Convergence in the QM-only and QM/MM modeling of enzymatic reactions: A case study for acetylene hydratase

Exploring the Reaction Mechanism of Polyethylene Terephthalate Biodegradation through QM/MM Approach

The enzyme PETase fromIdeonella sakaiensis (IsPETase) strain 201-F6 can catalyze the hydrolysis of polyethylene terephthalate (PET), mainly converting it into mono(2-hydroxyethyl) terephthalic acid (MHET). In this study, we used quantum mechanics/molecular mechanics (QM/MM) simulations to explore the molecular details of the catalytic reaction mechanism of IsPETase in the formation of MHET. The QM region was described with AM1d/PhoT and M06-2X/6-31+G(d,p) potential. QM/MM simulations unveil the complete enzymatic PET hydrolysis mechanism and identify two possible reaction pathways for acylation and deacylation steps. The barrier obtained at M06-2X/6-31+G(d,p)/MM potential for the deacylation step corresponds to 20.4 kcal/mol, aligning with the experimental value of 18 kcal/mol. Our findings indicate that deacylation is the rate-limiting step of the process. Furthermore, per-residue interaction energy contributions revealed unfavorable contributions to the transition state of amino acids located at positions 200-230, suggesting potential sites for targeted mutations. These results can contribute to the development of more active and selective enzymes for PET depolymerization.

The Effect of Selenium-Based Ligands on Tungsten Acetylene Complexes

Bioinspired tungsten acetylene complexes containing pyridine-2-selenolato (PySe) or 6-methyl-pyridine-2-selenolato (6-MePySe) ligands were synthesized. 77Se NMR spectroscopy allowed for an assessment of the resonance structures in the pyridine-2-selenolato ligands and the rationalization of chemoselectivity observed in regard to 1,2 migratory insertion of HC≡CH. [W(CO)(C2H2)(CHCH-PySe)(PySe)] is formed exclusively via insertion of HC≡CH into the W-N bond, while the use of bulkier 6-MePySe allows for the isolation of [W(CO)(C2H2)(6-MePySe)2], which only partially reacts with excess HC≡CH to give [W(CO)(C2H2)(CHCH-6-MePySe)(6-MePySe)]. Oxidation of [W(CO)(C2H2)(6-MePySe)2] with pyridine-N-oxide gave the tungsten(IV) complex [WO(C2H2)(6-MePySe)2]. Complexes [W(CO)(C2H2)(6-MePySe)2] and [WO(C2H2)(6-MePySe)2] react with trimethyl phosphine to carbyne complex [W(CO)(CCH2PMe3)(PMe3)2(6-MePySe)]Cl and alkylidene complex [WO(CHCHPMe3)(PMe3)2(6-MePySe)]Cl, respectively. The addition of substituted alkynes to [W(CO)3(PySe)2] via thermal decarbonylation gave complexes [W(CO)(MeC≡CMe)(PySe)2] and [W(CO)(HC≡Ct-Bu)(PySe)2], respectively. The here presented complexes are relevant for the modeling of the active site of acetylene hydratase from Pelobacter acetylenicus, in which a tungsten atom is enclosed in a sulfur-rich coordination sphere. A recently published theoretical study concluded that the exchange of sulfur for selenium would increase the activity of the enzyme. Our findings contrast this claim as comparative analysis concludes negligible structural and electronic differences between the selenium-based and previously published sulfur-based complexes.

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.

Cysteine Radical and Glutamate Collaboratively Enable C-H Bond Activation and C-N Bond Cleavage in a Glycyl Radical Enzyme HplG

