Comparison of ab Initio, DFT, and Semiempirical QM/MM Approaches for Description of Catalytic Mechanism of Hairpin Ribozyme

Simulation-Guided Conformational Space Exploration to Assess Reactive Conformations of a Ribozyme

Self-splicing ribozymes are small ribonucleic acid (RNA) enzymes that catalyze their own cleavage through a transphosphoesterification reaction. While this process is involved in some specific steps of viral RNA replication and splicing, it is also of importance in the context of the (putative) first autocatalytic RNA-based systems that could have preceded the emergence of modern life. The uncatalyzed phosphoester bond formation is thermodynamically very unfavorable, and many experimental studies have focused on understanding the molecular features of catalysis in these ribozymes. However, chemical reaction paths are short-lived and not easily characterized by experimental approaches, so molecular simulation approaches appear as an ideal tool to unveil the molecular details of the reaction. Here, we focus on the model hairpin ribozyme. We show that identifying a relevant initial conformation for reactivity studies, which is frequently overlooked in mixed quantum-classical studies that predominantly concentrate on the chemical reaction itself, can be highly challenging. These challenges stem from limitations in both available experimental structures (which are chemically altered to prevent self-cleavage) and the accuracy of force fields, together with the necessity for comprehensive sampling. We show that molecular dynamics simulations, combined with extensive conformational phase space exploration with Hamiltonian replica-exchange simulations, enable us to characterize the relevant conformational basins of the minimal hairpin ribozyme in the ligated state prior to self-cleavage. We find that what is usually considered a canonical reactive conformation with active site geometries and hydrogen-bond patterns that are optimal for the addition-elimination reaction with general acid/general base catalysis is metastable and only marginally populated. The thermodynamically stable conformation appears to be consistent with the expectations of a mechanism that does not require the direct participation of ribozyme residues in the reaction. While these observations may suffer from forcefield inaccuracies, all investigated forcefields lead to the same conclusions upon proper sampling, contrasting with previous investigations on shorter timescales suggesting that at least one reparametrization of the Amber99 forcefield allowed to stabilize aligned active site conformations. Our study demonstrates that identifying the most pertinent reactant state conformation holds equal importance alongside the accurate determination of the thermodynamics and kinetics of the chemical steps of the reaction.

QM/MM Free Energy Calculations of Long-Range Biological Protonation Dynamics by Adaptive and Focused Sampling

Water-mediated proton transfer reactions are central for catalytic processes in a wide range of biochemical systems, ranging from biological energy conversion to chemical transformations in the metabolism. Yet, the accurate computational treatment of such complex biochemical reactions is highly challenging and requires the application of multiscale methods, in particular hybrid quantum/classical (QM/MM) approaches combined with free energy simulations. Here, we combine the unique exploration power of new advanced sampling methods with density functional theory (DFT)-based QM/MM free energy methods for multiscale simulations of long-range protonation dynamics in biological systems. In this regard, we show that combining multiple walkers/well-tempered metadynamics with an extended system adaptive biasing force method (MWE) provides a powerful approach for exploration of water-mediated proton transfer reactions in complex biochemical systems. We compare and combine the MWE method also with QM/MM umbrella sampling and explore the sampling of the free energy landscape with both geometric (linear combination of proton transfer distances) and physical (center of excess charge) reaction coordinates and show how these affect the convergence of the potential of mean force (PMF) and the activation free energy. We find that the QM/MM-MWE method can efficiently explore both direct and water-mediated proton transfer pathways together with forward and reverse hole transfer mechanisms in the highly complex proton channel of respiratory Complex I, while the QM/MM-US approach shows a systematic convergence of selected long-range proton transfer pathways. In this regard, we show that the PMF along multiple proton transfer pathways is recovered by combining the strengths of both approaches in a QM/MM-MWE/focused US (FUS) scheme and reveals new mechanistic insight into the proton transfer principles of Complex I. Our findings provide a promising basis for the quantitative multiscale simulations of long-range proton transfer reactions in biological systems.

Prebiotic chemical reactivity in solution with quantum accuracy and microsecond sampling using neural network potentials

While RNA appears as a good candidate for the first autocatalytic systems preceding the emergence of modern life, the synthesis of RNA oligonucleotides without enzymes remains challenging. Because the uncatalyzed reaction is extremely slow, experimental studies bring limited and indirect information on the reaction mechanism, the nature of which remains debated. Here, we develop neural network potentials (NNPs) to study the phosphoester bond formation in water. While NNPs are becoming routinely applied to nonreactive systems or simple reactions, we demonstrate how they can systematically be trained to explore the reaction phase space for complex reactions involving several proton transfers and exchanges of heavy atoms. We then propagate at moderate computational cost hundreds of nanoseconds of a variety of enhanced sampling simulations with quantum accuracy in explicit solvent conditions. The thermodynamically preferred reaction pathway is a concerted, dissociative mechanism, with the transient formation of a metaphosphate transition state and direct participation of water solvent molecules that facilitate the exchange of protons through the nonbridging phosphate oxygens. Associative-dissociative pathways, characterized by a much tighter pentacoordinated phosphate, are higher in free energy. Our simulations also suggest that diprotonated phosphate, whose reactivity is never directly assessed in the experiments, is significantly less reactive than the monoprotonated species, suggesting that it is probably never the reactive species in normal pH conditions. These observations rationalize unexplained experimental results and the temperature dependence of the reaction rate, and they pave the way for the design of more efficient abiotic catalysts and activating groups.

