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

PLoS Comput Biol. 2016 Dec 13;12(12):e1005236. doi: 10.1371/journal.pcbi.1005236. eCollection 2016 Dec.


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.

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Algorithms
  • Calcium / metabolism
  • Cell Biology*
  • Cell Polarity
  • Computational Biology / methods*
  • Computer Simulation*
  • Models, Biological*
  • Reproducibility of Results
  • Stochastic Processes


  • Calcium