Hammerhead ribozymes: true metal or nucleobase catalysis? Where is the catalytic power from?

Surface-Accelerated String Method for Locating Minimum Free Energy Paths

We present a surface-accelerated string method (SASM) to efficiently optimize low-dimensional reaction pathways from the sampling performed with expensive quantum mechanical/molecular mechanical (QM/MM) Hamiltonians. The SASM accelerates the convergence of the path using the aggregate sampling obtained from the current and previous string iterations, whereas approaches like the string method in collective variables (SMCV) or the modified string method in collective variables (MSMCV) update the path only from the sampling obtained from the current iteration. Furthermore, the SASM decouples the number of images used to perform sampling from the number of synthetic images used to represent the path. The path is optimized on the current best estimate of the free energy surface obtained from all available sampling, and the proposed set of new simulations is not restricted to being located along the optimized path. Instead, the umbrella potential placement is chosen to extend the range of the free energy surface and improve the quality of the free energy estimates near the path. In this manner, the SASM is shown to improve the exploration for a minimum free energy pathway in regions where the free energy surface is relatively flat. Furthermore, it improves the quality of the free energy profile when the string is discretized with too few images. We compare the SASM, SMCV, and MSMCV using 3 QM/MM applications: a ribozyme methyltransferase reaction using 2 reaction coordinates, the 2'-O-transphosphorylation reaction of Hammerhead ribozyme using 3 reaction coordinates, and a tautomeric reaction in B-DNA using 5 reaction coordinates. We show that SASM converges the paths using roughly 3 times less sampling than the SMCV and MSMCV methods. All three algorithms have been implemented in the FE-ToolKit package made freely available.

MetBP: A Software Tool for Detection of Interaction between Metal Ion-RNA Base Pairs

MOTIVATION

The role of metals in shaping and functioning of RNA is a well established fact and the understanding of that through the analysis of structural data has biological relevance. Often metal ions bind to one or more atoms of the nucleobase of an RNA. This fact becomes more interesting when such bases form a base pair with any other base. Furthermore, when metal ions bind to any residue of an RNA, the secondary structural features of the residue (helix, loop, unpaired etc) are also biologically important. The available metal binding related software tools cannot address such type specific queries.

RESULTS

To fill this limitation, we have designed a software tool, called MetBP, that meets the goal. This tool is a stand-alone command line based tool and has no dependency on the other existing software. It accepts a structure file in mmCIF or PDB format and computes the base pairs and thereafter reports all metals that bind to one or more nucleotides that form pairs with another. It reports binding distance, angles along with base pair stability. It also reports several other important aspects, e.g. secondary structure of the residue in the RNA. MetBP can be used as a generalized metal binding site detection tool for Proteins and DNA as well.

AVAILABILITY

https://github.com/computational-biology/metbp.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

RNA Back and Forth: Looking through Ribozyme and Viroid Motifs

Current cellular facts allow us to follow the link from chemical to biochemical metabolites, from the ancient to the modern world. In this context, the "RNA world" hypothesis proposes that early in the evolution of life, the ribozyme was responsible for the storage and transfer of genetic information and for the catalysis of biochemical reactions. Accordingly, the hammerhead ribozyme (HHR) and the hairpin ribozyme belong to a family of endonucleolytic RNAs performing self-cleavage that might occur during replication. Furthermore, regarding the widespread occurrence of HHRs in several genomes of modern organisms (from mammals to small parasites and elsewhere), these small ribozymes have been regarded as living fossils of a primitive RNA world. They fold into 3D structures that generally require long-range intramolecular interactions to adopt the catalytically active conformation under specific physicochemical conditions. By studying viroids as plausible remains of ancient RNA, we recently demonstrated that they replicate in non-specific hosts, emphasizing their adaptability to different environments, which enhanced their survival probability over the ages. All these results exemplify ubiquitous features of life. Those are the structural and functional versatility of small RNAs, ribozymes, and viroids, as well as their diversity and adaptability to various extreme conditions. All these traits must have originated in early life to generate novel RNA populations.

Interaction of Na+, K+, Mg2+ and Ca2+ counter cations with RNA

Data on the location of alkaline and alkaline earth ions at RNA from crystallography, spectroscopy and computational modeling are reviewed.

Divalent Metal Ion Activation of a Guanine General Base in the Hammerhead Ribozyme: Insights from Molecular Simulations

The hammerhead ribozyme is a well-studied nucleolytic ribozyme that catalyzes the self-cleavage of the RNA phosphodiester backbone. Despite experimental and theoretical efforts, key questions remain about details of the mechanism with regard to the activation of the nucleophile by the putative general base guanine (G12). Straightforward interpretation of the measured activity-pH data implies the pK_a value of the N1 position in the G12 nucleobase is significantly shifted by the ribozyme environment. Recent crystallographic and biochemical work has identified pH-dependent divalent metal ion binding at the N7/O6 position of G12, leading to the hypothesis that this binding mode could induce a pK_a shift of G12 toward neutrality. We present computational results that support this hypothesis and provide a model that unifies the interpretation of available structural and biochemical data and paints a detailed mechanistic picture of the general base step of the reaction. Experimentally testable predictions are made for mutational and rescue effects on G12, which will give further insights into the catalytic mechanism. These results contribute to our growing knowledge of the potential roles of divalent metal ions in RNA catalysis.

