Specific Reaction Parametrization of the AM1/d Hamiltonian for Phosphoryl Transfer Reactions: H, O, and P Atoms

Improved Sugar Puckering Profiles for Nicotinamide Ribonucleoside for Hybrid QM/MM Simulations

The coenzyme nicotinamide adenine dinucleotide (NAD⁺) and its reduced form (NADH) play ubiquitous roles as oxidizing and reducing agents in nature. The binding, and possibly the chemical redox step, of NAD⁺/NADH may be influenced by the cofactor conformational distribution and, in particular, by the ribose puckering of its nicotinamide-ribonucleoside (NR) moiety. In many hybrid quantum mechanics-molecular mechanics (QM/MM) studies of NAD⁺/NADH dependent enzymes, the QM region is treated by semiempirical (SE) methods. Recent work suggests that SE methods do not adequately describe the ring puckering in sugar molecules. In the present work we adopt an efficient and practical strategy to correct for this deficiency for NAD⁺/NADH. We have implemented a cost-effective correction to a SE Hamiltonian by adding a correction potential, which is defined as the difference between an accurate benchmark density functional theory (DFT) potential energy surface (PES) and the SE PES. In practice, this is implemented via a B-spline interpolation scheme for the grid-based potential energy difference surface. We find that the puckering population distributions obtained from free energy QM(SE)/MM simulations are in good agreement with DFT and in fair accord with experimental results. The corrected PES should facilitate a more accurate description of the ribose puckering in the NAD⁺/NADH cofactor in simulations of biological systems.

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.

Toward Determining ATPase Mechanism in ABC Transporters: Development of the Reaction Path-Force Matching QM/MM Method

Adenosine triphosphate (ATP)-binding cassette (ABC) transporters are ubiquitous ATP-dependent membrane proteins involved in translocations of a wide variety of substrates across cellular membranes. To understand the chemomechanical coupling mechanism as well as functional asymmetry in these systems, a quantitative description of how ABC transporters hydrolyze ATP is needed. Complementary to experimental approaches, computer simulations based on combined quantum mechanical and molecular mechanical (QM/MM) potentials have provided new insights into the catalytic mechanism in ABC transporters. Quantitatively reliable determination of the free energy requirement for enzymatic ATP hydrolysis, however, requires substantial statistical sampling on QM/MM potential. A case study shows that brute force sampling of ab initio QM/MM (AI/MM) potential energy surfaces is computationally impractical for enzyme simulations of ABC transporters. On the other hand, existing semiempirical QM/MM (SE/MM) methods, although affordable for free energy sampling, are unreliable for studying ATP hydrolysis. To close this gap, a multiscale QM/MM approach named reaction path-force matching (RP-FM) has been developed. In RP-FM, specific reaction parameters for a selected SE method are optimized against AI reference data along reaction paths by employing the force matching technique. The feasibility of the method is demonstrated for a proton transfer reaction in the gas phase and in solution. The RP-FM method may offer a general tool for simulating complex enzyme systems such as ABC transporters.

Effects of protonation on the hydrolysis of triphosphate in vacuum and the implications for catalysis by nucleotide hydrolyzing enzymes

BACKGROUND

Nucleoside triphosphate (NTP) hydrolysis is a key reaction in biology. It involves breaking two very stable bonds (one P-O bond and one O-H bond of water), in either a concurrent or a sequential way. Here, we systematically examine how protonation of the triphosphate affects the mechanism of hydrolysis.

RESULTS

The hydrolysis reaction of methyl triphosphate in vacuum is computed with protons in various numbers and position on the three phosphate groups. Protonation is seen to have a strong catalytic effect, with the reaction mechanism depending highly on the protonation pattern.

CONCLUSION

This dependence is apparently complicated, but is shown to obey a well-defined set of rules: Protonation of the α- and β-phosphate groups favors a sequential hydrolysis mechanism, whereas γ-protonation favors a concurrent mechanism, the two effects competing with each other in cases of simultaneous protonation. The rate-limiting step is always the breakup of the water molecule while it attacks the γ-phosphorus, and its barrier is lowered by γ-protonation. This step has significantly lower barriers in the sequential reactions, because the dissociated γ-metaphosphate intermediate (PγO3-) is a much better target for water attack than the un-dissociated γ-phosphate (-PγO42-). The simple chemical logic behind these rules helps to better understand the catalytic strategy used by NTPase enzymes, as illustrated here for the catalytic pocket of myosin. A set of rules was determined that describes how protonating the phosphate groups affects the hydrolysis mechanism of methyl triphosphate: Protonation of the α- and/or β- phosphate groups promotes a sequential mechanism in which P-O bond breaking precedes the breakup of the attacking water, whereas protonation of the γ-phosphate promotes a concurrent mechanism and lowers the rate-limiting barrier of water breakup. The role played by individual protein residues in the catalytic pocket of triphosphate hydrolysing enzymes can be assigned accordingly.

