Insight into the role of Mg in hammerhead ribozyme catalysis from X-ray crystallography and molecular dynamics simulation

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.

Theoretical Studies of the Self Cleavage Pistol Ribozyme Mechanism

Ribozymes are huge complex biological catalysts composed of a combination of RNA and proteins. Nevertheless, there is a reduced number of small ribozymes, the self-cleavage ribozymes, that are formed just by RNA and, apparently, they existed in cells of primitive biological systems. Unveiling the details of these “fossils” enzymes can contribute not only to the understanding of the origins of life but also to the development of new simplified artificial enzymes. A computational study of the reactivity of the pistol ribozyme carried out by means of classical MD simulations and QM/MM hybrid calculations is herein presented to clarify its catalytic mechanism. Analysis of the geometries along independent MD simulations with different protonation states of the active site basic species reveals that only the canonical system, with no additional protonation changes, renders reactive conformations. A change in the coordination sphere of the Mg2+ ion has been observed during the simulations, which allows proposing a mechanism to explain the unique mode of action of the pistol ribozyme by comparison with other ribozymes. The present results are at the center of the debate originated from recent experimental and theoretical studies on pistol ribozyme.

The L-platform/L-scaffold framework: a blueprint for RNA-cleaving nucleic acid enzyme design

We develop an L-platform/L-scaffold framework we hypothesize may serve as a blueprint to facilitate site-specific RNA-cleaving nucleic acid enzyme design. Building on the L-platform motif originally described by Suslov and coworkers, we identify new critical scaffolding elements required to anchor a conserved general base guanine ("L-anchor") and bind functionally important metal ions at the active site ("L-pocket"). Molecular simulations, together with a broad range of experimental structural and functional data, connect the L-platform/L-scaffold elements to necessary and sufficient conditions for catalytic activity. We demonstrate that the L-platform/L-scaffold framework is common to five of the nine currently known naturally occurring ribozyme classes (Twr, HPr, VSr, HHr, Psr), and intriguingly from a design perspective, the framework also appears in an artificially engineered DNAzyme (8-17dz). The flexibility of the L-platform/L-scaffold framework is illustrated on these systems, highlighting modularity and trends in the variety of known general acid moieties that are supported. These trends give rise to two distinct catalytic paradigms, building on the classifications proposed by Wilson and coworkers and named for the implicated general base and acid. The "G + A" paradigm (Twr, HPr, VSr) exclusively utilizes nucleobase residues for chemistry, and the "G + M + " paradigm (HHr, 8-17dz, Psr) involves structuring of the "L-pocket" metal ion binding site for recruitment of a divalent metal ion that plays an active role in the chemical steps of the reaction. Finally, the modularity of the L-platform/L-scaffold framework is illustrated in the VS ribozyme where the "L-pocket" assumes the functional role of the "L-anchor" element, highlighting a distinct mechanism, but one that is functionally linked with the hammerhead ribozyme.

Dynamical ensemble of the active state and transition state mimic for the RNA-cleaving 8-17 DNAzyme in solution

We perform molecular dynamics simulations, based on recent crystallographic data, on the 8-17 DNAzyme at four states along the reaction pathway to determine the dynamical ensemble for the active state and transition state mimic in solution. A striking finding is the diverse roles played by Na+ and Pb2+ ions in the electrostatically strained active site that impact all four fundamental catalytic strategies, and share commonality with some features recently inferred for naturally occurring hammerhead and pistol ribozymes. The active site Pb2+ ion helps to stabilize in-line nucleophilic attack, provides direct electrostatic transition state stabilization, and facilitates leaving group departure. A conserved guanine residue is positioned to act as the general base, and is assisted by a bridging Na+ ion that tunes the pKa and facilitates in-line fitness. The present work provides insight into how DNA molecules are able to solve the RNA-cleavage problem, and establishes functional relationships between the mechanism of these engineered DNA enzymes with their naturally evolved RNA counterparts. This adds valuable information to our growing body of knowledge on general mechanisms of phosphoryl transfer reactions catalyzed by RNA, proteins and DNA.

