On the Convergence of QM/MM Energies

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.

The CuB site in particulate methane monooxygenase may be used to produce hydrogen peroxide

Particulate methane monooxygenase (pMMO) is the most efficient of the two groups of enzymes that can hydroxylate methane. The enzyme is membrane bound and therefore hard to study experimentally. For that reason, there is still no consensus regarding the location and nature of the active site. We have used combined quantum mechanical and molecular mechanical (QM/MM) methods to study the reactivity of the CuB site with a histidine brace and two additional histidine ligands. We compare it with the similar active site of lytic polysaccharide monooxygenases. We show that the CuB site can form a reactive [CuO]+ state by the addition of three electrons and two protons, starting from a resting Cu(II) state, with a maximum barrier of 72 kJ mol-1. The [CuO]+ state can abstract a proton from methane, forming a Cu-bound OH- group, which may then recombine with the CH3 group, forming the methanol product. The two steps have barriers of 59 and 52 kJ mol-1, respectively. However, in many of the steps, formation and dissociation of H2O2 or HO2- compete with the formation of the [CuO]+ state and the former steps are typically more favourable. Thus, our calculations indicate that the CuB site is not employed for methane oxidation, but may rather be used for the formation of hydrogen peroxide. This conclusion concurs with recent experimental investigations that excludes the CuB site as the site for methane oxidation.

QM/MM study reveals novel mechanism of KRAS and KRASG12R catalyzed GTP hydrolysis

As a crucial drug target, KRAS can regulate most cellular processes involving guanosine triphosphate (GTP) hydrolysis. However, the mechanism of GTP hydrolysis has remained controversial over the past decades. Here, several different GTP hydrolysis mechanisms catalyzed by wild-type KRAS (WT-KRAS) and KRASG12R mutants were discussed via four QM/MM calculation models. Based on the computational results, a Mg2+-coordinated H2O-mediated GTP hydrolysis mechanism was proposed. In this mechanism, a Mg2+-coordinated H2O first protonates the fully deprotonated GTP, and then the Mg2+ coordinated hydroxyl anion is generated. The Pγ-O bond is formed via the SN2 attack of the second H2O on the Pγ atom of the GTP, leading to the simultaneous cleavage of the Pγ-O bond. Meanwhile, the hydroxyl anion coordinated to Mg2+ and generated in the first step acts as a proton acceptor from water. This Mg2+ coordinated H2O-involved GTP hydrolysis mechanism may also be suitable for Mg2+-catalyzed ATP hydrolysis. Furthermore, the mechanism of GTP hydrolysis catalyzed by the KRASG12R mutant, whose hydrolysis rate was approximately 40-fold slower than WT-KRAS, was also discussed. Our QM/MM calculations reveal that GTP is easily protonated by the residue R12, and the energy barrier of GTP hydrolysis catalyzed by the KRASG12R mutant is lower than the corresponding barrier for WT-KRAS. Nevertheless, molecular dynamics (MD) simulations reveal that R12, a residue characterized by significant steric hindrance, is positioned at the GTP site where the nucleophilic attack by water occurs during Pγ-O bond formation, thereby strongly impeding the approach of water molecules to GTP. As a result, the GTP hydrolysis rate catalyzed by the KRASG12R mutant was severely impaired. Uncovering the GTP hydrolysis mechanism catalyzed by the WT-KRAS and KRASG12R mutant may also give a reasonable explanation for the relationship between the KRASG12R mutation and the occurrence of cancer. We hope this finding will provide useful guidance for drug discovery that targets KRAS.

Investigating the Substrate Oxidation Mechanism in Lytic Polysaccharide Monooxygenase: H2O2- versus O2-Activation

Lytic polysaccharide monooxygenases (LPMOs) form a copper-dependent family of enzymes classified under the auxiliary activity (AA) superfamily. The LPMOs are known for their boosting of polysaccharide degradation through oxidation of the glycosidic bonds that link the monosaccharide subunits. This oxidation has been proposed to be dependent on either O2 or H2O2 as cosubstrate. Theoretical investigations have previously supported both mechanisms, although this contrasts with recent experiments. A possible explanation is that the theoretical results critically depend on how the Cu active site is modeled. This has also led to different results even when employing only H2O2 as cosubstrate. In this paper, we investigate both the O2- and H2O2-driven pathways, employing LsAA9 as the underlying LPMO and a theoretical model based on a quantum mechanics/molecular mechanics (QM/MM) framework. We ensure to consistently include all residues known to be important by using extensive QM regions of up to over 900 atoms. We also investigate several conformers that can partly explain the differences seen in previous studies. We find that the O2-driven reaction is unfeasible, in contrast with our previous QM/MM calculations with smaller QM regions. Meanwhile, the H2O2-driven pathway is feasible, showing that for LsAA9, only H2O2 is a viable cosubstrate as proposed experimentally.

