A structure-based kinetic model of transcription

ABSTRACT

During transcription, RNA polymerase moves downstream along the DNA template and maintains a transcription bubble. Several recent structural studies of transcription complexes with a complete transcription bubble provide new insights into how RNAP couples the nucleotide addition reaction to its directional movement.

KEYWORDS:

• nucleotide addition cycle
• pyrophosphate release
• RNA polymerase
• transcription bubble
• transcription initiation
• transcription elongation
• translocation

During transcription, the DNA-dependent RNA polymerase (RNAP) moves downstream along template DNA and synthesizes RNA molecules composed of hundreds to thousands of nucleotides without the need of a helicase to unwind nucleic acid duplexes. The net effect of each RNA extension step during transcription is that RNAP takes one nucleoside triphosphate, extends the nascent RNA by one nucleotide, and generates one pyrophosphate ion (PPi). This is an energetically favorable reaction with free energy change of about −5.6 kcal/mol under standard conditions.^1,2 It remains obscure how the RNAP couples this chemical energy output to its directional movement along the DNA template.

RNAP and the transcription bubble

Cellular RNAP are large multi-subunit protein complexes that display a crab-claw-shaped architecture with a central cleft and two pincers, one of which, the “clamp,” is mobile.^3,4 The DNA template binds in the central cleft, and NTP substrates enter the active center through one channel, while the RNA product exits the active center through another channel. The NTP entrance channel (secondary channel) is separated from the central cleft (primary channel) by the long bridge helix (BH) that traverses the central cleft. The RNAP active center is located deep inside on the floor of the central cleft, and next to the secondary channel.

While moving along the DNA during transcription, RNAP maintains a transcription bubble with single-stranded non-template DNA and a segment of hybrid formed by the template-strand DNA and the nascent RNA. Several conserved structural elements lining the inner surface of the RNAP channels play critical roles in maintaining the downstream and upstream edges of the transcription bubble (Fig. 1).

Figure 1. (A) The mammalian transcription elongation complex (TEC)¹⁸ and (B) the E. coli s^S-transcription initiation complex (s^S-TIC)¹⁷ with a complete bubble. The nucleic acids are shown as colored spheres: nontemplate strand, blue; template strand, purple; RNA, green. The RNAP core enzymes are shown as grey surface diagrams and the structure elements critical for bubble maintenance are shown as colored tubes or ribbons: lid, orange; rudder, red; FL1, wheat; FL2, yellow; BH, red; TL, cyan. (C) and (D) are schematic representations of a post-translocated TEC and a pre-translocated TIC respectively. The TEC contains a 10-nt bubble with no extra unpaired DNA residues at both edges of the bubble.

The downstream edge of the transcription bubble is essentially the same for both transcription initiation and elongation. The downstream DNA separation is maintained by the conserved structural element called the fork loop 2 (FL2); and blocking at the downstream end of the DNA–RNA hybrid are the bridge helix and a conserved mobile element called trigger loop (TL). Conformational changes of the bridge helix and the trigger loop remodel the active site and modulates the enzymatic activity of cellular RNAP.^3-10

The bacterial FL2 is rigid and well-ordered even in the absence of downstream DNA. Various structural studies of bacterial transcription complexes show that the downstream edge of the DNA bubble is well-defined and maintained by the rigid FL2 of the bacterial RNAP, and there are no single stranded residues bridging the downstream DNA duplex and the templating DNA residue at the active site. The eukaryotic FL2 appears to be flexible, and there remains some uncertainty about the downstream edge of a eukaryotic transcription bubble.

