Local error estimates for adaptive simulation of the Reaction-Diffusion Master Equation via operator splitting.

Area of Science:

• Computational biology
• Biophysics
• Chemical kinetics

Background:

• Exact simulation of the reaction-diffusion master equation (RDME) is computationally expensive due to numerous diffusion events.
• Approximate and hybrid methods improve efficiency by splitting reaction and diffusion processes, but introduce temporal discretization errors.
• Current methods lack systematic error estimation and control, forcing users to guess appropriate timesteps.

Purpose of the Study:

• To derive local error estimates for first-order operator splitting in RDME simulations.
• To propose a strategy for adaptive timestep selection to control temporal discretization error.
• To enhance the Diffusive Finite-State Projection (DFSP) method with temporal adaptivity.

Main Methods:

• Derivation of local error estimates for operator splitting methods.
• Development of a general strategy for adaptive timestep selection.
• Extension of the Diffusive Finite-State Projection (DFSP) method to incorporate adaptive timesteps.

Main Results:

• Successfully derived estimates for local temporal discretization error.
• Proposed and exemplified a strategy for adaptive timestep selection.
• Integrated temporal adaptivity into the DFSP method, improving its usability and efficiency.

Conclusions:

• Adaptive timestep selection provides a systematic way to control errors in operator-split RDME simulations.
• The proposed strategy is broadly applicable to various approximate and hybrid simulation methods.
• Temporal adaptivity enhances the practical utility and computational efficiency of methods like DFSP for RDME simulations.