Altered Mechanisms for Acid-Catalyzed RNA Cleavage and Isomerization Reactions Models.

RNA strand cleavage by 2'-O-transphosphorylation is catalyzed not only by numerous nucleolytic RNA enzymes (ribozymes) but also by hydroxide or hydronium ions. In experiments, both cleavage of the 5'-linked nucleoside and isomerization between 3',5'- and 2',5'-phosphodiesters occur under acidic conditions, while only the cleavage reaction is observed under basic conditions. An ab initio path-integral approach for simulating kinetic isotope effects is used to reveal the reaction mechanisms for RNA cleavage and isomerization reactions under acidic conditions. Moreover, the proposed mechanisms can also be combined through the experimental pH-rate profiles.

Theoretical Simulations of Kinetic Isotope Effects on Decarboxylation of 3-Carboxybenzisoxazole.

Kinetic isotope effect values on the decarboxylation of 3-carboxybenzisoxazole have been computed using the second-order Kleinert's variational perturbation theory in the framework of Feynman's path integrals along with the potential energy surface obtained at the MP2/6-31+G(d) level. Good agreement with the experimental data was obtained, demonstrating that this novel computational approach for computing KIE values of organic reaction is a viable alternative to the traditional method employing the Bigeleisen equation and harmonic vibrational frequencies. Compared with the experimental measurements, consideration of anharmonicity and tunneling effects can significantly improve the calculated KIE values, reducing the root-mean-square deviation from 1.19 % for traditional method to 0.20 % for path-integral method.

Theoretical Simulations of Heavy-Atom Kinetic Isotope Effects in Aliphatic Claisen Rearrangement.

The aliphatic Claisen rearrangement of allyl vinyl ether has attracted great interest for its broad applications in chemical synthesis and biosynthesis. Although it is well agreed that this reaction proceeds via a concerted, "chair-like" transition state, certain inconsistencies of kinetic isotope effect (KIE) data between experimental measurements and theoretical simulations or between independent experiments indicate that the nature and mechanism of this important reaction need to be investigated in more detail. In order to verify two independent sets of experimental data, we present theoretical calculations on heavy-atom KIE values of alipahtic Claisen rearrangement, using our recently developed path-integral method with the second-order Kleinert's variational perturbation theory, which goes beyond the traditional method for computing KIE values by employing the Bigeleisen equation. Amazingly, the results demonstrate that both sets of experimental measurements are correct, while the inconsistency originates from the fact that the aliphatic Claisen rearrangement undergoes similar but different mechanisms in gas and solution phases. Different experimental conditions will alter the actual reactant state by tuning the population distribution of reactant conformers. According to the comparison between experimental and theoretical results, a more clear reaction mechanism of aliphatic Claisen rearrangement is revealed.

Association between high cumulative dose of benzodiazepine in Chinese patients and risk of dementia: a preliminary retrospective case-control study.

BACKGROUND: Evidence describing the association between high-dose benzodiazepine use and dementia has been conflicting. Most previous studies involved Caucasian populations, with only limited data on Chinese subjects. Possible differences exist between Chinese and Caucasian populations with regard to metabolism and prescription practice. This study aimed to assess the association between high-dose benzodiazepine use and dementia in a Chinese population. METHOD: A retrospective case-control study was carried out in all public hospitals under the Hong Kong Hospital Authority Hong Kong West Cluster between 2000 and 2015. The study recruited 273 Chinese adults (91 cases, 182 controls) aged 75 and over, with at least 6 years of follow-up data. Each dementia case was matched with two controls according to sex, age group, and duration of follow-up. The number of patients with benzodiazepine ever-use and the exposure density based on the prescribed daily doses were assessed. Prescribed daily doses were categorized as either <1096 or ≥1096. Odds ratios and 95% confidence intervals were computed by multivariate analysis. RESULTS: The difference in exposure density between the dementia and control groups was statistically significant between prescribed daily doses <1096 and ≥1096 (P = 0.02). There were two multivariate analyses models; one factored in depression (model 1), and the other (model 2) did not. Model 2 showed a statistically significant association (odds ratio = 1.71, 95% confidence intervals = 1.02-2.89, P = 0.04) between benzodiazepine exposure density and dementia. CONCLUSION: High-dose benzodiazepine use may be associated with dementia in the Chinese population. Prospective studies are required.

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

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

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

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

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

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

Roadmaps through free energy landscapes calculated using the multi-dimensional vFEP approach.

