## 3 _E. coli_\(\sigma\)[70] Promoter Recognition
### Kinetics and Mechanism of Open Complex Dissociation
Determining the DNA Closing Rate Constant (k-2) and the Stabilization (K\({}_{\rm 3}\)) of the Initial Open Complex  
Fast salt-upshift dissociation experiments provide a valuable method of determining the DNA closing rate constant k-2 [24]. For \(\lambda\)P\({}_{\rm R}\) (and presumably other promoters with long-lived open complexes), the stabilization equilibrium constant K\({}_{\rm 3}\) decreases strongly with increasing salt or urea concentration, so a fast salt or urea upshift rapidly converts the initial population of RP\({}_{\rm O}\) to I\({}_{\rm 2}\)[24]. Because the DNA closing step is found to be independent of salt concentration, a transient burst of I\({}_{\rm 2}\) is obtained, suitable for determining the DNA closing rate constant k-2 [24] and for fast DNA footprinting of I\({}_{\rm 2}\)[23]. Moreover, once determined at high salt concentration, k-2 is used at lower salt concentrations to dissect k\({}_{\rm d}\) and determine K\({}_{\rm 3}\) from Equation (9). For \(\lambda\)P\({}_{\rm R}\) at 37 \({}^{\circ}\)C, RP\({}_{\rm O}\) lifetime (1/k\({}_{\rm d}\)) is approximately 11 hours, while that of I\({}_{\rm 2}\) (1/k\({}_{\rm 2}\)) is about 1 second. Therefore, K\({}_{\rm 3}\) is about 10\({}^{5}\), and RP\({}_{\rm O}\) is approximately 10\({}^{5}\) fold more stable than I\({}_{\rm 2}\). The strong dependences of K\({}_{\rm 3}\) on urea and KCl concentration [18,24] and the effect on K\({}_{\rm 3}\) of deleting the \(\beta\)' jaw or the downstream duplex [134] indicate that a major part of this stabilization involves assembly of the jaw and other DMEs on the downstream duplex, schematically illustrated in Figure 3. Movements of the downstream (discriminator) region of the nontemplate strand [23] and of RNAP elements in the cleft in concert with tightening of interactions in the cleft are also implicated in stabilization of the initial open complex. Fundamental Similarities of the RNAP-Promoter Mechanism to a Mechanism of Enzyme Catalysis; Implications for Regulation of Open Complex Formation and Lifetime  
Mechanism 1 is of course formally the same as the minimal two-step mechanism of enzyme catalysis. The hyperbolic dependence of k\({}_{\rm obs}\) on [RNAP] in Equation (1) is completely analogous to the hyperbolic dependence of the initial velocity of the enzyme catalyzed reaction on substrate concentration for noncooperative enzymes; K\({}_{\rm 1}\) and k\({}_{\rm 2}\) are the counterparts of 1/K\({}_{\rm M}\) and k\({}_{\rm cat}\) in enzyme kinetic analysis. Another fundamental analogy, at least for \(\lambda\)P\({}_{\rm R}\), is that the DNA opening-closing step in mid-mechanism is rate-determining in both directions of the mechanism, just as the central catalytic steps are typically rate determining for both directions of an enzyme catalyzed reaction. Regulation of the kinetics of enzyme catalyzed reactions by ligands or cooperativity of multi-subunit enzymes is primarily at the level of the initial reversible steps of substrate binding and conformational change that precede the central catalytic step, while the catalytic step itself is typically not regulated. Is this also true of the kinetics of open complex formation and the lifetime of the stable open complex? Both the initial binding step and the conformational changes in the I\({}_{1}\) ensemble that prepare the DNA to be opened are highly regulated; equilibrium constants for these steps are strong functions of promoter sequence and length [142] and of concentrations of transcription factors, ligands, solutes and salts [63, 64, 65, 24, 60, 66]. Likewise, the steps converting the initial open complex I\({}_{2}\) to the stable open complex (RPo at \(\lambda\)P\({}_{\mathrm{R}}\)) are strong functions of promoter sequence and solute and salt concentrations, and are, thus, also likely targets of regulation. On the other hand, evidence to date indicates that while the DNA opening and closing rates are strongly temperature dependent (especially DNA opening), these analogs of the catalytic step are relatively insensitive to solution variables.