Investigation of the pK_a of the Nucleophilic O2′ of the Hairpin Ribozyme

Abstract

Small ribozymes cleave their RNA phosphodiester backbone by catalyzing a transphosphorylation reaction wherein a specific O2′ functions as the nucleophile. While deprotonation of this alcohol through its acidification would increase its nucleophilicity, little is known about the pK_a of this O2′ in small ribozymes, in part because high pK_a’s are not readily accessible experimentally. Herein, we turn to molecular dynamics to calculate the pK_a of the nucleophilic O2′ in the hairpin ribozyme and to study interactions within the active site that may impact its value. We estimate the pK_a of the nucleophilic O2′ in the wild type hairpin ribozyme to be 18.5 ± 0.8, which is higher than the reference compound, and identify a correlation between proper positioning of the O2′ for nucleophilic attack and elevation of its pK_a. We find that monovalent ions may play a role in depression of the O2′ pK_a, while the exocyclic amine appears to be important for organizing the ribozyme active site. Overall, this study suggests that the pK_a of the O2′ is raised in the ground state and lowers during the course of the reaction owing to positioning and metal ion interactions.

Graphical Abstract

Introduction

The hairpin ribozyme is one of ten families of small, self-cleaving RNA enzymes that catalyzes a site-specific cleavage along its RNA backbone.¹ The mechanism involves a transphosphorylation reaction wherein the nucleophilic O2′ attacks the scissile phosphate and results in a 2′,3′-cyclic phosphate and displacement of the adjacent O5′ leaving group (Figure 1). Ribozymes can employ various catalytic strategies to increase the rate of the reaction.^2,3 In the hairpin ribozyme, residues G8 and A38 donate hydrogen bonds to the scissile phosphate, stabilize the transition state through electrostatics, and may facilitate proton transfer as general base and acid, respectively (Figure 1).^4-9 It has also been suggested that water positioned near the nucleophilic O2′ or one of the nonbridging phosphoryl oxygens (NPOs) of the scissile phosphate could function as a specific or general base in the reaction, respectively.^5,9-13

Figure 1.

The active site of the hairpin ribozyme. An MD configuration of the entire ribozyme is shown to the left with the active site colored red and magnified as a drawing on the right. In the drawing, the electron pushing arrows illustrate how transphosphorylation occurs between A-1 and G1. G8 and A38 are catalytically important residues that hydrogen bond with the scissile phosphate. Hydrogen bonds observed in the WT hairpin ribozyme simulations in this study are drawn. The G8(N2)-to-G1(pro-S_P NPO) hydrogen bond is colored blue and is absent in simulations of the G8I variant.

Deprotonation of the nucleophilic O2′ is a catalytic strategy that could result in substantial rate enhancement since the resulting oxyanion is much more nucleophilic than the neutral alcohol.^2,14 Experiments on model compounds and unstructured oligonucleotides have shown that the pK_a values of the O2′ range from 12 to 14, making their deprotonation unfavorable by bases present in the functional deprotonated form at neutrality, which by definition have pK_a’s of about 7 or less.^14-17 However, functional groups within ribozymes often have shifted pK_a values, and depression of the pK_a of the nucleophilic O2′ within the ribozyme could, in principle, favor the formation of its more nucleophilic, deprotonated state. Despite such implications for catalysis, the pK_a of the nucleophilic O2′ remains unknown for many small ribozymes, including the hairpin ribozyme. This is due in part to the difficulty of experimentally measuring such a high pK_a since the ribozyme would need to be subjected to solutions with pH values exceeding the O2′ pK_a, resulting in alkaline denaturation of the RNA fold and/or degradation of the backbone.¹⁸ To circumvent this issue, we turned to calculations where we employed molecular dynamics (MD) to estimate the pK_a of the nucleophilic O2′ in the hairpin ribozyme and to assess underlying factors that might cause shifts in the pK_a.

Among the many potential contributors to a pK_a perturbation, we were interested in how monovalent cations could influence the pK_a of the nucleophilic O2′. This is because many small ribozymes, including the hairpin ribozyme, can readily catalyze transphosphorylation without the aid of divalent ions when high (molar) concentrations of monovalent ions are present.^19-22 It is thus possible that monovalent ions could play a role in depressing the pK_a of the nucleophilic O2′ either in the ground state or during nucleophilic attack. We also wanted to study whether the exocyclic amine of guanine influences the pK_a. In a previous cheminformatic study, we showed that the exocyclic amine of a guanine is positioned near the nucleophilic O2′ within the hairpin, hammerhead, twister, and glmS ribozymes.²³ This feature was especially prominent for the hairpin ribozyme, making it an excellent candidate for this particular study.

In many small ribozymes, the nucleophilic O2′ donates a hydrogen bond to one of the adjacent nonbridging phosphoryl oxygens.^24-27 This interaction is considered inhibitory as it ties up the O2′ proton from abstraction by the general base. Because hydrogen bonds would influence the O2′ pK_a, we considered whether a similar interaction occurred in the hairpin ribozyme. Another catalytic feature of small ribozymes is orientation of the nucleophilic O2′ relative to the scissile phosphate. When the O2′ is close to the phosphorus and in-line with the O5′-P bond, the scissile linkage is considered fit for in-line nucleophilic attack.^2,28 The cleavage reaction in the hairpin ribozyme is accompanied by inversion of stereochemistry at the scissile phosphate, illustrating that the reaction occurs through an S_N2-like mechanism where good in-line fitness is critical.²⁹

Herein, we investigate the pK_a of the nucleophilic O2′ in the hairpin ribozyme. We chose to study the hairpin ribozyme because the exocyclic amine of G8 is positioned close to the O2′. The wild type (WT) hairpin ribozyme was investigated using MD to estimate the O2′ pK_a. These MD simulations were extended to a system with a Na⁺ ion restrained to interact with the O2′ to gauge the impact of monovalent cations and then to a G8-to-inosine (G8I) variant to study the influence of the exocyclic amine. The results were compared with past theoretical and experimental studies from our lab and others. We found that the O2′ has a substantially elevated pK_a and identify several factors that may lead to this upward shift. Additionally, we show that monovalent cations depress the O2′ pK_a during rare instances when a Na⁺ ion directly coordinates the protonated O2′.

Methods

The systems studied herein were built using PyMOL^30,31 and/or programs included with AmberTools.³² Initial coordinates for the hairpin ribozyme were based on a crystal structure with 2.05 Å resolution of the pre-cleaved ribozyme inhibited by a 2′-methoxy substituted for the nucleophilic O2′ (PDB ID 2OUE).¹³ The direct coordination of a Na⁺ ion to the nucleophilic O2′ could have important implications on its pKa; however, monovalent ions equilibrate slowly with nucleic acids.^33,34 To avoid any issues with the association time of Na⁺ ions with the nucleophilic O2′, all ribozyme systems were built with a Na⁺ ion placed 2.2 Å from the alcohol, and distance restraints were used to hold the ion in position during minimization and equilibration. Unless otherwise noted, these restraints were released during equilibration and not used during production MD.

