Late Steps in the Formation of E. coli RNA Polymerase-λP_R Promoter Open Complexes: Characterization of Conformational Changes by Rapid [Perturbant] Upshift Experiments

Abstract

The formation of the transcriptionally-competent open complex (RP_o) by E. coli RNA polymerase at the λP_R promoter involves at least three steps and two kinetically-significant intermediates (I₁ and I₂). Understanding the sequence of conformational changes (rearrangements in the jaws of RNAP, DNA opening) that occur in the conversion of I₁ to RP_o requires: 1) dissecting the rate constant k_d for the dissociation of RP_o into contributions from individual steps and 2) isolating and characterizing I₂. To deconvolute k_d, we develop experiments involving rapid upshifts to elevated concentrations of RP_o-destabilizing solutes (“perturbants”: urea and KCl) to create a burst in the population of I₂. At high concentrations of either perturbant, k_d approaches the same [perturbant]-independent value at both 10 °C and 37 °C, interpreted as the rate constant k₋₂ for I₂ → I₁. The large effects of [urea] and [salt] on K₃ (the equilibrium constant for I₂ ⇄ RP_o) indicate that a large-scale folding transition in polymerase forms a new interface with the DNA late in the mechanism. We deduce that I₂ at the λP_R promoter is always unstable relative to RP_o, even at 0 °C, explaining previous difficulties in detecting it by using temperature downshifts. Evidence for an additional unstable intermediate (I₃) in the mechanism between I₂ and RP_o is presented. The large positive enthalpy change associated with open complex formation is divided between the steps converting I₁ to RP_o, consistent with a mechanism in which DNA opening occurs in several stages.

INTRODUCTION

To initiate RNA synthesis, RNA polymerase (RNAP) locally separates the complementary strands of promoter DNA around the transcription start site and places the start site base on the template strand into its active site. Defining the cascade of conformational changes that occur during initiation and how they are regulated by promoter sequence and transcription factors is essential for understanding genetic expression, for defining the input into transcriptional networks, and for designing inhibitors of this essential process in disease-causing organisms. For the bacterial RNAP, open complex formation occurs in the absence of NTP hydrolysis or a helicase cofactor. For eukaryotic RNAP, additional protein cofactors are required to open the start site, although their roles in opening the DNA remain unclear ¹. Despite evolutionary differences in complexity, the extensive structural and functional homology between multi-subunit RNAPs from all kingdoms ² renders the relatively simple E. coli enzyme a relevant model for the key steps in initiation, as well as providing a reference point for comparison with transcription by eukaryotic RNAP.

For E. coli RNAP holoenzyme (core enzyme (α₂, β, β’, and ω subunits) and σ⁷⁰ specificity subunit), formation of the transcriptionally-competent open complex (RP_o) proceeds through a series of steps following the recognition of a specific promoter DNA sequence. In RP_o, the DNA is unpaired and unstacked from the AT-rich −10 hexamer to just downstream of the transcription start site, a span of ~14 base pairs. At the λP_R promoter, this open region extends from position −11 to +3 ^{3; 4; 5}, with numbering relative to the start site, +1. Despite decades of study of open complex formation, fundamental questions remain regarding this essential cellular process. For example, it is still unclear what conformational changes in RNAP are required for DNA opening and whether opening occurs in a single step or in several.

Addressing these mechanistic questions requires kinetic studies to provide essential information regarding the numbers of steps and intermediates involved in the overall process of forming RP_o and the characteristic rate and/or equilibrium constants of these steps. Kinetic data for formation and dissociation of RP_o involving E. coli RNAP (R) and the λP_R promoter (P) is described by a mechanism consisting of a minimum of three steps with two kinetically significant intermediates ^{6; 7; 8}:

$$\mathrm{R}+\mathrm{P}\underset{{\mathrm{k}}_{-1}}{\overset{{\mathrm{k}}_1}{\rightleftarrows }}{\mathrm{I}}_1\underset{{\mathrm{k}}_{-2}}{\overset{{\mathrm{k}}_2}{\rightleftarrows }}{\mathrm{I}}_2\underset{{\mathrm{k}}_{-3}}{\overset{{\mathrm{k}}_3}{\rightleftarrows }}\mathrm{R}{\mathrm{P}}_{\mathrm{o}}$$ (Mechanism I)

In Mechanism I, under conditions typically used in studies of open complex formation (4 – 42 °C, moderate salt concentration), I₁ rapidly equilibrates with free RNAP and promoter DNA on the time scale required for I₁ to convert to I₂, and I₂ rapidly equilibrates with RP_o on the time scale required for I₂ to convert to I₁. Notably, the interconversion I₁ ⇄ I₂ is the rate-limiting step in both the forward and reverse directions ^{6; 9; 10}. Additional intermediates between the free species and I₁ and between I₂ and RP_o may exist. However, they are not included in Mechanism I because evidence for them has not been obtained from previous kinetic studies. (Other intermediate complexes must be included in nested sets of rapid equilibria that determine K₁ and K₃.)

In excess RNAP, the kinetics of formation of open complexes between free RNAP and λP_R promoter DNA are single exponential. In this case, measurements of the [RNAP]-dependence of the observed association rate constant are unambiguously interpreted in terms of K₁ (K₁ = k₁/k₋₁; the equilibrium constant for R + P ⇄ I₁) and k₂ (the rate constant for I₁ → I₂) ^{9; 10}. The behaviors of K₁ and k₂ as functions of reaction conditions (such as temperature ⁹ and solute concentrations ¹¹) provide insight into the driving forces and molecular processes involved in the formation of I₁ from free RNAP and DNA and its conversion to the subsequent transition state, (I₁-I₂)^‡. For example, the small dependence of K₁ on urea concentration ¹¹ implies that no large-scale folding transitions in RNAP occur concurrently with binding in R + P ⇄ I₁ (see Background Section).

Analogous information regarding the molecular processes that occur in the steps of the latter half of Mechanism I (the conversion of (I₁-I₂^‡) into RP_o via I₂) is contained in the kinetics of conversion of RPo back into free reactants (dissociation). At a minimum, the kinetically-significant steps of irreversible dissociation (initiated by addition of an excess of the polyanionic competitor heparin, which acts as a DNA mimic to sequester free RNAP) are ¹⁰:

$$\mathrm{R}{\mathrm{P}}_{\mathrm{o}}\underset{{\mathrm{k}}_3}{\overset{{\mathrm{k}}_{-3}}{\rightleftarrows }}{\mathrm{I}}_2\stackrel{{\mathrm{k}}_{-2}}{\to }\text{undetected species}({\mathrm{I}}_1,\mathrm{P})$$ (Mechanism II)

Previous studies of the kinetics of dissociation indicate that large-scale conformational changes occur in the latter half of Mechanism I. The large increases in the rate of dissociation with increasing concentrations of univalent salt ^{7; 12; 13} and urea ¹¹ indicate that a new RNAP-DNA interface forms and that ~120 amino acid residues fold in (I₁-I₂)^‡⇄I₂ ⇄ RP_o (see Background Section). The large positive activation heat capacity change ^{8; 13} associated with the rate constant for dissociation (k_d; see Background Section) is also consistent with the hypothesis that a large-scale folding transition in RNAP occurs in (I₁-I₂)^‡ ⇄ I₂ ⇄ RP_o (as a heat capacity change in a biopolymer process often signals a protein folding event ¹⁴). The strong acceleration of RP_o dissociation by the in vivo regulatory factors ppGpp and DksA at all promoters studied to date^{15; 16} indicates that they bind to (I₁-I₂)^‡ and/or I₂ more strongly than to RP_o. These large effects are consistent with the existence of large-scale conformational changes occurring in the conversions between these species. For example, we have proposed that ppGpp and DksA accelerate dissociation by disfavoring the folding transition involved in converting I₂ to RP_o ¹¹.

Evidence also shows that DNA opening at the λP_R promoter may occur, at least in part, during the latter half of Mechanism I. In I₁, promoter DNA around the transcription start site is unreactive to KMnO₄ and therefore presumably still double helical ^{3; 17}, while fourteen base pairs (−11 to +3) are deduced to be open in RP_o ^{3; 4; 5}. Thus, DNA opening must occur in I₁ → I₂ and/or I₂ → RP_o. Large positive enthalpy changes are also associated with these steps, consistent with the large enthalpic cost associated with melting DNA. A large positive activation energy (activation enthalpy) is observed for the conversion of I₁ to (I₁-I₂)^‡ (E_{a (2)} = 34 kcal/mol ⁹), and the negative activation energy of dissociation indicates that the van’t Hoff enthalpy change ΔH^o₍₃₎ for I₂ ⇄ RP_o must be large and positive at low temperature ^{8; 13}.

