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Analysis of a Model Biological Switch

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.

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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.

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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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Army Research Office (ARO)DAAG29-81-K-0107
Issue or Number:6
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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)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32189
Deposited By: Ruth Sustaita
Deposited On:02 Jul 2012 16:14
Last Modified:09 Nov 2021 21:25

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