FIGURE 6.

The time-dependent activity profile C(t) with TF for the three-step models. For each case, we show five lines: the un-repressed case without TF (top, dashed lines); the repressed cases by TF with the binding rate and the unbinding rate s⁻¹ (top, solid lines); 0.01 s⁻¹ (middle, solid lines); 0.001 s⁻¹ (bottom, solid lines); and with TF that never unbinds (bottom, dashed lines). The arrows indicate C_max given by Eq. 34 and t_pl given by Eq. 30. For all cases, the bare activity is Ω₀ ≈ 0.05 s⁻¹, but we focus on the promoters with fast open complex formation, namely, the larger effective on-rate = 10/11 s⁻¹. The case in panel a corresponds with a strong closed complex binding k_u/k_b ≪ 1, whereas panels b and c deals with a weakly binding RNAP. The difference between panels b and c illustrates the effect of a 10-times faster RNAP binding rate to the promoter.