Equilibrium and stopped-flow kinetic studies of interaction between T7 RNA polymerase and its promoters measured by protein and 2-aminopurine fluorescence changes.

The mechanism of bacteriophage T7 RNA polymerase binding to its promoter DNA was investigated using stopped-flow and equilibrium methods. To measure the kinetics of protein-DNA interactions in real time, changes in tryptophan fluorescence in the polymerase and 2-aminopurine (2-AP) fluorescence in the promoter DNA upon binary complex formation were used as probes. The protein fluorescence changes measured conformational changes in the polymerase whereas the fluorescence changes of 2-AP base, substituted in place of dA in the initiation region (−4 to +4), measured structural changes in the promoter DNA, such as DNA melting. The kinetic studies, carried out in the absence of the initiating nucleotide, are consistent with a two-step DNA binding mechanism, where the RNA polymerase forms an initial weak EDa complex rapidly with an equilibrium association constant K1. The EDa complex then undergoes a conformational change to EDb, wherein RNA polymerase is specifically and tightly bound to the promoter DNA. Both the polymerase and the promoter DNA may undergo structural changes during this isomerization step. The isomerization of EDa to EDb is a fast step relative to the rate of transcription initiation and its rate does not limit transcription initiation. To understand how T7 RNA polymerase modulates its transcriptional efficiency at various promoters at the level of DNA binding, comparative studies with two natural T7 promoters, Φ10 and Φ3.8, were conducted. The results indicate that kinetics, the bimolecular rate constant of DNA binding, kon (K1k2), and the dissociation rate constant, koff (k−2), and thermodynamics, the equilibrium constants of the two steps (K1 and k2/k−2) both play a role in modulating the transcriptional efficiency at the level of DNA binding. Thus, the 2-fold lower kon, the 4-fold higher koff, and the 2-5-fold weaker equilibrium interactions together make Φ3.8 a weaker promoter relative to Φ10.

tary in sequence to the template DNA (1). The phage enzymes are among the simplest RNA polymerases known, as no accessory proteins are necessary for specific initiation, elongation, or termination of transcription (2,3). The 17 promoters of bacteriophage T7 direct specific initiation of RNA synthesis that occurs in a rapid and processive manner (4,5). Due to their simplicity these enzymes serve as model systems to understand, in depth, the mechanisms of transcription initiation, elongation, or termination.
Initiation of transcription occurs by recognition and binding of the RNA polymerase to a promoter DNA sequence. This event is recognized as one of the important steps at which transcription and gene expression is regulated. The 17 bacteriophage T7 promoters share consensus sequence from Ϫ17 to ϩ6 position relative to the transcription start site at ϩ1 (6). The class III gene promoters of T7 are absolutely conserved in DNA sequence, whereas the class II gene promoters differ at a number of positions within the consensus sequence. The sequence of the promoter DNA is a primary factor that determines the strength of the promoter and the efficiency of initiation. However, the relationship between promoter DNA sequence and transcriptional efficiency is not well understood at the mechanistic level. In general, the detailed kinetics and thermodynamics of transcription are less well understood, in part, due to its complexity. The T7 promoters and the phage RNA polymerase, owing to their simplicity, should serve as a good starting model to understand the mechanism and regulation of transcription in greater detail.
The present study consists of the kinetic and thermodynamic investigations of the steps involved in promoter recognition and DNA binding. The interaction of the RNA polymerase with its promoter DNAs has not been examined previously using fast kinetic methods. Since DNA binding is a fast step, it is necessary to use rapid kinetic methods to directly observe intermediate binary species that accumulate transiently during initiation. The stopped-flow methods used in this study allow us to elucidate the mechanism of DNA binding and to determine the rate and equilibrium constants of steps leading to intermediate species. To examine DNA binding in real time we use the change in the intrinsic fluorescence of protein upon promoter binding as a signal. In addition, we have taken advantage of the fluorescent properties of 2-aminopurine (2-AP) 1 base, an analog of dA, which can be incorporated into the promoter DNAs and used as a probe to monitor promoter opening in real time. The present studies have been carried out in the absence of the NTP substrate. Comparative studies with two natural T7 promoters, ⌽10 and ⌽3.8, representing strong class III and weak class II promoters, respectively, provide insights into the mechanism by which T7 RNA polymerase regulates its transcriptional efficiency at the level of DNA binding.

