Kath, W. L. and Murray, J. D. (1985) Analysis of a Model Biological Switch. SIAM Journal on Applied Mathematics, 45 (6). pp. 943-955. ISSN 0036-1399. doi:10.1137/0145057. https://resolver.caltech.edu/CaltechAUTHORS:20120629-085150399
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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.
| Item Type: | Article | |||||||||
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| 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. | |||||||||
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| Issue or Number: | 6 | |||||||||
| DOI: | 10.1137/0145057 | |||||||||
| Record Number: | CaltechAUTHORS:20120629-085150399 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120629-085150399 | |||||||||
| Official Citation: | Analysis of a Model Biological Switch W. L. Kath, J. D. Murray SIAM J. Appl. Math. 45-6 (1985), pp. 943-955 (13 pages) http://dx.doi.org/10.1137/0145057 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 32189 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 02 Jul 2012 16:14 | |||||||||
| Last Modified: | 09 Nov 2021 21:25 |
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