Several crystal structures of the pre-cleaved hairpin ribozyme with native residues in the active site, except for a methoxy substituted for the nucleophilic alcohol to inhibit the reaction, show that the A-1 sugar adopts the rare 2′-endo pucker.^4,13,35 This is consistent with theoretical and biochemical findings that the cleavage reaction in RNA is more favorable when the sugar of the residue bearing the nucleophilic O2′ adopts a 2′-endo pucker.³⁶ The ff99 force field with modified α, γ, and χ dihedrals (ff99bsc0χ_OL3) is generally recommended for MD simulations of RNA using AMBER.^32,37-39 However, Mlýnský and colleagues showed that the A-1 sugar quickly flips from a 2′-endo to a 3′-endo pucker conformation in simulations of the hairpin ribozyme using this force field.⁴⁰ They further found that the A-1 sugar could maintain its 2′-endo pucker in simulations when additional modifications to the ε and ζ dihedral (εζ_OL1)⁴¹ were used with this force field. Therefore, we opted to use the ff99bsc0χ_OL3εζ_OL1 force field for all simulations presented in this study. In the ff99bsc0χ_OL3εζ_OL1 simulations of the hairpin ribozyme by Mlýnský and colleagues, the scissile phosphate was flipped from its original position towards A38, similar to what is seen in crystal structures of vanadate transition state mimics of the hairpin ribozyme.^5,42 For the work presented here, distance restraints were used to promote the formation and/or retention of several hydrogen bonds in the active site of the hairpin ribozyme during the minimization and the first part of the equilibration. These restraints flipped the scissile phosphate towards A38 and helped maintain the hydrogen bonding network in the active site during equilibration when a Na⁺ ion was restrained to the nucleophilic O2′. They were released during the latter part of the equilibration and not used during production MD. During our simulations, with the phosphate flipped towards A38, G8(N2) donates a hydrogen bond to the pro-S_P NPO of G1, as observed in the simulations by Mlýnský and colleagues⁴⁰ and vanadate transition state mimic crystal structures,^5,42 rather than to the pro-R_P NPO that was observed in other previous simulations^43,44 and crystal structures of the pre-cleavage ribozyme.^13,35 Experimental studies using phosphorothioate substitutions at the scissile phosphate do not provide much evidence for which conformation is operative during the reaction.^45-48

The pK_a of A-1(O2′) within the various systems was calculated herein using thermodynamic integration,^49,50 which involved running a series of simulations with the atomic charges of A-1 ranging in values between those of the O2′-protonated and deprotonated states (0<λ<1). Three replicates were performed for each pK_a calculation, and production MD trajectories were propagated at least until convergence of the running <∂V/∂λ> values were achieved (Table S1). Classical MD trajectories of the systems in the O2′-protonated (λ=0) and O2′-deprotonated (λ=1) states were also propagated. These simulations were not necessary for the pK_a calculations but provided insight into changes in hydrogen bonding, O2′ hydration, and other interactions that occurred upon deprotonation of the O2′. A single 500 ns trajectory was propagated for each of these two protonation states. Details of the methods are described in the Supporting Information.

Results

Thermodynamic integration (TI) was employed to calculate the pK_a of A-1(O2′) of the hairpin ribozyme.^49,50 TI relies on two series of simulations, one for the system of interest with an unknown pK_a and one for a reference system with a predetermined pK_a. In our case, the ribozyme is the system of interest, and we chose the ApG dinucleotide as the reference system since the hairpin ribozyme itself cleaves at an ApG linkage (Figure 1, residues −1 and 1). To gain insight into factors that may cause perturbations in the pK_a and to assess whether the phosphate linkage was oriented such that O2′ nucleophilic attack could occur, classical MD trajectories of the O2′-protonated and deprotonated states were propagated and analyzed. All results should be viewed as qualitatively rather than quantitatively accurate due to sampling and force field limitations.

We carried out three studies: (1) calculation of the pK_a of the nucleophilic O2′ in the WT hairpin ribozyme and comparative simulations of the ribozyme to those of ApG, (2) calculation of the pK_a with a Na⁺ ion restrained to the O2′ to assess its effect on the pK_a, and (3) simulations of the G8I variant of the hairpin ribozyme to assess the importance of a guanine at the general base position, as seen in numerous ribozymes.²³

The A-1(O2′) pK_a of the Hairpin Ribozyme

Acharya and colleagues experimentally measured a pK_a of 12.3 for A-1(O2′) in ApG via analysis of its transphosphorylation rate-pH profile in the background of 1 M NaCl,¹⁶ consistent with other experiments.^14,17,51,52 This pK_a was estimated to increase to 12.5 in the presence of 0.19 M NaCl,¹⁴ the average concentration of the three replicates of the ApG system. We hypothesized that the pK_a of the nucleophilic O2′ in the ribozyme is depressed below that of ApG as a strategy to increase the population of the more nucleophilic, deprotonated O2′. On the contrary, we calculated the ribozyme pK_a to be shifted upward by 6.0 ± 0.8 units, from 12.5 to 18.5 ± 0.8 (Table S2). The pK_a of a given functional group in a biomolecule is ultimately modulated by interactions that stabilize or destabilize the protonated or deprotonated states. Considering this, we compared ApG to the ribozyme when the O2′ is protonated and deprotonated in terms of four interactions of the O2′: 1) Na⁺ ion binding, 2) interactions with solvent, 3) hydrogen bonding to the adjacent NPOs, and 4) electrostatic repulsion from the NPOs.

1). Na⁺ ion binding.

We compared how Na⁺ ions interact with the nucleophilic O2′ alcohol in the ribozyme and its ApG dinucleotide counterpart. Strong interaction of the deprotonated O2′ with Na⁺ ions would favor its deprotonation and thus lower its pK_a. For the O2′-protonated state, a plot of Na⁺ ion isodensity reveals diffuse density between the alcohol and G8(O6) (Figure 2A). However, plots of the running coordination number of Na⁺ ions with respect to the O2′ indicate that an average of just 0.05 and 0.02 Na⁺ ions reside within 3 Å of the O2′ for the ribozyme and ApG, respectively (Figure 2B). These short interaction distances are indicative of Na⁺ ions binding via an inner-sphere coordination, but they are extremely rare. For the O2′-deprotonated state, plots of Na⁺ ion isodensity for the ribozyme are quite different. They show high localized density between the O2′ and G8(O6), as well as between the O2′ and the pro-S_P NPO of G1 (Figure 2C, top and bottom, respectively). Notably, the latter Na⁺ ion binding location is close to where the O2′ proton is located in the O2′-protonated state. An average of 1.9 Na⁺ ions reside within 3 Å of the O2′ of the deprotonated ribozyme (Figure 2D, blue), signifying that both the O2′-G8(O6) and O2′-pro-S_P sites are occupied throughout most of the trajectory. In contrast, only 1.3 Na⁺ ions reside within 3 Å of the O2′ of the deprotonated ApG. These data suggest that deprotonation generally favors inner-sphere coordination of Na⁺ ions to the oxyanions in both systems, with more Na⁺ ions coordinating the O2′ of the ribozyme than ApG.

Figure 2.

Na⁺ ion binding to A-1(O2′) in ApG and the hairpin ribozyme. A) Na⁺ ion isodensity plots for the O2′ protonated ribozyme. The transparent purple corresponds to the top 70% of Na⁺ ion density within a 10x10x10 ų region centered near the O2′. Residues A-1 and G8 are labeled, an arrow points to the O2′, and the carbons of A-1 and G1 are cyan while all others are grey. B) Running coordination number of Na⁺ ions to the protonated O2′ for ApG (black) and the ribozyme (blue). C) Same as panel A except for the deprotonated O2′, and the opaque and transparent purple correspond to the top 30% and 85%, respectively, of Na⁺ ion density. D) Same as panel B except for the deprotonated O2′. Also note the differences in the y-axis values between panels B and D.

