Stochastic Modeling and Statistical Inference of Intrinsic Noise in Gene Regulation System via the Chemical Master Equation

Intrinsic noise, the stochastic cell-to-cell fluctuations in mRNAs and proteins, has been observed and proved to play an important roles in cellular systems. Due to recent developments in single-cell-level measurement technology, the studies on intrinsic noise are becoming increasingly popular among scholars. The chemical master equation (CME) has been used to model the evolution of complex chemical and biological systems since 1940, and is often put forth as the standard tool for modeling intrinsic noise in gene regulation systems. A CME-based model can capture the discrete, stochastic, and dynamical nature of gene regulation systems, and may offer causal and physical explanations of the observed data at single-cell level. Nonetheless, the complexity of the CME also poses a serious challenge for researchers in proposing practical modeling and inference frameworks. In this article, we will review the existing works on the modeling and inference of intrinsic noise in gene regulation systems within the framework of the CME model. We will explore the principles of constructing a CME model for studying gene regulation systems and discuss the popular approximations of the CME. Then we will study the simulation simulation methods as well as the analytical and numerical approaches that can be used to solve the CME model. Finally we will summarize the existing statistical methods that can be used to infer unknown parameters or structures in the CME model using single-cell-level gene expression data.