How Large Should the QM Region Be in QM/MM Calculations? The Case of Catechol O-Methyltransferase

Multiscale Workflow for Modeling Ligand Complexes of Zinc Metalloproteins

Zinc metalloproteins are ubiquitous, with protein zinc centers of structural and functional importance, involved in interactions with ligands and substrates and often of pharmacological interest. Biomolecular simulations are increasingly prominent in investigations of protein structure, dynamics, ligand interactions, and catalysis, but zinc poses a particular challenge, in part because of its versatile, flexible coordination. A computational workflow generating reliable models of ligand complexes of biological zinc centers would find broad application. Here, we evaluate the ability of alternative treatments, using (nonbonded) molecular mechanics (MM) and quantum mechanics/molecular mechanics (QM/MM) at semiempirical (DFTB3) and density functional theory (DFT) levels of theory, to describe the zinc centers of ligand complexes of six metalloenzyme systems differing in coordination geometries, zinc stoichiometries (mono- and dinuclear), and the nature of interacting groups (specifically the presence of zinc-sulfur interactions). MM molecular dynamics (MD) simulations can overfavor octahedral geometries, introducing additional water molecules to the zinc coordination shell, but this can be rectified by subsequent semiempirical (DFTB3) QM/MM MD simulations. B3LYP/MM geometry optimization further improved the accuracy of the description of coordination distances, with the overall effectiveness of the approach depending upon factors, including the presence of zinc-sulfur interactions that are less well described by semiempirical methods. We describe a workflow comprising QM/MM MD using DFTB3 followed by QM/MM geometry optimization using DFT (e.g., B3LYP) that well describes our set of zinc metalloenzyme complexes and is likely to be suitable for creating accurate models of zinc protein complexes when structural information is more limited.

The Influence of Electronic Polarization on Nonlinear Optical Spectroscopy

The environment surrounding a chromophore can dramatically affect the energy absorption and relaxation process, as manifested in optical spectra. Simulations of nonlinear optical spectroscopy, such as two-dimensional electronic spectroscopy (2DES) and transient absorption (TA), will be influenced by the computational model of the environment. We here compare a fixed point charge molecular mechanics model and a quantum mechanical (QM) model of the environment in computed 2DES and TA spectra of Nile red in water and the chromophore of photoactive yellow protein (PYP) in water and protein environments. In addition to simulating these nonlinear optical spectra, we directly juxtapose the computed excitation energy correlation function to the dynamic Stokes shift function often used to analyze environment dynamics. Overall, we find that for the three systems studied here the mutual electronic polarization provided by the QM environment manifests in broader 2DES signals, as well as a larger reorganization energy and a larger static Stokes shift due to stronger coupling between the chromophore and the environment.

Computational investigations of selected enzymes from two iron and α-ketoglutarate-dependent families

DNA alkylation is used as the key epigenetic mark in eukaryotes, however, most alkylation in DNA can result in deleterious effects. Therefore, this process needs to be tightly regulated. The enzymes of the AlkB and Ten-Eleven Translocation (TET) families are members of the Fe and alpha-ketoglutarate-dependent superfamily of enzymes that are tasked with dealkylating DNA and RNA in cells. Members of these families span all species and are an integral part of transcriptional regulation. While both families catalyze oxidative dealkylation of various bases, each has specific preference for alkylated base type as well as distinct catalytic mechanisms. This perspective aims to provide an overview of computational work carried out to investigate several members of these enzyme families including AlkB, ALKB Homolog 2, ALKB Homolog 3 and Ten-Eleven Translocate 2. Insights into structural details, mutagenesis studies, reaction path analysis, electronic structure features in the active site, and substrate preferences are presented and discussed.

Machine Learning Force Fields

In recent years, the use of machine learning (ML) in computational chemistry has enabled numerous advances previously out of reach due to the computational complexity of traditional electronic-structure methods. One of the most promising applications is the construction of ML-based force fields (FFs), with the aim to narrow the gap between the accuracy of ab initio methods and the efficiency of classical FFs. The key idea is to learn the statistical relation between chemical structure and potential energy without relying on a preconceived notion of fixed chemical bonds or knowledge about the relevant interactions. Such universal ML approximations are in principle only limited by the quality and quantity of the reference data used to train them. This review gives an overview of applications of ML-FFs and the chemical insights that can be obtained from them. The core concepts underlying ML-FFs are described in detail, and a step-by-step guide for constructing and testing them from scratch is given. The text concludes with a discussion of the challenges that remain to be overcome by the next generation of ML-FFs.

On the Accuracy of QM/MM Models: A Systematic Study of Intramolecular Proton Transfer Reactions of Amino Acids in Water

This work presents a systematic assessment of QM/QM' and QM/MM models with respect to direct QM calculations for the tautomerization (neutral to zwitterion) reactions of amino acids (glycine, alanine, valine, aspartate, and neutral and protonated histidine) solvated in a 160 water cluster. The effect of varying QM region size and choice of embedding potentials, including fixed-charge and polarizable molecular mechanics force fields (TIP3P and EFP) and various semiempirical QM methods (PM7, GFN2-xTB, DFTBA, DFTB3, HF-3c, and PBEh-3c), on the accuracy of the models was examined. A surprising finding was that molecular mechanics force fields outperformed many of the semiempirical methods. Generally, the errors in the QM/QM' and QM/MM models converge slowly with respect to the QM region size, requiring 50 or more waters to be included in the QM region before the error in the model falls below 1 kcal mol^-1 of its pure QM result. Different QM region selection schemes were also compared, and it was found that selection based on Natural Population Analysis (NPA) atomic charges significantly reduced the error in the QM/QM' and QM/MM models particularly if a low-quality embedding potential was used. It is envisaged that these results will be useful for the development of future hybrid QM models.