Molecular simulations of the pistol ribozyme: unifying the interpretation of experimental data and establishing functional links with the hammerhead ribozyme

The pistol ribozyme (Psr) is among the most recently discovered RNA enzymes and has been the subject of experiments aimed at elucidating the mechanism. Recent biochemical studies have revealed exciting clues about catalytic interactions in the active site not apparent from available crystallographic data. The present work unifies the interpretation of the existing body of structural and functional data on Psr by providing a dynamical model for the catalytically active state in solution from molecular simulation. Our results suggest that a catalytic Mg2+ ion makes inner-sphere contact with G33:N7 and outer-sphere coordination to the pro-RP of the scissile phosphate, promoting electrostatic stabilization of the dianionic transition state and neutralization of the developing charge of the leaving group through a metal-coordinated water molecule that is made more acidic by a hydrogen bond donated from the 2'OH of P32. This model is consistent with experimental activity-pH and mutagenesis data, including sensitivity to G33(7cG) and phosphorothioate substitution/metal ion rescue. The model suggests several experimentally testable predictions, including the response of cleavage activity to mutations at G42 and P32 positions in the ribozyme, and thio substitutions of the substrate in the presence of different divalent metal ions. Further, the model identifies striking similarities of Psr to the hammerhead ribozyme (HHr), including similar global fold, organization of secondary structure around an active site three-way junction, catalytic metal ion binding mode, and guanine general base. However, the specific binding mode and role of the Mg2+ ion, as well as a conserved 2'-OH in the active site, are interrelated but subtly different between the ribozymes.

Assessing the Performance of the Nonbonded Mg2+ Models in a Two-Metal-Dependent Ribonuclease

Magnesium ions (Mg²⁺), abundant in living cells, are essential for biomolecular structure, dynamics, and function. The biological importance of Mg²⁺ has motivated continuous development and improvement of various Mg²⁺ models for molecular dynamics (MD) simulations during the last decades. There are four types of nonbonded Mg²⁺ models: the point charge models based on a 12-6 or 12-6-4 type Lennard-Jones (LJ) potential, and the multisite models based on a 12-6 or 12-6-4 LJ potential. Here, we systematically assessed the performance of these four types of nonbonded Mg²⁺ models (21 models in total) in terms of maintaining a challenging intermediate state configuration captured in the structure of a prototypical two-metal-ion RNase H complex with an RNA/DNA hybrid. Our data demonstrate that the 12-6-4 multisite models, which account for charge-induced dipole interactions, perform the best in reproducing all the unique coordination modes in this intermediate state and maintaining the correct carboxylate denticity. Our benchmark work provides a useful guideline for MD simulations and structural refinement of Mg²⁺-containing biomolecular systems.

Structural Simplicity and Mechanistic Complexity in the Hammerhead Ribozyme

Natural or full-length hammerhead ribozymes are up to 1000-fold more active than their minimal counterparts that lack a complex tertiary interaction that pre-organizes and stabilizes the ribozyme active site, positioning RNA functional groups to facilitate acid-base catalysis. The recent discovery that a single tertiary contact (an AU Hoogsteen pair) between Stems I and II confers essentially all of the enhanced activity greatly simplifies our understanding of the structural requirements for hammerhead ribozyme activity. In contrast, the simplest mechanistic interpretations are challenged with the presentation of more complex alternatives. These alternatives are elucidated and critically analyzed in the context of several of the active hammerhead ribozyme structures now available.

RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview

With both catalytic and genetic functions, ribonucleic acid (RNA) is perhaps the most pluripotent chemical species in molecular biology, and its functions are intimately linked to its structure and dynamics. Computer simulations, and in particular atomistic molecular dynamics (MD), allow structural dynamics of biomolecular systems to be investigated with unprecedented temporal and spatial resolution. We here provide a comprehensive overview of the fast-developing field of MD simulations of RNA molecules. We begin with an in-depth, evaluatory coverage of the most fundamental methodological challenges that set the basis for the future development of the field, in particular, the current developments and inherent physical limitations of the atomistic force fields and the recent advances in a broad spectrum of enhanced sampling methods. We also survey the closely related field of coarse-grained modeling of RNA systems. After dealing with the methodological aspects, we provide an exhaustive overview of the available RNA simulation literature, ranging from studies of the smallest RNA oligonucleotides to investigations of the entire ribosome. Our review encompasses tetranucleotides, tetraloops, a number of small RNA motifs, A-helix RNA, kissing-loop complexes, the TAR RNA element, the decoding center and other important regions of the ribosome, as well as assorted others systems. Extended sections are devoted to RNA-ion interactions, ribozymes, riboswitches, and protein/RNA complexes. Our overview is written for as broad of an audience as possible, aiming to provide a much-needed interdisciplinary bridge between computation and experiment, together with a perspective on the future of the field.

