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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 phosphorylation/dephosphorylation cycles, by using the quasi-steady state approximation of enzymatic kinetics. The CME dynamics is written from the coefficients of the deterministic reaction-rate equations and the stationary distribution is computed explicitly, according to a recently developed realization scheme. Simulations are included to provide a comparison with Monte Carlo methods in terms of computational complexity.