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

We consider a mathematical formulation of the problem of protein production during segment determination in the Drosophila blastoderm, together with s ome 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 statemen t of the problem with a small parameter. Some results of the comparison met hod applied to the model are obtained, and exact stationary upper solutions are derived. They exhibit distinctive features of localized bell-shaped st ructures. (C) 2001 American Institute of Physics.