How noise statistics impact models of enzyme cycles

Theoretical tools for adequately treating stochastic effects are important for understanding their role in biological processes. Although master equations provide rigorous means for investigating effects associated with fluctuations of discrete molecular copy numbers, they can be very challenging to treat analytically and numerically. Approaches based on the Langevin approximation are often more tractable, but care must be used to ensure that it is justified in each situation. Here, we examine a model of an enzyme cycle for which noise qualitatively alters the behavior of the system: fluctuations in the population of an enzyme can result in amplification and multistability in the distribution of its product. We compare master equation and Langevin treatments of this system and show that results derived previously with a white noise Langevin equation M. Samoilov et al., Proc. Natl. Acad. Sci. U.S.A. 102, 2310 (2005)] are inconsistent with the master equation. A colored noise Langevin equation captures some, but not all, of the essential physics of the system. The advantages and disadvantages of the Langevin approximation for modeling biological processes are discussed.