Electrostatically embedded symmetry-adapted perturbation theory

Symmetry-adapted perturbation theory (SAPT) is an ab initio approach that directly computes noncovalent interaction energies in terms of electrostatics, exchange repulsion, induction/polarization, and London dispersion components. Due to its high computational scaling, routine applications of even the lowest order of SAPT are typically limited to a few hundred atoms. To address this limitation, we report here the addition of electrostatic embedding to the SAPT (EE-SAPT) and ISAPT (EE-ISAPT) methods. We illustrate the embedding scheme using water trimer as a prototype example. Then, we show that EE-SAPT/EE-ISAPT can be applied for efficiently and accurately computing noncovalent interactions in large systems, including solvated dimers and protein-ligand systems. In the latter application, particular care must be taken to properly handle the quantum mechanics/molecular mechanics boundary when it cuts covalent bonds. We investigate various schemes for handling charges near this boundary and demonstrate which are most effective in the context of charge-embedded SAPT.

Reaction Mechanism for CO Reduction by Mo-Nitrogenase Studied by QM/MM

We have studied the conversion of two molecules of carbon monoxide to ethylene catalyzed by nitrogenase. We start from a recent crystal structure showing the binding of two carbon monoxide molecules to nitrogenase and employ the combined quantum mechanics and molecular mechanics approach. Our results indicate that the reaction is possible only if S2B dissociates as H2S (i.e., the charge of the FeMo cluster remains the same as in the E0 state, indicating that the Fe ions are formally reduced two steps when CO binds). Eight electrons and protons are needed for the reaction, and our mechanism suggests that the first four bind alternatively to the two carbon atoms. The C-C bond formation takes place already after the first protonation (in the E3 state). The next two protons bind to the same O atom, which then dissociates as water. In the same state (E8), the second C-O bond is cleaved, forming the ethylene product. The last two electrons and protons are used to form a water molecule that can be exchanged by S2B or by two CO molecules to start a new reaction cycle.

Putative reaction mechanism of nitrogenase with a half-dissociated S2B ligand

We have studied whether dissociation of the S2B sulfide ligand from one of its two coordinating Fe ions may affect the later parts of the reaction mechanism of nitrogenase. Such dissociation has been shown to be favourable for the E2-E4 states in the reaction mechanism, but previous studies have assumed that S2B either remains bridging or has fully dissociated from the active-site FeMo cluster. We employ combined quantum mechanical and molecular mechanical (QM/MM) calculations with two density-functional theory methods, r2SCAN and TPSSh. To make dissociation of S2B possible, we have added a proton to this group throughout the reaction. We study the reaction starting from the E4 state with N2H2 bound to the cluster. Our results indicate that half-dissociation of S2B is unfavourable in most steps of the reaction mechanism. We observe favourable half-dissociation of S2B only when NH or NH2 is bound to the cluster, bridging Fe2 and Fe6. However, the former state is most likely not involved in the reaction mechanism and the latter state is only an intermittent intermediate of the E7 state. Therefore, half-dissociation of S2B seems to play only a minor role in the later parts of the reaction mechanism of nitrogenase. Our suggested mechanism with a protonated S2B is alternating (the two N atoms of the substrate is protonated in an alternating manner) and the substrate prefers to bind to Fe2, in contrast to the preferred binding to Fe6 observed when S2B is unprotonated and bridging Fe2 and Fe6.

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.

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.

Relative cooperativity in neutral and charged molecular clusters using QM/MM calculations

QM/MM methods have been used to study electronic structure properties and chemical reactivity in complex molecular systems where direct electronic structure calculations are not feasible. In our previous work, we showed that non-polarizable force fields, by design, describe intermolecular interactions through pairwise interactions, overlooking many-body interactions involving three or more particles. In contrast, polarizable force fields account partially for many-body effects through polarization, but still handle van der Waals and permanent electrostatic interactions pairwise. We showed that despite those limitations, polarizable and non-polarizable force fields can reproduce relative cooperativity achieved using density functional theory due to error compensation mechanisms. In this contribution, we assess the performance of QM/MM methods in reproducing these phenomena. Our study highlights the significance of the QM region size and force field choice in QM/MM calculations, emphasizing the importance of parameter validation to obtain accurate interaction energy predictions.

