Effect of Geometry Optimizations on QM-Cluster and QM/MM Studies of Reaction Energies in Proteins

Quick-and-Easy Validation of Protein-Ligand Binding Models Using Fragment-Based Semiempirical Quantum Chemistry

Electronic structure calculations in enzymes converge very slowly with respect to the size of the model region that is described using quantum mechanics (QM), requiring hundreds of atoms to obtain converged results and exhibiting substantial sensitivity (at least in smaller models) to which amino acids are included in the QM region. As such, there is considerable interest in developing automated procedures to construct a QM model region based on well-defined criteria. However, testing such procedures is burdensome due to the cost of large-scale electronic structure calculations. Here, we show that semiempirical methods can be used as alternatives to density functional theory (DFT) to assess convergence in sequences of models generated by various automated protocols. The cost of these convergence tests is reduced even further by means of a many-body expansion. We use this approach to examine convergence (with respect to model size) of protein-ligand binding energies. Fragment-based semiempirical calculations afford well-converged interaction energies in a tiny fraction of the cost required for DFT calculations. Two-body interactions between the ligand and single-residue amino acid fragments afford a low-cost way to construct a "QM-informed" enzyme model of reduced size, furnishing an automatable active-site model-building procedure. This provides a streamlined, user-friendly approach for constructing ligand binding-site models that requires neither a priori information nor manual adjustments. Extension to model-building for thermochemical calculations should be straightforward.

CO Oxidation Mechanism of Silver-Substituted Mo/Cu CO-Dehydrogenase - Analogies and Differences to the Native Enzyme

The aerobic oxidation of carbon monoxide to carbon dioxide is catalysed by the Mo/Cu-containing CO-dehydrogenase enzyme in the soil bacterium Oligotropha carboxidovorans, enabling the organism to grow on the small gas molecule as carbon and energy source. It was shown experimentally that silver can be substituted for copper in the active site of Mo/Cu CODH to yield a functional enzyme. In this study, we employed QM/MM calculations to investigate whether the reaction mechanism of the silver-substituted enzyme is similar to that of the native enzyme. Our results suggest that the Ag-substituted enzyme can oxidize CO and release CO2 following the same reaction steps as the native enzyme, with a computed rate-limiting step of 10.4 kcal/mol, consistent with experimental findings. Surprisingly, lower activation energies for C-O bond formation have been found in the presence of silver. Furthermore, comparison of rate constants for reduction of copper- and silver-containing enzymes suggests a discrepancy in the transition state stabilization upon silver substitution. We also evaluated the effects that differences in the water-active site interaction may exert on the overall energy profile of catalysis. Finally, the formation of a thiocarbonate intermediate along the catalytic pathway was found to be energetically unfavorable for the Ag-substituted enzyme. This finding aligns with the hypothesis proposed for the wild-type form, suggesting that the creation of such species may not be necessary for the enzymatic catalysis of CO oxidation.

Perspective: multi-configurational methods in bio-inorganic chemistry

Transition metal ions play crucial roles in the structure and function of numerous proteins, contributing to essential biological processes such as catalysis, electron transfer, and oxygen binding. However, accurately modeling the electronic structure and properties of metalloproteins poses significant challenges due to the complex nature of their electronic configurations and strong correlation effects. Multiconfigurational quantum chemistry methods are, in principle, the most appropriate tools for addressing these challenges, offering the capability to capture the inherent multi-reference character and strong electron correlation present in bio-inorganic systems. Yet their computational cost has long hindered wider adoption, making methods such as density functional theory (DFT) the method of choice. However, advancements over the past decade have substantially alleviated this limitation, rendering multiconfigurational quantum chemistry methods more accessible and applicable to a wider range of bio-inorganic systems. In this perspective, we discuss some of these developments and how they have already been used to answer some of the most important questions in bio-inorganic chemistry. We also comment on ongoing developments in the field and how the future of the field may evolve.

Nanoscale chemical reaction exploration with a quantum magnifying glass

Nanoscopic systems exhibit diverse molecular substructures by which they facilitate specific functions. Theoretical models of them, which aim at describing, understanding, and predicting these capabilities, are difficult to build. Viable quantum-classical hybrid models come with specific challenges regarding atomistic structure construction and quantum region selection. Moreover, if their dynamics are mapped onto a state-to-state mechanism such as a chemical reaction network, its exhaustive exploration will be impossible due to the combinatorial explosion of the reaction space. Here, we introduce a "quantum magnifying glass" that allows one to interactively manipulate nanoscale structures at the quantum level. The quantum magnifying glass seamlessly combines autonomous model parametrization, ultra-fast quantum mechanical calculations, and automated reaction exploration. It represents an approach to investigate complex reaction sequences in a physically consistent manner with unprecedented effortlessness in real time. We demonstrate these features for reactions in bio-macromolecules and metal-organic frameworks, diverse systems that highlight general applicability.

