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Biophys J. 2015 Jan 20;108(2):230-6. doi: 10.1016/j.bpj.2014.11.3457.

Local perturbation analysis: a computational tool for biophysical reaction-diffusion models.

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Department of Mathematics, University of Melbourne, Parkville, Australia; Center for Mathematical and Computational Biology, Center for Complex Biological Systems, Department of Mathematics, University of California Irvine, Irvine, California. Electronic address:
I. K. Barber School of Arts and Sciences, University of British Columbia Okanagan, Kelowna, British Columbia, Canada; Department of Math, Physics, and Computer Science, University of the Philippines Mindanao, Davao City, Philippines.
Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada.


Diffusion and interaction of molecular regulators in cells is often modeled using reaction-diffusion partial differential equations. Analysis of such models and exploration of their parameter space is challenging, particularly for systems of high dimensionality. Here, we present a relatively simple and straightforward analysis, the local perturbation analysis, that reveals how parameter variations affect model behavior. This computational tool, which greatly aids exploration of the behavior of a model, exploits a structural feature common to many cellular regulatory systems: regulators are typically either bound to a membrane or freely diffusing in the interior of the cell. Using well-documented, readily available bifurcation software, the local perturbation analysis tracks the approximate early evolution of an arbitrarily large perturbation of a homogeneous steady state. In doing so, it provides a bifurcation diagram that concisely describes various regimes of the model's behavior, reducing the need for exhaustive simulations to explore parameter space. We explain the method and provide detailed step-by-step guides to its use and application.

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