Because RP_o and I₂ equilibrate rapidly on the time scale of converting I₂ to I₁, it has proven difficult to separate the steps that determine the dissociation kinetics (Mechanism II) and to isolate and characterize I₂. The goal of the present study is to unambiguously dissect, for the first time, the contributions of RP_o ⇄ I₂ and I₂ → I₁ to the rate of open complex dissociation. This information can, in turn, be used to characterize the molecular processes occurring in the steps and to design experiments to trap and characterize the elusive I₂.

One method of deconvoluting the kinetics of dissociation is a so-called “burst” experiment, in which a reaction variable is rapidly shifted in an attempt to destabilize RP_o and increase the population of I₂. Use of temperature downshift bursts after initially forming RP_o at high temperatures were attempted based on the conclusion that ΔH^o₍₃₎ for I₂ ⇄ RP_o is large and positive and the inference that a downshift in temperature will therefore rapidly depopulate RP_o ^{3; 18; 19; 20}. However, the difficulty of performing a temperature downshift rapidly, the temperature dependence of the rate of KMnO₄ reactivity (activation energy ~ 8 kcal/mol; M. Capp, unpublished data), and the possibility of artifacts (such as off-pathway complexes formed in the downshifts ^{21; 22}) may have complicated the interpretations of these experiments.

In this study, we have designed isothermal burst (upshift) experiments, in which preformed open complexes are rapidly shifted to elevated concentrations of either urea or KCl and the dissociation kinetics are followed. We find that the rate constant for dissociation of open complexes (k_d) reaches or approaches a [urea]- and [KCl]-independent value at both 10 and 37 °C, signifying that either k₋₃ (RP_o → I₂) or k₋₂ (I₂ → I₁) is independent of [perturbant]. Based on an analogy between our data and the effect of [urea] on the kinetics and equilibria of protein folding, we propose that the plateau value of k_d represents the rate constant k₋₂, and that the entire effects of [urea] and [salt] on k_d are contained in RP_o ⇄ I₂ (i.e. k₋₃ and k₃). Implications of these results for the nature of I₂ and of the steps converting I₁ to RP_o are discussed.

BACKGROUND

Formulation of the dissociation rate constant k_d

For systems where the kinetics of dissociation of open complexes are single exponential (as observed for the λP_R promoter under almost all conditions studied ^{6; 7; 11}), the dissociation rate constant k_d is interpreted without approximation as ¹⁰:

$${\mathrm{k}}_{\mathrm{d}}=\frac{{\mathrm{k}}_{-2}{\mathrm{k}}_{-3}}{{\mathrm{k}}_{-2}+{\mathrm{k}}_{-3}+{\mathrm{k}}_3}=\frac{{\mathrm{k}}_{-2}}{1+{\mathrm{K}}_3+{\mathrm{k}}_{-2}/{\mathrm{k}}_{-3}}$$ (1)

where K₃ = k₃/k₋₃.

Under conditions where the interconversion of RP_o and I₂ in Mechanism II rapidly equilibrates on the time scale required for I₂ to convert to I₁ (k₃ ≫ k₋₂), deduced experimentally from the negative activation energy of k_d ^{6; 8; 13}, eq 1 can be simplified, depending on the relative magnitude of K₃ ¹⁰:

$${\mathrm{k}}_{\mathrm{d}}=\frac{{\mathrm{k}}_{-2}}{\mathrm{1}+{\mathrm{K}}_3}\text{where}{\mathrm{K}}_3~1$$ (2a)

or

$${\mathrm{k}}_{\mathrm{d}}=\frac{{\mathrm{k}}_{-2}}{{\mathrm{K}}_3}\text{where}{\mathrm{K}}_3\gg 1$$ (2b)

Interpretation of the effect of nondenaturing concentrations of urea on a biopolymer process and application to the study of the kinetics of open complex formation

Urea has been shown to interact preferentially (i.e. relative to interactions with water) primarily with amide groups (specifically with the polar N and O atoms) of proteins and model compounds ^{23; 24; 25; 26; 27; 28; 29; 30}. Preferential interactions of urea with other groups on proteins and nucleic acids (such as predominantly nonpolar or charged groups) have not been detected in studies with biopolymers ^{24; 25}. We have quantified this interaction per unit of polar amide surface area (ASA_{polar amide}) ^{24; 28; 30}, thus making [urea] an effective quantitative probe of changes in the solvent exposure of amide surface area associated with biopolymer processes:

$$\text{dln}{\mathrm{K}}_{\text{obs}}/{\text{dm}}_{\text{urea}}=\left(1.4\times {10}^{-3}\right)\mathrm{\Delta }{\text{ASA}}_{\text{polar amide}}$$ (3)

where K_obs is the observed equilibrium quotient for a biopolymer process and ΔASA_{polar amide} is the change in the amount of water-accessible polar amide surface area in converting the reactant state to the product state. A test of the usefulness of [urea] as a probe of ΔASA_{polar amide} was provided by a study of lac repressor binding to operator DNA; the observed effect of [urea] on the binding constant K_obs agrees with that predicted from structural information on the amount of polar amide surface buried in complex formation ³⁰.

This method of analysis has been used to interpret the [urea]-dependences of K₁, k₂, and k_d in Mechanism I and Mechanism II ¹¹. The moderate initial dependence of K₁ on [urea] is consistent with the polar amide surface area known or predicted to be buried in the large RNAP-DNA interface formed in R + P ⇄ I₁, without having to invoke additional large-scale folding transitions. The lack of a dependence of k₂ on [urea] implies that there is no net exposure of polar amide surface in the conversion of I₁ to the subsequent transition state (I₁-I₂)^‡. The large dependence of k_d on [urea] was interpreted as a large-scale folding transition in a region of RNAP in (I₁-I₂)^‡ ⇄ RP_o. Specifically, we proposed that disordered regions in the C-terminus of the β’ subunit, including the downstream jaw, fold in I₂ ⇄ RP_o.

Experiments performed at moderate urea concentrations under reversible conditions, where the kinetics of the association and dissociation reactions can be measured simultaneously (Supporting Information of ¹¹ and unpublished data), result in values for k_d that are the same within error as those obtained from irreversible dissociation experiments at the same urea concentrations. This result provides evidence that the intermediates involved in the forward and reverse processes in the presence of perturbant are the same.

RESULTS

The dissociation of RNAP-promoter open complexes following upshifts in perturbant (urea or KCl) concentration shows single exponential kinetics

The rate of dissociation of open complexes (RP_o) formed between E. coli RNAP and λP_R promoter DNA is greatly accelerated by increasing concentrations of urea ¹¹ and salt ^{6; 7; 12}. We monitored the dissociation of pre-formed open complexes following a rapid upshift in either [urea] (up to 5.0 M) or [KCl] (up to 1.10 M) in order to dissect the contributions of RP_o ⇄ I₂ and I₂ → I₁ (Mechanism II) to the overall [perturbant] dependences of k_d. [Evidence that these experiments monitor the dissociation kinetics of RP_o by Mechanism II and not by an alternative mechanism induced by high [salt] or [urea] (such as holoenzyme or DNA denaturation) is presented in the Analysis Section.] Representative data for these dissociation experiments are shown in Figure 1([urea] upshifts) and Figure 2 ([KCl] upshifts). These data are well fit by single-exponential decays (eq 4, Methods) under every set of reaction conditions studied; fits are represented by solid lines for the 10 °C data and dashed lines for the 37 °C data. Values of the dissociation rate constant k_d from fits to eq 4 are given in Table 1 (for the [urea] upshifts) and Table 2 (for the [KCl] upshifts). The single exponential character of the data validates the use of eq 1 (Background Section) in the analysis of all values of k_d ¹⁰.

Figure 1.

Dissociation of RNA polymerase (RNAP)-λP_R promoter open complexes after upshifts in urea concentration. Preformed open complexes in Dissociation Buffer (DB) were mixed with a solution of DB containing urea and heparin to obtain the urea concentrations listed. Data are plotted as the fraction of DNA originally bound in open complexes remaining bound after upshift (θ_t/θ₀). Black symbols represent data taken at 37 °C. White symbols represent data taken at 10 °C. Lines are fits of the data to a single exponential decay (eq 4 in the text). Dashed lines are fits to the 37 °C data, and solid lines are fits to the 10 °C data. Rate constants (k_d) from the fits are contained in Table 1. (a) Upshifts to 0 (circles), 0.5 (triangles), and 1.0 (squares) M urea. (b) Upshifts to 1.5 (circles), 2.0 (triangles), and 3.0 (squares) M urea. (c) Upshifts to 3.5 (circles), 4.0 (triangles), and 4.5 (squares) M urea.

Figure 2.