SCINE-Software for chemical interaction networks

The software for chemical interaction networks (SCINE) project aims at pushing the frontier of quantum chemical calculations on molecular structures to a new level. While calculations on individual structures as well as on simple relations between them have become routine in chemistry, new developments have pushed the frontier in the field to high-throughput calculations. Chemical relations may be created by a search for specific molecular properties in a molecular design attempt, or they can be defined by a set of elementary reaction steps that form a chemical reaction network. The software modules of SCINE have been designed to facilitate such studies. The features of the modules are (i) general applicability of the applied methodologies ranging from electronic structure (no restriction to specific elements of the periodic table) to microkinetic modeling (with little restrictions on molecularity), full modularity so that SCINE modules can also be applied as stand-alone programs or be exchanged for external software packages that fulfill a similar purpose (to increase options for computational campaigns and to provide alternatives in case of tasks that are hard or impossible to accomplish with certain programs), (ii) high stability and autonomous operations so that control and steering by an operator are as easy as possible, and (iii) easy embedding into complex heterogeneous environments for molecular structures taken individually or in the context of a reaction network. A graphical user interface unites all modules and ensures interoperability. All components of the software have been made available as open source and free of charge.

Eliminating Imaginary Vibrational Frequencies in Quantum-Chemical Cluster Models of Enzymatic Active Sites

In constructing finite models of enzyme active sites for quantum-chemical calculations, atoms at the periphery of the model must be constrained to prevent unphysical rearrangements during geometry relaxation. A simple fixed-atom or "coordinate-lock" approach is commonly employed but leads to undesirable artifacts in the form of small imaginary frequencies. These preclude evaluation of finite-temperature free-energy corrections, limiting thermochemical calculations to enthalpies only. Full-dimensional vibrational frequency calculations are possible by replacing the fixed-atom constraints with harmonic confining potentials. Here, we compare that approach to an alternative strategy in which fixed-atom contributions to the Hessian are simply omitted. While the latter strategy does eliminate imaginary frequencies, it tends to underestimate both the zero-point energy and the vibrational entropy while introducing artificial rigidity. Harmonic confining potentials eliminate imaginary frequencies and provide a flexible means to construct active-site models that can be used in unconstrained geometry relaxations, affording better convergence of reaction energies and barrier heights with respect to the model size, as compared to models with fixed-atom constraints.

The influence of model building schemes and molecular dynamics sampling on QM-cluster models: the chorismate mutase case study

Most QM-cluster models of enzymes are constructed based on X-ray crystal structures, which limits comparison to in vivo structure and mechanism. The active site of chorismate mutase from Bacillus subtilis and the enzymatic transformation of chorismate to prephenate is used as a case study to guide construction of QM-cluster models built first from the X-ray crystal structure, then from molecular dynamics (MD) simulation snapshots. The Residue Interaction Network ResidUe Selector (RINRUS) software toolkit, developed by our group to simplify and automate the construction of QM-cluster models, is expanded to handle MD to QM-cluster model workflows. Several options, some employing novel topological clustering from residue interaction network (RIN) information, are evaluated for generating conformational clustering from MD simulation. RINRUS then generates a statistical thermodynamic framework for QM-cluster modeling of the chorismate mutase mechanism via refining 250 MD frames with density functional theory (DFT). The 250 QM-cluster models sampled provide a mean ΔG‡ of 10.3 ± 2.6 kcal mol-1 compared to the experimental value of 15.4 kcal mol-1 at 25 °C. While the difference between theory and experiment is consequential, the level of theory used is modest and therefore "chemical" accuracy is unexpected. More important are the comparisons made between QM-cluster models designed from the X-ray crystal structure versus those from MD frames. The large variations in kinetic and thermodynamic properties arise from geometric changes in the ensemble of QM-cluster models, rather from the composition of the QM-cluster models or from the active site-solvent interface. The findings open the way for further quantitative and reproducible calibration in the field of computational enzymology using the model construction framework afforded with the RINRUS software toolkit.

QM/MM study of the catalytic reaction of aphid myrosinase

Brevicoryne brassicae, an aphid species, exclusively consumes plants from the Brassicaceae family and employs a sophisticated defense mechanism involving a myrosinase enzyme that breaks down glucosinolates obtained from its host plants. In this work, we employed combined quantum mechanical and molecular mechanical (QM/MM) calculations and molecular dynamics (MD) simulations to study the catalytic reaction of aphid myrosinase. A proper QM region to study the myrosinase reaction should contain the whole substrate, models of Gln-19, His-122, Asp-124, Asn-166, Glu-167, Lys-173, Tyr-180, Val-228, Tyr-309, Tyr-346, Ile-347, Glu-374, Glu-423, Trp-424, and a water molecule. The calculations show that Asp-124 and Glu-423 must be charged, His-122 must be protonated on NE2, and Glu-167 must be protonated on OE2. Our model reproduces the anomeric retaining characteristic of myrosinase and indicates that the deglycosylation reaction is the rate-determining step of the reaction. Based on the calculations, we propose a reaction mechanism for aphid myrosinase-mediated hydrolysis of glucosinolates with an overall barrier of 15.2 kcal/mol. According to the results, removing a proton from Arg-312 or altering it to valine or methionine increases glycosylation barriers but decreases the deglycosylation barrier.

