ANALYSIS AND DESIGN OF JUMP COEFFICIENTS IN DISCRETE STOCHASTIC DIFFUSION MODELS

Area of Science:

• Computational Systems Biology
• Mathematical Modeling
• Stochastic Processes

Background:

• Reaction-diffusion kinetics are modeled using Markov processes.
• Discretization of diffusion equations for stochastic simulation can yield non-physical negative coefficients.
• Existing methods modify coefficients but introduce errors.

Purpose of the Study:

• To quantify the error introduced by modifying non-negative jump coefficients.
• To develop a backward analysis algorithm for error assessment.
• To propose a novel method for deriving non-negative coefficients that minimizes error.

Main Methods:

• Interpreting modified discretization matrices as discretizations of perturbed equations.
• Bounding forward error by backward error.
• Developing and applying a backward analysis algorithm to compute diffusion coefficients.

Main Results:

• A method to quantify errors in stochastic diffusion simulation coefficients was developed.
• A backward analysis algorithm was presented to compute diffusion coefficients.
• Numerical experiments demonstrated the superiority of the new method in minimizing both backward and forward errors.

Conclusions:

• The proposed backward analysis and coefficient derivation method accurately quantifies and minimizes errors in stochastic reaction-diffusion models.
• This approach enhances the reliability of simulations using unstructured meshes.
• The method offers a superior alternative for generating non-negative jump coefficients in computational systems biology.