Sodium and Potassium Interactions with Nucleic Acids

Metal ions are essential cofactors for the structure and functions of nucleic acids. Yet, the early discovery in the 70s of the crucial role of Mg(2+) in stabilizing tRNA structures has occulted for a long time the importance of monovalent cations. Renewed interest in these ions was brought in the late 90s by the discovery of specific potassium metal ions in the core of a group I intron. Their importance in nucleic acid folding and catalytic activity is now well established. However, detection of K(+) and Na(+) ions is notoriously problematic and the question about their specificity is recurrent. Here we review the different methods that can be used to detect K(+) and Na(+) ions in nucleic acid structures such as X-ray crystallography, nuclear magnetic resonance or molecular dynamics simulations. We also discuss specific versus non-specific binding to different structures through various examples.

Assessment of metal-assisted nucleophile activation in the hepatitis delta virus ribozyme from molecular simulation and 3D-RISM

The hepatitis delta virus ribozyme is an efficient catalyst of RNA 2'-O-transphosphorylation and has emerged as a key experimental system for identifying and characterizing fundamental features of RNA catalysis. Recent structural and biochemical data have led to a proposed mechanistic model whereby an active site Mg(2+) ion facilitates deprotonation of the O2' nucleophile, and a protonated cytosine residue (C75) acts as an acid to donate a proton to the O5' leaving group as noted in a previous study. This model assumes that the active site Mg(2+) ion forms an inner-sphere coordination with the O2' nucleophile and a nonbridging oxygen of the scissile phosphate. These contacts, however, are not fully resolved in the crystal structure, and biochemical data are not able to unambiguously exclude other mechanistic models. In order to explore the feasibility of this model, we exhaustively mapped the free energy surfaces with different active site ion occupancies via quantum mechanical/molecular mechanical (QM/MM) simulations. We further incorporate a three-dimensional reference interaction site model for the solvated ion atmosphere that allows these calculations to consider not only the rate associated with the chemical steps, but also the probability of observing the system in the presumed active state with the Mg(2+) ion bound. The QM/MM results predict that a pathway involving metal-assisted nucleophile activation is feasible based on the rate-controlling transition state barrier departing from the presumed metal-bound active state. However, QM/MM results for a similar pathway in the absence of Mg(2+) are not consistent with experimental data, suggesting that a structural model in which the crystallographically determined Mg(2+) is simply replaced with Na(+) is likely incorrect. It should be emphasized, however, that these results hinge upon the assumption of the validity of the presumed Mg(2+)-bound starting state, which has not yet been definitively verified experimentally, nor explored in depth computationally. Thus, further experimental and theoretical study is needed such that a consensus view of the catalytic mechanism emerges.

Review of computer simulations of isotope effects on biochemical reactions: From the Bigeleisen equation to Feynman's path integral

Enzymatic reactions are integral components in many biological functions and malfunctions. The iconic structure of each reaction path for elucidating the reaction mechanism in details is the molecular structure of the rate-limiting transition state (RLTS). But RLTS is very hard to get caught or to get visualized by experimentalists. In spite of the lack of explicit molecular structure of the RLTS in experiment, we still can trace out the RLTS unique "fingerprints" by measuring the isotope effects on the reaction rate. This set of "fingerprints" is considered as a most direct probe of RLTS. By contrast, for computer simulations, oftentimes molecular structures of a number of TS can be precisely visualized on computer screen, however, theoreticians are not sure which TS is the actual rate-limiting one. As a result, this is an excellent stage setting for a perfect "marriage" between experiment and theory for determining the structure of RLTS, along with the reaction mechanism, i.e., experimentalists are responsible for "fingerprinting", whereas theoreticians are responsible for providing candidates that match the "fingerprints". In this Review, the origin of isotope effects on a chemical reaction is discussed from the perspectives of classical and quantum worlds, respectively (e.g., the origins of the inverse kinetic isotope effects and all the equilibrium isotope effects are purely from quantum). The conventional Bigeleisen equation for isotope effect calculations, as well as its refined version in the framework of Feynman's path integral and Kleinert's variational perturbation (KP) theory for systematically incorporating anharmonicity and (non-parabolic) quantum tunneling, are also presented. In addition, the outstanding interplay between theory and experiment for successfully deducing the RLTS structures and the reaction mechanisms is demonstrated by applications on biochemical reactions, namely models of bacterial squalene-to-hopene polycyclization and RNA 2'-O-transphosphorylation. For all these applications, we used our recently-developed path-integral method based on the KP theory, called automated integration-free path-integral (AIF-PI) method, to perform ab initio path-integral calculations of isotope effects. As opposed to the conventional path-integral molecular dynamics (PIMD) and Monte Carlo (PIMC) simulations, values calculated from our AIF-PI path-integral method can be as precise as (not as accurate as) the numerical precision of the computing machine. Lastly, comments are made on the general challenges in theoretical modeling of candidates matching the experimental "fingerprints" of RLTS. This article is part of a Special Issue entitled: Enzyme Transition States from Theory and Experiment.

