Complete dissection of transcription elongation reveals slow translocation of RNA polymerase II in a linear ratchet mechanism

1Transcription constitutes the first and a central regulatory step for gene expression. During the process of RNA synthesis, RNA polymerase (RNAP) converts the energy from chemical catalysis of the nucleoside triphosphate (NTP) into mechanical translocation along the DNA template. Two classes of mechanisms have been offered to describe the mechanochemical coupling of transcription elongation. The first class, known as the ‘power stroke’ mechanism, suggests that the forward translocation of RNAP is directly driven by a chemical step such as the release of the pyrophosphate (PPi). The second class, known as the ‘Brownian ratchet’ mechanism, postulates that the polymerase oscillates back and forth on the DNA template between a pre- and a post-translocated state at the beginning of each nucleotide addition cycle, and that such thermally-driven motions are rectified to the post-translocated state by the incorporation of the incoming NTP. After extensive structural and biochemical investigations, it is now generally thought that multi-subunit RNAPs, including bacterial and eukaryotic enzymes, function through the Brownian ratchet mechanism. This mechanism received further support from single-molecule studies, which followed the dynamics of individual transcription elongation complexes (TECs). Nonetheless, in order to explain the relationship between the elongation velocity and the external force applied to RNAP obtained from single-molecule experiments, the classical linear ratchet mechanism (Figure 1) had to be modified such that the incoming NTP must also bind to the pre-translocated TEC (Figure 1—figure supplement 1). In the pre-translocated TEC, the primary nucleotide binding site is occupied by the 3′-end of the nascent transcript. Thus, the branched Brownian ratchet scheme necessarily requires a secondary NTP binding site on the enzyme. However, the precise location of this secondary site and the mechanism by which the NTP is transferred to the primary site remain poorly defined.

2Pausing is an off-pathway process that plays crucial roles in the regulation of transcription elongation. In one view of the mechanisms of transcriptional pausing, RNAP first enters an elemental pause state, whose structural evidence was recently presented in bacterial RNAP. However, similar evidence is lacking for eukaryotic polymerases. These elemental pauses can be subsequently stabilized into longer-lived pauses by the formation of a hairpin structure in the nascent RNA transcript or by RNAP backtracking. The backtracking process is caused by upstream movements of the polymerase, displacing the 3′-end of the nascent RNA away from the active site into the secondary channel of the enzyme. An alternative view poses that most pauses are attributed to backtracking, which can be described as a one-dimensional random walk of the enzyme along the DNA template. RNA synthesis resumes when the polymerase diffusively realigns its active site with the 3′-end of the transcript.

3Both the nucleotide addition phase and the pausing phase are closely regulated by conserved structural motifs near the active center of the polymerase, namely the bridge helix and the trigger loop (TL). In order to understand the mechanism of transcription and its regulation, it is important to achieve a detailed description of both on- and off-pathway kinetics of the elongation reaction. Previous efforts to dissect the kinetic scheme of transcription elongation have assumed that the forward and reverse translocation steps of the Brownian ratchet occur in rapid equilibrium relative to the chemical steps in the nucleotide addition cycle. However, the assumption of fast translocation equilibrium has never been experimentally validated. In fact, recent studies suggested that the translocation step may be partially rate-limiting for the nucleotide addition cycle, which gives rise to the heterogeneous elongation rates at different template positions.

4In this work, we sought to achieve a comprehensive kinetic characterization of transcription elongation without making any assumption about the rate-limiting mechanism of the reaction. We used an optical tweezers assay to follow the transcription trajectories of single yeast RNA polymerase II (Pol II) molecules under a variety of conditions, including varying NTP concentrations, assisting and opposing applied forces, and different tracks (bare and nucleosomal DNA). In vivo, eukaryotic DNA is organized around histone octamers to form nucleosomes, which impose physical barriers to transcription elongation. We have previously demonstrated that a transcribing Pol II cannot actively unravel a wrapped nucleosome. Instead, the polymerase pauses and waits until the local nucleosomal DNA spontaneously unwraps and permits Pol II to advance. Here we used the nucleosomal barrier as a tool to specifically perturb forward translocation of a transcribing Pol II and separately measured the forward and reverse translocation rates. Surprisingly, we found that the forward translocation rate is of the same order of magnitude as the catalysis rate, in contradiction to previous assumptions of fast translocation. This finding reveals that translocation and catalysis together constitute the rate-limiting steps in the nucleotide addition cycle. As a consequence, we were able to rationalize the observed force–velocity relationship of the enzyme with a linear Brownian ratchet scheme in which the incoming NTP only binds to the post-translocated TEC, thus reconciling bulk and single-molecule data and arriving at a unifying view of the transcription elongation process. We further obtained all the major kinetic parameters in the nucleotide addition phase and the pausing phase of the elongation cycle. The energy landscape for transcription elongation derived from these parameters shows that: (i) the enzyme thermodynamically favors the pre-translocated state to the post-translocated state; (ii) entry into the 1-basepair (bp) backtracked state is easier than into further backtracked states; and (iii) from the pre-translocated state, the enzyme thermodynamically favors the backtracked states, but kinetically favors forward translocation. We also applied this analysis to a TL mutant Pol II, Rpb1-E1103G, to quantitatively elucidate the roles of the TL in transcription elongation. Our results indicate that the conformational transitions of the TL control enzyme translocation, catalysis, and pausing, rendering it a vital target element for transcriptional regulation.

