The +2 NTP Binding Drives Open Complex Formation in T7 RNA Polymerase*

Transcription initiation as catalyzed by T7 RNA polymerase consists primarily of promoter binding, strand separation, nucleotide binding, and synthesis of the first phosphodiester bond. The promoter strand separation process occurs at a very fast rate, but promoter opening is incomplete in the absence of the initiating NTPs. In this paper, we investigate how initiating NTPs affect the kinetics and thermodynamics of open complex formation. Transient state kinetic studies show that the open complex, EDo, is formed via an intermediate EDc, and the conversion of EDc toEDo occurs with an unfavorable equilibrium constant. In the presence of the initiating NTP that base-pairs with the template at position +2, the process of open complex formation is nearly complete. Our studies reveal that the nucleotide that drives open complex formation needs to be a triphosphate and to be correctly base-paired with the template. These results indicate that the melted template DNA in the open complex is positioned to bind the +2 NTP. The addition of +1 NTP alone does not stabilize the open complex; nor is it required for +2 NTP binding. However, there appears to be cooperativity in initiating NTP binding in that the binding of +2 NTP facilitates +1 NTP binding. The dissection of the initiation pathway provides insights into how open complex formation steps that are sensitive to the promoter sequence upstream from the initiation start site modulate the affinity of initiating NTPs and allow transcription initiation to be regulated by initiating NTP concentration.

The efficiency of transcription is regulated to produce the required amount of RNA in the cell, and this can occur in numerous ways. Transcriptional efficiency is intrinsically regulated by the promoter DNA sequence during initiation through complex protein-DNA interactions. In addition, several extrinsic factors such as accessory proteins or ligands that bind to the RNAP 1 -DNA complex regulate transcription by allosteric mechanisms. The efficiency of transcription is also regulated by the concentration of substrate NTPs when the cellular NTP concentration is close to the K d of NTPs. This is found in Escherichia coli RNAP-rRNA promoter complexes, such as the rrnB P1 promoters, that have relatively weak affinity for initiating NTP, and thus rRNA synthesis is controlled by the initiating NTP concentration that varies with the cellular growth rate (1). The bacteriophage T7 RNAP is similar in that it also has a relatively weak affinity for initiating NTPs; hence, transcription is regulated by the initiating NTP concentration (2)(3)(4). It is interesting that RNAP-promoter complexes with the same initiation start sequence but different promoter core sequences respond differently to initiating NTP concentrations, because they show different affinities for initiating NTPs (3,5). In these promoters, the template sequence at the initiation site is the same, and thus the interactions of the incoming NTP with the template and RNAP are expected to be the same; thus, it is not obvious how the core sequence regulates the affinity of initiating NTP.
Both rrn P1 and T7 promoters show a common feature, and that is an unfavorable equilibrium constant for closed to open complex formation in the absence of initiating NTP. The observed K d of the initiating NTP is dependent on the efficiency of steps preceding NTP binding, such as promoter binding and opening; hence, these steps can potentially modulate the K d of the initiating NTP. Kinetic studies of T7 RNAP have shown that the observed rate of promoter opening is fast (Ͼ100 s Ϫ1 ) in the absence of initiating NTP (6 -8). However, both kinetic and structural studies suggest that the equilibrium constant of the promoter opening step is unfavorable. Fluorescence studies indicate that open complex formation is incomplete even at RNAP and DNA concentrations much above the K d of the T7 RNAP-DNA complex (8). Similarly, much of the Ϫ4 to Ϫ1 TATA region of the T7 dsDNA promoter that melts in the open complex cannot be modified by KMnO 4 , unless initiating nucleotides are present (9 -11).
Incomplete conversion of closed to open complex is also observed in the rrn P1 promoters of E. coli RNAP. A closed complex between E. coli RNAP with rrn P1 promoter is formed readily, but it is not stoichiometrically converted to the open complex in the absence of initiating nucleotides (1,12,13). The presence of ATP and CTP, the initiating nucleotides, is required to both make the complex heparin-resistant and open the Ϫ10 dsDNA region (1,12,13). The instability of the open complex may be the reason for this weaker K m of the initiating NTP in rrnB P1 as well as T7 promoters (1,5).
This study was undertaken to investigate the effect of initiating NTPs on the promoter opening steps, which in turn provides information on how open complex formation steps play a role in regulating initiating NTP binding. We use transient state kinetic methods to dissect the pathway of initiation and to identify the steps that are affected by the initiating NTP. The steps of DNA binding and promoter opening were monitored in real time using 2-AP-modified promoter DNAs. Such methods have been used previously to probe the promoter opening steps in T7 RNAP (2, 6 -8) and in E. coli RNAP (14). The kinetic data were globally fit to derive the transcription initiation pathway including the steps of promoter strand separation and initiating NTP binding. The results indicate that the promoter strand separation and initiating NTP binding steps are linked. We find that the binding of ϩ2 NTP drives open complex formation, which in turn makes the ϩ1 position available for ϩ1 NTP binding, resulting in cooperative ϩ1 and ϩ2 NTP binding. The mechanism derived from these studies provides a better understanding of the transcription initiation pathway and provides insights into how open complex formation steps can regulate the affinity of the initiating nucleotides.

