Nascent RNA kinetics with complex promoter architecture: Analytic results and parameter inference

Abstract

The stochastic kinetics of transcription can be accurately inferred from the distribution of nascent RNA . However, the inferences using conventional gene-expression models with exponential waiting times between promoter active and inactive states would be inaccurate since these waiting times may follow non-exponential distributions. For instance, the refractory period of the prolactin gene in mammalian cells obeys a bimodal distribution. In this paper, we have developed a general stochastic model for nascent RNA that takes into account the complexity of promoter structure and encompasses various traditional models of gene transcription as its special cases. Importantly, we have derive the exact distribution and moments of nascent RNA using techniques in queuing theory, which provides insight into the effect of molecular memory on transcription dynamics. Based on the derived analytical results, we further developed a method to infer non-exponential waiting-time distributions between promoter states from stationary nascent RNA distributions. Data analysis of a realistic example verifies the validity of this inference method.