Figure 1.

Mechanical coupling between RNAP translocation and the DNA torsional response. (A) RNAP translocation on a torsionally constrained DNA segment is accompanied by undertwisting of the DNA upstream (σ_b < 0) and overtwisting of the DNA downstream (σ_f > 0). The supercoiled DNA, in turn, applies a restoring torque on the RNAP (τ_b and τ_f). (B) In agreement with the experimental data (10), we used a sigmoid curve (Equation 3) to model the RNAP velocity-DNA restoring torque dependence. (C) As the RNAP moves away from the transcription start site (TSS), its translocation rate () and rotation rate () continuously decreases, while the rate of DNA twisting by the RNAP () exhibits a non-monotonic trend. The behavior shown here is for the case of a torsionally constrained genomic segment. (D) Ratio of the average RNAP velocity in the presence of different supercoiling generators to the average RNAP velocity in the absence of any supercoiling generators. Here, Φ₀ and Φ_L are the rates of supercoiling injection upstream and downstream from the gene body, respectively. See Eqs. (S5) and (S6) for further details. (E) Ratio of the average RNAP velocity in the presence of different torque generators to the average RNAP velocity in the absence of any torque generators. Here, T₀ and T_L are the torques applied by an external agent or process upstream and downstream from the gene body, respectively. See Eqs. (S7) and (S8) for further details. In (D) and (E), the white line demarcates the region where the average RNAP velocity is lower in the presence of the generators from the region where the presence of generators increases the average RNAP velocity. The average RNAP velocity is defined as the gene length divided by the total time taken by the RNAP to transcribe the gene.