EXPERIMENTAL PROCEDURES
Synthetic DNA and Other Materials-The oligodeoxynucleotides (unmodified and 2-AP-modified) were custom-synthesized by Integrated DNA Technologies (Coralville, IA). The oligodeoxynucleotides were purified on a 16% polyacrylamide gel containing 3 M urea. The ssDNA of desired length was excised and electroeluted, and the ssDNA was ethanol-precipitated, resuspended in water, and stored at Ϫ20°C. The purity of ssDNA was Ͼ95%, and its concentration was determined from absorption and calculated molar extinction coefficients at 260 nm for each DNA. Complementary ssDNAs were titrated against each other to confirm both duplex formation and the absence of free ssDNA as reported previously (15). The 3Ј-dGTP was purchased from TriLink Biotechnologies (San Diego, CA).
Protein-T7 RNAP was overexpressed in E. coli strain BL21 (16). The enzyme was purified as previously described (2,4,7) with the exception that the CM-Sephadex separation step was eliminated. The purified enzyme was checked for the lack of DNA exonuclease activity and was stored at -80°C in 20 mM sodium phosphate, pH 7.7, 1 mM trisodium EDTA, 1 mM dithiothreitol, 100 mM sodium chloride, and 50% (v/v) glycerol. The enzyme stock was diluted for each experiment, resulting in final glycerol concentrations ranging from 0.02 to 1%. The enzyme concentration was calculated from its absorbance at 280 nm and molar extinction coefficient of 1.4 ϫ 10 5 M Ϫ1 cm Ϫ1 (17). All of the experiments were carried out at 25°C in buffer A (50 mM Tris acetate, pH 7.5, 50 mM sodium acetate, 10 mM magnesium acetate, 5 mM dithiothreitol), unless stated otherwise.
Equilibrium Fluorescence Measurements-Experiments measuring the fraction of open complex formation were performed as follows. Using a 200-l quartz cuvette, the fluorescence of T7 RNAP (4 M) mixed with 1 M dsDNA or p-dsDNA promoter containing a single 2-AP, either at t(Ϫ4) or t(Ϫ2), was measured first and then again upon the addition of 500 M nucleotide. The sample was excited with 315-nm light (2-nm bandwidth), and the resulting fluorescence intensity at 370 nm (2 nm bandwidth) was measured on a FluoroMax-2 spectrofluorometer (Jobin Yvon-Spex Instruments S.A., Inc.) using the DataMax software program. After volume correction, the fluorescence of free T7 RNAP was corrected by carrying out a control experiment with nonfluorescent promoter DNA. The corrected fluorescence was F c (f) Ϫ F c (nf), where F c (f) and F c (nf) are the fluorescence intensities of samples containing 2-AP-modified promoter and nonfluorescent (unmodified) promoter DNA, respectively. Under these conditions, the RNAP fluorescence contributes 28% to the total signal. The signal produced from the 2-AP is therefore easily detected over this background.
The equilibrium RNAP titration binding experiment was carried out at 25°C in a 3-ml quartz cuvette. The titration was performed by adding small aliquots of T7 RNAP to a (GGG)40-bp dsDNA t(Ϫ4) (0.1 M) (Fig. 1) in the presence of 3Ј-dGTP (500 M). The sample was excited with 315-nm light (3-nm bandwidth), and the resulting fluorescence intensity at 370 nm (3-nm bandwidth) was measured. The measured fluorescence intensity value was corrected for inner filter using Equation 1, where F i,c represents the corrected fluorescence intensity, F i,obs is the observed fluorescence intensity, Abs i,ex is the absorbance of the solution at point i in the titration at 315 nm, and Abs i,em is the absorbance of the same solution at 370 nm. The concentrations of total RNAP and DNA at each point in the titration were determined from Equations 2 and 3, where The corrected fluorescence was plotted as a function of total T7 RNAP concentration, and the data were simultaneously fit to Equation 4 and the quadratic equation (Equation 5) to obtain the RNAP K d value.
where C is a constant, f D , f E , and f ED are the fluorescence coefficients for 2-AP DNA (D), T7 RNAP (E), and T7 RNAP-DNA complex (ED), respectively. The ED is defined by the quadratic Equation 5.