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.

Development of Site-Specific Mg(2+)-RNA Force Field Parameters: A Dream or Reality? Guidelines from Combined Molecular Dynamics and Quantum Mechanics Simulations

The vital contribution of Mg²⁺ ions to RNA biology is challenging to dissect at the experimental level. This calls for the integrative support of atomistic simulations, which at the classical level are plagued by limited accuracy. Indeed, force fields intrinsically neglect nontrivial electronic effects that Mg²⁺ exerts on its surrounding ligands in varying RNA coordination environments. Here, we present a combined computational study based on classical molecular dynamics (MD) and Density Functional Theory (DFT) calculations, aimed at characterizing (i) the performance of five Mg²⁺ force field (FF) models in RNA systems and (ii) how charge transfer and polarization affect the binding of Mg²⁺ ions in different coordination motifs. As a result, a total of ∼2.5 μs MD simulations (100/200 ns for each run) for two prototypical Mg²⁺-dependent ribozymes showed remarkable differences in terms of populations of inner-sphere coordination site types. Most importantly, complementary DFT calculations unveiled that differences in charge transfer and polarization among recurrent Mg²⁺-RNA coordination motifs are surprisingly small. In particular, the charge of the Mg²⁺ ions substantially remains constant through different coordination sites, suggesting that the common philosophy of developing site-specific Mg²⁺ ion parameters is not in line with the physical origin of the Mg²⁺-RNA MD simulations inaccuracies. Overall, this study constitutes a guideline for an adept use of current Mg²⁺ models and provides novel insights for the rational development of next-generation Mg²⁺ FFs to be employed for atomistic simulations of RNA.

A Two-Metal-Ion-Mediated Conformational Switching Pathway for HDV Ribozyme Activation

RNA enzymes serve as a potentially powerful platform from which to design catalysts and engineer new biotechnology. A fundamental understanding of these systems provides insight to guide design. The hepatitis delta virus ribozyme (HDVr) is a small, self-cleaving RNA motif widely distributed in nature, that has served as a paradigm for understanding basic principles of RNA catalysis. Nevertheless, questions remain regarding the precise roles of divalent metal ions and key nucleotides in catalysis. In an effort to establish a reaction mechanism model consistent with available experimental data, we utilize molecular dynamics simulations to explore different conformations and metal ion binding modes along the HDVr reaction path. Building upon recent crystallographic data, our results provide a dynamic model of the HDVr reaction mechanism involving a conformational switch between multiple non-canonical G25:U20 base pair conformations in the active site. These local nucleobase dynamics play an important role in catalysis by modulating the metal binding environments of two Mg²⁺ ions that support catalysis at different steps of the reaction pathway. The first ion plays a structural role by inducing a base pair flip necessary to obtain the catalytic fold in which C75 moves towards to the scissile phosphate in the active site. Ejection of this ion then permits a second ion to bind elsewhere in the active site and facilitate nucleophile activation. The simulations collectively describe a mechanistic scenario that is consistent with currently available experimental data from crystallography, phosphorothioate substitutions, and chemical probing studies. Avenues for further experimental verification are suggested.

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.