Dissociation of RNAP-λP_R promoter open complexes after upshifts in KCl concentration. Preformed open complexes in Dissociation Buffer (DB) were mixed with a solution of DB containing additional KCl and heparin to obtain the KCl concentrations listed. Data are plotted as the fraction of DNA originally bound in open complexes remaining bound after upshift (θ_t/θ₀). Black symbols represent data taken at 37 °C. White symbols represent data taken at 10 °C. Lines are fits of the data to a single exponential decay (eq 4 in the text). Dashed lines are fits to the 37 °C data, and solid lines are fits to the 10 °C data. Rate constants (k_d) from the fits are contained in Table 2. (a) Upshifts to 0.12 (circles), 0.15 (triangles), and 0.18 (squares) M KCl. (b) Upshifts to 0.24 (circles), 0.30 (triangles), and 0.38 (squares) M KCl. (c) Upshifts to 0.60 (circles), 0.80 (triangles), and 1.10 (squares) M KCl. Note: The data at 0 M urea in Figure 1 is the same as the data at 0.12 M KCl in Figure 2 (replotted for comparison).

Table 1.

Values of the rate constant for the dissociation of open complexes (k_d) following upshift in urea concentration.

	kd (s−1)a
[urea] (M)	37 °C	10 °C
0	1.9 (±0.6) × 10−5	2.1 (±0.2) × 10−4
0.5	6.0 (±1.2) × 10−5	1.35 (±0.06) × 10−3
1.0	3.2 (±0.6) × 10−4	7.1 (±0.5) × 10−3
1.5	1.4 (±0.3) × 10−3	4.1 (±0.7) × 10−2
2.0	8.9 (±2.2) × 10−3	1.2 (±0.2) × 10−1
2.5	3.8 (±1.5) × 10−2	2.0 (±0.2) × 10−1
3.0	9.4 (±1.4) × 10−2	3.1 (±0.2) × 10−1
3.5	2.5 (±0.7) × 10−1	4.7 (±0.2) × 10−1
4.0	5.5 (±2.2) × 10−1	7.0 (±1.2) × 10−1
4.5	6.9 (±0.4) × 10−1	7.0 (±0.6) × 10−1
5.0	1.4 ±0.2	-

^ak_d is calculated by fitting the dissociation data represented in Figure 1 with eq 4 in the text.

Table 2.

Values of the rate constant for the dissociation of open complexes (k_d) following upshift in KCl concentration.

	kd (s−1)a
[KCl] (M)	37 °C	10 °C
0.12	1.9 (±0.6) × 10−5	2.1 (±0.2) × 10−4
0.15	7.3 (±0.7) × 10−5	6.9 (±0.4) × 10−4
0.18	1.9 (±0.4) × 10−4	1.6 (±0.2) × 10−3
0.24	1.3 (±0.1) × 10−3	1.15 (±0.07) × 10−2
0.30	1.0 (±0.3) × 10−2	5.3 (±0.9) × 10−2
0.38	9.1 (±5.2) × 10−2	1.1 (±0.1) × 10−1
0.48	4.8 (±0.6) × 10−1	-
0.60	1.6 ±0.7	4.2 (±0.7) × 10−1
0.80	2.3 ±0.8	5.5 (±1.4) × 10−1
1.10	3.3 ±0.2	7.3 (±0.6) × 10−1

^ak_d is calculated by fitting the dissociation data represented in Figure 2 with eq 4 in the text.

The rate of open complex dissociation is strongly driven by [perturbant] at low perturbant concentrations but independent of [perturbant] at high perturbant concentrations

In Figure 3, the natural logarithm of k_d (ln k_d) is plotted versus [urea] (panel a), and against ln [KCl] (panel b). At the lowest concentrations of both urea (up to ~1.5 M at 10 °C and ~2.5 M at 37 °C) and KCl (up to ~0.30 M at 10 °C and ~0.48 M at 37 °C), ln k_d increases dramatically with increasing [perturbant] (linearly versus [urea] and with a slight positive (upward) curvature versus ln [KCl]). At higher concentrations of both perturbants, the rate of open complex dissociation becomes less dependent on [perturbant], resulting in negative (downward) curvature in the data in Figure 3. For example, while dlnk_d/d[urea] at 10 °C between 0 M urea and 0.5 M urea is ~3.5 M⁻¹, dlnk_d/d[urea] is only ~1 M⁻¹ between 2.0 M urea and 3.0 M urea (Fig 3a). Likewise, at 37 °C, between 0.30 M KCl and 0.38 M KCl, dlnk_d/dln[KCl] = ~9.3, while between 0.48 M KCl and 0.60 M KCl, dlnk_d/dln[KCl] = ~5.4 (Fig 3b).

Figure 3.

The natural logarithm (ln) of the dissociation rate constant k_d (from fits of the kinetic data represented in Fig 1 and Fig 2 to eq 4) plotted versus [urea] (a) and ln [KCl] (b). Black points are for data taken at 37 °C; white points are for data taken at 10 °C. In (a), solid lines are fits of the data to an expression (utilizing eq 5, eq 7, and eq 8 in the text) in which dependences of the equilibrium constant K₃ (I₂ ⇄ RP_o) and the rate constant k₋₃ (RP_o → I₂) on [urea] are incorporated into the general expression for k_d (eq 1). Dashed lines are fits of the data to an expression (utilizing eq 6 and eq 7) in which only the dependence of K₃ on [urea] is incorporated into a simplified expression for k_d (eq 2a). In (b), solid lines are fits of the data to an expression (utilizing eq 6, eq 9–eq 11) in which a dependence of K₃ on [KCl] was incorporated into the simplified expression for k_d (eq 2a). Horizontal dotted lines represent values of ln k₋₂ determined from the fits.

At the highest concentrations of either perturbant, the rate of open complex dissociation becomes essentially independent of [perturbant]. This is particularly evident in Figure 3b, where k_d appears to have reached a [KCl]-independent plateau at both 10 and 37 °C (for example, at 37 °C, k_d = 2.3 ± 0.8 s⁻¹ at 0.80 M KCl and 3.3 ± 0.2 s⁻¹ at 1.10 M KCl (Fig. 2c, Table 2)). Similarly, in Fig 3a, k_d at 10 °C appears to have reached a [urea]-independent plateau (k_d =7.0 (± 1.2) × 10⁻¹ s⁻¹ at 4.0 M urea and 7.0 (± 0.6) × 10⁻¹ s⁻¹ at 4.5 M urea (Fig. 1c, Table 1)). While k_d at 37 °C is still increasing with [urea] at the highest urea concentration studied (k_d = 6.9 (± 0.4) × 10⁻¹ s⁻¹ at 4.5 M urea and 1.4 ± 0.2 s⁻¹ at 5.0 M urea (Fig. 1c, Table 1)), it also appears to be gradually approaching a plateau at even higher [urea] (Fig 3a).

The dissociation of open complexes is characterized by a negative activation energy at low perturbant concentrations and a positive activation energy at high perturbant concentrations

At the lowest urea and KCl concentrations studied, k_d is much larger at 10 °C than at 37 °C (Fig 3 and Table 1 and Table 2). This difference is vividly demonstrated in Fig 1a and Fig 2a: dissociation of open complexes is much faster at 10 °C than at 37 °C in 0, 0.5, and 1.0 M urea (Fig 1a) and in 0.12, 0.15, and 0.18 M KCl (Fig 2a). The negative activation energy for k_d implies that a rapidly equilibrating initial step (or steps) precedes the rate-determining step in dissociation (because an elementary rate constant cannot have a negative activation energy). The earlier observation of this negative activation energy originally motivated the inclusion of a second kinetically-significant intermediate (I₂) into Mechanism I ^{6; 8; 19}.

As the perturbant concentrations are increased, the differences between k_d at 10 and 37 °C decrease (i.e. the negative activation energy in each perturbant decreases in magnitude) until, after upshift to some [urea] and [KCl], the values of k_d at 10 and 37 °C converge (where the activation energy is zero) (Fig 3 and Table 1 and Table 2). As seen in Fig 1c, this occurs at ~4.5 M urea, where open complexes dissociate at roughly the same rate at 10 and 37 °C (k_d is 6.9 (± 0.4) × 10⁻¹ s⁻¹ at 37 °C and 7.0 (± 0.6) × 10⁻¹ s⁻¹ at 10 °C). In Fig 2b, the rate of dissociation is essentially independent of temperature at 0.38 M KCl (k_d = 9.1 (± 5.2) × 10⁻² s⁻¹ at 37 °C and 1.1 (± 0.1) × 10⁻¹ s⁻¹ at 10 °C).