Highly robust quantum mechanics and umbrella sampling studies on inclusion complexes of curcumin and β-cyclodextrin

The poor aqueous solubility of curcumin (CUR) obstructs its wide utilization in nutraceuticals, cosmetics, and pharmaceutical companies. This study is dedicated to investigate the stability of CUR inside the hydrophobic pocket of β-cyclodextrin (β-CD), hydroxypropyl-β-CD (HP-β-CD), and 2,6-Di-O-methyl-β-CD (DM-β-CD). Initially, molecular mechanics (MM) calculations and subsequently quantum mechanical (QM) calculations were performed on inclusion complexes to strengthen the MM results. We performed microsecond timescale MD simulations to observe the structural dynamics of CUR inside the cavity of CDs. We elucidated the most stable binding orientations of CUR inside the cavity of CDs based on binding free energy obtained from the Molecular Mechanics Poisson-Boltzmann Surface Area (MM-PBSA) and umbrella sampling simulations. Furthermore, the two-layered ONIOM (B3LYP/6-311+G(2d,p):PM7) method with CPCM implicit water model was used to derive the complete energetics and thermodynamics of inclusion complexes at 1:1 stoichiometry. Each inclusion reaction was exothermic and spontaneous. The chemical reactivity and kinetic stability of inclusion complexes were described by HOMO-LUMO molecular orbital energies. In conclusion, our studies revealed that HP-β-CD had the highest binding affinity for CUR with the most negative complexation energy (-6520.69 kJ/mol) and Gibb's free energy change (-6448.20 kJ/mol). The atomic-level investigation of noncovalent interactions between CUR and the hydroxypropyl groups in HP-β-CD/CUR complex may be helpful to drive new derivatives of HP-β-CD with better host capacity. The computational strategy adopted here might serve as a benchmark for increasing the solubility of numerous clinically significant molecules.

Catalytic Effects of Active Site Conformational Change in the Allosteric Activation of Imidazole Glycerol Phosphate Synthase

Imidazole glycerol phosphate synthase (IGPS) is a class-I glutamine amidotransferase (GAT) that hydrolyzes glutamine. Ammonia is produced and transferred to a second active site, where it reacts with N1-(5'-phosphoribosyl)-formimino-5-aminoimidazole-4-carboxamide ribonucleotide (PrFAR) to form precursors to purine and histidine biosynthesis. Binding of PrFAR over 25 Å away from the active site increases glutaminase efficiency by ∼4500-fold, primarily altering the glutamine turnover number. IGPS has been the focus of many studies on allosteric communication; however, atomic details for how the glutamine hydrolysis rate increases in the presence of PrFAR are lacking. We present a density functional theory study on 237-atom active site cluster models of IGPS based on crystallized structures representing the inactive and allosterically active conformations and investigate the multistep reaction leading to thioester formation and ammonia production. The proposed mechanism is supported by similar, well-studied enzyme mechanisms, and the corresponding energy profile is consistent with steady-state kinetic studies of PrFAR + IGPS. Additional active site models are constructed to examine the relationship between active site structural change and transition-state stabilization via energy decomposition schemes. The results reveal that the inactive IGPS conformation does not provide an adequately formed oxyanion hole structure and that repositioning of the oxyanion strand relative to the substrate is vital for a catalysis-competent oxyanion hole, with or without the hVal51 dihedral flip. These findings are valuable for future endeavors in modeling the IGPS allosteric mechanism by providing insight into the atomistic changes required for rate enhancement that can inform suitable reaction coordinates for subsequent investigations.

Impacts of QM region sizes and conformation numbers on modelling enzyme reactions: a case study of polyethylene terephthalate hydrolase

A quantum mechanics/molecular mechanics (QM/MM) approach is a broadly used tool in computational enzymology. Treating the QM region with a high-level DFT method is one of the important branches. Here, taking leaf-branch compost cutinase-catalyzed polyethylene terephthalate depolymerization as an example, the convergence behavior of energy barriers as well as key structural and charge features with respect to the size of the QM region (up to 1000 atoms) is systematically investigated. BP86/6-31G(d)//CHARMM and M06-2X/6-311G(d,p)//CHARMM level of theories were applied for geometry optimizations and single-point energy calculations, respectively. Six independent enzyme conformations for all the four catalytic steps (steps (i)-(iv)) were considered. Most of the twenty-four cases show that at least 500 QM atoms are needed while only two rare cases show that ∼100 QM atoms are sufficient for convergence when only a single conformation was considered. This explains why most previous studies showed that 500 or more QM atoms are required while a few others showed that ∼100 QM atoms are sufficient for DFT/MM calculations. More importantly, average energy barriers and key structural/charge features from six conformations show an accelerated convergence than that in a single conformation. For instance, to reach energy barrier convergence (within 2.0 kcal mol-1) for step (ii), only ∼100 QM atoms are required if six conformations are considered while 500 or more QM atoms are needed with a single conformation. The convergence is accelerated to be more rapid if hundreds and thousands of conformations were considered, which aligns with previous findings that only several dozens of QM atoms are required for convergence with semi-empirical QM/MM MD simulations.

