Probing Mechanisms of Transcription Elongation Through Cell-to-Cell Variability of RNA Polymerase

Abstract

The process of transcription initiation and elongation are primary points of control in the regulation of gene expression. Although biochemical studies have uncovered the mechanisms involved in controlling transcription at each step, how these mechanisms manifest in vivo at the level of individual genes is still unclear. Recent experimental advances have enabled single-cell measurements of RNA polymerase (RNAP) molecules engaged in the process of transcribing a gene of interest. In this article, we use Gillespie simulations to show that measurements of cell-to-cell variability of RNAP numbers and interpolymerase distances can reveal the prevailing mode of regulation of a given gene. Mechanisms of regulation at each step, from initiation to elongation dynamics, produce qualitatively distinct signatures, which can further be used to discern between them. Most intriguingly, depending on the initiation kinetics, stochastic elongation can either enhance or suppress cell-to-cell variability at the RNAP level. To demonstrate the value of this framework, we analyze RNAP number distribution data for ribosomal genes in Saccharomyces cerevisiae from three previously published studies and show that this approach provides crucial mechanistic insights into the transcriptional regulation of these genes.

Figure 1

Model of transcription elongation. (A) The promoter for the gene of interest switches between two states: an active and an inactive one. The rate of switching from the active state to the inactive state is k_OFF and from the inactive to the active state is k_ON. From the active state, transcription initiation proceeds at a rate k_INI. Once on the gene, each polymerase molecule can either be in an active or a paused state, independent of the state of other RNAPs. A polymerase molecule in the active state can switch stochastically to the paused state with a rate k_P+, whereas it can again switch back to the active state with a rate k_P−. In the active state, the polymerases move from one bp to the next at a rate k_EL until they reach the end of the gene and fall off at the same rate. From this model, we compute the mean and the variance of the number of RNA polymerases (RNAPs), in steady state, and the interpolymerase distances along the gene as a function of the initiation rate. (B) A histogram of the RNAP number distribution is shown for an rrn gene in yeast (adapted from (17)) obtained from EM images of the DNA extracted from single cells. (C) A histogram of interpolymerase distances along a gene in E. coli (adapted from (18)) is shown. EM images also provide interpolymerase distances along a gene of interest. To see this figure in color, go online.

Figure 2

Noise profiles for different models of transcription elongation. (A and B) Using Gillespie simulations (50), we computed the Fano factor of the RNAP number distribution and the coefficient of variation (CV) of the interpolymerase distance distribution along the gene, as a function of the initiation rate of the gene being transcribed, for the two different models of transcription elongation: simple elongation (blue) and the pausing model (red). The two different models give qualitatively distinct predictions. To illustrate this point, we use the rates, as shown in Table 1. (C) The probability that a nucleotide on a gene is occupied by an RNAP for simple elongation (k_INI = 1 s⁻¹ shown in blue) and pausing model (k_INI = 1 s⁻¹, k_P+ = 0.1 s⁻¹, and k_P− = 0.1 s⁻¹ shown red) is shown. (D and E) A kymograph shows bunch formation at different initiation rates for simple elongation (D) and the pausing model (E). For simple elongation, the polymerases collide and move with a uniform speed, whereas in the pausing model, a paused RNAP molecule creates a roadblock, forming bunches of polymerases. To see this figure in color, go online.

Figure 3

Effect of elongation dynamics on RNAP noise for a bursty promoter. (A) We computed the Fano factor of the nascent RNA number distribution and (B) the coefficient of variation (CV) of the interpolymerase distance distribution as a function of the initiation rate for the three different models of elongation: ON-OFF promoter dynamics alone (dashed line), simple elongation (blue), pausing model (green) for k_P+ = 0.1 s⁻¹ and k_P− = 0.05 s⁻¹. Whereas for the simple elongation, the Fano factor goes down as the initiation rate is increased, for the pausing model, for lower initiation rates, an increment in the initiation rate enhances the Fano factor. However, for higher initiation rates, any increase in initiation rate decreases Fano factor. (C and D) A kymograph of RNA polymerase (RNAP) in a bursty promoter is shown. (C) Bunch formation does not occur for simple elongation. (D) In the pausing model, bunch formation varies as initiation rate is tuned. For a low initiation rate (k_INI = 0.02 s⁻¹, left panel), bunch formation is rare. For an intermediate rate (k_INI = 0.2 s⁻¹, middle panel), bunch formation becomes frequent, and for a high initiation rate (k_INI = 1 s⁻¹, right panel), bunches become very frequent. To see this figure in color, go online.

Figure 4

Noise in the RNAP number distributions for ribosomal genes in budding yeast. The Fano factor of RNAP number distribution is plotted as a function of mean from the published experimental data (55, 56, 57). For each data set, shown in red squares with error bars, we fit the control stain (WT, solid squares) with the ON-OFF model to extract the parameters (k_INI, k_ON, and k_OFF; see Table 2) and then vary each of them separately keeping the other parameters fixed. Simulation results from varying the initiation rate only (dashed light gray line), promoter activation rate only (dashed dark gray line), and promoter inactivation rate only (solid blue line) are shown for each. Error bars for mean in (A) and (B) represent standard error of the mean. There are no error bars for the Fano factor because of unavailability of raw data sets. Error bars in (C) represent standard error of the mean and standard deviation (SD) of the Fano factor. The errors in the Fano factor are determined by bootstrapping each experimental RNAP number distribution 1000 times and calculating the SD in the Fano factor for those independent bootstrapped data sets. To see this figure in color, go online.