RNAP makes sequence-specific interactions with the upstream promoter DNA during transcription initiation. In bacteria, the σ factor of the RNAP holoenzyme recognizes the consensus −35 and −10 hexamers and forms base-specific interactions with the −11A and −7T residues of the promoter DNA. The sequence-specific interactions help separate the DNA strands starting from the promoter −11 position, and the DNA bubble expands as RNAP moves downstream for RNA synthesis. Bacterial RNA polymerase preferentially initiates RNA synthesis seven or eight nucleotides (nt) downstream from the −10 hexamer,^11,12 suggesting that an initiation bubble of about 13 nt is likely the energetically most favorable state. Structural studies show that RNAP comfortably accommodates both the non-template and template DNA strands of a 13-nt bubble.^13-15 When the initiation bubble expands to 14 nt or larger, the non-template strand DNA starts to loop out and the template strand DNA presses onto the σ₃ domain (DNA scrunching), and the transcription complex becomes stressed.^16,17 An initiation bubble of 16 nt or larger would start causing the σ₃ domain to separate from the RNAP core. It is likely that the DNA bubble never expands significantly larger than 16 nt during transcription initiation before σ₃–σ₄ domains separate from the core for transition into the elongation phase.

There remains no consensus about the upstream edge of an elongation bubble. A recent Cryo-EM study of the mammalian transcription elongation complexes with a complete DNA bubble suggests that the template strand DNA base pairs with the non-template DNA immediately after DNA–RNA separation by the “lid” element.¹⁸ The DNA separation is maintained by the universally conserved “rudder” element and the fork loop 1 (FL1). This DNA annealing immediately after DNA–RNA separation was evident for the single-subunit RNAP,¹⁹ and may also be true in the crystal structure of a yeast RNAP II transcription elongation complex.²⁰ It was shown that bacterial transcription elongation complexes contain a 9- or 10-bp hybrid depending on the translocation status.^5,21 If there are no single-stranded DNA residues bridging the upstream DNA duplex and the hybrid, the transcription bubble might be maintained at a size as small as 10 nt by bacterial RNAPs during processive transcription elongation. Since the free energy levels associated with different translocation states of a transcription complex would be profoundly affected by the making and breaking of nucleic acid base stacking at both edges of the transcription bubble, this lack of extra unpaired DNA residues at both edges of an elongation bubble could be of critical importance in coordinating transcription translocation by the RNAPs.

Nucleotide addition cycle

RNA synthesis in both transcription initiation and elongation involves nucleotide addition cycles (NAC) comprising four fundamental steps: translocation, NTP binding, catalysis, and PPi release (Fig. 2). At the end of the previous NAC, the nascent RNA 3′-end still occupies the nucleotide addition site. After RNAP translocates along the DNA template to move the RNA 3′ residue upstream and bring the next template DNA base into the active site, NTP is allowed to enter the active site and base pair with the DNA template to extend the RNA by one nucleotide, generating a PPi and putting the new RNA 3′-end at the nucleotide addition site. Release of PPi completes the cycle and resets the stage for the next round of nucleotide addition. The reverse reaction, called pyrophosphate exchange or pyrophosphorolysis, also happens in the presence of excessive PPi and leads to formation of NTP and cleavage of the terminal nucleotides.^22-24

Figure 2. The steps of the nucleotide addition cycle are related to six basic states E₁ to E₆ with regard to translocation, NTP/PPi association and active site opening. These six states include three quickly equilibrating groups QE₁ (pre-translocated E₁ and post-translocated E₂), QE2 (NTP-associated E₃ and E₄) and QE3 (PPi-associated E₅ and E₆), which are connected by slower diffusion-controlled and chemical reaction steps. E₁ and E₂ states are also likely equilibrating quickly with others states such as active site closed E₀, backtracked E₇ and hypertranslocated E₈ states. Both E₇ and E₈ represent ensembles of translocation states, however, it is likely that only the 1-nt backtracking and 1-nt hyper forward translocation states are of significance in many cases. Solid arrows represent rapid processes; dashed arrows represent potentially rate-limiting processes. Some states (such as the active site-open E₁, E₂, E₇ and E₈ states) are more ratchetable and could become ratcheted/clamp-opened (E₉ states). The off-pathway ratcheting processes (rate constants kr's) are expected to be slower than the on-pathway processes. TL/open, active site-open trigger loop conformation; TH/close, active site-closed trigger helices conformation.