Stopped-flow Kinetics-The stopped-flow experiments were carried out using a SF-2001 instrument spectrophotometer equipped with a photomultiplier detection system from KinTek Corp. (Austin, TX). T7 RNAP (in buffer A) (with or without GTP or 3Ј-dGTP) was placed in one syringe, and the t(Ϫ4) 2-AP-containing (GGG)40-bp dsDNA promoter in buffer A was placed in the second syringe. At 25°C, the two solutions (40 l from each syringe) were rapidly mixed (flow rate of 6.0 ml s Ϫ1 ), and the 2-AP was excited by light with a wavelength of 315 nm. The progress of the reaction was monitored by measuring the intensity of the fluorescence emission using a cut-on filter Ͼ360 nm (WG360; Hi-Tech Scientific, serial no. 273129). Multiple traces (3-10 traces) were averaged to optimize the signal. The KinTek stopped-flow kinetic software was used to fit the stopped-flow kinetic traces to Equation 6 describing single or multiple exponential changes, where F is the fluorescence intensity 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 nth term, respectively; and C is the fluorescence intensity at t ϭ 0.
The obtained rate constants were plotted as a function of T7 RNAP concentration, and the corresponding plots were fit by nonlinear regression analysis to a hyperbolic equation (18), using SigmaPlot (Jandel Scientific).
where k max is the maximum rate of promoter opening, K1 ⁄2 is the concentration of E (T7 RNAP) where the rate is k max /2, and C is the y intercept.
The decrease in the observed rate (k obs ) as a function of nucleotide concentration was fit to a decreasing hyperbola, Equation 8 (19).
where k 3 Ј and k 4 Ј are approximately equal to rate constants k 3 and k 4 in the reaction shown in Table I, and K dGTP Ј is approximately equal to the intrinsic K d of GTP or 3Ј-dGTP. The K d of ϩ1 GTP was measured by preincubating T7 RNAP with (GAC)40-bp t(Ϫ2) dsDNA and ATP in one syringe and mixing this solution with increasing concentrations of GTP from a second syringe in a stopped flow and measuring the decrease in 2-AP fluorescence over time. The observed rate was plotted as a function of GTP concentration and was fit to a hyperbola. Equation 7, where k max represents a conformational change upon GTP binding, K1 ⁄2 is the K d of GTP in the presence of 200 M ATP, and C is the y intercept.
Global Fitting of the Kinetic Data-The stopped-flow kinetic data (a total of 29 time courses) from three sets of experiments (Figs. 4, a and c, and 5a) were globally fit by the nonlinear least-squares method using the software MATLAB from The MathWorks, Inc. (Natick, MA). The overall equilibrium constant of DNA binding (K d,overall ) in the presence of 500 M 3Ј-dGTP (18 nM) was used as a constraint in the fitting process. Differential equations were written for each of the kinetic species in the mechanism (Table I) An assumption was made that the fluorescence of ED c complex was the same as free 2-AP-labeled dsDNA. The differential equations (ODE) were solved using the MATLAB built-in ODE solver ode15s. Nonlinear least squares global fitting routine was carried out, using randomly chosen starting parameters, at least 33 times, to ensure that the solution represents the global minimum. The fitting converged to one set of parameters that provided the best global fit as judged by the sum of squared residuals. The correlation matrix for the fitted parameters (Table I) was calculated from the Jacobian at the fitting solution. The 95% confidence intervals for each parameter were calculated by 257 rounds of the Monte Carlo method (20). Each of the rounds involved the generation of a new set of pseudoexperimental data by adding noise normalized by weights to the data predicted by the model. Each set of pseudoexperimental data was fit as described above to produce a new set of optimal parameters. The confidence intervals were obtained by analysis of multiple sets of parameters. The use of MATLAB for analysis of enzyme kinetics data is discussed in Ref. 21. The MATLAB code is available from S. S. P.