5The Brownian ratchet kinetic scheme for the nucleotide addition cycle of transcription elongation (Figure 1) can be simplified to: where k1 and k−1 are the forward and reverse translocation rate constants, k2 and k−2 are the NTP binding and dissociation rate constants, and k3 is the combined catalysis rate constant that includes NTP sequestration, bond formation, and PPi release. Because of the large equilibrium constant of transcription elongation and the very low PPi concentration (1 μM) in the buffer, k3 was considered essentially irreversible. Using the concept of net rate constants, we can replace the reversible rate constants between two adjacent states with a single net rate constant and re-write the above scheme as: and are the net rate constants for translocation and NTP binding, respectively, which are given by:

6The time the enzyme takes to finish one nucleotide addition cycle (τ) equals the step size of the polymerase (d = 1 nt) divided by the pause-free velocity (v), and also equals the sum of the inverse of each net rate:

7Plugging Equations 1 and 2 into Equation 3 yields the following expression for the pause-free velocity:

8We note that this expression is more general than those shown in previous studies, as it is derived without assuming local equilibration of translocation and NTP binding. In particular, we describe the kinetics of the translocation step with k1 and k−1, instead of a single equilibrium constant Kδ = k−1/k1. Such treatment is a prerequisite to explicitly determine the forward and reverse translocation rates. Equation 4 can be simplified to the Michaelis–Menten equation form:where, and.

9We followed the transcriptional dynamics of individual Pol II molecules with a dual-trap optical tweezers instrument. One laser trap holds a polystyrene bead attached to a stalled Pol II molecule, while the other trap holds another bead attached to the upstream DNA template (assisting force geometry; Figure 2A) or to the downstream template (opposing force geometry, not shown). Upon addition of NTP, transcription restarts, resulting in a change of the DNA tether length and thereby a variation of the force applied to Pol II. Single-molecule transcription trajectories were collected at a range of NTP concentrations (35 μM–2 mM) (Figure 2B,C). The relationship between pause-free velocity (v) and [NTP] for the wild-type enzyme fits well to Equation 5, with Vmax = 25 ± 3 nt/s and KM = 39 ± 12 μM (errors are SEM) (Figure 2D, gray line). We also examined the dynamics of the E1103G mutant Pol II, which is known to transcribe DNA at a faster overall velocity than the wild-type (Figure 2B,C). We found that the maximum pause-free velocity of the mutant is ∼1.5-fold higher than that of the wild-type, with Vmax = 38 ± 5 nt/s and KM = 62 ± 15 μM (Figure 2D, blue line).

10As shown in the example trajectories (Figure 2B,C), transcription elongation is punctuated by pauses of various durations. Pause density, ρpause, is defined as the average number of pauses per bp of template transcribed. As the concentration of NTP goes up, the pause-free velocity increases and the apparent ρpause, which counts pauses lasting longer than 1 s, decreases (Figure 2E). The same trend was also observed for the mutant Pol II (Figure 2F). The inverse relationship between v and ρpause indicates that elongation and pausing are in kinetic competition and that pausing occurs prior to NTP binding. Note that pausing has also been observed to occur after NTP binding at certain sequences for Escherichia coli RNAP; however, yeast Pol II does not seem to employ such mechanism. The pause-free velocities and apparent pause densities at various NTP concentrations are summarized in Table 1.

11Backtracking is a major mechanism for transcriptional pauses. We have previously modeled backtracking as a one-dimensional random walk of the enzyme along the DNA template. In this model, Pol II diffuses back and forth on DNA with a forward stepping rate constant kf and a backward stepping rate constant kb during a backtracked pause. These rate constants are dependent on the applied force (F, which is positive for assisting forces and negative for opposing forces) according to:where k0 is the intrinsic zero-force stepping rate constant of Pol II diffusing along DNA during backtracking, Δ is the distance to the transition state for each step (taken to be 0.5 bp, or 0.17 nm), kB is the Boltzmann constant, and T is the temperature (kBT = 4.11 pN·nm at 25ºC). The probability density of pause durations, ψ(t), is equivalent to the distribution of first-passage times for a particle diffusing on a one-dimensional lattice to return to the origin, and is given by:where I1 is the modified Bessel function of the first kind. We fit the distribution of pause durations for the wild-type enzyme on bare DNA to this model and extracted a characteristic k0 of 1.3 ± 0.3 s−1 (Figure 2—figure supplement 1, gray dashed line). Using the values of k0 and the applied force in our experiment (6.5 pN), we calculated kf and kb to be 1.7 ± 0.4 s−1 and 1.0 ± 0.3 s−1, respectively (Equations 6 and 7).

