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dc.contributor.authorMarciniak-Czochra, Anna
dc.contributor.editorAntoniouk, Alexandra V.
dc.contributor.editorMelnik, Roderick V. N.
dc.date.accessioned2019-11-19 23:55
dc.date.accessioned2020-01-07 16:47:06
dc.date.accessioned2020-04-01T09:26:49Z
dc.date.available2020-04-01T09:26:49Z
dc.date.issued2012
dc.identifier1006424
dc.identifier.urihttp://library.oapen.org/handle/20.500.12657/23720
dc.description.abstractIn this paper we present mathematical approaches to understand a symmetry break and formation of spatially heterogenous structures during development. We focus on the models given by reaction-diffusion equations and approach the question of possible mechanisms of development of spatially heterogeneous structures. We discuss two mechanisms of pattern formation: diffusion-driven instability (Turing instability) and a hysteresis-driven mechanism, and demonstrate their possibilities and constraints in explaining different aspects of structure formation in cell systems. Depending on the type of nonlinearities, we show the existence of Turing patterns, the maxima of which may be of the spike or plateau type, and the existence of transition layer stationary solutions. These concepts are discussed on example of morphogenesis of the fresh water polyp Hydra, which is a model organism in developmental biology.
dc.languageEnglish
dc.subject.classificationbic Book Industry Communication::K Economics, finance, business & management::KN Industry & industrial studies::KND Manufacturing industries::KNDR Road vehicle manufacturing industry
dc.subject.classificationbic Book Industry Communication::P Mathematics & science::PB Mathematics::PBK Calculus & mathematical analysis::PBKS Numerical analysis
dc.subject.classificationbic Book Industry Communication::P Mathematics & science::PB Mathematics::PBW Applied mathematics
dc.subject.classificationbic Book Industry Communication::P Mathematics & science::PS Biology, life sciences::PSA Life sciences: general issues
dc.subject.otherMathematical Method
dc.subject.otherStatistical Method
dc.subject.otherModeling Method
dc.subject.otherLife Sciences Application
dc.titleChapter 8.1 Reaction-Diffusion Models of Pattern Formation in Developmental Biology
dc.typechapter
oapen.identifier.doi10.1515/9783110288537.191
oapen.relation.isPublishedBy2b386f62-fc18-4108-bcf1-ade3ed4cf2f3
virtual.oapen_relation_isPublishedBy.publisher_nameDe Gruyter
virtual.oapen_relation_isPublishedBy.publisher_websitehttps://www.degruyter.com/
oapen.relation.isPartOfBook971c4d04-5c8e-442e-b04d-c7f4af74d703
virtual.oapen_relation_isPartOfBook.dc_titleMathematics and Life Sciences
oapen.relation.isFundedBy7292b17b-f01a-4016-94d3-d7fb5ef9fb79
virtual.oapen_relation_isFundedBy.grantor_name FP7 Ideas: European Research Council
oapen.relation.isbn9783110273724
oapen.collectionEuropean Research Council (ERC)
oapen.place.publicationBerlin/Boston
oapen.grant.number210680
oapen.grant.acronymBIOSTRUCT


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