Accurate QM/MM Free Energy Calculations of Enzyme Reactions: Methylation by CatecholO-Methyltransferase

Convergence criteria for single-step free-energy calculations: the relation between the Π bias measure and the sample variance

Free energy calculations play a crucial role in simulating chemical processes, enzymatic reactions, and drug design. However, assessing the reliability and convergence of these calculations remains a challenge. This study focuses on single-step free-energy calculations using thermodynamic perturbation. It explores how the sample distributions influence the estimated results and evaluates the reliability of various convergence criteria, including Kofke's bias measure Π and the standard deviation of the energy difference ΔU, σ ΔU . The findings reveal that for Gaussian distributions, there is a straightforward relationship between Π and σ ΔU , free energies can be accurately approximated using a second-order cumulant expansion, and reliable results are attainable for σ ΔU up to 25 kcal mol-1. However, interpreting non-Gaussian distributions is more complex. If the distribution is skewed towards more positive values than a Gaussian, converging the free energy becomes easier, rendering standard convergence criteria overly stringent. Conversely, distributions that are skewed towards more negative values than a Gaussian present greater challenges in achieving convergence, making standard criteria unreliable. We propose a practical approach to assess the convergence of estimated free energies.

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.

The Glycine N-Methyltransferase Case Study: Another Challenge for QM-Cluster Models?

The methyl transfer reaction between SAM and glycine catalyzed by glycine N-methyltransferase (GNMT) was examined using QM-cluster models generated by Residue Interaction Network ResidUe Selector (RINRUS). RINRUS is a Python-based tool that can build QM-cluster models with rules-based processing of the active site residue interaction network. This way of enzyme model-building allows quantitative analysis of residue and fragment contributions to kinetic and thermodynamic properties of the enzyme. Many residue fragments are important for the GNMT catalytic reaction, such as Gly137, Asn138, and Arg175, which interact with the glycine substrate, and Trp30, Asp85, and Tyr242, which interact with the SAM cofactor. Our study shows that active site fragments that interact with the glycine substrate and the SAM cofactor must both be included in the QM-cluster models. Even though the proposed mechanism is a simple one-step reaction, GNMT may be a rather challenging case study for QM-cluster models because convergence in energetics requires models with >350 atoms. "Maximal" QM-cluster models built with either qualitative contact count ranking or quantitative interaction energies from functional group symmetry adapted perturbation theory provide acceptable results. Hence, important residue fragments that contribute to the energetics of the methyl-transfer reaction in GNMT are correctly identified in the RIN. Observations from this work suggest new directions to better establish an effective approach for constructing atomic-level enzyme models.

High-throughput computational investigation of protein electrostatics and cavity for SAM-dependent methyltransferases

S-adenosyl methionine (SAM)-dependent methyl transferases (MTases) are a ubiquitous class of enzymes catalyzing dozens of essential life processes. Despite targeting a large space of substrates with diverse intrinsic reactivity, SAM MTases have similar catalytic efficiency. While understanding of MTase mechanism has grown tremendously through the integration of structural characterization, kinetic assays, and multiscale simulations, it remains elusive how these enzymes have evolved to fit the diverse chemical needs of their respective substrates. In this work, we performed a high-throughput molecular modeling analysis of 91 SAM MTases to better understand how their properties (i.e., electric field [EF] strength and active site volumes) help achieve similar catalytic efficiency toward substrates of different reactivity. We found that EF strengths have largely adjusted to make the target atom a better methyl acceptor. For MTases that target RNA/DNA and histone proteins, our results suggest that EF strength accommodates formal hybridization state and variation in cavity volume trends with diversity of substrate classes. Metal ions in SAM MTases contribute negatively to EF strength for methyl donation and enzyme scaffolds tend to offset these contributions.

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.

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.

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.

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.

Adaptive-Partitioning Multilayer Dynamics Simulations: 1. On-the-Fly Switch between Two Quantum Levels of Theory

We propose to generalize the previously developed two-layer permuted adaptive-partitioning quantum-mechanics/molecular-mechanics (QM/MM), which reclassifies atoms as QM or MM on-the-fly in dynamics simulations, to multilayer adaptive-partitioning algorithms that enable multiple levels of theory. In this work, we formulate two new algorithms that smoothly interpolate the energy between two QM (Q1 and Q2) levels of theory. The first "permuted adaptive-partitioning" scheme is based on the weighted many-body expansion of the potential, as in the adaptive-partitioning QM/MM. Unconventional and potentially more efficient, the second "interpolated adaptive-partitioning" method employs alchemical QM calculations with Q1/Q2-mixed basis sets, Fock matrices, and overlap matrices. To our knowledge, this is the first time that such alchemical calculations are performed in QM, although they are routinely done in MM. Test calculations on water-cluster models show that both new algorithms indeed yield smooth energy curves when water molecules shift between Q1 and Q2.

