  Mathematical modeling is now used commonly in the analysis of signaling
networks. With advances in high resolution microscopy, the spatial location of
different signaling molecules and the spatio-temporal dynamics of signaling
microdomains are now widely acknowledged as key features of biochemical signal
transduction. Reaction-diffusion mechanisms are commonly used to model such
features, often with a heavy reliance on numerical simulations to obtain
results. However, simulations are parameter dependent and may not be able to
provide an understanding of the full range of the system responses. Analytical
approaches on the other hand provide a framework to study the entire phase
space. In this tutorial, we provide a largely analytical method for studying
reaction-diffusion models and analyzing their stability properties. Using two
representative biological examples, we demonstrate how this approach can guide
experimental design.
