Numerical solution of compartment-based reaction/diffusion models with DABOSS algorithm

The intracellular diffusive movement of molecular substances that are buffered by diffusing chelators is often modeled as movement between compartments with constant concentrations within which the buffering occurs. Here, an algorithm to solve such a system of time-dependent differential equations is presented. This Dynamic and Balanced Operator Splitting Scheme (DABOSS) combines dynamic time stepping and operator splitting techniques. The time stepping minimizes the number of time steps while bounding local errors. The balanced operator splitting separates the diffusion and reaction components (each of which is solved efficiently) in a way that preserves the correct steady-state behavior. Analysis shows that DABOSS scales almost linearly in the number of compartments and remains accurate over very long simulations. Moreover, DABOSS works efficiently for nanometer-sized compartments with sources of flux, showing that it is applicable to situations where more spatial resolution is desired.