Fig 1.
Experimental methods to count nascent RNA (transcribing RNA polymerase molecules).
(A) Electron micrographs of intact chromosomes extracted from cells provide images of transcribing polymerases along a gene (also referred to as Miller spreads). This method allows one to count the number of RNAP molecules that are actively transcribing a gene of interest across a population of genetically identical cells. Histograms for the distribution of number of Pol I molecules is shown along rDNA, for a wild type yeast cell (adapted from [67]). (B) Fluorescence in Situ Hybridization (FISH) in single cells provide the intensity of the transcription site, which can then be used to count the number of nascent RNAs for a particular gene. Histogram for the nascent RNA distribution is shown for MDN1 gene in yeast (adapted from [25]) (C) Such measurements can be used to count the number of nascent RNA transcripts using the fact that the length of nascent RNA transcripts are shorter than the mRNA transcripts. Histograms for mRNA distribution [68] in ES cells is shown.
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].)
Fig 3.
(A) Mean number of nascent RNAs for six different yeast genes.
We use the nascent RNA distribution data for six constitutively expressed yeast genes: KAP104, TAF5, TAF6, TAF12, RPB2, RPB3 and plot the mean of the distributions as a function of the gene length. The mean of the distribution increases linearly with the gene length indicating that the transcription of all six genes is initiating at the same rate. The initiation rate of these genes extracted from the data is 0.145±0.025/min, where the rate of elongation is taken to be 0.8 kb/min [4]. (B) Fano factor for the nascent RNA distribution of six different yeast genes. Using the data for the nascent RNA distributions for the same six yeast genes described in (A) we compute the Fano factor and compare it to predictions from our model. The shaded region shows the possible values that the Fano factor can take depending on the ratio of kLOAD and kESC given the initiation rate determined from the mean in part (A). The boundary of the shaded region corresponds to the minimum amount of noise (as measured by the Fano factor) given the extracted rate of initiation in part (A), and it is obtained when the two rates are the same, i.e., kLOAD = kESC = 0.29±0.013/min. Interestingly enough the Fano factors characterizing the nascent RNA distribution for these six yeast genes seem to lie on this boundary. (The nascent RNA data for the six yeast genes used in our analysis is taken from ref. [25].)
Fig 4.
Comparison of predicted and measured Fano factors for cytoplasmic mRNA distributions.
Fano factors for the cytoplasmic mRNA distributions, as predicted by the one-step (RPB1), two-step (KAP104, TAF5, TAF6, TAF12, RPB2, RPB3, MDN1) and three-step (PUP1, PRE3, PRE7, PRP8) mechanisms of initiation, are shown as blue bars. These are compared with the measured cytoplasmic mRNA distributions, shown in green bars, as reported in ref [25]. In cases when the measured distributions have higher Fano factors than predicted, this is indicative of significant sources of noise downstream to transcription initiation and elongation that affect the cell-to-cell variability of cytoplasmic mRNA.