Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium ‘sparks’ as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.
CITATION STYLE
Schaff, J. C., Gao, F., Li, Y., Novak, I. L., & Slepchenko, B. M. (2016). Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology. PLoS Computational Biology, 12(12). https://doi.org/10.1371/journal.pcbi.1005236
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