Before revision: Mathematical models, with some simplifying assumptions, can provide clarity into the workings of complex biological systems. Despite their seeming simplicity, even so-called 'minimal' models can exhibit a diverse range of behavior in various regions of the parameter space. These models can be studied using simulations and analytical methods. Simulations are often parameter dependent and fall short of providing a complete understanding of the full range of  system responses.
After revision: 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 fall short of providing a complete understanding of the full range of system responses.