Anharmonic Vibrational Calculations Based on Group-Localized Coordinates: Applications to Internal Water Molecules in Bacteriorhodopsin

An efficient anharmonic vibrational method is developed exploiting the locality of molecular vibration. Vibrational coordinates localized to a group of atoms are employed to divide the potential energy surface (PES) of a system into intra- and inter-group contributions. Then, the vibrational Schrödinger equation is solved based on a PES, in which the inter-group coupling is truncated at the harmonic level while accounting for the intra-group anharmonicity. The method is applied to a pentagonal hydrogen bond network (HBN) composed of internal water molecules and charged residues in a membrane protein, bacteriorhodopsin. The PES is calculated by the quantum mechanics/molecular mechanics (QM/MM) calculation at the level of B3LYP-D3/aug-cc-pVDZ. The infrared (IR) spectrum is computed using a set of coordinates localized to each water molecule and amino acid residue by second-order vibrational quasi-degenerate perturbation theory (VQDPT2). Benchmark calculations show that the proposed method yields the N-D/O-D stretching frequencies with an error of 7 cm-1 at the cost reduced by more than five times. In contrast, the harmonic approximation results in a severe error of 150 cm-1. Furthermore, the size of QM regions is carefully assessed to find that the QM regions should include not only the pentagonal HBN itself but also its HB partners. VQDPT2 calculations starting from transient structures obtained by molecular dynamics simulations have shown that the structural sampling has a significant impact on the calculated IR spectrum. The incorporation of anharmonicity, sufficiently large QM regions, and structural samplings are of essential importance to reproduce the experimental IR spectrum. The computational spectrum paves the way for decoding the IR signal of strong HBNs and helps elucidate their functional roles in biomolecules.

Harder, better, faster, stronger: Large-scale QM and QM/MM for predictive modeling in enzymes and proteins

Computational prediction of enzyme mechanism and protein function requires accurate physics-based models and suitable sampling. We discuss recent advances in large-scale quantum mechanical (QM) modeling of biochemical systems that have reduced the cost of high-accuracy models. Tradeoffs between sampling and accuracy have motivated modeling with molecular mechanics (MM) in a multiscale QM/MM or iterative approach. Limitations to both conventional density-functional theory and classical MM force fields remain for describing noncovalent interactions in comparison to experiment or wavefunction theory. Because predictions of enzyme action (i.e. electrostatics), free energy barriers, and mechanisms are sensitive to the protocol and embedding method in QM/MM, convergence tests and systematic methods for quantifying QM-level interactions are a needed, active area of development.

Cheminformatic quantum mechanical enzyme model design: A catechol-O-methyltransferase case study

To accurately simulate the inner workings of an enzyme active site with quantum mechanics (QM), not only must the reactive species be included in the model but also important surrounding residues, solvent, or coenzymes involved in crafting the microenvironment. Our lab has been developing the Residue Interaction Network Residue Selector (RINRUS) toolkit to utilize interatomic contact network information for automated, rational residue selection and QM-cluster model generation. Starting from an x-ray crystal structure of catechol-O-methyltransferase, RINRUS was used to construct a series of QM-cluster models. The reactant, product, and transition state of the methyl transfer reaction were computed for a total of 550 models, and the resulting free energies of activation and reaction were used to evaluate model convergence. RINRUS-designed models with only 200-300 atoms are shown to converge. RINRUS will serve as a cornerstone for improved and automated cheminformatics-based enzyme model design.

Combining Evolutionary Conservation and Quantum Topological Analyses To Determine Quantum Mechanics Subsystems for Biomolecular Quantum Mechanics/Molecular Mechanics Simulations

Selection of residues and other molecular fragments for inclusion in the quantum mechanics (QM) region for QM/molecular mechanics (MM) simulations is an important step for these calculations. Here, we present an approach that combines protein sequence/structure evolution and electron localization function (ELF) analyses. The combination of these two analyses allows the determination of whether a residue needs to be included in the QM subsystem or can be represented by the MM environment. We have applied this approach on two systems previously investigated by QM/MM simulations, 4-oxalocrotonate tautomerase (4OT) and ten-eleven translocation-2 (TET2), that provide examples where fragments may or may not need to be included in the QM subsystem. Subsequently, we present the use of this approach to determine the appropriate QM subsystem to calculate the minimum energy path (MEP) for the reaction catalyzed by human DNA polymerase λ (Polλ) with a third cation in the active site. Our results suggest that the combination of protein evolutionary and ELF analyses provides insights into residue/molecular fragment selection for QM/MM simulations.

Protein Dynamics and Substrate Protonation States Mediate the Catalytic Action of trans-4-Hydroxy-l-Proline Dehydratase

The enzyme trans-4-hydroxy-l-proline (Hyp) dehydratase (HypD) is among the most abundant glycyl radical enzymes (GREs) in the healthy human gut microbiome and is considered a promising antibiotic target for the prominent antibiotic-resistant pathogen Clostridium difficile. Although an enzymatic mechanism has been proposed, the role of the greater HypD protein environment in mediating radical reactivity is not well understood. To fill this gap in understanding, we investigate HypD across multiple time- and length-scales using electronic structure modeling and classical molecular dynamics. We observe that the Hyp substrate protonation state significantly alters both its enzyme-free reactivity and its dynamics within the enzyme active site. Accurate coupled-cluster modeling suggests the deprotonated form of Hyp to be the most reactive protonation state for C5-H_pro-S activation. In the protein environment, hydrophobic interactions modulate the positioning of the Cys434 radical to enhance the reactivity of C5-H_pro-S abstraction. Long-time dynamics reveal that changing Hyp protonation states triggers the switching of a Leu643-gated water tunnel, a functional feature that has not yet been observed for members of the GRE superfamily.

