derived from non-equilibrium statistical mechanics (Cellular Potts Model) and continuous reaction-diffusion models. A state diagram with associated rules and a set of ordinary differential equations</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A Hybrid Discrete-Continuum Model for 3-D Skeletogenesis of the Vertebrate Limb","attachmentId":43907973,"attachmentType":"pdf","work_url":"https://www.academia.edu/14767357/A_Hybrid_Discrete_Continuum_Model_for_3_D_Skeletogenesis_of_the_Vertebrate_Limb","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/14767357/A_Hybrid_Discrete_Continuum_Model_for_3_D_Skeletogenesis_of_the_Vertebrate_Limb"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="64137526" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/64137526/Reaction_Diffusion_Systems_and_External_Morphogen_Gradients_The_Two_Dimensional_Case_with_an_Application_to_Skeletal_Pattern_Formation">Reaction–Diffusion Systems and External Morphogen Gradients: The Two-Dimensional Case, with an Application to Skeletal Pattern Formation</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="209622622" href="https://independent.academia.edu/StuartNewman4">Stuart Newman</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Bulletin of Mathematical Biology, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">We investigate a reaction-diffusion system consisting of an activator and an inhibitor in a two-dimensional domain. There is a morphogen gradient in the domain. The production of the activator depends on the concentration of the morphogen. Mathematically, this leads to reactiondiffusion equations with explicitly space-dependent terms. It is well known that in the absence of an external morphogen, the system can produce either spots or stripes via the Turing bifurcation. We derive first order expansions for the possible patterns in the presence of an external morphogen and show how both stripes and spots are affected. This work generalizes previous one-dimensional results to two dimensions. Specifically, we consider the quasi-one-dimensional case of a thin rectangular domain and the case of a square domain. We apply the results to a model of skeletal pattern formation in vertebrate limbs. In the framework of reaction-diffusion models, our results suggest a simple explanation for some recent experimental findings in the mouse limb which are much harder to explain in positional-information-type models.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Reaction–Diffusion Systems and External Morphogen Gradients: The Two-Dimensional Case, with an Application to Skeletal Pattern Formation","attachmentId":76309871,"attachmentType":"pdf","work_url":"https://www.academia.edu/64137526/Reaction_Diffusion_Systems_and_External_Morphogen_Gradients_The_Two_Dimensional_Case_with_an_Application_to_Skeletal_Pattern_Formation","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/64137526/Reaction_Diffusion_Systems_and_External_Morphogen_Gradients_The_Two_Dimensional_Case_with_an_Application_to_Skeletal_Pattern_Formation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="89548623" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/89548623/Dynamical_mechanisms_for_skeletal_pattern_formation_in_the_vertebrate_limb">Dynamical mechanisms for skeletal pattern formation in the vertebrate limb</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="130094744" href="https://independent.academia.edu/TGlimm">Tilmann Glimm</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proceedings of the Royal Society of London. Series B: Biological Sciences, 2004</p><p class="ds-related-work--abstract ds2-5-body-sm">We describe a 'reactor-diffusion' mechanism for precartilage condensation based on recent experiments on chondrogenesis in the early vertebrate limb and additional hypotheses. Cellular differentiation of mesenchymal cells into subtypes with different fibroblast growth factor (FGF) receptors occurs in the presence of spatio-temporal variations of FGFs and transforming growth factor-betas (TGF-βs). One class of differentiated cells produces elevated quantities of the extracellular matrix protein fibronectin, which initiates adhesion-mediated preskeletal mesenchymal condensation. The same class of cells also produces an FGFdependent laterally acting inhibitor that keeps condensations from expanding beyond a critical size. We show that this 'reactor-diffusion' mechanism leads naturally to patterning consistent with skeletal form, and describe simulations of spatio-temporal distribution of these differentiated cell types and the TGF-β and inhibitor concentrations in the developing limb bud.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Dynamical mechanisms for skeletal pattern formation in the vertebrate limb","attachmentId":93333077,"attachmentType":"pdf","work_url":"https://www.academia.edu/89548623/Dynamical_mechanisms_for_skeletal_pattern_formation_in_the_vertebrate_limb","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/89548623/Dynamical_mechanisms_for_skeletal_pattern_formation_in_the_vertebrate_limb"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="57362346" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/57362346/A_Finite_Element_Model_Based_on_Discontinuous_Galerkin_Methods_on_Moving_Grids_for_Vertebrate_Limb_Pattern_Formation">A Finite Element Model Based on Discontinuous Galerkin Methods on Moving Grids for Vertebrate Limb Pattern Formation</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33732628" href="https://independent.academia.edu/MarkAlber">Mark