Molecular mechanism of the site-specific self-cleavage of the RNA phosphodiester backbone by a twister ribozyme
The catalytic activity of some classes of natural RNA, named as ribozymes, has been discovered just in the past decades. In this paper, the cleavage of the RNA phosphodiester backbone has been studied in aqueous solution and in a twister ribozyme from Oryza sativa. The free energy profiles associated with a baseline substrate-assisted mechanism for the reaction in the enzyme and in solution were computed by means of free energy perturbation methods within hybrid QM/MM potentials, describing the chemical system by the M06-2× functional and the environment by means of the AMBER and TIP3P force fields. The results confirm that this is a stepwise mechanism kinetically controlled by the second step that involves the P–O5′ breaking bond concomitant with the proton transfer from the OP1 atom to the leaving O5′ atom. 18O kinetic isotope effects on the nucleophile and leaving oxygen atoms, in very good agreement with experiments, also support this description. Nevertheless, the free energy profiles in the enzyme and in solution are almost coincident which, despite that the rate-limiting activation free energy is in very good agreement with experimental data of counterpart reactions in solution, rule out this substrate-assisted catalysis mechanism for the twister ribozyme from O. sativa. Catalysis must come from the role of alternative acid–base species not available in aqueous solution, but the rate-limiting transition state must be associated with the P–O5′ bond cleavage.
KeywordsTwister ribozyme Reaction mechanism QM/MM Free energy profiles KIEs
Chemical reactions are traditionally known to be catalysed in nature by protein enzymes, but in the early 80s it was discovered that natural RNA molecules, named as ribozymes, present catalytic activity [1, 2]. According to their size, these natural ribozymes can be divided into three families: small self-cleaving RNAs (less than 200 nucleotides), medium-sized self-splicing introns and larger catalytic ribonuclear protein (RNP) complexes . Some authors assemble the two last families in the same one . The class of small ribozymes includes the hammerhead , hairpin , hepatitis delta virus (HDV) , Varkud satellite (VS) , glmS , twister , twister sister , pistol  and hatchet . The reaction that is catalysed by these ribozymes is the site-specific self-cleavage of the RNA phosphodiester backbone, as well as the reverse ligation process.
It has been proposed that different ribozymes employ different agents to activate the nucleophile and the leaving group. Thus, experimental studies and theoretical calculations have suggested that the nucleophile is activated in the HDV ribozyme through a divalent cation located in the active site, which can be partially hydrated, and would serve either as a Lewis acid, a Brønsted base or both [13, 14]. In the case of the hammerhead, experimental and computational studies suggest that an adenine (A38) and a guanine (G8) have an important role in the catalytic mechanism, the later acting as an acid (“AH” in Scheme 1) whose hydroxyl O2′ is activated by the presence of a Mg2+ cation [15, 16]. In the rest of small ribozymes, Mg2+ cation does not play a chemical but only structural role. The activation of the nucleophile and leaving groups, if occurred, has been proposed to take place through nucleosides located in the active site as general acid or base catalysts (“AH” and “B” in Scheme 1).
Recent kinetic studies of the pH dependence of the rate constant on the wild-type Oryza sativa and several mutants suggested that G33 must be the base activating the nucleophile (“B” in Scheme 1) , while A1 must be acting as a general acid capable of donating a proton to the oxyanion leaving group (“AH” in Scheme 1) . Moreover, the structures also support the role of G33 in stabilizing the negative charge developed on the phosphate group in the TS through the interaction between the exocyclic NH2 group and the non-bridging oxygen atoms of the phosphate. Surprisingly, atomic mutagenesis of the nitrogen atoms of the A1 nucleobase has established that the pH dependence of the cleavage reaction arises in part from the protonation state of the N3 ring nitrogen of that adenine, and not of the N1 atom, that usually is the acid position . The standard pKa value of N3 of adenine in solution is 1.5, and consequently, a dramatic shift must be suffered in order to be protonated at physiological conditions. Lilley and co-workers suggested that the origin of this shift must be found in the local environment, since the six-membered ring of A1 lies between three phosphate groups . This pKa shift was predicted by Gaines and York from computational simulations that rendered a variation of the pKa at the N3 position of A1 towards neutrality by approximately five units .