Machine Learning for Chemical Reactions

Machine learning (ML) techniques applied to chemical reactions have a long history. The present contribution discusses applications ranging from small molecule reaction dynamics to computational platforms for reaction planning. ML-based techniques can be particularly relevant for problems involving both computation and experiments. For one, Bayesian inference is a powerful approach to develop models consistent with knowledge from experiments. Second, ML-based methods can also be used to handle problems that are formally intractable using conventional approaches, such as exhaustive characterization of state-to-state information in reactive collisions. Finally, the explicit simulation of reactive networks as they occur in combustion has become possible using machine-learned neural network potentials. This review provides an overview of the questions that can and have been addressed using machine learning techniques, and an outlook discusses challenges in this diverse and stimulating field. It is concluded that ML applied to chemistry problems as practiced and conceived today has the potential to transform the way with which the field approaches problems involving chemical reactions, in both research and academic teaching.

Vibronic and Environmental Effects in Simulations of Optical Spectroscopy

Including both environmental and vibronic effects is important for accurate simulation of optical spectra, but combining these effects remains computationally challenging. We outline two approaches that consider both the explicit atomistic environment and the vibronic transitions. Both phenomena are responsible for spectral shapes in linear spectroscopy and the electronic evolution measured in nonlinear spectroscopy. The first approach utilizes snapshots of chromophore-environment configurations for which chromophore normal modes are determined. We outline various approximations for this static approach that assumes harmonic potentials and ignores dynamic system-environment coupling. The second approach obtains excitation energies for a series of time-correlated snapshots. This dynamic approach relies on the accurate truncation of the cumulant expansion but treats the dynamics of the chromophore and the environment on equal footing. Both approaches show significant potential for making strides toward more accurate optical spectroscopy simulations of complex condensed phase systems.

Accelerated Computation of Free Energy Profile at Ab Initio Quantum Mechanical/Molecular Mechanics Accuracy via a Semiempirical Reference Potential. 4. Adaptive QM/MM

Although quantum mechanical/molecular mechanics (QM/MM) methods are now routinely applied to the studies of chemical reactions in condensed phases and enzymatic reactions, they may experience technical difficulties when the reactive region is varying over time. For instance, when the solvent molecules are directly participating in the reaction, the exchange of water molecules between the QM and MM regions may occur on a time scale comparable to the reaction time. To cope with this situation, several adaptive QM/MM schemes have been proposed. However, these methods either add significantly to the computational cost or introduce artificial restraints to the system. In this work, we developed a novel adaptive QM/MM scheme and applied it to the study of a nucleophilic addition reaction. In this scheme, the configuration sampling was performed with a small QM region (without solvent molecules), and the thermodynamic properties under another potential energy function with a larger QM region (with a certain number of solvent molecules and/or different levels of QM theory) are computed via extrapolation using the reference-potential method. Our simulation results show that this adaptive QM/MM scheme is numerically stable, at least for the case studied in this work. Furthermore, this method also offers an inexpensive way to examine the convergence of the QM/MM calculation with respect to the size of the QM region.

Mechanism of covalent binding of ibrutinib to Bruton's tyrosine kinase revealed by QM/MM calculations

Ibrutinib is the first covalent inhibitor of Bruton's tyrosine kinase (BTK) to be used in the treatment of B-cell cancers. Understanding the mechanism of covalent inhibition will aid in the design of safer and more selective covalent inhibitors that target BTK. The mechanism of covalent inhibition in BTK has been uncertain because there is no appropriate residue nearby that can act as a base to deprotonate the cysteine thiol prior to covalent bond formation. We investigate several mechanisms of covalent modification of C481 in BTK by ibrutinib using combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics reaction simulations. The lowest energy pathway involves direct proton transfer from C481 to the acrylamide warhead in ibrutinib, followed by covalent bond formation to form an enol intermediate. There is a subsequent rate-limiting keto-enol tautomerisation step (ΔG ^‡ = 10.5 kcal mol^-1) to reach the inactivated BTK/ibrutinib complex. Our results represent the first mechanistic study of BTK inactivation by ibrutinib to consider multiple mechanistic pathways. These findings should aid in the design of covalent drugs that target BTK and other similar targets.

Biomolecular QM/MM Simulations: What Are Some of the "Burning Issues"?

QM/MM simulations have become an indispensable tool in many chemical and biochemical investigations. Considering the tremendous degree of success, including recognition by a 2013 Nobel Prize in Chemistry, are there still "burning challenges" in QM/MM methods, especially for biomolecular systems? In this short Perspective, we discuss several issues that we believe greatly impact the robustness and quantitative applicability of QM/MM simulations to many, if not all, biomolecules. We highlight these issues with observations and relevant advances from recent studies in our group and others in the field. Despite such limited scope, we hope the discussions are of general interest and will stimulate additional developments that help push the field forward in meaningful directions.