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.

QM/MM investigation of the discriminatory pre-transfer editing mechanism operated by Lysyl-tRNA synthetase

Aminoacyl-tRNA synthetases (aaRSs) are essential enzymes that remarkable facilitate the aminoacylation process during translation. With a high fidelity, the mischarged tRNA is prevented through implementing pre- and post-transfer proofreading mechanisms. For instance, Lysine-tRNA synthetase charges the native substrate, lysine, to its cognate tRNA. In spite of the great structural similarity between lysine to the noncognate and toxic ornithine, with the side chain of lysine being only one methylene group longer, LysRS is able to achieve this discrimination with a high efficiency. In this work, the hybrid quantum mechanics/molecular mechanics (QM/MM) investigation was applied to probe the pre-transfer editing mechanism catalyzed by lysyl-tRNA synthetase to reject the noncognte aminoacyl, L-ornityl (Orn), compared to the cognate substrate, L-lysyl. Particularly, the self-cyclization pre-transfer editing mechanism was explored for the two substrates. The substrate-assisted self-cyclization editing of Orn-AMP, where its phosphate moiety acts as the catalytic base, is found to be the rate-determining step with an energy barrier of 101.2 kJ mol-1. Meanwhile, the corresponding rate-limiting pathway for the native Lys-AMP lies at 140.2 kJ mol-1. This observation clearly indicated the infeasibility of this catalytic scenario in the presence of the native substrate. Interestingly, a thermodynamically favorable cyclic product of -92.9 kJ mol-1 with respect to the aminoacyl reactant complex demonstrated evidence of a successful pre-transfer editing. This reaction resulted in the discharge of the on-cognate -ornithine derivative from LysU's active site. These valuable mechanistic insights are valuable to enrich our knowledge of this extremely efficient and specific catalytic machinery of LysRS.Communicated by Ramaswamy H. Sarma.

H2 formation from the E2-E4 states of nitrogenase

Nitrogenase is the only enzyme that can cleave the strong triple bond in N2, making nitrogen available for biological lifeforms. The active site is a MoFe7S9C cluster (the FeMo cluster) that binds eight electrons and protons during one catalytic cycle, giving rise to eight intermediate states E0-E7. It is experimentally known that N2 binds to the E4 state and that H2 is a compulsory byproduct of the reaction. However, formation of H2 is also an unproductive side reaction that should be avoided, especially in the early steps of the reaction mechanism (E2 and E3). Here, we study the formation of H2 for various structural interpretations of the E2-E4 states using combined quantum mechanical and molecular mechanical (QM/MM) calculations and four different density-functional theory methods. We find large differences in the predictions of the different methods. B3LYP strongly favours protonation of the central carbide ion and H2 cannot form from such structures. On the other hand, with TPSS, r2SCAN and TPSSh, H2 formation is strongly exothermic for all structures and En and therefore need strict kinetic control to be avoided. For the E2 state, the kinetic barriers for the low-energy structures are high enough to avoid H2 formation. However, for both the E3 and E4 states, all three methods predict that the best structure has two hydride ions bridging the same pair of Fe ions (Fe2 and Fe6) and these two ions can combine to form H2 with an activation barrier of only 29-57 kJ mol-1, corresponding to rates of 7 × 102 to 5 × 107 s-1, i.e. much faster than the turnover rate of the enzyme (1-5 s-1). We have also studied H-atom movements within the FeMo cluster, showing that the various protonation states can quite freely be interconverted (activation barriers of 12-69 kJ mol-1).

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.

Two local minima for structures of [4Fe-4S] clusters obtained with density functional theory methods

[4Fe-4S] clusters are essential cofactors in many proteins involved in biological redox-active processes. Density functional theory (DFT) methods are widely used to study these clusters. Previous investigations have indicated that there exist two local minima for these clusters in proteins. We perform a detailed study of these minima in five proteins and two oxidation states, using combined quantum mechanical and molecular mechanical (QM/MM) methods. We show that one local minimum (L state) has longer Fe-Fe distances than the other (S state), and that the L state is more stable for all cases studied. We also show that some DFT methods may only obtain the L state, while others may obtain both states. Our work provides new insights into the structural diversity and stability of [4Fe-4S] clusters in proteins, and highlights the importance of reliable DFT methods and geometry optimization. We recommend r2SCAN for optimizing [4Fe-4S] clusters in proteins, which gives the most accurate structures for the five proteins studied.

