Stochastic analysis of a complex gene-expression model. (July 2022) - Chen, Aimin; Tian, Tianhai; Chen, Yiren; Zhou, Tianshou
Abstract: Gene expression has been extensively studied in terms of Markov processes, but its stochastic mechanisms including how noisy sources contribute to expression levels still remain not fully understood. To reveal more reasonable mechanisms, it is needed to consider more molecular events occurring in gene-expression processes. Here we introduce and analyze a general gene-expression model described by a chemical master equation. This model simultaneously considers negative feedback, bursting and promoter cyclic structure, thus extending most gene-expression models in the existing literature. First, we uncover the hierarchy of this complex transcription process by deriving the probability-generating function expressed by an Euler integral formula. Second, we further derive analytical mRNA distribution, which includes previous results as its special cases and provides new insights into the roles of chromatin remodeling and feedback in fine-tuning the mRNA noise. Third, we show that the multi-OFF mechanism always reduces the mRNA noise, but the effect of feedback on the mRNA noise is complex, depending on the detail of the multi-OFF mechanism. The overall analysis provides a paradigm for investigation into expression noise and gene-expression mechanisms in more complex cases. Highlights: A general but biologically reasonable model of stochastic gene expression is constructed, which includes almost previously studied gene-expression models as its special cases; The hierarchy of complex transcription processes is revealed; Analytical mRNA distribution is derived, which extends previous theoretical results; The multi-OFF mechanism always reduces the mRNA noise, independently of feedback forms.