A radial distribution function (RDF) plot of Na⁺ ions with respect to the O2′ reveals two major peaks for the ribozyme in the O2′-protonated state (Figure S1A, blue). The first peak is centered at 2.4 Å and corresponds to the inner-sphere coordinated Na⁺ ions discussed above. The second peak is centered at 4.6 Å and extends to about 5.6 Å. There is an average of 0.91 Na⁺ ions within 5.6 Å of the O2′, most of which are represented by the second peak at 4.6 Å (Figure S1B, blue). Ions at this distance could interact with the O2′ via outer-sphere coordination (Figure S2A) or could simply be interacting with other nearby moieties (Figure S2B). We were interested in outer-sphere coordination since it might influence the reaction. Because of the ambiguity indicated in Figure S2, information beyond the RDF is needed to determine how often Na⁺ ions formed an outer-sphere coordination with the O2′. For every 10^th configuration of the trajectory, we assessed 1) whether water resided within hydrogen bonding distance to the O2′ and 2) if there was a nearby water, whether a Na⁺ ion resided close to that water (see Supporting Information). These criteria were satisfied for 37.1% of the trajectory, indicating that outer-sphere coordination to the O2′ occurs during this fraction of the trajectory. For ApG with a protonated O2′, outer-sphere coordination only occurs during 3.0% of the trajectory, 12-fold less than the ribozyme.

We also considered the O2′-deprotonated state. As mentioned above, there is an initial peak in the RDF, now centered slightly closer at 2.2 Å, for both the ribozyme and ApG, representing inner-sphere coordination. The second peak near 4.6 Å is much smaller in amplitude than the first for both the ribozyme and ApG (Figure S1C inset), potentially representing minor populations of outer-sphere coordination. Further analysis revealed that the Na⁺ ions interact with the O2′ oxyanions of the ribozyme and ApG via outer-sphere coordination during 6.8% and 7.6% of the trajectory, respectively. In sum, the O2′ of the ribozyme interacts with at least one outer-sphere Na⁺ ion during 37.1% of the trajectory in the O2′-protonated state but interacts with nearly two inner-sphere Na⁺ ions throughout the trajectory of the O2′-deprotonated state. The O2′ of ApG interacts strongly with Na⁺ ions only in the O2′-deprotonated state, specifically 1.3 ions via inner-sphere coordination. The stronger interactions of the deprotonated O2′ with Na⁺ ions in the ribozyme relative to ApG favor a decreased pK_a relative to ApG. Given that we calculated an increase in pK_a in the ribozyme, we were particularly interested in additional molecular level contributions to the O2′ pK_a.

2). Interactions with solvent.

Next, we considered how the solvent accessible surface areas (SASAs) of the O2′ oxygen atoms of the ribozyme and ApG change upon deprotonation. The linear combinations of pairwise overlaps method was used to estimate these SASA values.^53,54 Strong interaction of the deprotonated O2′ with solvent would favor its deprotonation and thus lower its pK_a. Distributions of the O2′ SASAs for the O2′-protonated and deprotonated states of the ribozyme reveal similar dominant values of 18 Ų and 19 Ų, respectively (Figure 3A, C, blue), suggesting that the SASA of the ribozyme O2′ changes little in response to deprotonation. On the other hand, distributions for ApG show dominant values of 14 Ų and 31 Ų for the O2′-protonated state that increase to 28 Ų and 35 Ų for the O2′-deprotonated state (Figure 3A, C, black). Therefore, upon deprotonation, the O2′ SASA of the ribozyme remains static at a single low value while that of ApG has two dominant values that increase.

Figure 3.

Solvent accessible surface areas and hydration of A-1(O2′) in ApG and the hairpin ribozyme. A) Distributions of the SASA of the protonated O2′ in ApG (black) and the ribozyme (blue). The area under each distribution is normalized to one. B) Running coordination number of water hydrogen atoms to the protonated O2′ in ApG (black) and the ribozyme (blue). C) and D) Same as panels A and B except for the deprotonated O2′.

It is possible that the increased SASA in ApG leads to greater interaction with water. To evaluate this, we plotted the running coordination number of hydrogens belonging to water with respect to the O2′. For the ribozyme, an average of 0.73 and 0.12 hydrogen atoms from water reside within 2.4 Å of the O2′ in the O2′-protonated and deprotonated states, respectively (Figure 3B, D, blue), indicating a significant loss of hydrogen bond donation from water upon O2′ deprotonation. The low O2′ surface area available combined with the binding of two Na⁺ ions likely exclude water upon deprotonation of the ribozyme. For ApG, an average of 0.98 and 2.0 hydrogen atoms from water are positioned within 2.4 Å from the O2′ in the O2′-protonated and deprotonated states, respectively (Figure 3B, D, black), indicating the opposite effect: a gain in hydrogen bond donation from water upon O2′ deprotonation. In sum, O2′ deprotonation leads to increased O2′ SASA (Figure 3A, C, black) and hydration for ApG (Figure 3B, D, black) but little change in O2′ SASA (Figure 3A, C, blue) with decreased hydration for the ribozyme (Figure 3B, D, blue) favoring a decreased O2′ pK_a in ApG relative to the ribozyme.

3). Hydrogen bonding of the O2′ to the adjacent NPOs.

We assessed hydrogen bond donation between the protonated O2′ and the two nearby NPOs (Figure 4A, B). Strong hydrogen bonding of the O2′ would disfavor its deprotonation and thus raise its pK_a. Heatmaps showing how the simulations sampled various hydrogen bonding distances and angles are compared between ApG and the ribozyme for both NPOs. For all potential hydrogen bonding interactions considered in this study, conformations where the donor-acceptor distance is less than or equal to 3.2 Å and where the donor-proton-acceptor angle is greater than or equal to 135° are regarded as hydrogen bonding. For ApG, hydrogen bonds from the O2′ to the pro-S_P and pro-R_P NPOs form during just 25.3% and 5.7%, respectively, of the trajectory (Figure 4C, D). In other words, a hydrogen bond between the O2′ and either NPO forms throughout 31% of the trajectory. The O2′ also donates hydrogen bonds to other, weaker acceptors, such as the O5′ of G1, leading to some type of hydrogen bond donation during 63% of the trajectory in total (Table S3). For the ribozyme, hydrogen bonding to the pro-S_P NPO of G1 occurs much more frequently, as it is maintained during 96.5% of the trajectory (Figure 4E). Furthermore, the bulk of the density resides at the bottom right corner of the heatmap, at a distance near 2.5 Å and an angle near 170°, indicating that the hydrogen bonding is strong. The hydrogen bond from the O2′ is stereospecific as well, as it practically never donates to the pro-R_P NPO of G1 (Figure 4F). Thus, the O2′ of the ribozyme donates a strong hydrogen bond to the pro-S_P NPO for almost the entire trajectory, while the O2′ of ApG donates a hydrogen bond to the NPOs during only 31% of the trajectory, including some donation to the pro-R_P NPO.

Figure 4.

Hydrogen bonding of the protonated O2′ to the NPOs in ApG and the hairpin ribozyme. MD configurations of the ApG simulations show an example of a hydrogen bond being donated from the O2′ (designated by the arrow) to A) the pro-S_P NPO or B) the pro-R_P NPO. C) and D) Heatmaps of hydrogen bonding distances and angles for ApG where the O2′ is the donor and the acceptors are either the pro-S_P NPO (panel C) or the pro-R_P NPO (panel D). E) and F) Same as panels C and D, respectively, except for the ribozyme. In all four heatmaps, the same number of data points are binned, and colors correspond with the color bar at the right. The red box in each heatmap designates good hydrogen bonding geometry with distances less than or equal to 3.2 Å and angles greater than or equal to 135°, and the percentages depicted represent the fraction of points that meet the hydrogen bonding criteria.