Effect of the Initiating Nucleotides on Promoter Melting-
Several studies, including crystal structural studies of the T7 RNAP-DNA complex, indicate that the promoter region from Ϫ4 to Ϫ1 is melted during preinitiation (open complex formation) (22)(23)(24). The process of promoter melting can be studied at equilibrium or followed in real time by monitoring the fluorescence of a 2-AP base incorporated in the Ϫ4 to Ϫ1 TATA region of T7 promoters (6 -8). When the Ϫ4 to Ϫ1 region melts, the adenines both unpair and unstack from the double helix, and since 2-AP fluorescence is sensitive to base-stacking interactions, the fluorescence of 2-AP increases as the promoter melts. The fluorescence of 2-AP incorporated in dsDNA or p-dsDNA increases relative to free DNA when the DNAs are bound to T7 RNAP (8). As shown in Fig. 2a, the increase in fluorescence of 2-AP in a T7 RNAP-dsDNA complex is 25-27% of the fluorescence of the RNAP-p-dsDNA complex, irrespective of the position of the 2-AP in the TATA box. The less than 100% increase in fluorescence of 2-AP in the T7 RNAP-(GGG)40-bp dsDNA promoter complex relative to the p-dsDNA complex is not due to free 2-AP DNA or T7 RNAP, because the concentrations of reacting species are 8.5 times the DNA K d value of the (GGG)40-bp dsDNA (470 nM) (15,25). We propose that the smaller fluorescence increase of the dsDNA complex is due to an incomplete conversion of the closed complex ED c to the open complex, ED o , in the (GGG)40-bp promoter. We explored the possibility that the partial opening may be due to nonspecifically bound T7 RNAP at the noncoding region of the dsDNA. We used a t(Ϫ4) (GGG)26-bp dsDNA promoter, which contains only 5 base pairs of coding region, and observed the same results as with the (GGG)40-bp promoter (data not shown). We have also measured the binding of T7 RNAP to a predefined random sequence 20-mer DNA and found the K d to be Ͼ100 M. 2 When the initiating nucleotide GTP was added to the complex of (GGG)40-bp dsDNA and T7 RNAP, a further increase in fluorescence was observed. In the presence of GTP, the fluorescence of (GGG)40-bp dsDNA reached nearly the same level as the p-dsDNA in complex. We found that the fluorescence of p-dsDNA, which is an analog of open complex, did not increase upon the addition of GTP but in fact decreased, which we believe is due to G-ladder synthesis as shown below. We propose that the fluorescence increase upon the addition of GTP is mostly due to the shift in the population of closed complex to the open complex. Thus, GTP binding (or phosphodiester bond formation between two GTPs) stabilizes the initiation complex and drives the conversion of ED c to ED o . We wished to address several questions as follows. Is it the ϩ1 GTP, or the ϩ2 GTP binding, or both, that drive the opening of promoter DNA? Is this effect specific to the initiating NTP? Is RNA synthesis required for stabilization of the open complex?
To investigate whether the above phenomenon was specific to the initiating nucleotide, GTP, other nucleotides were examined. The addition of GMP had no effect on the fluorescence of (GGG)40-bp dsDNA in complex with T7 RNAP (Fig. 2a). Note that GMP can initiate RNA synthesis when added with GTP (26), but it is not known whether GMP can bind to T7 RNAP-DNA complex in the absence of ϩ2 NTP. The absence of an effect with GMP indicates that either GMP binding does not drive open complex formation or GMP alone binds poorly. Thus, the triphosphate moiety in GTP is important for binding and stabilizing the open complex. Similarly, ATP had no effect on the fluorescence of (GGG)40-bp dsDNA in complex with T7 RNAP, indicating that correct base-pairing interactions are necessary.
To determine whether RNA synthesis is required for stabi-2 R. Bandwar and S. S. Patel, unpublished data. lizing the open complex, we used the GTP analog, 3Ј-dGTP, that cannot be elongated to pppGpG because the analog lacks the 3Ј-OH group. When 3Ј-dGTP was added to dsDNA in complex with T7 RNAP, the fluorescence of 2-AP increased as observed with GTP and reached about 75% of the fluorescence of p-dsDNA in complex with T7 RNAP. The fluorescence of p-dsDNA, on the other hand, did not change upon the addition of 3Ј-dGTP. These results indicate that pppGpG synthesis is not required and simply binding of 3Ј-dGTP or GTP is sufficient to stabilize a fully open complex. Interestingly, GpG that can bind to the ϩ1/ϩ2-position opposite the template showed no effect. This again indicates that the triphosphate moiety of GTP is important for interactions and for driving open complex formation. Similar increases in the fluorescence of 2-AP at other positions in the TATA box, including nt(Ϫ1), nt(Ϫ3), and t(Ϫ2) upon the addition of 3Ј-dGTP were observed (the data for t(Ϫ2) is shown in Fig. 2a).
Most polymerases use two metal ion catalysis for nucleic acid synthesis, and two Mg(II) ions are postulated to be involved in RNA synthesis (27). It has been proposed that one of these Mg(II) ions interacts with the ␤,␥-phosphate groups of ϩ2 NTP and the other with the 3Ј-OH group of ϩ1 NTP to activate the -OH group for nucleophilic attack on the ␣-phosphate of ϩ2 NTP for phosphodiester bond formation. The Mg(II) concentration in all of the experiments described above was 10 mM; we therefore examined Mg(II) concentrations ranging from 0 to 30 mM (Fig. 2b). In the absence of Mg(II), the addition of GTP did not increase the fluorescence of (GGG)40-bp in complex with T7 RNAP, but in fact the fluorescence decreased. The reason for the decrease is not clear. As little as 1 mM Mg(II) added with GTP was, however, sufficient for maximal increase in fluorescence of (GGG)40-bp in complex. These results indicate that it is the MgGTP complex that is necessary for binding and/or stabilizing the ED o complex. In the absence of GTP, increasing concentrations of Mg 2ϩ caused a decrease in the fluorescence of (GGG)40-bp in complex with T7 RNAP perhaps due to inhibition of open complex formation as observed in E. coli RNAP (28).