Hydroxyprolines are abundant in nature and widely utilized by many living organisms. Isomerization of trans-4-hydroxy-d-proline (t4D-HP) to generate 2-amino-4-ketopentanoate has been found to need a glycyl radical enzyme HplG, which catalyzes the cleavage of the C-N bond, while dehydration of trans-4-hydroxy-l-proline involves a homologous enzyme of HplG. Herein, molecular dynamics simulations and quantum mechanics/molecular mechanics (QM/MM) calculations are employed to understand the reaction mechanism of HplG. Two possible reaction pathways of HplG have been explored to decipher the origin of its chemoselectivity. The QM/MM calculations reveal that the isomerization proceeds via an initial hydrogen shift from the Cγ site of t4D-HP to a catalytic cysteine radical, followed by cleavage of the Cδ-N bond in t4D-HP to form a radical intermediate that captures a hydrogen atom from the cysteine. Activation of the Cδ-H bond in t4D-HP to bring about dehydration of t4D-HP possesses an extremely high energy barrier, thus rendering the dehydration pathway implausible in HplG. On the basis of the current calculations, conserved residue Glu429 plays a pivotal role in the isomerization pathway: the hydrogen bonding between it and t4D-HP weakens the hydroxyalkyl Cγ-Hγ bond, and it acts as a proton acceptor to trigger the cleavage of the C-N bond in t4D-HP. Our current QM/MM calculations rationalize the origin of the experimentally observed chemoselectivity of HplG and propose an H-bond-assisted bond activation strategy in radical-containing enzymes. These findings have general implications on radical-mediated enzymatic catalysis and expand our understanding of how nature wisely and selectively activates the C-H bond to modulate catalytic selectivity.

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.

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.

Perspective: Reference-Potential Methods for the Study of Thermodynamic Properties in Chemical Processes: Theory, Applications, and Pitfalls

In silico investigations of enzymatic reactions and chemical reactions in condensed phases often suffer from formidable computational costs due to a large number of degrees of freedom and enormous important volume in phase space. Usually, accuracy must be compromised to trade for efficiency by lowering the reliability of the Hamiltonians employed or reducing the sampling time. Reference-potential methods (RPMs) offer an alternative approach to reaching high accuracy of simulation without much loss of efficiency. In this Perspective, we summarize the idea of RPMs and showcase some recent applications. Most importantly, the pitfalls of these methods are also discussed, and remedies to these pitfalls are presented.

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.

Dioxygen Activation by a Bioinspired Tungsten(IV) Complex

An increasing number of discovered tungstoenzymes raises interest in the biomimetic chemistry of tungsten complexes in oxidation states +IV, +V, and +VI. Bioinspired (sulfur-rich) tungsten(VI) dioxido complexes are relatively prevalent in literature. Still, their energetically demanding reduction directly correlates with a small number of known tungsten(IV) oxido complexes, whose chemistry is not well explored. In this paper, a reduction of the [WO₂(6-MePyS)₂] (6-MePyS = 6-methylpyridine-2-thiolate) complex with PMe₃ to a phosphine-stabilized tungsten(IV) oxido complex [WO(6-MePyS)₂(PMe₃)₂] is described. This tungsten(IV) complex partially releases one PMe₃ ligand in solution, creating a vacant coordination site capable of activating dioxygen to form [WO₂(6-MePyS)₂] and OPMe₃. Therefore, [WO₂(6-MePyS)₂] can be used as a catalyst for the aerobic oxidation of PMe₃, rendering this complex a rare example of a tungsten system utilizing dioxygen in homogeneous catalysis. Additionally, the investigation of the reactivity of the tungsten(IV) oxido complex with acetylene, substrate of a tungstoenzyme acetylene hydratase (AH), revealed the formation of the tungsten(IV) acetylene adduct. Although this adduct was previously reported as an oxidation product of the tungsten(II) acetylene carbonyl complex, here it is obtained via substitution at the sulfur-rich tungsten(IV) center, mimicking the initial step of the first shell mechanism for AH as suggested by computational studies.

QM Calculations Revealed that Outer-Sphere Electron Transfer Boosted O-O Bond Cleavage in the Multiheme-Dependent Cytochrome bd Oxygen Reductase

The cytochrome bd oxygen reductase catalyzes the four-electron reduction of dioxygen to two water molecules. The structure of this enzyme reveals three heme molecules in the active site, which differs from that of heme-copper cytochrome c oxidase. The quantum chemical cluster approach was used to uncover the reaction mechanism of this intriguing metalloenzyme. The calculations suggested that a proton-coupled electron transfer reduction occurs first to generate a ferrous heme b₅₉₅. This is followed by the dioxygen binding at the heme d center coupled with an outer-sphere electron transfer from the ferrous heme b₅₉₅ to the dioxygen moiety, affording a ferric ion superoxide intermediate. A second proton-coupled electron transfer produces a heme d ferric hydroperoxide, which undergoes efficient O-O bond cleavage facilitated by an outer-sphere electron transfer from the ferrous heme b₅₉₅ to the O-O σ* orbital and an inner-sphere proton transfer from the heme d hydroxyl group to the leaving hydroxide. The synergistic benefits of the two types of hemes rationalize the highly efficient oxygen reduction repertoire for the multi-heme-dependent cytochrome bd oxygen reductase family.