At concentrations of KCl higher than 0.38 M, k_d is significantly larger at 37 °C than at 10 °C (Fig 3b and Table 2); this is dramatically apparent in Fig 2c, where dissociation of open complexes is clearly faster at 37 °C than at 10 °C in 0.60, 0.80, and 1.10 M KCl. This temperature dependence of dissociation at high [KCl] results in a positive activation energy for the process. The data indicate that a positive activation energy is likely at high concentrations of urea as well. While k_d is the same at 10 and 37 °C at 4.5 M urea (the highest concentration for which there is data at both temperatures), k_d has reached its [urea]-independent value already by 4.5 M urea at 10 °C (Fig. 3a, Table 1), and so would be expected to have that same value at all higher concentrations of urea. However, at 37 °C, k_d is still increasing: at 5.0 M urea, k_d = 1.4 ± 0.2 s⁻¹. Thus, at urea concentrations greater than 4.5 M, k_d is likely larger at 37 °C than at 10 °C. Because values of k_d at high [KCl] and [urea] at both 10 and 37 °C are independent of perturbant concentration, the positive activation energy of k_d in this regime is also independent of perturbant concentration.

ANALYSIS

Interpretation of k_d at high perturbant concentrations: The rate of dissociation is determined by the rate of I₂ → I₁

The simplest interpretation of the [perturbant]-independent positive activation energy for open complex dissociation at high perturbant concentrations (represented by the higher plateau value of k_d at 37 °C than at 10 °C in Fig 3) is that I₂ no longer rapidly converts back to the higher enthalpy state RP_o on the time scale over which I₂ converts to I₁. In order for the rapid equilibrium in I₂ ⇄ RP_o to break down, I₂ → I₁ must become faster than I₂ → RP_o, resulting in a mechanism of dissociation consisting of two sequential uni-directional steps at high [perturbant]:

$$\mathrm{R}{\mathrm{P}}_{\mathrm{o}}\stackrel{{\mathrm{k}}_{-3}}{\to }{\mathrm{I}}_2\stackrel{{\mathrm{k}}_{-2}}{\to }\text{undected species}\left({\mathrm{I}}_1,\mathrm{P}\right)$$ (Mechanism III)

In general, analysis of Mechanism III for the situation where both RP_o and I₂ are detectable and where k₋₃ and k₋₂ are of comparable magnitude yields a lag phase in the dissociation of detectable complexes. Since the data in Fig 1c and Fig 2c (for dissociation of detectable complexes at high perturbant concentrations) are well fit by a single exponential decay (without an apparent lag phase), one of the rate constants in the back direction, either k₋₂ or k₋₃, must be large enough that it does not contribute to the overall observable kinetics of dissociation. In this high [perturbant] regime, dissociation of detectable complexes must therefore be represented by one or the other of the following mechanisms:

$$\mathrm{R}{\mathrm{P}}_{\mathrm{o}}\stackrel{{\mathrm{k}}_{-3}}{\to }\text{undected species}\left({\mathrm{I}}_2,{\mathrm{I}}_1,\mathrm{P}\right)$$ (Mechanism IVa)

or

$${\mathrm{I}}_2\stackrel{{\mathrm{k}}_{-2}}{\to }\text{undetected species}\left({\mathrm{I}}_1,\mathrm{P}\right)$$ (Mechanism IVb)

For Mechanism IVa to be applicable, k₋₂ would have to exceed k₋₃ by enough so that no I₂ accumulates on the time scale of the conversion of RP_o to I₂. For Mechanism IVb to be applicable, k₋₃ would have to exceed k₋₂ by enough so that all RP_o converts to I₂ before significant dissociation of I₂ commences (and within the time resolution of the experiment). Because the plateaus at high perturbant concentrations are independent of [perturbant], whichever rate constant determines k_d in this regime (either k₋₃ or k₋₂) is independent of [perturbant].

Although the data alone do not allow us to distinguish between Mechanism IVa and Mechanism IVb because of the symmetry between k₋₂ and k₋₃ in the general expression for k_d (eq 1), we propose that Mechanism IVb describes the dissociation of detectable complexes at high [perturbant]. Our reasoning is based on an analogy between the [urea]-dependent step in open complex formation and the two-state process of folding a single-domain globular protein. In general, for proteins for which the rates of folding (k_fold) and unfolding (k_unfold) have been determined as functions of urea concentration, the overall [urea]-dependence of the equilibrium constant (K_obs = k_fold/k_unfold) is distributed to some extent (between 30 and 70% of the overall effect on each) between k_fold and k_unfold (see ³¹). The rate constants k₂ (I₁ → I₂) and k₋₂ (I₂ → I₁) are the forward and reverse elementary rate constants that make up the equilibrium K₂ (I₁ ⇄ I₂); because we previously found that k₂ is independent of [urea] ¹¹, it is unlikely that k₋₂ would contain a significant [urea]-dependence. Thus, it is most likely that the [urea]-dependence is contained within k₃ and k₋₃. (While a situation in which the [urea]-dependence of a biopolymer process is fully contained within only one of the rate constants that make up the equilibrium constant for the process may not be physically impossible, to our knowledge no examples of it exist.)

The behavior of k_d at high concentrations of urea and KCl strongly supports our conclusion that Mechanism II (at low [perturbant]) and Mechanism IVb (at high [perturbant]) characterize the dissociation of RNAP-promoter complexes, and that other mechanisms (such as RNAP or DNA denaturation) are not significant. In particular, if perturbant-induced denaturation were occurring, we would expect the rate of dissociation to continue increasing with perturbant concentration, rather than reaching [perturbant]-independent plateaus, as are seen in the data. Moreover, the native forms of RNAP holoenzyme ³² and DNA ³³ are stable at high salt concentrations, so upshifts in KCl concentration cannot be inducing denaturation. The observation that the rate of dissociation at high [perturbant] is independent of the identity of perturbant (most explicitly evident at 10 °C; Fig 3) implies that the same dissociation process is occurring at both high [urea] and high [KCl]. Thus, we conclude that if other salt- or urea-induced processes do occur, they do so only after the transition state (I₁-I₂)^‡ has been formed in the dissociation direction, and therefore do not influence the observed kinetics of dissociation.

The step I₁ ⇄ I₂ is highly endothermic

From the values of k₋₂ at 10 and 37 °C (Table 3), we estimate the activation energy for k₋₂ (E_a(−2) = −RΔlnk₋₂/Δ (1/T)) to be 9.9 kcal/mol. This activation energy is smaller than that of k₂ (E_a(2) = 34 kcal/mol)⁹, resulting in an estimated enthalpy change for the overall step (I₁ ⇄ I₂) that is large and positive (ΔH₂^o = 24 kcal/mol). Our calculation assumes that there is no activation heat capacity change for k₋₂(ΔC_p^‡₍₋₂₎ = ΔE_a(−2)/ΔT ~0), and thus that E_a(−2) is constant between 10 and 37 °C. This assumption is consistent with the observed lack of an activation heat capacity change for the forward rate constant k₂ ⁹, and is analogous to the argument (above) that the lack of a [urea]-dependence of k₂ implies that k₋₂ is independent of [urea] as well. A heat capacity change in a biopolymer process, like a [urea]-dependence, is often a sign of a conformational change in which biopolymer surface is either buried from or exposed to the solvent ¹⁴. We propose that the [urea]-dependence and the heat capacity change in k_d both result from the same folding transition in RNAP; the extension of this proposal is that both are contained in the same step (I₂ ⇄ RP_o).

Table 3.

Parameters from the analysis of the [urea] and [KCl] upshifts at 37 and 10 °C

	37 °C	10 °C
k−2 (s−1)	3.3 ± 0.7	7.2 (±0.7) × 10−1
K3o a	2.7 (±0.9) × 105	3.2 (±0.6) × 103
dlnK3/d[urea] b	−3.3 ± 0.1 M−1	−3.5 ± 0.1 M−1
k−3o (s−1) a c	1.1 (±0.7) × 10−2	3.3 (±1.0) × 10−2
k3o (s−1) a d	3.0 (±2.2) × 103	1.0 (±0.4) × 102
dlnk−3/d[urea] c	1.1 ± 0.2 M−1
dlnk3/d[urea] e	−2.2 ± 0.2 M−1	−2.5 ± 0.2 M−1

^aX^o is the value of X in DB (containing 0.12 M KCl and no urea)

^bDetermined from a fit of the linear regions of the data in Fig 3a (0–1.5 M urea at 10 °C and 0–2.5 M urea at 37 °C)

^cCalculated from fits of the data in Figure 3a to eq 5 in the text

^dCalculated from values of K₃ (= k₃/k₋₃) and k₋₃ in this table

^eCalculated from: dlnk₃/d[urea] = dlnK₃/d[urea] + dlnk₋₃/d[urea]

Interpretation of k_d at low perturbant concentrations: The [perturbant]-dependence of the rate of dissociation is determined by the [perturbant]-dependence of RP_o ⇄ I₂