Quantifying Uncertainties in Solvation Procedures for Modeling Aqueous Phase Reaction Mechanisms

Computational quantum chemistry provides fundamental chemical and physical insights into solvated reaction mechanisms across many areas of chemistry, especially in homogeneous and heterogeneous renewable energy catalysis. Such reactions may depend on explicit interactions with ions and solvent molecules that are nontrivial to characterize. Rigorously modeling explicit solvent effects with molecular dynamics usually brings steep computational costs while the performance of continuum solvent models such as polarizable continuum model (PCM), charge-asymmetric nonlocally determined local-electric (CANDLE), conductor-like screening model for real solvents (COSMO-RS), and effective screening medium method with the reference interaction site model (ESM-RISM) are less well understood for reaction mechanisms. Here, we revisit a fundamental aqueous hydride transfer reaction-carbon dioxide (CO₂) reduction by sodium borohydride (NaBH₄)-as a test case to evaluate how different solvent models perform in aqueous phase charge migrations that would be relevant to renewable energy catalysis mechanisms. For this system, quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations almost exactly reproduced energy profiles from QM simulations, and the Na⁺ counterion in the QM/MM simulations plays an insignificant role over ensemble averaged trajectories that describe the reaction pathway. However, solvent models used on static calculations gave much more variability in data depending on whether the system was modeled using explicit solvent shells and/or the counterion. We pinpoint this variability due to unphysical descriptions of charge-separated states in the gas phase (i.e., self-interaction errors), and we show that using more accurate hybrid functionals and/or explicit solvent shells lessens these errors. This work closes with recommended procedures for treating solvation in future computational efforts in studying renewable energy catalysis mechanisms.

The influence of base pair tautomerism on single point mutations in aqueous DNA

The relationship between base pair hydrogen bond proton transfer and the rate of spontaneous single point mutations at ambient temperatures and pressures in aqueous DNA is investigated. By using an ensemble-based multiscale computational modelling method, statistically robust rates of proton transfer for the A:T and G:C base pairs within a solvated DNA dodecamer are calculated. Several different proton transfer pathways are observed within the same base pair. It is shown that, in G:C, the double proton transfer tautomer is preferred, while the single proton transfer process is favoured in A:T. The reported range of rate coefficients for double proton transfer is consistent with recent experimental data. Notwithstanding the approximately 1000 times more common presence of single proton transfer products from A:T, observationally there is bias towards G:C to A:T mutations in a wide range of living organisms. We infer that the double proton transfer reactions between G:C base pairs have a negligible contribution towards this bias for the following reasons: (i) the maximum half-life of the G*:C* tautomer is in the range of picoseconds, which is significantly smaller than the milliseconds it takes for DNA to unwind during replication, (ii) statistically, the majority of G*:C* tautomers revert back to their canonical forms through a barrierless process, and (iii) the thermodynamic instability of the tautomers with respect to the canonical base pairs. Through similar reasoning, we also deduce that proton transfer in the A:T base pair does not contribute to single point mutations in DNA.

Modeling Excited-State Proton Transfer to Solvent: A Dynamics Study of a Super Photoacid with a Hybrid Implicit/Explicit Solvent Model

The rapid growth of time-resolved spectroscopies and the theoretical advances in ab initio molecular dynamics (AIMD) pave the way to look at the real-time molecular motion following the electronic excitation. Here, we exploited the capabilities of AIMD combined with a hybrid implicit/explicit model of solvation to investigate the ultrafast excited-state proton transfer (ESPT) reaction of a super photoacid, known as QCy9, in water solution. QCy9 transfers a proton to a water solvent molecule within 100 fs upon the electronic excitation in aqueous solution, and it is the strongest photoacid reported in the literature so far. Because of the ultrafast kinetics, it has been experimentally hypothesized that the ESPT escapes the solvent dynamics control (Huppert et al., J. Photochem. Photobiol. A2014,277, 90). The sampling of the solvent configuration space on the ground electronic state is the first key step toward the simulation of the ESPT event. Therefore, several configurations in the Franck–Condon region, describing an average solvation, were chosen as starting points for the excited-state dynamics. In all cases, the excited-state evolution spontaneously leads to the proton transfer event, whose rate is strongly dependent on the hydrogen bond network around the proton acceptor solvent molecule. Our study revealed that the explicit representation at least of three solvation shells around the proton acceptor molecule is necessary to stabilize the excess proton. Furthermore, the analysis of the solvent molecule motions in proximity of the reaction site suggested that even in the case of the strongest photoacid, the ESPT is actually assisted by the solvation dynamics of the first and second solvation shells of the water accepting molecule.

Molecular Photochemistry: Recent Developments in Theory

Photochemistry is a fascinating branch of chemistry that is concerned with molecules and light. However, the importance of simulating light-induced processes is reflected also in fields as diverse as biology, material science, and medicine. This Minireview highlights recent progress achieved in theoretical chemistry to calculate electronically excited states of molecules and simulate their photoinduced dynamics, with the aim of reaching experimental accuracy. We focus on emergent methods and give selected examples that illustrate the progress in recent years towards predicting complex electronic structures with strong correlation, calculations on large molecules, describing multichromophoric systems, and simulating non-adiabatic molecular dynamics over long time scales, for molecules in the gas phase or in complex biological environments.

