Published December 1985
| Published
Journal Article
Open
Analysis of a Model Biological Switch
- Creators
- Kath, W. L.
- Murray, J. D.
Abstract
A model mechanism proposed by Murray [Phil. Traps. Roy. Soc. London B, 295 (1981), pp. 473–496] for generating wing patterns and eyespots on butterflies and moths is based on a morphogen (S) activated biological switch for a gene product (g). We analyse one of the resulting partial differential equation systems, namely S_t = DΔS - kS, g_t = k_tS + αg (g-k_2) (g_c-g ), where D,k,k_1 ,k_2 ,g_c > k_2 and α are positive constants. We determine analytically the size of the spatial domain where g → g_c as t → ∞ after an influx of S at the origin. This gives the size of the eyespot in terms of the mechanism parameters. The analytical problem is a nontrivial singular perturbation expansion which we discuss in detail.
Additional Information
© 1985 Society for Industrial and Applied Mathematics. Published online: 12 July 2006. Received by the editors December 20, 1983, and in final revised form February 15, 1985. This work was partially supported by the National Science Foundation under grant NCS-8205407 and by the U.S. Army Research Office under contract DAAG29-81-K-0107.Attached Files
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Additional details
- Eprint ID
- 32189
- Resolver ID
- CaltechAUTHORS:20120629-085150399
- NCS-8205407
- NSF
- DAAG29-81-K-0107
- Army Research Office (ARO)
- Created
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2012-07-02Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field