Bridging the gap between theory and experiment to derive a detailed understanding of hammerhead ribozyme catalysis

Herein we summarize our progress toward the understanding of hammerhead ribozyme (HHR) catalysis through a multiscale simulation strategy. Simulation results collectively paint a picture of HHR catalysis: HHR first folds to form an electronegative active site pocket to recruit a threshold occupation of cationic charges, either a Mg(2+) ion or multiple monovalent cations. Catalytically active conformations that have good in-line fitness are supported by specific metal ion coordination patterns that involve either a bridging Mg(2+) ion or multiple Na(+) ions, one of which is also in a bridging coordination pattern. In the case of a single Mg(2+) ion bound in the active site, the Mg(2+) ion undergoes a migration that is coupled with deprotonation of the nucleophile (C17:O2'). As the reaction proceeds, the Mg(2+) ion stabilizes the accumulating charge of the leaving group and significantly increases the general acid ability of G8:O2'. Further computational mutagenesis simulations suggest that the disruptions due to mutations may severely impact HHR catalysis at different stages of the reaction. Catalytic mechanisms supported by the simulation results are consistent with available structural and biochemical experiments, and together they advance our understanding of HHR catalysis.

Ground-state coordination of a catalytic metal to the scissile phosphate of a tertiary-stabilized Hammerhead ribozyme

Although the Hammerhead ribozyme (HHRz) has long been used as a model system in the field of ribozyme enzymology, several details of its mechanism are still not well understood. In particular, significant questions remain concerning the disposition and role of catalytic metals in the HHRz. Previous metal-rescue experiments using a "minimal" HHRz resulted in prediction of a catalytic metal that is bound in the A9/G10.1 site in the ground state of the reaction and that bridges to the scissile phosphate further along the reaction pathway. "Native" or extended HHRz constructs contain tertiary contacts that stabilize a more compact structure at moderate ionic strength. We performed Cd(2+) rescue experiments on an extended HHRz from Schistosoma mansoni using stereo-pure scissile phosphorothioate-substituted substrates in order to determine whether a metal ion makes contact with the scissile phosphate in the ground state or further along the reaction coordinate. Inhibition in Ca(2+)/Mg(2+) and rescue by thiophilic Cd(2+) was specific for the R(p)-S stereoisomer of the scissile phosphate. The affinity of the rescuing Cd(2+), measured in two different ionic strength backgrounds, increased fourfold to 17-fold when the pro-R(p) oxygen is replaced by sulfur. These data support a model in which the rescuing metal ion makes a ground-state interaction with the scissile phosphate in the native HHRz. The resulting model for Mg(2+) activation in the HHRz places a metal ion in contact with the scissile phosphate, where it may provide ground-state electrostatic activation of the substrate.

Characterization of the Structure and Dynamics of the HDV Ribozyme at Different Stages Along the Reaction Path

The structure and dynamics of the hepatitis delta virus ribozyme (HDVr) are studies using molecular dynamics simulations at several stages along its catalytic reaction path, including reactant, activated precursor, transition state mimic and product states, departing from an initial structure based on the C75U mutant crystal structure (PDB: 1VC7). Results of five 350 ns molecular dynamics simulations reveal a spontaneous rotation of U-1 that leads to an in-line conformation and support the role of protonated C75 as the general acid in the transition state. Our results provide rationale for the interpretation of several important experimental results, and make experimentally testable predictions regarding the roles of key active site residues that are not obvious from any available crystal structures.

Computational mutagenesis studies of hammerhead ribozyme catalysis

Computational studies of the mutational effects at the C3, G8, and G5 positions of the hammerhead ribozyme (HHR) are reported, based on a series of twenty-four 100-ns molecular dynamics simulations of the native and mutated HHR in the reactant state and in an activated precursor state (G8:2'OH deprotonated). Invoking the assumptions that G12 acts as the general base while the 2'OH of G8 acts as a general acid, the simulations are able to explain the origins of experimentally observed mutational effects, including several that are not easily inferred from the crystal structure. Simulations suggest that the Watson-Crick base-pairing between G8 and C3, the hydrogen bond network between C17 and G5, and the base stacking interactions between G8 and C1.1, collectively, are key to maintaining an active site structure conducive for catalytic activity. Mutation-induced disruption of any of these interactions will adversely affect activity. The simulation results predict that the C3U/G8D double mutant, where D is 2,6-diaminopurine, will have a rescue effect relative to the corresponding single mutations. Two general conclusions about the simulations emerge from this work. First, mutation simulations may require 30 ns or more to suitably relax such that the mutational effects become apparent. Second, in some cases, it is necessary to look beyond the reactant state in order to interpret mutational effects in terms of catalytically active structure. The present simulation results lead to better understanding of the origin of experimental mutational effects and provide insight into the key conserved features necessary to maintain the integrity of the active site architecture.