Characterization of the three-dimensional free energy manifold for the uracil ribonucleoside from asynchronous replica exchange simulations

Replica exchange molecular dynamics has emerged as a powerful tool for efficiently sampling free energy landscapes for conformational and chemical transitions. However, daunting challenges remain in efficiently getting such simulations to scale to the very large number of replicas required to address problems in state spaces beyond two dimensions. The development of enabling technology to carry out such simulations is in its infancy, and thus it remains an open question as to which applications demand extension into higher dimensions. In the present work, we explore this problem space by applying asynchronous Hamiltonian replica exchange molecular dynamics with a combined quantum mechanical/molecular mechanical potential to explore the conformational space for a simple ribonucleoside. This is done using a newly developed software framework capable of executing >3,000 replicas with only enough resources to run 2,000 simultaneously. This may not be possible with traditional synchronous replica exchange approaches. Our results demonstrate 1.) the necessity of high dimensional sampling simulations for biological systems, even as simple as a single ribonucleoside, and 2.) the utility of asynchronous exchange protocols in managing simultaneous resource requirements expected in high dimensional sampling simulations. It is expected that more complicated systems will only increase in computational demand and complexity, and thus the reported asynchronous approach may be increasingly beneficial in order to make such applications available to a broad range of computational scientists.

Multipolar Ewald methods, 2: applications using a quantum mechanical force field

A fully quantum mechanical force field (QMFF) based on a modified “divide-and-conquer” (mDC) framework is applied to a series of molecular simulation applications, using a generalized Particle Mesh Ewald method extended to multipolar charge densities. Simulation results are presented for three example applications: liquid water, p-nitrophenylphosphate reactivity in solution, and crystalline N,N-dimethylglycine. Simulations of liquid water using a parametrized mDC model are compared to TIP3P and TIP4P/Ew water models and experiment. The mDC model is shown to be superior for cluster binding energies and generally comparable for bulk properties. Examination of the dissociative pathway for dephosphorylation of p-nitrophenylphosphate shows that the mDC method evaluated with the DFTB3/3OB and DFTB3/OPhyd semiempirical models bracket the experimental barrier, whereas DFTB2 and AM1/d-PhoT QM/MM simulations exhibit deficiencies in the barriers, the latter for which is related, in part, to the anomalous underestimation of the p-nitrophenylate leaving group pKa. Simulations of crystalline N,N-dimethylglycine are performed and the overall structure and atomic fluctuations are compared with the experiment and the general AMBER force field (GAFF). The QMFF, which was not parametrized for this application, was shown to be in better agreement with crystallographic data than GAFF. Our simulations highlight some of the application areas that may benefit from using new QMFFs, and they demonstrate progress toward the development of accurate QMFFs using the recently developed mDC framework.

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.

Simple Link Atom Saccharide Hybrid (SLASH) Treatment for Glycosidic Bonds at the QM/MM Boundary

We investigated link atom approaches for treating the polar C-O bond with particular reference to the glycosidic bond found in complex carbohydrates. We show that cutting this bond after the oxygen in the QM region and saturating the QM system with a hydrogen link atom leads to greater conformational and configurational accuracy at the boundary compared with cutting the bond before oxygen and saturating the QM system with a halogen link atom to represent the oxygen. Furthermore, we find that balancing the MM atom charges and redistributing the boundary atom charges at the QM/MM boundary minimizes the effect of the link atom, both energetically and structurally. This is illustrated via a series of calculations on a set of carbohydrate and carbohydrate-like model compounds. Finally, we confirm the validity of our model by performing molecular dynamics simulations for a typical disaccharide model compound in water. Our postsimulation conformational and configurational analyses show that the oxygen-to-water hydrogen pair distribution functions and the Φ,Ψ distributions at the glycosidic boundary between the quantum and classical regions compare favorably with results obtained from complete QM and complete MM treatments of the saccharide.

Development of Semiempirical Models for Proton Transfer Reactions in Water

This letter presents a method for the parametrization of semiempirical models for proton transfer reactions in water clusters. Two new models are developed: AM1-W, which is a reparameterization of the classic AM1 model, and AM1PG-W, which is a modified AM1-like model including a pairwise correction to the core repulsion function. Both models show good performance on hydrogen-bonding energies and on proton transfer energy profiles, which are of great importance for proton transfer reactions in large water clusters and in proteins. The parametrization method introduced is general and can be used to develop any other system-specific semiempirical models.

Theoretical Modeling on the Reaction Mechanism of p-Nitrophenylmethylphosphate Alkaline Hydrolysis and its Kinetic Isotope Effects

We have studied the alkaline hydrolysis of p-nitrophenylmethylphosphate (p-NPmP) in aqueous solution by means of polarizable continuum models and by hybrid quantum-mechanical/molecular-mechanical (QM/MM) methods. The theoretical predictions of kinetic isotope effects (KIEs) are in very good agreement with the experimental data, confirming a concerted asynchronous molecular mechanism. In addition, comparison of high level DFT theory with semiempirical AM1/d Hamiltonian has allowed checking the reliability of the later to be used in modeling very large molecular models containing phosphorus atoms.

