Multiscale Modeling of Chemical Kinetics via the Master Equation

Multiscale Modeling of Chemical Kinetics via the Master Equation

We present numerical methods for both the direct solution and simulation of the chemical master equation (CME), and, compared to popular methods in current use, such as the Gillespie stochastic simulation algorithm (SSA) and τ -Leap approximations, this new approach has the advantage of being able to detect when the system has settled down to equilibrium. This improved performance is due to the...

Order Reduction of the Chemical Master Equation via Balanced Realisation

We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension might be large even for trivial systems. Here, we derive a reduced ODE set that accurately approximates the probabilities of subspaces of interest with a known...

Stochastic Modeling and Statistical Inference of Intrinsic Noise in Gene Regulation System via Chemical Master Equation

Intrinsic noise, the stochastic cell-to-cell fluctuations in mRNAs and proteins, have been observed and proved to play important roles in cellular systems. Due to the recent development in single-cell-level measurement technology, the studies on intrinsic noise are becoming increasingly popular among scholars. The chemical master equation (CME) has been used to model the evolutions of complex c...

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