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.

Challenges in Protein QM/MM Simulations with Intra-Backbone Link Atoms

Hybrid quantum mechanical/molecular mechanical (QM/MM) simulations fuel discoveries in many fields of science including computational biochemistry and enzymology. Development of more convenient tools leads to an increase in the number of works in which mechanical insights into enzymes' mode of operation are obtained. Most commonly, these tools feature hydrogen-capping (link atom) approach to provide coupling between QM and MM subsystems across a covalent bond. Extensive studies were conducted to provide a solid foundation for the correctness of such an approach when a bond to a nonpolar MM atom is considered. However, not every task may be accomplished this way. Certain scenarios of using QM/MM in computational enzymology encourage or even necessitate the incorporation of backbone atoms into the QM region. Two out of three backbone atoms are polar, and in QM/MM with electrostatic embedding, a neighboring link atom will be hyperpolarized. Several schemes to mitigate this effect were previously proposed alongside a rigorous assessment of quantitative effects on model systems. However, it was not clear whether they may translate into qualitatively different results and how link atom hyperpolarization may manifest itself in a real-life enzymological scenario. Here, we show that the consequences of such an artifact may be severe and may completely overturn the conclusions drawn from the simulations. Our case advocates for the use of charge redistribution schemes whenever intra-backbone QM/MM boundaries are considered. Moreover, we addressed how different boundary types and charge redistribution schemes influence backbone dynamics. We showed that the results are heavily dependent on which boundary MM terms are retained, with charge alteration being of secondary importance. In the worst case, only three intra-backbone boundaries may be used with relative confidence in the adequacy of resulting simulations, irrespective of the hyperpolarization mitigation scheme. Thus, advances in the field are certainly needed to fuel new discoveries. As of now, we believe that issues raised in this work might encourage authors in the field to report what boundaries, boundary MM terms, and charge redistribution schemes they are using, so their results may be correctly interpreted.

Effect of the QM Size, Basis Set, and Polarization on QM/MM Interaction Energy Decomposition Analysis

Herein, an Energy Decomposition Analysis (EDA) scheme extended to the framework of QM/MM calculations in the context of electrostatic embeddings (QM/MM-EDA) including atomic charges and dipoles is applied to assess the effect of the QM region size on the convergence of the different interaction energy components, namely, electrostatic, Pauli, and polarization, for cationic, anionic, and neutral systems interacting with a strong polar environment (water). Significant improvements are found when the bulk solvent environment is described by a MM potential in the EDA scheme as compared to pure QM calculations that neglect bulk solvation. The predominant electrostatic interaction requires sizable QM regions. The results reported here show that it is necessary to include a surprisingly large number of water molecules in the QM region to obtain converged values for this energy term, contrary to most cluster models often employed in the literature. Both the improvement of the QM wave function by means of a larger basis set and the introduction of polarization into the MM region through a polarizable force field do not translate to a faster convergence with the QM region size, but they lead to better results for the different interaction energy components. The results obtained in this work provide insight into the effect of each energy component on the convergence of the solute-solvent interaction energy with the QM region size. This information can be used to improve the MM FFs and embedding schemes employed in QM/MM calculations of solvated systems.

Convergence in determining enzyme functional descriptors across Kemp eliminase variants

