There are several sources of fluctuations in gene expression. Here we study the effects of time-dependent DNA replication, itself a tightly controlled process, on noise in mRNA levels. Stochastic simulations of constitutive and regulated gene expression are used to analyze the time-averaged mean and variation in each case. The simulations demonstrate that to capture mRNA distributions correctly, chromosome replication must be realistically modeled. Slow relaxation of mRNA from the low copy number steady state before gene replication to the high steady state after replication is set by the transcript's half-life and contributes significantly to the shape of the mRNA distribution. Consequently both the intrinsic kinetics and the gene location play an important role in accounting for the mRNA average and variance. Exact analytic expressions for moments of the mRNA distributions that depend on the DNA copy number, gene location, cell doubling time, and the rates of transcription and degradation are derived for the case of constitutive expression and subsequently extended to provide approximate corrections for regulated expression and RNA polymerase variability. Comparisons of the simulated models and analytical expressions to experimentally measured mRNA distributions show that they better capture the physics of the system than previous theories.
Keywords: analytical solutions; chromosome replication; master equation; stochastic gene expression; stochastic simulation.