12Next, we investigated the transcriptional dynamics of Pol II through the nucleosome by loading a histone octamer on the 601 nucleosome positioning sequence (NPS) (Figure 2B,C, Figure 2—figure supplements 2–5). The wild-type enzyme displays a two-fold increase in the apparent pause density upon encountering the nucleosome (Table 2). The mean pause duration on nucleosomal DNA is significantly longer than that on bare DNA (Table 2; Figure 2—figure supplement 1). Similarly, the mutant Pol II displays higher pause density and longer pause duration in the presence of a nucleosome (Table 2).

13It has been shown that the nucleosomal DNA can spontaneously unwrap and rewrap around the histones. The increased pause duration of Pol II on nucleosomal DNA can be explained by rewrapping of the DNA downstream of a backtracked Pol II, which prevents the polymerase from diffusing back to the 3′-end of the nascent RNA to resume transcription. Because one bp of nucleosomal DNA fluctuates much faster (>1000 s−1; see ‘Materials and methods’ for the derivation) than Pol II stepping (∼1 s−1), the nucleosomal DNA in front of the polymerase reaches wrapping/unwrapping equilibrium between each backtracking step. It follows that the pause durations on nucleosomal DNA can be drawn from the same distribution as on bare DNA, except that the effective forward stepping rate is reduced by a factor, γu, corresponding to the fraction of time the local nucleosomal DNA is unwrapped, that is. The backward stepping rate kb is not affected by the nucleosome, because little histone transfer occurs in our experimental geometry where the DNA template is under tension and therefore the polymerase does not encounter any roadblock when it diffuses backward. The distribution of pause durations for wild-type Pol II on nucleosomal DNA can be correctly fit by this model with a γu value of 0.6 ± 0.2 (Figure 2—figure supplement 1, red dashed line).

14Having understood the effect of the nucleosomal barrier on the pausing dynamics, we then turned our attention to its effect on the on-pathway elongation kinetics. Interestingly, we found that the nucleosome also delays the transcribing enzyme by modulating its pause-free velocity. As the wild-type Pol II transcribes through nucleosomal DNA at saturating [NTP], its mean pause-free velocity decreases by 14% from 26.9 ± 0.8 nt/s to 23.2 ± 0.6 nt/s (Figure 3A). The mutant Pol II is even more dramatically slowed down by the nucleosome, with its mean pause-free velocity reduced by 35% from 39.8 ± 0.6 nt/s to 26.0 ± 0.7 nt/s (Figure 3B).

15We have previously shown that a transcribing Pol II cannot actively open a wrapped nucleosome; instead, the enzyme passively waits for the DNA immediately in front of it to spontaneously unwrap and then translocates forward through a locally unwrapped nucleosome. Since the fluctuations of local nucleosomal DNA occur orders of magnitude faster than the translocations of Pol II during backtracking, we assume that they are also much faster than the on-pathway translocation steps of Pol II. Under this assumption, local DNA reaches wrapping/unwrapping equilibrium before Pol II makes a translocation step and the forward translocation rate (k1) is effectively reduced by the fraction of time the local nucleosomal DNA is unwrapped (γu). The reverse translocation rate (k−1) is unlikely to be affected, again due to the lack of a roadblock against reverse translocation. Thus, according to Equation 5, the maximum pause-free velocity for nucleosomal DNA transcription is:

16In comparison, the maximum pause-free velocity for bare DNA transcription is:

17Using an optimal γu value of 0.6, we solved Equations 9 and 10 and obtained k1 = 112 ± 30 s−1 (indeed much slower than local DNA wrapping/unwrapping) and k3 = 35 ± 3 s−1 for the wild-type. Importantly, these values show that the forward translocation rate is only three times faster than the catalysis rate and, therefore, has a significant contribution to the overall elongation velocity. For the mutant Pol II, translocation becomes even slower than catalysis (k1 = 50 ± 4 s−1 and k3 = 195 ± 65 s−1). The mutant’s higher k3 compensates for its lower k1, rendering its overall velocity faster than that of the wild type. We note that these numbers were extracted by using the average values of the pause-free velocity and γu over the whole nucleosomal region. Such a simplifying treatment is based on the observations that both the pause-free velocity (Figure 3) and the local DNA wrapping equilibrium do not change substantially along the NPS.