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.

Histidine oxidation in lytic polysaccharide monooxygenase

The lytic polysaccharide monooxygenases (LPMOs) comprise a super-family of copper enzymes that boost the depolymerisation of polysaccharides by oxidatively disrupting the glycosidic bonds connecting the sugar units. Industrial use of LPMOs for cellulose depolymerisation has already begun but is still far from reaching its full potential. One issue is that the LPMOs self-oxidise and thereby deactivate. The mechanism of this self-oxidation is unknown, but histidine residues coordinating to the copper atom are the most susceptible. An unusual methyl modification of the NE2 atom in one of the coordinating histidine residues has been proposed to have a protective role. Furthermore, substrate binding is also known to reduce oxidative damage. We here for the first time investigate the mechanism of histidine oxidation with combined quantum and molecular mechanical (QM/MM) calculations, with outset in intermediates previously shown to form from a reaction with peroxide and a reduced LPMO. We show that an intermediate with a [Cu-O]⁺ moiety is sufficiently potent to oxidise the nearest C-H bond on both histidine residues, but methylation of the NE2 atom of His-1 increases the reaction barrier of this reaction. The substrate further increases the activation barrier. We also investigate a [Cu-OH]²⁺ intermediate with a deprotonated tyrosine radical. This intermediate was previously proposed to have a protective role, and we also find it to have higher barriers than the corresponding a [Cu-O]⁺ intermediate.

Accelerated Quantum Mechanics/Molecular Mechanics Simulations via Neural Networks Incorporated with Mechanical Embedding Scheme

A powerful tool to study the mechanism of reactions in solutions or enzymes is to perform the ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations. However, the computational cost is too high due to the explicit electronic structure calculations at every time step of the simulation. A neural network (NN) method can accelerate the QM/MM-MD simulations, but it has long been a problem to accurately describe the QM/MM electrostatic coupling by NN in the electrostatic embedding (EE) scheme. In this work, we developed a new method to accelerate QM/MM calculations in the mechanic embedding (ME) scheme. The potentials and partial point charges of QM atoms are first learned in vacuo by the embedded atom neural networks (EANN) approach. MD simulations are then performed on this EANN/MM potential energy surface (PES) to obtain free energy (FE) profiles for reactions, in which the QM/MM electrostatic coupling is treated in the mechanic embedding (ME) scheme. Finally, a weighted thermodynamic perturbation (wTP) corrects the FE profiles in the ME scheme to the EE scheme. For two reactions in water and one in methanol, our simulations reproduced the B3LYP/MM free energy profiles within 0.5 kcal/mol with a speed-up of 30-60-fold. The results show that the strategy of combining EANN potential in the ME scheme with the wTP correction is efficient and reliable for chemical reaction simulations in liquid. Another advantage of our method is that the QM PES is independent of the MM subsystem, so it can be applied to various MM environments as demonstrated by an S_N2 reaction studied in water and methanol individually, which used the same EANN PES. The free energy profiles are in excellent accordance with the results obtained from B3LYP/MM-MD simulations. In future, this method will be applied to the reactions of enzymes and their variants.

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.

Quantum Mechanical Calculations of Redox Potentials of the Metal Clusters in Nitrogenase

We have calculated redox potentials of the two metal clusters in Mo-nitrogenase with quantum mechanical (QM) calculations. We employ an approach calibrated for iron-sulfur clusters with 1-4 Fe ions, involving QM-cluster calculations in continuum solvent and large QM systems (400-500 atoms), based on structures from combined QM and molecular mechanics (QM/MM) geometry optimisations. Calculations on the P-cluster show that we can reproduce the experimental redox potentials within 0.33 V. This is similar to the accuracy obtained for the smaller clusters, although two of the redox reactions involve also proton transfer. The calculated P1+/PN redox potential is nearly the same independently of whether P1+ is protonated or deprotonated, explaining why redox titrations do not show any pH dependence. For the FeMo cluster, the calculations clearly show that the formal oxidation state of the cluster in the resting E0 state is MoIIIFe3IIFe4III , in agreement with previous experimental studies and QM calculations. Moreover, the redox potentials of the first five E0-E4 states are nearly constant, as is expected if the electrons are delivered by the same site (the P-cluster). However, the redox potentials are insensitive to the formal oxidation states of the Fe ion (i.e., whether the added protons bind to sulfide or Fe ions). Finally, we show that the later (E4-E8) states of the reaction mechanism have redox potential that are more positive (i.e., more exothermic) than that of the E0/E1 couple.

