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The Use of Chemostats in Microbial Systems Biology
Published on: October 14, 2013
Deterministic limit of stochastic chemical kinetics
1Dan T. Gillespie Consulting, 30504 Cordoba Pl., Castaic, California 91384, USA. GillespieDT@mailaps.org
The Journal of Physical Chemistry. B
|January 23, 2009
Summary
This study analyzes assumptions for deriving deterministic reaction rate equations from stochastic chemical kinetics. Findings show these assumptions are valid for most homogeneous systems near the thermodynamic limit.
Area of Science:
- Chemical Kinetics
- Statistical Mechanics
- Physical Chemistry
Background:
- Traditional deterministic reaction rate equations are widely used.
- Discrete-stochastic formulations offer a more fundamental description of chemical kinetics.
- Bridging these two descriptions requires understanding underlying approximations.
Purpose of the Study:
- To analyze the approximating assumptions in a recent derivation of deterministic reaction rate equations from discrete-stochastic chemical kinetics.
- To determine the conditions under which these approximations are valid.
Main Methods:
- Analysis of approximating assumptions.
- Investigation of the thermodynamic limit (infinite molecular populations and volume, finite concentrations).
- Examination of spatially homogeneous systems.
Main Results:
- The approximating assumptions are justified for systems sufficiently close to the thermodynamic limit.
- This justification holds for practically all encountered spatially homogeneous systems.
Conclusions:
- The derivation of deterministic reaction rate equations from stochastic formulations is robust under common conditions.
- The thermodynamic limit provides a rigorous basis for the validity of these approximations in chemical kinetics.
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