Effects of the promoter open complex formation on gene expression dynamics

Little is known about the biological mechanisms that shape the distribution of intervals between the completion of RNA molecules $\left(T_p^{\text{RNA}}\right)$, and thus transcriptional noise. We characterize numerically and analytically how the promoter open complex delay $\left({\tau }_P\right)$ and the transcription initiation rate $\left(k_t\right)$ shape $T_p^{\text{RNA}}$. From this, we assess the noise and mean of transcript levels and show that these can be tuned both independently and simultaneously by ${\tau }_P$ and $k_t$. Finally, we characterize how ${\tau }_P$ affects bursting in RNA production and show that the ${\tau }_P$ measured for a lac promoter best fits independent measurements of the burst distribution of the same promoter. Since ${\tau }_P$ affects noise in gene expression, and given that it is sequence dependent, it is likely to be evolvable.

Figure 1

Normalized MC and analytical $T_p^{\text{RBS}}$ distributions for ${\tau }_P\sim \text{N}\left(40,4^2\right)$ and ${\tau }_P=0$. Lines correspond to the analytical predictions.

Figure 2

Contour plot for the mean and coefficient of variation $\left(c_v\right)$ of the RNA level as a function of ${\tau }_P$ and $k_t$. The mean stays constant when moving along the solid lines and the $c_v$ stays constant when moving along the dashed lines.

Figure 3

$p$-values from the two-sampled K-S test between the distribution of variations in RNA amounts in experiments and model for various values of ${\tau }_P$ (from 0 to 100, step size of 1).