As seen in Fig 3, k_d increases dramatically with increasing [perturbant] at low perturbant concentrations. The logarithm of k_d increases linearly with increasing [urea] (up to ~1.5 M urea at 10 °C and ~2.5 M urea at 37 °C; Figure 3a) and nonlinearly (with slight upward curvature) with ln [KCl] (up to ~0.30 M KCl at 10 °C and to ~0.48 M KCl at 37 °C; Figure 3b). These trends in k_d correspond closely to the behaviors expected for the equilibrium constants for protein unfolding and for disruption of a protein-DNA interface, respectively. In studies of protein unfolding, ln K_obs is almost invariably a linear function of [urea] (giving rise to the so-called ‘m-value’), even to zero urea ²⁹. For studies of the dissociation of positively charged ligands from DNA in the presence of both univalent salt and Mg²⁺, ln K_obs shows a nonlinear dependence on ln [univalent salt], with curvature resulting from the [univalent salt]-dependent association of Mg²⁺ with the DNA phosphate backbone ³⁴. The trends in the data at low [perturbant] in Fig 3, coupled with the assumption that k₋₂ is independent of [perturbant], imply that the denominator of the expression for k_d (eq 1) is completely dominated by K₃ (K₃ ≫ 1 + k₋₂/k₋₃). The expression for k_d at low [perturbant] can therefore be simplified to eq 2b: k_d = k₋₂/K₃. Thus, the initial dependences of k_d on [urea] and [KCl] are equal in magnitude to the dependences of K₃ on those perturbants: dlnk_d/d[urea] = −dlnK₃/d[urea] and Sk_d (=dlnk_d/dln[KCl]) = −SK₃.

Fits of the linear regions of the [urea] upshift data in Fig 3a give the following values of dlnK₃/d[urea]: −3.3 ± 0.2 M⁻¹ at 37 °C and −3.5 ± 0.1 M⁻¹ at 10 °C. These dependences agree well with that determined previously at 17 °C over a smaller range of urea concentrations (dlnk_d/d[urea] (= −dlnK₃/d[urea]) = 3.1 ± 0.1 M⁻¹ from 0 to 0.6 M urea ¹¹). Using eq 3 (Background Section), these values of dlnK₃/d[urea] reveal that ~2.4 × 10₃ Ų of polar amide biopolymer surface (corresponding to ~120 amino acid residues) is buried in the conversion of I₂ to RP_o.

I₂ is unstable under typical transcription assay conditions

One implication of the values of k₋₂ and K₃ obtained from the fits of the upshift data (Table 3) is that I₂ is unstable relative to both I₁ and RP_o at the λP_R promoter under typical assay conditions. In Dissociation Buffer, the equilibrium constant K₂ for I₁ ⇄ I₂ is ~3 × 10⁻³ at 10 °C and ~0.2 at 37 °C (with K₂ = k₂/k₋₂ calculated using the values of k₋₂ from Table 3 and values of k₂ determined previously ⁹). The equilibrium constant K₃ for I₂ ⇄ RP_o is 3.2 (± 0.6) × 10³ at 10 °C and 2.7 (± 0.9) × 10⁵ at 37 °C (Table 3). Calculation of K₂ and K₃ between 0 and 42 °C (data not shown) shows that essentially none of the promoter DNA exists as I₂ at equilibrium at any temperature, explaining previous difficulties in isolating and characterizing I₂. [Notably, at 0 °C, K₃ is calculated to be ~120, indicating that our previous attempt to rapidly populate I₂ through means of a temperature downshift to 0 °C ³⁵ was unsuccessful and therefore incorrectly interpreted.]

Interpretation of k_d at intermediate perturbant concentrations

At moderate perturbant concentrations, K₃ has decreased by enough such that it contributes less to the denominator of k_d than it did at low concentrations (where it so completely dominated the denominator that dlnk_d/d(ln)[perturbant] = −dlnK₃/d(ln)[perturbant]), but not by so much that it is negligible compared to unity (as is the case at high [perturbant], where k_d = k₋₂). Thus, the dependences of K₃ on [perturbant] contribute progressively less to the overall dependences of k_d, and these overall dependences begin to decrease in magnitude. These transition regions between the low (k_d = k₋₂/K₃) and high (k_d = k₋₂) [perturbant] regimes are characterized by downward (negative) curvature in the trends in ln k_d with [urea] (~1.5–3.5 M at 10 °C and >2.5 M at 37 °C) and with ln [KCl] (~0.30–0.80 M at 10 °C and ~0.48–0.80 M at 37 °C) (Fig 3).

The exact dependences of k_d on [perturbant] in the transition regions depend on the relationship between the individual rate constants that comprise k_d: k₋₂, k₃, and k₋₃. There are two possible scenarios: either all three terms (1 + K₃ + k₋₂/k₋₃) contribute to the denominator of k_d (eq 1), or only two terms (1 + K₃) contribute to the denominator of k_d (eq 2a). These scenarios are considered below for the [urea] and [KCl] upshifts.

i) Intermediate urea concentrations: Evidence that an additional kinetically significant intermediate (I₃) may exist between I₂ and RP_o

We initially attempted fits of ln k_d versus [urea] (Fig 3a) to eq 6 (Methods), in which we assume that only the expression 1+ K₃ (and not k₋₂/k₋₃) contributes to the denominator of k_d throughout the entire range of urea concentrations studied (using values of k₋₂, K₃, and dlnK₃/d[urea] in Table 3 for the fits). It is visually apparent that these fits, shown as dashed lines in Fig 3a, are not optimal. While the fits are good at low and high [urea], the fitted curves lie systematically and significantly above the data points at intermediate [urea] (i.e. k_d approaches the plateau values of k₋₂ at high [urea] more slowly than predicted by the fits). While this discrepancy exists for both the 10 and 37 °C data sets, it is much more pronounced at 37 °C.

One possible reason for this discrepancy is that the k₋₂/k₋₃ term contributes significantly to k_d in this range of urea concentrations. To test this possibility, the data in Figure 3a were refit to eq 5 (Methods), in which the k₋₂/k₋₃ term is included. The fits to eq 5, shown as solid lines, clearly agree with the experimental data at intermediate urea concentrations better than the fits to eq 6. Values of k₋₃^o (the value in Dissociation Buffer in the absence of urea) and dlnk₋₃/d[urea] for 10 and 37 °C determined from these fits are given in Table 3.

One interesting feature of these fits is that the resultant value of k₋₃^o at 10 °C (3.3 (± 1.0) × 10⁻² s⁻¹) is larger than the value at 37 °C (1.1 (± 0.7) × 10⁻² s⁻¹). This difference results from the fact that the discrepancy between the data and the fit to eq 6 for the 37 °C data set is larger than that for the 10 °C data set; thus, the 37 °C data set requires a larger value of k₋₂/k₋₃ in the denominator of the expression for k_d to correct for the discrepancy. The resulting negative activation energy for k₋₃ (E_{a (−3)} ~ −7 kcal/mol, based on a two-point fit) implies that, in the context of this analysis, k₋₃ is not an elementary rate constant. If k₋₃ were in fact non-elementary, it would contain one or more additional equilibrium steps, resulting in the following minimal mechanism:

$$\mathrm{R}+\mathrm{P}\underset{{\mathrm{k}}_{-1}}{\overset{{\mathrm{k}}_1}{\rightleftarrows }}{\mathrm{I}}_1\underset{{\mathrm{k}}_{-2}}{\overset{{\mathrm{k}}_2}{\rightleftarrows }}{\mathrm{I}}_2\underset{{{\mathrm{k}}_{-3}}^{*}}{\overset{{\mathrm{k}}_3}{\rightleftarrows }}{\mathrm{I}}_3\underset{{\mathrm{k}}_{-4}}{\overset{{\mathrm{k}}_4}{\rightleftarrows }}\mathrm{R}{\mathrm{P}}_{\mathrm{o}}$$ (Mechanism V)

where k₃ ≫ k₋₂ (rapid equilibrium in I₂ ⇄ I₃) and ${\mathrm{k}}_4\gg {\mathrm{k}}_{-3}^{*}$ (rapid equilibrium in I₃ ⇄ RP_o). The quantity k₋₃ from Mechanism I (RP_o → I₂) would be a composite rate constant containing ${\mathrm{k}}_{-3}^{*}$, k₄, and k₋₄.