The variational free energy profile (vFEP) method is extended to two dimensions and tested with molecular simulation applications. The proposed 2D-vFEP approach effectively addresses the two major obstacles to constructing free energy profiles from simulation data using traditional methods: the need for overlap in the re-weighting procedure and the problem of data representation. This is especially evident as these problems are shown to be more severe in two dimensions. The vFEP method is demonstrated to be highly robust and able to provide stable, analytic free energy profiles with only a paucity of sampled data. The analytic profiles can be analyzed with conventional search methods to easily identify stationary points (e.g. minima and first-order saddle points) as well as the pathways that connect these points. These "roadmaps" through the free energy surface are useful not only as a post-processing tool to characterize mechanisms, but can also serve as a basis from which to direct more focused "on-the-fly" sampling or adaptive force biasing. Test cases demonstrate that 2D-vFEP outperforms other methods in terms of the amount and sparsity of the data needed to construct stable, converged analytic free energy profiles. In a classic test case, the two dimensional free energy profile of the backbone torsion angles of alanine dipeptide, 2D-vFEP needs less than 1% of the original data set to reach a sampling accuracy of 0.5 kcal/mol in free energy shifts between windows. A new software tool for performing one and two dimensional vFEP calculations is herein described and made publicly available.

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.

Experimental and computational analysis of the transition state for ribonuclease A-catalyzed RNA 2'-O-transphosphorylation.

Enzymes function by stabilizing reaction transition states; therefore, comparison of the transition states of enzymatic and nonenzymatic model reactions can provide insight into biological catalysis. Catalysis of RNA 2'-O-transphosphorylation by ribonuclease A is proposed to involve electrostatic stabilization and acid/base catalysis, although the structure of the rate-limiting transition state is uncertain. Here, we describe coordinated kinetic isotope effect (KIE) analyses, molecular dynamics simulations, and quantum mechanical calculations to model the transition state and mechanism of RNase A. Comparison of the (18)O KIEs on the 2'O nucleophile, 5'O leaving group, and nonbridging phosphoryl oxygens for RNase A to values observed for hydronium- or hydroxide-catalyzed reactions indicate a late anionic transition state. Molecular dynamics simulations using an anionic phosphorane transition state mimic suggest that H-bonding by protonated His12 and Lys41 stabilizes the transition state by neutralizing the negative charge on the nonbridging phosphoryl oxygens. Quantum mechanical calculations consistent with the experimental KIEs indicate that expulsion of the 5'O remains an integral feature of the rate-limiting step both on and off the enzyme. Electrostatic interactions with positively charged amino acid site chains (His12/Lys41), together with proton transfer from His119, render departure of the 5'O less advanced compared with the solution reaction and stabilize charge buildup in the transition state. The ability to obtain a chemically detailed description of 2'-O-transphosphorylation transition states provides an opportunity to advance our understanding of biological catalysis significantly by determining how the catalytic modes and active site environments of phosphoryl transferases influence transition state structure.

Exact Relation between Potential of Mean Force and Free-Energy Profile.

We apply concepts of covariant and contravariant vector space in differential geometry and general relativity to derive new, general, exact relations between potential of mean force and free-energy profile. These relations are immensely practical in free-energy simulations because a full Jacobian transformation (which is usually unknown) is not required; rather, only knowledge of the (constraint) coordinate of interest is needed. We reveal that in addition to the Jacobian determinant, the Jacobian scale factor and Leibnizian contributions must also be considered, as well a Fixman term with correct mass dependence. Our newly derived relations are verified with new non-trivial benchmark numerical examples for which exact results can be computed, and compared with relations available in the literature that turn out to exhibit significant deviations from the exact values.

Insight into the phosphodiesterase mechanism from combined QM/MM free energy simulations.

Molecular dynamics simulations employing a combined quantum mechanical and molecular mechanical potential have been carried out to elucidate the reaction mechanism of the hydrolysis of a cyclic nucleotide cAMP substrate by phosphodiesterase 4B (PDE4B). PDE4B is a member of the PDE superfamily of enzymes that play crucial roles in cellular signal transduction. We have determined a two-dimensional potential of mean force (PMF) for the coupled phosphoryl bond cleavage and proton transfer through a general acid catalysis mechanism in PDE4B. The results indicate that the ring-opening process takes place through an S(N)2 reaction mechanism, followed by a proton transfer to stabilize the leaving group. The computed free energy of activation for the PDE4B-catalyzed cAMP hydrolysis is about 13 kcal·mol(-1) and an overall reaction free energy is about -17 kcal·mol(-1), both in accord with experimental results. In comparison with the uncatalyzed reaction in water, the enzyme PDE4B provides a strong stabilization of the transition state, lowering the free energy barrier by 14 kcal·mol(-1). We found that the proton transfer from the general acid residue His234 to the O3' oxyanion of the ribosyl leaving group lags behind the nucleophilic attack, resulting in a shallow minimum on the free energy surface. A key contributing factor to transition state stabilization is the elongation of the distance between the divalent metal ions Zn(2+) and Mg(2+) in the active site as the reaction proceeds from the Michaelis complex to the transition state.

