PLoS Computational Biology (Dec 2016)

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology.

  • James C Schaff,
  • Fei Gao,
  • Ye Li,
  • Igor L Novak,
  • Boris M Slepchenko

DOI
https://doi.org/10.1371/journal.pcbi.1005236
Journal volume & issue
Vol. 12, no. 12
p. e1005236

Abstract

Read online

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.