Elimination of fast variables in stochastic nonlinear kinetics

Area of Science:

• Chemical kinetics
• Stochastic processes
• Nonlinear dynamics

Background:

• Reduced chemical schemes simplify complex reactions but may fail in specific systems.
• Accurate modeling is crucial for understanding phenomena like fluorescence correlation spectroscopy (FCS) and explosive reactions.

Purpose of the Study:

• To define the validity domain of the quasi-steady-state approximation and fast concentration elimination.
• To assess the accuracy of reduced models in predicting fluctuations in small and mesoscopic systems.

Main Methods:

• Developing and comparing three-variable and two-variable chemical models.
• Utilizing stochastic approaches, including master equations and Langevin equations.
• Analyzing variances and covariances of slow variable fluctuations.

Main Results:

• Two-variable models inaccurately predict variances and covariances, even for large systems.
• Reduced schemes exhibit significant weaknesses in mesoscopic systems with few molecules.
• Langevin equations show shortcomings compared to the master equation for stochastic simulations.

Conclusions:

• Reduced chemical schemes cannot adequately describe fluctuations and their coupling with nonlinear dynamics.
• Stochastic effects are critical in small and mesoscopic systems, necessitating more complex models.