Alber</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Mathematical Modelling of Natural Phenomena, 2009</p><p class="ds-related-work--abstract ds2-5-body-sm">Skeletal patterning in the vertebrate limb, i.e., the spatiotemporal regulation of cartilage differentiation (chondrogenesis) during embryogenesis and regeneration, is one of the best studied examples of a multicellular developmental process. Recently [Alber et al., The morphostatic limit for a model of skeletal pattern formation in the vertebrate limb, Bulletin of Mathematical Biology, 2008, v70, pp. 460-483], a simplified two-equation reaction-diffusion system was developed to describe the interaction of two of the key morphogens: the activator and an activator-dependent inhibitor of precartilage condensation formation. A discontinuous Galerkin (DG) finite element method was applied to solve this nonlinear system on complex domains to study the effects of domain geometry on the pattern generated [Zhu et al., Application of Discontinuous Galerkin Methods for reaction-diffusion systems in developmental biology, Journal of Scientific Computing, 2009, v40, pp. 391-418]. In this paper, we extend these previous results and develop a DG finite element model in a moving and deforming domain for skeletal pattern formation in the vertebrate limb. Simulations reflect the actual dynamics of limb development and indicate the important role played by the geometry of the undifferentiated apical zone.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A Finite Element Model Based on Discontinuous Galerkin Methods on Moving Grids for Vertebrate Limb Pattern Formation","attachmentId":72302007,"attachmentType":"pdf","work_url":"https://www.academia.edu/57362346/A_Finite_Element_Model_Based_on_Discontinuous_Galerkin_Methods_on_Moving_Grids_for_Vertebrate_Limb_Pattern_Formation","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/57362346/A_Finite_Element_Model_Based_on_Discontinuous_Galerkin_Methods_on_Moving_Grids_for_Vertebrate_Limb_Pattern_Formation"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="89548634" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/89548634/Mathematical_modeling_of_chondrogenic_pattern_formation_during_limb_development_Recent_advances_in_continuous_models">Mathematical modeling of chondrogenic pattern formation during limb development: Recent advances in continuous models</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="130094744" href="https://independent.academia.edu/TGlimm">Tilmann Glimm</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Mathematical Biosciences, 2020</p><p class="ds-related-work--abstract ds2-5-body-sm">This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Mathematical modeling of chondrogenic pattern formation during limb development: Recent advances in continuous models","attachmentId":93333018,"attachmentType":"pdf","work_url":"https://www.academia.edu/89548634/Mathematical_modeling_of_chondrogenic_pattern_formation_during_limb_development_Recent_advances_in_continuous_models","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/89548634/Mathematical_modeling_of_chondrogenic_pattern_formation_during_limb_development_Recent_advances_in_continuous_models"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="65542618" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/65542618/A_Mathematical_Model_for_Outgrowth_and_Spatial_Patterning_of_the_Vertebrate_Limb_Bud">A Mathematical Model for Outgrowth and Spatial Patterning of the Vertebrate Limb Bud</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="42371274" href="https://independent.academia.edu/HansOthmer">Hans Othmer</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Theoretical Biology, 1999</p><p class="ds-related-work--abstract ds2-5-body-sm">The average stage length is 4 hours up to stage 23, and about 6 hours thereafter. F. 1. (a) The orientation of axes used to describe the limb; (b) a schematic of the adult wing skeleton in chick. * A diffusible substance that induces a concentration-dependent response at some step in the patterning process. * S is the volumetric growth per unit volume per unit time. * The AER-competent region is of fixed size, but the ZPA-competent region elongates. Because of morphogen coupling, the active region of the ZPA species is localized distally and the size of the active region is roughly constant.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A Mathematical Model for Outgrowth and Spatial Patterning of the Vertebrate Limb Bud","attachmentId":77091689,"attachmentType":"pdf","work_url":"https://www.academia.edu/65542618/A_Mathematical_Model_for_Outgrowth_and_Spatial_Patterning_of_the_Vertebrate_Limb_Bud","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/65542618/A_Mathematical_Model_for_Outgrowth_and_Spatial_Patterning_of_the_Vertebrate_Limb_Bud"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="1228473" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/1228473/Computational_Models_for_Mechanics_of_Morphogenesis">Computational Models for Mechanics of Morphogenesis</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="1957813" href="https://wustl.academia.edu/ZiChen">Zi Chen</a></div><p class="ds-related-work--abstract ds2-5-body-sm">In the developing embryo, tissues differentiate, deform, and move in an orchestrated manner to generate various biological shapes driven by the complex interplay between genetic, epigenetic, and