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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

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A general moment expansion method for stochastic kinetic models.

Angelique Ale¹, Paul Kirk, Michael P H Stumpf

¹Division of Molecular Biosciences, Theoretical Systems Biology Group, Imperial College London, London SW7 2AZ, United Kingdom. a.ale@imperial.ac.uk

The Journal of Chemical Physics

|May 10, 2013

Summary

Moment approximation methods offer efficient ways to model chemical reaction systems. This study introduces a general method, showing its effectiveness for complex systems where simpler approximations fail.

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Area of Science:

Computational Chemistry
Chemical Kinetics
Systems Biology

Background:

Moment approximation methods are increasingly used for stochastic chemical kinetics.
Existing methods like linear noise approximation have limitations for complex systems.
Higher-order moments are crucial for accurately describing system dynamics.

Purpose of the Study:

To derive a general moment expansion method applicable to any propensity functions and moment orders.
To assess the method's accuracy and efficiency compared to stochastic simulations.
To explore its utility in parameter sensitivity analysis and estimation.

Main Methods:

Developed a general moment expansion technique for stochastic reaction systems.
Applied the method to dimerisation, Michaelis-Menten kinetics, and an oscillating p53 model.
Analyzed computational costs and parameter sensitivity quantification.

Main Results:

The method accurately captures system behavior, including higher moments.
For some systems (e.g., p53), multiple moments are needed for convergence.
Lower-order moment agreement doesn't guarantee higher-order agreement.
The approach is numerically efficient compared to stochastic simulations.

Conclusions:

The generalized moment expansion method provides an efficient and accurate tool for analyzing stochastic chemical kinetics.
It offers insights into higher-order moments and parameter sensitivity.
Guidance is provided for determining appropriate moment orders for accurate distribution approximation.