We also investigated whether interactions of the O2′ with other atoms accompany the rare instances when the O2′-to-pro-S_P NPO hydrogen bond in the O2′-protonated ribozyme does not form. This was done by inspecting the trajectories for Na⁺ ion binding and other hydrogen bonding interactions. At least one Na⁺ ion resides within 3 Å of the O2′ during 5.2% of the trajectory. However, this value drops to 0.28% for the fraction of the trajectory when the O2′-to-pro-S_P NPO hydrogen bond does not form. Thus, Na⁺ ion binding does not appear to be the cause of the disruption of this hydrogen bond. This is consistent with the observation that the Na⁺ ion does not bind between the O2′ and pro-S^P NPO in the O2′-protonated state (Figure 2A). In regard to other hydrogen bonding interactions, the pro-S_P NPO typically accepts a hydrogen bond from G8(N2) in addition to that from the O2′ (Figure 1). This NPO accepts hydrogen bonds from other donors during only 16.1% of the fraction of the trajectory when it also accepts a hydrogen bond from G8(N2) but not from the O2′. Furthermore, the O2′ donates a hydrogen bond to an acceptor other than the pro-S_P NPO during only 8.5% of the fraction of the trajectory when it is not donating a hydrogen bond to the pro-S_P NPO. These low percentages indicate that the loss of the O2′-to-pro-S_P NPO hydrogen bond is generally not compensated by alternative hydrogen bond donors and acceptors. Absence of compensation means that the energetic penalty for not forming this hydrogen bond is high, consistent with the observation that it is broken in only 3.5% of the trajectory (Figure 4E). Overall, hydrogen bonding of the O2′ is stronger for the ribozyme than for ApG, favoring an increased pK_a in the ribozyme.

4). Electrostatic repulsion from the NPOs.

After considering the hydrogen bonding angle and distance in the O2′-protonated state, we turned to assessing the O2′-to-NPO distances in the O2′-deprotonated state, where the proton is no longer present and hydrogen bonding is no longer possible. Short O2′-NPO distances would result in high electrostatic energies and thus disfavor deprotonation and raise the pK_a of the O2′. For ApG, the deprotonated O2′-pro-S_P and O2′-pro-R_P NPO distances vary greatly, extending up to 5 Å during a substantial fraction of the trajectory, especially for the O2′-pro-R_P interaction (Figure 5A, B). In contrast, for the ribozyme these distances consistently fluctuate near 3 Å for the O2′-pro-S_P interaction and a little over 4 Å for the O2′-pro-R_P interaction (Figure 5C, D). Overall, the O2′ to NPO distances are smaller for the ribozyme than for ApG, favoring an increased electrostatic repulsion for the oxyanion in the ribozyme and an increase in its O2′ pK_a. On the whole, three of the four contributions (decreased interactions of the deprotonated O2′ with solvent, increased hydrogen bond donation of the protonated O2′ to the NPOs, and greater electrostatic repulsion of the deprotonated O2′ from the NPOs) favor an O2′ pK_a increase in the ribozyme relative to ApG, consistent with our calculations.

Figure 5.

Distances between the deprotonated O2′ and NPOs in ApG and the hairpin ribozyme. A) and B) O2′ to pro-S_P NPO (panel A) and pro-R_P NPO (panel B) distances throughout the 500 ns trajectory for ApG (black). C) and D) Same as panels A and B, respectively, except for the hairpin ribozyme (blue).

Tradeoff Between In-Line Fitness and the A-1(O2′) pK_a

The previous section revealed an elevated O2′ pK_a in the hairpin ribozyme and some potential factors leading to this elevation. In the ribozyme, the O2′ resides close to the pro-S_P NPO in both the O2′-protonated (Figure 4E) and deprotonated (Figure 5C) states. These distances stabilize the O2′-protonated state through hydrogen bond donation and destabilize the O2′-deprotonated state through electrostatic repulsion, with both effects leading to an increase in O2′ pK_a. For nucleophilic attack to occur, the O2′ and the scissile phosphate must have reasonable in-line fitness. The smaller the O2′-P distance and the closer the O2′-P-O5′ angle is to 180°, the better the in-line fitness. It is possible that there is a correlation between in-line fitness, which drives the reaction, and O2′-NPO proximity, which elevates the O2′ pK_a. To address this, we assessed whether and how often the geometries of the phosphate linkage in ApG and the scissile phosphate in the ribozyme sample conformations with good in-line fitness and assessed corresponding O2′-NPO distances in ApG.

Conformations with O2′-P distances below 3.5 Å and with O2′-P-O5′ angles above 125° are considered fit for in-line nucleophilic attack (Figure 6), as has been used previously for the hairpin ribozyme.⁴⁴ A heatmap for ApG reveals that only 2.6% of the population falls within the established cutoffs for in-line fitness during the O2′-protonated state trajectory (Figure 6A). These values increase dramatically to 92.7% for the ribozyme (Figure 6B). Plots showing the protonated O2′ isodensities relative to the phosphate groups reveal that the density is dispersed around the phosphate in ApG but concentrated near the pro-S_P NPO in the ribozyme (Figures 6D, 6E, S3). We overlaid cones with the structures to designate the in-line fitness cutoffs. A much smaller portion of the O2′ density falls within the accompanying cone for ApG as compared to the ribozyme (Figures 6D, 6E, S3). Similar results are observed for the O2′-deprotonated state, with strong in-line fitness for only the ribozyme and much of the concentrated O2′ density inside the cone (Figures S3, S4). Overall, the ribozyme has good in-line fitness, which is true whether the O2′ is protonated or deprotonated, while the reference dinucleotide has poor in-line fitness. Apparently, the scaffold of the ribozyme serves a role in enforcing in-line fitness.

Figure 6.

In-line fitness of ApG and the hairpin ribozyme in the O2′ protonated state. A) and B) Heatmaps of in-line fitness distances and angles for ApG (panel A) and the ribozyme (panel B). Points that fall within the green box are considered fit for nucleophilic attack, and the percentages depicted represent the fraction of points that meet the in-line fitness cutoffs. In both heatmaps, the same number of data points are binned, and colors correspond with the color bar in panel B. C) Drawing of the phosphate linkage showing the O2′ positioned for in-line nucleophilic attack, with the O2′, phosphorus, and O5′ circled in green. D) and E) Isodensity plots of the O2′ relative to the phosphate of G1 in ApG (panel D) and the ribozyme (panel E). The top 90% of O2′ density is shown in red and overlayed on an MD configuration for reference. Density that falls within the cone is considered fit for in-line nucleophilic attack. Alternative perspectives are shown in Figure S3.

Placement of the O2′ within a majority of the in-line fitness cone also positions it in close proximity to the NPOs. Because it samples many positions relative to the nearby phosphate, the O2′ in ApG provides a good opportunity to study how close this moiety approaches the NPOs for those rare instances when ApG samples conformations with good in-line fitness. For ApG in the O2′-protonated state, a heatmap shows that the O2′ samples conformations placing it at a wide range of distances from either NPO (Figure 7A). A subplot of only those conformations that fall within the in-line fitness boundaries reveals two distinct populations of comparable weight, each close to one of the two NPOs (Figure 7B). For ApG in the O2′-deprotonated state, similar results are observed, except that there appears to be a preference for the O2′ being close to the pro-S_P NPO rather than the pro-R_P NPO when in-line fitness cutoffs are satisfied (Figure S5). This analysis suggests that O2′-NPO proximity is an intrinsic property of good in-line fitness. Such close distances would likely raise the pK_a of the O2′ and be a tradeoff for improved fitness for O2′ nucleophilic attack.

Figure 7.

Distances of the protonated O2′ to the NPOs of ApG. A) Heatmap of the O2′ to pro-R_P and pro-S_P NPO distances for the entire trajectory of ApG. Colors correspond to the color bar at the right, and the diagonal line shows where the O2′ to pro-R_P and pro-S_P NPO distances are equal. B) Same as panel A except the analysis is performed for only the fraction of the trajectory where the O2′ is positioned for in-line nucleophilic attack. Note that the counts are lower due to this being a subpopulation of the whole trajectory.