From the fits of the data to eq 5, the [urea]-dependence of I₂ → RP_o (dlnk₃/d[urea] = −2.2 ± 0.2 M⁻¹ at 37 °C) is larger in magnitude than that of the reverse process RP_o → I₂ (dlnk₋₃/d[urea] = 1.1 ± 0.2 M⁻¹). While the [urea]-dependence of RP_o → I₂ (k₋₃) could conceivably be distributed between I₃ → I₂ (k₋₃^*) and I₃ ⇄ RP_o (K₄ = k₄/k₋₄) in the context of Mechanism V, we assume that the [urea]-dependence of k₋₃ is wholly contained in k₋₃^* for the following reason. The ratio of the calculated values of dlnk₃/d[urea] and dlnk₋₃/d[urea] places roughly 70% of the overall [urea]-dependence of I₂⇄ RP_o in k₃; this ratio is typical of the two-state folding of a globular protein, for which the forward rate constant (k_fold) generally contains ~70% of the overall [urea] dependence, with the back rate constant (k_unfold) providing the remaining ~30% ³¹. Since the forward elementary rate constant k₃ contains 70% of the overall [urea]-dependence, we surmise that the corresponding back direction elementary rate constant k₋₃^* contains the remainder of the [urea]-dependence. The extension of this assumption is that the folding transition in RNAP implied by the [urea]-dependence is wholly contained within ${\mathrm{I}}_2\rightleftarrows {\mathrm{I}}_3\left({{\mathrm{K}}_3}^{*}={\mathrm{k}}_3/{\mathrm{k}}_{-3}^{*}\right)$.

ii) Intermediate KCl concentrations

For the [KCl] upshift experiments, we find that eq 6 adequately models the dependence of ln k_d on ln [KCl] throughout the range of KCl concentrations studied. For the fits of the data to eq 6, shown as solid lines in Fig 3b, we used the values of k₋₂ and K₃^o in Dissociation Buffer at 37 and 10 °C determined from the fits of the [urea] upshift data (Table 3). As detailed in the Methods Section, the best fits to the data necessitated the inclusion of a small temperature dependence of the equilibrium constant for the interaction of Mg²⁺ with the DNA phosphate backbone.

Fits of the [KCl] upshift data (Fig 3b) to eq 5 (which includes the k₋₂/k₋₃ term in the expression for k_d; eq 1) did not improve the quality of the fit (not shown), suggesting that the quantity k₋₂/k₋₃ does not significantly contribute to k_d at any KCl concentration. Use of eq 6 is consistent with the fact that the large [salt]-dependence of I₂ ⇄ RP_o (K₃ = k₃/k₋₃) likely stems from the formation of a new interface between RNAP and DNA. In general, for the formation of a protein-DNA interface, the dissociation-direction rate constant (the breaking of the interface, concurrent with the re-association of salt cations with the DNA phosphate backbone) is expected to be much more salt dependent (by roughly 6-fold ³⁶) than the forward-direction rate constant (in our case making Sk₋₃ ≈ 6Sk₃). Thus, k₋₂/k₋₃ never becomes significant compared to K₃ while K₃ still measurably contributes to k_d because K₃ (= k₃/k₋₃) is much greater than k₋₂/k₋₃ at low [KCl] and both terms decrease with similar [KCl]-dependences (Sk_d ≈ Sk₋₃). This is demonstrated in Figure 4, which shows the values of K₃ and k₋₂/k₋₃ predicted by the parameters determined from our fits throughout the range of salt concentrations studied. In contrast to the [KCl] upshifts, the k₋₂/k₋₃ term does become significant in our analysis of the [urea] upshifts because most of the [urea]-dependence of K₃ is contained in k₃ (~70%). Thus, while K₃ is much larger than k₋₂/k₋₃ at low [urea], and though both quantities decrease with increasing [urea], the [urea]-dependence of K₃ is much larger than that of k₋₂/k₋₃, and the two terms become comparable at an intermediate urea concentration (Figure 5).

Figure 4.

Predicted values of the terms in the denominator of the general expression for k_d (= k₋₂/(1 + K₃ + k₋₂/k₋₃); eq 1) as functions of ln [KCl] at 37 °C (a) and 10 °C (b). k₋₂/k₋₃ is shown as a dashed line, K₃ (= k₃/k₋₃) is shown as a solid line, and unity is shown as a horizontal dotted line. Values of K₃ were calculated throughout the range of [KCl] shown from the values of K₃^o in DB (Table 3) and eq 9–eq 11 in the text. Values of k₋₃ used to calculate k₋₂/k₋₃ were calculated from values of k₋₃^o (Table 3) and eq 9–eq 11 in the text (with K₃ in the equations replaced by k₋₃). The value of Sk₋₃ ^−Mg used in eq 9 for calculating k₋₃ was 7.9 (assuming that Sk₋₃ is ~(6/7)SK₃; see Analysis Section). Values of k₋₂ used to calculate k₋₂/k₋₃ were calculated from the plateau values of k_d in Figure 3b (Table 3).

Figure 5.

Values of the terms in the denominator of the general expression for k_d (= k₋₂/(1 + K₃ + k₋₂/k₋₃); eq 1) as functions of [urea] at 37 °C (a) and 10 °C (b). k₋₂/k₋₃ is shown as a dashed line, K₃ (= k₃/k₋₃) is shown as a solid line, and unity is shown as a horizontal dotted line. Values of K₃ were calculated throughout the range of [urea] shown from the values of K₃^o and dlnK₃/d[urea] (Table 3) and eq 7 in the text. Values of k₋₃ used to calculate k₋₂/k₋₃ were calculated from values of k₋₃^o and dlnk₋₃/d[urea] (Table 3) and eq 8 in the text. Values of k₋₂ used to calculate k₋₂/k₋₃ were calculated from the plateau values of k_d in Figure 3a (Table 3).

Although it is likely that the [salt]-dependence of the composite rate constant for RP_o → I₂ is much larger than that for I₂ → RP_o, the individual contributions of I₂ ⇄ I₃ and I₃ ⇄ RP_o in Mechanism V to the overall [salt]-dependence of I₂ ⇄ RP_o cannot be determined from our data. Since the [salt]-dependence of k_d is assumed to result from the formation of a new RNAP-DNA interface, which is, in turn, likely coupled to the folding of a region of RNAP implied by the [urea]-dependence, we would expect most, if not all, of the [salt]-dependence of k_d to reside in the conversion of I₃ to I₂.

DISCUSSION

The large [urea]- and [salt]-dependences of ${\mathrm{I}}_2\stackrel{{\mathrm{K}}_3}{\rightleftarrows }\mathrm{R}{\mathrm{P}}_{\mathrm{o}}$ are consistent with the proposed large-scale folding transition late in open complex formation to form a new RNAP-DNA interface

We previously interpreted the large increase in the rate of dissociation of RNAP-λP_R open complexes with increasing [urea] as reflecting the large-scale burial of polar amide surface (corresponding to the folding of ~120 amino acid residues) in the conversion of the transition state (I₁-I₂)^‡ into RP_o ¹¹. We proposed that the major folding process in which this surface is buried is the transition of disordered regions in the C-terminus of the β’ subunit, including parts of the downstream jaw of RNAP, to an ordered state, and that this transition occurs in I₂ ⇄ RP_o (K₃ in Mechanism I) ¹¹. (Over 100 conserved residues in this region of the C-terminus of β’ are predicted to be intrinsically disordered in free RNAP by the computer algorithm PONDR (Predictor of Naturally Disordered Regions ^{37; 38}).) The present study corroborates this large [urea] effect and provides strong evidence (see Analysis Section) that the folding transition does in fact occur in the conversion of I₂ to RP_o. Our deduction that the equilibrium constant K₃ for I₂ ⇄ RP_o is also strongly [salt]-dependent implies that a new RNAP-DNA interface is formed in the step. Located at the downstream end of the active site channel, the downstream jaw appears ideally positioned to fold onto the downstream DNA in RP_o formation, an interaction that could be the origin of the large [salt]-dependence of K₃.

The lack of significant [urea] and [salt] effects on ${\mathrm{I}}_1\stackrel{{\mathrm{K}}_2}{\rightleftarrows }{\mathrm{I}}_2$ indicate no change in the exposure of polar amide surface to the solvent and no net release/uptake of salt ions in this bottleneck step

We previously reported that the rate constant k₂ for I₁ → I₂ is independent of urea concentration ¹¹. Based on the analysis of our current results described above, we deduce that the rate constant k₋₂ for I₂ → I₁ and thus the equilibrium constant K₂ (= k₂/k₋₂) for I₁ ⇄ I₂ are also independent of urea concentration. The lack of a measurable effect of [urea] on K₂ suggests that there is no significant net change in the amount of polar amide biopolymer surface exposed to the solvent, such as would result from a folding/unfolding transition in a region of RNAP, in I₁ ⇄ I₂. We also deduce that k₋₂ is independent of salt concentration. In a separate study, we find that k₂ is only slightly affected by salt concentration (dlnk₂/dln[KCl] = Sk₂ ~ −1 in the absence of Mg²⁺) (Kontur et al. in prep). Thus, K₂ has only a slight dependence on salt concentration (SK₂ ~−1), revealing that no significant net uptake or release of ions occurs in I₁ ⇄ I₂, such as would result from the burial/exposure of DNA phosphates and cationic groups on RNAP in the formation/disruption of an RNAP-DNA interface. The lack of significant [urea] or [salt] effects on K₂ is surprising, as the interconversion of I₁ and I₂ is the rate-limiting bottleneck step in both the formation and dissociation of open complexes and would therefore be expected to involve large-scale conformational changes in RNAP and/or DNA. These findings lead us to propose that the major conformational change in I₁ ⇄ I₂ may occur within the active site channel of RNAP, largely shielded from the solution (and thus solute-inaccessible). This proposal is consistent with DNA backbone footprinting experiments ^{3; 17}, which reveal that both strands of the DNA are protected from cleavage from the −10 hexamer to ~+15 in both I₁ and RP_o.

