title: Local perturbation analysis: a computational tool for biophysical reaction-diffusion models.
abstract: 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.
authors.affiliation: 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: holmesw@unimelb.edu.au.
authors.forename: William R
authors.initials: WR
authors.lastname: Holmes
authors.affiliation: 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.
authors.forename: May Anne
authors.initials: MA
authors.lastname: Mata
authors.affiliation: Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada.
authors.forename: Leah
authors.initials: L
authors.lastname: Edelstein-Keshet
mesh_terms: D004058:Diffusion; D008954:Models, Biological; D012984:Software; D020741:rho GTP-Binding Proteins / Q000737:chemistry / Q000378:metabolism*
chemical_list: D020741:rho GTP-Binding Proteins