Given that O2′-NPO distance is an intrinsic property of good in-line fitness, we turned to the ribozyme to assess whether there is a subpopulation with good in-line fitness but poor O2′-to-NPO hydrogen bonding. Such a subpopulation might be especially well prepared for reaction and help solve the paradox of reaction-promoting in-line fitness being associated with reaction-inhibiting O2′-to-NPO hydrogen bonding. While the O2′-deprotonated state depends primarily on distance because of electrostatic repulsion, both distance and orientation are important when in the O2′-protonated state owing to hydrogen bonding. In fact, for most of the 3.5% of the ribozyme trajectory when the O2′-to-pro-S_P NPO hydrogen bond is not formed, it is the hydrogen bonding angle rather than distance that is poor (Figure 4E). We investigated whether this 3.5% subpopulation, dominated by poor hydrogen bonding angles, retained good in-line fitness. Strikingly, a heatmap of in-line fitness distances and angles of this subpopulation (Figure S6A) reveals that good in-line fitness is maintained, with most of the subpopulation (76%) meeting the cutoffs for good in-line fitness (Figure S6B). Furthermore, when considering only the subpopulation that resides extremely far from the hydrogen bonding cutoffs (hydrogen bond angle less than 90°), good in-line fitness is still largely maintained (71%) (Figure S6C, D). It is thus possible that this 3.5% subpopulation represents the configurations that undergo deprotonation and reaction since the O2′ is positioned for in-line nucleophilic attack but the hydrogen bonding to the NPOs is absent.

Impact of Na⁺ Ion Presence on the pK_a of A-1(O2′)

The previous sections reported that the O2′ pK_a is elevated to 18.5 ± 0.8 and identified significant factors of ion binding, solvent interaction, hydrogen bonding, and electrostatic interaction that could result in a pK_a shift in a qualitative fashion. We now present a more quantitative assessment of the effect of Na+ ion association with the O2' on the pK_a. Then, in the next section, we turn to the effect of a guanine functional group on the pK_a.

In the simulations discussed above, Na⁺ ions were allowed to move freely without the use of any restraints. At least one Na⁺ ion resides within 3 Å of the protonated O2′ during 5.2% of the trajectory, a small but still appreciable enough fraction of the trajectory to consider. When the O2′ is deprotonated, one or more Na⁺ ions reside within 3 Å of the oxyanion for the entire trajectory. We wondered what the O2′ pK_a was during the fraction of the trajectory (5.2%) when at least one Na⁺ ion was nearby during the O2′-protonated state since that might favor the reaction by lowering the pK_a. In attempt to measure this microscopic O2′ pK_a for those rare events, we performed thermodynamic integration with a Na⁺ ion restrained near the O2′ (see Supporting Information). These simulations resulted in an O2′ pK_a of 16.1 ± 1.0, 2.4 units below that of the unrestrained simulations (Table S2).

For the O2′-protonated state, plots of Na⁺ isodensity reveal high occupation near the O2′, a consequence of the Na⁺−O2′ distance restraint biasing the Na⁺ ion to the O2′ bound state (Figure S7A). Substantial ion density is found in two regions: between the O2′ and G8(O6) (Figure S7A, upper right) and between the O2′ and solvent (Figure S7A, lower left). A plot of running coordination number of Na⁺ ions with respect to the O2′ shows an average of nearly one Na⁺ ion residing within 3 Å of the protonated O2′ (Figure S7B), moving between these two regions. We rationalized that the proximity of a Na⁺ ion to the O2′ may disrupt the O2′-to-pro-S_P hydrogen bond and thus facilitate the reaction for those instances in which a Na⁺ ion is nearby and the O2′ pK_a is lowered; however, the presence of the ion did not appear to have this effect, as strong hydrogen bonding is maintained (Figure S8). Given that Na⁺ ion binding is rare in the unrestrained simulation, that it only depresses the pK_a to 16.1 ± 1.0, and that it does not prevent the dominant O2′-to-pro-S_P hydrogen bond, it seems unlikely that Na⁺ ion binding in the fully O2′-protonated state initiates the reaction.

For the O2′-deprotonated state, the Na⁺ ion running coordination number and isodensity plots are close to those observed for the trajectories without a restrained Na⁺ ion (Figure S7C, D). There is an average of 1.9 Na⁺ ions within 3 Å of the O2′, with one ion occupying the space between the O2′ and pro-S_P NPO and the other ion in the space between the O2′ and G8(O6).

Impact of the Exocyclic Amine of G8 on the pK_a of A-1(O2′)

We next focused on how the O2′ pK_a was impacted by G8(N2), which predominantly donates a hydrogen bond to the pro-S_P NPO of G1 in our simulations but also resides near the O2′ (Figure 1). We rationalized that the N2 could depress the pK_a of the O2′ by competing with it for NPO hydrogen bonding in the O2′-protonated state, by interacting with the O2′ oxyanion in the O2′-deprotonated state, or a combination of these. We therefore ran simulations on the G8I variant and hypothesized that the resulting O2′ pK_a would be higher than that observed for the WT ribozyme. In the G8I variant, the guanine at position 8 is replaced by inosine, which differs from guanine in that the exocyclic amine is replaced by a hydrogen.

We propagated trajectories of G8I for both the O2′-protonated and deprotonated states (Figure 8). In the O2′-protonated G8I trajectory, the phosphate flips away from A38 (Figure 8A, black) and then the sugar pucker of A-1 quickly flips from the southern conformation (2′-endo) observed in the WT ribozyme simulations to a northern conformation (3‱-endo) near 345 ns in the trajectory (Figure 8A, blue; Figure 8C, panel 3). The phosphate remains flipped away, and the pucker remains in the northern conformation for the rest of the trajectory. The same conformational changes occur in the O2′-deprotonated trajectory, with the phosphate flipping away from A38 near 29.1 ns (Figure 8B, black; Figure 8C, panel 2) and the sugar pucker flipping near 426.6 ns in the trajectory (Figure 8B, blue; Figure 8C, panel 3). The TI trajectories were propagated for shorter lengths (see Supporting Information), and a pucker flip was only observed for one lambda value (λ = 0.08198) of replicate 2 (Table S1). The trajectory within this lambda window was propagated again, and A-1 does not flip to a northern conformation in the second trajectory. Thus, the resulting O2′ pK_a calculations are reflective of the G8I variant when the A-1 sugar remains near the southern pucker conformation, consistent with the WT ribozyme simulations performed in this study and the crystal structure of the G8I variant (PDB ID 1ZFT).¹³

Figure 8.

Conformational changes in the G8I variant hairpin ribozyme simulations. The values of in-line fitness (grey), the epsilon dihedral (black) and the sugar pucker (blue) of A-1 throughout the 500 ns trajectory are shown when the O2′ is A) protonated and B) deprotonated. The red vertical lines separate regions with different conformations and are drawn at 345 ns in panel A and at 29.1 ns and 426.6 ns in panel B. For comparison of the G8I variant to WT, the dashed red horizontal lines mark the average in-line fitness from the WT simulations, which are 0.45 for the protonated state (panel A) and 0.43 for the deprotonated state (panel B). C) MD configurations from the O2′ deprotonated trajectory exemplify the different conformations observed in panels A and B. Atoms that form the epsilon dihedral plotted in panels A and B are identified by the black traces. Residues A-1 and I8 are labeled. Red numbers depicted in each configuration correspond to the regions in the plots, separated by red vertical lines and also labeled with red numbers.