18The pause density, ρpause, is governed by the kinetic competition between pause entry and elongation. Previously, an overall elongation rate, which includes translocation, NTP binding, and catalysis, was used in the expression for ρpause. A more accurate treatment is to use the elementary rate constant in the elongation pathway directly connected to pausing, which is the net rate constant for forward translocation, (Figure 1; Equation 2):where kb1 is the rate constant of entering the 1-bp backtracked pausing state. At saturating NTP concentrations ([NTP]>>k−1(k−2+k3)/(k2k3)), becomes equivalent to k1. Hencewhere ρpause(sat) is the pause density at saturating NTP concentration. In order to obtain a true pause density, the apparent ρpause needs to be corrected to include pauses shorter than 1 s that are missed by our pause detection algorithm. After such a correction (‘Materials and methods’), the total ρpause(sat) is 0.045 ± 0.012 bp−1. Solving Equation 12 yields kb1 = 5.3 ± 2.0 s−1. This value is approximately five times larger than subsequent backward stepping rates, which are force-biased stepping rates obtained from Equation 7 (kbn = 1.0 ± 0.3 s−1, n≥2). The difference between kb1 and kbn indicates that the first backtracking transition is easier to make than subsequent backtracking transitions. Using this value of kb1, along with the value of γu obtained above, we can predict a nucleosomal pause density of 0.035 ± 0.015 bp−1 for pauses longer than 1 s, which agrees with the experimental measurement (Table 2).

19We then compared the pausing kinetics between the wild-type and the mutant enzymes. Interestingly, on bare DNA, the mutation only affects the distribution of pauses that are shorter than 2 s (Figure 4A, p=0.003, Kolmogorov-Smirnov test). In contrast, the distributions of longer pauses are indistinguishable between the mutant and the wild-type Pol II (Figure 4—figure supplement 1, p=0.9). It is possible to rationalize this observation if the mutation selectively influences the kinetics of the first backtracking step (kb1 and/or kf1) without affecting subsequent backtracking steps, given that pauses of short durations involve small backtracking excursions and that entering the 1-bp backtracked state is distinct from entering longer backtracked ones (kb1 is different from kbn, n≥2). The first backward stepping rate (kb1) only influences the pause density but not the pause duration, while the first forward stepping rate (kf1) does affect the pause duration. Specifically, the increase in short pauses can be explained if the mutation increases kf1 and accelerates the return from a pause to active elongation. Indeed, Monte Carlo kinetic simulations show that setting kf1 to be larger than 4 s−1—2.4-fold higher than the wild-type value (1.7 ± 0.4 s−1; Equation 6)—can reproduce the experimentally observed pause duration distributions for the mutant Pol II on bare DNA (Figure 4A, blue dashed line) and nucleosomal DNA (Figure 4B, green dashed line, and Figure 4—figure supplement 2). Moreover, by comparing the experimentally measured and simulated pause densities using different kb1 values, we can set a lower bound for the mutant’s kb1 to be 2.8 s−1.

20Taken together, we have shown that the rate of entering the 1-bp backtracked state is higher than those of entering further backtracked states, and that the E1103G mutation modulates the transition kinetics between the 1-bp backtracked state and the pre-translocated state. Until now, kf1 and kb1 have been assumed to be identical with the other stepping rates during backtracking (kfn and kbn, n≥2). Our data here suggest that the first backtracking step should be treated differently, consistent with published structural data (see ‘Discussion’).

21We have determined the rates of forward translocation (k1) and catalysis (k3) in the nucleotide addition cycle and shown that they are comparable. What remains unknown is the reverse translocation rate k−1, which may also affect the elongation velocity under sub-saturating NTP conditions (Equation 4). To determine k−1, we examined the pause densities measured at various NTP concentrations. Equation 11 can be re-written as:where K = (k−2+k3)/k2. The total ρpause as a function of [NTP] fits well to Equation 13 (Figure 5A,B). Using the values of k1, k3, and kb1 determined above, we obtained k−1K equal to (4.7 ± 0.5) × 103 µM·s−1 and (2.5 ± 0.4) × 104 µM·s−1 for the wild-type and the mutant enzymes, respectively.

22We then revisited the relationship between the pause-free velocity and [NTP] (Figure 2D), which follows Michaelis–Menten kinetics. According to Equation 5, the Michaelis constant KM is expressed as:

23Plugging the values of KM, k1, k3, and k−1K into Equation 14 yields the values of K and k−1 for the wild-type Pol II: K = 9.2 µM and k−1 = 510 s−1. We could further calculate the translocation equilibrium constant, Kδ = [pre-translocated]/[post-translocated] = k−1/k1 = 4.6. This result indicates that the enzyme favors the pre-translocated state to the post-translocated one, in agreement with most previous reports. For the mutant enzyme, we could set an upper bound of K to be 100 µM and a lower bound of k−1 to be 210 s−1 (Figure 5—figure supplement 1). Assuming that the mutant shares a similar K value with the wild-type, we calculated k−1 to be ∼2700 s−1 and Kδ to be ∼54 for the mutant Pol II (see ‘Materials and methods’ for a discussion of this assumption).