Molecular simulations have been extensively employed to accelerate biocatalytic discoveries. Enzyme functional descriptors derived from molecular simulations have been leveraged to guide the search for beneficial enzyme mutants. However, the ideal active-site region size for computing the descriptors over multiple enzyme variants remains untested. Here, we conducted convergence tests for dynamics-derived and electrostatic descriptors on 18 Kemp eliminase variants across six active-site regions with various boundary distances to the substrate. The tested descriptors include the root-mean-square deviation of the active-site region, the solvent accessible surface area ratio between the substrate and active site, and the projection of the electric field (EF) on the breaking C-H bond. All descriptors were evaluated using molecular mechanics methods. To understand the effects of electronic structure, the EF was also evaluated using quantum mechanics/molecular mechanics methods. The descriptor values were computed for 18 Kemp eliminase variants. Spearman correlation matrices were used to determine the region size condition under which further expansion of the region boundary does not substantially change the ranking of descriptor values. We observed that protein dynamics-derived descriptors, including RMSD_{active_site} and SASA_ratio, converge at a distance cutoff of 5 Å from the substrate. The electrostatic descriptor, EF_C-H, converges at 6 Å using molecular mechanics methods with truncated enzyme models and 4 Å using quantum mechanics/molecular mechanics methods with whole enzyme model. This study serves as a future reference to determine descriptors for predictive modeling of enzyme engineering.

Assessment of Reversibility for Covalent Cysteine Protease Inhibitors Using Quantum Mechanics/Molecular Mechanics Free Energy Surfaces

We have used molecular dynamics (MD) simulations with hybrid quantum mechanics/molecular mechanics (QM/MM) potentials to investigate the reaction mechanism for covalent inhibition of cathepsin K and assess the reversibility of inhibition. The computed free energy profiles suggest that a nucleophilic attack by the catalytic cysteine on the inhibitor warhead and proton transfer from the catalytic histidine occur in a concerted manner. The results indicate that the reaction is more strongly exergonic for the alkyne-based inhibitors, which bind irreversibly to cathepsin K, than for the nitrile-based inhibitor odanacatib, which binds reversibly. Gas-phase energies were also calculated for the addition of methanethiol to structural prototypes for a number of warheads of interest in cysteine protease inhibitor design in order to assess electrophilicity. The approaches presented in this study are particularly applicable to assessment of novel warheads, and computed transition state geometries can be incorporated into molecular models for covalent docking.

Enhanced-Sampling Simulations for the Estimation of Ligand Binding Kinetics: Current Status and Perspective

The dissociation rate (k off) associated with ligand unbinding events from proteins is a parameter of fundamental importance in drug design. Here we review recent major advancements in molecular simulation methodologies for the prediction of k off. Next, we discuss the impact of the potential energy function models on the accuracy of calculated k off values. Finally, we provide a perspective from high-performance computing and machine learning which might help improve such predictions.

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.

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.

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.

The Effect of Pyridine-2-thiolate Ligands on the Reactivity of Tungsten Complexes toward Oxidation and Acetylene Insertion

Intending to deepen our understanding of tungsten acetylene (C₂H₂) chemistry, with regard to the tungstoenzyme acetylene hydratase, here we explore the structure and reactivity of a series of tungsten acetylene complexes, stabilized with pyridine-2-thiolate ligands featuring tungsten in both +II and +IV oxidation states. By varying the substitution of the pyridine-2-thiolate moiety with respect to steric and electronic properties, we examined the details and limits of the previously reported intramolecular nucleophilic attack on acetylene followed by the formation of acetylene inserted complexes. Here, we demonstrate that only the combination of high steric demand and electron-withdrawing features prevents acetylene insertion. Nevertheless, although variable synthetic approaches are necessary for their synthesis, tungsten acetylene complexes can be stabilized predictably with a variety of pyridine-2-thiolate ligands.

Probing the Suitability of Different Ca2+ Parameters for Long Simulations of Diisopropyl Fluorophosphatase

Organophosphate hydrolases are promising as potential biotherapeutic agents to treat poisoning with pesticides or nerve gases. However, these enzymes often need to be further engineered in order to become useful in practice. One example of such enhancement is the alteration of enantioselectivity of diisopropyl fluorophosphatase (DFPase). Molecular modeling techniques offer a unique opportunity to address this task rationally by providing a physical description of the substrate-binding process. However, DFPase is a metalloenzyme, and correct modeling of metal cations is a challenging task generally coming with a tradeoff between simulation speed and accuracy. Here, we probe several molecular mechanical parameter combinations for their ability to empower long simulations needed to achieve a quantitative description of substrate binding. We demonstrate that a combination of the Amber19sb force field with the recently developed 12-6 Ca2+ models allows us to both correctly model DFPase and obtain new insights into the DFP binding process.

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

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

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.

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

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

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.