Efficient automatic construction of atom-economical QM regions with point-charge variation analysis

The setup of QM/MM calculations is not trivial since many decisions have to be made by the simulation scientist to achieve reasonable and consistent results. The main challenge to be tackled is the construction of the QM region to make sure to take into account all important parts of the adjacent environment and exclude less important ones. In our previous work [F. Brandt and Ch. R. Jacob, Systematic QM Region Construction in QM/MM Calculations Based on Uncertainty Quantification, J. Chem. Theory Comput., 2022, 18, 2584-2596.], we introduced the point charge variation analysis (PCVA) as a simple and reliable tool to systematically construct QM regions based on the sensitivity of the reaction energy with respect to variations of the MM point charges. Here, we assess several simplified variants of this PCVA approach for the example of catechol O-methyltransferase and apply PCVA for another system, the triosephosphate isomerase. Furthermore, we extend its scope by applying it to a DNA system. Our results indicate that PCVA offers an efficient and versatile approach of the automatic construction of atom-economical QM regions, but also identify possible pitfalls and limitations.

Catalytic Reaction Mechanism of Glyoxalase II: A Quantum Mechanics/Molecular Mechanics Study

Methylglyoxal (MG) is a reactive and toxic compound produced in carbohydrate, lipid, and amino acid metabolism. The glyoxalase system is the main detoxifying route for MG and consists of two enzymes, glyoxalase I (GlxI) and glyoxalase II (GlxII). GlxI catalyzes the formation of S-d-lactoylglutathione from hemithioacetal, and GlxII converts this intermediate to d-lactate. A relationship between the glyoxalase system and some diseases like diabetes has been shown, and inhibiting enzymes of this system may be an effective means of controlling certain diseases. A detailed understanding of the reaction mechanism of an enzyme is essential to the rational design of competitive inhibitors. In this work, we use quantum mechanics/molecular mechanics (QM/MM) calculations and energy refinement utilizing the big-QM and QM/MM thermodynamic cycle perturbation methods to propose a mechanism for the GlxII reaction that starts with a nucleophilic attack of the bridging OH^- group on the substrate. The coordination of the substrate to the Zn ions places its electrophilic center close to the hydroxide group, enabling the reaction to proceed. Our estimated reaction energies are in excellent agreement with experimental data, thus demonstrating the reliability of our approach and the proposed mechanism. Additionally, we examined alternative protonation states of Asp-29, Asp-58, Asp-134, and the bridging hydroxide ion in the catalytic process. However, these give less favorable reactions, a poorer reproduction of the crystal structure geometry of the active site, and higher root-mean-squared deviations of the active site residues in molecular dynamics simulations.

Fragment-Based Calculations of Enzymatic Thermochemistry Require Dielectric Boundary Conditions

Electronic structure calculations on enzymes require hundreds of atoms to obtain converged results, but fragment-based approximations offer a cost-effective solution. We present calculations on enzyme models containing 500-600 atoms using the many-body expansion, comparing to benchmarks in which the entire enzyme-substrate complex is described at the same level of density functional theory. When the amino acid fragments contain ionic side chains, the many-body expansion oscillates under vacuum boundary conditions but rapid convergence is restored using low-dielectric boundary conditions. This implies that full-system calculations in the gas phase are inappropriate benchmarks for assessing errors in fragment-based approximations. A three-body protocol retains sub-kilocalorie per mole fidelity with respect to a supersystem calculation, as does a two-body calculation combined with a full-system correction at a low-cost level of theory. These protocols pave the way for application of high-level quantum chemistry to large systems via rigorous, ab initio treatment of many-body polarization.

Evaluating the active site-substrate interplay between x-ray crystal structure and molecular dynamics in chorismate mutase

Designing realistic quantum mechanical (QM) models of enzymes is dependent on reliably discerning and modeling residues, solvents, and cofactors important in crafting the active site microenvironment. Interatomic van der Waals contacts have previously demonstrated usefulness toward designing QM-models, but their measured values (and subsequent residue importance rankings) are expected to be influenceable by subtle changes in protein structure. Using chorismate mutase as a case study, this work examines the differences in ligand-residue interatomic contacts between an x-ray crystal structure and structures from a molecular dynamics simulation. Select structures are further analyzed using symmetry adapted perturbation theory to compute ab initio ligand-residue interaction energies. The findings of this study show that ligand-residue interatomic contacts measured for an x-ray crystal structure are not predictive of active site contacts from a sampling of molecular dynamics frames. In addition, the variability in interatomic contacts among structures is not correlated with variability in interaction energies. However, the results spotlight using interaction energies to characterize and rank residue importance in future computational enzymology workflows.

