The Chemical Langevin and Fokker−Planck Equations for the Reversible Isomerization Reaction

Abstract

This paper uses the simple reversible isomerization reaction to illustrate and clarify the roles played in chemical kinetics by recently proposed forms for the chemical Langevin equation and chemical Fokker−Planck equation. It is shown that the stationary solution of the chemical Fokker−Planck equation for this model reaction provides, for most purposes, an excellent approximation to the stationary solution of the chemical master equation. It is also shown that, when allowance is made for the stipulated macroscopic nature of the time increment dt in the chemical Langevin equation, the changes in molecular population during dt predicted by that equation for this model reaction closely approximate the changes prescribed by the chemical master equation. The discussion highlights the role of the chemical Langevin equation as not only a potential computational aid but also a conceptual bridge between the stochastic chemical master equation and the traditional deterministic reaction rate equation.