Chemically Accurate Vibrational Free Energies of Adsorption from Density Functional Theory Molecular Dynamics: Alkanes in Zeolites

We present a methodology to compute, at reduced computational cost, Gibbs free energies, enthalpies, and entropies of adsorption from molecular dynamics. We calculate vibrational partition functions from vibrational energies, which we obtain from the vibrational density of states by projection on the normal modes. The use of a set of well-chosen reference structures along the trajectories accounts for the anharmonicities of the modes. For the adsorption of methane, ethane, and propane in the H-CHA zeolite, we limit our treatment to a set of vibrational modes localized at the adsorption site (zeolitic OH group) and the alkane molecule interacting with it. Only two short trajectories (1–20 ps) are required to reach convergence (<1 kJ/mol) for the thermodynamic functions. The mean absolute deviations from the experimentally measured values are 2.6, 2.8, and 4.7 kJ/mol for the Gibbs free energy, the enthalpy, and the entropy term (−TΔS), respectively. In particular, the entropy terms show a major improvement compared to the harmonic approximation and almost reach the accuracy of the previous use of anharmonic frequencies obtained with curvilinear distortions of individual modes. The thermodynamic functions so obtained follow the trend of the experimental values for methane, ethane, and propane, and the Gibbs free energy of adsorption at experimental conditions is correctly predicted to change from positive for methane (5.9 kJ/mol) to negative for ethane (−4.8 kJ/mol) and propane (−7.1 kJ/mol).

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.

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.

Quantum Chemical and QM/MM Models in Biochemistry

Quantum chemical (QC) calculations provide a basis for deriving a microscopic understanding of enzymes and photobiological systems. Here we describe how QC models can be used to explore the electronic structure, dynamics, and energetics of biomolecules. We introduce the hybrid quantum mechanics/classical mechanics (QM/MM) approach, where a quantum mechanically described system of interest is embedded in a classically described force field representation of the biochemical surroundings. We also discuss the QM cluster model approach, as well as embedding theories, that provide complementary methodologies to model quantum mechanical effects in biomolecules. The chapter also provides some practical guides for building quantum biochemical models using the quinone reduction catalysis in respiratory complex I and a model reaction in solution as examples.

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

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

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.

Accelerating the Calculation of Solute-Solvent Interaction Energies through Systematic Molecular Fragmentation

The method of systematic molecular fragmentation by annihilation (SMFA) is modified to apply to the interaction energy between a solute and solvent, where the solute is a pair of reacting molecules. For NH₃ + CH₃Cl as the solute, it is shown that SMFA can estimate (to chemical accuracy) the average binding energy of the solute in large water clusters containing up to 160 water molecules, at an appropriate level of electronic structure theory. The SMFA calculation can be carried out in a computation time that makes it feasible to estimate the solvation contribution to free energies of activation and reaction by ensemble averaging.

Development of a Robust Indirect Approach for MM → QM Free Energy Calculations That Combines Force-Matched Reference Potential and Bennett's Acceptance Ratio Methods

We use the PBE0/6-31G* density functional method to perform ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations under periodic boundary conditions with rigorous electrostatics using the ambient potential composite Ewald method in order to test the convergence of MM → QM/MM free energy corrections for the prediction of 17 small-molecule solvation free energies and eight ligand binding free energies to T4 lysozyme. The "indirect" thermodynamic cycle for calculating free energies is used to explore whether a series of reference potentials improve the statistical quality of the predictions. Specifically, we construct a series of reference potentials that optimize a molecular mechanical (MM) force field's parameters to reproduce the ab initio QM/MM forces from a QM/MM simulation. The optimizations form a systematic progression of successively expanded parameters that include bond, angle, dihedral, and charge parameters. For each reference potential, we calculate benchmark quality reference values for the MM → QM/MM correction by performing the mixed MM and QM/MM Hamiltonians at 11 intermediate states, each for 200 ps. We then compare forward and reverse application of Zwanzig's relation, thermodynamic integration (TI), and Bennett's acceptance ratio (BAR) methods as a function of reference potential, simulation time, and the number of simulated intermediate states. We find that Zwanzig's equation is inadequate unless a large number of intermediate states are explicitly simulated. The TI and BAR mean signed errors are very small even when only the end-state simulations are considered, and the standard deviations of the TI and BAR errors are decreased by choosing a reference potential that optimizes the bond and angle parameters. We find a robust approach for the data sets of fairly rigid molecules considered here is to use bond + angle reference potential together with the end-state-only BAR analysis. This requires QM/MM simulations to be performed in order to generate reference data to parametrize the bond + angle reference potential, and then this same simulation serves a dual purpose as the full QM/MM end state. The convergence of the results with respect to time suggests that computational resources may be used more efficiently by running multiple simulations for no more than 50 ps, rather than running one long simulation.

