Spatially extended model of kinase-receptor interaction in cells

We consider a spatially-extended model describing mutual
phosphorylation of cytosolic kinase molecules and membrane receptors. The analyzed regulatory subsystem is a part of signal transduction mechanisms characteristic for immune receptors and Src family kinases. It couples differential equations defined in a domain and on its boundary via
nonlinear Robin boundary conditions. Assuming a spherically symmetric framework, our approach is to consider an auxiliary problem in which a uniform Dirichlet boundary condition is imposed on the external boundary of the spherical shell  instead of the Robin boundary condition. This method allows us to find the stationary spherically-symmetric solutions, both stable and unstable.