Efficient Low-Order Approximation of First-Passage Time Distributions.

Area of Science:

• Computational Chemistry
• Biophysics
• Chemical Kinetics

Background:

• Master equations are fundamental for modeling reaction dynamics but computing first-passage times is often intractable.
• Stochastic simulations are common but computationally intensive for complex systems.

Purpose of the Study:

• To develop an efficient computational method for determining first-passage time distributions in reaction processes.
• To link the intractable problem of first-passage times to a solvable Bayesian inference framework.

Main Methods:

• Reformulating the first-passage time problem as a sequential Bayesian inference task for an auxiliary process.
• Approximating the solution by solving a closed set of coupled ordinary differential equations for low-order moments.
• Validating the approach using stochastic simulations for specific chemical and biological models.

Main Results:

• Demonstrated the equivalence between first-passage time computation and Bayesian inference.
• Developed an efficient approximation method using coupled ordinary differential equations.
• Achieved good agreement between the approximated results and stochastic simulations for tested models.

Conclusions:

• The proposed method provides an efficient and scalable approach to compute first-passage time distributions.
• This work bridges the gap between master equation modeling and Bayesian inference techniques.
• The findings have implications for analyzing complex reaction dynamics in various scientific fields.