Mechanistic insights into RNA transphosphorylation from kinetic isotope effects and linear free energy relationships of model reactions

Phosphoryl transfer reactions are ubiquitous in biology and the understanding of the mechanisms whereby these reactions are catalyzed by protein and RNA enzymes is central to reveal design principles for new therapeutics. Two of the most powerful experimental probes of chemical mechanism involve the analysis of linear free energy relations (LFERs) and the measurement of kinetic isotope effects (KIEs). These experimental data report directly on differences in bonding between the ground state and the rate-controlling transition state, which is the most critical point along the reaction free energy pathway. However, interpretation of LFER and KIE data in terms of transition-state structure and bonding optimally requires the use of theoretical models. In this work, we apply density-functional calculations to determine KIEs for a series of phosphoryl transfer reactions of direct relevance to the 2'-O-transphosphorylation that leads to cleavage of the phosphodiester backbone of RNA. We first examine a well-studied series of phosphate and phosphorothioate mono-, di- and triesters that are useful as mechanistic probes and for which KIEs have been measured. Close agreement is demonstrated between the calculated and measured KIEs, establishing the reliability of our quantum model calculations. Next, we examine a series of RNA transesterification model reactions with a wide range of leaving groups in order to provide a direct connection between observed Brønsted coefficients and KIEs with the structure and bonding in the transition state. These relations can be used for prediction or to aid in the interpretation of experimental data for similar non-enzymatic and enzymatic reactions. Finally, we apply these relations to RNA phosphoryl transfer catalyzed by ribonuclease A, and demonstrate the reaction coordinate-KIE correlation is reasonably preserved. A prediction of the secondary deuterium KIE in this reaction is also provided. These results demonstrate the utility of building up knowledge of mechanism through the systematic study of model systems to provide insight into more complex biological systems such as phosphoryl transfer enzymes and ribozymes.

Ab initio path-integral calculations of kinetic and equilibrium isotope effects on base-catalyzed RNA transphosphorylation models

Detailed understandings of the reaction mechanisms of RNA catalysis in various environments can have profound importance for many applications, ranging from the design of new biotechnologies to the unraveling of the evolutionary origin of life. An integral step in the nucleolytic RNA catalysis is self-cleavage of RNA strands by 2'-O-transphosphorylation. Key to elucidating a reaction mechanism is determining the molecular structure and bonding characteristics of transition state. A direct and powerful probe of transition state is measuring isotope effects on biochemical reactions, particularly if we can reproduce isotope effect values from quantum calculations. This article significantly extends the scope of our previous joint experimental and theoretical work in examining isotope effects on enzymatic and nonenzymatic 2'-O-transphosphorylation reaction models that mimic reactions catalyzed by RNA enzymes (ribozymes), and protein enzymes such as ribonuclease A (RNase A). Native reactions are studied, as well as reactions with thio substitutions representing chemical modifications often used in experiments to probe mechanism. Here, we report and compare results from eight levels of electronic-structure calculations for constructing the potential energy surfaces in kinetic and equilibrium isotope effects (KIE and EIE) computations, including a "gold-standard" coupled-cluster level of theory [CCSD(T)]. In addition to the widely used Bigeleisen equation for estimating KIE and EIE values, internuclear anharmonicity and quantum tunneling effects were also computed using our recently developed ab initio path-integral method, that is, automated integration-free path-integral method. The results of this work establish an important set of benchmarks that serve to guide calculations of KIE and EIE for RNA catalysis.

