Figure 8. A) Time Evolution of Populations of Unbound Promoter DNA, Intermediates in the {CC} Ensemble and the Stable λP_R Promoter OC.

Simulations of population fractions of reactant, intermediates and product vs time (0.01 s to 400 s) for 5-step Mechanism 2 at 50 nM final concentrations of RNAP and promoter DNA, 19 ° C, using rate constants (Table 3) from analysis of FRET and PIFE kinetic data. Free promoter DNA _{— .. –}; closed complex intermediates RP_{C – – –}, I_{1,E – – –} , I_{1M– – –} , I_{1,L – – –}, OC ──. The dashed vertical line at 10 s marks the onset of OC formation from the equilibrium mixture of {CC} and free promoter DNA predicted from filter binding and MnO₄⁻ kinetic data (Fig. 2B). B) Standard Free Energy (G°) vs. Progress Diagram for OC Formation with FL λP_R Promoter DNA. G° values for CC intermediates and the stable OC are obtained from the equilibrium constants of Table 3 (ΔG° = −RT lnK_i) and are expressed relative to RP_C, which is arbitrarily assigned G° = 0 kcal. The G° value for I₂ is obtained from K₅ = k₅/k₋₅, where k₋₅ = 1.2 s⁻¹ (see Fig. 5, there designated k_{I2 → I1}). Activation free energies G^o‡ relative to the same reference are calculated from the relationship ΔG^o‡ = − RTln(k/k _max) where k_max is the (maximum) rate constant for the hypothetical situation ΔG^o‡ = 0.⁴ For purposes of illustration, we choose k_max= 5 x 10³ s⁻¹ for all steps.