## 3 _E. coli_\(\sigma\)[70] Promoter Recognition
### The Promoter Search and Initial Specific Binding to Form RPc  
During initiation, RNAP holoenzyme first searches for and specifically recognizes promoter DNA, forming an initial closed complex generally called RPc (Figure 3). The bimolecular rate constant for formation of a closed complex between Eo70 and _rrmB_ P1 promoter on a short (204 bp) DNA is \(2\times 10^{8}\) M\({}^{-1}\cdot\)s\({}^{-1}\)[71]; that for a closed complex between Eo54 RNAP and an 853 bp fragment containing the _S. typhimurium glnAp2_ promoter is \(2.1\times 10^{7}\) M\({}^{-1}\cdot\)s\({}^{-1}\)[21]. These provide lower bounds on the rate constant for RPc formation at these promoters, which are one or two orders of magnitude less than the theoretical three-dimensional (3D) diffusion limit (\(\sim\)\(6\times 10^{9}\) M\({}^{-1}\cdot\)s\({}^{-1}\) for equal-sized reactants). Is the rate of formation of the initial specific complex RPc determined by 3D diffusion of RNAP and promoter DNA, or by nonpromoter binding followed by 1D diffusion (_i.e._, sliding) and/or hopping of RNAP which  
Figure 3: Schematic representation of proposed intermediates in open complex formation and dissociation at \(\lambda\)P\({}_{\rm R}\) promoter. Closed complexes like RPc, I\({}_{1,\rm E}\) (early), or I\({}_{1,\rm L}\) (late) can be significant members of the rapidly equilibrating I\({}_{1}\) ensemble. The \(\alpha\)CTDs are shown in cyan; other colors are the same as in Figure 1.  
can increase the rate constant above the 3D limit? Although some early studies (including [114, 115, 116, 117, 118]) argued in favor of RNAP sliding, recent single-molecule studies provide evidence against it [119, 120], while suggesting a role for RNAP hopping [121]. Since thermodynamics is path-independent, sliding or hopping should not affect the equilibrium constant for forming RP\({}_{\rm C}\). This equilibrium constant and not the second order rate constant for forming RP\({}_{\rm C}\) is generally the significant quantity for the kinetics of open complex formation (see Section 5). Hence sliding or hopping (if they occur) will increase the rate of open complex formation and initiation only if RP\({}_{\rm C}\) formation is irreversible. Nonpromoter binding of RNAP [122] can have either a competitive or facilitating effect on promoter binding, depending on DNA length and solution conditions.  
The initial specific closed complex RP\({}_{\rm C}\) (Figure 3) and/or other early specific promoter complexes have been characterized by real time OH and permanganate footprinting of the T7A1 promoter [25, 26] and by low temperature DNase, OH and permanganate footprinting of other promoters [58, 123, 124, 125, 126, 127]. Footprinting reveals that RP\({}_{\rm C}\) is closed and that RNAP is bound to the UP element, \(-\)35, spacer and \(-\)10 regions, protecting the upstream DNA from \(-\)55 to \(-\)5. Since no sites of enhanced DNase reactivity are observed in RP\({}_{\rm C}\)[58, 123, 124, 125, 126, 127] the downstream duplex is presumably unbent. At \(\lambda\)P\({}_{\rm R}\), only more advanced closed complexes than RP\({}_{\rm C}\) have been detected, indicating that RP\({}_{\rm C}\) must be significantly less stable than these extended-footprint closed complexes under the conditions studied.