Transition-State Vibrational Analysis and Isotope Effects for COMT-Catalyzed Methyl Transfer

Isotopic partition-function ratios (IPFRs) computed for transition structures (TSs) of the methyl-transfer reaction catalyzed by catechol O-methyltransferase and modeled by hybrid QM/MM methods are analyzed. The ability of smaller Hessians to reproduce trends in α-3H3 and 14Cα IPFRs as obtained using the much larger subset QM/MM Hessians from which they are extracted is investigated critically. A 6-atom-extracted Hessian reproduces perfectly the α-T3 IPFR values from the full-subset Hessians of all the TSs but not the α-14CIPFRs. Average AM1/OPLS-AA harmonic frequencies and mean-square amplitudes are presented for the 12 normal modes of the α-CH3 moiety within the active site of several enzymic transition structures, together with QM/MM potential energy scans along each of these modes to assess the degree of anharmonicity. A novel investigation of ponderal effects upon IPFRs suggests that the value for α-14C tends toward a limiting minimum whereas that for α-T3 tends toward a limiting maximum as the mass of the rest of the system increases. The transition vector is dominated by motions of atoms within the donor and acceptor moieties and is very well described as a simple combination of Walden-inversion "umbrella" bending and asymmetric stretching of the SCα and CαO bonds. The contribution of atoms of the protein residues Met40, Tyr68, and Asp141 to the transition vector is extremely small. Average valence force constants for the COMT TS show significant differences from early BEBOVIB estimates which were used in support of the compression hypothesis for catalysis. There is no correlation between TS IPFRs and the nonbonded distances for close contacts between the S atom of SAM and Tyr68 or between any of the H atoms of the transferring methyl group and either Met40 or Asp141.

Electronic Structure Modeling of Metal-Organic Frameworks

Owing to their molecular building blocks, yet highly crystalline nature, metal-organic frameworks (MOFs) sit at the interface between molecule and material. Their diverse structures and compositions enable them to be useful materials as catalysts in heterogeneous reactions, electrical conductors in energy storage and transfer applications, chromophores in photoenabled chemical transformations, and beyond. In all cases, density functional theory (DFT) and higher-level methods for electronic structure determination provide valuable quantitative information about the electronic properties that underpin the functions of these frameworks. However, there are only two general modeling approaches in conventional electronic structure software packages: those that treat materials as extended, periodic solids, and those that treat materials as discrete molecules. Each approach has features and benefits; both have been widely employed to understand the emergent chemistry that arises from the formation of the metal-organic interface. This Review canvases these approaches to date, with emphasis placed on the application of electronic structure theory to explore reactivity and electron transfer using periodic, molecular, and embedded models. This includes (i) computational chemistry considerations such as how functional, k-grid, and other model variables are selected to enable insights into MOF properties, (ii) extended solid models that treat MOFs as materials rather than molecules, (iii) the mechanics of cluster extraction and subsequent chemistry enabled by these molecular models, (iv) catalytic studies using both solids and clusters thereof, and (v) embedded, mixed-method approaches, which simulate a fraction of the material using one level of theory and the remainder of the material using another dissimilar theoretical implementation.

Improved Basis-Set Incompleteness Potentials for Accurate Density-Functional Theory Calculations in Large Systems

The accurate calculation of chemical properties using density-functional theory (DFT) requires the use of a nearly complete basis set. In chemical systems involving hundreds to thousands of atoms, the cost of the calculations place practical limitations on the number of basis functions that can be used. Therefore, in most practical applications of DFT to large systems, there exists a basis-set incompleteness error (BSIE). In this article, we present the next iteration of the basis-set incompleteness potentials (BSIPs), one-electron potentials designed to correct for basis-set incompleteness error. The ultimate goal associated with the development of BSIPs is to allow the calculation of molecular properties using DFT with near-complete-basis-set results at a computational cost that is similar to a small basis set calculation. In this work, we develop BSIPs for 10 atoms in the first and second rows (H, B-F, Si-Cl) and 15 common basis sets of the Pople, Dunning, Karlsruhe, and Huzinaga types. Our new BSIPs are constructed to minimize BSIE in the calculation of reaction energies, barrier heights, noncovalent binding energies, and intermolecular distances. The BSIPs were obtained using a training set of 15 944 data points. The fitting approach employed a regularized linear least-squares method with variable selection (the LASSO method), which results in a much better fit to the training data than our previous BSIPs while, at the same time, reducing the computational cost of BSIP development. The proposed BSIPs are tested on various benchmark sets and demonstrate excellent performance in practice. Our new BSIPs are also transferable; i.e., they can be used to correct BSIE in calculations that employ density functionals other than the one used in the BSIP development (B3LYP). Finally, BSIPs can be used in any quantum chemistry program that have implemented effective-core potentials without changes to the software.

Hydrogen deuterium exchange defines catalytically linked regions of protein flexibility in the catechol O-methyltransferase reaction

Human catechol O-methyltransferase (COMT) has emerged as a model for understanding enzyme-catalyzed methyl transfer from S-adenosylmethionine (AdoMet) to small-molecule catecholate acceptors. Mutation of a single residue (tyrosine 68) behind the methyl-bearing sulfonium of AdoMet was previously shown to impair COMT activity by interfering with methyl donor-acceptor compaction within the activated ground state of the wild type enzyme [J. Zhang, H. J. Kulik, T. J. Martinez, J. P. Klinman, Proc. Natl. Acad. Sci. U.S.A. 112, 7954-7959 (2015)]. This predicts the involvement of spatially defined protein dynamical effects that further tune the donor/acceptor distance and geometry as well as the electrostatics of the reactants. Here, we present a hydrogen/deuterium exchange (HDX)-mass spectrometric study of wild type and mutant COMT, comparing temperature dependences of HDX against corresponding kinetic and cofactor binding parameters. The data show that the impaired Tyr68Ala mutant displays similar breaks in Arrhenius plots of both kinetic and HDX properties that are absent in the wild type enzyme. The spatial resolution of HDX below a break point of 15-20 °C indicates changes in flexibility across ∼40% of the protein structure that is confined primarily to the periphery of the AdoMet binding site. Above 20 °C, Tyr68Ala behaves more like WT in HDX, but its rate and enthalpic barrier remain significantly altered. The impairment of catalysis by Tyr68Ala can be understood in the context of a mutationally induced alteration in protein motions that becomes manifest along and perpendicular to the primary group transfer coordinate.

