An Analytic Approach to a Stochastic Enzyme Kinetic Model

In this paper we study a stochastic model of the enzyme-substrate reaction system. We investigate the block structure of the transition rate matrix of the model and find a formula for the exact solution to the chemical master equation of the model. The solution of the model is represented in terms of the eigenvalues and eigenvectors of block matrices whose dimensions are much lower than the original transition rate matrix. The method presented in the paper can reduce greatly computational complexity when the solution of stochastic enzyme-substrate model is sought. We show the accuracy and efficiency of the method by simulating examples.