24A central piece of evidence previously used to favor a branched kinetic scheme (Figure 1—figure supplement 1) over a simpler linear scheme (Figure 1) for the nucleotide addition cycle is the relationship between the pause-free velocity (v) and the applied force (F). However, in those studies, translocation was assumed to be in rapid equilibrium relative to catalysis. Having explicitly determined the translocation rates (k±1) and found that the forward translocation rate (k1) is comparable to the catalysis rate (k3), we went on to examine whether a linear kinetic scheme (Figure 1) is sufficient to explain the F–v relationship, which for such scheme can be expressed as:

25We assume that only the translocation transitions in the nucleotide addition cycle are force-sensitive and that the translocation rates depend on force according to the Boltzmann-type equation:, and, where δ is the distance to the transition state for forward translocation, the only unknown variable left in Equation 15. We measured the pause-free velocity at different applied forces for both wild-type and mutant enzymes and obtained values in good agreement with previously published single-molecule data (Figure 6A,B). The velocity of the wild-type enzyme shows a weak but detectable dependence on force, while the velocity of the mutant displays a much stronger force dependence. The F–v plots can be fit well to Equation 15 with δ of 0.46 ± 0.09 bp for the wild-type (Figure 6A) and 0.24 ± 0.05 bp for the mutant (Figure 6B). Therefore, it is indeed possible to explain the observed force–velocity relationship of transcription elongation with a classic, non-branched Brownian ratchet mechanism, in which NTP binding occurs after translocation.

26RNAP transcribes DNA through a multi-step kinetic pathway. The rate-limiting nature of the various steps in the nucleotide addition cycle has so far remained largely conjectural. Almost all the existing kinetic studies of transcription elongation relied on the major assumption that translocation and NTP binding follow rapid equilibrium kinetics. As a result, the catalytic step occurring after NTP binding has been assigned to be rate-limiting of the overall elongation reaction.

27The linear Brownian ratchet mechanism that assumes fast translocation equilibrium predicts that, as the NTP concentration increases, the force-sensitivity of the elongation velocity decreases and eventually vanishes, because the enzyme spends less time in the load-sensitive translocation steps. However, the F–v relationships of the enzyme obtained from optical tweezers studies have shown significant dependence of elongation velocity on external force even at saturating NTP concentrations, in contradiction to the above prediction. To account for this discrepancy, a modified, branched ratchet model was proposed in which the NTP must also bind to a secondary site on the polymerase in the pre-translocated configuration. Although the existence of such additional binding site may be rationalized by the downstream allosteric site, the ‘E’ site or pre-insertion site, or the tilted hybrid structure, whether it constitutes a significant pathway in the elongation reaction and how it is related to the primary nucleotide binding pathway remain obscure. More importantly, the branched model neglects the possibility that the translocation steps may not be as fast as assumed.

28In this study, we tested this possibility of slow translocation by placing a nucleosome in the path of the transcribing polymerase and directly determining the rates of forward and reverse translocation. Our analyses show that the forward translocation rate is in fact within the same order of magnitude as the catalysis rate. For the wild-type Pol II, k1 is only 2.5 times higher than k3 (Figure 7A; Table 3). For the E1103G mutant, k1 even becomes the slowest step in the nucleotide addition cycle (Table 3). Hence, the translocation step is one of the rate-limiting transitions during transcription elongation. Translocation and catalysis together control the overall elongation velocity. These findings naturally explain the observed F–v relationship: because the enzyme always spends a considerable amount of time in the force-sensitive pre-translocated state even at high [NTP], we should always expect a force-dependence of the velocity. Moreover, a lower k1 renders the velocity more sensitive to force, consistent with the experimental observation that the mutant Pol II shows a steeper F–v curve than the wild-type (Figure 6A,B). Therefore, our results demonstrate that a linear ratchet model can explain the transcriptional kinetics of Pol II and that it is not necessary to invoke a conceptually more complicated branched model, as long as the constraint of fast translocation equilibrium is relieved. Note that although our data argue against rapid oscillation of the ratchet, they still support the notion that the enzyme is able to spontaneously diffuse along the DNA between the pre- and post-translocated states, as suggested by the Brownian ratchet mechanism.

29We extracted the values of k1 and k3 by comparing the maximum pause-free velocities on bare DNA and nucleosomal DNA (Equations 9 and 10). In principle, k1 and k3 can also be determined by examining Vmax as a function of applied force:where. Using our data and the previously published data collected at saturating [NTP] (1 mM) and various forces (Figure 6), we fit the Vmax–F dependence to Equation 16 and obtained the values of k1 = 87 ± 61 s−1, k3 = 33 ± 8 s−1, and δ = 0.64 ± 0.58 bp for the wild-type Pol II, and k1 = 65 ± 37 s−1, k3 = 62 ± 32 s−1, and δ = 0.64 ± 0.50 bp for the mutant Pol II. Thus, the same qualitative conclusion that both translocation and catalysis are rate-limiting for the elongation reaction can be drawn from this alternative approach. Compared to the approach of using the nucleosomal barrier as a tool to determine k1 and k3, fitting the Vmax–F relationship involves one additional free parameter (δ) and the values are less constrained (larger errors). In the future, it is worthwhile to use either of these two approaches or both to test whether prokaryotic transcription also employs a linear ratchet mechanism.