Computational study on the polymerization reaction of d-aminopeptidase for the synthesis of d-peptides

Almost all natural proteins are composed exclusively of l-amino acids, and this chirality influences their properties, functions, and selectivity. Proteases can recognize proteins composed of l-amino acids but display lower selectivity for their stereoisomers, d-amino acids. Taking this as an advantage, d-amino acids can be used to develop polypeptides or biobased materials with higher biostability. Chemoenzymatic peptide synthesis is a technique that uses proteases as biocatalysts to synthesize polypeptides, and d-stereospecific proteases can be used to synthesize polypeptides incorporating d-amino acids. However, engineered proteases with modified catalytic activities are required to allow the incorporation of d-amino acids with increased efficiency. To understand the stereospecificity presented by proteases and their involvement in polymerization reactions, we studied d-aminopeptidase. This enzyme displays the ability to efficiently synthesize poly d-alanine-based peptides under mild conditions. To elucidate the mechanisms involved in the unique specificity of d-aminopeptidase, we performed quantum mechanics/molecular mechanics simulations of its polymerization reaction and determined the energy barriers presented by the chiral substrates. The enzyme faces higher activation barriers for the acylation and aminolysis reactions with the l-stereoisomer than with the d-substrate (10.7 and 17.7 kcal mol-1 higher, respectively). The simulation results suggest that changes in the interaction of the substrate with Asn155 influence the stereospecificity of the polymerization reaction.

How accurate are approximate quantum chemical methods at modelling solute-solvent interactions in solvated clusters?

In this paper, the performance of a wide range of DFT methods is assessed for the calculation of interaction energies of thermal clusters of a solute in water. Three different charge states (neutral, proton transfer transition state and zwitterion) of glycine were solvated by 1 to 40 water molecules as sampled from molecular dynamics simulations. While some ab initio composite methods that employ insufficiently large basis sets incurred significant errors even for a cluster containing only 5 water molecules relative to the W1X-2 benchmark, the DLPNO-CCSD(T)/CBS and DSD-PBEP86 (triple zeta basis set) levels of theory predicted very accurate interaction energies. These levels of theory were used to benchmark the performance of 16 density functionals from different rungs of Jacob's Ladder. Of the Rung 4 functionals examined, the ωB97M-V and ωB97X-V functionals stood out for predicting absolute interaction energies in 40-water clusters with mean absolute deviations (MAD) ∼4 kJ mol-1. The B3LYP-D3(BJ) functional performed exceptionally well with a MAD ∼1.7 kJ mol-1 and is the overall best performing method. Calculations of relative interaction energies allow for cancellation of systematic errors, including basis set truncation and superposition errors, and the ωB97M-V and B3LYP-D3(BJ) double zeta basis set calculations yielded relative interaction energies that are within ∼3 kJ mol-1 of the benchmark. The ONIOM approximation provides another strategy for accelerating the calculation of accurate absolute interaction energies provided that the calculations have converged with respect to the size of the "high-level-layer".

Embedding Methods for Quantum Chemistry: Applications from Materials to Life Sciences

Quantum mechanical embedding methods hold the promise to transform not just the way calculations are performed, but to significantly reduce computational costs and improve scaling for macro-molecular systems containing hundreds if not thousands of atoms. The field of embedding has grown increasingly broad with many approaches of different intersecting flavors. In this perspective, we lay out the methods into two streams: QM:MM and QM:QM, showcasing the advantages and disadvantages of both. We provide a review of the literature, the underpinning theories including our contributions, and we highlight current applications with select examples spanning both materials and life sciences. We conclude with prospects and future outlook on embedding, and our view on the use of universal test case scenarios for cross-comparisons of the many available (and future) embedding theories.

Using Atomic Confining Potentials for Geometry Optimization and Vibrational Frequency Calculations in Quantum-Chemical Models of Enzyme Active Sites

Quantum-chemical studies of enzymatic reaction mechanisms sometimes use truncated active-site models as simplified alternatives to mixed quantum mechanics molecular mechanics (QM/MM) procedures. Eliminating the MM degrees of freedom reduces the complexity of the sampling problem, but the trade-off is the need to introduce geometric constraints in order to prevent structural collapse of the model system during geometry optimizations that do not contain a full protein backbone. These constraints may impair the efficiency of the optimization, and care must be taken to avoid artifacts such as imaginary vibrational frequencies. We introduce a simple alternative in which terminal atoms of the model system are placed in soft harmonic confining potentials rather than being rigidly constrained. This modification is simple to implement and straightforward to use in vibrational frequency calculations, unlike iterative constraint-satisfaction algorithms, and allows the optimization to proceed without constraint even though the practical result is to fix the anchor atoms in space. The new approach is more efficient for optimizing minima and transition states, as compared to the use of fixed-atom constraints, and also more robust against unwanted imaginary frequencies. We illustrate the method by application to several enzymatic reaction pathways where entropy makes a significant contribution to the relevant reaction barriers. The use of confining potentials correctly describes reaction paths and facilitates calculation of both vibrational zero-point and finite-temperature entropic corrections to barrier heights.