QM/MM Study of Partial Dissociation of S2B for the E2 Intermediate of Nitrogenase

Nitrogenase is the only enzyme that can cleave the triple bond in N2, making nitrogen available for all lifeforms. Previous computational studies have given widely diverging results regarding the reaction mechanism of the enzyme. For example, some recent studies have suggested that one of the μ2-bridging sulfide ligands (S2B) may dissociate from one of the Fe ions when protonated in the doubly reduced and protonated E2 state, whereas other studies indicated that such half-dissociated states are unfavorable. We have examined how the relative energies of 26 structures of the E2 state depend on details of combined quantum mechanical and molecular mechanical (QM/MM) calculations. We show that the selection of the broken-symmetry state, the basis set, relativistic effects, the size of the QM system, relaxation of the surroundings, and the conformations of the bound protons may affect the relative energies of the various structures by up to 12, 22, 9, 20, 37, and 33 kJ/mol, respectively. However, they do not change the preferred type of structures. On the other hand, the choice of the DFT functional strongly affects the preferences. The hybrid B3LYP functional strongly prefers doubly protonation of the central carbide ion, but such a structure is not consistent with experimental EPR data. Other functionals suggest structures with a hydride ion, in agreement with the experiments, and show that the ion bridges between Fe2 and Fe6. Moreover, there are two structures of the same type that are degenerate within 1-5 kJ/mol, in agreement with the observation of two EPR signals. However, the pure generalized gradient approximation (GGA) functional TPSS favors structures with a protonated S2B also bridging Fe2 and Fe6, whereas r2SCAN (meta-GGA) and TPSSh (hybrid) prefer structures with S2B dissociated from Fe2 (but remaining bound to Fe6). The energy difference between the two types of structure is so small (7-18 kJ/mol) that both types need to be considered in future investigations of the mechanism of nitrogenase.

Improving the Accuracy of Quantum Mechanics/Molecular Mechanics (QM/MM) Models with Polarized Fragment Charges

This paper introduces an economical approach for improving the accuracy and convergence of quantum mechanics/molecular mechanics (QM/MM) models. The approach is tested on a series of neutral and charged amino acids embedded in a 160-water cluster, where their intramolecular proton transfer energies (neutral amino acid → zwitterionic amino acid) were previously obtained at the ωB97X-D/6-31G(d) level of theory. When the charges on the MM atoms were replaced with those obtained at the same QM level of theory used to treat the QM atoms, this significantly improved the accuracy and convergence of the QM/MM models. In particular, the QM/MM model converged to within 1.4 kcal mol^-1 of directly calculated DFT energies for smaller (by as many as 20 waters) QM regions. The use of atomic charges obtained from the natural population analysis yielded the most significant improvement, while other charge schemes such as Mulliken, electrostatic potential, or CM5 led to poorer outcomes. It is further demonstrated that the QM atomic charges can be accurately estimated in a highly efficient manner using an iterative fragmentation approach based on the moving-domain QM/MM method. Similar observations were made when the approach was used to predict the barrier of an S_N2 reaction. Thus, the use of QM-quality atomic charges on MM atoms represents a simple and easy-to-implement strategy for improving the accuracy of QM/MM models.

Influence of the Greater Protein Environment on the Electrostatic Potential in Metalloenzyme Active Sites: The Case of Formate Dehydrogenase

The Mo/W-containing metalloenzyme formate dehydrogenase (FDH) is an efficient and selective natural catalyst that reversibly converts CO₂ to formate under ambient conditions. In this study, we investigate the impact of the greater protein environment on the electrostatic potential (ESP) of the active site. To model the enzyme environment, we used a combination of classical molecular dynamics and multiscale quantum-mechanical (QM)/molecular-mechanical (MM) simulations. We leverage charge shift analysis to systematically construct QM regions and analyze the electronic environment of the active site by evaluating the degree of charge transfer between the core active site and the protein environment. The contribution of the terminal chalcogen ligand to the ESP of the metal center is substantial and dependent on the chalcogen identity, with similar, less negative ESPs for Se and S terminal chalcogens in comparison to O regardless of whether the metal is Mo or W. The orientation of the side chains and conformations of the cofactor also affect the ESP, highlighting the importance of sampling dynamic fluctuations in the protein. Overall, our observations suggest that the terminal chalcogen ligand identity plays an important role in the enzymatic activity of FDH, suggesting opportunities for a rational bioinspired catalyst design.