A Deep Potential model for liquid-vapor equilibrium and cavitation rates of water

Computational studies of liquid water and its phase transition into vapor have traditionally been performed using classical water models. Here, we utilize the Deep Potential methodology-a machine learning approach-to study this ubiquitous phase transition, starting from the phase diagram in the liquid-vapor coexistence regime. The machine learning model is trained on ab initio energies and forces based on the SCAN density functional, which has been previously shown to reproduce solid phases and other properties of water. Here, we compute the surface tension, saturation pressure, and enthalpy of vaporization for a range of temperatures spanning from 300 to 600 K and evaluate the Deep Potential model performance against experimental results and the semiempirical TIP4P/2005 classical model. Moreover, by employing the seeding technique, we evaluate the free energy barrier and nucleation rate at negative pressures for the isotherm of 296.4 K. We find that the nucleation rates obtained from the Deep Potential model deviate from those computed for the TIP4P/2005 water model due to an underestimation in the surface tension from the Deep Potential model. From analysis of the seeding simulations, we also evaluate the Tolman length for the Deep Potential water model, which is (0.091 ± 0.008) nm at 296.4 K. Finally, we identify that water molecules display a preferential orientation in the liquid-vapor interface, in which H atoms tend to point toward the vapor phase to maximize the enthalpic gain of interfacial molecules. We find that this behavior is more pronounced for planar interfaces than for the curved interfaces in bubbles. This work represents the first application of Deep Potential models to the study of liquid-vapor coexistence and water cavitation.

Computer Aided Development of Nucleic Acid Applications in Nanotechnologies

Utilization of nucleic acids (NAs) in nanotechnologies and nanotechnology-related applications is a growing field with broad application potential, ranging from biosensing up to targeted cell delivery. Computer simulations are useful techniques that can aid design and speed up development in this field. This review focuses on computer simulations of hybrid nanomaterials composed of NAs and other components. Current state-of-the-art molecular dynamics simulations, empirical force fields (FFs), and coarse-grained approaches for the description of deoxyribonucleic acid and ribonucleic acid are critically discussed. Challenges in combining biomacromolecular and nanomaterial FFs are emphasized. Recent applications of simulations for modeling NAs and their interactions with nano- and biomaterials are overviewed in the fields of sensing applications, targeted delivery, and NA templated materials. Future perspectives of development are also highlighted.

Carbon Nanodots from an In Silico Perspective

Carbon nanodots (CNDs) are the latest and most shining rising stars among photoluminescent (PL) nanomaterials. These carbon-based surface-passivated nanostructures compete with other related PL materials, including traditional semiconductor quantum dots and organic dyes, with a long list of benefits and emerging applications. Advantages of CNDs include tunable inherent optical properties and high photostability, rich possibilities for surface functionalization and doping, dispersibility, low toxicity, and viable synthesis (top-down and bottom-up) from organic materials. CNDs can be applied to biomedicine including imaging and sensing, drug-delivery, photodynamic therapy, photocatalysis but also to energy harvesting in solar cells and as LEDs. More applications are reported continuously, making this already a research field of its own. Understanding of the properties of CNDs requires one to go to the levels of electrons, atoms, molecules, and nanostructures at different scales using modern molecular modeling and to correlate it tightly with experiments. This review highlights different in silico techniques and studies, from quantum chemistry to the mesoscale, with particular reference to carbon nanodots, carbonaceous nanoparticles whose structural and photophysical properties are not fully elucidated. The role of experimental investigation is also presented. Hereby, we hope to encourage the reader to investigate CNDs and to apply virtual chemistry to obtain further insights needed to customize these amazing systems for novel prospective applications.

QM/MM Well-Tempered Metadynamics Study of the Mechanism of XBP1 mRNA Cleavage by Inositol Requiring Enzyme 1α RNase

A range of in silico methodologies were herein employed to study the unconventional XBP1 mRNA cleavage mechanism performed by the unfolded protein response (UPR) mediator Inositol Requiring Enzyme 1α (IRE1). Using Protein-RNA molecular docking along with a series of extensive restrained/unrestrained atomistic molecular dynamics (MD) simulations, the dynamical behavior of the system was evaluated and a reliable model of the IRE1/XBP1 mRNA complex was constructed. From a series of well-converged quantum mechanics molecular mechanics well-tempered metadynamics (QM/MM WT-MetaD) simulations using the Grimme dispersion interaction corrected semiempirical parametrization method 6 level of theory (PM6-D3) and the AMBER14SB-OL3 force field, the free energy profile of the cleavage mechanism was determined, along with intermediates and transition state structures. The results show two distinct reaction paths based on general acid-general base type mechanisms, with different activation energies that perfectly match observations from experimental mutagenesis data. The study brings unique atomistic insights into the cleavage mechanism of XBP1 mRNA by IRE1 and clarifies the roles of the catalytic residues H910 and Y892. Increased understanding of the details in UPR signaling can assist in the development of new therapeutic agents for its modulation.

RNA-ligand molecular docking: advances and challenges

With rapid advances in computer algorithms and hardware, fast and accurate virtual screening has led to a drastic acceleration in selecting potent small molecules as drug candidates. Computational modeling of RNA-small molecule interactions has become an indispensable tool for RNA-targeted drug discovery. The current models for RNA-ligand binding have mainly focused on the docking-and-scoring method. Accurate docking and scoring should tackle four crucial problems: (1) conformational flexibility of ligand, (2) conformational flexibility of RNA, (3) efficient sampling of binding sites and binding poses, and (4) accurate scoring of different binding modes. Moreover, compared with the problem of protein-ligand docking, predicting ligand binding to RNA, a negatively charged polymer, is further complicated by additional effects such as metal ion effects. Thermodynamic models based on physics-based and knowledge-based scoring functions have shown highly encouraging success in predicting ligand binding poses and binding affinities. Recently, kinetic models for ligand binding have further suggested that including dissociation kinetics (residence time) in ligand docking would result in improved performance in estimating in vivo drug efficacy. More recently, the rise of deep-learning approaches has led to new tools for predicting RNA-small molecule binding. In this review, we present an overview of the recently developed computational methods for RNA-ligand docking and their advantages and disadvantages.