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

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

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

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

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.

Roles of Closed- and Open-Loop Conformations in Large-Scale Structural Transitions of l-Lactate Dehydrogenase

The mechanism of l-lactate generation from pyruvate by l-lactate dehydrogenase (LDH) from the rabbit muscle was studied theoretically by the multistructural microiteration (MSM) method combined with the quantum mechanics/molecular mechanics (QM/MM)-ONIOM method, where the MSM method describes the MM environment as a weighted average of multiple different structures that are fully relaxed during geometry optimization or a reaction path calculation for the QM part. The results showed that the substrate binding and product states were stabilized only in the open-loop conformation of LDH and the reaction occurred in the closed-loop conformation. In other words, before and after the chemical reaction, a large-scale structural transition from the open-loop conformation to the closed-loop conformation and vice versa occurred. The closed-loop conformation stabilized the transition state of the reaction. In contrast, the open-loop conformation stabilized the substrate binding and final states. In other words, the closed- to open-loop transition at the substrate binding state urges capture of the substrate molecule, the subsequent open- to closed-loop transition promotes the product generation, and the final closed- to open-loop transition at the final state prevents the reverse reaction going back to the substrate binding state. It is thus suggested that the exchange of stability between the closed- and open-loop conformations at different states promotes the catalytic cycle.

Reaction Mechanism of [NiFe] Hydrogenase Studied by Computational Methods

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

A Comparison of QM/MM Simulations with and without the Drude Oscillator Model Based on Hydration Free Energies of Simple Solutes

Maintaining a proper balance between specific intermolecular interactions and non-specific solvent interactions is of critical importance in molecular simulations, especially when predicting binding affinities or reaction rates in the condensed phase. The most rigorous metric for characterizing solvent affinity are solvation free energies, which correspond to a transfer from the gas phase into solution. Due to the drastic change of the electrostatic environment during this process, it is also a stringent test of polarization response in the model. Here, we employ both the CHARMM fixed charge and polarizable force fields to predict hydration free energies of twelve simple solutes. The resulting classical ensembles are then reweighted to obtain QM/MM hydration free energies using a variety of QM methods, including MP2, Hartree⁻Fock, density functional methods (BLYP, B3LYP, M06-2X) and semi-empirical methods (OM2 and AM1 ). Our simulations test the compatibility of quantum-mechanical methods with molecular-mechanical water models and solute Lennard⁻Jones parameters. In all cases, the resulting QM/MM hydration free energies were inferior to purely classical results, with the QM/MM Drude force field predictions being only marginally better than the QM/MM fixed charge results. In addition, the QM/MM results for different quantum methods are highly divergent, with almost inverted trends for polarizable and fixed charge water models. While this does not necessarily imply deficiencies in the QM models themselves, it underscores the need to develop consistent and balanced QM/MM interactions. Both the QM and the MM component of a QM/MM simulation have to match, in order to avoid artifacts due to biased solute⁻solvent interactions. Finally, we discuss strategies to improve the convergence and efficiency of multi-scale free energy simulations by automatically adapting the molecular-mechanics force field to the target quantum method.

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.

On the convergence of multi-scale free energy simulations

In this work we employ simple model systems to evaluate the relative performance of two of the most important free energy methods: The Zwanzig equation (also known as "Free energy perturbation") and Bennett's acceptance ratio method (BAR). Although our examples should be transferable to other kinds of free energy simulations, we focus on applications of multi-scale free energy simulations. Such calculations are especially complex, since they connect two different levels of theory with very different requirements in terms of speed, accuracy, sampling and parallelizability. We try to reconcile all those different factors by developing some simple criteria to guide the early stages of the development of a free energy protocol. This is accomplished by quantifying how many λ intermediate steps and how many potential energy evaluations are necessary in order to reach a certain level of convergence.

