Size-dependent symmetry breaking in models for morphogenesis
A general property of dynamical systems is the appearance of spatial and temporal patterns due to a change of stability of a homogeneous steady state. Such spontaneous symmetry breaking is observed very frequently in all kinds of real systems, including the development of shape in living organisms....
| Main Authors: | , , , |
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| Format: | Conference item |
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2002
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| _version_ | 1797079614603919360 |
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| author | Barrio, R Maini, P Aragon, J Torres, M |
| author_facet | Barrio, R Maini, P Aragon, J Torres, M |
| author_sort | Barrio, R |
| collection | OXFORD |
| description | A general property of dynamical systems is the appearance of spatial and temporal patterns due to a change of stability of a homogeneous steady state. Such spontaneous symmetry breaking is observed very frequently in all kinds of real systems, including the development of shape in living organisms. Many nonlinear dynamical systems present a wide variety of patterns with different shapes and symmetries. This fact restricts the applicability of these models to morphogenesis, since one often finds a surprisingly small variation in the shapes of living organisms. For instance, all individuals in the Phylum Echinodermata share a persistent radial fivefold symmetry. In this paper, we investigate in detail the symmetry-breaking properties of a Turing reaction-diffusion system confined in a small disk in two dimensions. It is shown that the symmetry of the resulting pattern depends only on the size of the disk, regardless of the boundary conditions and of the differences in the parameters that differentiate the interior of the domain from the outer space. This study suggests that additional regulatory mechanisms to control the size of the system are of crucial importance in morphogenesis. (C) 2002 Elsevier Science B.V. All rights reserved. |
| first_indexed | 2024-03-07T00:48:25Z |
| format | Conference item |
| id | oxford-uuid:857ddc33-a1d8-405c-86d8-840c8b66e06b |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:48:25Z |
| publishDate | 2002 |
| record_format | dspace |
| spelling | oxford-uuid:857ddc33-a1d8-405c-86d8-840c8b66e06b2022-03-26T21:57:59ZSize-dependent symmetry breaking in models for morphogenesisConference itemhttp://purl.org/coar/resource_type/c_5794uuid:857ddc33-a1d8-405c-86d8-840c8b66e06bSymplectic Elements at Oxford2002Barrio, RMaini, PAragon, JTorres, MA general property of dynamical systems is the appearance of spatial and temporal patterns due to a change of stability of a homogeneous steady state. Such spontaneous symmetry breaking is observed very frequently in all kinds of real systems, including the development of shape in living organisms. Many nonlinear dynamical systems present a wide variety of patterns with different shapes and symmetries. This fact restricts the applicability of these models to morphogenesis, since one often finds a surprisingly small variation in the shapes of living organisms. For instance, all individuals in the Phylum Echinodermata share a persistent radial fivefold symmetry. In this paper, we investigate in detail the symmetry-breaking properties of a Turing reaction-diffusion system confined in a small disk in two dimensions. It is shown that the symmetry of the resulting pattern depends only on the size of the disk, regardless of the boundary conditions and of the differences in the parameters that differentiate the interior of the domain from the outer space. This study suggests that additional regulatory mechanisms to control the size of the system are of crucial importance in morphogenesis. (C) 2002 Elsevier Science B.V. All rights reserved. |
| spellingShingle | Barrio, R Maini, P Aragon, J Torres, M Size-dependent symmetry breaking in models for morphogenesis |
| title | Size-dependent symmetry breaking in models for morphogenesis |
| title_full | Size-dependent symmetry breaking in models for morphogenesis |
| title_fullStr | Size-dependent symmetry breaking in models for morphogenesis |
| title_full_unstemmed | Size-dependent symmetry breaking in models for morphogenesis |
| title_short | Size-dependent symmetry breaking in models for morphogenesis |
| title_sort | size dependent symmetry breaking in models for morphogenesis |
| work_keys_str_mv | AT barrior sizedependentsymmetrybreakinginmodelsformorphogenesis AT mainip sizedependentsymmetrybreakinginmodelsformorphogenesis AT aragonj sizedependentsymmetrybreakinginmodelsformorphogenesis AT torresm sizedependentsymmetrybreakinginmodelsformorphogenesis |