Duality-based calculations for transition probabilities in stochastic chemical reactions

Area of Science:

• Chemical Kinetics
• Computational Chemistry
• Systems Biology

Background:

• Evaluating transition probabilities in chemical reaction systems often requires computationally intensive direct time evolutions.
• Recalculating these probabilities for each change in rate constants is inefficient for systems with many parameters.

Purpose of the Study:

• To propose an efficient computational method for evaluating transition probabilities in chemical reaction systems.
• To reduce computational cost associated with varying rate constants.

Main Methods:

• The proposed method utilizes duality relations, focusing on an extended dual process instead of direct time evolution of the original system.
• A single solution of the dual process can be reused for multiple rate constant scenarios.

Main Results:

• The novel approach significantly enhances efficiency for repeated calculations involving different rate constants.
• Demonstrated successful application in a parameter estimation problem for the Lotka-Volterra system.

Conclusions:

• The duality-based method offers a computationally advantageous alternative for analyzing chemical reaction systems.
• This technique is particularly beneficial for parameter estimation and sensitivity analyses where rate constants are frequently varied.