Evaluating QM/MM Free Energy Surfaces for Ranking Cysteine Protease Covalent Inhibitors

One tactic for cysteine protease inhibition is to form a covalent bond between an electrophilic atom of the inhibitor and the thiol of the catalytic cysteine. In this study, we evaluate the reaction free energy obtained from a hybrid quantum mechanical/molecular mechanical (QM/MM) free energy profile as a predictor of affinity for reversible, covalent inhibitors of rhodesain. We demonstrate that the reaction free energy calculated with the PM6/MM potential is in agreement with the experimental data and suggest that the free energy profile for covalent bond formation in a protein environment may be a useful tool for the inhibitor design.

User-Friendly Quantum Mechanics: Applications for Drug Discovery

Quantum mechanics (QM) methods provide a fine description of receptor-ligand interactions and of chemical reactions. Their use in drug design and drug discovery is increasing, especially for complex systems including metal ions in the binding sites, for the design of highly selective inhibitors, for the optimization of bi-specific compounds, to understand enzymatic reactions, and for the study of covalent ligands and prodrugs. They are also used for generating molecular descriptors for predictive QSAR/QSPR models and for the parameterization of force fields. Thanks to the continuous increase of computational power offered by GPUs and to the development of sophisticated algorithms, QM methods are becoming part of the standard tools used in computer-aided drug design (CADD). We present the most used QM methods and software packages, and we discuss recent representative applications in drug design and drug discovery.

Finding Reactive Configurations: A Machine Learning Approach for Estimating Energy Barriers Applied to Sirtuin 5

Sirtuin 5 is a class III histone deacetylase that, unlike its classification, mainly catalyzes desuccinylation and demanoylation reactions. It is an interesting drug target that we use here to test new ideas for calculating reaction pathways of large molecular systems such as enzymes. A major issue with most schemes (e.g., adiabatic mapping) is that the resulting activation barrier height heavily depends on the chosen educt conformation. This makes the selection of the initial structure decisive for the success of the characterization. Here, we apply machine learning to a large number of molecular dynamics frames and potential energy barriers obtained by quantum mechanics/molecular mechanics calculations in order to identify (1) suitable start-conformations for reaction path calculations and (2) structural features relevant for the first step of the desuccinylation reaction catalyzed by Sirtuin 5. The latter generally aids the understanding of reaction mechanisms and important interactions in active centers. Using our novel approach, we found eleven key features that govern the reactivity. We were able to estimate reaction barriers with a mean absolute error of 3.6 kcal/mol and identified reactive configurations.

Examining the Origin of Catalytic Power of Catechol O-Methyltransferase

For decades, there has been debate regarding the origin of the catalytic power of enzymes. In this work, we use the approach of computational chemistry to study the enzyme catechol O-methyltransferase (COMT) and reveal that the two current views on the catalytic mechanism of enzymes, the rate-promoting vibrations and the electric field, may both be viewed as part of the chemical step catalyzed by COMT. However, we show that the rate-promoting vibrations cause the electrostatic effect. This work provides insight into the catalytic mechanism of COMT and resolves a longstanding controversy regarding this enzyme's mechanism.

Towards large scale hybrid QM/MM dynamics of complex systems with advanced point dipole polarizable embeddings

In this work, we present a general route to hybrid Quantum Mechanics/Molecular Mechanics (QM/MM) Molecular Dynamics for complex systems using a polarizable embedding. We extend the capabilities of our hybrid framework, combining the Gaussian and Tinker/Tinker-HP packages in the context of the AMOEBA polarizable force field to treat large (bio)systems where the QM and the MM subsystems are covalently bound, adopting pseudopotentials at the boundaries between the two regions. We discuss in detail the implementation and demonstrate the global energy conservation of our QM/MM Born-Oppenheimer molecular dynamics approach using Density Functional Theory. Finally, the approach is assessed on the electronic absorption properties of a 16 500 atom complex encompassing an organic dye embedded in a DNA matrix in solution, extending the hybrid method to a time-dependent Density Functional Theory approach. The results obtained comparing different partitions between the quantum and the classical subsystems also suggest that large QM portions are not necessary if accurate polarizable force fields are used in a variational formulation of the embedding, properly including the QM/MM mutual polarization.

Quantum Mechanical Description of Electrostatics Provides a Unified Picture of Catalytic Action Across Methyltransferases

Methyl transferases (MTases) are a well-studied class of enzymes for which competing enzymatic enhancement mechanisms have been suggested, ranging from structural methyl group CH···X hydrogen bonds (HBs) to electrostatic- and charge-transfer-driven stabilization of the transition state (TS). We identified all Class I MTases for which reasonable resolution (<2.0 Å) crystal structures could be used to form catalytically competent ternary complexes for multiscale (i.e., quantum-mechanical/molecular-mechanical or QM/MM) simulation of the S_N2 methyl transfer reaction coordinate. The four Class I MTases studied have both distinct functions (e.g., protein repair or biosynthesis) and substrate nucleophiles (i.e., C, N, or O). While CH···X HBs stabilize all reactant complexes, no universal TS stabilization role is found for these interactions in MTases. A consistent picture is instead obtained through analysis of charge transfer and electrostatics, wherein much of cofactor-substrate charge separation is maintained in the TS region, and electrostatic potential is correlated with substrate nucleophilicity (i.e., intrinsic reactivity).

Projector-Based Embedding Eliminates Density Functional Dependence for QM/MM Calculations of Reactions in Enzymes and Solution

Combined quantum mechanics/molecular mechanics (QM/MM) methods are increasingly widely utilized in studies of reactions in enzymes and other large systems. Here, we apply a range of QM/MM methods to investigate the Claisen rearrangement of chorismate to prephenate, in solution, and in the enzyme chorismate mutase. Using projector-based embedding in a QM/MM framework, we apply treatments up to the CCSD(T) level. We test a range of density functional QM/MM methods and QM region sizes. The results show that the calculated reaction energetics are significantly more sensitive to the choice of density functional than they are to the size of the QM region in these systems. Projector-based embedding of a wave function method in DFT reduced the 13 kcal/mol spread in barrier heights calculated at the DFT/MM level to a spread of just 0.3 kcal/mol, essentially eliminating dependence on the functional. Projector-based embedding of correlated ab initio methods provides a practical method for achieving high accuracy for energy profiles derived from DFT and DFT/MM calculations for reactions in condensed phases.