NTP binds to the post-translocated RNAP with an open active site. In T7 RNA polymerase, it was proposed that PPi release is tightly coupled with active site opening and RNAP translocation.²⁵ In E. coli RNA polymerase, this tight coupling was not observed, but it was suggested that the PPi release occurs shortly before or concurrently with the translocation,²⁶ and that transcription translocation might require an unfolded TL.²⁷ TL unfolding allows access to the active site through the secondary channel. Previous structural studies of cellular RNAP complexes with nucleic acids displayed an overwhelming preference for the post-translocated state with an open active site,¹⁷ and thus gave an impression that both post-translocation and RNAP active site opening are energetically favorable. However, recent studies showed a pre-translocated complex with a closed RNAP active site in both the presence and absence of a bound PPi, suggesting that PPi release, TL unfolding, and transcript translocation are separable events during transcription.^16,17 Since the active site opening of a closed complex appears to be too small for a PPi to freely pass through,¹⁷ TL unfolding might be necessary before PPi can dissociate from the RNAP active site. The cycling process of nucleotide addition might be divided into six basic states (E₁ to E₆ in Fig. 2). NTP binds only to the E₂ state and would shift the equilibrium of transcription to the post-translocated states as was shown previously,²⁸ whereas PPi favors binding to the pre-translocated E₁ state and would shift the equilibrium in the opposite direction.

The movement of RNAP along the nucleic acid scaffold might be visualized in terms of thermally controlled transitions between free energy minima associated with translocation states along the template. This thermally controlled transition is expected to be a rapid event that happens in microseconds time scale. In addition to the quick motion between the pre- and post-translocation states, it is known that translocation can go further in both directions, forming the backtracked E₇ and the hyper forward translocated E₈ states. It is likely that, after each nucleotide addition, enzyme states E₀, E₁, E₂, E₇, and E₈ equilibrate quickly (QE1, Fig. 2). The enzyme distribution among these equilibrating states is determined by the relative free energy levels, which might be estimated using the nearest-neighbor stacking parameters of nucleic acids.^29,30 Quick changes in equilibrium are also expected between states E₃ and E₄ (QE2) and between states E₅ and E₆ (QE3) as they involve only local conformational changes in RNAP. Two diffusion-controlled processes (between E₂ and E₃ and between E₆ and E₁) and the chemical reaction step (between E₄ and E₅) connect these quickly equilibrating groups to form the nucleotide addition cycle.

A kinetic model of the nucleotide addition cycle

According to the diagram shown in Fig. 2, the net rate of nucleotide addition might be represented as(1) $v=k_{\text{5}}\times E_{\text{4}}-k_{\text{−5}}\times E_{\text{5}}\text{,}$(1) where E_n represents the concentration of individual enzyme species E_n, and the k_n's are the reaction constants as shown in Fig. 2. The following analyses are based on the assumption that the chemical reaction (E₄ to E₅) is the rate-limiting step with quick changes in equilibrium among species of each QE group and between E₂ and E₃ after each nucleotide addition. Under assay conditions with very low NTP concentrations, the diffusion-controlled E₂ to E₃ step could become the rate-limiting step, and similar analyses might also be made but are not included here.