environmental factors. Mechanics plays a key role in regulating and controlling morphogenesis, and quantitative models help us understand how various mechanical forces combine to shape the embryo. Models allow for the quantitative, unbiased testing of physical mechanisms, and when used appropriately, can motivate new experimentaldirections. This knowledge benefits biomedical researchers who aim to prevent and treat congenital malformations, as well as engineers working to create replacement tissues in the laboratory. In this review, we first give an overview of fundamental mechanical theories for morphogenesis, and then focus on models for specific processes, including pattern formation, gastrulation, neurulation, organogenesis, and wound healing. The role of mechanical feedback in development is also discussed. Finally, some perspectives aregiven on the emerging challenges in morphomechanics and mechanobiology.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Computational Models for Mechanics of Morphogenesis","attachmentId":18663030,"attachmentType":"pdf","work_url":"https://www.academia.edu/1228473/Computational_Models_for_Mechanics_of_Morphogenesis","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/1228473/Computational_Models_for_Mechanics_of_Morphogenesis"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="14767299" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/14767299/Multi_model_simulations_of_chicken_limb_morphogenesis">Multi-model simulations of chicken limb morphogenesis</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33732628" href="https://independent.academia.edu/MarkAlber">Mark Alber</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2003</p><p class="ds-related-work--abstract ds2-5-body-sm">Early development of multicellular organisms (morphogenesis) is a complex phenomenon. We present COMPUCELL, a multi-model software framework for simulations of morphogenesis. As an example, we simulate the formation of the skeletal pattern in the avian limb bud, which requires simulations based on interactions of the genetic regulatory network with generic cellular mechanisms (cell adhesion, haptotaxis, and chemotaxis). A combination of a rule-based state automaton and sets of differential equations, both subcellular ordinary differential equations (ODEs) and domain-level reaction-diffusion partial differential equations (PDEs) models genetic regulation. This regulation controls the differentiation of cells, and also cell-cell and cell-extracellular matrix interactions that give rise to cell pattern formation and cell rearrangements such as mesenchymal condensation. The cellular Potts model (CPM) models cell dynamics (cell movement and rearrangement). These models couple; COMPUCELL provides an integrated framework for such computations. Binaries for Microsoft Windows and Solaris are available 1 . Source code is available on request, via email: compucell@cse.nd.edu.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Multi-model simulations of chicken limb morphogenesis","attachmentId":43908000,"attachmentType":"pdf","work_url":"https://www.academia.edu/14767299/Multi_model_simulations_of_chicken_limb_morphogenesis","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/14767299/Multi_model_simulations_of_chicken_limb_morphogenesis"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":44049637,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":44049637,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_44049637" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. You can download the paper by clicking the button above.</p></div></div></div></div><div class="ds-sidebar--container js-work-sidebar"><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="0" data-entity-id="14760893" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/14760893/On_multiscale_approaches_to_three_dimensional_modelling_of_morphogenesis">On multiscale approaches to three-dimensional modelling of morphogenesis</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33732628" href="https://independent.academia.edu/MarkAlber">Mark Alber</a><span>, </span><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33728423" href="https://pan-pl.academia.edu/BogdanKazmierczak">Bogdan Kazmierczak</a><span>, </span><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="25883662" href="https://indiana.academia.edu/JGlazier">James A Glazier</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of The Royal Society Interface, 2005</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On multiscale approaches to three-dimensional modelling of morphogenesis","attachmentId":43910456,"attachmentType":"pdf","work_url":"https://www.academia.edu/14760893/On_multiscale_approaches_to_three_dimensional_modelling_of_morphogenesis","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a 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Alber</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2018</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On Multiscale Approaches to 3-Dimensional Modeling of Morphogenesis","attachmentId":86468799,"attachmentType":"pdf","work_url":"https://www.academia.edu/79913081/On_Multiscale_Approaches_to_3_Dimensional_Modeling_of_Morphogenesis","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/79913081/On_Multiscale_Approaches_to_3_Dimensional_Modeling_of_Morphogenesis"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 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