The Kinetics of Promoter DNA Binding in the Presence of Initiating GTP-To investigate the effect of initiating NTP on the steps of DNA binding and opening, we measured the kinetics of open complex formation in the absence and in the presence of 3Ј-dGTP. The kinetics of promoter opening were measured by following the time-dependent increase in fluorescence of (GGG)40-bp dsDNA modified with 2-AP at t(Ϫ4) using a stopped-flow instrument (Fig. 3a). Representative kinetic traces are shown in Fig. 3b, with and without 3Ј-dGTP. A single exponential increase in 2-AP DNA fluorescence was observed with and without nucleotide. The same kinetics were observed irrespective of whether 3Ј-dGTP was preincubated with T7 RNAP or with the DNA. When we compare the kinetics of promoter opening with and without 3Ј-dGTP (Fig. 3b), it is clear that both the amplitude of the fluorescence increase and the observed rate of promoter opening are affected. The data show that the initial increase in fluorescence with time is similar with or without 3Ј-dGTP, but equilibrium is reached much faster in the reaction without 3Ј-dGTP as compared with the reaction with 3Ј-dGTP. Thus, the apparent rate of promoter opening is faster in the reaction without 3Ј-dGTP. The same results were obtained with GTP, but nucleotides such as ATP or GMP showed no effect on the DNA binding kinetics (data not shown).
To dissect the elementary steps of DNA binding and promoter opening, the stopped-flow kinetics (see Fig. 3a) were measured both in the absence (Fig. 4a) and in the presence of 3Ј-dGTP (Fig. 4c) at various concentrations of T7 RNAP. The kinetic traces were computer-fit to equation 6, and the observed exponential rate was plotted against [T7 RNAP] as shown in Fig. 4e. The observed rate increases in a hyperbolic manner with increasing [T7 RNAP] with or without 3Ј-dGTP, indicating that DNA binding and promoter opening occurs by a minimal two-step mechanism outlined below.
where E represents T7 RNAP, and D is the dsDNA promoter that forms an initial complex that we propose is the closed complex ED c (with intrinsic rate constants, k 1 and k 2 ). The closed complex undergoes a conformational change to form the open complex ED o (with intrinsic rate constants, k 3 and k 4 ). If we assume that the formation of ED c is a rapid equilibrium step, then the rate constants of the hyperbolic fit (Equation 7) can be interpreted (18). With a rapid equilibrium assumption, the maximum observed rate of promoter opening in the absence of 3Ј-dGTP, k max ϭ k 3 ϩ k 4 , is 180 s Ϫ1 ; the concentration of T7 RNAP required to reach the half-maximal rate, K1 ⁄2 (equal to k 2 /k 1 ), is 1 M; and C is k 4 , which the fit indicated was close to 0. In the presence of 500 M 3Ј-dGTP, the k max is about 6-fold slower (30 s Ϫ1 ) with no change in the T7 RNAP K1 ⁄2 (1 M). If ED c formation is not a rapid equilibrium step, then the meaning of k max and K1 ⁄2 is complicated, because the observed rate at any given concentration of E and D is dependent on all four intrinsic rate constants (18). In this case, the only way to extract the intrinsic rate constants is to globally fit the kinetics of DNA binding to a model. Global fitting was performed (described in detail below), and the solid lines going through the kinetic data in Fig. 4, a and c (residuals shown in Fig. 4, b and  d), are fits to Reaction 2 (see below) with intrinsic constants listed in Table I.  Fig. 5a. We found that the observed exponential rate decreased with increasing [3Ј-dGTP] or [GTP] (Fig. 5c), and the corresponding fluorescence amplitude increased (Fig. 5d).