30With the same transcript length, RNAP is able to move back and forth on the DNA template, forming different TEC configurations (Figure 7A,B). Each translocation state corresponds to a local energy minimum. Transitions between the pre- and post-translocated states, together with NTP binding and catalysis, constitute the active elongation pathway (Figure 7—figure supplement 1, green). The enzyme can also enter the pausing pathway by transiting from the pre-translocated state to the backtracked states (Figure 7—figure supplement 1, blue). The hyper-translocated states, in which the enzyme undergoes further forward translocation beyond 1 bp, are energetically unfavorable. The rate constants extracted from our single-molecule experiments translate into a free energy landscape for Pol II’s mechanical translocations and chemical transitions (Figure 7B, Figure 7—figure supplement 1; ‘Materials and methods’), which reveals many detailed features of the kinetics of Pol II transcription.

31First, the staircase shape formed by the energy minima of post-translocated, pre-translocated, and 1-bp backtracked states shows that the off-pathway backtracked states are thermodynamically more stable than the on-pathway states (Figure 7B). This feature confers the enzyme its propensity to enter the pausing pathway, which is the central mechanism for various types of transcriptional control, such as arrest, proofreading, co-transcriptional RNA folding, and recruitment of regulators.

32Second, the energy barrier from the pre-translocated to the 1-bp backtracked state is 2.5 kBT higher than the barrier from the pre-translocated to the post-translocated state, causing k1 to be more than 10 times faster than kb1. Thus, at the beginning of each nucleotide addition cycle, the pre-translocated TEC favors the catalysis-competent post-translocated state kinetically over the 1-bp backtracked state, even though it is thermodynamically more favorable to move in the opposite direction. This property ensures that pausing only occurs sporadically so that the transcript can be synthesized within a reasonable amount of time. In addition, the barriers between neighboring backtracked states are also relatively high, preventing the enzyme from backtracking too far, which could lead to transcriptional arrest.

33Third, the first backtracking step appears to be unique from further backtracking steps in two aspects. Kinetically, entering the 1-bp backtracked state is easier than entering subsequent backtracked states, as reflected by the difference between kb1 and kbn (n≥2). Such a difference is supported by structural data: the structure of an arrested Pol II complex suggests that backtracking beyond 1 bp is disfavored as it is sterically hindered by a ‘gating’ tyrosine (Rpb2-Y769). Thermodynamically, transiting from the pre-translocated state to the 1-bp backtracked state is favorable, while backtracking for more steps yields no additional energetic benefit. This result can also find structural support: the first backtracked nucleotide is stabilized by a binding pocket formed by several Pol II residues, whereas the second or third backtracked nucleotide makes no additional contact to the enzyme.

34Thus, our model depicts an enzyme with a delicate balance between active elongation and inactive pausing. This model can serve as a framework to study the effects of DNA sequence and nascent RNA structure on transcriptional dynamics. Moreover, this model may improve our understanding of the control of transcription fidelity. The 1-bp backtracked state is closely associated with the proofreading process of Pol II, as the enzyme in this location preferentially cleaves the 3′ dinucleotide of the RNA containing the mismatched base, empting the active site for NTP binding. It is possible that nucleotide misincorporation slows down forward translocation, thereby promoting the entry to the pausing pathway and the removal of the dinucleotide.

35It is worth noting that we cannot definitively rule out the alternative scenario in which the first unique pausing state corresponds to a non-backtracked intermediate. Nonetheless, no evidence has been found for the universal occurrence of such an intermediate in Pol II transcription. The interpretation that most pauses in Pol II transcription are caused by enzyme backtracking is more parsimonious, especially given the corroborating structural data mentioned above.

36The kinetic characterization of the E1103G mutant Pol II reveals that this TL mutation results in many modifications to the enzyme dynamics (Table 3). Between the pre-translocated state and the post-translocated state, the mutant is significantly more biased toward the former than the wild type (Figure 7B). This property, together with its lower forward translocation rate, renders the mutant’s elongation velocity more sensitive to perturbations of its forward translocation, such as an externally applied force (Figure 6B) or the presence of a nucleosomal barrier (Figure 3B). It has been shown that the inter-conversion between pre- and post-translocated states involves the transitions of the TL between an open conformation and a wedged conformation. It is plausible that the mutation modulates the enzyme’s translocation kinetics by altering the rates of transition between these two conformations.