EXPERIMENTAL PROCEDURES
Protein Purification-T7 RNA polymerase was purified from the Escherichia coli BL21/pAR1219 cell line (kindly provided by Alan Rosenberg and Bill Studier, Brookhaven National Laboratories) (2). The enzyme was Ͼ95% pure after three chromatography columns consisting of SP-Sephadex, CM-Sephadex, and DEAE-Sephacel purchased from Sigma (7). The polymerase was stored in 50% glycerol, and buffer containing 20 mM sodium phosphate (pH 7.7), 1 mM trisodium EDTA, 1 mM dithiothreitol, 100 mM NaCl at Ϫ80°C. The concentration of the polymerase was determined by absorbance measurement at 280 nm and from its molar extinction coefficient of 1.4 ϫ 10 5 M Ϫ1 cm Ϫ1 (8).
Synthesis of DNAs: Normal and 2-AP DNA-The DNA promoters were synthesized on a Millipore Nucleic Acid synthesis system 899. DMT-deoxynucleoside (benzoyl or isobutyryl) ␤-cyanoethylphosphoramidites were purchased from PerSeptive Biosystems. 2-Aminopurine CE phosphoramidite and Ac-dC-CE phosphoramidite were purchased from Glen Research Corp. Ac-dC-CE phosphoramidite was used for dC incorporation in 2-AP DNA. Coupling time of 15 min for 2-AP base incorporation and ultrafast cleavage and deprotection systems were used for the synthesis of 2-AP containing DNAs (deprotection was performed with a mixture of equal volumes of ammonium hydroxide and 40% methylamine aqueous solution, following the procedure provided by Glen Research). 2-AP base was incorporated at position Ϫ3, Ϫ1, and ϩ4 for ⌽10 and ⌽3.8 nontemplate strands, position Ϫ4 and Ϫ2 for ⌽10 template strand, and position Ϫ4 for the ⌽3.8 template strand (Fig. 1).
All synthetic promoters used in this study were purified on 16% polyacrylamide, 5 M urea gels. The DNA was visualized by UV shadowing, and electroeluted from the gel using an Elutrap apparatus (Schleicher & Schuell). The concentration of purified DNA was determined by absorbance measurement at 260 nm using the following extinction coefficients (M Ϫ1 cm Ϫ1 ) for the bases: dA, 15,200; dC, 7050; dG, 12,010; dT, 8400. The extinction coefficient of 2-AP, at 260 nm, equal to 1000 M Ϫ1 cm Ϫ1 was used in the calculation of 2-AP DNA concentration (9). The double-stranded (ds) DNAs were prepared by annealing the individual single-stranded DNA strands. The exact ratio of the two single-stranded DNA strands to prepare the dsDNAs was determined routinely from titration experiments performed on an 18% native polyacrylamide gel that resolves dsDNA from the singlestranded DNAs.
Fluorescence Titrations-The fluorimetric titration experiments were performed on a Perkin Elmer LS50B Luminescence Spectrometer. The emission spectra of 2-AP containing DNAs were obtained by excitation at 315 nm (excitation slit width ϭ 5 nm, and emission slit width ϭ 5 nm). Fluorimetric titration experiments were performed in the reaction buffer (50 mM Tris acetate, pH 7.5, 50 mM sodium acetate, 10 mM magnesium acetate, 5 mM dithiothreitol, 0.05% Tween 20) at 25°C. The fluorescence changes recorded in all these experiments are an average of 5 measurements which were taken after at least 1 min of incubation when the readings no longer changed. A constant amount of 2-AP dsDNA (0.05 M) was titrated against increasing concentration of T7 RNA polymerase. A control experiment was carried out in the presence of normal DNA (0.05 M) and increasing amounts of the polymerase, and the spectra were subtracted from the above to obtain fluorescence changes due to polymerase⅐2-AP DNA complex formation.