The catalytic mechanism of the mitochondrial methylenetetrahydrofolate dehydrogenase/cyclohydrolase (MTHFD2)

Methylenetetrahydrofolate dehydrogenase/cyclohydrolase (MTHFD2) is a new drug target that is expressed in cancer cells but not in normal adult cells, which provides an Achilles heel to selectively kill cancer cells. Despite the availability of crystal structures of MTHFD2 in the inhibitor- and cofactor-bound forms, key information is missing due to technical limitations, including (a) the location of absolutely required Mg2+ ion, and (b) the substrate-bound form of MTHFD2. Using computational modeling and simulations, we propose that two magnesium ions are present at the active site whereby (i) Arg233, Asp225, and two water molecules coordinate MgA2+, while MgA2+ together with Arg233 stabilize the inorganic phosphate (Pi); (ii) Asp168 and three water molecules coordinate MgB2+, and MgB2+ further stabilizes Pi by forming a hydrogen bond with two oxygens of Pi; (iii) Arg201 directly coordinates the Pi; and (iv) through three water-mediated interactions, Asp168 contributes to the positioning and stabilization of MgA2+, MgB2+ and Pi. Our computational study at the empirical valence bond level allowed us also to elucidate the detailed reaction mechanisms. We found that the dehydrogenase activity features a proton-coupled electron transfer with charge redistribution connected to the reorganization of the surrounding water molecules which further facilitates the subsequent cyclohydrolase activity. The cyclohydrolase activity then drives the hydration of the imidazoline ring and the ring opening in a concerted way. Furthermore, we have uncovered that two key residues, Ser197/Arg233, are important factors in determining the cofactor (NADP+/NAD+) preference of the dehydrogenase activity. Our work sheds new light on the structural and kinetic framework of MTHFD2, which will be helpful to design small molecule inhibitors that can be used for cancer treatment.

Benchmark Study of Redox Potential Calculations for Iron-Sulfur Clusters in Proteins

Redox potentials have been calculated for 12 different iron–sulfur sites of 6 different types with 1–4 iron ions. Structures were optimized with combined quantum mechanical and molecular mechanical (QM/MM) methods, and the redox potentials were calculated using the QM/MM energies, single-point QM methods in a continuum solvent or by QM/MM thermodynamic cycle perturbations. We show that the best results are obtained with a large QM system (∼300 atoms, but a smaller QM system, ∼150 atoms, can be used for the QM/MM geometry optimization) and a large value of the dielectric constant (80). For absolute redox potentials, the B3LYP density functional method gives better results than TPSS, and the results are improved with a larger basis set. However, for relative redox potentials, the opposite is true. The results are insensitive to the force field (charges of the surroundings) used for the QM/MM calculations or whether the protein and solvent outside the QM system are relaxed or kept fixed at the crystal structure. With the best approach for relative potentials, mean absolute and maximum deviations of 0.17 and 0.44 V, respectively, are obtained after removing a systematic error of −0.55 V. Such an approach can be used to identify the correct oxidation states involved in a certain redox reaction.

We have studied redox potentials of 12 iron−sulfur sites of 6 types with 1−4 iron ions. Structures were optimized with combined quantum mechanical and molecular mechanical (QM/MM) methods, and the redox potentials were calculated with QM/MM, QM calculations in a continuum solvent or by QM/MM thermodynamic cycle perturbations. The best results are obtained with the second approach using ∼300 atoms in the QM model and a large dielectric constant.