Theoretical studies of RNA catalysis: hybrid QM/MM methods and their comparison with MD and QM

Hybrid QM/MM methods combine the rigor of quantum mechanical (QM) calculations with the low computational cost of empirical molecular mechanical (MM) treatment allowing to capture dynamic properties to probe critical atomistic details of enzyme reactions. Catalysis by RNA enzymes (ribozymes) has only recently begun to be addressed with QM/MM approaches and is thus still a field under development. This review surveys methodology as well as recent advances in QM/MM applications to RNA mechanisms, including those of the HDV, hairpin, and hammerhead ribozymes, as well as the ribosome. We compare and correlate QM/MM results with those from QM and/or molecular dynamics (MD) simulations, and discuss scope and limitations with a critical eye on current shortcomings in available methodologies and computer resources. We thus hope to foster mutual appreciation and facilitate collaboration between experimentalists and theorists to jointly advance our understanding of RNA catalysis at an atomistic level.

Comparative enzymology and structural biology of RNA self-cleavage

Self-cleaving hammerhead, hairpin, hepatitis delta virus, and glmS ribozymes comprise a family of small catalytic RNA motifs that catalyze the same reversible phosphodiester cleavage reaction, but each motif adopts a unique structure and displays a unique array of biochemical properties. Recent structural, biochemical, and biophysical studies of these self-cleaving RNAs have begun to reveal how active site nucleotides exploit general acid-base catalysis, electrostatic stabilization, substrate destabilization, and positioning and orientation to reduce the free energy barrier to catalysis. Insights into the variety of catalytic strategies available to these model RNA enzymes are likely to have important implications for understanding more complex RNA-catalyzed reactions fundamental to RNA processing and protein synthesis.

Probing general acid catalysis in the hammerhead ribozyme

Recent crystallographic and computational studies have provided fresh insights into the catalytic mechanism of the RNA-cleaving hammerhead ribozyme. Based on these findings, specific ribozyme functional groups have been hypothesized to act directly as the general acid and base catalysts, although the catalytic role of divalent metal cations (M(2+)) remains uncertain. We now report a functional characterization of the general acid catalysis mechanism and the role of an M(2+) cofactor therein, for the S. mansoni hammerhead (an "extended" hammerhead ribozyme). We have compared hammerhead cleavage of substrates with natural (ribo-phosphodiester) versus bridging-5'-phosphorothioate scissile linkages, in the contexts of active site mutations and M(2+) substitution. Cleavage of the natural substrate is inhibited by modification of the G8 2'-OH ribozyme residue and depends strongly upon the presence and identity of an M(2+) cofactor; in contrast, cleavage of the bridging-phosphorothioate substrate is conspicuously insensitive to any of these factors. These results imply that (1) both an M(2+) cofactor and the G8 2'-OH play crucial roles in hammerhead general acid catalysis and (2) the M(2+) cofactor does not contribute to general acid catalysis via Lewis acid stabilization of the leaving group. General acid pK(a) perturbation was also demonstrated for both M(2+) substitution and G8 2'-OH modification, which suggests transition state M(2+) coordination of the G8 2'-OH, to lower its pK(a) and improve its ability to transfer a proton to the leaving group. We also report a simple method for synthesizing radiolabeled bridging-5'-phosphorothioate substrates.

