Figure 2.

Emergence of DNA supercoiling-mediated collective RNAP behavior. (A) In our simulation setup, RNAPs are recruited to the transcription start site at a rate k_on and the supercoiling throughout the genomic segment is relaxed at a rate k_relax. (B) When a second RNAP is recruited to the TSS before the first RNAP has finished transcribing (event indicated by the vertical dashed black line), the translocation rate of the already recruited RNAP increases (shown by the solid green curve). The translocation rate of the first RNAP in the absence of subsequent RNAP recruitment is indicated by the dashed green curve. Inset: when the DNA segment is torsionally constrained (clamped DNA), the velocity of the first RNAP is higher if more RNAPs are subsequently recruited to the same gene. The effect disappears if there is no supercoiling accumulation (torsionally unconstrained or free DNA) or if the RNAP-generated supercoiling is quickly relaxed (high k_relax). In each case, the behavior for 256 independent runs is shown. (C) The average RNAP velocity varies non-monotonically with k_on in the case of torsionally constrained DNA. Collective RNAP behavior, which emerges for k_on > 10⁻² s⁻¹ (shaded region), increases the overall transcription elongation rate. However, for very high k_on (k_on > 1.0 s⁻¹), a ‘traffic jam’-like scenario decreases the average RNAP velocity. For different transcription initiation rates, the average RNAP velocity increases with the rate of DNA torsional stress relaxation (k_relax). (D) The average number of co-transcribing RNAPs for different values of k_on and k_relax. The shaded regions in panels (C) and (D) indicate the range of k_on values corresponding to the regime of collective RNAP behavior. Comparison with the case of torsionally unconstrained DNA is shown in Supplementary Figure S7.