Role of Protein Dynamics in Allosteric Control of the Catalytic Phosphoryl Transfer of Insulin Receptor Kinase

The catalytic and allosteric mechanisms of insulin receptor kinase (IRK) are investigated by a combination of ab initio and semiempirical quantum mechanical and molecular mechanical (QM/MM) methods and classical molecular dynamics (MD) simulations. The simulations reveal that the catalytic reaction proceeds in two steps, starting with the transfer of a proton from substrate Tyr to the catalytic Asp1132, followed by the phosphoryl transfer from ATP to substrate Tyr. The enhancement of the catalytic rate of IRK upon phosphorylations in the enzyme's activation loop is found to occur mainly via changes to the free energy landscape of the proton transfer step, favoring the proton transfer in the fully phosphorylated enzyme. In contrast, the effects of the phosphorylations on the phosphoryl transfer are smaller. Equilibrium MD simulations show that IRK phosphorylations affect the protein dynamics of the enzyme before the proton transfer to Asp1132 with only a minor effect after the proton transfer. This finding is consistent with the large change in the proton transfer free energy and the smaller change in the free energy barrier of phosphoryl transfer found by QM/MM simulations. Taken together, the present results provide details on how IRK phosphorylation exerts allosteric control of the catalytic activity via modifications of protein dynamics and free energy landscape of catalytic reaction. The results also highlight the importance of protein dynamics in connecting protein allostery and catalysis to control catalytic activity of enzymes.

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.

A computational study of the phosphoryl transfer reaction between ATP and Dha in aqueous solution

Phosphoryl transfer reactions are ubiquitous in biology, being involved in processes ranging from energy and signal transduction to the replication genetic material. Dihydroxyacetone phosphate (Dha-P), an intermediate of the synthesis of pyruvate and a very important building block in nature, can be generated by converting free dihydroxyacetone (Dha) through the action of the dihydroxyacetone kinase enzyme. In this paper the reference uncatalyzed reaction in solution has been studied in order to define the foundations of the chemical reaction and to determine the most adequate computational method to describe this electronically complex reaction. In particular, the phosphorylation reaction mechanism between adenosine triphosphate (ATP) and Dha in aqueous solution has been studied by means of quantum mechanics/molecular mechanics (QM/MM) Molecular Dynamics (MD) simulations with the QM subset of atoms described with semi-empirical and DFT methods. The results appear to be strongly dependent on the level of calculation, which will have to be taken into account for future studies of the reaction catalyzed by enzymes. In particular, PM3/MM renders lower free energy barriers and a less endergonic process than AM1d/MM and PM6/MM methods. Nevertheless, the concerted pathway was not located with the former combination of potentials.

Nucleic acid reactivity: challenges for next-generation semiempirical quantum models

Semiempirical quantum models are routinely used to study mechanisms of RNA catalysis and phosphoryl transfer reactions using combined quantum mechanical (QM)/molecular mechanical methods. Herein, we provide a broad assessment of the performance of existing semiempirical quantum models to describe nucleic acid structure and reactivity to quantify their limitations and guide the development of next-generation quantum models with improved accuracy. Neglect of diatomic differential overlap and self-consistent density-functional tight-binding semiempirical models are evaluated against high-level QM benchmark calculations for seven biologically important datasets. The datasets include: proton affinities, polarizabilities, nucleobase dimer interactions, dimethyl phosphate anion, nucleoside sugar and glycosidic torsion conformations, and RNA phosphoryl transfer model reactions. As an additional baseline, comparisons are made with several commonly used density-functional models, including M062X and B3LYP (in some cases with dispersion corrections). The results show that, among the semiempirical models examined, the AM1/d-PhoT model is the most robust at predicting proton affinities. AM1/d-PhoT and DFTB3-3ob/OPhyd reproduce the MP2 potential energy surfaces of 6 associative RNA phosphoryl transfer model reactions reasonably well. Further, a recently developed linear-scaling "modified divide-and-conquer" model exhibits the most accurate results for binding energies of both hydrogen bonded and stacked nucleobase dimers. The semiempirical models considered here are shown to underestimate the isotropic polarizabilities of neutral molecules by approximately 30%. The semiempirical models also fail to adequately describe torsion profiles for the dimethyl phosphate anion, the nucleoside sugar ring puckers, and the rotations about the nucleoside glycosidic bond. The modeling of pentavalent phosphorus, particularly with thio substitutions often used experimentally as mechanistic probes, was problematic for all of the models considered. Analysis of the strengths and weakness of the models suggests that the creation of robust next-generation models should emphasize the improvement of relative conformational energies and barriers, and nonbonded interactions.

First quantum mechanics/molecular mechanics studies of the inhibition mechanism of cruzain by peptidyl halomethyl ketones

Cruzain is a primary cysteine protease expressed by the protozoan parasite Trypanosoma cruzi during Chagas disease infection, and thus, the development of inhibitors of this protein is a promising target for designing an effective therapy against the disease. In this paper, the mechanism of inhibition of cruzain by two different irreversible peptidyl halomethyl ketones (PHK) inhibitors has been studied by means of hybrid quantum mechanics/molecular mechanics-molecular dynamics (MD) simulations to obtain a complete representation of the possible free energy reaction paths. These have been traced on free energy surfaces in terms of the potential of mean force computed at AM1d/MM and DFT/MM levels of theory. An analysis of the possible reaction mechanisms of the inhibition process has been performed showing that the nucleophilic attack of an active site cysteine, Cys25, on a carbon atom of the inhibitor and the cleavage of the halogen-carbon bond take place in a single step. PClK appears to be much more favorable than PFK from a kinetic point of view. This result would be in agreement with experimental studies in other papain-like enzymes. A deeper analysis of the results suggests that the origin of the differences between PClK and PFK can be the different stabilizing interactions established between the inhibitors and the residues of the active site of the protein. Any attempt to explore the viability of the inhibition process through a stepwise mechanism involving the formation of a thiohemiketal intermediate and a three-membered sulfonium intermediate has been unsuccessful. Nevertheless, a mechanism through a protonated thiohemiketal, with participation of His159 as a proton donor, appears to be feasible despite showing higher free energy barriers. Our results suggest that PClK can be used as a starting point to develop a proper inhibitor of cruzain.