Threshold occupancy and specific cation binding modes in the hammerhead ribozyme active site are required for active conformation

The relationship between formation of active in-line attack conformations and monovalent (Na(+)) and divalent (Mg(2+)) metal ion binding in hammerhead ribozyme (HHR) has been explored with molecular dynamics simulations. To stabilize repulsions between negatively charged groups, different requirements of the threshold occupancy of metal ions were observed in the reactant and activated precursor states both in the presence and in the absence of a Mg(2+) in the active site. Specific bridging coordination patterns of the ions are correlated with the formation of active in-line attack conformations and can be accommodated in both cases. Furthermore, simulation results suggest that the HHR folds to form an electronegative recruiting pocket that attracts high local concentrations of positive charge. The present simulations help to reconcile experiments that probe the metal ion sensitivity of HHR catalysis and support the supposition that Mg(2+), in addition to stabilizing active conformations, plays a specific chemical role in catalysis.

Extension of adaptive tree code and fast multipole methods to high angular momentum particle charge densities

The development and implementation of a tree code (TC) and fast multipole method (FMM) for the efficient, linear-scaling calculation of long-range electrostatic interactions of particle distributions with variable shape and multipole character are described. The target application of these methods are stochastic boundary molecular simulations with polarizable force fields and/or combined quantum mechanical/molecular mechanical potentials. Linear-scaling is accomplished through the adaptive decomposition of the system into a hierarchy of interacting particle sets. Two methods for effecting this decomposition are evaluated: fluc-splitting and box-splitting, for which the latter is demonstrated to be generally more accurate. In addition, a generalized termination criterion is developed that delivers optimal performance at fixed error tolerance that, in the case of quadrupole-represented Drude water, effects a speed-up by a factor of 2-3 relative to a multipole-independent termination criteria. The FMM is shown to be approximately 2-3 times faster than the TC, independent of the system size and multipole order of the particles. The TC and FMM are tested for a variety of static and polarizable water systems, and for the the 70S ribosome functional complex containing an assembly of transfer and messenger RNAs.

Solvent structure and hammerhead ribozyme catalysis

Although the hammerhead ribozyme is regarded as a prototype for understanding RNA catalysis, the mechanistic roles of associated metal ions and water molecules in the cleavage reaction remain controversial. We have investigated the catalytic potential of observed divalent metal ions and water molecules bound to a 2 A structure of the full-length hammerhead ribozyme by using X-ray crystallography in combination with molecular dynamics simulations. A single Mn(2+) is observed to bind directly to the A9 phosphate in the active site, accompanying a hydrogen-bond network involving a well-ordered water molecule spanning N1 of G12 (the general base) and 2'-O of G8 (previously implicated in general acid catalysis) that we propose, based on molecular dynamics calculations, facilitates proton transfer in the cleavage reaction. Phosphate-bridging metal interactions and other mechanistic hypotheses are also tested with this approach.

Origin of mutational effects at the C3 and G8 positions on hammerhead ribozyme catalysis from molecular dynamics simulations

A series of ten 60 ns molecular dynamics (MD) simulations of the native and mutated full length hammerhead ribozymes in the reactant state and in an activated precursor state (G8:2'OH deprotonated) are reported. Mutant simulations include the C3U, G8A, and G8I single mutants and a C3U/G8A double mutant that exhibits an experimental rescue effect. The results provide critical details into the origin of the observed mutation effects and support a mechanism where the 2'OH of G8 acts as a general acid catalyst that is held in position through Watson-Crick hydrogen bonding between G8 and C3.

Quantum mechanical/molecular mechanical simulation study of the mechanism of hairpin ribozyme catalysis

The molecular mechanism of hairpin ribozyme catalysis is studied with molecular dynamics simulations using a combined quantum mechanical and molecular mechanical (QM/MM) potential with a recently developed semiempirical AM1/d-PhoT model for phosphoryl transfer reactions. Simulations are used to derive one- and two-dimensional potentials of mean force to examine specific reaction paths and assess the feasibility of proposed general acid and base mechanisms. Density-functional calculations of truncated active site models provide complementary insight to the simulation results. Key factors utilized by the hairpin ribozyme to enhance the rate of transphosphorylation are presented, and the roles of A38 and G8 as general acid and base catalysts are discussed. The computational results are consistent with available experimental data, provide support for a general acid/base mechanism played by functional groups on the nucleobases, and offer important insight into the ability of RNA to act as a catalyst without explicit participation by divalent metal ions.