Molecular dynamics simulations have been carried out by Hammes-Schiffer and co-workers to elucidate the self-cleavage mechanism and structural properties of the env22 twister ribozyme . One of the two Mg2+ ions located in the active site interacting with the non-bridging oxygen atoms of the scissile phosphate and a water molecule could stabilize the TS, and the activated water molecule could play the role of general acid. Furthermore, a Na+ located between A1(N3) and A1(O5′) could stabilize the negative charge developed during the reaction. It was observed that these ions retained their position during the molecular dynamics simulations. Thus, a relatively rigid network of hydrogen bonding, electrostatic and π-stacking interactions around the self-cleavage site was then proposed as being important in either the stabilization of the geometry and catalysis. The study of Hammes-Schiffer and co-workers , published just after the work of Gaines and York , suggested a quite different mechanism for the Oryza sativa and env22 twister ribozymes.
2 Computational methods
The computational study of the site-specific self-cleavage reaction of the RNA phosphodiester backbone in terms of free energies presents two problems. First, as previously demonstrated by Mulholland and Otyepka for the catalytic mechanism of a hairpin ribozyme, the use of semiempirical methods to describe the QM region in multiscale schemes can predict reaction pathways significantly different than the ones obtained at more accurate level using more expensive methods . The second computational problem is related to the amount of internal coordinates associated with the chemical reaction. The reaction involves, at least, six bond forming and breaking processes. Then, a complete exploration of multidimensional free energy surfaces based on, for instance, umbrella sampling (US) methods, is not viable. Consequently, in this work the exploration of the free energy profile has been carried out by means of free energy perturbation (FEP) methods. These methods imply the sampling of the environment (usually the MM region) along a previously traced IRC from TS located at QM/MM level. Keeping in mind that the sampling is performed along the IRC, the free energy profile is obtained along a realistic reaction coordinate. Nevertheless, a possible limitation of the technique is that, since there is no sampling on the chemical system, the result could be biased by the fact that just one TS structure is used. In our case, since the QM subset of atoms, or chemical system, cannot present significant different conformations, this limitation is not expected to be dramatic. Moreover, the use of FEP methods has the advantage that the QM geometries along the reaction path can be obtained from IRC that can be traced at high level of theory. The M06-2X hybrid functional developed by Truhlar’s group [29, 30] with the standard 6-31+G(d,p) basis set has been selected to treat the QM subset of atoms. The rest of the system (RNA, water molecules and counterions) was described using the AMBER  and TIP3P  force fields, as implemented in the fDYNAMO library [33, 34]. Therefore, the QM wave function is polarized by the charges of the MM subset of atoms.
The coordinates of the initial structure of the twister ribozyme from Oryza sativa were chosen from the X-ray structures deposited in the PDB with code 4OJI . This X-ray structure contains 5 Mg2+ cations, but none of them located in the cleavage site. Then, the RNA was solvated in a truncated octahedral box by adding 10 Å buffer of water molecules around RNA system (the resulting systems were of 85 × 105 × 92 Å3). A total of 43 Na+ counterions were required to electrostatically balance the system which were placed into optimal electrostatic positions around the protein. The coordinates of the hydrogen atoms were added using the AMBER tools, considering the standard pKa values of the titratable residues. After properly modified, water molecules with an oxygen atom lying within 2.8 Å of any heavy atom of the RNA were removed. The resulting QM/MM system consisted of 19 atoms in the QM region and 36135 atoms in the MM region.
Additionally, in order to compare the enzymatic reaction with the uncatalysed process in water solution, the same QM atoms (including the corresponding link atoms) were placed in a pre-equilibrated cubic box of 50 Å of lattice. The removal of the overlapping waters led to a model composed by 22 QM atoms and 4156 mobile TIP3P water molecules, which was studied with the same methodology as the ribozyme.