Water interactions with hydrophobic groups: assessment and recalibration of semiempirical molecular orbital methods

In this work, we present a study of the ability of different semiempirical methods to describe intermolecular interactions in water solution. In particular, we focus on methods based on the Neglect of Diatomic Differential Overlap approximation. Significant improvements of these methods have been reported in the literature in the past years regarding the description of non-covalent interactions. In particular, a broad range of methodologies has been developed to deal with the properties of hydrogen-bonded systems, with varying degrees of success. In contrast, the interactions between water and a molecule containing hydrophobic groups have been little analyzed. Indeed, by considering the potential energy surfaces obtained using different semiempirical Hamiltonians for the intermolecular interactions of model systems, we found that none of the available methods provides an entirely satisfactory description of both hydrophobic and hydrophilic interactions in water. In addition, a vibrational analysis carried out in a model system for these interactions, a methane clathrate cluster, showed that some recent methods cannot be used to carry out studies of vibrational properties. Following a procedure established in our group [M. I. Bernal-Uruchurtu, M. T. C. Martins-Costa, C. Millot, and M. F. Ruiz-López, J. Comput. Chem. 21, 572 (2000); W. Harb, M. I. Bernal-Uruchurtu, and M. F. Ruiz-López, Theor. Chem. Acc. 112, 204 (2004)], we developed new parameters for the core-core interaction terms based on fitting potential energy curves obtained at the MP2 level for our model system. We investigated the transferability of the new parameters to describe a system, having both hydrophilic and hydrophobic groups, interacting with water. We found that only by introducing two different sets of parameters for hydrophilic and hydrophobic hydrogen atom types we are able to match the features of the ab initio calculated properties. Once this assumption is made, a good agreement with the MP2 reference is achieved. The results reported in this work provide therefore a direction for future developments of semiempirical approaches that are still required to investigate chemical processes in biomolecules and in large disordered systems.

The adaptive buffered force QM/MM method in the CP2K and AMBER software packages

The implementation and validation of the adaptive buffered force (AdBF) quantum-mechanics/molecular-mechanics (QM/MM) method in two popular packages, CP2K and AMBER are presented. The implementations build on the existing QM/MM functionality in each code, extending it to allow for redefinition of the QM and MM regions during the simulation and reducing QM-MM interface errors by discarding forces near the boundary according to the buffered force-mixing approach. New adaptive thermostats, needed by force-mixing methods, are also implemented. Different variants of the method are benchmarked by simulating the structure of bulk water, water autoprotolysis in the presence of zinc and dimethyl-phosphate hydrolysis using various semiempirical Hamiltonians and density functional theory as the QM model. It is shown that with suitable parameters, based on force convergence tests, the AdBF QM/MM scheme can provide an accurate approximation of the structure in the dynamical QM region matching the corresponding fully QM simulations, as well as reproducing the correct energetics in all cases. Adaptive unbuffered force-mixing and adaptive conventional QM/MM methods also provide reasonable results for some systems, but are more likely to suffer from instabilities and inaccuracies. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Multiscale methods for computational RNA enzymology

RNA catalysis is of fundamental importance to biology and yet remains ill-understood due to its complex nature. The multidimensional "problem space" of RNA catalysis includes both local and global conformational rearrangements, changes in the ion atmosphere around nucleic acids and metal ion binding, dependence on potentially correlated protonation states of key residues, and bond breaking/forming in the chemical steps of the reaction. The goal of this chapter is to summarize and apply multiscale modeling methods in an effort to target the different parts of the RNA catalysis problem space while also addressing the limitations and pitfalls of these methods. Classical molecular dynamics simulations, reference interaction site model calculations, constant pH molecular dynamics (CpHMD) simulations, Hamiltonian replica exchange molecular dynamics, and quantum mechanical/molecular mechanical simulations will be discussed in the context of the study of RNA backbone cleavage transesterification. This reaction is catalyzed by both RNA and protein enzymes, and here we examine the different mechanistic strategies taken by the hepatitis delta virus ribozyme and RNase A.

Explicit Drug Re-positioning: Predicting Novel Drug-Target Interactions of the Shelved Molecules with QM/MM Based Approaches

With the demand to enhance the speed of the drug discovery process there has been an increased usage of computational approaches in drug discovery studies. However because of their probabilistic outcomes, the challenge is to exactly mimic the natural environment which can provide the exact charge polarization effect while estimating the binding energy between protein and ligand. There has been a large number of scoring functions from simple one to the complex one available for estimating binding energy. The quantum mechanics/molecular mechanics (QM/MM) hybrid approach has been the preferred choice of interest since last decade for modeling reactions in biomolecular systems. The application of QM/MM approach has been expanded right from rescoring the already known complexes and depicting the correct position of some novel molecule to ranking a large number of molecules. It is expected that the application of QM/MM-based scoring will grow in all areas of drug discovery. However, the most promising area will be its application in repositioning, that is, assigning novel functions or targets to the already existing drugs, as this would stop the rising attrition rates as well as reduce the overall time and cost of drug discovery procedure.

