DNA Supercoiling Drives a Transition between Collective Modes of Gene Synthesis

Transcription of genes can be affected by both biochemical and mechanical factors. Recent experiments suggested that the mechanical stress associated with transcription-induced DNA supercoiling is responsible for the transition from cooperative to antagonistic group dynamics of RNA polymerases (RNAPs) upon promoter repression. To underpin the mechanism behind this drastic transition, we developed a continuum deterministic model for transcription under torsion. In our model, the speed of an RNAP is affected by the local DNA supercoiling, as well as two global factors: (i) the number of RNAPs on the gene affecting the torsional stress experienced by individual RNAPs and (ii) transcription factors blocking the diffusion of DNA supercoils. Our minimal model can successfully reproduce the experimental findings and helps elucidate the interplay of mechanical and biological factors in the collective dynamics of molecular machines involved in gene expression.

Figure 1

The model. (a) Excess negative supercoiling in DNA segments and restoring torque on ${\mathrm{RNAP}}_i$. (b) ON and OFF states of the promoter regulated by a repressor TF. (c) Time series of the promoter state for four different initiation rates $\alpha$.

Figure 2

Model parameters. (a) Initiation rates $\alpha$ used in the simulations (blue triangles) based on experimental data (red solid circles) in Ref. [10]. (b) Speed of an RNAP $v$ as a function of torque $\tau /{\tau }_c$.

Figure 3

Time series of $\tau /{\tau }_c$ and $v$ of the first 3–4 RNAPs for the case of active promoter (a)–(b) and promoter repression at $T=90\mathrm{s}$ (c)–(d) at the intermediate initiation rate $\alpha =0.033{\mathrm{s}}^{-1}$. We only plot $\tau /{\tau }_c\in (-2,2)$ for clarity. Gray dashed lines demarcate the time range for Supplemental Material, Fig. S2 [29].

Figure 4

Comparison of our model (blue) with the experimental results of Ref. [10] (red) on the speed of RNAPs $v_{\mathrm{ON}}$ as a function of initiation rates $\alpha$. The inset shows the effect of promoter repression. Low initiation rate represents ${\alpha }_{\mathrm{sim}}=0.006{\mathrm{s}}^{-1}$ (${\alpha }_{\mathrm{expt}}=0.009{\mathrm{s}}^{-1}$), yielding roughly a single RNAP on the gene at a given time. Intermediate and high initiation rates are from ${\alpha }_{\mathrm{sim}}=0.033{\mathrm{s}}^{-1}$ (${\alpha }_{\mathrm{expt}}=0.035{\mathrm{s}}^{-1}$) and ${\alpha }_{\mathrm{sim}}=0.127{\mathrm{s}}^{-1}$ (${\alpha }_{\mathrm{expt}}=0.127{\mathrm{s}}^{-1}$), respectively.

Figure 5

Consequences of relaxing the central assumptions of our model. Red and blue bars represent experimental data and simulation results from $f(n)=1$, respectively. (Dark blue) Free DNA: TF does not constrain supercoils even when bound near the promoter. (Light blue) Clamped DNA: supercoils are always constrained near the promoter, even when TF is unbound.