Stopped-flow Studies-The stopped-flow instrument from KinTek Corp. (State College, PA) was used to measure the DNA binding kinetics. Equal volumes of protein and DNA in buffer (50 mM Tris acetate, pH 7.5, 50 mM sodium acetate, 10 mM magnesium acetate, 5 mM dithiothreitol) from separate syringes were rapidly mixed in the stopped-flow instrument at 25°C. Changes in fluorescence emission of the protein were measured using a cut-on long pass filter Ͼ348 nm (Oriel Corp., catalog number 51260) after excitation at 290 nm (1-mm slits). 2-AP fluorescence emission was measured using a cut-on filter Ͼ360 nm (WG360, Hi-Tech Scientific, serial number 273129), after excitation at 315 nm (1-5 mm slit width). About 5-10 kinetic traces for 2-AP DNAs and 20 -30 for normal DNAs were routinely averaged for each experiment.
Data Analysis-The equilibrium binding and kinetic data were fit using SigmaPlot (Jandel Scientific) or KaleidaGraph (Abelbeck) softwares. Stopped-flow kinetic traces were fit using the KinTek stoppedflow kinetic program software to single or sum of exponential as in the equation, F ϭ ⌺ A n ϫ exp(-k obs,n t) ϩ C, where F is the fluorescence at time t, n is the number of exponential terms, A n and k obs,n are the amplitude and the observed rate constant of the n th term, respectively, and C is the fluorescence intensity at t ϭ 0. The error bars for k obs values shown in the Figs. 5 and 7 represent errors in the fit. The errors shown for the rate constants represents the mean of deviation of the reported rate constants from the values computed from the maximum and minimum k obs values.

RESULTS
Studies in the literature (10 -13), mainly using E. coli RNA polymerase, have shown that binding of the RNA polymerase to the promoter DNA is a multistep process, involving formation of several closed and open polymerase-DNA binary complexes. We studied the equilibrium and kinetic interactions between T7 RNA polymerase and T7 promoters with the goal of dissecting the steps involved in the process of promoter recognition during transcription initiation. The kinetics of DNA binding were measured using stopped-flow methods. The decrease in intrinsic protein fluorescence that results upon promoterpolymerase binary complex formation was used as the probe for kinetic measurements. To investigate the kinetics of promoter opening, 2-AP containing promoter DNAs were prepared. 2-AP is a fluorescent base analog of dA that base pairs with dT. The fluorescence of 2-AP is sensitive to local changes that result from melting of dsDNA (9,14,15). This is evident from the fluorescence spectra in Fig. 2, a and b, which shows the 2-4fold higher fluorescence of 2-AP in the single-stranded DNA form versus the dsDNA form. Both DNA binding and DNA melting during transcription initiation should be observable in real time by following the change in fluorescence of 2-AP DNA promoters.
T7 Promoter DNAs-The consensus sequence recognized by T7 RNA polymerase consists of bases in the region Ϫ17 to ϩ6 relative to the transcription start site at ϩ1 (16 -18). We have synthesized promoter DNAs, 40-base pairs in length, containing the natural ⌽10 and ⌽3.8 sequences from positions Ϫ21 to ϩ19 (Fig. 1). The sequence of ⌽10, a class III promoter, is absolutely conserved whereas the sequence of ⌽3.8, a class II promoter, differs at several positions (Ϫ2, Ϫ11, Ϫ12, and Ϫ13) from the consensus sequence. We compare here the equilibrium and kinetic interactions of these two promoters to better understand how transcriptional efficiency is regulated at the DNA binding steps during initiation.
Fluorescent promoter DNAs were chemically synthesized by incorporating 2-AP bases in place of dA bases in both the template and the nontemplate DNA strands in the region between Ϫ4 and ϩ4 (Fig. 1). We chose to incorporate the 2-AP bases in this region because the region Ϫ6 to ϩ2 has been shown (19,20) to be in the single-stranded form in the open binary complex. The fluorescence of 2-AP bases at those positions should be sensitive to changes in DNA structure, such as DNA melting that occurs during initiation. Changing the dA bases to 2-AP at those positions does not affect transcription initiation. The steady state and pre-steady state kinetics of 2-mer to 19-mer RNA product formation were the same with the 2-AP-modified versus the unmodified promoters (data not shown). We have also synthesized partially dsDNA promoters that contain single-stranded template region from Ϫ5 onward as mimics of open promoter DNAs (Fig. 1).