In contrast to our hypothesis, simulations of the G8I variant did not lead to an elevated pK_a for the O2′. Instead, they resulted in a somewhat lower O2′ pK_a relative to the WT ribozyme, with a value of 16.4 ± 1.7 obtained from averaging over the three G8I replicates. While the sugar pucker does not flip to a northern conformation in any of these G8I simulations, the scissile phosphate flips away from A38 in some λ windows within replicate 2. Additionally, the I8(N1)-to-O2′ hydrogen bond does not form during part or all of several of the G8I λ windows in replicates 1 and 2. Lower O2′ pK_a values of 15.4 and 15.0 were calculated from G8I replicates 1 and 2, respectively, while a WT-like O2′ pK_a of 18.3 was calculated from G8I replicate 3 (Table S4, bottom row). Notably, G8I replicate 3, with a calculated O2′ pK_a similar to that of the WT ribozyme, is more reflective of the WT simulations in terms of phosphate orientation and I8(N1)-to-O2′ hydrogen bonding (Table S4, compare “G8I Ribozyme” column 3 to “WT Ribozyme” columns). Apparently, the O2′ pK_a of G8I is either decreased when WT-like hydrogen bonding is lost (G8I replicates 1 and 2) or the same when WT-like hydrogen bonding is maintained (G8I replicate 3); however, in no case is the O2′ pK_a of G8I elevated relative to WT like we hypothesized.

We then considered whether changes to in-line fitness accompanied the changes in conformation at the active site. In-line fitness angles and distances were quantified by using an equation similar to that published by the Breaker group (see Supporting Information).²⁸ Ideal in-line fitness geometries receive a score near unity, and poor geometries receive a score near zero (Figure 8A, B, top panels). Overall, the alternative conformations sampled by the G8I variant have poorer values of in-line fitness than the average in-line fitness of the WT ribozyme in the O2′-protonated and especially in the O2′-deprotonated states (Figure 8A, B top panel, compare gray to red dash). This difference can also be seen by comparing in-line fitness heatmaps of the different conformations sampled in the G8I variant simulations (Figure S9) to the in-line fitness heatmaps of the WT ribozyme (Figures 6B, S4B), where fitness is especially poor for conformations 2 and 3. The points in the heatmaps of these alternative conformations fall primarily outside of the in-line fitness cutoffs.

We also examined Na⁺ ion and solvent occupancy near the O2′ for the G8I variant. For the following analysis, we only considered the trajectory up to 340 ns for the O2′-protonated state and up to 420 ns for the O2′-deprotonated state. The sugar pucker of A-1 remains in the southern conformation during these times. Plots of Na⁺ ion isodensity reveal ion density between the O2′ and solvent for the O2′-protonated state and between the O2′ and pro-S^P NPO and the O2′ and I8(O6) for the O2′-deprotonated state (Figure S10A, C), similar to the WT ribozyme (Figure 2A, C). An average of 0.06 and 2.0 Na⁺ ions reside within 3 Å of the O2′ for the O2′-protonated and deprotonated states, respectively, again similar to the WT ribozyme (Figure S10B, D). The solvent accessible surface area of the O2′ is either similar to or somewhat below that observed for the WT ribozyme (Figure S11A, B, C). Except for when the phosphate is flipped away from A38, plots of the running coordination number of hydrogen atoms belonging to water with respect to the O2′ are similar to those observed for the WT ribozyme (Figure S11D, E). After the phosphate flips during the O2′-deprotonated state trajectory, an average of 0.85 hydrogen atoms from water reside within 2.4 Å of the O2′, greater than what was observed for the WT ribozyme (Figure S11F). Overall, our observations indicate that the exocyclic amine may play an important role in keeping the active site oriented for nucleophilic attack but not in pK_a perturbation. Furthermore, when the G8I variant moves into alternate conformations, the O2′ pK_a is depressed, but when it happens to stay in a WT-like conformation, the O2′ pK_a is unperturbed.

Discussion

By running simulations of the hairpin ribozyme, we calculated that its nucleophilic O2′ has an elevated pK_a of 18.5 ± 0.8 and identified several factors that may contribute to this upward shift. These included the presence of a hydrogen bond in the O2′-protonated state along with reduced O2′ hydration and a short distance from the O2′ to the adjacent NPOs in the O2′-deprotonated state. In comparison to ApG, the O2′ of the ribozyme binds more Na⁺ ions in both the O2′-protonated and deprotonated states, and it is much better set up for in-line attack despite the elevated pK_a. We also found a correlation between O2′ orientation for nucleophilic attack and interaction with the nearby NPOs of the scissile phosphate, which would likely contribute to the pK_a elevation. Simulations with a Na⁺ ion restrained to the O2′ revealed a microscopic pK_a of 16.1 ± 1.0, indicating that the pK_a is depressed during the rare instances when a Na⁺ ion directly coordinates the protonated O2′; however, this did not serve to prevent the O2′-to-pro-S_P hydrogen bond. To ascertain the impact of the exocyclic amine of G8 on the O2′ pK_a, simulations on the G8I variant ribozyme were performed and resulted in an O2′ pK_a of 16.4 ± 1.7. However, the active site of the G8I variant sampled alternative conformations not observed in the WT ribozyme that led to overall poorer values of in-line fitness.

In the following sections, we consider O2′ pK_a shifting in RNAs and re-evaluate the idea that an elevated O2′ pK_a is inhibitory to catalysis. We consider the importance of positioning of the O2′ for nucleophilic attack. Finally, we compare observations on Na⁺ ion binding with experimental data and consider potential roles monovalent ions may have in catalysis.

Considerations for Shifting of the Nucleophilic O2′ pK_a

The pK_a values of functional groups within RNAs are often perturbed. For instance, Watson-Crick (WC) base pairing shifts the pK_a of all moieties involved in hydrogen bonding away from neutrality, with acceptors shifting lower and donors shifting higher. For example, while unpaired adenosine typically has a pK_a of 3.5, NMR spectroscopy revealed that base paired adenosines have pK_a values of ≤ 3.1.^55,56 When in a WC base pair, the U(N3)-to-A(N1) hydrogen bond stabilizes the N1 in its deprotonated state, making it more energetically unfavorable to protonate. The molecular basis behind these shifts is that protonation or deprotonation of RNA is coupled to folding: protonating or deprotonating a WC base pairing weakens RNA structure,¹⁸ evident by the pH dependence of RNA helix melting temperature.⁵⁷

With the limited repertoire of four nucleobases, pK_a perturbation in RNA extends the diversity of roles the nucleobases can play. For instance, a protonated adenine or cytosine can partake in unique base pairing inaccessible to their neutral forms^58,59 and can also serve as a general acid in a ribozyme.⁶⁰ Indeed, functional residues within the active sites of ribozymes frequently have shifted pK_a values. Raman crystallography revealed that C75 in the HDV ribozyme has a pK_a of 6.40 in the presence of 2 mM Mg²⁺, far above its unperturbed value of 4.2.^55,61 This pK_a near neutrality promotes the protonation of C75, enabling its function as general acid in the cleavage mechanism of the ribozyme.⁶²

We calculated a pK_a of 18.5 ± 0.8 for the nucleophilic O2′ in the hairpin ribozyme, well above that of the internucleotidic O2′ in ApG of 12.5, and so we investigated what factors might perturb this pK_a. We considered changes between the O2′-protonated and deprotonated states with respect to binding of Na⁺ ions, hydration of the O2′, hydrogen bond donation to the NPOs, and electrostatic repulsion from the NPOs as four potential contributors to the upward shifted O2′ pK_a. Among this list, Na⁺ ion binding does not appear to contribute to the increased O2′ pK_a. In both the O2′-protonated and deprotonated states, the O2′ in the ribozyme binds more Na⁺ ions than that in ApG (Figures 2, S1), although the amount bound in the fully O2′-protonated state is relatively small, suggesting a minor effect on O2′ pK_a. On the other hand, the O2′ in the ribozyme has reduced hydration upon O2′ deprotonation, which signifies that hydrogen bonds from water are broken; in contrast, ApG has enhanced hydration upon O2′ deprotonation (Figure 3). Additionally, the O2′ of the ribozyme, but not of ApG, donates a strong hydrogen bond to the pro-S_P NPO, stabilizing the proton (Figure 4), akin to what is observed in WC base pairs. And finally, the deprotonated O2′ remains closer to the negatively charged NPOs in the ribozyme than in ApG, which leads to greater electrostatic repulsion in the ribozyme (Figure 5). Collectively, these interactions would lead to an increased O2′ pK_a, consistent with our pK_a calculations. Additionally, we tested the hypothesis that the nearby exocyclic amine of G8 functions to reduce the pK_a of the O2′. Calculations of the G8I variant ribozyme resulted in an O2′ pK_a of 16.4 ± 1.7, suggesting that the exocyclic amine has little effect on or may even increase the O2′ pK_a. We will next consider what implications an elevated O2′ pK_a has on the mechanism of catalysis in the hairpin ribozyme.

