A closure scheme for chemical master equations

A closure scheme for chemical master equations.

Probability reigns in biology, with random molecular events dictating the fate of individual organisms, and propelling populations of species through evolution. In principle, the master probability equation provides the most complete model of probabilistic behavior in biomolecular networks. In practice, master equations describing complex reaction networks have remained unsolved for over 70 yea...

Chemical Master Equations - A Mathematical Scheme for the Multi-site Phosphorylation Case

The Chemical Master Equation (CME) provides a fruitful approach for the stochastic description of complex biochemical processes, because it is able to cope with random fluctuations of the chemical agents and to fit the experimental behavior in a more accurate way than deterministic concentration equations. In this work, our attention is focused on modeling and simulation of multisite phosphoryl...

Solving a system of Master Equations for parallel chemical interactions

A Genetic Programming-based Scheme for Solving Fuzzy Differential Equations

This paper deals with a new approach for solving fuzzy differential equations based on genetic programming. This method produces some trial solutions and seeks the best of them. If the solution cannot be expressed in a closed analytical form then our method produces an approximation with a controlled level of accuracy. Furthermore, the numerical results reveal the potential of the proposed appr...

Approximation scheme for master equations: Variational approach to multivariate case.

We study an approximation scheme based on a second quantization method for a chemical master equation. Small systems, such as cells, could not be studied by the traditional rate equation approach because fluctuation effects are very large in such small systems. Although a Fokker-Planck equation obtained by the system size expansion includes the fluctuation effects, it needs large computational ...