title: Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.
abstract: 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.
authors.affiliation: Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, Connecticut, United States of America.
authors.forename: James C
authors.identifier: 0000-0003-3286-7736
authors.initials: JC
authors.lastname: Schaff
authors.affiliation: Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, Connecticut, United States of America.
authors.forename: Fei
authors.initials: F
authors.lastname: Gao
authors.affiliation: Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, Connecticut, United States of America.
authors.forename: Ye
authors.initials: Y
authors.lastname: Li
authors.affiliation: Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, Connecticut, United States of America.
authors.forename: Igor L
authors.initials: IL
authors.lastname: Novak
authors.affiliation: Richard D. Berlin Center for Cell Analysis and Modeling, Department of Cell Biology, University of Connecticut Health Center, Farmington, Connecticut, United States of America.
authors.forename: Boris M
authors.initials: BM
authors.lastname: Slepchenko
mesh_terms: D000465:Algorithms; D002118:Calcium / Q000378:metabolism; D003585:Cell Biology; D016764:Cell Polarity; D019295:Computational Biology / Q000379:methods*; D003198:Computer Simulation; D008954:Models, Biological; D015203:Reproducibility of Results; D013269:Stochastic Processes
chemical_list: D002118:Calcium