Chemical reactivity and binding interactions in ribonucleic acid-peptide complexes

The covalent and noncovalent backbone binding interactions in RNA-peptide complexes were studied by DFT methods. Four RNA structures R1(GGCUAGCC), R2(AAUCGAUU), R3(GGGAUCCC), and R4(AAAGCUUU) has been selected for eight protonated peptides (DR, ER, GR, KR, NGR, RR, tmeGnd (tme), and VR) interactions based on an experimental study (Anal Chem. 2019; 91:1659-1664). Chemical reactivity theory is used to study the reactivity of eight peptides with global descriptors. Lower hardness values reflected low stability and high reactivity for the protonated peptides. DR, ER, GR, KR, NGR, RR, and VR show lower value of ω, μ while tme has high value of ω, μ. Larger highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap for ER, GR, and KR showed greater structural stability for peptides. AutoDock and PatchDock results indicated that R1, R2, and R4 retain hairpin structures while interacting with peptide complexes. The calculated binding energies of (R1-R4)-peptide complexes from AutoDock tools are (1.49-11.12) kcal/mol. Results showed that the noncovalent interactions are stronger than the covalent interactions for R1-peptide complexes. The reason might be the transfer of proton from protonated ligand to deprotonated RNA, which has initiated the loss of the ligand. Also it has been observed that proton transfer has become energetically unfavorable in presence of additional hydrogen bonds which is predicted in the experimental results.

Dissecting the Mechanism of (R)-3-Hydroxybutyrate Dehydrogenase by Kinetic Isotope Effects, Protein Crystallography, and Computational Chemistry

The enzyme (R)-3-hydroxybutyrate dehydrogenase (HBDH) catalyzes the enantioselective reduction of 3-oxocarboxylates to (R)-3-hydroxycarboxylates, the monomeric precursors of biodegradable polyesters. Despite its application in asymmetric reduction, which prompted several engineering attempts of this enzyme, the order of chemical events in the active site, their contributions to limit the reaction rate, and interactions between the enzyme and non-native 3-oxocarboxylates have not been explored. Here, a combination of kinetic isotope effects, protein crystallography, and quantum mechanics/molecular mechanics (QM/MM) calculations were employed to dissect the HBDH mechanism. Initial velocity patterns and primary deuterium kinetic isotope effects establish a steady-state ordered kinetic mechanism for acetoacetate reduction by a psychrophilic and a mesophilic HBDH, where hydride transfer is not rate limiting. Primary deuterium kinetic isotope effects on the reduction of 3-oxovalerate indicate that hydride transfer becomes more rate limiting with this non-native substrate. Solvent and multiple deuterium kinetic isotope effects suggest hydride and proton transfers occur in the same transition state. Crystal structures were solved for both enzymes complexed to NAD⁺:acetoacetate and NAD⁺:3-oxovalerate, illustrating the structural basis for the stereochemistry of the 3-hydroxycarboxylate products. QM/MM calculations using the crystal structures as a starting point predicted a higher activation energy for 3-oxovalerate reduction catalyzed by the mesophilic HBDH, in agreement with the higher reaction rate observed experimentally for the psychrophilic orthologue. Both transition states show concerted, albeit not synchronous, proton and hydride transfers to 3-oxovalerate. Setting the MM partial charges to zero results in identical reaction activation energies with both orthologues, suggesting the difference in activation energy between the reactions catalyzed by cold- and warm-adapted HBDHs arises from differential electrostatic stabilization of the transition state. Mutagenesis and phylogenetic analysis reveal the catalytic importance of His150 and Asn145 in the respective orthologues.

Deciphering the Self-Cleavage Reaction Mechanism of Hairpin Ribozyme

Hairpin ribozyme catalyzes the reversible self-cleavage of phosphodiester bonds which plays prominent roles in key biological processes involving RNAs. Despite impressive advances on ribozymatic self-cleavage, critical aspects of its molecular reaction mechanism remain controversially debated. Here, we generate and analyze the multidimensional free energy landscape that underlies the reaction using extensive QM/MM metadynamics simulations to investigate in detail the full self-cleavage mechanism. This allows us to answer several pertinent yet controversial questions concerning activation of the 2'-OH group, the mechanistic role of water molecules present in the active site, and the full reaction pathway including the structures of transition states and intermediates. Importantly, we find that a sufficiently unrestricted reaction subspace must be mapped using accelerated sampling methods in order to compute the underlying free energy landscape. It is shown that lower-dimensional sampling where the bond formation and cleavage steps are coupled does not allow the system to sufficiently explore the landscape. On the basis of a three-dimensional free energy surface spanned by flexible generalized coordinates, we find that 2'-OH is indirectly activated by adjacent G8 nucleobase in conjunction with stabilizing H-bonding involving water. This allows the proton of the 2'-OH group to directly migrate toward the 5'-leaving group via a nonbridging oxygen of the phosphodiester link. At variance with similar enzymatic processes where water wires connected to protonable side chains of the protein matrix act as transient proton shuttles, no such de/reprotonation events of water molecules are found to be involved in this ribozymatic transesterification. Overall, our results support an acid-catalyzed reaction mechanism where A38 nucleobase directly acts as an acid whereas G8, in stark contrast, participates only indirectly via stabilizing the nascent nucleophile for subsequent attack. Moreover, we conclude that self-cleavage of hairpin ribozyme follows an A_N + D_N two-step associative pathway where the rate-determining step is the cleavage of the phosphodiester bond. These results provide a major advancement in our understanding of the unique catalytic mechanism of hairpin ribozyme which will fruitfully impact on the design of synthetic ribozymes.