The strongly endothermic steps in the conversion of I₁ to RP_o may signify DNA opening

At λP_R, DNA opening occurs at some point or points in the steps I₁ ⇄ I₂ ⇄ RP_o ^{3; 17}. DNA melting is a highly endothermic process (ΔH^o_obs = ~5 kcal/(mol base pair) for converting a duplex to partially stacked single strands at 20 °C ³⁹). Thus, the step(s) in Mechanism I in which melting occurs is (are) expected to be characterized by a large positive enthalpy change. Our previous and current results suggest that the latter two steps of Mechanism I, I₁ ⇄ I₂ and I₂ ⇄ RP_o, are both accompanied by large positive enthalpy changes. [ΔH^o₍₂₎ = 24 kcal/mol, based on the activation energy of k₂ ⁹ and a two-point estimate of the activation energy of k₋₂; see Analysis Section. ΔH₃^o for I₂ ⇄ RP_o may exceed ~45 kcal/mol at low temperatures; see below.] Is DNA opening distributed to some extent between I₁ ⇄ I₂ and I₂ ⇄ RP_o?

Indirect experimental evidence suggests that local DNA melting occurs in discrete steps for the Bacillus subtilis RNAP ^{40; 41}, as well as for mutant ^{42; 43} and wild type ^{21; 44; 45} E. coli RNAP. However, the mechanism of DNA opening and the precise temporal sequence of opening events have not been established for any multi-subunit RNAP at any promoter. We propose that DNA opening by E. coli RNAP at the λP_R promoter may be distributed between I₁ ⇄ I₂ and I₂ ⇄ RP_o. The large activation energy and slow kinetics of I₁ → I₂ are consistent with the initiation of DNA opening in the −10 region, and the large positive enthalpy change of I₂ ⇄ RP_o may reflect further opening downstream to +3. We are currently developing [KCl] upshift experiments in conjunction with MnO4⁻ footprinting reactions to test this prediction.

Evidence for an additional step in the mechanism of open complex formation

As detailed in the Analysis Section (and demonstrated in Fig 3a), the dependence of k_d on [urea] between ~1.5 and 3.5 M urea at 10 °C and above ~2.5 M urea at 37 °C provides evidence for the possible existence of an additional kinetically significant intermediate (I₃) late in the mechanism of open complex formation:

$$\mathrm{R}+\mathrm{P}\underset{{\mathrm{k}}_{-1}}{\overset{{\mathrm{k}}_1}{\rightleftarrows }}{\mathrm{I}}_1\underset{{\mathrm{k}}_{-2}}{\overset{{\mathrm{k}}_2}{\rightleftarrows }}{\mathrm{I}}_2\underset{{{\mathrm{k}}_{-3}}^{*}}{\overset{{\mathrm{k}}_3}{\rightleftarrows }}{\mathrm{I}}_3\underset{{\mathrm{k}}_{-4}}{\overset{{\mathrm{k}}_4}{\rightleftarrows }}\mathrm{R}{\mathrm{P}}_{\mathrm{o}}$$ (Mechanism V)

In the context of this mechanism, the folding transition in RNAP and the formation of a new RNAP-DNA interface in I₂ ⇄ RP_o likely occurs in I₂ ⇄ I₃ and not in I₃ ⇄ RP_o (see Analysis Section).

The conversion of I₂ into RP_o is characterized by a large positive enthalpy change, but we cannot conclusively divide the thermodynamics of this step between the formation of I₃ and its conversion to RP_o. The activation energy of the composite rate constant k₋₃ for RP_o → I₂ (E_{act (−3)}) is ~−7 kcal/mol (based on a two-point determination using the values of k₋₃ at 10 and 37 °C from Table 3). Because of this negative activation energy, the conversion of I₃ into RP_o (K₄ = k₄/k₋₄) must be highly endothermic, although we lack sufficient information (such as the activation energy for the elementary rate constant k₋₃^* (I₃ → I₂)) to conclusively determine the thermodynamics of K₃^* (= k₃/k₋₃^* for I₂ ⇄ I₃).

An analysis of the thermodynamics of folding for various proteins indicates that the value of T_H (the temperature at which ΔH^o = 0) is typically low (0–10 °C) (R. Saecker, unpublished data). We previously found that k_d is characterized by a large negative activation energy at low temperatures (E_a(d) = ~−35 kcal/mol at 7 °C ¹³ and ~−30 kcal/mol between 10 and 15 °C ⁸), which implies a large positive enthalpy change for the conversion of I₂ to RP_o at low temperatures (ΔH^o₍₃₎ = ~45 kcal/mol at 7 °C, calculated from E_{a (d)} and E_{a (−2)} (Analysis Section)). If the T_H of the folding step in open complex formation is near 7 °C (by analogy to the T_H values for protein folding), then this folding step (predicted to be part of I₂ ⇄ I₃) would not contribute significantly to this large enthalpy change. Thus, the majority of the large enthalpy change in I₂ ⇄ RP_o is likely in I₃ ⇄ RP_o and not in I₂ ⇄ I₃. In this scenario, if the enthalpy changes do reflect DNA opening, the two steps in which opening occurs are I₁ ⇄ I₂ and I₃ ⇄ RP_o, separated by the folding of a region of RNAP to form a new interface with the promoter DNA in I₂ ⇄ I₃:

$$\mathrm{R}+\mathrm{P}\stackrel{\text{interface formation}}{\rightleftarrows }{\mathrm{I}}_1\stackrel{\text{DNA opening}}{\rightleftarrows }{\mathrm{I}}_2\stackrel{\text{RNAP folding/interface formation}}{\rightleftarrows }{\mathrm{I}}_3\stackrel{\text{DNA opening}}{\rightleftarrows }\mathrm{R}{\mathrm{P}}_{\mathrm{o}}$$ (Mechanism VI)

We are currently testing this proposed mechanism with RNAP and DNA variants and with MnO₄⁻ footprinting experiments following upshift to high concentrations of KCl.

MATERIALS AND METHODS

Buffers

Storage Buffer for RNAP holoenzyme contained 50% glycerol (v/v), 10 mM Tris-HCl (pH 7.5 at 4 °C), 100 mM NaCl, 0.1 mM DTT, and 0.1 mM Na₂EDTA. Dissociation Buffer (DB) contained 10 mM (10.7 mm (millimolal)) MgCl₂, 41 mM (44 mm) Tris-HCl buffer (pH 8.0 at temperature of experiment), 884 mM (948 mm) glycerol, 1 mM (1mm) DTT, 100 µg/mL BSA, 13 mM (13.9 mm) NaCl, at least 120 mM (129 mm) KCl, and the final desired dissociation concentration of urea or additional KCl. In [urea] upshift experiments, concentrations of all species were held constant on the molal scale. In [KCl] upshift experiments, concentrations of all species were held constant on the molar scale. Wash Buffer contained 0.1 M NaCl, 10 mM Tris-HCl (pH 8.0 at room temperature), and 0.1 mM Na₂EDTA.

Wild-type Eσ⁷⁰ RNA polymerase holoenzyme

E. coli K12 wild type RNA polymerase holoenzyme was purified as described ⁴⁶ and stored in storage buffer in 500 µL samples at −70 °C. All RNAP concentrations reported here refer to active concentrations, determined as described ⁶. Individual samples of RNAP used were 45–60% active.

λP_R promoter DNA

A DNA fragment containing the λP_R promoter was obtained from the plasmid pBR81 and labeled at the 3’ end with ³²P as described ⁴⁷. The resulting blunt-ended fragment contains the λP_R wild type sequence (from positions −60 to +20, relative to the transcription start site) centrally located in a DNA fragment extending from position −115 to +76. The specific activity of the fragment was generally ~10¹⁷ cpm/mole.