(1). When the concentration of pyrophosphate is low and E₅ is negligible, then(2) $v \cong k_{\text{5}}\times E_{\text{4}}$(2)

By applying the equilibrating processes, we can get a Michaelis–Menten equation(3) $v=v_{\text{max}}\times \frac{S}{K_{\text{m}}+S}$(3) with(4) $v_{\text{max}}= k_{\text{5}}\times E_{\text{Total}}\times \frac{K_{\text{eq4}}}{1+K_{\text{eq4}}}$(4) (5) $K_{\text{m}}=\frac{K_{\text{dS}}}{f_{\text{E}}{}_{\text{2}}\times \left(1+K_{\text{eq4}}\right)}$(5) where E_Total is the total concentration of all the E_n species actively involved in the nucleotide addition cycle; S is the concentration of substrate NTP, K_dS is the NTP dissociation constant,(6) $K_{\text{dS}}=\frac{k_{\text{−3}}}{k_{\text{3}}}$(6)

K_eq4 is the equilibrium constant between QE2 species,(7) $K_{\text{eq4}}=\frac{k_{\text{4}}}{k_{\text{−4}}}$(7) and f_E2 is the fraction of E₂ in QE1 species,(8) $f_{\text{E}}{}_{\text{2}}=\frac{E_{\text{2}}}{E_{\text{0}}+E_{\text{1}}+E_{\text{2}}+E_{\text{7}}+E_{\text{8}}}$(8)

Based on this kinetic model, K_m increases significantly if the post-translocated state is energetically unfavorable, and v_max is strongly affected by the QE2 equilibrium. Non-cognate substrates likely disfavor active site closure and would display reduced v_max values.

(2). When pyrophosphate is present in a significant amount, such as in vivo, PPi-containing species become non-negligible, then(9) $v=\frac{k_{\text{5}}\times K_{\text{eq4}}\times E_{\text{Total}}\times f_{\text{E}}{}_{\text{2}}\times \frac{S}{K_{\text{dS}}}–k_{\text{−5}}\times K_{\text{eq6}}\times E_{\text{Total}}\times f_{\text{E}}{}_{\text{1}}\times \frac{P}{K_{\text{dP}}}}{1+\left(1+K_{\text{eq4}}\right)\times f_{\text{E}}{}_{\text{2}}\times \frac{S}{K_{\text{dS}}}+\left(1+K_{\text{eq6}}\right)\times f_{\text{E}}{}_{\text{1}}\times \frac{P}{K_{\text{dP}}}}$(9) where P is the concentration of pyrophosphate, and K_dP is the pyrophosphate dissociation constant,(10) $K_{\text{dP}}=\frac{k_{\text{1}}}{k_{\text{−1}}}$(10)

K_eq6 is the equilibrium constant between QE3 species,(11) $K_{\text{eq6}}=\frac{k_{\text{−6}}}{k_{\text{6}}}$(11) and f_E1 is the fraction of E₁ in QE1 species,(12) $f_{\text{E}}{}_{\text{1}}=\frac{E_{\text{1}}}{E_{\text{0}}+E_{\text{1}}+E_{\text{2}}+E_{\text{7}}+E_{\text{8}}}$(12)

Since $k_{\text{−5}}<<k_{\text{5}}$, the reverse pyrophosphorolysis reaction is negligible under normal assay conditions, and equation (9(9) $v=\frac{k_{\text{5}}\times K_{\text{eq4}}\times E_{\text{Total}}\times f_{\text{E}}{}_{\text{2}}\times \frac{S}{K_{\text{dS}}}–k_{\text{−5}}\times K_{\text{eq6}}\times E_{\text{Total}}\times f_{\text{E}}{}_{\text{1}}\times \frac{P}{K_{\text{dP}}}}{1+\left(1+K_{\text{eq4}}\right)\times f_{\text{E}}{}_{\text{2}}\times \frac{S}{K_{\text{dS}}}+\left(1+K_{\text{eq6}}\right)\times f_{\text{E}}{}_{\text{1}}\times \frac{P}{K_{\text{dP}}}}$(9) ) could be simplified to a Michaelis–Menten equation-like form with the same v_max as shown in equation (4(4) $v_{\text{max}}= k_{\text{5}}\times E_{\text{Total}}\times \frac{K_{\text{eq4}}}{1+K_{\text{eq4}}}$(4) ) and a K_m of the form(13) $K_{\text{m}}=\frac{K_{\text{dS}}}{f_{\text{E}}{}_{\text{2}}\times \left(1+K_{\text{eq4}}\right)}\times \left(1+\left(1+K_{\text{eq6}}\right)\times \frac{f_{\text{E}}{}_{\text{1}}\times P}{K_{\text{dP}}}\right)$(13)