Equilibrium Binding of T7 RNA Polymerase to 2-AP-modified Promoter DNAs-Binding of T7 RNA polymerase to 2-AP modified promoter DNAs resulted in about 6 -7-fold enhancement in 2-AP-DNA fluorescence, as shown in Fig. 2, a and b. This increase in fluorescence is greater than the expected change from simply melting the duplex DNA. Therefore, at least a part of the increase in fluorescence appears to be due to the interaction of the DNA with the protein active site. The increase in 2-AP DNA fluorescence change upon binary com-plex formation was used to measure the equilibrium dissociation constant (K d ) of ⌽10 and ⌽3.8 promoters. The fluorimetric titrations were carried out at constant [DNA] and increasing [polymerase] at 25°C. The 2-AP DNA was excited at 315 nm (to minimize protein absorption) and emission was measured at 370 nm. The final equilibrium binding isotherms were obtained by subtracting the fluorescence of protein. The binding isotherms were fit to a hyperbola ( Fig. 3, a and b) to calculate the apparent K d values. The measured K d values for ⌽10 and ⌽3.8 were 0.015 (Ϯ0.002) and 0.035 (Ϯ0.009) M, respectively. The ⌽10 promoter DNA therefore binds to the polymerase more strongly than the ⌽3.8 promoter.
Stopped-flow Kinetics of RNA Polymerase Binding to Unmodified Promoter DNAs-The kinetic mechanism of RNA polymerase binding to DNA was investigated using the stoppedflow method. The binding of ⌽10 and ⌽3.8 promoter DNAs to the polymerase leads to quenching of protein tryptophan fluorescence. This intrinsic change in protein fluorescence was used to measure the kinetics of DNA binding, under conditions of excess polymerase over DNA as well as excess DNA over polymerase. Except for an extra kinetic phase under excess DNA conditions, the kinetics under the two conditions were comparable. Fig. 4 shows representative kinetic traces under excess [DNA] conditions, where 0.3 M ⌽10 DNA (Fig. 4a) or ⌽3.8 DNA (Fig. 4b) was mixed with 0.05 M polymerase. The kinetics fit best to two exponentials. To elucidate the mechanism of DNA binding and determine the bimolecular rate constant of DNA binding, the kinetics were measured as a function of increasing [DNA]. As shown in Fig. 5, a and b, the observed rate constant (k obs ) of the fast phase increased linearly with increasing [DNA]. If DNA binding occurred with a simple onestep mechanism: The slope of k obs versus [DNA] provided the bimolecular rate constant, k on , and the intercept provided the dissociation rate constant, k off (21). DNA binding is most likely a multistep process. Therefore, the derived k on and k off are macroscopic rate constants that describe the overall kinetics of DNA binding and dissociation and do not necessarily represent the intrinsic rate constants. The stopped-flow kinetic results show that ⌽10 dsDNA promoter binds to the polymerase with a k on of 72 Ϯ 7 M Ϫ1 s Ϫ1 (slope), and dissociates from the binary complex with a k off of 4.0 Ϯ 0.3 s Ϫ1 (intercept). The ⌽3.8 dsDNA promoter binds to the polymerase with about 2-fold slower k on (42 Ϯ 4 M Ϫ1 s Ϫ1 ) and also dissociates faster from the complex with a 4-fold higher k off (17.7 Ϯ 1.0 s Ϫ1 ). Control experiments with a dsDNA containing a non-promoter DNA sequence (Fig. 1), that is a DNA with random sequence, showed no measurable fluorescence changes confirming that the above rate constants measure specific interactions of the polymerase with the respective promoter sequences.
