Gene expression time delays and turing pattern formation systems
The incorporation of time delays can greatly affect the behaviour of partial differential equations and dynamical systems. In addition, there is evidence that time delays in gene expression due to transcription and translation play an important role in the dynamics of cellular systems. In this paper...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2006
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| _version_ | 1826271359033933824 |
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| author | Gaffney, E Monk, N |
| author_facet | Gaffney, E Monk, N |
| author_sort | Gaffney, E |
| collection | OXFORD |
| description | The incorporation of time delays can greatly affect the behaviour of partial differential equations and dynamical systems. In addition, there is evidence that time delays in gene expression due to transcription and translation play an important role in the dynamics of cellular systems. In this paper, we investigate the effects of incorporating gene expression time delays into a one-dimensional putative reaction diffusion pattern formation mechanism on both stationary domains and domains with spatially uniform exponential growth. While oscillatory behaviour is rare, we find that the time taken to initiate and stabilise patterns increases dramatically as the time delay is increased. In addition, we observe that on rapidly growing domains the time delay can induce a failure of the Turing instability which cannot be predicted by a naive linear analysis of the underlying equations about the homogeneous steady state. The dramatic lag in the induction of patterning, or even its complete absence on occasions, highlights the importance of considering explicit gene expression time delays in models for cellular reaction diffusion patterning. © Society for Mathematical Biology 2006. |
| first_indexed | 2024-03-06T21:55:25Z |
| format | Journal article |
| id | oxford-uuid:4cc28fc2-33d0-4127-a70e-d18e491bc16d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:55:25Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:4cc28fc2-33d0-4127-a70e-d18e491bc16d2022-03-26T15:51:19ZGene expression time delays and turing pattern formation systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4cc28fc2-33d0-4127-a70e-d18e491bc16dEnglishSymplectic Elements at Oxford2006Gaffney, EMonk, NThe incorporation of time delays can greatly affect the behaviour of partial differential equations and dynamical systems. In addition, there is evidence that time delays in gene expression due to transcription and translation play an important role in the dynamics of cellular systems. In this paper, we investigate the effects of incorporating gene expression time delays into a one-dimensional putative reaction diffusion pattern formation mechanism on both stationary domains and domains with spatially uniform exponential growth. While oscillatory behaviour is rare, we find that the time taken to initiate and stabilise patterns increases dramatically as the time delay is increased. In addition, we observe that on rapidly growing domains the time delay can induce a failure of the Turing instability which cannot be predicted by a naive linear analysis of the underlying equations about the homogeneous steady state. The dramatic lag in the induction of patterning, or even its complete absence on occasions, highlights the importance of considering explicit gene expression time delays in models for cellular reaction diffusion patterning. © Society for Mathematical Biology 2006. |
| spellingShingle | Gaffney, E Monk, N Gene expression time delays and turing pattern formation systems |
| title | Gene expression time delays and turing pattern formation systems |
| title_full | Gene expression time delays and turing pattern formation systems |
| title_fullStr | Gene expression time delays and turing pattern formation systems |
| title_full_unstemmed | Gene expression time delays and turing pattern formation systems |
| title_short | Gene expression time delays and turing pattern formation systems |
| title_sort | gene expression time delays and turing pattern formation systems |
| work_keys_str_mv | AT gaffneye geneexpressiontimedelaysandturingpatternformationsystems AT monkn geneexpressiontimedelaysandturingpatternformationsystems |