37Furthermore, our analyses lead to the conclusion that the faster overall elongation velocity of the mutant is due to its much greater catalysis rate despite a slower translocation step. The increase of the catalysis rate is most likely due to a faster NTP sequestration step induced by the closure of the TL. The lack of hydrogen bonding between T1095 and the mutated E1103 residue may destabilize the open state of the TL and speed up its closure.

38The E1103G mutation also affects the pausing kinetics. Specifically, a decrease in the activation energy required to return from the first backtracked state to the pre-translocated state accelerates the recovery from a pause (Figure 7B). Consequently, the mutant populates the 1-bp backtracked state less than the wild-type. This property might affect the overall fidelity of transcription. It has been previously shown that E1103G mutation strongly promotes incorporation of non-cognate NMP and mismatch extension. The destabilization of the 1-bp backtracked state relative to the pre-translocated state in the E1103G mutant, established in this work, is consistent with its efficient mismatch extension and suggests that this mutation might also confer a defect in proofreading activity.

39Together, our results suggest that the dynamics of TL are involved in multiple phases of transcription elongation, including translocation, catalysis, and pausing. In vivo, various transcription factors and small molecules can directly manipulate the TL dynamics and regulate transcription elongation. For example, transcription factor IIS (TFIIS) stimulates the endonuclease activity of Pol II by replacing the TL with its zinc finger domain, and thus, rescues transcription elongation by creating a new 3′-end of the transcript at Pol II’s active site. In fact, the viability of yeast cells expressing only the E1103G mutant Pol II is strictly dependent on TFIIS. It is interesting to investigate how these trans-acting factors modify the rate-limiting mechanism and detailed kinetics of the elongation reaction. Finally, the elementary rate constants extracted from our analyses should provide a reference frame for future computational studies aiming to fully describe the molecular trajectory of a transcribing polymerase.

40Biotinylated wild-type and E1103G S. cerevisae Pol II (unphosphorylated C-terminal domain) were purified as previously described. The 3-kb DNA handle was prepared by PCR from Lambda DNA (NEB, Ipswich, MA) using a digoxigenin-labeled primer. The 574-bp DNA template was prepared by PCR from a modified pUC19 plasmid containing the 601 nucleosome positioning sequence (NPS). Each histone protein was recombinantly expressed and purified from E. coli, reconstituted to octamers, and loaded on the NPS-containing DNA using salt gradient dialysis.

41The transcription elongation complexes (TECs) were assembled by annealing a 9-nt RNA primer (IDT, Coralville, IA) to a 93-nt template DNA, incubating the hybrid with a biotinylated Pol II, and subsequently annealing a 96-nt complementary DNA using previously published sequences and procedures. The TEC was walked to a stall site by addition of ATP, CTP and GTP. In the assisting force geometry, the downstream end of the stalled TEC was ligated to the 574-bp DNA containing the 601 NPS (with or without a preloaded nucleosome), while its upstream end was ligated to the 3-kb DNA handle. In the opposing force geometry, the downstream end of the TEC was ligated to a 4-kb DNA amplified from Lambda DNA. The complexes were incubated with 2.1-μm streptavidin-coated beads (Spherotech, Lake Forest, IL), and DNA tethers were formed in a dual-trap optical tweezers instrument by attaching the digoxigenin-labeled DNA handle to a 2.1-μm anti-digoxigenin IgG-coated bead. In the assisting force geometry, Pol II and its upstream DNA were under tension, while no external force was applied to the downstream nucleosome (Figure 2A). The tension in the upstream DNA prevented intra-nucleosomal loop transfer and thus ensured that the nucleosome was always ahead of the transcribing polymerase. Transcription was restarted in optical tweezers by addition of NTPs (Thermo Fisher Scientific, Waltham, MA). The transcription buffer contains 20 mM Tris-HCl (pH 7.9), 5 mM MgCl2, 10 μM ZnCl2, 1 mM β-mercaptoethanol, 1 μM pyrophosphate, 300 mM KCl, and NTPs ranging from 35 μM to 2 mM each.

42Position data were recorded at 2 kHz, averaged and decimated to 50 Hz, and filtered using a second-order Savitzky-Golay filter with a time constant of 1 s. The contour length of the DNA was calculated from the extension and force using the worm-like-chain formula of DNA elasticity with a persistent length of 30 nm. This value of persistent length was obtained from pulling 3-kb DNA in our transcription buffer (data not shown). To alleviate calibration error and improve positional accuracy, single-molecule transcription traces that passed 85% of the template were aligned using both the stall site and the expected run-off length. Shorter traces were also proportionally extended based on the average error from the run-off traces. To identify pauses, we computed the dwell time of Pol II at each nucleotide position. Pauses were identified from dwell times that were longer the average dwell time by at least a factor of two. Due to the limited spatial resolution, we joined pauses that were separated by 3 bp or fewer into a single continuous pause. Pauses longer than 1 s are most likely caused by backtracking and were counted. Pause-free velocities were calculated from time derivatives of the filtered position data, with a threshold of 2 nt/s to remove pauses. All curve fittings were performed by non-linear regression of the means weighted by the inverse of the variance.

