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. Analytical approaches on the other hand provide a framework to study the entire phase space. Here, we outline a largely analytical method for studying reaction-diffusion models . Using a prototypic model of cell polarization, we characterize protein activation in response to an external stimulus and highlight the importance of phase-space analysis. We demonstrate how comprehensive treatment of the phase space can guide experimental design and supplement simulation studies.In order to make such analyses more accessible, we provide an easy-to-use graphical user interface URL
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 .
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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
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
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In this tutorial, we provide
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. Using a prototypic model of cell polarization, we characterize protein activation in response to an external stimulus and highlight the importance of phase-space analysis. We demonstrate how comprehensive treatment of the phase space
and analyzing their stability properties. Using two representative biological examples, we demonstrate how this approach
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and supplement simulation studies.In order to make such analyses more accessible, we provide an easy-to-use graphical user interface URL
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