Fig 1.
Model schematics of supercoiling-dependent transcription.
(A) During transcription initiation, a negatively supercoiled (blue circle) promoter is favored over a positively supercoiled (red circle) promoter for RNAP (green oval) binding and open complex formation [7]. (B) During transcription elongation, the translocation of RNAP induces positive supercoiling in front and negative supercoiling behind [4,5], which consequently influences whether the RNAP remains processive (green) in elongation or becomes stalled (grey) [10,11]. (C) Transcription terminates when RNAP is released from the mRNA. The transcribed mRNA is subsequently degraded in the model. (D) Supercoils can diffuse on DNA within a topological domain flanked by two domain barriers and interact with RNAP and topoisomerases. (E) Topo I (blue oval) removes one negative supercoil at a time [32]. (F) Gyrase (red oval) converts one positive supercoil to one negative supercoil at a time [31]. (G) Formation and dissolution of a topological domain upon the binding and unbinding of domain anchoring proteins (domain barriers, grey block).
Table 1.
Timescale for key processes in supercoiling dissipation and generation.
Fig 2.
Cooperation of RNAP transcription is favored by high initiation rates and antagonized by low initiation rates.
(A) The apparent RNAP elongation rate increases and reaches maxima (blue shaded region) as the initiation rate increases. Error bars are standard deviations from 1000 simulations. (B) Pearson correlation coefficient of adjacent RNAP trajectories increases and approaches unity (blue shaded region) as the initiation rate increases. The correlation coefficient is normalized such that “0” corresponds to the case of independently transcribing RNAP trajectories and “1” corresponds to the case of the co-transcribing RNAP trajectories in the highest expressed gene. The unnormalized curve is in S4 Fig. (C) The mean distance (dots in boxes) between neighboring RNAP molecules decreases as the initiation rate increases. When the maximal cooperation is reached (intersect with blue shaded region, initiate rate at which maximal elongation rate is reached) the distance is ~ 500 bp. Box borders indicate first and third quartiles of the data, vertical lines standard deviations, and horizontal lines in the box media. (D) Stacked histograms of supercoil density upstream (top), downstream (middle) and torque (bottom) RNAP molecules face during transcription. Supercoil densities of processive and stalled RNAP molecules are shown in green and red, respectively. The torque value above the stall threshold is shaded in grey. (E) Representative kymographs of RNAP translocation trajectories (black lines) with the corresponding supercoiling density (positive in orange and negative in blue) in its vicinity. A time interval of 750–950 s was chosen to maintain a constant mean mRNA copy number at a steady-state under each condition (S3 Fig). The slope of the trajectory reflects the elongation speed of the associated RNAP molecule. Left and right white dashed lines indicate the start and end positions of the transcribing region, respectively. The asteroid in the left kymograph indicates that a slow-moving RNAP molecule started to move with a higher speed after a new RNAP molecule is loaded at the promoter on the left. The arrowhead in the middle kymograph indicates a transcribing RNAP molecule drastically reduces its elongation speed after the leading RNAP (right) terminates its transcription and dissociates.
Fig 3.
Cooperation holds under the condition of fast Topo I unbinding and moderate supercoiling diffusion.
(A to C) Examples of the elongation rate–initiation rate curves (blue dots) and the corresponding piecewise linear fitting (red lines) for three different combinations of the Topo I unbinding rate and supercoil diffusion rate. Fitting is only performed for scenarios where the maximum empirical initiation rate is greater than 0.05 s−1 (i.e., C is not fitted). The fitted slope (k) values and fitting goodness (r2) were displayed in the legend. Grey stars correspond to the experimental data in Kim et al. [13]. (D) Heatmap of RNAP cooperativity, characterized by the slope of the elongation rate–initiation rate curve, under different supercoiling diffusion coefficients and Topo I unbinding rates. The grey region corresponds to the regime where the fitting goodness r2 is below 0.85, or the fitting is not performed (maximum initiation rate < 0.05 s−1). The red star indicates parameters used in the rest of the paper. (E) Heatmap of the mean squared error (MSE) between the model and the experimental data from Kim et al. [13].
Fig 4.
Dynamic topological domain formation results in bursty and noisy transcription from strong promoters through the accumulation and release of supercoiling.
(A-F) Comparison of a weak promoter (kmax = 0.005 s−1, top panel) and a strong promoter (kmax = 0.1 s−1, bottom panel) in their responses to supercoil density (A and D), mRNA copy number distribution when the DNA is open (unlooped, B and E) and when the DNA dynamically loops and unloops (C and F). (G-H) Exemplary mRNA production time traces (top panel) and the corresponding supercoil density of the DNA (bottom panel) for the strong promoter in the open-DNA condition (G) and the dynamically looping condition (H). The pink-shaded regions in H indicate the time when the loop is open. (I) Comparison of the Fano factor as a function of mean mRNA copy number for genes in an open DNA (blue) and that in a dynamically looping DNA condition (orange). The grey line denotes Fano factor = 1. (J) Comparison of the average initiation rate of genes when the DNA is open (green) and when the DNA is closed (red) in the dynamically looping DNA condition.
Fig 5.
Intergenic supercoiling affects the level of mRNA production of two neighboring genes.
(A) The construct for convergently, divergently and codirectionally arranged genes with the intergenic length fixed at 1.2 kb. The mRNA copy number distribution (B) and intergenic supercoiling distribution (C) for cases with (orange bar) and without (blue bar) intergenic supercoiling. The bar plot for initiation rate (D) and elongation rate (E) for cases with (orange bar) and without (blue bar) intergenic supercoiling. Error bar suggests standard deviation.
Fig 6.
The effects of the initiation rate on the expression of adjacent genes.
(A) The construct for convergently, divergently, and codirectionally arranged genes where the initiation rate of one gene is varied (kmax = 0.001, 0.005, 0.01, 0.02, 0.05, 0.1, 0.2 s−1) and the initiation rate of the other gene is monitored in response to that of the first gene with an upper limit of kmax = 0.05 s−1. (B) The mean mRNA copy number of the monitored gene as a function of the maximum initiation rate (kmax) of the first gene, for the four constructs shown in (A). The dot is the mean and the shaded area is mean ± SEM. (C) The intergenic supercoiling density as a function the maximum initiation rate (kmax) of the adjacent gene. The dot is the mean and shaded area is mean ± SEM. (D) The empirical elongation rate of the monitored gene as a function of the maximum initiation rate (kmax) of the gene whose initiation rate is varied. The elongation rate is calculated for transcription events after 750 s, where the mean mRNA copy number already reaches a steady state (S14 Fig).