43From an elongation-competent state, Pol II can either elongate by 1 nt with the net forward translocation rate and incorporate an NMP to the RNA transcript, or enter a backtracked pause by 1 nt. During a pause, Pol II diffuses forward and backward with force-biased rate constants kf and kb, respectively. For each condition, we simulated 100 trajectories and extracted the pause durations and densities to compare with the experimentally measured values.

44Fluorescence correlation spectroscopy and fluorescence resonance energy transfer experiments showed that the first 20–30 bp of DNA at the nucleosome ends spontaneously unwrap and rewrap on the histone surface every 10–250 ms. The timescale of the 1-bp DNA fluctuations has not been directly reported but can be estimated from the experimental results above for longer DNA fluctuations. Assuming the wrapping/unwrapping kinetics is uniform along the DNA, we can model the unwrapping of a 25-bp DNA segment as:where ku and kw are the local unwrapping and wrapping rate constants of each basepair, respectively. Since the local wrapping equilibrium constant has been shown to be close to 1, we further approximate ku and kw with a single value k:

45A net rate constant can substitute for each pair of forward and reverse rate constants:

46The net rate constants are given by:

47The time required for unwrapping 25 bp of DNA equals the total time of unwrapping each bp of DNA:

48Thus, the time for 1-bp DNA to unwrap from the nucleosome is expected to be less than 1 ms:

49In the same way, we can also show that the 1-bp DNA rewrapping occurs on a similar timescale (τ1→0 < 1 ms). In addition, molecular dynamics simulations also suggested that the local nucleosomal DNA fluctuates very fast (ns–µs timescale). Therefore, we assume that the 1 bp of DNA in front of the polymerase unwraps and rewraps much faster than the translocation of the enzyme.

50Experimentally we only counted pauses with lifetimes between 1 s and 120 s. The total pause density ρpause, total is given by:

51The correction factor can be solved analytically to be 2.9 for the wild-type Pol II. For the mutant enzyme, the values of kf1 and kb1 are different from those for the wild-type (Table 3). We simulated transcriptional pauses using the lower bounds of kf1 and kb1 and obtained a correction factor of ∼7 for the mutant Pol II.

52The value of K for the mutant Pol II (Kmutant) cannot be constrained by Equation 14 due to the relatively large experimental error. We took a different approach to constrain Kmutant by simulating the ρpause–[NTP] relationship with varying Kmutant values and then comparing it to the experimental data (Figure 5—figure supplement 1). We found that the simulated curve substantially deviates from the experimental curve when Kmutant becomes larger than 100 µM. Hence, we set the upper bound of Kmutant to be 100 µM. Using the k−1K value of (2.5 ± 0.4) × 104 µM·s−1 obtained from Equation 13, we set the lower bound of k−1 for the mutant to be 210 s−1. The notion that the NTP dissociation rate is much faster than the catalysis rate (k−2 >> k3) has been widely used in the kinetic studies of RNA and DNA polymerases, and is supported by biochemical evidence. It follows from this notion that K = (k−2+k3)/k2 ≈ k−2/k2. Thus, K becomes virtually identical to KD, the NTP dissociation constant. Because the mutated residue (Glu1103) is located distal from the NTP-interacting part of TL and the E1103G mutation affects TL closure and NTP sequestration after the initial docking step, the NTP binding/dissociation kinetics are unlikely to be markedly affected by the mutation. Therefore, it is reasonable to assume that the wild-type and the mutant enzymes share similar KD values (∼9.2 µM). Under this assumption, we could estimate the k−1 value for the mutant to be ∼2700 s−1.

53The free energy difference (ΔΔG) between two neighboring translocation states was computed using the forward and reverse rate constants between these states (k+ and k−):

54The height of the activation energy barrier (ΔG†) was calculated according to the Arrhenius equation:where k is the corresponding rate constant and A is the pre-exponential factor. In this study, for illustration purposes, we made a simplifying assumption that all reaction steps share the same pre-exponential factor. A was calculated using the stepping rate constant during backtracking k0 = 1.3 s−1 and the barrier height between neighboring backtracked states ΔGb†. We assumed that one DNA–RNA hybrid basepair and one DNA–DNA basepair in the transcription bubble must be broken before any other bonds are formed and that no other interactions contribute to the barrier. Using the available free energy data for basepairing, we estimated ΔGb† to be ∼8.5 kBT, which translates to an Arrhenius pre-factor of ∼6.4 × 103 s−1. The catalysis step is essentially irreversible in our experimental condition. The free energy drop after each nucleotide addition cycle is arbitrarily set to be 10 kBT.