Implications of an Elevated O2′ pK_a for Rate Acceleration

With a pK_a of 18.5 ± 0.8, removal of the proton from O2′ is quite unfavorable in the ground state. This raises the question of how rate acceleration occurs. We consider three scenarios for reaction: one involving O2′ pK_a perturbation towards neutrality in a rare ground state, and two others involving O2′ pK_a perturbation upon approach to the transition state. It is possible that deprotonation occurs during a rare ground state when the microscopic O2′ pK_a falls far below 18.5 ± 0.8. A strong inhibitory, O2′-to-pro-S_P NPO hydrogen bond forms throughout 96.5% of the WT ribozyme trajectory (Figure 4E). One would expect the O2′ pK_a would fall during the 3.5% of the trajectory when this hydrogen bond does not form. Furthermore, a Na⁺ ion directly binds the protonated O2′ during 5.2% of the WT ribozyme trajectory, and an O2′ pK_a of 16.1 ± 1.0 was calculated from the simulations with a Na⁺ ion restrained to the O2′. This indicates that the O2′ pK_a drops during the 5.2% of trajectory when a Na⁺ ion directly binds. Therefore, during the rare instances when both 1) the inhibitory hydrogen bond is not formed and 2) a Na⁺ ion directly binds the O2′, the pK_a of the O2′ could drop several units, favoring proton abstraction by a general base.

In the case of the glmS ribozyme, our lab previously found experimental evidence suggesting the nucleophilic O2′ is tied up in an inhibitory hydrogen bonding interaction with the pro-R_P NPO of the scissile phosphate.^24,25 Substituting the pro-R_P NPO with a sulfur (a weaker hydrogen bond acceptor) in the cofactor-free ribozyme increased the catalytic rate 30-fold, representing a large inverse thio effect. Similar findings were also recently reported for the Varkud satellite ribozyme with a 6-fold inverse thio effect.²⁶ For the hairpin ribozyme investigated herein, two separate studies reported slight inverse thio effects where replacing the pro-S_P NPO with a sulfur enhanced the catalytic rates by 1.2-fold and 1.8-fold.^47,48 However, these experiments were performed using a two-way junction hairpin ribozyme where the rate-limiting step may be docking rather than chemistry.⁶³ Rate enhancements in cleavage due to release of hydrogen bonding from the sulfur substitutions may not be observed if this is the case. Nonetheless, even if the O2′ pK_a was lowered by several units in a rare state, no general base, which needs a pK_a near neutrality to be in the functional deprotonated form, could effectively compete for this proton since the O2′ pK_a would still be too high. Finally, binding of a Na⁺ ion and loss of the inhibitory hydrogen bond are not correlated, making their coincidence especially rare. This does not mean that this 3.5% population is necessarily unimportant for the reaction. For instance, this subpopulation could still be important in freeing up the O2′ proton for removal from the general base.

We now consider O2′ pK_a perturbation near the transition state. It is possible, for instance, that deprotonation occurs concomitant with nucleophilic attack. In this case, the O2′ pKa would drop to a value between the pK_a of the alcohol on the ribozyme calculated here (18.5 ± 0.8) and a pK_a similar to that of a protonated ether (roughly −4), which is a massive 22 pK_a unit difference.⁶⁴ This relates to Jencks’s libido rule for general acid-base catalysis, which states that general base catalysis is only possible when 1) the pK_a of the nucleophile changes considerably after completion of the reaction and 2) the pK_a of the general base resides between that of the nucleophile in its substrate (high pK_a) and product (low pK_a) forms.⁶⁵ For the glmS ribozyme, non-linear Poisson-Boltzmann with Linear Response Approximation calculations were previously performed to predict the pK_a of the nucleophilic O2′, resulting in a similarly high value of 19.6 ± 0.8.⁶⁶ Quantum mechanical/molecular mechanical (QM/MM) MD simulations were also performed for the glmS ribozyme with the general base (G40) in its deprotonated functional form, which indicated that the O2′ is deprotonated by G40 during nucleophilic attack, when in the course of the reaction the pK_a of the O2′ would be lower. We propose that a similar mechanism is operative in the hairpin ribozyme, enabling the O2′ to relinquish its proton to a suitable general base (i.e., one with a pK_a near neutrality so that it is in its deprotonated form in the reactant state) or to buffer or water during the course of the reaction.^5,13,67,68

Until now, we have considered the O2′-to-pro-S_P NPO hydrogen bond as an inhibitory interaction since it likely raises the pK_a of the nucleophile. However, if the pro-S_P NPO functions as the catalytic general base, the high frequency of hydrogen bond formation would actually favor catalysis. An NPO typically has a pK_a near 1 for a phosphodiester and would thus function poorly as a general base.⁵⁵ During the reaction, the scissile phosphate temporarily becomes a phosphorane either as an intermediate or during the transition state. Prior studies have reported pK_a values ranging from 11.3 to 15 for the ionization of phosphorane monoanions.^69-74 Therefore, similar to how the O2′ pK_a may decrease upon nucleophilic attack, the pro-S_P NPO pK_a may elevate during the reaction, increasing its feasibility to act as general base. Using QM/MM calculations, four previous studies on the hairpin ribozyme found that one or both NPOs were suitable general bases in the reaction.^9-12 The dominant O2′-to-pro-S_P NPO hydrogen bonding observed in our simulations might suggest that the pro-S_P NPO could act as the general base. However, given that experiments did not show a strong thio effect at either NPO,^46,48 it seems unlikely that the NPOs accept the O2′ proton.

The Importance of Nucleophile Positioning for Catalysis

The hairpin ribozyme and ApG differ widely in the rates at which transphosphorylation occurs. Nesbitt and colleagues reported an experimentally observed rate constant (k_obs) of 0.19 min⁻¹ for the hairpin ribozyme (pH 7.5, 25 °C, 2.5 M KCl).²⁰ We can estimate the k_obs for ApG at pH 7.5 using the methods of Li and Breaker.¹⁴ They measured a k_obs of a chimeric RNA/DNA oligonucleotide where cleavage primarily occurred at a phosphate flanked by an A and G under a variety of experimental conditions. Equations were formulated to extrapolate the measured k_obs to other experimental conditions. Under conditions similar to those mentioned above for the ribozyme (pH 7.5, 23 °C, 3.16 M KCl), the chimeric ApG substrate has a predicted k_obs of 3.7 × 10⁻⁸ min⁻¹. Therefore, the hairpin ribozyme enhances the rate of transphosphorylation roughly 10⁷-fold, similar to estimates for the hammerhead ribozyme.⁷⁵

Part of this rate enhancement could arise from the hairpin ribozyme positioning the nucleophilic O2′ for attack. In our simulations, the ribozyme samples in-line fit conformations much more frequently than ApG (Figures 6, S4). The ribozyme facilitates catalysis by orienting the active site for chemistry, specifically through in-line fitness. It has previously been estimated that orienting the O2′ for nucleophilic attack in ribozymes can increase the rate up to 100-fold.^2,76 Indeed, going from an in-line fitness of 2.6% to 92.7% from ApG to the ribozyme in our O2′-protonated trajectories (Figure 6A, B) represents a 36-fold increase, which is within this 100-fold upper limit. This result is also consistent with the findings from a prior theoretical study on an RNA splicing endonuclease, which predicted that promoting in-line fitness increased the rate by about 12-fold.⁷⁷ Because in-line fitness only accounts for a fraction of the estimated 10⁷-fold rate increase in the ribozyme, the remainder of this rate acceleration must come from other factors such as neutralizing the negative NPO charges as the substrate proceeds to the transition state or from proper positioning of general acids and bases in their functional protonated and deprotonated forms, respectively.^2,10

