Stochastic theory of large-scale enzyme-reaction networks: finite copy number corrections to rate equation models.

Numerical modeling for nonlinear biochemical reaction networks

Nowadays, numerical models have great importance in every field of science, especially for solving the nonlinear differential equations, partial differential equations, biochemical reactions, etc. The total time evolution of the reactant concentrations in the basic enzyme-substrate reaction is simulated by the Runge-Kutta of order four (RK4) and by nonstandard finite difference (NSFD) method. A...

Dimensional Reduction of the Fokker-Planck Equation for Stochastic Chemical Reactions

The Fokker-Planck equation models chemical reactions on a mesoscale. The solution is a probability density function for the copy number of the different molecules. The number of dimensions of the problem can be large making numerical simulation of the reactions computationally intractable. The number of dimensions is reduced here by deriving partial differential equations for the first moments ...

A scalable moment-closure approximation for large-scale biochemical reaction networks

Motivation Stochastic molecular processes are a leading cause of cell-to-cell variability. Their dynamics are often described by continuous-time discrete-state Markov chains and simulated using stochastic simulation algorithms. As these stochastic simulations are computationally demanding, ordinary differential equation models for the dynamics of the statistical moments have been developed. The...

Determining the long-term behavior of cell populations: A new procedure for detecting ergodicity in large stochastic reaction networks

A reaction network consists of a finite number of species, which interact through predefined reaction channels. Traditionally such networks were modeled deterministically, but it is now well-established that when reactant copy numbers are small, the random timing of the reactions create internal noise that can significantly affect the macroscopic properties of the system. To understand the role...

The application of DEA and queuing models to large scale computer networks