Molecular Mechanism of Substrate Oxidation in Lytic Polysaccharide Monooxygenases: Insight from Theoretical Investigations

Lytic polysaccharide monooxygenases (LPMOs) are copper enzymes that today comprise a large enzyme superfamily, grouped into the distinct members AA9-AA17 (with AA12 exempted). The LPMOs have the potential to facilitate the upcycling of biomass waste products by boosting the breakdown of cellulose and other recalcitrant polysaccharides. The cellulose biopolymer is the main component of biomass waste and thus comprises a large, unexploited resource. The LPMOs work through a catalytic, oxidative reaction whose mechanism is still controversial. For instance, the nature of the intermediate performing the oxidative reaction is an open question, and the same holds for the employed co-substrate. Here we review theoretical investigations addressing these questions. The applied theoretical methods are usually based on quantum mechanics (QM), often combined with molecular mechanics (QM/MM). We discuss advantages and disadvantages of the employed theoretical methods and comment on the interplay between theoretical and experimental results.

Systematic QM Region Construction in QM/MM Calculations Based on Uncertainty Quantification

While QM/MM studies of enzymatic reactions are widely used in computational chemistry, the results of such studies are subject to numerous sources of uncertainty, and the effect of different choices by the simulation scientist that are required when setting up QM/MM calculations is often unclear. In particular, the selection of the QM region is crucial for obtaining accurate and reliable results. Simply including amino acids by their distance to the active site is mostly not sufficient as necessary residues are missing or unimportant residues are included without evidence. Here, we take a first step toward quantifying uncertainties in QM/MM calculations by assessing the sensitivity of QM/MM reaction energies with respect to variations of the MM point charges. We show that such a point charge variation analysis (PCVA) can be employed to judge the accuracy of QM/MM reaction energies obtained with a selected QM region and devise a protocol to systematically construct QM regions that minimize this uncertainty. We apply such a PCVA to the example of catechol O-methyltransferase and demonstrate that it provides a simple and reliable approach for the construction of the QM region. Our PCVA-based scheme is computationally efficient and requires only calculations for a system with a minimal QM region. Our work highlights the promise of applying methods of uncertainty quantification in computational chemistry.

Can water act as a nucleophile in CO oxidation catalysed by Mo/Cu CO-dehydrogenase? Answers from theory

The aerobic CO dehydrogenase from Oligotropha carboxidovorans is an environmentally crucial bacterial enzyme for maintenance of subtoxic concentration of CO in the lower atmosphere, as it allows for the oxidation of CO to CO₂ which takes place at its Mo−Cu heterobimetallic active site. Despite extensive experimental and theoretical efforts, significant uncertainties still concern the reaction mechanism for the CO oxidation. In this work, we used the hybrid quantum mechanical/molecular mechanical approach to evaluate whether a water molecule present in the active site might act as a nucleophile upon formation of the new C−O bond, a hypothesis recently suggested in the literature. Our study shows that activation of H₂O can be favoured by the presence of the Mo=O_eq group. However, overall our results suggest that mechanisms other than the nucleophilic attack by Mo=O_eq to the activated carbon of the CO substrate are not likely to constitute reactive channels for the oxidation of CO by the enzyme.

Predicting Effects of Site-Directed Mutagenesis on Enzyme Kinetics by QM/MM and QM Calculations: A Case of Glutamate Carboxypeptidase II

Quantum and molecular mechanics (QM/MM) and QM-only (cluster model) modeling techniques represent the two workhorses in mechanistic understanding of enzyme catalysis. One of the stringent tests for QM/MM and/or QM approaches is to provide quantitative answers to real-world biochemical questions, such as the effect of single-point mutations on enzyme kinetics. This translates into predicting the relative activation energies to 1-2 kcal·mol^-1 accuracy; such predictions can be used for the rational design of novel enzyme variants with desired/improved characteristics. Herein, we employ glutamate carboxypeptidase II (GCPII), a dizinc metallopeptidase, also known as the prostate specific membrane antigen, as a model system. The structure and activity of this major cancer antigen have been thoroughly studied, both experimentally and computationally, which makes it an ideal model system for method development. Its reaction mechanism is quite well understood: the reaction coordinate comprises a "tetrahedral intermediate" and two transition states and experimental activation Gibbs free energy of ∼17.5 kcal·mol^-1 can be inferred for the known k_cat ≈ 1 s^-1. We correlate experimental kinetic data (including the E424H variant, newly characterized in this work) for various GCPII mutants (k_cat = 8.6 × 10^-5 s^-1 to 2.7 s^-1) with the energy profiles calculated by QM/MM and QM-only (cluster model) approaches. We show that the near-quantitative agreement between the experimental values and the calculated activation energies (ΔH^⧧) can be obtained and recommend the combination of the two protocols: QM/MM optimized structures and cluster model (QM) energetics. The trend in relative activation energies is mostly independent of the QM method (DFT functional) used. Last but not least, a satisfactory correlation between experimental and theoretical data allows us to provide qualitative and fairly simple explanations of the observed kinetic effects which are thus based on a rigorous footing.

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.