Pairing structural reconstruction with catalytic competence to evaluate the mechanisms of key enzymes in the folate-mediated one-carbon pathway

Mammalian metabolism comprises a series of interlinking pathways that include two major cycles: the folate and methionine cycles. The folate-mediated metabolic cycle uses several oxidation states of tetrahydrofolate to carry activated one-carbon units to be readily used and interconverted within the cell. They are required for nucleotide synthesis, methylation and metabolism, and particularly for proliferation of cancer cells. Based on the latest progress in genome-wide CRISPR loss-of-function viability screening of 789 cell lines, we focus on the most cancer-dependent enzymes in this pathway, especially those that are hyperactivated in cancer, to provide new insight into the chemical basis for cancer drug development. Since the complete 3D structure of several of these enzymes of the one-carbon pathway in their active form are not available, we used homology modelling integrated with the interpretation of the reaction mechanism. In addition, have reconstructed the most likely scenario for the reactions taking place paired with their catalytic competence that provides a testable framework for this pathway.

Thermodynamically Favourable States in the Reaction of Nitrogenase without Dissociation of any Sulfide Ligand

We have used combined quantum mechanical and molecular mechanical (QM/MM) calculations to study the reaction mechanism of nitrogenase, assuming that none of the sulfide ligands dissociates. To avoid the problem that there is no consensus regarding the structure and protonation of the E₄ state, we start from a state where N₂ is bound to the cluster and is protonated to N₂H₂, after dissociation of H₂. We show that the reaction follows an alternating mechanism with HNNH (possibly protonated to HNNH₂) and H₂NNH₂ as intermediates and the two NH₃ products dissociate at the E₇ and E₈ levels. For all intermediates, coordination to Fe6 is preferred, but for the E₄ and E₈ intermediates, binding to Fe2 is competitive. For the E₄, E₅ and E₇ intermediates we find that the substrate may abstract a proton from the hydroxy group of the homocitrate ligand of the FeMo cluster, thereby forming HNNH₂, H₂NNH₂ and NH₃ intermediates. This may explain why homocitrate is a mandatory component of nitrogenase. All steps in the suggested reaction mechanism are thermodynamically favourable compared to protonation of the nearby His‐195 group and in all cases, protonation of the NE2 atom of the latter group is preferred.

Factors That Determine the Variation of Equilibrium and Kinetic Properties of QM/MM Enzyme Simulations: QM Region, Conformation, and Boundary Condition

To analyze the impact of various technical details on the results of quantum mechanical (QM)/molecular mechanical (MM) enzyme simulations, including the QM region size, catechol-O-methyltransferase (COMT) is studied as a model system using an approximate QM/MM method (DFTB3/CHARMM). The results show that key equilibrium and kinetic properties for methyl transfer in COMT exhibit limited variations with respect to the size of the QM region, which ranges from ∼100 to ∼500 atoms in this study. With extensive sampling, local and global structural characteristics of the enzyme are largely conserved across the studied QM regions, while the nature of the transition state (e.g., secondary kinetic isotope effect) and reaction exergonicity are largely maintained. Deviations in the free energy profile with different QM region sizes are similar in magnitude to those observed with changes in other simulation protocols, such as different initial enzyme conformations and boundary conditions. Electronic structural properties, such as the covariance matrix of residual charge fluctuations, appear to exhibit rather long-range correlations, especially when the peptide backbone is included in the QM region; this observation holds when a range-separated DFT approach is used as the QM region, suggesting that delocalization error is unlikely the origin. Overall, the analyses suggest that multiple simulation details determine the results of QM/MM enzyme simulations with comparable contributions.

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.

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.

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.

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.

Reaction mechanism of lysyl oxidase-like 2 (LOXL2) studied by computational methods

Lysyl oxidase-like 2 (LOXL2) is a copper-dependent amine oxidase that catalyzes the oxidative deamination of the ε-amino group of lysines/hydroxylysines on substrate proteins (collagen and elastin) to form aldehyde groups. The generated aldehyde groups are of significance in crosslinking with the adjacent aldehyde or ε-amino group on proteins in extracellular matrix. In this paper, we have studied the reaction mechanism of LOXL2 by means of quantum mechanics (QM) and combined QM and molecular mechanics (QM/MM) methods. This study is divided into two parts, i.e. the biosynthesis of lysine tyrosylquinone (LTQ) cofactor and oxidative deamination of ε-amino group of lysine by LTQ. For the former part, the reaction is driven by a large exothermicity of about 284 kJ/mol. Dopaquinone radical (DPQr) is suggested to be an intermediate state in this reaction. In addition, His652 residue is predicted to serve as proton acceptor. The rate-determining step for the biosynthesis of LTQ is found to be hydrogen-atom abstraction from the benzene ring on substrate by Cu²⁺-hydroxide, which is a proton-coupled electron transfer (PCET) process with an energy barrier of 84 kJ/mol. For the latter part, the reaction is exothermic by about 145 kJ/mol, and the copper ion is proposed to play a role of redox catalyst in the last step to generate the product of aldehyde. However, the copper ion might not be indispensable for the latter part, which is consistent with the previous study.

