Synergetics and Biological Morphogenesis. In: Krinsky VI, editor. Self-Organization Autowaves and Structures Far from Equilibrium. Berlin: Springer Berlin Heidelberg; 1984. pp. 204-8. [DOI: 10.1007/978-3-642-70210-5_38]

How gap genes make their domains: An analytical study based on data driven approximations

We consider a mathematical formulation of the problem of protein production during segment determination in the Drosophila blastoderm, together with some preliminary results of its analytical study. We reformulate the spatial difference equations as a set of nonlinear partial differential equations and obtain their dimensionless form in the continuum limit. Using previous results obtained by the gene circuit method, we find an asymptotic statement of the problem with a small parameter. Some results of the comparison method applied to the model are obtained, and exact stationary upper solutions are derived. They exhibit distinctive features of localized bell-shaped structures. (c) 2001 American Institute of Physics.