Benchmarking quantum mechanical methods for calculating reaction energies of reactions catalyzed by enzymes

To assess the accuracy of different quantum mechanical methods for biochemical modeling, the reaction energies of 20 small model reactions (chosen to represent chemical steps catalyzed by commonly studied enzymes) were calculated. The methods tested included several popular Density Functional Theory (DFT) functionals, second-order Møller Plesset perturbation theory (MP2) and its spin-component scaled variant (SCS-MP2), and coupled cluster singles and doubles and perturbative triples (CCSD(T)). Different basis sets were tested. CCSD(T)/aug-cc-pVTZ results for all 20 reactions were used to benchmark the other methods. It was found that MP2 and SCS-MP2 reaction energy calculation results are similar in quality to CCSD(T) (mean absolute error (MAE) of 1.2 and 1.3 kcal mol−1, respectively). MP2 calculations gave a large error in one case, and are more subject to basis set effects, so in general SCS-MP2 calculations are a good choice when CCSD(T) calculations are not feasible. Results with different DFT functionals were of reasonably good quality (MAEs of 2.5–5.1 kcal mol−1), whereas popular semi-empirical methods (AM1, PM3, SCC-DFTB) gave much larger errors (MAEs of 11.6–14.6 kcal mol−1). These results should be useful in guiding methodological choices and assessing the accuracy of QM/MM calculations on enzyme-catalyzed reactions.

Quantum Chemical and QM/MM Models in Biochemistry

Quantum chemical (QC) calculations provide a basis for deriving a microscopic understanding of enzymes and photobiological systems. Here we describe how QC models can be used to explore the electronic structure, dynamics, and energetics of biomolecules. We introduce the hybrid quantum mechanics/classical mechanics (QM/MM) approach, where a quantum mechanically described system of interest is embedded in a classically described force field representation of the biochemical surroundings. We also discuss the QM cluster model approach, as well as embedding theories, that provide complementary methodologies to model quantum mechanical effects in biomolecules. The chapter also provides some practical guides for building quantum biochemical models using the quinone reduction catalysis in respiratory complex I and a model reaction in solution as examples.

Mechanistic role of nucleobases in self-cleavage catalysis of hairpin ribozyme at ambient versus high-pressure conditions

Ribozymes catalyze the site-specific self-cleavage of intramolecular phosphodiester bonds. Initially thought to act as metalloenzymes, they are now known to be functional even in the absence of divalent metal ions and specific nucleobases directly participate in the self-cleavage reaction. Here, we use extensive replica exchange molecular dynamics simulations to probe the precise mechanistic role of nucleobases by simulating precatalytic reactant and active precursor states of a hairpin ribozyme along its reaction path at ambient as well as high-pressure conditions. The results provide novel key insights into the self-cleavage of ribozymes. We find that deprotonation of the hydroxyl group is crucial and might be the penultimate step to the self-cleavage. The G8 nucleobase is found to stabilize the activated precursor into inline arrangement for facile nucleophilic attack of the scissile phosphate only after deprotonation of the hydroxyl group. The protonated A38 nucleobase, in contrast, mainly acts a proton donor to the O5'-oxygen leaving group that eventually leads to the self-cleavage. Indeed, systematic high-pressure simulations of catalytically relevant states confirm these findings and, moreover, provide support to the role of ribozymes as piezophilic biocatalysts with regard to their relevance in early life under extreme conditions in the realm of RNA world hypothesis.

Studying the phosphoryl transfer mechanism of the E. coli phosphofructokinase-2: from X-ray structure to quantum mechanics/molecular mechanics simulations

Phosphofructokinases catalyze the ATP-dependent phosphorylation of fructose-6-phosphate and they are highly regulated.

Phosphofructokinases (Pfks) catalyze the ATP-dependent phosphorylation of fructose-6-phosphate (F6P) and they are regulated in a wide variety of organisms. Although numerous aspects of the kinetics and regulation have been characterized for Pfks, the knowledge about the mechanism of the phosphoryl transfer reaction and the transition state lags behind. In this work, we describe the X-ray crystal structure of the homodimeric Pfk-2 from E. coli, which contains products in one site and reactants in the other, as well as an additional ATP molecule in the inhibitory allosteric site adjacent to the reactants. This complex was previously predicted when studying the kinetic mechanism of ATP inhibition. After removing the allosteric ATP, molecular dynamic (MD) simulations revealed conformational changes related to domain packing, as well as stable interactions of Lys27 and Asp256 with donor (ATP) and acceptor (fructose-6-) groups, and of Asp166 with Mg²⁺. The phosphoryl transfer reaction mechanism catalyzed by Pfk-2 was investigated through Quantum Mechanics/Molecular Mechanics (QM/MM) simulations using a combination of the string method and a path-collective variable for the exploration of its free energy surface. The calculated activation free energies showed that a dissociative mechanism, occurring with a metaphosphate intermediate formation followed by a proton transfer to Asp256, is more favorable than an associative one. The structural analysis reveals the role of Asp256 acting as a catalytic base and Lys27 stabilizing the transition state of the dissociative mechanism.