Applications of quantum mechanical/molecular mechanical methods to the chemical insertion step of DNA and RNA polymerization

We review theoretical attempts to model the chemical insertion reactions of nucleoside triphosphates catalyzed by the nucleic acid polymerases using combined quantum mechanical/molecular mechanical methodology. Due to an existing excellent database of high-resolution X-ray crystal structures, the DNA polymerase β system serves as a useful template for discussion and comparison. The convergence of structures of high-quality complexes and continued developments of theoretical techniques suggest a bright future for understanding the global features of nucleic acid polymerization.

AM1/d-CB1: A Semiempirical Model for QM/MM Simulations of Chemical Glycobiology Systems

A semiempirical method based on the AM1/d Hamiltonian is introduced to model chemical glycobiological systems. We included in the parameter training set glycans and the chemical environment often found about them in glycoenzymes. Starting with RM1 and AM1/d-PhoT models we optimized H, C, N, O, and P atomic parameters targeting the best performing molecular properties that contribute to enzyme catalyzed glycan reaction mechanisms. The training set comprising glycans, amino acids, phosphates and small organic model systems was used to derive parameters that reproduce experimental data or high-level density functional results for carbohydrate, phosphate and amino acid heats of formation, amino acid proton affinities, amino acid and monosaccharide dipole moments, amino acid ionization potentials, water-phosphate interaction energies, and carbohydrate ring pucker relaxation times. The result is the AM1/d-Chemical Biology 1 or AM1/d-CB1 model that is considerably more accurate than existing NDDO methods modeling carbohydrates and the amino acids often present in the catalytic domains of glycoenzymes as well as the binding sites of lectins. Moreover, AM1/d-CB1 computed proton affinities, dipole moments, ionization potentials and heats of formation for transition state puckered carbohydrate ring conformations, observed along glycoenzyme catalyzed reaction paths, are close to values computed using DFT M06-2X. AM1/d-CB1 provides a platform from which to accurately model reactions important in chemical glycobiology.

Recent advances in QM/MM free energy calculations using reference potentials

Background

Recent years have seen enormous progress in the development of methods for modeling (bio)molecular systems. This has allowed for the simulation of ever larger and more complex systems. However, as such complexity increases, the requirements needed for these models to be accurate and physically meaningful become more and more difficult to fulfill. The use of simplified models to describe complex biological systems has long been shown to be an effective way to overcome some of the limitations associated with this computational cost in a rational way.

Scope of review

Hybrid QM/MM approaches have rapidly become one of the most popular computational tools for studying chemical reactivity in biomolecular systems. However, the high cost involved in performing high-level QM calculations has limited the applicability of these approaches when calculating free energies of chemical processes. In this review, we present some of the advances in using reference potentials and mean field approximations to accelerate high-level QM/MM calculations. We present illustrative applications of these approaches and discuss challenges and future perspectives for the field.

Major conclusions

The use of physically-based simplifications has shown to effectively reduce the cost of high-level QM/MM calculations. In particular, lower-level reference potentials enable one to reduce the cost of expensive free energy calculations, thus expanding the scope of problems that can be addressed.

General significance

As was already demonstrated 40 years ago, the usage of simplified models still allows one to obtain cutting edge results with substantially reduced computational cost. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

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We present some of the advances to accelerate high-level QM/MM calculations.

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Quantitative limitations of low-level methods can be overcome by these approaches.

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Reference potentials make free energy simulations feasible for large systems.

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Automated fitting reduces the need of expensive sampling of high-level approaches.

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Application of reference potentials can be extended to a wide range of processes.

Reaction Path Force Matching: A New Strategy of Fitting Specific Reaction Parameters for Semiempirical Methods in Combined QM/MM Simulations

We present a general strategy of reparametrizing semiempirical (SE) methods against ab initio (AI) methods for combined quantum mechanical and molecular mechanical (QM/MM) simulations of specific chemical reactions in condensed phases. The resulting approach, designated Reaction Path Force Matching (RP-FM), features cycles of sampling configurations along a reaction path on an efficient SE/MM potential energy surface (PES) and adjusting specific reaction parameters (SRPs) in the SE method such that the atomic forces computed at the target AI/MM level are reproduced. Iterative applications of the RP-FM cycle make possible achieving the accuracy of AI/MM simulations without explicitly sampling the computationally expensive AI/MM PES. The bypassed sampling, nevertheless, is implicitly accomplished through the aid of the efficient SE-SRP/MM PES, on which the target-level reaction path is expected to be obtained upon convergence. We demonstrate the effectiveness of the RP-FM procedure for a symmetric proton transfer reaction in the gas phase and in solution. The remarkable agreements between the RP-FM optimized SE-SRP methods and the target AI method on various properties, including energy profiles, potential of mean force free energy profiles, atomic forces, charge populations, and solvation effects, suggest that RP-FM can be used as an efficient and reliable strategy for simulating condensed-phase chemical reactions.

