Inferring Transcriptional Dynamics with Time-Dependent Reaction Rates Using Stochastic Simulation

Abstract

Gene transcription is a stochastic process. Single-cell experiments show that transcription occurs in bursty fashion. It has been shown that stochastic switching between promoter active (ON) and inactive (OFF) states results in bursts. However, increasing evidence on promoter switching between ON and OFF states suggests that promoter states’ times can be non-exponential and exhibits multi-OFF mechanism. All these experimental facts motivate to present a multi-state promoter model of gene expression for characterizing promoter architecture. In this paper, we develop a model for promoter with arbitrary number of promoter OFF states and single ON state using Erlang-distributed ON/OFF times. In this paper, we use Monte Carlo approach of Expectation–Maximization (MCEM) that uses direct method of Gillespie’s Stochastic Simulation Algorithm (SSA) to infer the unknown kinetic rates, number of promoter states and parameters representing estimation errors of inferred parameters. We use graphics processing units (GPUs) to accelerate the MCEM. Application of MCEM to time-series data of endogenous mouse glutaminase promoter shows that promoter switching between ON and OFF states effects bursting. The production of mRNAs becomes consistent as the number of OFF states increases and arrives at deterministic time intervals. The main objective is to analyse the impact of promoter switching on bursty production of mRNAs. Our analysis demonstrates that bursting kinetics depends on the promoter ON/OFF states.