Ab initio molecular dynamics of Na⁺ and Mg²⁺ countercations at the backbone of RNA in water solution

The interactions between sodium or magnesium ions and phosphate groups of the RNA backbone represented as dinucleotide fragments in water solution have been studied using ab initio Born-Oppenheimer molecular dynamics. All systems have been simulated at 300 and 320 K. Sodium ions have mobility higher than that of the magnesium ions and readily change their position with respect to the phosphate groups, from directly bonded to completely solvated state, with a rough estimate of the lifetime of bonded Na(+) of about 20-30 ps. The coordination number of the sodium ions frequently changes in irregular intervals ranging from several femtoseconds to about 10 ps with the most frequently encountered coordination number five, followed by six. The magnesium ion is stable both as directly bonded to an oxygen atom from the phosphate group and completely solvated by water. In both states the Mg(2+) ion has exactly six oxygen atoms in the first coordination shell; moreover, during the whole simulation of more than 100 ps no exchange of ligand in the first coordination shells has been observed. Solvation of the terminal phosphate oxygen atoms by water molecules forming hydrogen bonds in different locations of the ions is also discussed. The stability of the system containing sodium ions essentially does not depend on the position of the ions with respect to the phosphate groups.

Site-specific platinum(II) cross-linking in a ribozyme active site

The function of RNA depends on its ability to adopt complex and dynamic structures, and the incorporation of site-specific cross-linking probes is a powerful method for providing distance constraints that are valuable in RNA structural biology. Here we describe a new RNA-RNA cross-linking strategy based on Pt(II) targeting of specific phosphorothioate substitutions. In this strategy cis-diammine Pt(II) complexes are kinetically recruited and anchored to a phosphorothioate substitution embedded within a structured RNA. Substitution of the remaining exchangeable Pt(II) ligand with a nucleophile supplied by a nearby RNA nucleobase results in metal-mediated cross-links that are stable during isolation. This type of cross-linking strategy was explored within the catalytic core of the Hammerhead ribozyme (HHRz). When a phosphorothioate substitution is installed at the scissile bond normally cleaved by the HHRz, Pt(II) cross-linking takes place to nucleotides G8 and G10 in the ribozyme active site. Both of these positions are predicted to be within ~8 Å of a phosphorothioate-bound Pt(II) metal center. Cross-linking depends on Mg(2+) ion concentration, reaching yields as high as 30%, with rates that indicate cation competition within the RNA three-helix junction. Cross-linking efficiency depends on accurate formation of the HHRz tertiary structure, and cross-links are not observed for RNA helices. Combined, these results show promise for using kinetically inert Pt(II) complexes as new site-specific cross-linking tools for exploring RNA structure and dynamics.

High-pressure analysis of a hammerhead ribozyme from Chrysanthemum chlorotic mottle viroid reveals two different populations of self-cleaving molecule

The activity of the full-length hammerhead ribozyme requires a tertiary interaction between its distal loops leading to the closure of the molecule and its stabilization in the active conformation. In this study, the conformational changes accompanying the cis-cleavage reaction of Chrysanthemum chlorotic mottle viroid hammerhead ribozyme were investigated by high-pressure experiments on the complete cleavage reaction. Two activation volumes (ΔV(≠)) were measured, pointing to the presence of two different populations of molecules corresponding to fast-cleaving and slow-cleaving ribozymes in the reaction mixture. The fast population, with a small ΔV(≠) of 2.6 mL·mol(-1), most likely represents molecules in the near-active conformation, whereas the slow population, with a larger ΔV(≠) of 11.6 mL·mol(-1 , represents molecules that need a larger conformational change to induce activity. In addition, pH-dependence experiments suggest that the group whose deprotonation is required for activity intervenes in the formation of the transition state or in the chemistry of the reaction, but not in the conformational change that precedes it.

Modeling the RNA 2'OH activation: possible roles of metal ion and nucleobase as catalysts in self-cleaving ribozymes

The RNA 2'OH activation as taking place in the first chemical step of self-cleaving ribozymes is studied theoretically by DFT and MP2 methods using a continuum solvation model (CPCM). The reaction of proton transfer is studied in the presence of two kinds of catalysts: a fully hydrated metal ion (Mg(2+)) or partially hydrated nucleobase (guanine), taken separately or together leading to three different modes of activation. The metal ion is either directly bound (inner-sphere) or indirectly bound (outer-sphere) to the 2'OH group and a hydroxide ion acts as a general or specific base; the nucleobase is taken in anionic or in neutral enol-tautomeric forms playing itself the role of general base. The presence of a close metal ion (outer-sphere) lowers the pK(a) value of the 2'OH group by several log units in both metal-ion and nuleobase catalysis. The direct metal coordination to the 2'OH group (inner-sphere) further stabilizes the developing negative charge on the nucleophile. The switching from the inner-sphere to the outer-sphere coordination appears to be driven by the energy cost for reorganizing the first coordination shell rather than by the electrostatic repulsion between the ligands. The metal-ion catalysis is more effective with a specific base in the dianionic mechanism. On the other hand, the nucleobase catalysis is more effective in the monoanionic mechanism and in the presence of a metal ion acting as a cofactor through nonspecific electrostatic interactions. The results establish a baseline to study the possible roles of metal and nucleobase catalysts and their environment in more realistic models for self-cleaving ribozymes.