Quantum mechanics/molecular mechanics studies of the mechanism of falcipain-2 inhibition by the epoxysuccinate E64

Because of the increasing resistance of malaria parasites to antimalarial drugs, the lack of highly effective vaccines, and an inadequate control of mosquito vectors, the problem is growing, especially in the developing world. New approaches to drug development are consequently required. One of the proteases involved in the degradation of human hemoglobin is named falcipain-2 (FP2), which has emerged as a promising target for the development of novel antimalarial drugs. However, very little is known about the inhibition of FP2. In this paper, the inhibition of FP2 by the epoxysuccinate E64 has been studied by molecular dynamics (MD) simulations using hybrid AM1d/MM and M06-2X/MM potentials to obtain a complete picture of the possible free energy reaction paths. A thorough analysis of the reaction mechanism has been conducted to understand the inhibition of FP2 by E64. According to our results, the irreversible attack of Cys42 on E64 can take place on both carbon atoms of the epoxy ring because both processes present similar barriers. While the attack on the C2 atom presents a slightly smaller barrier (12.3 vs 13.6 kcal mol(-1)), the inhibitor-protein complex derived from the attack on C3 appears to be much more stabilized. In contrast to previous hypotheses, our results suggest that residues such as Gln171, Asp170, Gln36, Trp43, Asn81, and even His174 would be anchoring the inhibitor in a proper orientation for the reaction to take place. These results may be useful for the rational design of new compounds with higher inhibitory activity.

Improvement of DNA and RNA Sugar Pucker Profiles from Semiempirical Quantum Methods

Neglect of diatomic differential overlap (NDDO) and self-consistent density-functional tight-binding (SCC-DFTB) semiempirical models commonly employed in combined quantum mechanical/molecular mechanical simulations fail to adequately describe the deoxyribose and ribose sugar ring puckers. This failure limits the application of these methods to RNA and DNA systems. In this work, we provide benchmark ab initio gas-phase two-dimensional potential energy scans of the RNA and DNA sugar puckering. The benchmark calculations are compared with semiempirical models. Pucker corrections are introduced into the semiempirical models via B-spline interpolation of the potential energy difference surface relative to the benchmark data. The corrected semiempirical models are shown to well reproduce the ab initio puckering profiles. Furthermore, we demonstrate that the uncorrected semiempirical models do not usually produce a transition state between the A-form and B-form sugar puckers, but the ab initio transition state is reproduced when the B-spline correction is used.

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

We have analyzed the capability of state-of-the-art multiscale computational approaches to provide atomic-resolution electronic structure insights into possible catalytic scenarios of the hairpin ribozyme by evaluating potential and free energy surfaces of the reactions by various hybrid QM/MM methods. The hairpin ribozyme is a unique catalytic RNA that achieves rate acceleration similar to other small self-cleaving ribozymes but without direct metal ion participation. Guanine 8 (G8) and adenine 38 (A38) have been identified as the catalytically essential nucleobases. However, their exact catalytic roles are still being investigated. In line with the available experimental data, we considered two reaction scenarios involving protonated A38H(+) as a general acid which is further assisted by either canonical G8 or deprotonated G8(-) forms. We used the spin-component scaled Møller-Plesset (SCS-MP2) method at the complete basis set limit as the reference method. The semiempirical AM1/d-PhoT and SCC-DFTBPR methods provided acceptable activation barriers with respect to the SCS-MP2 data but predicted significantly different reaction pathways. DFT functionals (BLYP and MPW1K) yielded the same reaction pathway as the SCS-MP2 method. The activation barriers were slightly underestimated by the GGA BLYP functional, although with accuracy comparable to the semiempirical methods. The SCS-MP2 method and hybrid MPW1K functional gave activation barriers that were closest to those derived from experimentally measured rate constants.

Quantum mechanical study of solvent effects in a prototype SN2 reaction in solution: Cl- attack on CH3Cl

The nucleophilic attack of a chloride ion on methyl chloride is an important prototype SN2 reaction in organic chemistry that is known to be sensitive to the effects of the surrounding solvent. Herein, we develop a highly accurate Specific Reaction Parameter (SRP) model based on the Austin Model 1 Hamiltonian for chlorine to study the effects of solvation into an aqueous environment on the reaction mechanism. To accomplish this task, we apply high-level quantum mechanical calculations to study the reaction in the gas phase and combined quantum mechanical/molecular mechanical simulations with TIP3P and TIP4P-ew water models and the resulting free energy profiles are compared with those determined from simulations using other fast semi-empirical quantum models. Both gas phase and solution results with the SRP model agree very well with experiment and provide insight into the specific role of solvent on the reaction coordinate. Overall, the newly parameterized SRP Hamiltonian is able to reproduce both the gas phase and solution phase barriers, suggesting it is an accurate and robust model for simulations in the aqueous phase at greatly reduced computational cost relative to comparably accurate ab initio and density functional models.

An extensible interface for QM/MM molecular dynamics simulations with AMBER

We present an extensible interface between the AMBER molecular dynamics (MD) software package and electronic structure software packages for quantum mechanical (QM) and mixed QM and classical molecular mechanical (MM) MD simulations within both mechanical and electronic embedding schemes. With this interface, ab initio wave function theory and density functional theory methods, as available in the supported electronic structure software packages, become available for QM/MM MD simulations with AMBER. The interface has been written in a modular fashion that allows straight forward extensions to support additional QM software packages and can easily be ported to other MD software. Data exchange between the MD and QM software is implemented by means of files and system calls or the message passing interface standard. Based on extensive tests, default settings for the supported QM packages are provided such that energy is conserved for typical QM/MM MD simulations in the microcanonical ensemble. Results for the free energy of binding of calcium ions to aspartate in aqueous solution comparing semiempirical and density functional Hamiltonians are shown to demonstrate features of this interface.