Soft Scorpionate Hydridotris(2-mercapto-1-methylimidazolyl) borate) Tungsten-Oxido and -Sulfido Complexes as Acetylene Hydratase Models

A series of WIV alkyne complexes with the sulfur-rich ligand hydridotris(2-mercapto-1-methylimidazolyl) borate) (TmMe ) are presented as bio-inspired models to elucidate the mechanism of the tungstoenzyme acetylene hydratase (AH). The mono- and/or bis-alkyne precursors were reacted with NaTmMe and the resulting complexes [W(CO)(C2 R2 )(TmMe )Br] (R=H 1, Me 2) oxidized to the target [WE(C2 R2 )(TmMe )Br] (E=O, R=H 4, Me 5; E=S, R=H 6, Me 7) using pyridine-N-oxide and methylthiirane. Halide abstraction with TlOTf in MeCN gave the cationic complexes [WE(C2 R2 )(MeCN)(TmMe )](OTf) (E=CO, R=H 10, Me 11; E=O, R=H 12, Me 13; E=S, R=H 14, Me 15). Without MeCN, dinuclear complexes [W2 O(μ-O)(C2 Me2 )2 (TmMe )2 ](OTf)2 (8) and [W2 (μ-S)2 (C2 Me2 )(TmMe )2 ](OTf)2 (9) could be isolated showing distinct differences between the oxido and sulfido system with the latter exhibiting only one molecule of C2 Me2 . This provides evidence that a fine balance of the softness at W is important for acetylene coordination. Upon dissolving complex 8 in acetonitrile complex 13 is reconstituted in contrast to 9. All complexes exhibit the desired stability toward water and the observed effective coordination of the scorpionate ligand avoids decomposition to disulfide, an often-occurring reaction in sulfur ligand chemistry. Hence, the data presented here point toward a mechanism with a direct coordination of acetylene in the active site and provide the basis for further model chemistry for acetylene hydratase.

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.

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

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

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

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

Theoretical Studies of Nickel-Dependent Enzymes

The advancements of quantum chemical methods and computer power allow detailed mechanistic investigations of metalloenzymes. In particular, both quantum chemical cluster and combined QM/MM approaches have been used, which have been proven to successfully complement experimental studies. This review starts with a brief introduction of nickel-dependent enzymes and then summarizes theoretical studies on the reaction mechanisms of these enzymes, including NiFe hydrogenase, methyl-coenzyme M reductase, nickel CO dehydrogenase, acetyl CoA synthase, acireductone dioxygenase, quercetin 2,4-dioxygenase, urease, lactate racemase, and superoxide dismutase.

QM/MM Study of the Uracil DNA Glycosylase Reaction Mechanism: A Competition between Asp145 and His148

Uracil DNA glycosylase catalyzes the N-glycosidic bond cleavage of uracil, thereby initiating the base excision repair mechanism for this DNA lesion. Here we employ hybrid quantum mechanics/molecular mechanics calculations to investigate the exact mechanism of the nucleophile attack and the role of the conserved His148 residue. Our calculations suggest that the C1'-N1 bond dissociation proceeds by a migration of the electrophilic sugar in the direction of the water nucleophile, resulting in a planar, oxocarbenium-like transition state. The subsequent nucleophile addition and proton transfer to a nearby base occur without a barrier. We assign the role of a proton acceptor to His148 and elucidate why mutations of this residue curtail the enzymatic activity but do not fully suppress it.

A benchmark for the size of the QM system required for accurate hybrid QM/MM calculations on the metal site of the protein copper, zinc superoxide dismutase

The protein superoxide dismutase 1 (SOD1) is a copper and zinc-binding protein that has been implicated in the pathogenesis of amyotrophic lateral sclerosis (ALS). The Zn(II) binding to SOD1 is critical for the stability of the protein, and has been by itself implicated in ALS pathogenesis. Hence, the quantum mechanical (QM) study of the Zn(II)-site of SOD1 is relevant for understanding ALS. The hybrid QM-molecular mechanics (QM/MM) approach commonly employed for the QM study of proteins is highly dependent on the size of the sub-system treated quantum-mechanically. The size of the QM system also determines the computational feasibility of a given method. In the present work, we compare optimized geometries for the metal site and Zn(II) dissociation energies obtained with a QM/MM methodology employing different sizes for the QM sub-system. We find that geometries converge rapidly to RMSDs of around 0.3 Å, and fails to converge further, while a QM system of 480 atoms was required for converging the Zn(II) interaction energy of SOD1 to within 5 kcal*mol^-1, and a 611-atoms QM system for a 1 kcal*mol^-1 convergence with respect to our reference, 1280 QM-atoms system. Graphical Abstract The size of the QM system is critical for both the accuracy and the computational cost of a QM/MM calculation. We have identified a optimum balance for the study of the active site of the coppper, zinc superoxide dismutase.

