Deciphering Transcriptional Dynamics In Vivo by Counting Nascent RNA Molecules
Fig 2
(A) Model of transcriptional regulation.
The promoter switches between two states: an active and an inactive one. The probability per unit time of switching from the active state to the inactive state is kOFF, and from the inactive to the active state is kON. From the active state transcription initiation occurs in two sequential steps: the formation of the pre-initiation complex at the promoter proceeds with rate kLOAD after which the RNA polymerase escapes the promoter at a constant probability per unit time kESC. Once on the gene the polymerases move from one base pair to the next with a rate k, until they reach the end of the gene and they fall off with the same rate. From this model we compute the mean and the variance of the number of RNA polymerases, present on the gene in steady state, as a function of all the rates and the length of the gene L. This calculation is aided by introducing the mi variables for every base, which keep track of the number of polymerases at that base. (B) Noise profile for different models of transcription initiation. From the master equation of the model described in (A) we computed the Fano factor of the nascent RNA distribution as a function of the length of the gene being transcribed, for the three different models of transcription initiation: one-step (red), "bursty"(blue), and two-step initiation (black). The three different models give qualitatively distinct predictions. To illustrate this point for the "bursting" model we use the following parameters: kOFF = 5/min, kON = 0.435/min, k = 0.8kb/min, kLOAD = 5/min and kESC = 0/min, which are characteristic of the PDR5 promoter in yeast, as reported in [4]. For the two-step model we use kLOAD = 0.14/min, kESC = 0.14/min, kOFF = 0/min, kON = 0/min, k = 0.8kb/min, characteristic of MDN1 promoter, which we find by analyzing the data reported in [25]. For the one-step model, we use kLOAD = 0.09/min, kESC = 0/min, kOFF = 0/min, kON = 0/min, k = 0.8kb/min, which are characteristics of the yeast gene RPB1, obtained by analyzing the data published in [25]. (C) Noise profiles for different regulatory mechanisms. In the "bursting" model of transcription, the transcriptional output can be modulated either by changing the burst size or the burst frequency, which in the model can be achieved by tuning kOFF or kON. The Fano factor for the nascent RNA distribution obtained from burst size and burst frequency mechanisms of regulation are plotted as a function of the fold change in mean. (i.e., the mean of the distribution normalized by the maximum mean number of nascent RNAs in the cell, which is obtained when there is no transcriptional regulation and the promoter is always active). Clearly the two modes of regulation give qualitatively distinct predictions for the noise profile. (To illustrate this point we use the following parameters: kOFF = 5/min, kON = 0.435/min, k = 0.8kb/min, L = 4436 bps, kINI = 5/min, which were reported for the PDR5 promoter in yeast [4].)