Theoretical analysis of kinetic isotope effects on proton transfer reactions between substituted alpha-methoxystyrenes and substituted acetic acids.

Primary kinetic isotope effects (KIEs) on a series of carboxylic acid-catalyzed protonation reactions of aryl-substituted alpha-methoxystyrenes (X-1) to form oxocarbenium ions have been computed using the second-order Kleinert variational perturbation theory (KP2) in the framework of Feynman path integrals (PI) along with the potential energy surface obtained at the B3LYP/6-31+G(d,p) level. Good agreement with the experimental data was obtained, demonstrating that this novel computational approach for computing KIEs of organic reactions is a viable alternative to the traditional method employing Bigeleisen equation and harmonic vibrational frequencies. Although tunneling makes relatively small contributions to the lowering of the free energy barriers for the carboxylic acid catalyzed protonation reaction, it is necessary to include tunneling contributions to obtain quantitative estimates of the KIEs. Consideration of anharmonicity can further improve the calculated KIEs for the protonation of substituted alpha-methoxystyrenes by chloroacetic acid, but for the reactions of the parent and 4-NO(2) substituted alpha-methoxystyrene with substituted carboxylic acids, the correction of anharmonicity overestimates the computed KIEs for strong acid catalysts. In agreement with experimental findings, the largest KIEs are found in nearly ergoneutral reactions, DeltaG(o) approximately 0, where the transition structures are nearly symmetric and the reaction barriers are relatively low. Furthermore, the optimized transition structures are strongly dependent on the free energy for the formation of the carbocation intermediate, that is, the driving force DeltaG(o), along with a good correlation of Hammond shift in the transition state structure.

Determination of the structure form of the fourth ligand of zinc in Acutolysin A using combined quantum mechanical and molecular mechanical simulation.

Acutolysin A, which is isolated from the snake venom of Agkistrodon acutus, is a member of the SVMPs subfamily of the metzincin family, and it is a snake venom zinc metalloproteinase possessing only one catalytic domain. The catalytic zinc ion, in the active site, is coordinated in a tetrahedral manner with three imidazole nitrogen atoms of histidine and one oxygen atom. It is uncertain whether this oxygen atom is a water molecule or a hydroxide ion just from the three-dimensional X-ray crystal structure. The identity of the fourth ligand of zinc is theoretically determined for the first time by performing both combined quantum mechanical and molecular mechanical (QM/MM) simulation and high-level quantum mechanical calculations. All of the results obtained indicate that the fourth ligand in the active site of the reported X-ray crystal structure is a water molecule rather than a hydroxide anion. On the basis of these theoretical results, we note that the experimental observed pH dependence of the proteolytic and hemorrhagic activity of Acutolysin A can be attributed to the deprotonation of the zinc-bound water to yield a better nucleophile, the hydroxide ion. Structural analyses revealed structural details useful for the understanding of acutolysin catalytic mechanism.

Hybrid quantum and classical methods for computing kinetic isotope effects of chemical reactions in solutions and in enzymes.

A method for incorporating quantum mechanics into enzyme kinetics modeling is presented. Three aspects are emphasized: 1) combined quantum mechanical and molecular mechanical methods are used to represent the potential energy surface for modeling bond forming and breaking processes, 2) instantaneous normal mode analyses are used to incorporate quantum vibrational free energies to the classical potential of mean force, and 3) multidimensional tunneling methods are used to estimate quantum effects on the reaction coordinate motion. Centroid path integral simulations are described to make quantum corrections to the classical potential of mean force. In this method, the nuclear quantum vibrational and tunneling contributions are not separable. An integrated centroid path integral-free energy perturbation and umbrella sampling (PI-FEP/UM) method along with a bisection sampling procedure was summarized, which provides an accurate, easily convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. In the ensemble-averaged variational transition state theory with multidimensional tunneling (EA-VTST/MT), these three aspects of quantum mechanical effects can be individually treated, providing useful insights into the mechanism of enzymatic reactions. These methods are illustrated by applications to a model process in the gas phase, the decarboxylation reaction of N-methyl picolinate in water, and the proton abstraction and reprotonation process catalyzed by alanine racemase. These examples show that the incorporation of quantum mechanical effects is essential for enzyme kinetics simulations.