[Solute] upshift-induced dissociation kinetics

The irreversible kinetics of dissociation of RNAP-promoter DNA open complexes were measured at 10 and 37 °C using either manual mixing or rapid mixing, and nitrocellulose filter binding. Dissociation was initiated by addition of either urea or additional KCl, and the polyanionic competitor heparin.

i) Manual mixing experiments

RNAP (final concentration 6–15 nM) and DNA (final concentration 0.05–0.5 nM) were combined in DB and allowed to associate to equilibrium or completion either at the temperature at which dissociation was to occur or at room temperature. The preformed open complexes were incubated at the temperature of dissociation for at least 20 minutes before dissociation was initiated. (Longer times of incubation had no effect on the kinetics of the process.) At time t = 0, the reaction was combined (in ≤ 10 s) with an equal volume of DB containing heparin and sufficient urea or additional KCl to obtain the final concentration of perturbant for the dissociation reaction (and 100 µg/mL heparin) for a final volume of 1–1.2 mL. At given time points, 100 µL of the reaction was filtered through nitrocellulose.

ii) Rapid quench mixing experiments

RNAP (final concentration 5–30 nM) and DNA (final concentration 0.05–0.5 nM) were combined in DB and allowed to associate to completion at room temperature (30–60 min). Samples of these pre-formed open complexes in DB and of DB containing heparin (final concentration 100 µg/mL) and either urea or additional KCl were loaded into sample ports of a rapid mixer (Chemical-Quench-Flow Model RQF-3; KinTek Co., Austin, TX) where they were incubated at the final temperature of dissociation for at least five minutes. A water bath was used to regulate the temperature of the reaction loops in the apparatus (monitored by a Fluke 51K/J temperature probe). At time zero, known (approximately equal) volumes of the two samples were rapidly mixed (in less than 20 ms) in the reaction loop, resulting in final concentrations of 100 µg/mL heparin and the reported dissociation concentrations of urea or KCl. The solutions used to push the two reactant solutions together matched the reactant solutions in composition. At time t, the reaction was rapidly combined with ‘quench solution’ (a buffered low [KCl] solution), effectively stopping the dissociation reaction by diluting perturbant concentrations to 0.08–0.12 M KCl and <1.5 M urea at room temperature. The quenched sample was collected and filtered through nitrocellulose at room temperature.

Nitrocellulose filter binding assays

Nitrocellulose filter binding assays were performed as described ¹¹. As nitrocellulose retains RNAP but not dsDNA, the only radioactive DNA remaining on the nitrocellulose after filtering and rinsing with Wash Buffer is that still complexed with RNAP. For manual mixing reactions, the total counts per minute filtered (cpm_TOT, generally ~1000–3500 cpm) was determined by spotting 20 µl from the reaction mixture onto a dried nitrocellulose filter. For rapid mixing reactions, cpm_TOT was determined by performing a reaction and applying the entire expelled sample to three dried nitrocellulose filters. Background retention of radiolabeled DNA on filters (cpm_bkgd) was determined by filtering an aliquot of the reaction mixture lacking RNAP. Filter efficiency (FE; the fraction of label retained on a filter under conditions where all promoter DNA in solution is complexed as open complexes) for a given perturbant concentration was determined by dividing the extrapolated intercept from a reaction performed at 37 °C by cpm_TOT from the reaction. Filter efficiencies were generally ~0.70–0.95, and were not found to be significantly affected by perturbant up to 0.24 M KCl and 1.5 M urea. (All higher concentrations of perturbant were diluted to lower perturbant concentrations before filtering). The observed fraction of promoter DNA in the form of open complexes at a given time point (θ_obs) was determined by dividing the counts per minute (cpm_t = cpm_obs − cpm_bkgd) by the total counts per minute, cpm_TOT. θ_obs was corrected for filter efficiency to determine the fraction of promoter DNA capable of binding to RNAP in the form of open complexes, ${\mathrm{\theta }}_{\mathrm{t}}(=\frac{1}{\mathrm{F}\mathrm{E}}{\mathrm{\theta }}_{\text{obs}})$.

DATA ANALYSIS

Fitting of dissociation data to single-exponential decay

The observed rate constant (k_d) for the irreversible dissociation of open complexes was determined by fitting θ_t versus time for a given perturbant concentration to a single-exponential decay equation:

$${\mathrm{\theta }}_{\mathrm{t}}={\mathrm{\theta }}_{\mathrm{t}}^{\mathrm{o}}{\mathrm{e}}^{-{\mathrm{k}}_{\mathrm{d}}\mathrm{t}}$$ (4)

where ${\mathrm{\theta }}_{\mathrm{t}}^{\mathrm{o}}$ is the value of θ_t at time t = 0

Dependences of ln k_d on [urea] and on ln [KCl]

Expressions for the dependence of ln k_d on [perturbant] are as follow (depending on whether k₋₂/k₋₃ is significant compared to K₃; see eq 1 and eq 2):

$$\text{ln}{\mathrm{k}}_{\mathrm{d}}=\text{ln}{\mathrm{k}}_{-2}-\ln \left(1+{\mathrm{K}}_3+\frac{{\mathrm{k}}_{-2}}{{\mathrm{k}}_{-3}}\right)\left(\text{based on eq 1}\right)$$ (5)

$$\text{ln}{\mathrm{k}}_{\mathrm{d}}=\text{ln}{\mathrm{k}}_{-2}-\text{ln}\left(1+{\mathrm{K}}_3\right)\left(\text{based on eq 2a}\right)$$ (6)

where both K₃ and k₋₃ are functions of KCl and urea concentration.

The expressions for K₃ and k₋₃ as functions of [urea] in eq 5 and eq 6 are (assuming that ln K₃ and ln k₋₃ are both linearly dependent on [urea]):

$${\mathrm{K}}_3={{\mathrm{K}}_3}^{\mathrm{o}}\text{exp}\left(\frac{\text{dln}{\mathrm{K}}_3}{\mathrm{d}\left[\text{urea}\right]}\left[\text{urea}\right]\right)$$ (7)

$${\mathrm{K}}_{-3}={{\mathrm{K}}_{-3}}^{\mathrm{o}}\text{exp}\left(\frac{\text{dln}{\mathrm{k}}_{-3}}{\mathrm{d}\left[\text{urea}\right]}\left[\text{urea}\right]\right)$$ (8)

where K₃^o and k₋₃^o are the values of K₃ and k₋₃ in DB in the absence of urea.

K₃ was determined as a function of [KCl] according to:

$$\text{ln}{\mathrm{K}}_3=\text{ln}{{\mathrm{K}}_3}^{\mathrm{o}}-{{\text{SK}}_3}^{-\text{Mg}}\text{ln}\left(\left[\text{KCl}\right]/0.120\right)-\left(\frac{{{\text{SK}}_3}^{-\text{Mg}}}{0.88}\right)\text{ln}({\mathrm{S}}^{120\text{mM}}/{\mathrm{S}}^{[\text{KCl}]})$$ (9)

where:

$$\begin{array}{c}{{\mathrm{K}}_3}^{\mathrm{o}}\text{is the value of}{\mathrm{K}}_3\text{in DB}\hfill \\ \mathrm{S}{{\mathrm{K}}_3}^{-\text{Mg}}\text{is the value of}\mathrm{S}{\mathrm{K}}_3\mathrm{in\; the\; absence\; of}{\text{Mg}}^{2+}\left(\mathrm{S}{{\mathrm{K}}_3}^{-\text{Mg}}=-9.2\left(\text{Kontur et al., in prep}\right)\right)\hfill \\ {\mathrm{S}}^{\left[\text{KCl}\right]}=0.5(1+{\left(1+4{\mathrm{K}}_{\text{obs}}^{\text{Mg}}\left[{\text{Mg}}^{2+}\right]\right)}^{0.5})\mathrm{at\; the\; KCl\; concentration\; being\; considered}\hfill \end{array}$$ (10)

${\mathrm{K}}_{\text{obs}}^{\text{Mg}}$ is the equilibrium constant for the association of Mg²⁺ with the DNA phosphate backbone. The best fits of the data at 10 and 37 °C necessitated using different expressions for ${\mathrm{K}}_{\text{obs}}^{\text{Mg}}$ as a function of [KCl], implying a temperature dependence of ${\mathrm{K}}_{\text{obs}}^{\text{Mg}}$ at a given KCl concentration:

$$\log {\mathrm{K}}_{\text{obs}}^{\text{Mg}}=-1.3\text{log}\left[\text{KCl}\right]+0.40\left(37°\mathrm{C}\right)$$ (11a)

$$\log {\mathrm{K}}_{\text{obs}}^{\text{Mg}}=-1.6\text{log}\left[\text{KCl}\right]+0.60\left(10°\mathrm{C}\right)$$ (11b)

Abbreviations used

RNAP

RNA polymerase

SK_obs = dlnκ_obs/dln[monovalent salt]

where κ_obs is a rate or equilibrium constant