In our G8I variant ribozyme simulations, the active site conformation within the variant departed from that observed in the WT ribozyme simulations and primarily sampled conformations where the in-line fitness cutoffs were not satisfied (Figures 8, S9). Additionally, an elevated O2′ pK_a relative to that of the WT ribozyme was not observed, contrary to our expectation. Thus, a principal consequence of removing the exocyclic amine appears to be loss of orientation of the O2′ for nucleophilic attack. By comparing the crystal structures of the G8I variant with the WT ribozyme, the Wedekind lab noted that the exocyclic amine appears to serve a role in aligning the active site for nucleophilic attack.¹³ This loss in alignment is consistent with the decrease in an experimentally measured k_obs of roughly 10-fold for the G8I variant relative to WT.⁸

We also reported that there appears to be an inherent connection between distance of the nucleophilic O2′ to the NPOs and good in-line fitness, which is a measure of the O2′-P distance and O2′-P-O5′ angle (Figure 7B). These close proximities enable the formation of an O2′-to-NPO hydrogen bond when the O2′ is protonated and results in electrostatic repulsion when the O2′ is deprotonated, both of which favor an upward shifted O2′ pK_a. A similar observation on the correlation between in-line fitness and O2′-to-NPO hydrogen bonding has been made previously for other simulations of the hairpin ribozyme.⁴⁴ Given the small rate enhancement of positioning the O2′ for nucleophilic attack, one may wonder why the scissile phosphate is organized in such a way. If the ribozyme stabilized a conformation with poor in-line fitness, the estimated 36-fold increase in rate would be lost, but the pK_a of the O2′ could potentially drop substantially. However, promoting such a conformation would not only result in a loss of rate enhancement, it would also cause a substantial rate decrease since the nucleophilic O2′ would seldom be able to attack the phosphorus. While this is a seemingly obvious point, it is an important one: maintaining good in-line fitness is confounded with this inhibitory interaction but does much in terms of avoiding the stabilization of conformations that would abolish any possible rate enhancement. A corollary is that in ordinary RNA, the inhibitory hydrogen bond may serve a productive function: it may be a way to prevent RNA degradation by capturing the O2′ when it does fluctuate into an in-line geometry. Data attained herein on the in-line fit sub-population of ApG supports this notion (Figure 7B). Experimentally, one might then expect RNA degradation to be accelerated upon dithio substitution; however, our lab previously found that this was not the case after measuring the cleavage kinetics of a chimeric RNA/DNA oligonucleotide.²⁵ It is possible that more complex compensating effects arise upon substitution of the NPOs with sulfur.

Participation of Ions in the Reaction

We now consider the potential for involvement of ions in the reaction on the basis of observations from our simulations and from the experimental literature. While only a low average of 0.05 Na⁺ ions directly coordinate to the O2′-protonated state, almost two Na⁺ ions directly coordinate to the O2′-deprotonated state in the hairpin ribozyme simulations (Figure 2). In the O2′-protonated state, binding primarily occurs between the O2′ and G8(O6), while in the O2′-deprotonated state, the two Na⁺ ions flank the O2′, with one ion again coordinating G8(O6) and the other ion coordinating the pro-S_P NPO. Moreover, an average of 0.91 Na⁺ ions reside within 5.6 Å of the protonated O2′ (Figure S1), sometimes interacting with the O2′ and other times simply coordinating other moieties near the alcohol (Figures S2).

Like most small ribozymes, the hairpin ribozyme is highly functional in solutions containing diverse divalent metal ions including Mg²⁺.⁷⁸ Prior studies have shown that the ribozyme maintains nearly full activity after replacing 10-12 mM Mg²⁺ with the outer-sphere ion mimic [Co(NH₃)₆]³⁺, indicating that precluding inner-sphere coordination with metal ions does not significantly affect catalysis.^46,48 Proficient cleavage in 10 mM [Co(NH₃)₅Cl]²⁺, which bears a +2 charge instead of a +3 charge, was also observed.⁴⁸ Scott and colleagues demonstrated that the ribozyme catalyzes the reaction in 4 M Li⁺ in the absence of polyvalent ions with only a 1.4-fold reduction in rate.¹⁹ In fact, the ribozyme is also active in high concentrations of other monovalent species, including NH₄⁺.²⁰ These findings indicate that monovalent ions alone can support catalysis and that the cationic monovalent species does not need to be a metal ion. Moreover, monovalent ions may serve a specific role. Intriguingly, relative to [Co(NH₃)₆]³⁺ alone, a mixture of 50 mM Na⁺ with 12 mM [Co(NH₃)₆]³⁺ increased the rate 4.1-fold,⁴⁶ and a mixture of 100 mM Na⁺ with 10 mM [Co(NH₃)₆]³⁺ enhanced folding.⁷⁹ Further addition of Na⁺ (up to 500 mM) does not result in an additional increase in rate, indicating a minimal amount of monovalent ions are needed to further stimulate the reaction.⁴⁶ Additionally, a Na⁺ ion was resolved in a 2.25 Å resolution crystal structure of a product mimic of the ribozyme and directly coordinates the O2′.⁴² While the monovalent ions may stabilize the fold, the fact that the rate reached a plateau at modest Na⁺ concentrations⁴⁶ in the [Co(NH₃)₆]³⁺ background suggests that the ions might serve a role beyond folding, perhaps by interacting directly in the transition state.

The observed binding of nearly two Na⁺ ions in our simulations to the deprotonated O2′ (Figure 2C, D) is reminiscent of the two-metal ion mechanism employed by many RNA and protein enzymes.^80,81 For instance, the group I ribozyme uses at least two Mg²⁺ ions in catalyzing RNA splicing, where both divalent ions coordinate one of the NPOs of the scissile phosphate and one functions to activate the nucleophile.⁸² While we were able to simulate the ribozyme with the O2′ fully deprotonated prior to nucleophilic attack, this precise state may not occur to any meaningful extent owing to the exceptionally high O2′ pK_a of 18.5 ± 0.8. More realistic is a mechanism in which the O2′ is deprotonated during the course of the reaction. If this is assumed to be the case, a two-metal ion mechanism may assemble on the way to the transition state.

Conclusions

Molecular dynamics simulations were employed to calculate a p1_a of 18.5 ± 0.8 for the nucleophilic O2′ in the hairpin ribozyme. An O2′-to-pro-S_P hydrogen bond, electrostatic repulsion between the deprotonated O2′ and the adjacent NPOs, and reduced hydration of the deprotonated O2′ are all factors likely contributing to this elevated pK_a. The former two contributors appear to be a consequence of positioning the O2′ for in-line nucleophilic attack, a critical requirement for the reaction to occur. While the exocyclic amine of G8 is positioned near the O2′, pK_a calculations on the G8I variant ribozyme suggest that it does not play an important role in pK_a depression. Due to the high O2′ pK_a, we favor a mechanism wherein deprotonation occurs during the course of nucleophilic attack when the pK_a would drop substantially. We also found that Na⁺ ions may play some role in depressing the O2′ pK_a, evident from higher Na⁺ ion occupancy near the O2′ in the ribozyme relative to ApG, and a lower microscopic pK_a of 16.1 ± 1.0 for the simulations with a restrained Na⁺ ion. Experimental data support the notion that monovalent ions could aid in deprotonation prior to or during nucleophilic attack.