A Systematic Approach for Computing Zero-Point Energy, Quantum Partition Function, and Tunneling Effect Based on Kleinert's Variational Perturbation Theory.

In this paper, we describe an automated integration-free path-integral (AIF-PI) method, based on Kleinert's variational perturbation (KP) theory, to treat internuclear quantum-statistical effects in molecular systems. We have developed an analytical method to obtain the centroid potential as a function of the variational parameter in the KP theory, which avoids numerical difficulties in path-integral Monte Carlo or molecular dynamics simulations, especially at the limit of zero-temperature. Consequently, the variational calculations using the KP theory can be efficiently carried out beyond the first order, i.e., the Giachetti-Tognetti-Feynman-Kleinert variational approach, for realistic chemical applications. By making use of the approximation of independent instantaneous normal modes (INM), the AIF-PI method can readily be applied to many-body systems. Previously, we have shown that in the INM approximation, the AIF-PI method is accurate for computing the quantum partition function of a water molecule (3 degrees of freedom) and the quantum correction factor for the collinear H(3) reaction rate (2 degrees of freedom). In this work, the accuracy and properties of the KP theory are further investigated by using the first three order perturbations on an asymmetric double-well potential, the bond vibrations of H(2), HF, and HCl represented by the Morse potential, and a proton-transfer barrier modeled by the Eckart potential. The zero-point energy, quantum partition function, and tunneling factor for these systems have been determined and are found to be in excellent agreement with the exact quantum results. Using our new analytical results at the zero-temperature limit, we show that the minimum value of the computed centroid potential in the KP theory is in excellent agreement with the ground state energy (zero-point energy) and the position of the centroid potential minimum is the expectation value of particle position in wave mechanics. The fast convergent property of the KP theory is further examined in comparison with results from the traditional Rayleigh-Ritz variational approach and Rayleigh-Schrödinger perturbation theory in wave mechanics. The present method can be used for thermodynamic and quantum dynamic calculations, including to systematically determine the exact value of zero-point energy and to study kinetic isotope effects for chemical reactions in solution and in enzymes.

Combined QM/MM and path integral simulations of kinetic isotope effects in the proton transfer reaction between nitroethane and acetate ion in water.

An integrated Feynman path integral-free energy perturbation and umbrella sampling (PI-FEP/UM) method has been used to investigate the kinetic isotope effects (KIEs) in the proton transfer reaction between nitroethane and acetate ion in water. In the present study, both nuclear and electronic quantum effects are explicitly treated for the reacting system. The nuclear quantum effects are represented by bisection sampling centroid path integral simulations, while the potential energy surface is described by a combined quantum mechanical and molecular mechanical (QM/MM) potential. The accuracy essential for computing KIEs is achieved by a FEP technique that transforms the mass of a light isotope into a heavy one, which is equivalent to the perturbation of the coordinates for the path integral quasiparticle in the bisection sampling scheme. The PI-FEP/UM method is applied to the proton abstraction of nitroethane by acetate ion in water through molecular dynamics simulations. The rule of the geometric mean and the Swain-Schaad exponents for various isotopic substitutions at the primary and secondary sites have been examined. The computed total deuterium KIEs are in accord with experiments. It is found that the mixed isotopic Swain-Schaad exponents are very close to the semiclassical limits, suggesting that tunneling effects do not significantly affect this property for the reaction between nitroethane and acetate ion in aqueous solution.

An automated integration-free path-integral method based on Kleinert's variational perturbation theory.

Based on Kleinert's variational perturbation (KP) theory [Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 3rd ed. (World Scientific, Singapore, 2004)], we present an analytic path-integral approach for computing the effective centroid potential. The approach enables the KP theory to be applied to any realistic systems beyond the first-order perturbation (i.e., the original Feynman-Kleinert [Phys. Rev. A 34, 5080 (1986)] variational method). Accurate values are obtained for several systems in which exact quantum results are known. Furthermore, the computed kinetic isotope effects for a series of proton transfer reactions, in which the potential energy surfaces are evaluated by density-functional theory, are in good accordance with experiments. We hope that our method could be used by non-path-integral experts or experimentalists as a "black box" for any given system.