A modified next reaction method for simulating chemical systems with time dependent propensities and delays

Area of Science:

• Computational Chemistry
• Chemical Kinetics
• Stochastic Modeling

Background:

• Chemical reaction systems with few molecules are modeled using discrete jump Markov processes.
• Existing simulation methods like the Gillespie algorithm provide statistically exact sample paths.

Purpose of the Study:

• To develop a more efficient simulation method for discrete Markov jump processes.
• To extend exact simulation techniques to systems with time-dependent propensities and delays.

Main Methods:

• Representing reaction initiation times as firing times of unit rate Poisson processes.
• Deriving a modified next reaction method based on this Poisson process representation.
• Extending the method to handle time-dependent propensities and reaction delays.

Main Results:

• The modified next reaction method achieves improved efficiency over existing approaches.
• The method is successfully extended to accurately simulate systems with time-dependent propensities.
• The approach effectively incorporates delays into the simulation of chemical reaction systems.

Conclusions:

• The novel simulation approach offers a significant efficiency gain for stochastic chemical kinetics.
• This method provides a powerful tool for analyzing complex chemical systems with dynamic and delayed reactions.