Relative Ligand-Binding Free Energies Calculated from Multiple Short QM/MM MD Simulations

We have devised a new efficient approach to compute combined quantum mechanical (QM) and molecular mechanical (MM, i.e. QM/MM) ligand-binding relative free energies. Our method employs the reference-potential approach with free-energy perturbation both at the MM level (between the two ligands) and from MM to QM/MM (for each ligand). To ensure that converged results are obtained for the MM → QM/MM perturbations, explicit QM/MM molecular dynamics (MD) simulations are performed with two intermediate mixed states. To speed up the calculations, we utilize the fact that the phase space can be extensively sampled at the MM level. Therefore, we run many short QM/MM MD simulations started from snapshots of the MM simulations, instead of a single long simulation. As a test case, we study the binding of nine cyclic carboxylate ligands to the octa-acid deep cavitand. Only the ligand is in the QM system, treated with the semiempirical PM6-DH+ method. We show that for eight of the ligands, we obtain well converged results with short MD simulations (1-15 ps). However, in one case, the convergence is slower (∼50 ps) owing to a mismatch between the conformational preferences of the MM and QM/MM potentials. We test the effect of initial minimization, the need of equilibration, and how many independent simulations are needed to reach a certain precision. The results show that the present approach is about four times faster than using standard MM → QM/MM free-energy perturbations with the same accuracy and precision.

On the Difference Between Additive and Subtractive QM/MM Calculations

The combined quantum mechanical (QM) and molecular mechanical (MM) approach (QM/MM) is a popular method to study reactions in biochemical macromolecules. Even if the general procedure of using QM for a small, but interesting part of the system and MM for the rest is common to all approaches, the details of the implementations vary extensively, especially the treatment of the interface between the two systems. For example, QM/MM can use either additive or subtractive schemes, of which the former is often said to be preferable, although the two schemes are often mixed up with mechanical and electrostatic embedding. In this article, we clarify the similarities and differences of the two approaches. We show that inherently, the two approaches should be identical and in practice require the same sets of parameters. However, the subtractive scheme provides an opportunity to correct errors introduced by the truncation of the QM system, i.e., the link atoms, but such corrections require additional MM parameters for the QM system. We describe and test three types of link-atom correction, viz. for van der Waals, electrostatic, and bonded interactions. The calculations show that electrostatic and bonded link-atom corrections often give rise to problems in the geometries and energies. The van der Waals link-atom corrections are quite small and give results similar to a pure additive QM/MM scheme. Therefore, both approaches can be recommended.

QM/MM study of the reaction mechanism of sulfite oxidase

Sulfite oxidase is a mononuclear molybdenum enzyme that oxidises sulfite to sulfate in many organisms, including man. Three different reaction mechanisms have been suggested, based on experimental and computational studies. Here, we study all three with combined quantum mechanical (QM) and molecular mechanical (QM/MM) methods, including calculations with large basis sets, very large QM regions (803 atoms) and QM/MM free-energy perturbations. Our results show that the enzyme is set up to follow a mechanism in which the sulfur atom of the sulfite substrate reacts directly with the equatorial oxo ligand of the Mo ion, forming a Mo-bound sulfate product, which dissociates in the second step. The first step is rate limiting, with a barrier of 39–49 kJ/mol. The low barrier is obtained by an intricate hydrogen-bond network around the substrate, which is preserved during the reaction. This network favours the deprotonated substrate and disfavours the other two reaction mechanisms. We have studied the reaction with both an oxidised and a reduced form of the molybdopterin ligand and quantum-refinement calculations indicate that it is in the normal reduced tetrahydro form in this protein.

A component analysis of the free energies of folding of 35 proteins: A consensus view on the thermodynamics of folding at the molecular level

What factors favor protein folding? This is a textbook question. Parsing the experimental free energies of folding/unfolding into diverse enthalpic and entropic components of solute and solvent favoring or disfavoring folding is not an easy task. In this study, we present a computational protocol for estimating the free energy contributors to protein folding semi-quantitatively using ensembles of unfolded and native states generated via molecular dynamics simulations. We tested the methodology on 35 proteins with diverse structural motifs and sizes and found that the calculated free energies correlate well with experiment (correlation coefficient ∼ 0.85), enabling us to develop a consensus view of the energetics of folding. As a more sensitive test of the methodology, we also investigated the free energies of folding of an additional 33 single point mutants and obtained a correlation coefficient of 0.8. A notable observation is that the folding free energy components appear to carry signatures of the fold (SCOP classification) of the protein. © 2017 Wiley Periodicals, Inc.