The presence of a second slow phase in the DNA binding kinetics (Fig. 4) suggested a second step in the DNA binding mechanism (21). Curiously, this slow phase was observed only when [DNA] was in excess of the polymerase. In addition, the observed rate constant of the second phase decreased with increasing [DNA] (Fig. 5, c and d). Both of these results suggest the presence of a conformational change before DNA binding, as shown in Reaction 2. The proposed conformational change is most likely a change in the polymerase, since biphasic kinetics were not observed when the polymerase concentration was in excess of the promoter DNA. REACTION 2 According to mechanism (Reaction 2), the RNA polymerase exists in two conformations, EЈ and E. The polymerase, E, is competent for DNA binding whereas polymerase, EЈ, needs to undergo a conformational change in order to bind DNA. k 1 and k Ϫ1 represent the forward and reverse rate constants of the conformational change, and K d is the dissociation constant of the binary complex ED. The rate constant of the second phase decreased with increasing [DNA] because of the following relationship between the observed rate constant and [DNA] (22).
At very low [DNA], the observed rate constant will be close to k 1 ϩ k Ϫ1 , whereas at very high [DNA], the observed rate will plateau at k 1 . Thus, Reaction 3 predicts that the observed rate constant will decrease from the sum of the rate constants (k 1 ϩ k Ϫ1 ) to k 1 with increasing [DNA]. This is clearly the case with the ⌽3.8 promoter as shown in Fig. 5d. In case of the ⌽10 promoter, the decrease is small (Fig. 5c). This is both because of the tighter K d of ⌽10 DNA relative to ⌽3.8, and since the kinetics were not measured at very low [DNA]. The nature of this slow conformational change in the polymerase required for DNA binding is not known. It may represent movement of one of the polymerase domains such as the thumb region that has been postulated to be flexible and involved in DNA binding (23). Judging from the relative amplitudes of the fluorescence changes in the kinetic experiments, we estimate that EЈ represents about 30% of the population of RNA polymerase. Thus, approximately 70% of the RNA polymerase is in a conformation that binds DNA with fast kinetics. The rest of the discussion in this paper is concerned with the kinetics of the fast form of the polymerase. To investigate the steps involved in DNA binding and to measure their rate constants, the stopped-flow kinetics of 2-AP DNA binding were measured at increasing [polymerase]. The kinetics fit best to a single exponential and as shown in Fig. 7, a and b, the observed rate constants increased linearly as a function of [polymerase], analogous to the dependence measured by protein fluorescence change. Both protein and DNA fluorescence changes therefore appear to measure essentially the same process. The k on and k off rate constants (Table I) (Table I), the K d value for the 2-AP modified ⌽3.8 DNA was about 2-fold higher relative to the ⌽10 promoter. The equilibrium K d values measured from the fluorimetric titrations are, however, lower than those derived from the kinetic rate constants. The different K d values from the two methods suggest the presence of an additional step after the bimolecular DNA binding step. This step must be very slow since it was not observed by stopped-flow kinetic measurements. Additional studies need to be carried out to understand the differences in the K d values by the two methods.  (Table I). Interestingly, the partially dsDNAs bind to the polymerase with much higher k on and dissociate with much lower k off values relative to the fully dsDNAs. For instance, the partially ds ⌽10 DNA binds with a 5-fold higher k on , and a 30 -200-fold lower k off relative to the fully dsDNA (Table I). Similarly, the partially ds ⌽3.8 DNAs bind with a 5-fold higher k on , but the k off values are 2-3-fold lower than those of the fully dsDNA. DISCUSSION We have investigated the equilibrium and kinetic interactions between T7 promoters and T7 RNA polymerase to dissect the steps in the mechanism of DNA binding during initiation of transcription. The polymerase-DNA binary complex formation was quantitated by following both the decrease in protein tryptophan fluorescence and the increase in 2-AP DNA fluorescence. Since the fluorescence of 2-AP dsDNA increases upon DNA melting, this change was used to probe the kinetics of promoter opening. The 2-AP base was introduced in place of dA bases in the region shown to be in the open form during initiation (19,20). Replacement of dA bases with 2-AP in this region did not affect transcription initiation, since the measured steady state and pre-steady state kinetics of 2-mer to 19-mer RNA formation with 2-AP-modified DNAs as templates were comparable to those with the unmodified DNAs.
