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

Area of Science:

• Computational Biology
• Biophysics
• Mathematical Biology

Background:

• Hybrid deterministic-stochastic methods offer efficiency for models with mixed stochasticity levels.
• General-purpose hybrid solvers for spatially resolved reaction-diffusion systems are scarce.

Purpose of the Study:

• To describe the fundamentals of a general-purpose spatial hybrid method.
• To provide a validated computational tool for complex biological simulations.

Main Methods:

• Integrating a deterministic partial differential equation solver with a particle-based stochastic simulator (Smoldyn).
• Generating spatially inhomogeneous hybrid system realizations.
• Validating the algorithm using a calcium 'sparks' model.

Main Results:

• The hybrid solver successfully generates realizations of spatially inhomogeneous systems.
• The method was rigorously validated on a calcium 'sparks' model.
• Application to a cell polarity model demonstrated its utility.

Conclusions:

• The developed spatial hybrid method is a general-purpose tool for reaction-diffusion systems.
• This approach facilitates the study of biological phenomena with disparate stochasticity.
• The method is compatible with biologist-friendly frameworks like Virtual Cell.