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An introduction to linear stability analysis for deciphering spatial patterns in signaling networks

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.