Theoretical Studies on Mechanism of Inactivation of Kanamycin A by 4'-O-Nucleotidyltransferase

This work is focused on mechanistic studies of the transfer of an adenylyl group (Adenoside-5'-monophosfate) from adenosine 5'-triphosphate (ATP) to a OH-4' hydroxyl group of an antibiotic. Using hybrid quantum mechanics/molecular mechanics (QM/MM) techniques, we study the substrate and base-assisted mechanisms of the inactivation process of kanamycin A (KAN) catalyzed by 4'-O-Nucleotidyltransferase [ANT(4')], an active enzyme against almost all aminoglycoside antibiotics. Free energy surfaces, obtained with Free Energy Perturbation methods at the M06-2X/MM level of theory, show that the most favorable reaction path presents a barrier of 12.2 kcal·mol-1 that corresponds to the concerted activation of O4' from KAN by Glu145. In addition, the primary and secondary 18O kinetic isotope effects (KIEs) have been computed for bridge O3α, and non-bridge O1α, O2α, and O5' atoms of ATP. The observed normal 1°-KIE of 1.2% and 2°-KIE of 0.07% for the Glu145-assisted mechanism are in very good agreement with experimentally measured data. Additionally, based on the obtained results, the role of electrostatic and compression effects in enzymatic catalysis is discussed.

QM/MM Calculations on Protein-RNA Complexes: Understanding Limitations of Classical MD Simulations and Search for Reliable Cost-Effective QM Methods

Although atomistic explicit-solvent Molecular Dynamics (MD) is a popular tool to study protein-RNA recognition, satisfactory MD description of protein-RNA complexes is not always achieved. Unfortunately, it is often difficult to separate MD simulation instabilities primarily caused by the simple point-charge molecular mechanics (MM) force fields from problems related to the notorious uncertainties in the starting structures. Herein, we report a series of large-scale QM/MM calculations on the U1A protein-RNA complex. This experimentally well-characterized system has an intricate protein-RNA interface, which is very unstable in MD simulations. The QM/MM calculations identify several H-bonds poorly described by the MM method and thus indicate the sources of instabilities of the U1A interface in MD simulations. The results suggest that advanced QM/MM computations could be used to indirectly rationalize problems seen in MM-based MD simulations of protein-RNA complexes. As the most accurate QM method, we employ the computationally demanding meta-GGA density functional TPSS-D3(BJ)/def2-TZVP level of theory. Because considerably faster methods would be needed to extend sampling and to study even larger protein-RNA interfaces, a set of low-cost QM/MM methods is compared to the TPSS-D3(BJ)/def2-TZVP data. The PBEh-3c and B97-3c density functional composite methods appear to be suitable for protein-RNA interfaces. In contrast, HF-3c and the tight-binding Hamiltonians DFTB3-D3 and GFN-xTB perform unsatisfactorily and do not provide any advantage over the MM description. These conclusions are supported also by similar analysis of a simple HutP protein-RNA interface, which is well-described by MD with the exception of just one H-bond. Some other methodological aspects of QM/MM calculations on protein-RNA interfaces are discussed.

Phosphoryl-Transfer Reaction in RNA under Alkaline Conditions

The phosphoryl-transfer reaction in RNA under alkaline conditions by exploring the influence of several solvents theoretically was studied. The calculations were carried out by using the M06-2X functional and the solvents were taken as a continuum by using the solvent model density (SMD) method. The main findings show that the O2'-P-O5' angle in the reactants, the free activation energies, and the reaction mechanism are clearly dependent on the dielectric constant of the environment, thus showing that the electrostatic term is the determining factor for this chemical system with two negative charges. Our study seems to indicate that water, the solvent with the greatest dielectric constant, would be the solvent that increases the reaction rate the most. As this outcome was not the case in enzymatic catalysis, one has to conclude that, in the case of proteins as well as for ribozymes, the enzymatic catalysis is not mainly due to the solvent reaction field, but to local electrical fields as a result of enzyme preorganization.

Analysis of Phosphoryl-Transfer Enzymes with QM/MM Free Energy Simulations

We discuss the application of quantum mechanics/molecular mechanics (QM/MM) free energy simulations to the analysis of phosphoryl transfers catalyzed by two enzymes: alkaline phosphatase and myosin. We focus on the nature of the transition state and the issue of mechanochemical coupling, respectively, in the two enzymes. The results illustrate unique insights that emerged from the QM/MM simulations, especially concerning the interpretation of experimental data regarding the nature of enzymatic transition states and coupling between global structural transition and catalysis in the active site. We also highlight a number of technical issues worthy of attention when applying QM/MM free energy simulations, and comment on a number of technical and mechanistic issues that require further studies.

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.

Prebiotic synthesis of nucleic acids and their building blocks at the atomic level - merging models and mechanisms from advanced computations and experiments

The origin of life on Earth is one of the most fascinating questions of contemporary science. Extensive research in the past decades furnished diverse experimental proposals for the emergence of first informational polymers that could form the basis of the early terrestrial life. Side by side with the experiments, the fast development of modern computational chemistry methods during the last 20 years facilitated the use of in silico modelling tools to complement the experiments. Modern computations can provide unique atomic-level insights into the structural and electronic aspects as well as the energetics of key prebiotic chemical reactions. Many of these insights are not directly obtainable from the experimental techniques and the computations are thus becoming indispensable for proper interpretation of many experiments and for qualified predictions. This review illustrates the synergy between experiment and theory in the origin of life research focusing on the prebiotic synthesis of various nucleic acid building blocks and on the self-assembly of nucleotides leading to the first functional oligonucleotides.