Charge-dependent model for many-body polarization, exchange, and dispersion interactions in hybrid quantum mechanical/molecular mechanical calculations

This work explores a new charge-dependent energy model consisting of van der Waals and polarization interactions between the quantum mechanical (QM) and molecular mechanical (MM) regions in a combined QMMM calculation. van der Waals interactions are commonly treated using empirical Lennard-Jones potentials, whose parameters are often chosen based on the QM atom type (e.g., based on hybridization or specific covalent bonding environment). This strategy for determination of QMMM nonbonding interactions becomes tedious to parametrize and lacks robust transferability. Problems occur in the study of chemical reactions where the "atom type" is a complex function of the reaction coordinate. This is particularly problematic for reactions, where atoms or localized functional groups undergo changes in charge state and hybridization. In the present work we propose a new model for nonelectrostatic nonbonded interactions in QMMM calculations that overcomes many of these problems. The model is based on a scaled overlap model for repulsive exchange and attractive dispersion interactions that is a function of atomic charge. The model is chemically significant since it properly correlates atomic size, softness, polarizability, and dispersion terms with minimal one-body parameters that are functions of the atomic charge. Tests of the model are examined for rare-gas interactions with neutral and charged atoms in order to demonstrate improved transferability. The present work provides a new framework for modeling QMMM interactions with improved accuracy and transferability.

Role of Mg2+ in hammerhead ribozyme catalysis from molecular simulation

Molecular dynamics simulations have been performed to investigate the role of Mg2+ in the full-length hammerhead ribozyme cleavage reaction. In particular, the aim of this work is to characterize the binding mode and conformational events that give rise to catalytically active conformations and stabilization of the transition state. Toward this end, a series of eight 12 ns molecular dynamics simulations have been performed with different divalent metal binding occupations for the reactant, early and late transition state using recently developed force field parameters for metal ions and reactive intermediates in RNA catalysis. In addition, hybrid QM/MM calculations of the early and late transition state were performed to study the proton-transfer step in general acid catalysis that is facilitated by the catalytic Mg2+ ion. The simulations suggest that Mg2+ is profoundly involved in the hammerhead ribozyme mechanism both at structural and catalytic levels. Binding of Mg2+ in the active site plays a key structural role in the stabilization of stem I and II and to facilitate formation of near attack conformations and interactions between the nucleophile and G12, the implicated general base catalyst. In the transition state, Mg2+ binds in a bridging position where it stabilizes the accumulated charge of the leaving group while interacting with the 2'OH of G8, the implicated general acid catalyst. The QM/MM simulations provide support that, in the late transition state, the 2'OH of G8 can transfer a proton to the leaving group while directly coordinating the bridging Mg2+ ion. The present study provides evidence for the role of Mg2+ in hammerhead ribozyme catalysis. The proposed simulation model reconciles the interpretation of available experimental structural and biochemical data, and provides a starting point for more detailed investigation of the chemical reaction path with combined QM/MM methods.

Structure-function relationships in RNA and RNP enzymes: recent advances

The structural biology of ribozymes and ribonucleoprotein (RNP) enzymes is now sufficiently advanced that a true dialogue between structural and functional studies is possible. In this review, we consider three important systems in which an integration of structural and biochemical data has recently led to major advances in mechanistic understanding. In the hammerhead ribozyme, application-driven biochemical studies led to the discovery of a key structural interaction that had been omitted from previously-studied constructs. A new crystal structure of the resulting, tertiary-stabilized hammerhead has resolved a remarkable number of longstanding paradoxes in the structure-function relationship of this ribozyme. In the Group I intron ribozyme, a flurry of high-resolution structures has largely confirmed, but in some cases refined or challenged, a detailed model of a metalloenzyme active site that had previously been derived by meticulous quantitative metal ion rescue experiments. Finally, for the peptidyl transferase center of the ribosome, recent biochemical and chemical results motivated by the pioneering crystal structures have suggested a picture of a catalytic mechanism dominated by proximity and orientation effects and substrate-assisted catalysis. These results refocus attention on catalysis as a property of the integrated RNP machinery as a whole, as opposed to a narrow concern with the RNA functional groups in immediate contact with the reactive center.