Modeling catalytic promiscuity in the alkaline phosphatase superfamily

In recent years, it has become increasingly clear that promiscuity plays a key role in the evolution of new enzyme function. This finding has helped to elucidate fundamental aspects of molecular evolution. While there has been extensive experimental work on enzyme promiscuity, computational modeling of the chemical details of such promiscuity has traditionally fallen behind the advances in experimental studies, not least due to the nearly prohibitive computational cost involved in examining multiple substrates with multiple potential mechanisms and binding modes in atomic detail with a reasonable degree of accuracy. However, recent advances in both computational methodologies and power have allowed us to reach a stage in the field where we can start to overcome this problem, and molecular simulations can now provide accurate and efficient descriptions of complex biological systems with substantially less computational cost. This has led to significant advances in our understanding of enzyme function and evolution in a broader sense. Here, we will discuss currently available computational approaches that can allow us to probe the underlying molecular basis for enzyme specificity and selectivity, discussing the inherent strengths and weaknesses of each approach. As a case study, we will discuss recent computational work on different members of the alkaline phosphatase superfamily (AP) using a range of different approaches, showing the complementary insights they have provided. We have selected this particular superfamily, as it poses a number of significant challenges for theory, ranging from the complexity of the actual reaction mechanisms involved to the reliable modeling of the catalytic metal centers, as well as the very large system sizes. We will demonstrate that, through current advances in methodologies, computational tools can provide significant insight into the molecular basis for catalytic promiscuity, and, therefore, in turn, the mechanisms of protein functional evolution.

Stabilization of different types of transition states in a single enzyme active site: QM/MM analysis of enzymes in the alkaline phosphatase superfamily

The first step for the hydrolysis of a phosphate monoester (pNPP(2-)) in enzymes of the alkaline phosphatase (AP) superfamily, R166S AP and wild-type NPP, is studied using QM/MM simulations based on an approximate density functional theory (SCC-DFTBPR) and a recently introduced QM/MM interaction Hamiltonian. The calculations suggest that similar loose transition states are involved in both enzymes, despite the fact that phosphate monoesters are the cognate substrates for AP but promiscuous substrates for NPP. The computed loose transition states are clearly different from the more synchronous ones previously calculated for diester reactions in the same AP enzymes. Therefore, our results explicitly support the proposal that AP enzymes are able to recognize and stabilize different types of transition states in a single active site. Analysis of the structural features of computed transition states indicates that the plastic nature of the bimetallic site plays a minor role in accommodating multiple types of transition states and that the high degree of solvent accessibility of the AP active site also contributes to its ability to stabilize diverse transition-state structures without the need of causing large structural distortions of the bimetallic motif. The binding mode of the leaving group in the transition state highlights that vanadate may not always be an ideal transition state analog for loose phosphoryl transfer transition states.

Molecular simulations of RNA 2'-O-transesterification reaction models in solution

We employ quantum mechanical/molecular mechanical umbrella sampling simulations to probe the free energy surfaces of a series of increasingly complex reaction models of RNA 2'-O-transesterification in aqueous solution under alkaline conditions. Such models are valuable for understanding the uncatalyzed processes underlying catalytic cleavage of the phosphodiester backbone of RNA, a reaction of fundamental importance in biology. The chemically reactive atoms are modeled by the AM1/d-PhoT quantum model for phosphoryl transfer, whereas the aqueous solvation environment is modeled with a molecular mechanics force field. Several simulation protocols were compared that used different ionic conditions and force field models. The results provide insight into how variation of the structural environment of the nucleophile and leaving group affects the free energy profile for the transesterification reaction. Results for a simple RNA backbone model are compared with recent experiments by Harris et al. on the specific base-catalyzed cleavage of a UpG dinucleotide. The calculated and measured free energies of activation match extremely well (ΔF(‡) = 19.9-20.8 vs 19.9 kcal/mol). Solvation is seen to play a crucial role and is characterized by a network of hydrogen bonds that envelopes the pentacoordinate dianionic phosphorane transition state and provides preferential stabilization relative to the reactant state.

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.

A New Maximum Likelihood Approach for Free Energy Profile Construction from Molecular Simulations

A novel variational method for construction of free energy profiles from molecular simulation data is presented. The variational free energy profile (VFEP) method uses the maximum likelihood principle applied to the global free energy profile based on the entire set of simulation data (e.g from multiple biased simulations) that spans the free energy surface. The new method addresses common obstacles in two major problems usually observed in traditional methods for estimating free energy surfaces: the need for overlap in the re-weighting procedure and the problem of data representation. Test cases demonstrate that VFEP outperforms other methods in terms of the amount and sparsity of the data needed to construct the overall free energy profiles. For typical chemical reactions, only ~5 windows and ~20-35 independent data points per window are sufficient to obtain an overall qualitatively correct free energy profile with sampling errors an order of magnitude smaller than the free energy barrier. The proposed approach thus provides a feasible mechanism to quickly construct the global free energy profile and identify free energy barriers and basins in free energy simulations via a robust, variational procedure that determines an analytic representation of the free energy profile without the requirement of numerically unstable histograms or binning procedures. It can serve as a new framework for biased simulations and is suitable to be used together with other methods to tackle with the free energy estimation problem.

