FIGURE 5.

The time-dependent activity profile C(t) with TF for the single-step (a) and the two-step models with k_on = 0.1 s⁻¹ (b) and 1 s⁻¹ (c). The bare activity is one transcription initiation per 20 s: Ω₀ = 1/20 s⁻¹. For each case, we show five curves: 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. 22 and t_pl given by Eq. 23 for the two-step models. For the single-step model in panel a, the RNAP activity is limited only by a binding event once every 20 s. For the case in panel b of the two-step model, each step takes 10 s, while in the case of panel c, where the on-rate is fast, the overall activity limited by an elongation initiation time of 19 s.