Mechanistic Insights into the Reaction of Chlorination of Tryptophan Catalyzed by Tryptophan 7-Halogenase

Tryptophan 7-halogenase catalyzes chlorination of free tryptophan to 7-chlorotryptophan, which is the first step in the antibiotic pyrrolnitrin biosynthesis. Many biologically and pharmaceutically active natural products contain chlorine and thus, an understanding of the mechanism of its introduction into organic molecules is important. Whilst enzyme-catalyzed chlorination is accomplished with ease, it remains a difficult task for the chemists. Therefore, utilizing enzymes in the synthesis of chlorinated organic compounds is important, and providing atomistic mechanistic insights about the reaction mechanism of tryptophan 7-halogenase is vital and timely. In this work, we examined a mechanism for the reaction of tryptophan chlorination, performed by tryptophan 7-halogenase, by calculating potential energy and free energy surfaces using two different Combined Quantum Mechanical/Molecular Mechanical (QM/MM) methods both employing Density Functional Theory (DFT) for the QM region. Both computational strategies agree on the nature of the rate-limiting step and provided close results for the reaction barriers of the two reaction steps. The calculations for both the potential energy and the free energy profiles showed very similar geometric features and hydrogen bonding interactions for the characterized stationary points.

Thermodynamics and kinetics of RNA tertiary structure formation in the junctionless hairpin ribozyme

The hairpin ribozyme consists of two RNA internal loops that interact to form the catalytically active structure. This docking transition is a rare example of intermolecular formation of RNA tertiary structure without coupling to helix annealing. We have used temperature-dependent surface plasmon resonance (SPR) to characterize the thermodynamics and kinetics of RNA tertiary structure formation for the junctionless form of the ribozyme, in which loops A and B reside on separate molecules. We find docking to be strongly enthalpy-driven and to be accompanied by substantial activation barriers for association and dissociation, consistent with the structural reorganization of both internal loops upon complex formation. Comparisons with the parallel analysis of a ribozyme variant carrying a 2'-O-methyl modification at the self-cleavage site and with published data in other systems reveal a surprising diversity of thermodynamic signatures, emphasizing the delicate balance of contributions to the free energy of formation of RNA tertiary structure.

Producing DFT/MM enzyme reaction trajectories from SCC-DFTB/MM driving forces to probe the underlying electronics of a glycosyltransferase reaction

The SCC-DFTB/MIO/CHARMM free energy surface for a glycosyltransferase, TcTS, is benchmarked against a DFT/MM reaction trajectory using the same CHARMM MM force field ported to the NWChem package. The popular B3LYP functional, against which the MIO parameter set was parameterized is used to optimize TS structures and run DFT reaction dynamics. A novel approach was used to generate reaction forces from a SCC-DFTB/MIO/CHARMM reaction surface to drive B3LYP/6-31G/MM and B3LYP/6-31G(d)/MM reaction trajectories. Although TS structures compare favorably, differences stemming primarily from a minimal basis set approximation prevented a successful 6-31G(d) FEARCF reaction dynamics trajectory. None the less, the dynamic evolution of the B3LYP/6-31G/MM-computed electron density provided an opportunity to perform NBO analysis along the reaction trajectory. Here, we illustrate that a successful ab initio reaction trajectory is computationally accessible when the underlying potential energy function of the semi-empirical method used to produce driving forces is sufficiently close to the ab initio potential. © 2017 Wiley Periodicals, Inc.

Understanding in-line probing experiments by modeling cleavage of nonreactive RNA nucleotides

Ribonucleic acid (RNA) is involved in many regulatory and catalytic processes in the cell. The function of any RNA molecule is intimately related with its structure. In-line probing experiments provide valuable structural data sets for a variety of RNAs and are used to characterize conformational changes in riboswitches. However, the structural determinants that lead to differential reactivities in unpaired nucleotides have not been investigated yet. In this work, we used a combination of theoretical approaches, i.e., classical molecular dynamics simulations, multiscale quantum mechanical/molecular mechanical calculations, and enhanced sampling techniques in order to compute and interpret the differential reactivity of individual residues in several RNA motifs, including members of the most important GNRA and UNCG tetraloop families. Simulations on the multinanosecond timescale are required to converge the related free-energy landscapes. The results for uGAAAg and cUUCGg tetraloops and double helices are compared with available data from in-line probing experiments and show that the introduced technique is able to distinguish between nucleotides of the uGAAAg tetraloop based on their structural predispositions toward phosphodiester backbone cleavage. For the cUUCGg tetraloop, more advanced ab initio calculations would be required. This study is the first attempt to computationally classify chemical probing experiments and paves the way for an identification of tertiary structures based on the measured reactivity of nonreactive nucleotides.

Perspective: Quantum mechanical methods in biochemistry and biophysics

In this perspective article, I discuss several research topics relevant to quantum mechanical (QM) methods in biophysical and biochemical applications. Due to the immense complexity of biological problems, the key is to develop methods that are able to strike the proper balance of computational efficiency and accuracy for the problem of interest. Therefore, in addition to the development of novel ab initio and density functional theory based QM methods for the study of reactive events that involve complex motifs such as transition metal clusters in metalloenzymes, it is equally important to develop inexpensive QM methods and advanced classical or quantal force fields to describe different physicochemical properties of biomolecules and their behaviors in complex environments. Maintaining a solid connection of these more approximate methods with rigorous QM methods is essential to their transferability and robustness. Comparison to diverse experimental observables helps validate computational models and mechanistic hypotheses as well as driving further development of computational methodologies.