In Eq. (4), the total partition function, Q, was computed as the product of the translational, rotational and vibrational partition functions for the isotopologs in reactants and TS in the active site of the open- and closed-loop conformation monomers. The Born–Oppenheimer, rigid rotor and harmonic oscillator approximations were considered to independently compute the different contributions. Keeping in mind that involved states, reactants and TS are in a condensed media (the active site of a protein), contribution of translation and rotation to KIEs are negligible. Nevertheless, the full 3 N × 3 N Hessians have been subjected to a projection procedure to eliminate translational and rotational modes, which transforms them into almost zero frequencies, as previously described . Thus, it has been assumed that the 3 N–6 vibrational degrees of freedom are separable from the six translational and rotational degrees of freedom of the substrate.
3 Results and discussion
These conclusions can be complemented with the analysis of the time evolution of the distance between the HO2′ and the OP1 atoms, and the O2′–P–O5′ angle (see Figure S1 in Supporting Information). The in-line conformation presents an adequate geometry for the direct transfer of the H2′ proton from the O2′ atom to the OP1 atom (the HO2′–OP1 interatomic distance is ca 1.9 Å along the simulation).
Relative potential energies of the different states appearing along the baseline mechanisms obtained at M06-2X/AMBER/TIP3P level in the ribozyme for the in-line and outline conformations, involving OP1 and OP2 atoms as proton shuttles
Free energy differences with reactants obtained from the M06-2X/AMBER/TIP3P FEPs in the ribozyme and in aqueous solution, before and after adding the zero-point vibrational energy (ZPVE)
The free energy profiles presented in Fig. 4 confirm that the mechanism of the nucleolytic self-cleavage of RNA proposed in Scheme 4 can take place in a stepwise manner through a stable intermediate. Interestingly, the free energy profile in the enzyme is almost coincident with the profile obtained in solution. The rate-limiting step corresponds to the second step involving the HO2′ transfer from OP1 to O5′ and the P–O5′ bond breaking. The quantum vibrational corrections diminish the activation free energy barrier of this step, TS2, by 2.7 and 2.9 kcal mol−1 in the ribozyme and in water, respectively. Thus, the rate-limiting activation free energy is 29.1 kcal mol−1 in both environments, suggesting no catalytic effect if the reaction would proceed in the ribozyme by means of this substrate-assisted mechanism. The reaction is endergonic in both media, although the product state is slightly more stabilized in solution than in the ribozyme (the reaction free energies are 7.6 and 2.3 kcal mol−1 in the ribozyme and in water, respectively).
Interatomic distances between key atoms on the different states appearing along the baseline mechanisms obtained at M06-2X/AMBER/TIP3P level (a) in the twister Oryza sativa ribozyme and (b) in aqueous solution
Atomic charges of key atoms obtained with the CHELPG method at M06-2X/6-31 + G(d,p)//AMBER level for the reaction in the (a) twister Oryza sativa ribozyme and (b) in aqueous solution, for the baseline mechanism starting from the in-line conformation of reactants
18O KIEs computed at M06-2X/6-31 + G(d,p)//AMBER level from TS1 and TS2 for the self-cleaving nucleolytic catalysed by the twister Oryza sativa ribozyme and in aqueous solution
O. sativa ribozyme
Our results for the 18O KIEs for the O2′ and O5′ substitutions in the ribozyme are 0.994 and 1.046, respectively, which are in good agreement with the experiments by Gu et al. . These authors reported 18O KIE values of 0.994 ± 0.002 for the substitution of the nucleophile O2′ and 1.014 ± 0.003 for the substitution of the leaving O5′, and with their previous QM results of 0.998 and 1.026, respectively .
The normal 18O KIE value for the substitution of O2′ in solution reflects the slightly differences detected in the geometries, as presented above. As observed, shorter interatomic distances involving the O2′ are detected in the TS2 located in the ribozyme than in solution, rendering slightly inverse 18O KIEs for the O2′ substitution in the ribozyme (0.994) and slightly normal in solution (1.010).