The Observed Rate of Open Complex Formation Depends on GTP Concentration-To
The decrease in the observed rates with increasing GTP or 3Ј-dGTP concentration is consistent with the mechanism shown in Reaction 2. In this mechanism, the DNA binding steps precede the GTP binding step. If ED c formation is a fast step relative to ED o formation and GTP binding is a rapid equilibrium step, the rate dependences can be fit to Equation 8 (19) to obtain approximate values of GTP or 3Ј-dGTP K d (26 M for GTP and 111 M for 3Ј-dGTP). The observed K d of GTP is lower than 3Ј-dGTP K d most likely because the ED o G intermediate reacts to give additional species resulting from RNA synthesis, and the observed K d of GTP is a function of the equilibrium constant of all of the subsequent species. In addition, it is also likely that the K d value of 3Ј-dGTP is higher because it lacks the 3Ј-OH group. The [GTP] or [3Ј-dGTP] dependence also provided estimates of the intrinsic rate constant k 3 or the promoter opening rate (between 16 and 19 s Ϫ1 ) and a lower estimate of k 4 or the promoter closing rate (between 70 and 80 s Ϫ1 ). The derived values indicate that the rate of promoter closing is at least ϳ5 times faster than the rate of promoter opening. Thus, the equilibrium constant between closed and open forms is Ͻ1, in agreement with the conclusions from the fluorescence equilibrium binding studies shown in Figs. 2 and 7.   )), where DNA binding K d,overall ϭ 0.018 Ϯ 0.002 M at [3Ј-dGTP] ϭ 500 M measured directly using fluorescent equilibrium titrations (Fig. 6). The fluorescence amplitudes obtained from fitting increased as a function of [3Ј-dGTP] and were fit to a hyperbola with an observed 3Ј-dGTP K d of 588 M. This K d of 3Ј-dGTP is about 5 times weaker than the K d obtained from the rate dependence in Fig. 5c. If 3Ј-dGTP binds to the ED o species, which due to the unfavorable equilibrium constant of the ED c to ED o step, is present in substoichiometric amounts, then the observed K d of 3Ј-dGTP ϭ K d,GTP (1 ϩ 1/K 2 ), where K d,GTP is the intrinsic K d of 3Ј-dGTP estimated to be 110 M from the rate dependence, and K 2 is the equilibrium constant of ED c to ED o conversion estimated to be 0.2 (16 s Ϫ1 /80 s Ϫ1 ). Thus, the observed K d,3Ј-dGTP ϭ 110 (1 ϩ 1/0.2) ϭ 660 M, which is close to the experimentally measured K d of 588 M from amplitude dependence. Thus, the kinetics of DNA binding in the presence of initiating GTP are consistent with the mechanism shown in Reaction 2. Note that the above treatment provides only estimates of intrinsic rate constants. To obtain accurate values of the intrinsic rate constants, the data were globally fit to Reaction 2 by numerical methods, as described below.
Global Fitting of the Kinetic Data-The goal of globally fitting the data is to test the model and derive a set of intrinsic parameters that satisfactorily explains all of the data. Previous work (8) examining T7 RNAP-promoter binding provided evi-dence for an intermediate before open complex formation and suggested that the closed to open complex formation step was unfavorable. In that work, it was assumed that the formation of the intermediate, the closed complex, occurred by a rapid equilibrium step. In order to account for these observations, promoter opening was proposed to occur via a three-step mechanism whereby the T7 RNAP and promoter DNA first formed a closed complex, which formed two open complex species sequentially. The RNAP-promoter binding data were globally fit to this three-step mechanism and yielded an intrinsic equilibrium constant of 0.13 and overall equilibrium constant of 0.8 M for the promoter opening step.
The current studies of promoter opening in the presence of initiating nucleotide provide additional details in the process of promoter opening, enabling the refinement of the previous model. Here three sets of kinetic data (Figs. 4, a and c, and 5a), representing 29 time courses, including the data that were fit previously (8), were globally fit to the solution of the differential equations describing Reaction 2. This is a minimal mechanism that satisfactorily describes the given experimental data sets. In contrast to the previous fittings, promoter binding was not assumed to be a rapid equilibrium. The fitting was constrained using the observed K d of the RNAP-(GGG)40-bp dsDNA complex formed in the presence of 3Ј-dGTP (18 Ϯ 2 nM) obtained from fluorescence equilibrium titration (Fig. 6). Global fitting of the kinetic data was performed using MATLAB software to obtain a consistent set of intrinsic rate and equilibrium constants. The set of intrinsic rate constants that fit the described data sets is shown in Table I, and simulated lines that describe the data are shown as solid lines in Figs.  4, a and c, and 5a with the corresponding residuals in Figs. 4,  b and d, and 5b. These parameters are considered to be more accurately determined than those previously reported, since the model in Reaction 2 was subject to more rigorous global fitting constraints.