Metal Fluorides: Tools for Structural and Computational Analysis of Phosphoryl Transfer Enzymes

The phosphoryl group, PO₃^-, is the dynamic structural unit in the biological chemistry of phosphorus. Its transfer from a donor to an acceptor atom, with oxygen much more prevalent than nitrogen, carbon, or sulfur, is at the core of a great majority of enzyme-catalyzed reactions involving phosphate esters, anhydrides, amidates, and phosphorothioates. The serendipitous discovery that the phosphoryl group could be labeled by "nuclear mutation," by substitution of PO₃^- by MgF₃^- or AlF₄^-, has underpinned the application of metal fluoride (MF _x ) complexes to mimic transition states for enzymatic phosphoryl transfer reactions, with sufficient stability for experimental analysis. Protein crystallography in the solid state and ¹⁹F NMR in solution have enabled direct observation of ternary and quaternary protein complexes embracing MF _x transition state models with precision. These studies have underpinned a radically new mechanistic approach to enzyme catalysis for a huge range of phosphoryl transfer processes, as varied as kinases, phosphatases, phosphomutases, and phosphohydrolases. The results, without exception, have endorsed trigonal bipyramidal geometry (tbp) for concerted, "in-line" stereochemistry of phosphoryl transfer. QM computations have established the validity of tbp MF _x complexes as reliable models for true transition states, delivering similar bond lengths, coordination to essential metal ions, and virtually identical hydrogen bond networks. The emergence of protein control of reactant orbital overlap between bond-forming species within enzyme transition states is a new challenging theme for wider exploration.

CADEE: Computer-Aided Directed Evolution of Enzymes

The tremendous interest in enzymes as biocatalysts has led to extensive work in enzyme engineering, as well as associated methodology development. Here, a new framework for computer-aided directed evolution of enzymes (CADEE) is presented which allows a drastic reduction in the time necessary to prepare and analyze in silico semi-automated directed evolution of enzymes. A pedagogical example of the application of CADEE to a real biological system is also presented in order to illustrate the CADEE workflow.

Intrinsic Base-Pair Rearrangement in the Hairpin Ribozyme Directs RNA Conformational Sampling and Tertiary Interface Formation

Dynamic fluctuations in RNA structure enable conformational changes that are required for catalysis and recognition. In the hairpin ribozyme, the catalytically active structure is formed as an intricate tertiary interface between two RNA internal loops. Substantial alterations in the structure of each loop are observed upon interface formation, or docking. The very slow on-rate for this relatively tight interaction has led us to hypothesize a double conformational capture mechanism for RNA-RNA recognition. We used extensive molecular dynamics simulations to assess conformational sampling in the undocked form of the loop domain containing the scissile phosphate (loop A). We observed several major accessible conformations with distinctive patterns of hydrogen bonding and base stacking interactions in the active-site internal loop. Several important conformational features characteristic of the docked state were observed in well-populated substates, consistent with the kinetic sampling of docking-competent states by isolated loop A. Our observations suggest a hybrid or multistage binding mechanism, in which initial conformational selection of a docking-competent state is followed by induced-fit adjustment to an in-line, chemically reactive state only after formation of the initial complex with loop B.

QM/MM free energy simulations: recent progress and challenges

Due to the higher computational cost relative to pure molecular mechanical (MM) simulations, hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations particularly require a careful consideration of balancing computational cost and accuracy. Here we review several recent developments in free energy methods most relevant to QM/MM simulations and discuss several topics motivated by these developments using simple but informative examples that involve processes in water. For chemical reactions, we highlight the value of invoking enhanced sampling technique (e.g., replica-exchange) in umbrella sampling calculations and the value of including collective environmental variables (e.g., hydration level) in metadynamics simulations; we also illustrate the sensitivity of string calculations, especially free energy along the path, to various parameters in the computation. Alchemical free energy simulations with a specific thermodynamic cycle are used to probe the effect of including the first solvation shell into the QM region when computing solvation free energies. For cases where high-level QM/MM potential functions are needed, we analyze two different approaches: the QM/MM-MFEP method of Yang and co-workers and perturbative correction to low-level QM/MM free energy results. For the examples analyzed here, both approaches seem productive although care needs to be exercised when analyzing the perturbative corrections.

A Projector-Embedding Approach for Multiscale Coupled-Cluster Calculations Applied to Citrate Synthase

Projector-based embedding has recently emerged as a robust multiscale method for the calculation of various electronic molecular properties. We present the coupling of projector embedding with quantum mechanics/molecular mechanics modeling and apply it for the first time to an enzyme-catalyzed reaction. Using projector-based embedding, we combine coupled-cluster theory, density-functional theory (DFT), and molecular mechanics to compute energies for the proton abstraction from acetyl-coenzyme A by citrate synthase. By embedding correlated ab initio methods in DFT we eliminate functional sensitivity and obtain high-accuracy profiles in a procedure that is straightforward to apply.

Ambient-Potential Composite Ewald Method for ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulation

A new approach for performing Particle Mesh Ewald in ab initio quantum mechanical/molecular mechanical (QM/MM) simulations with extended atomic orbital basis sets is presented. The new approach, the Ambient-Potential Composite Ewald (CEw) method, does not perform the QM/MM interaction with Mulliken charges nor electrostatically fit charges. Instead the nuclei and electron density interact directly with the MM environment, but in a manner that avoids the use of dense Fourier transform grids. By performing the electrostatics with the underlying QM density, the CEw method avoids self-consistent field instabilities that have been encountered with simple charge mapping procedures. Potential of mean force (PMF) profiles of the p-nitrophenyl phosphate dissociation reaction in explicit solvent are computed from PBE0/6-31G* QM/MM molecular dynamics simulations with various electrostatic protocols. The CEw profiles are shown to be stable with respect to real-space Ewald cutoff, whereas the PMFs computed from truncated and switched electrostatics produce artifacts. PBE0/6-311G**, AM1/d-PhoT, and DFTB2 QM/MM simulations are performed to generate two-dimensional PMF profiles of the phosphoryl transesterification reactions with ethoxide and phenoxide leaving groups. The semiempirical models incorrectly produce a concerted ethoxide mechanism, whereas PBE0 correctly produces a stepwise mechanism. The ab initio reaction barriers agree more closely to experiment than the semiempirical models. The failure of Mulliken-charge QM/MM-Ewald is analyzed.