The DNA and RNA sugar-phosphate backbone emerges as the key player. An overview of quantum-chemical, structural biology and simulation studies

Knowledge of geometrical and physico-chemical properties of the sugar-phosphate backbone substantially contributes to the comprehension of the structural dynamics, function and evolution of nucleic acids. We provide a side by side overview of structural biology/bioinformatics, quantum chemical and molecular mechanical/simulation studies of the nucleic acids backbone. We highlight main features, advantages and limitations of these techniques, with a special emphasis given to their synergy. The present status of the research is then illustrated by selected examples which include classification of DNA and RNA backbone families, benchmark structure-energy quantum chemical calculations, parameterization of the dihedral space of simulation force fields, incorporation of arsenate into DNA, sugar-phosphate backbone self-cleavage in small RNA enzymes, and intricate geometries of the backbone in recurrent RNA building blocks. Although not apparent from the current literature showing limited overlaps between the QM, simulation and bioinformatics studies of the nucleic acids backbone, there in fact should be a major cooperative interaction between these three approaches in studies of the sugar-phosphate backbone.

QM/MM analysis suggests that Alkaline Phosphatase (AP) and nucleotide pyrophosphatase/phosphodiesterase slightly tighten the transition state for phosphate diester hydrolysis relative to solution: implication for catalytic promiscuity in the AP superfamily

Several members of the Alkaline Phosphatase (AP) superfamily exhibit a high level of catalytic proffciency and promiscuity in structurally similar active sites. A thorough characterization of the nature of transition state for different substrates in these enzymes is crucial for understanding the molecular mechanisms that govern those remarkable catalytic properties. In this work, we study the hydrolysis of a phosphate diester, MpNPP(-), in solution, two experimentally well-characterized variants of AP (R166S AP, R166S/E322Y AP) and wild type Nucleotide pyrophosphatase/phosphodiesterase (NPP) by QM/MM calculations in which the QM method is an approximate density functional theory previously parametrized for phosphate hydrolysis (SCC-DFTBPR). The general agreements found between these calculations and available experimental data for both solution and enzymes support the use of SCC-DFTBPR/MM for a semiquantitative analysis of the catalytic mechanism and nature of transition state in AP and NPP. Although phosphate diesters are cognate substrates for NPP but promiscuous substrates for AP, the calculations suggest that their hydrolysis reactions catalyzed by AP and NPP feature similar synchronous transition states that are slightly tighter in nature compared to that in solution, due in part to the geometry of the bimetallic zinc motif. Therefore, this study provides the first direct computational support to the hypothesis that enzymes in the AP superfamily catalyze cognate and promiscuous substrates via similar transition states to those in solution. Our calculations do not support the finding of recent QM/MM studies by López-Canut and co-workers, who suggested that the same diester substrate goes through a much looser transition state in NPP/AP than in solution, a result likely biased by the large structural distortion of the bimetallic zinc site in their simulations. Finally, our calculations for different phosphate diester orientations and phosphorothioate diesters highlight that the interpretation of thio-substitution experiments is not always straightforward.

QM/MM studies of hairpin ribozyme self-cleavage suggest the feasibility of multiple competing reaction mechanisms

The hairpin ribozyme is a prominent member of small ribozymes since it does not require metal ions to achieve catalysis. Guanine 8 (G8) and adenine 38 (A38) have been identified as key participants in self-cleavage and -ligation. We have carried out hybrid quantum-mechanical/molecular mechanical (QM/MM) calculations to evaluate the energy along several putative reaction pathways. The error of our DFT description of the QM region was tested and shown to be ~1 kcal/mol. We find that self-cleavage of the hairpin ribozyme may follow several competing microscopic reaction mechanisms, all with calculated activation barriers in good agreement with those from experiment (20-21 kcal/mol). The initial nucleophilic attack of the A-1(2'-OH) group on the scissile phosphate is predicted to be rate-limiting in all these mechanisms. An unprotonated G8(-) (together with A38H(+)) yields a feasible activation barrier (20.4 kcal/mol). Proton transfer to a nonbridging phosphate oxygen also leads to feasible reaction pathways. Finally, our calculations consider thio-substitutions of one or both nonbridging oxygens of the scissile phosphate and predict that they have only a negligible effect on the reaction barrier, as observed experimentally.

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

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

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.

Polarized Molecular Orbital Model Chemistry. II. The PMO Method

We present a new semiempirical molecular orbital method based on neglect of diatomic differential overlap. This method differs from previous NDDO-based methods in that we include p orbitals on hydrogen atoms to provide a more realistic modeling of polarizability. As in AM1-D and PM3-D, we also include damped dispersion. The formalism is based on the original MNDO one, but in the process of parameterization we make some specific changes to some of the functional forms. The present article is a demonstration of the capability of the new approach, and it presents a successful parametrization for compounds composed only of hydrogen and oxygen atoms, including the important case of water clusters.