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

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

Activation and Photoinduced Release of Alkynes on a Biomimetic Tungsten Center: The Photochemical Behavior of the W-S-Phoz System

The synthesis and structural determination of four tungsten alkyne complexes coordinated by the bio-inspired S,N-donor ligand 2-(4',4'-dimethyloxazoline-2'-yl)thiophenolate (S-Phoz) is presented. A previously established protocol that involved the reaction of the respective alkyne with the bis-carbonyl precursor [W(CO)2 (S-Phoz)2 ] was used for the complexes [W(CO)(C2 R2 )(S-Phoz)2 ] (R=H, 1 a; Me, 1 b; Ph, 1 c). Oxidation with pyridine-N-oxide gave the corresponding W-oxo species [WO(C2 R2 )(S-Phoz)2 ] (R=H, 2 a; Me, 2 b; Ph, 2 c). All W-oxo-alkyne complexes (2 a, b, c) were found to be capable of alkyne release upon light irradiation to afford five-coordinate [WO(S-Phoz)2 ] (3). The photoinduced release of the alkyne ligand was studied in detail by in situ 1 H NMR measurements, which revealed correlation of the photodissociation rate constant (2 b>2 a>2 c) with the elongation of the alkyne C≡C bond in the molecular structures. Oxidation of [WO(S-Phoz)2 ] (3) with pyridine-N-oxide yielded [WO2 (S-Phoz)2 ] (4), which shows highly fluxional behavior in solution. Variable-temperature 1 H NMR spectroscopy revealed three isomeric forms with respect to the ligand arrangement versus each other. Furthermore, compound 4 rearranges to tetranuclear oxo compound [W4 O4 (μ-O)6 (S-Phoz)4 ] (5) and dinuclear [{WO(μ-O)(S-Phoz)}2 ] (6) over time. The latter two were identified by single-crystal X-ray diffraction analyses.

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.

Computational Understanding of the Selectivities in Metalloenzymes

Metalloenzymes catalyze many different types of biological reactions with high efficiency and remarkable selectivity. The quantum chemical cluster approach and the combined quantum mechanics/molecular mechanics methods have proven very successful in the elucidation of the reaction mechanism and rationalization of selectivities in enzymes. In this review, recent progress in the computational understanding of various selectivities including chemoselectivity, regioselectivity, and stereoselectivity, in metalloenzymes, is discussed.

Do Better Quality Embedding Potentials Accelerate the Convergence of QM/MM Models? The Case of Solvated Acid Clusters

This study examines whether the use of more accurate embedding potentials improves the convergence of quantum mechanics/molecular mechanics (QM/MM) models with respect to the size of the QM region. In conjunction with density functional theory calculations using the ωB97X-D functional, various embedding potentials including the TIP3P water model, the effective fragment potential (EFP), and semi-empirical methods (PM6, PM7, and DFTB) were used to simulate the deprotonation energies of solvated acid clusters. The calculations were performed on solvated neutral (HA) and cationic (HB⁺) acids clusters containing 160 and 480 water molecules using configurations sampled from molecular dynamics simulations. Consistently, the ωB97X-D/EFP model performed the best when using a minimal QM region size. The performance for the other potentials appears to be highly sensitive to the charge character of the acid/base pair. Neutral acids display the expected trend that semi-empirical methods generally perform better than TIP3P; however, an opposite trend was observed for the cationic acids. Additionally, electronic embedding provided an improvement over mechanical embedding for the cationic systems, but not the neutral acids. For the best performing ωB97X-D/EFP model, a QM region containing about 6% of the total number of solvent molecules is needed to approach within 10 kJ mol^-1 of the pure QM result if the QM region was chosen based on the distance from the reaction centre.

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.