Chemical feasibility of the general acid/base mechanism of glmS ribozyme self-cleavage

In numerous Gram-positive bacteria, the glmS ribozyme or catalytic riboswitch regulates the expression of glucosamine-6-phosphate (GlcN6P) synthase via site-specific cleavage of its sugar-phosphate backbone in response to GlcN6P ligand binding. Biochemical data have suggested a crucial catalytic role for an active site guanine (G40 in Thermoanaerobacter tengcongensis, G33 in Bacillus anthracis). We used hybrid quantum chemical/molecular mechanical (QM/MM) calculations to probe the mechanism where G40 is deprotonated and acts as a general base. The calculations suggest that the deprotonated guanine G40(-) is sufficiently reactive to overcome the thermodynamic penalty arising from its rare protonation state, and thus is able to activate the A-1(2'-OH) group toward nucleophilic attack on the adjacent backbone. Furthermore, deprotonation of A-1(2'-OH) and nucleophilic attack are predicted to occur as separate steps, where activation of A-1(2'-OH) precedes nucleophilic attack. Conversely, the transition state associated with the rate-determining step corresponds to concurrent nucleophilic attack and protonation of the G1(O5') leaving group by the ammonium moiety of the GlcN6P cofactor. Overall, our calculations help to explain the crucial roles of G40 (as a general base) and GlcN6P (as a general acid) during glmS ribozyme self-cleavage. In addition, we show that the QM/MM description of the glmS ribozyme self-cleavage reaction is significantly more sensitive to the size of the QM region and the quality of the QM-MM coupling than that of other small ribozymes.

The role of an active site Mg(2+) in HDV ribozyme self-cleavage: insights from QM/MM calculations

The hepatitis delta virus (HDV) ribozyme is a catalytic RNA motif embedded in the human pathogenic HDV RNA. It catalyzes self-cleavage of its sugar-phosphate backbone with direct participation of the active site cytosine C75. Biochemical and structural data support a general acid role of C75. Here, we used hybrid quantum mechanical/molecular mechanical (QM/MM) calculations to probe the reaction mechanism and changes in Gibbs energy along the ribozyme's reaction pathway with an N3-protonated C75H(+) in the active site, which acts as the general acid, and a partially hydrated Mg(2+) ion with one deprotonated, inner-shell coordinated water molecule that acts as the general base. We followed eight reaction paths with a distinct position and coordination of the catalytically important active site Mg(2+) ion. For six of them, we observed feasible activation barriers ranging from 14.2 to 21.9 kcal mol(-1), indicating that the specific position of the Mg(2+) ion in the active site is predicted to strongly affect the kinetics of self-cleavage. The deprotonation of the U-1(2'-OH) nucleophile and the nucleophilic attack of the resulting U-1(2'-O(-)) on the scissile phosphodiester are found to be separate steps, as deprotonation precedes the nucleophilic attack. This sequential mechanism of the HDV ribozyme differs from the concerted nucleophilic activation and attack suggested for the hairpin ribozyme. We estimate the pKa of the U-1(2'-OH) group to range from 8.8 to 11.2, suggesting that it is lowered by several units from that of a free ribose, comparable to and most likely smaller than the pKa of the solvated active site Mg(2+) ion. Our results thus support the notion that the structure of the HDV ribozyme, and particularly the positioning of the active site Mg(2+) ion, facilitate deprotonation and activation of the 2'-OH nucleophile.

Molecular dynamic simulations of protein/RNA complexes: CRISPR/Csy4 endoribonuclease

BACKGROUND

Many prokaryotic genomes comprise Clustered Regularly Interspaced Short Palindromic Repeats (CRISPRs) offering defense against foreign nucleic acids. These immune systems are conditioned by the production of small CRISPR-derived RNAs matured from long RNA precursors. This often requires a Csy4 endoribonuclease cleaving the RNA 3'-end.

METHODS

We report extended explicit solvent molecular dynamic (MD) simulations of Csy4/RNA complex in precursor and product states, based on X-ray structures of product and inactivated precursor (55 simulations; ~3.7μs in total).

RESULTS

The simulations identify double-protonated His29 and deprotonated terminal phosphate as the likely dominant protonation states consistent with the product structure. We revealed potential substates consistent with Ser148 and His29 acting as the general base and acid, respectively. The Ser148 could be straightforwardly deprotonated through solvent and could without further structural rearrangements deprotonate the nucleophile, contrasting similar studies investigating the general base role of nucleobases in ribozymes. We could not locate geometries consistent with His29 acting as general base. However, we caution that the X-ray structures do not always capture the catalytically active geometries and then the reactive structures may be unreachable by the simulation technique.

CONCLUSIONS

We identified potential catalytic arrangement of the Csy4/RNA complex but we also report limitations of the simulation technique. Even for the dominant protonation state we could not achieve full agreement between the simulations and the structural data.

GENERAL SIGNIFICANCE

Potential catalytic arrangement of the Csy4/RNA complex is found. Further, we provide unique insights into limitations of simulations of protein/RNA complexes, namely, the influence of the starting experimental structures and force field limitations. This article is part of a Special Issue entitled Recent developments of molecular dynamics.