Stochastic analysis of genetic promoter architectures with memory

Stochasticity in the gene-expression process can create variability in the level of a given mRNA/protein across a homogenous population of living cells. Random fluctuations between different promoter states have been implicated as a major source of noise in the expression of many genes. These fluctuations are typically modeled through a two-state promoter architecture, where the promoter of a gene transitions between an active (ON) and inactive (OFF) state, spending an exponentially distributed time-interval in each state. High levels of mRNA production occur from the active state, while the inactive state allows for a low basal rate of production. Recent data has shown the existence of three-state promoter architectures with memory, where the time spent in the inactive state is gamma distributed. Here we analyze stochastic models of both two-state and three-state promoter architectures and identify key differences in their stochastic dynamics. Quantifying distance between probability distributions using standard metrics reveals that the difference in the mRNA copy number distributions for both promoter architectures is maximum when the stability of the active promoter state is comparable to the stability of the mRNA transcript. Our results further show that mRNA auto-correlations decay more rapidly for a three-state promoter architecture compared to a two-state promoter architecture. Interestingly, we find that in certain parameter regimes the three-state promoter architecture can yield negative mRNA auto-correlations. Finally, we discuss how these results can be useful for identifying genetic promoter architectures from single-cell mRNA data.