Several interesting features are revealed from the intrinsic parameters obtained by global fitting. The derived rate constants reveal that T7 RNAP binds the dsDNA promoter to form a closed complex ED c with a bimolecular rate constant of 255 M Ϫ1 s Ϫ1 , which is close to diffusion-limited. The ED c dissociates into free RNAP and DNA at a relatively slow rate of 9.4 s Ϫ1 . The ED c isomerizes to ED o with a rate constant of 15.8 s Ϫ1 . The ED o species is not stable and reverses back to ED c with a faster rate constant close to 125 s Ϫ1 . Thus, ED c to ED o conver-  Table I) sion occurs with an unfavorable equilibrium constant, K 2 of 0.13 Ϯ 0.01 (k 3 /k 4 ϭ 15.8 s Ϫ1 /125 s Ϫ1 ), consistent with the mechanism derived from studies in the absence of GTP (8). The correlation matrix in Table I reveals that except for one, all of the parameters have low dependences on one another. Only the value of k 3 is highly dependent on k 4 , which indicates that additional constraints are necessary to accurately determine the value of k 3 . The mechanism also indicates that the initiating NTP binds to ED o with a K d of 69 M, but the observed GTP K d is weaker due to the unfavorable equilibrium constant of the promoter opening step. Previous studies (29) have shown that the cumulative K d of ϩ1 and ϩ2 GTP is around 400 M, and the K d of ϩ2 GTP is around 100 M. Since the intrinsic K d of 3Ј-dGTP (69 M) derived from global fit is close to the estimated K d of ϩ2 GTP, it suggests that the open complex formation may be driven by the binding of GTP that base-pairs with the template at the ϩ2-position. Confirmation of this hypothesis was obtained using a modified promoter with the initiating sequence, GAC (see below).
The Binding of ϩ2 NTP Drives Open Complex Formation-The consensus promoter used in the above studies starts with the sequence ϩ1 GGG, where both ϩ1 and ϩ2 template positions base-pair with GTP; hence, we cannot determine using the (GGG)40-bp promoter which GTP binding step, the ϩ1 or ϩ2, drives open complex formation. We made a DNA starting with the coding sequence ϩ1 GAC (Fig. 1) to investigate whether ϩ1, ϩ2, or both initiating NTPs play a role in stabilizing the open complex. In the GAC promoter, the ϩ1-position base-pairs with G, the ϩ2 base-pairs with A, and ϩ3 base-pairs with C; thus, we can study the effects of GTP, ATP, or CTP binding on open complex formation.
Experiments similar to those in Fig. 2 were carried out with the GAC promoters. The fluorescence of 2-AP at t(Ϫ4) in both dsDNA and p-dsDNA was measured in an equilibrium experiment under various conditions (Fig. 7). Similar to the GGG promoter, the fluorescence of T7 RNAP-(GAC)40-bp dsDNA complex in the absence of initiating NTPs is about 30% of the fluorescence of (GAC)p-dsDNA complex. Interestingly, when GTP or 3Ј-dGTP or GMP that base-pairs with the ϩ1-position was added to the (GAC)40-bp complex, no change in fluorescence was observed. On the other hand, when ATP that basepairs with the ϩ2-position was added, the fluorescence of dsDNA complex increased and reached the same level as that of the p-dsDNA complex. The addition of CTP alone that basepairs with ϩ3 had no effect (data not shown). These results indicate that the NTP that base-pairs with the template at the ϩ2-position drives open complex formation. When ATP was  Table I using the relationship k ϭ kT/h exp(Ϫ⌬G ‡ /RT), where k is the first order rate constant, k is the Boltzmann constant, h is the Plank constant, T is absolute temperature, ⌬G ‡ is the free energy of activation, and R is the gas constant. At 25°C, kT/h is 6.212 ϫ 10 12 s Ϫ1 . The free energies of the intermediates were calculated relative to free T7 RNAP and DNA for various concentrations of DNA and 3Ј-dGTP (1 M, dotted and dashed line; 1 mM, dashed line; standard state 1 M, solid line). The ground state of the GTP-bound species were calculated using the equation ⌬G ϭ ⌬G 0 ϩ RT ln(products/substrates), assuming that ϩ1 GTP binds with a K d value of 422 M. The activation energies shown for these steps are arbitrary. The schematic diagram shows the hypothetical structures of the intermediate species in the pathway of initiation. added with GTP, conditions under which phosphodiester bond formation occurs, no additional increase of fluorescence over the level with ATP alone was observed. These results indicate that ATP binding is sufficient and that RNA synthesis is not necessary for ED c to ED o conversion. In addition, the t(Ϫ4) base unstacking reaction is complete in the absence of RNA synthesis. These results are somewhat different from the reported KMnO 4 modification experiments (10,30), where the reactivity of Ϫ3 and Ϫ1 Ts in the template strand was found to increase significantly only when RNA synthesis occurred. A possible explanation is that the reactivity of KMnO 4 is influenced by the accessibility of MnO 4 Ϫ to the DNA bound to RNAP (31), and Ϫ3 and Ϫ1 Ts become reactive to KMnO 4 only when a 4-or 5-mer RNA is made.