Computer-aided understanding and engineering of enzymatic selectivity

Enzymes offering chemo-, regio-, and stereoselectivity enable the asymmetric synthesis of high-value chiral molecules. Unfortunately, the drawback that naturally occurring enzymes are often inefficient or have undesired selectivity toward non-native substrates hinders the broadening of biocatalytic applications. To match the demands of specific selectivity in asymmetric synthesis, biochemists have implemented various computer-aided strategies in understanding and engineering enzymatic selectivity, diversifying the available repository of artificial enzymes. Here, given that the entire asymmetric catalytic cycle, involving precise interactions within the active pocket and substrate transport in the enzyme channel, could affect the enzymatic efficiency and selectivity, we presented a comprehensive overview of the computer-aided workflow for enzymatic selectivity. This review includes a mechanistic understanding of enzymatic selectivity based on quantum mechanical calculations, rational design of enzymatic selectivity guided by enzyme-substrate interactions, and enzymatic selectivity regulation via enzyme channel engineering. Finally, we discussed the computational paradigm for designing enzyme selectivity in silico to facilitate the advancement of asymmetric biosynthesis.

QM/MM Study of the Catalytic Reaction of Myrosinase; Importance of Assigning Proper Protonation States of Active-Site Residues

Myrosinase from Sinapis alba hydrolyzes glycosidic bonds of β-d-S-glucosides. The enzyme shows an enhanced activity in the presence of l-ascorbic acid. In this work, we employed combined quantum mechanical and molecular mechanical (QM/MM) calculations and molecular dynamics simulations to study the catalytic reaction of wild-type myrosinase and its E464A, Q187A, and Q187E mutants. Test calculations show that a proper QM region to study the myrosinase reaction must contain the whole substrate, models of Gln-187, Glu-409, Gln-39, His-141, Asn-186, Tyr-330, Glu-464, Arg-259, and a water molecule. Furthermore, to make the deglycosylation step possible, Arg-259 must be charged, Glu-464 must be protonated on OE2, and His-141 must be protonated on the NE2 atom. The results indicate that assigning proper protonation states of the residues is more important than the size of the model QM system. Our model reproduces the anomeric retaining characteristic of myrosinase and also reproduces the experimental fact that ascorbate increases the rate of the reaction. A water molecule in the active site, positioned by Gln-187, helps the aglycon moiety of the substrate to stabilize the buildup of negative charge during the glycosylation reaction and this in turn makes the moiety a better leaving group. The water molecule also lowers the glycosylation barrier by ∼9 kcal/mol. The results indicate that the Q187E and E464A mutants but not the Q187A mutant can perform the glycosylation step. However, the energy profiles for the deglycosylation step of the mutants are not similar to that of the wild-type enzyme. The Glu-464 residue lowers the barriers of the glycosylation and deglycosylation steps. The ascorbate ion can act as a general base in the reaction of the wild-type enzyme only if the Glu-464 and His-141 residues are properly protonated.

QM/MM study of the binding of H2 to MoCu CO dehydrogenase: development and applications of improved H2 van der Waals parameters

The MoCu CO dehydrogenase enzyme not only transforms CO into CO₂ but it can also oxidise H₂. Even if its hydrogenase activity has been known for decades, a debate is ongoing on the most plausible mode for the binding of H₂ to the enzyme active site and the hydrogen oxidation mechanism. In the present work, we provide a new perspective on the MoCu-CODH hydrogenase activity by improving the in silico description of the enzyme. Energy refinement—by means of the BigQM approach—was performed on the intermediates involved in the dihydrogen oxidation catalysis reported in our previously published work (Rovaletti, et al. “Theoretical Insights into the Aerobic Hydrogenase Activity of Molybdenum–Copper CO Dehydrogenase.” Inorganics 7 (2019) 135). A suboptimal description of the H₂–HN(backbone) interaction was observed when the van der Waals parameters described in previous literature for H₂ were employed. Therefore, a new set of van der Waals parameters is developed here in order to better describe the hydrogen–backbone interaction. They give rise to improved binding modes of H₂ in the active site of MoCu CO dehydrogenase. Implications of the resulting outcomes for a better understanding of hydrogen oxidation catalysis mechanisms are proposed and discussed.

Two-Substrate Glyoxalase I Mechanism: A Quantum Mechanics/Molecular Mechanics Study

Glyoxalase I (GlxI) is an important enzyme that catalyzes the detoxification of methylglyoxal (MG) with the help of glutathione (H-SG). It is currently unclear whether MG and H-SG are substrates of GlxI or whether the enzyme processes hemithioacetal (HTA), which is nonenzymatically formed from MG and H-SG. Most previous studies have concentrated on the latter mechanism. Here, we study the two-substrate reaction mechanism of GlxI from humans (HuGlxI) and corn (ZmGlxI), which are Zn(II)-active and -inactive, respectively. Hybrid quantum mechanics/molecular mechanics calculations were used to obtain geometrical structures of the stationary points along reaction paths, and big quantum mechanical systems with more than 1000 atoms and free-energy perturbations were used to improve the quality of the calculated energies. We studied, on an equal footing, all reasonable reaction paths to the S- and R-enantiomers of HTA from MG and H-SG (the latter was considered in two different binding modes). The results indicate that the MG and H-SG reaction in both enzymes can follow the same path to reach S-HTA. However, the respective overall barriers and reaction energies are different for the two enzymes (6.1 and -9.8 kcal/mol for HuGlxI and 15.7 and -2.2 kcal/mol for ZmGlxI). The first reaction step to produce S-HTA is facilitated by a crystal water molecule that forms hydrogen bonds with a Glu and a Thr residue in the active site. The two enzymes also follow similar paths to R-HTA. However, the reactions reach a deprotonated and protonated R-HTA in the human and corn enzymes, respectively. The production of deprotonated R-HTA in HuGlxI is consistent with other theoretical and experimental works. However, our calculations show a different behavior for ZmGlxI (both S- and R-HTA can be formed in the enzyme with the alcoholic proton on HTA). This implies that Glu-144 of corn GlxI is not basic enough to keep the alcoholic proton. In HuGlxI, the two binding modes of H-SG that lead to S- and R-HTA are degenerate, but the barrier leading to R-HTA is lower than the barrier to S-HTA. On the other hand, ZmGlxI prefers the binding mode, which produces S-HTA; this observation is consistent with experiments. Based on the results, we present a modification for a previously proposed two-substrate reaction mechanism for ZmGlxI.

