On Reduced Models for the Chemical Master Equation

On Reduced Models for the Chemical Master Equation

Abstract. The chemical master equation plays a fundamental role for the understanding of gene regulatory networks and other discrete stochastic reaction systems. Solving this equation numerically, however, is usually extremely expensive or even impossible due to the huge size of the state space. Thus, the chemical master equationmust often be replaced by a reducedmodel which operates with a con...

Hybrid method for the chemical master equation

The chemical master equation is solved by a hybrid method coupling a macroscopic, deterministic description with a mesoscopic, stochastic model. The molecular species are divided into one subset where the expected values of the number of molecules are computed and one subset with species with a stochastic variation in the number of molecules. The macroscopic equations resemble the reaction rate...

Numerical Methods for the Chemical Master Equation

Numerical Methods for the Chemical Master Equation

The numerical solution of chemical reactions described at the meso-scale is the topic of this thesis. This description, the master equation of chemical reactions, is an accurate model of reactions where stochastic effects are crucial for explaining certain effects observed in real life. In particular, this general equation is needed when studying processes inside living cells where other macro-...

Dimensional reduction of the master equation for stochastic chemical networks: The reduced-multiplane method.

Chemical reaction networks which exhibit strong fluctuations are common in microscopic systems in which reactants appear in low copy numbers. The analysis of these networks requires stochastic methods, which come in two forms: direct integration of the master equation and Monte Carlo simulations. The master equation becomes infeasible for large networks because the number of equations increases...