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.

N2H2 binding to the nitrogenase FeMo cluster studied by QM/MM methods

We have made a systematic combined quantum mechanical and molecular mechanical (QM/MM) investigation of possible structures of the N₂ bound state of nitrogenase. We assume that N₂ is immediately protonated to a N₂H₂ state, thereby avoiding the problem of determining the position of the protons in the cluster. We have systematically studied both end-on and side-on structures, as well as both HNNH and NNH₂ states. Our results indicate that the binding of N₂H₂ is determined more by interactions and steric clashes with the surrounding protein than by the intrinsic preferences of the ligand and the cluster. The best binding mode with both the TPSS and B3LYP density-functional theory methods has trans-HNNH terminally bound to Fe2. It is stabilised by stacking of the substrate with His-195 and Ser-278. However, several other structures come rather close in energy (within 3-35 kJ/mol) at least in some calculations: The corresponding cis-HNNH structure terminally bound to Fe2 is second best with B3LYP. A structure with HNNH₂ terminally bound to Fe6 is second most stable with TPSS (where the third proton is transferred to the substrate from the homocitrate ligand). Structures with trans-HNNH, bound to Fe4 or Fe6, or cis-HNNH bound to Fe6 are also rather stable. Finally, with the TPSS functional, a structure with cis-HNNH side-on binding to the Fe3-Fe4-Fe5-Fe7 face of the cluster is also rather low in energy, but all side-on structures are strongly disfavoured by the B3LYP method.

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.

What Is the Structure of the E4 Intermediate in Nitrogenase?

Nitrogenase is the only enzyme that can cleave the strong triple bond in N₂. The active site contains a complicated MoFe₇S₉C cluster. It is believed that it needs to accept four protons and electrons, forming the E₄ state, before it can bind N₂. However, there is no consensus on the atomic structure of the E₄ state. Experimental studies indicate that it should contain two hydride ions bridging two pairs of Fe ions, and it has been suggested that both hydride ions as well as the two protons bind on the same face of the cluster. On the other hand, density functional theory (DFT) studies have indicated that it is energetically more favorable with either three hydride ions or with a triply protonated carbide ion, depending on the DFT functional. We have performed a systematic combined quantum mechanical and molecular mechanical (QM/MM) study of possible E₄ states with two bridging hydride ions. Our calculations suggest that the most favorable structure has hydride ions bridging the Fe2/6 and Fe3/7 ion pairs. In fact, such structures are 14 kJ/mol more stable than structures with three hydride ions, showing that pure DFT functionals give energetically most favorable structures in agreement with experiments. An important reason for this finding is that we have identified a new type of broken-symmetry state that involves only two Fe ions with minority spin, in contrast to the previously studied states with three Fe ions with minority spin. The energetically best structures have the two hydride ions on different faces of the FeMo cluster, whereas better agreement with ENDOR data is obtained if they are on the same face; such structures are only 6–22 kJ/mol less stable.

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.

Ewald-based methods for Gaussian integral evaluation: application to a new parameterization of GEM

The development of accurate potentials for computational simulations has been an active area of research. Our group has been involved in the development of the Gaussian electrostatic model (GEM), a force field based on molecular densities. The philosophy of GEM is based on the pioneering work of N. Gresh and co-workers of the reproduction of individual inter-molecular interaction components obtained from quantum mechanical (QM) energy decomposition analysis (EDA). The molecular densities used in GEM are represented by fitting accurate QM molecular densities using auxiliary basis sets (comprised of Hermite Gaussians). The use of these molecular densities results in the need to evaluate a large number of Gaussian integrals. We have previously shown that the particle-mesh Ewald (PME), and fast Fourier Poisson (FFP) methods can be used for efficiently evaluating these types of integrals. Here, we present the latest parameterization of GEM* and its application for an extensive study of PME and FFP for molecular dynamics (MD) simulations using a hybrid version of our potential, GEM*. The temperature dependence of various bulk properties is presented and discussed, as well as the effect of various parameters affecting the performance/accuracy of both methods.

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.