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Incorporating postleap checks in tau-leaping.

David F Anderson¹

¹Department of Mathematics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA. anderson@math.wisc.edu

The Journal of Chemical Physics

|February 13, 2008

Summary

This study introduces a novel adaptive tau-leaping method for chemical systems. It ensures accuracy and avoids negative populations by using Poisson processes and post-leap checks, improving simulation reliability.

Area of Science:

Computational chemistry
Stochastic modeling
Chemical kinetics

Background:

Discrete chemical systems are often modeled using stochastic simulation algorithms.
Existing methods like tau-leaping can face challenges with accuracy and negative population values.
Efficient and reliable simulation of chemical reactions is crucial for understanding complex systems.

Purpose of the Study:

To develop a new adaptive tau-leaping procedure for discrete chemical systems.
To guarantee simulation accuracy through novel post-leap checks.
To create a method that inherently avoids negative population values.

Main Methods:

Representing reaction times as firing times of independent, unit rate Poisson processes.
Implementing an adaptive tau-leaping algorithm with explicit post-leap checks.

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Separating system state from model randomness to prevent bias in sample path statistics.

Main Results:

The developed procedure guarantees accuracy via post-leap checks.
Rejection of leaps does not bias the statistics of generated sample paths.
The simulation method naturally avoids negative population values due to leap conditions being ensured with probability one.

Conclusions:

The new adaptive tau-leaping method offers improved accuracy and reliability for simulating discrete chemical systems.
This approach provides a robust way to handle stochasticity in chemical kinetics.
The method effectively prevents non-physical negative populations in simulations.