When the PPi-containing species become non-negligible ($f_{\text{E}}{}_{\text{1}}\times P>>K_{\text{dP}}$), the K_m for the substrate NTP would be significantly affected by the presence of pyrophosphate. When ($f_{\text{E}}{}_{\text{1}}\times P >>f_{\text{E}}{}_{\text{2}}\times S$) and pyrophosphorolysis remains negligible, the nucleotide addition rate might become relatively slow and proportional to f_E2/f_E1:(14) $v \cong \frac{v_{\text{max}}\times \left(1+K_{\text{eq4}}\right)\times S\times K_{\text{dP}}}{\left(1+K_{\text{eq6}}\right)\times P\times K_{\text{dS}}}\times \left(\frac{f_{\text{E2}}}{f_{\text{E1}}}\right)$(14)

Since f_E1 and f_E2 are expected to be strongly sequence-dependent, this might be the mechanistic basis for the sequence-dependent frequent short pauses during transcription. By applying nearest-neighbor stacking analyses^29,31 to the transcription bubble models shown in Fig. 1, it can be seen that some sequences strongly prefer the pre-translocated E₁ state over the post-translocated E₂ state ($f_{\text{E1}}>>f_{\text{E2}}$). This kinetic model makes predictions consistent with the observed pauses during transcription elongation^32,33 (unpublished analyses).

On the other hand, this model also suggests that the presence of the NTP that is complementary to the next template residue would promote PPi dissociation, which could be used to explain the effects of the incoming NTP in the measured rates of PPi release²⁴ and nucleotide addition³⁴ without involving a secondary NTP-binding site in the RNAP. Structural studies of transcription complexes showed no evidence for a secondary NTP-binding site in the RNAP.

In an extreme case, when the reverse pyrophosphorolysis reaction becomes non-negligible, the chemical reaction might reach equilibrium or even be reversed. According to equation (9(9) $v=\frac{k_{\text{5}}\times K_{\text{eq4}}\times E_{\text{Total}}\times f_{\text{E}}{}_{\text{2}}\times \frac{S}{K_{\text{dS}}}–k_{\text{−5}}\times K_{\text{eq6}}\times E_{\text{Total}}\times f_{\text{E}}{}_{\text{1}}\times \frac{P}{K_{\text{dP}}}}{1+\left(1+K_{\text{eq4}}\right)\times f_{\text{E}}{}_{\text{2}}\times \frac{S}{K_{\text{dS}}}+\left(1+K_{\text{eq6}}\right)\times f_{\text{E}}{}_{\text{1}}\times \frac{P}{K_{\text{dP}}}}$(9) ), an equilibrium of nucleotide addition ($v=0$) can be reached by increasing the [PPi]/[NTP] ratio so that(15) $\frac{P}{S}=\frac{k_{\text{5}}\times K_{\text{eq4}}\times f_{\text{E2}}\times K_{\text{dP}}}{k_{\text{−5}}\times K_{\text{eq6}}\times f_{\text{E1}}\times K_{\text{dS}}}$(15)

Although k₅ is expected to be about 10⁴ faster than k₋₅, when ($f_{\text{E1}}>>f_{\text{E2}}$), the chemical reaction could easily reach equilibrium in an in vitro assay as PPi accumulates with each nucleotide addition, which is probably what we observed in the σ^S-TIC crystals.¹⁷