Equatorial Active Site Compaction and Electrostatic Reorganization in Catechol-O-methyltransferase

Catechol-O-methyltransferase (COMT) is a model S-adenosyl-l-methionine (SAM) dependent methyl transferase, which catalyzes the methylation of catecholamine neurotransmitters such as dopamine in the primary pathway of neurotransmitter deactivation in animals. Despite extensive study, there is no consensus view of the physical basis of catalysis in COMT. Further progress requires experimental data that directly probes active site geometry, protein dynamics and electrostatics, ideally in a range of positions along the reaction coordinate. Here we establish that sinefungin, a fungal-derived inhibitor of SAM-dependent enzymes that possess transition state-like charge on the transferring group, can be used as a transition state analog of COMT when combined with a catechol. X-ray crystal structures and NMR backbone assignments of the ternary complexes of the soluble form of human COMT containing dinitrocatechol, Mg2+ and SAM or sinefungin were determined. Comparison and further analysis with the aid of density functional theory calculations and molecular dynamics simulations provides evidence for active site "compaction", which is driven by electrostatic stabilization between the transferring methyl group and "equatorial" active site residues that are orthogonal to the donor-acceptor (pseudo reaction) coordinate. We propose that upon catecholamine binding and subsequent proton transfer to Lys 144, the enzyme becomes geometrically preorganized, with little further movement along the donor-acceptor coordinate required for methyl transfer. Catalysis is then largely facilitated through stabilization of the developing charge on the transferring methyl group via "equatorial" H-bonding and electrostatic interactions orthogonal to the donor-acceptor coordinate.

The extra virgin olive oil phenolic oleacein is a dual substrate-inhibitor of catechol-O-methyltransferase

Catechol-containing polyphenols present in coffee and tea, while serving as excellent substrates for catechol-O-methyltransferase (COMT)-catalyzed O-methylation, can also operate as COMT inhibitors. However, little is known about the relationship between COMT and the characteristic phenolics present in extra virgin olive oil (EVOO). We here selected the EVOO dihydroxy-phenol oleacein for a computational study of COMT-driven methylation using classic molecular docking/molecular dynamics simulations and hybrid quantum mechanical/molecular mechanics, which were supported by in vitro activity studies using human COMT. Oleacein could be superimposed onto the catechol-binding site of COMT, maintaining the interactions with the atomic positions involved in methyl transfer from the S-adenosyl-L-methionine cofactor. The transition state structure for the meta-methylation in the O5 position of the oleacein benzenediol moiety was predicted to occur preferentially. Enzyme analysis of the conversion ratio of catechol to O-alkylated guaiacol confirmed the inhibitory effect of oleacein on human COMT, which remained unaltered when tested against the protein version encoded by the functional Val¹⁵⁸Met polymorphism of the COMT gene. Our study provides a theoretical determination of how EVOO dihydroxy-phenols can be metabolized via COMT. The ability of oleacein to inhibit COMT adds a new dimension to the physiological and therapeutic utility of EVOO secoiridoids.

Linear Response Functions of Densities and Spin Densities for Systematic Modeling of the QM/MM Approach for Mono- and Poly-Nuclear Transition Metal Systems

We applied our analysis, based on a linear response function of density and spin density, to two typical transition metal complex systems-the reaction centers of P450, and oxygen evolving center in Photosystem II, both of which contain open-shell transition metal ions. We discuss the relationship between LRF of electron density and spin density and the types of units and interactions of the systems. The computational results are discussed in relation to quantum mechanics (QM) cluster and quantum mechanics/molecular mechanics (QM/MM) modeling that are employed to compute the reaction centers of enzymes.

Revealing quantum mechanical effects in enzyme catalysis with large-scale electronic structure simulation

Enzymes have evolved to facilitate challenging reactions at ambient conditions with specificity seldom matched by other catalysts. Computational modeling provides valuable insight into catalytic mechanism, and the large size of enzymes mandates multi-scale, quantum mechanical-molecular mechanical (QM/MM) simulations. Although QM/MM plays an essential role in balancing simulation cost to enable sampling with full QM treatment needed to understand electronic structure in enzyme active sites, the relative importance of these two strategies for understanding enzyme mechanism is not well known. We explore challenges in QM/MM for studying the reactivity and stability of three diverse enzymes: i) Mg2+-dependent catechol O-methyltransferase (COMT), ii) radical enzyme choline trimethylamine lyase (CutC), and iii) DNA methyltransferase (DNMT1), which has structural Zn2+ binding sites. In COMT, strong non-covalent interactions lead to long range coupling of electronic structure properties across the active site, but the more isolated nature of the metallocofactor in DNMT1 leads to faster convergence of some properties. We quantify these effects in COMT by computing covariance matrices of by-residue electronic structure properties during dynamics and along the reaction coordinate. In CutC, we observe spontaneous bond cleavage following initiation events, highlighting the importance of sampling and dynamics. We use electronic structure analysis to quantify the relative importance of CHO and OHO non-covalent interactions in imparting reactivity. These three diverse cases enable us to provide some general recommendations regarding QM/MM simulation of enzymes.