The  (Table I). We also attempted to directly measure the K d of ϩ1 GTP using the (GAC)40-bp promoter. In the absence of ATP, no detectable fluorescence change was observed even at high millimolar concentrations of GTP. However, when a solution of T7 RNAP, (GAC)40-bp dsDNA, and ATP (200 M) was mixed with GTP (see scheme in Fig. 8), a small decrease in fluorescence was observed. Both the rate and amplitude increased with increasing [GTP] as shown in Fig. 8. The rate dependence provided a GTP K d of 422 Ϯ 183 M, which is an estimate of the GTP K d in the presence of 200 M ATP. Thus, the K d of ϩ1 NTP is 10 times weaker than the K d of ϩ2 NTP.
Pathway of Transcription Initiation and Initiating NTP Binding-The kinetic and equilibrium binding studies described above provide a detailed pathway of initiation in T7 RNAP. The kinetics of DNA binding in the presence of initiating NTP provide direct evidence for the unfavorable equilibrium constant of the promoter opening step. It is clear from the free energy diagram (Fig. 9) shown at 1 M, 1 mM, and 1 M DNA and initiating NTP concentrations that the binding energy of the initiating nucleotide is required to stabilize the preinitiation open complex in T7 RNAP. Our results show that phosphodiester bond formation is not necessary and that simply high concentrations of initiating nucleotide (ϾK d of ϩ2 NTP) provides sufficient energy to drive the ED c to ED o conversion. The results reported here also show that the initiating NTP that base-pairs with the template at the ϩ2position is responsible for stabilizing the open complex. These results indicate that the template DNA in the preinitiation complex is positioned in the active site to bind the ϩ2 NTP and that the ϩ1 NTP binding step is not required for ϩ2 NTP binding.
It has been postulated that the stacking interactions of the Ϫ1 T in the template with Trp 422 and the ϩ1 base play a role in positioning the melted template strand within the T7 RNAP active site for correct initiation at the ϩ1-position (24,32,33). It also appears that the interactions of T7 RNAP with the upstream promoter binding region are important in the correct positioning of the template strand (29). The binding of the incoming NTP is directed both by the positioning of the Ϫ1 base and possible interactions with H 784 (34). The studies reported in this paper indicate that ϩ2 NTP binds before ϩ1 NTP and that ϩ2 NTP binding plays a role in start site selection by directing the binding of ϩ1 NTP at the T7 RNAP active site. The affinity of ϩ2 NTP is about 10 times higher than that of the ϩ1 NTP, most likely because the ϩ2 NTP and the Mg(II) ion bound to the ␤-␥ phosphate of ϩ2 NTP interacts extensively with the amino acids at the active site of the RNAP-DNA complex. The tighter interactions of ϩ2 Mg-NTP complex can therefore lock the template DNA in place to facilitate ϩ1 NTP binding.
How Does the Promoter Opening Step Modulate the K d of the Initiating NTP?-Although the intrinsic K d of the ϩ2 NTP (in this case 3Ј-dGTP) is 50 M, the observed K d is close to 10 times weaker. This is because the initiating NTP binds to the ED o complex, which is present in substoichiometric level. The observed K d of the initiating NTP is a function of both its intrinsic K d and the equilibrium constant of ED c to ED o conversion, which, being unfavorable, limits the binding of initiating NTP. These observations reveal an interesting mechanism by which promoter bases upstream from the start site (bases in the promoter specificity region) can influence the apparent K d values of the initiating NTPs. A promoter can have the same sequence at the start site, but the apparent K d of the initiating NTPs can be different, depending on the equilibrium constant of the promoter opening step. For example, T7 promoters ⌽3.8 and ⌽10 both have the same initiation sequence, ϩ1 GGGAGA, but the ⌽3.8 promoter with nonconsensus base pairs at positions Ϫ2, Ϫ11, Ϫ12, and Ϫ13 has a weaker affinity for the initiating GTPs (29). The nonconsensus base pairs alter the protein-DNA interactions decreasing the intrinsic equilibrium constant of the promoter opening step, which in turn affects the K d of the initiating NTPs. The same reason may explain why E. coli rrnB P1 promoters have a high K m for the initiating NTP and why base changes in the promoter core region affect the K m of the initiating NTP (5). Thus, base changes upstream from the start site can modulate initiating NTP binding and make transcription respond to cellular NTP pools. In general, any accessory factor that binds to the RNAP-DNA complex, such as transcription factors that change the conformation of the RNAP or the DNA, can regulate the intrinsic parameters of DNA binding and promoter opening steps, which in turn can regulate the efficiency of transcription.