Analysis of a Model Biological Switch

W. L. Kath, J. D. Murray
1985 SIAM Journal on Applied Mathematics  
A model mechanism proposed by Murray [Phil. Trans. 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 where D, k, k., k2, gc > kz and a are positive constants. We determine analytically the size of the spatial domain where g-+ gc as t-+ oo after an influx of S at the origin. This
more » ... gives the size of the eyes pot in terms of the mechanism parameters. The analytical problem is a nontrivial singular perturbation expansion which we discuss in detail.
doi:10.1137/0145057 fatcat:guazcojh5bcnxkmyw67rm7mdt4