Successes, challenges, and opportunities for quantum chemistry in understanding metalloenzymes for solar fuels research

Overview of the rich and diverse contributions of quantum chemistry to understanding the structure and function of the biological archetypes for solar fuel research, photosystem II and hydrogenases.

Both Configuration and QM Region Size Matter: Zinc Stability in QM/MM Models of DNA Methyltransferase

Quantum-mechanical/molecular-mechanical (QM/MM) methods are essential to the study of metalloproteins, but the relative importance of sampling and degree of QM treatment in achieving quantitative predictions is poorly understood. We study the relative magnitude of configurational and QM-region sensitivity of energetic and electronic properties in a representative Zn²⁺ metal binding site of a DNA methyltransferase. To quantify property variations, we analyze snapshots extracted from 250 ns of molecular dynamics simulation. To understand the degree of QM-region sensitivity, we perform analysis using QM regions ranging from a minimal 49-atom region consisting only of the Zn²⁺ metal and its four coordinating Cys residues up to a 628-atom QM region that includes residues within 12 Å of the metal center. Over the configurations sampled, we observe that illustrative properties (e.g., rigid Zn²⁺ removal energy) exhibit large fluctuations that are well captured with even minimal QM regions. Nevertheless, for both energetic and electronic properties, we observe a slow approach to asymptotic limits with similarly large changes in absolute values that converge only with larger (ca. 300-atom) QM region sizes. For the smaller QM regions, the electronic description of Zn²⁺ binding is incomplete: the metal binds too tightly and is too stabilized by the strong electrostatic potential of MM point charges, and the Zn-S bond covalency is overestimated. Overall, this work suggests that efficient sampling with QM/MM in small QM regions is an effective method to explore the influence of enzyme structure on target properties. At the same time, accurate descriptions of electronic and energetic properties require a larger QM region than the minimal metal-coordinating residues in order to converge treatment of both metal-local bonding and the overall electrostatic environment.

Quantum Mechanics/Molecular Mechanics Study of the Reaction Mechanism of Glyoxalase I

Glyoxalase I (GlxI) is a member of the glyoxalase system, which is important in cell detoxification and converts hemithioacetals of methylglyoxal (a cytotoxic byproduct of sugar metabolism that may react with DNA or proteins and introduce nucleic acid strand breaks, elevated mutation frequencies, and structural or functional changes of the proteins) and glutathione into d-lactate. GlxI accepts both the S and R enantiomers of hemithioacetal, but converts them to only the S-d enantiomer of lactoylglutathione. Interestingly, the enzyme shows this unusual specificity with a rather symmetric active site (a Zn ion coordinated to two glutamate residues; Glu-99 and Glu-172), making the investigation of its reaction mechanism challenging. Herein, we have performed a series of combined quantum mechanics and molecular mechanics calculations to study the reaction mechanism of GlxI. The substrate can bind to the enzyme in two different modes, depending on the direction of its alcoholic proton (H2; toward Glu-99 or Glu-172). Our results show that the S substrate can react only if H2 is directed toward Glu-99 and the R substrate only if H2 is directed toward Glu-172. In both cases, the reactions lead to the experimentally observed S-d enantiomer of the product. In addition, the results do not show any low-energy paths to the wrong enantiomer of the product from neither the S nor the R substrate. Previous studies have presented several opposing mechanisms for the conversion of R and S enantiomers of the substrate to the correct enantiomer of the product. Our results confirm one of them for the S substrate, but propose a new one for the R substrate.

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.

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.

