An efficient and assumption-free method to approximate protein level distribution in the two-states gene expression model

Stochastic fluctuations at each step of gene expression might influence protein levels distributions across cell populations. However, current methods to model protein distribution of intrinsic gene expression dynamics are either computationally inefficient or rely on ad hoc assumptions, e.g., that the gene is always active. Taking advantage of the simple form of lower-order moments of distribution, we developed an efficient and assumption-free protein distribution approximation method (EFPD), for the two state gene expression model to accurately approximate the distribution. By EFPD, we computed nearly identical intensity of gene expression regulation at mRNA and protein level, implying a profound link between transcription and translation. Finally, by extending EFPD to approximate the distribution of protein level at any arbitrary temporal state, we proposed an explanation for the role of stochastic noise in gene expression in the context of a continuously changing environment. EFPD can be a powerful tool for modeling the particular molecular mechanisms of targeted gene expression pattern.