A singular perturbation approach to diffusion reaction equations containing a point source, with application to the hemolytic plaque assay.

Many cells secrete factors which diffuse and bind to receptors on neighboring cells. These processes can be described by a nonlinear diffusion equation with a point source and spatially distributed binding reaction. We show via perturbation analysis how approximate solutions can be obtained for such equations when the binding reaction is fast compared to diffusive transport. We base our analysis on an example which is of great practical importance in immunology, the hemolytic plaque technique.