Regulation of transcription

As shown in Fig. 2, transcription can be regulated at various steps of the nucleotide addition cycle. Some factors, such as NTP or PPi analogs, modulate the formation or distribution of QE2 or QE3 species, and thus might act as competitive regulators; whereas many other factors act at the translocation step and affect the distribution of QE1 species. It is known that upstream RNA hairpin formation could also be coupled to RNAP forward translocation, and similarly, DNA or RNA translocases could interact directly with the nucleic acid and power either forward or backward translocation by ATP hydrolysis.³⁵ Some DNA sequences favor the pre-translocation state and cause transcriptional pauses^32,33; whereas sequence-specific interactions between the RNAP and the DNA could also alter the translocation preference and play a role in regulating transcription efficiency.^33,36

As shown by Sekine et al.,³⁷ transcription complexes at some states are more ratchetable, and thus could become ratcheted. A ratcheted complex contains a wide-open central cleft caused by the swing movement of the clamp and a ratcheting movement between the core and shelf modules that form the active center.³⁸ Ratchetable and ratcheted states are expected to be inter-convertible, presumably at a slow rate. A known slow process similar to the ratcheting movement is the rate-limiting I₁ to I₂ conversion, which likely involves RNAP clamp opening, during the formation of an RNAP-promoter open complex.³⁹ Some of the ratcheted complexes, such as those with extensive backtracking or an RNA hairpin in the RNA exit channel, are long-lived. Since ratcheting involves BH bending, it is likely that only those states with an unfolded TL, such as states E₁, E₂, E₇, and E₈, are ratchetable. Extended pauses at some ratchetable states would increase the chance to form long-lived ratcheted states. Apparently, formation of the off-pathway ratcheted complexes would decrease the effective total amount of complexes in active transcription (E_Total in equations (4(4) $v_{\text{max}}= k_{\text{5}}\times E_{\text{Total}}\times \frac{K_{\text{eq4}}}{1+K_{\text{eq4}}}$(4) ) and (9(9) $v=\frac{k_{\text{5}}\times K_{\text{eq4}}\times E_{\text{Total}}\times f_{\text{E}}{}_{\text{2}}\times \frac{S}{K_{\text{dS}}}–k_{\text{−5}}\times K_{\text{eq6}}\times E_{\text{Total}}\times f_{\text{E}}{}_{\text{1}}\times \frac{P}{K_{\text{dP}}}}{1+\left(1+K_{\text{eq4}}\right)\times f_{\text{E}}{}_{\text{2}}\times \frac{S}{K_{\text{dS}}}+\left(1+K_{\text{eq6}}\right)\times f_{\text{E}}{}_{\text{1}}\times \frac{P}{K_{\text{dP}}}}$(9) )).

The universally conserved NusG-family proteins bind the clamp helices of the RNAP near the upstream edge of the transcription bubble, and make bridging interactions between the two pincers of the RNAP central cleft. NusG bridging of the two pincers could potentially prevent RNAP from ratcheting open. This inhibition of RNAP ratcheting is likely what makes NusG essential for E. coli viability. Ratcheted or more ratchetable complexes, such as those with backtracked residues, are frequently targeted by Gre factors from the secondary channel for cleavage of backtracked RNA residues. ppGpp binds on the outer surface of RNAP⁴⁰ and thus could increase the ratchetability of RNAP for its cooperative role with DksA, another RNAP secondary channel-binding protein.⁴¹ It is known that RapA binds at the RNA exit channel and could potentially suppress RNA hairpin formation and promote backtranslocation.³⁵ It remains to be revealed how other factors, such as NusA, interact with the exiting RNA to modulate transcription termination or antitermination.

Abbreviations

BH	=	bridge helix
NTP	=	nucleoside triphosphate
PPi	=	pyrophosphate
RNAP	=	RNA polymerase
TL	=	trigger loop

Disclosure of potential conflicts of interest

No potential conflicts of interest were disclosed.

Funding

This work was supported by NIH grant GM22778 (to T.A.S.). T.A.S. is an investigator of the Howard Hughes Medical Institute.