Travelling waves in a tissue interaction model for skin pattern formation
Tissue interaction plays a major role in many morphogenetic processes, particularly those associated with skin organ primordia. We examine travelling wave solutions in a tissue interaction model for skin pattern formation which is firmly based on the known biology. From a phase space analysis we con...
| Main Authors: | , , |
|---|---|
| Format: | Journal article |
| Published: |
1994
|
| _version_ | 1826265230494138368 |
|---|---|
| author | Cruywagen, G Maini, P Murray, J |
| author_facet | Cruywagen, G Maini, P Murray, J |
| author_sort | Cruywagen, G |
| collection | OXFORD |
| description | Tissue interaction plays a major role in many morphogenetic processes, particularly those associated with skin organ primordia. We examine travelling wave solutions in a tissue interaction model for skin pattern formation which is firmly based on the known biology. From a phase space analysis we conjecture the existence of travelling waves with specific wave speeds. Subsequently, analytical approximations to the wave profiles are derived using perturbation methods. We then show numerically that such travelling wave solutions do exist and that they are in good agreement with our analytical results. Finally, the biological implications of our analysis are discussed. |
| first_indexed | 2024-03-06T20:20:24Z |
| format | Journal article |
| id | oxford-uuid:2d9b0923-3ce7-405d-a865-1b3f1f42a7af |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:20:24Z |
| publishDate | 1994 |
| record_format | dspace |
| spelling | oxford-uuid:2d9b0923-3ce7-405d-a865-1b3f1f42a7af2022-03-26T12:43:57ZTravelling waves in a tissue interaction model for skin pattern formationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:2d9b0923-3ce7-405d-a865-1b3f1f42a7afMathematical Institute - ePrints1994Cruywagen, GMaini, PMurray, JTissue interaction plays a major role in many morphogenetic processes, particularly those associated with skin organ primordia. We examine travelling wave solutions in a tissue interaction model for skin pattern formation which is firmly based on the known biology. From a phase space analysis we conjecture the existence of travelling waves with specific wave speeds. Subsequently, analytical approximations to the wave profiles are derived using perturbation methods. We then show numerically that such travelling wave solutions do exist and that they are in good agreement with our analytical results. Finally, the biological implications of our analysis are discussed. |
| spellingShingle | Cruywagen, G Maini, P Murray, J Travelling waves in a tissue interaction model for skin pattern formation |
| title | Travelling waves in a tissue interaction model for skin pattern formation |
| title_full | Travelling waves in a tissue interaction model for skin pattern formation |
| title_fullStr | Travelling waves in a tissue interaction model for skin pattern formation |
| title_full_unstemmed | Travelling waves in a tissue interaction model for skin pattern formation |
| title_short | Travelling waves in a tissue interaction model for skin pattern formation |
| title_sort | travelling waves in a tissue interaction model for skin pattern formation |
| work_keys_str_mv | AT cruywageng travellingwavesinatissueinteractionmodelforskinpatternformation AT mainip travellingwavesinatissueinteractionmodelforskinpatternformation AT murrayj travellingwavesinatissueinteractionmodelforskinpatternformation |