We compare here the mechanism of polymerase binding to two natural T7 promoters: ⌽10, a strong class III promoter, and ⌽3.8, a weaker class II promoter that has base changes at positions Ϫ2, Ϫ11, Ϫ12, Ϫ13 from the consensus sequence. The base changes in class II promoters affect their efficiency of transcription, however, the regulatory mechanisms are unclear. There are several ways by which transcriptional efficiency can be regulated. A promoter may have weaker equilibrium (K d ) or unfavorable kinetic interactions with the polymerase, that is, low k on and high k off values. Thus, both kinetic and thermodynamic interactions can play a role in dictating the efficiency of transcription. Efficiency of transcription is also controlled by steps following initial DNA binding, such as open complex formation, binding of initiating nucleotides, phosphodiester bond formation, and processivity of RNA synthesis. The equilibrium interactions of ⌽10 and ⌽3.8 promoters with the polymerase were measured using fluorimetric titrations. The increase in fluorescence of 2-AP-modified promoters upon binding to the polymerase was used to determine the apparent K d values. The derived K d values indicate that T7 RNA polymerase does discriminate against ⌽3.8 promoter at the DNA binding step. ⌽3.8 promoter interaction with the polymerase was at least 2-fold weaker relative to the strong ⌽10 promoter. Investigation of the stopped-flow kinetics of DNA binding showed that the weaker interactions of the ⌽3.8 DNA were due to slower k on , the bimolecular rate constant of DNA binding, as well as faster k off , the dissociation rate con- stant. The K d values calculated from the ratio of k off /k on for the various ⌽3.8 promoters are also consistently weaker relative to the ⌽10 promoters (see Table I). The kinetics of protein-DNA interactions (the k on and k off values) must play a significant role in promoter discrimination in vivo. The slow k on and faster k off translates into unfavorable kinetic interactions that could decrease promoter utilization. The 2-fold lower k on and the 2-fold higher k off together make ⌽3.8 a weaker promoter relative to ⌽10. Exactly which base change in ⌽3.8 is responsible for the weaker binding cannot be determined from this study. Most likely candidates are bases at positions Ϫ11, Ϫ12, and Ϫ13 because base changes at these positions occur in T7 promoters at lower frequencies (6 -18%) than changes at, say, position Ϫ2 (30%) (6).
The initial steps of DNA binding, including closed and open binary complex formation, have been studied to a large extent with E. coli RNA polymerase (13). Techniques such as DNA footprinting and nitrocellulose membrane binding have been used to measure the kinetics of DNA binding. Similarly, sensitivity of open single-stranded DNA to KMnO 4 (24,25), and nitrocellulose filter binding (26) and polyacrylamide gel-retardation assay with heparin chase (27,28) have been used to probe open complex formation steps. All of these methods are manual and cannot measure transient complexes formed with rapid kinetics. The stopped-flow method, especially with promoter DNAs containing the fluorescent base 2-AP, is ideal for measuring the kinetics of DNA binding as well as the kinetics of promoter opening in real time. The fluorescence of 2-AP is sensitive to changes in the state of the DNA. Thus, stoppedflow kinetic studies with promoter DNAs containing 2-AP bases placed in the initiation region allow measurement of local conformational changes, such as DNA melting, that occur during initiation. Additionally, these experiments provide both kinetic and equilibrium information necessary to elucidate the detailed mechanism of DNA binding during transcription.
To dissect the various steps in the mechanism of promoter binding, the kinetics of DNA binding were measured by following both the changes in the fluorescence of protein and the 2-AP DNA. These experiments indicated that both protein and DNA fluorescence changes measured the same bimolecular process of DNA binding to the protein. No distinct kinetic phase due to promoter opening was observed with the fluorescent 2-AP DNAs. Stopped-flow study of both protein and DNA fluorescence changes provided the k on and k off rate constants that describe the overall rate of binary complex formation and dissociation. Comparison of the kinetic constants for different promoters shows that the strength of binary complex is determined by both the k on and the k off values (Table I). Partially dsDNA promoters bind to the polymerase with the highest affinity. The strong binding of partially dsDNAs is due to both a higher k on (5-10-fold) and a lower k off (2-200 fold) compared to the fully dsDNAs. Furthermore, it is also seen, that the ds ⌽10 promoter binds to the polymerase strongly, and with a higher k on (about 2-fold) and a lower k off (about 2-fold) relative to the weaker ds ⌽3.8 promoter. The lower k off values indicate that the binary complex is kinetically stable. Thus, the partially dsDNAs form the most kinetically stable binary complexes whereas the ⌽3.8 dsDNAs the least.