Finally, considering the values of the 18O KIE computed from the TS1, we can assert that a hypothetical mechanism kinetically controlled by the nucleophilic attack of O2′ to the P atom, concomitant with the HO2′ proton transfer to OP1, can be discarded.
The molecular mechanism for the cleavage of the RNA phosphodiester backbone has been studied in aqueous solution and catalysed by a twister ribozyme from Oryza sativa. In particular, the present paper shows the results of exploring the baseline or substrate-assisted mechanism by means of QM/MM MD simulations where the QM subset of atoms is described by a DFT functional (M06-2X). An initial equilibration of the ribozyme system was carried out by means of unbiased MD simulations with two different starting conformations of the reacting system: an outline conformation where the angle between the O2′–P forming bond and the P–O5′ breaking bond is equal to the values presented in the X-ray structure of the Oryza sativa twister ribozyme, and an in-line conformation where this angle was initially forced to be 145°, which is the value taken from the X-ray structure of the env22 ribozyme. Both conformations revealed to be stable during the MD trajectories but, keeping in mind the reaction under examination, it appears that the crystal structure of Oryza sativa is not a reactive conformation for the mechanism analysed in this work. This result justifies the need of performing MD simulations before starting the study of a chemical reaction in condensed media.
The reaction was studied by generating the corresponding PES from in-line and outline reactants state conformations and exploring the possibility of the two oxygen atoms of the phosphate group, OP1 and OP2, acting as the atoms involved in the transfer of the HO2′ atom. The potential energy barriers clearly indicate that the most favourable reaction mechanism would be the one starting from the in-line conformation and involving the OP1 atom as proton shuttle. Then, the free energy profile was computed at M06-2X/AMBER/TIP3P level by means of FEP methods only for this mechanistic route. The full free energy profile was also explored in solution, and the results confirmed that the proposed reaction mechanism takes place, in both media, through a stepwise mechanism kinetically controlled by the second step. The rate-limiting TS involves the P–O5′ breaking bond concomitant with the proton transfer from the OP1 atom to the leaving O5′ atom. The fact that the free energy profiles in the enzyme and in solution are almost coincident, rendering a rate-limiting activation free energy of 29.1 kcal mol−1, suggests no catalytic effect of the Oryza sativa twister ribozyme, if the reaction proceeds through a baseline substrate-assisted mechanism.
Warshel and co-workers, in a comparative study of the peptide bond formation reaction in water and catalysed by the ribosome , already pointed out that catalytic effects cannot be attributed to substrate-assisted mechanisms. Nevertheless, calculation of 18O KIEs for the substitution of the nucleophile and leaving oxygen atoms (O2′ and O5′) in solution and in the ribozyme gives a high normal KIE value of 1.04 for the isotopic substitution on O5′ position when computed for rate-limiting TS (TS2), which is in excellent agreement with previous experiments and calculations by Gu et al. .
All in all, our results suggest that the ribozyme-catalysed reaction should take place by a different mechanism whereby different species belonging to the active site of the ribozyme could act as the HO2′ proton acceptor and the proton donor to the O5′ leaving oxygen atom (B and AH species in Scheme 1). In other words, catalysis must come from the role of alternative acid–base species not available in aqueous solution. Nevertheless, on the basis of the agreement between our predicted 18O KIEs and the experimental data, the rate-limiting step of the cleavage of the RNA phosphodiester backbone catalysed by the twister ribozyme from Oryza sativa must be associated with the P–O5′ bond cleavage.
This work was supported by the Spanish Ministerio de Economía y Competitividad for project CTQ2015-66223-C2, Universitat Jaume I (project P1•1B2014-26), Generalitat Valenciana (PROMETEOII/2014/022) and the Polish Ministry of Science and Higher Education (“Iuventus Plus” programme project no. 0478/IP3/2015/73, 2015-2016). V.M. is grateful to the University of Bath for the award of a David Parkin Visiting Professorship. Authors acknowledge computational resources from the Servei d’Informàtica of Universitat de València on the “Tirant” supercomputer and the Servei d’Informat̀ica of Universitat Jaume I.
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