Reaction Mechanism of [NiFe] Hydrogenase Studied by Computational Methods

[NiFe] hydrogenases catalyze the reversible conversion of molecular hydrogen to protons and electrons. This seemingly simple reaction has attracted much attention because of the prospective use of H₂ as a clean fuel. In this paper, we have studied the full reaction mechanism of this enzyme with various computational methods. Geometries were obtained with combined quantum mechanical and molecular mechanics (QM/MM) calculations. To get more accurate energies and obtain a detailed account of the surroundings, we performed big-QM calculations with 819 atoms in the QM region. Moreover, QM/MM thermodynamic cycle perturbation calculations were performed to obtain free energies. Finally, density matrix renormalisation group complete active space self-consistent field calculations were carried out to study the electronic structures of the various states in the reaction mechanism. Our calculations indicate that the Ni-L state is not involved in the reaction mechanism. Instead, the Ni-C state is reduced by one electron and then the bridging hydride ion is transferred to the sulfur atom of Cys546 as a proton and the two electrons transfer to the Ni ion. This step turned out to be rate-determining with an energy barrier of 58 kJ/mol, which is consistent with the experimental rate of 750 ± 90 s^-1 (corresponding to ∼52 kJ/mol). The cleavage of the H-H bond is facile with an energy barrier of 33 kJ/mol, according to our calculations. We also find that the reaction energies are sensitive to the size of the QM system, the basis set, and the density functional theory method, in agreement with previous studies.

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

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

Large-scale QM/MM free energy simulations of enzyme catalysis reveal the influence of charge transfer

Hybrid quantum mechanical-molecular mechanical (QM/MM) simulations provide key insights into enzyme structure-function relationships. Numerous studies have demonstrated that large QM regions are needed to systematically converge ground state, zero temperature properties with electrostatic embedding QM/MM. However, it is not well known if ab initio QM/MM free energy simulations have this same dependence, in part due to the hundreds of thousands of energy evaluations required for free energy estimations that in turn limit QM region size. Here, we leverage recent advances in electronic structure efficiency and accuracy to carry out range-separated hybrid density functional theory free energy simulations in a representative methyltransferase. By studying 200 ps of ab initio QM/MM dynamics for each of five QM regions from minimal (64 atoms) to one-sixth of the protein (544 atoms), we identify critical differences between large and small QM region QM/MM in charge transfer between substrates and active site residues as well as in geometric structure and dynamics that coincide with differences in predicted free energy barriers. Distinct geometric and electronic structure features in the largest QM region indicate that important aspects of enzymatic rate enhancement in methyltransferases are identified with large-scale electronic structure.

A novel mechanism of heme degradation to biliverdin studied by QM/MM and QM calculations

Heme degradation by heme oxygenase enzymes is important for maintaining iron homeostasis and prevention of oxidative stress.

Jensen HJ, Hedegård ED. Exploration of H2 binding to the [NiFe]-hydrogenase active site with multiconfigurational density functional theory

The combination of density functional theory (DFT) with a multiconfigurational wave function is an efficient way to include dynamical correlation in calculations with multiconfiguration self-consistent field wave functions.

QM/MM Study of the Conversion of Oxophlorin into Verdoheme by Heme Oxygenase

Heme oxygenase is an enzyme that degrades heme, thereby recycling iron in most organisms, including humans. Pervious density functional theory (DFT) calculations have suggested that iron(III) hydroxyheme, an intermediate generated in the first step of heme degradation by heme oxygenase, is converted to iron(III) superoxo oxophlorin in the presence of dioxygen. In this article, we have studied the detailed mechanism of conversion of iron(III) superoxo oxophlorin to verdoheme by using combined quantum mechanics and molecular mechanics (QM/MM) calculations. The calculations employed the B3LYP method and the def2-QZVP basis set, considering dispersion effects with the DFT-D3 approach, obtaining accurate energies with large QM regions of almost 1000 atoms. The reaction was found to be exothermic by -35 kcal/mol, with a rate-determining barrier of 19 kcal/mol in the doublet state. The protein environment and especially water in the enzyme pocket significantly affects the reaction by decreasing the reaction activation energies and changing the structures by providing strategic hydrogen bonds.

Quantum chemical approaches to [NiFe] hydrogenase

The mechanism by which [NiFe] hydrogenase catalyses the oxidation of molecular hydrogen is a significant yet challenging topic in bioinorganic chemistry. With far-reaching applications in renewable energy and carbon mitigation, significant effort has been invested in the study of these complexes. In particular, computational approaches offer a unique perspective on how this enzyme functions at an electronic and atomistic level. In this article, we discuss state-of-the art quantum chemical methods and how they have helped deepen our comprehension of [NiFe] hydrogenase. We outline the key strategies that can be used to compute the (i) geometry, (ii) electronic structure, (iii) thermodynamics and (iv) kinetic properties associated with the enzymatic activity of [NiFe] hydrogenase and other bioinorganic complexes.

Quantum-Chemical Study of the Discrimination against dNTP in the Nucleotide Addition Reaction in the Active Site of RNA Polymerase II

Eukaryotic RNA polymerase II catalyzes the transcription of DNA into mRNA very efficiently and with an extremely low error rate with regard to matching base and sugar moiety. Despite its importance, little is known about how it discriminates against 2'-deoxy NTPs during the chemical reaction. To investigate the differences in the addition reactions of ATP and dATP, we used FF-MD and QM/MM calculations within a nudged elastic band approach, which allowed us to find the energetically accessible reaction coordinates. By converging the QM size, we found that 800 QM atoms are necessary to properly describe the active site. We show how the absence of a single hydrogen bond between the enzyme and the NTP 2'-OH group leads to an increase of the reaction barrier by 16 kcal/mol and therefore conclude that Arg446 is the key residue in the discrimination process.