The lower than diffusion limited k on and the differences in k on values between various promoter DNAs suggest that DNA binding occurs by a two-step mechanism, The first step in the above mechanism represents the diffusioncontrolled binding of the DNA to the polymerase to form ED a , with an equilibrium association constant K 1 . The interactions of the DNA with polymerase in this complex are weak, and the free polymerase, DNA, and the ED a species are in rapid equi-  librium (that is, the rates of binding and dissociation are faster relative to k 2 and k Ϫ2 ). Therefore, although there are two steps in the DNA binding mechanism, due to fast formation of ED a , the stopped-flow kinetics showed only one phase. The second step leading to the formation of ED b is a conformational change, wherein the interactions between the polymerase and the DNA are more stable. If we compare the above mechanism to that proposed for DNA binding to E. coli RNA polymerase (13), the ED a complex would be analogous to one of the closed binary complexes, and the ED b species may be analogous to one of the open complexes. Since the stopped-flow kinetics of DNA binding measured by protein or DNA fluorescence changes were identical, the isomerization step may be global. In other words, both polymerase and DNA may change their conformation concomitantly during the isomerization step leading to formation of ED b . Studies with partially dsDNA promoters (both 2-AP and unmodified DNAs) provide clues as to the nature of this second step. Since the partially dsDNAs are already open, we did not expect the 2-AP fluorescence to change. However, the 2-AP fluorescence in the partially dsDNAs increased in an analogous manner as in the fully dsDNAs. These results can be explained in two ways. The 2-AP fluorescence increase may be due to a conformational change that occurs in both fully doublestranded and partially dsDNAs such as DNA twisting or DNA bending, distortions which could lead to promoter opening (29). Thus, DNA bending or twisting may represent the second step in mechanism (Reaction 3), and the resulting ED b complex in the fully dsDNA promoters may be an intermediate open binary complex. Alternatively, the increase in 2-AP fluorescence may simply be due to the change in the protein conformation which may result in changes in the local environment around the DNA.
According to the proposed mechanism (Reaction 3), the bimolecular rate constant, k on listed in Table I is equal to K 1 k 2 and the measured dissociation rate constant, k off is equal to k Ϫ2 . The lower-than-diffusion-limited k on values for the fully dsDNA promoters can result both from a weaker ED a complex or a slower conformational change (k 2 ). The ⌽3.8 promoter, which has a lower k on , therefore forms a weaker ED a complex or undergoes a slower conformational change, or both, relative to the ⌽10 promoter. Since the partially dsDNAs are already open, they do not have to go through a "closed" complex, and therefore the k on values of partially dsDNAs are higher and close to diffusion-limited. The above two-step mechanism of DNA binding predicts that the observed rate constants should saturate at k 2 ϩ k Ϫ2 at high DNA or polymerase concentrations. Since no saturation was observed in our measurements up to rate constant of 100 s Ϫ1 , the second step in the above mechanism must be fast (Ͼ100 s Ϫ1 ) for both the ⌽10 and ⌽3.8 promoters. Relative to the rates of transcription initiation, 2 ED b , the intermediate open binary complex, is formed with fast kinetics that cannot limit transcription initiation. This does not mean that regulation cannot occur at the DNA binding step. Although promoter opening is not rate-limiting, the equilibrium constants of DNA binding and isomerization steps can modulate the efficiency of transcription initiation. For instance, the faster k off (or k Ϫ2 ) of ⌽3.8 makes the isomerization of ED a to ED b to occur with an unfavorable equilibrium relative to the ⌽10 promoter. Thus, efficiency of transcription initiation is modulated kinetically by the macroscopic rate constants k on and k off , and thermodynamically by the equilibrium constants (K 1 and k 2 /k Ϫ2 ) of the two steps during DNA binding.