Numerically efficient analysis of a one- dimensional stochastic Lac operon model

Abstract

Gene expression models and their analysis play a key role to understand gene regulation mechanisms. The lac operon mechanism has been largely studied to analyze its bistable behavior. In this paper a stochastic quasi steady- state lac operon model which is indeed a one dimensional birth- death process is considered. Nevertheless the well known closed- from solutions, due to the nonlinearity of parameters, the intermediate computed values become out of the representation range with the increase of the state space size. An aggregation- based two step algorithm is proposed to compute the steady- state distribution efficiently. The results of the stochastic model give the same parameter range for the bistable behavior as with the deterministic ODE model.