Multistructural microiteration technique for geometry optimization and reaction path calculation in large systems

We propose a multistructural microiteration (MSM) method for geometry optimization and reaction path calculation in large systems. MSM is a simple extension of the geometrical microiteration technique. In conventional microiteration, the structure of the non-reaction-center (surrounding) part is optimized by fixing atoms in the reaction-center part before displacements of the reaction-center atoms. In this method, the surrounding part is described as the weighted sum of multiple surrounding structures that are independently optimized. Then, geometric displacements of the reaction-center atoms are performed in the mean field generated by the weighted sum of the surrounding parts. MSM was combined with the QM/MM-ONIOM method and applied to chemical reactions in aqueous solution or enzyme. In all three cases, MSM gave lower reaction energy profiles than the QM/MM-ONIOM-microiteration method over the entire reaction paths with comparable computational costs. © 2017 Wiley Periodicals, Inc.

Perspective: Quantum mechanical methods in biochemistry and biophysics

In this perspective article, I discuss several research topics relevant to quantum mechanical (QM) methods in biophysical and biochemical applications. Due to the immense complexity of biological problems, the key is to develop methods that are able to strike the proper balance of computational efficiency and accuracy for the problem of interest. Therefore, in addition to the development of novel ab initio and density functional theory based QM methods for the study of reactive events that involve complex motifs such as transition metal clusters in metalloenzymes, it is equally important to develop inexpensive QM methods and advanced classical or quantal force fields to describe different physicochemical properties of biomolecules and their behaviors in complex environments. Maintaining a solid connection of these more approximate methods with rigorous QM methods is essential to their transferability and robustness. Comparison to diverse experimental observables helps validate computational models and mechanistic hypotheses as well as driving further development of computational methodologies.

Computing converged free energy differences between levels of theory via nonequilibrium work methods: Challenges and opportunities

We demonstrate that Jarzynski's equation can be used to reliably compute free energy differences between low and high level representations of systems. The need for such a calculation arises when employing the so-called "indirect" approach to free energy simulations with mixed quantum mechanical/molecular mechanical (QM/MM) Hamiltonians; a popular technique for circumventing extensive simulations involving quantum chemical computations. We have applied this methodology to several small and medium sized organic molecules, both in the gas phase and explicit solvent. Test cases include several systems for which the standard approach; that is, free energy perturbation between low and high level description, fails to converge. Finally, we identify three major areas in which the difference between low and high level representations make the calculation of ΔAlow→high difficult: bond stretching and angle bending, different preferred conformations, and the response of the MM region to the charge distribution of the QM region. © 2016 Wiley Periodicals, Inc.

Averaged Condensed Phase Model for Simulating Molecules in Complex Environments

The need for configurational sampling dramatically increases the cost of combined quantum mechanics/molecular mechanics (QM/MM) simulations of chemical processes in solution. We developed an averaged condensed phase environment (ACPE) model that constructs an effective polarizable environment directly from explicitly sampled molecular dynamics configurations via the K-means++ algorithm and a mathematically rigorous translation of the molecular mechanics parameters. The model captures detailed heterogeneous features in the environment that may be difficult to describe using a conventional polarizable continuum model. Instead of performing repeated QM/MM calculations for each new configuration of the environment, the ACPE approach allows one to perform a single QM calculation on an averaged configuration. Here, we demonstrate the model by computing electronic excitation energies for several small molecules in solution. The ACPE model predicts the excitation energies in excellent agreement with conventional configurational averaging yet with orders of magnitude of reduction in the computational cost.

Human Ferrochelatase: Insights for the Mechanism of Ferrous Iron Approaching Protoporphyrin IX by QM/MM and QTCP Free Energy Studies

Ferrochelatase catalyzes the insertion of ferrous iron into protoporphyrin IX, the terminal step in heme biosynthesis. Some disputes in its mechanism remain unsolved, especially for human ferrochelatase. In this paper, high-level quantum mechanical/molecular mechanics (QM/MM) and free-energy studies were performed to address these controversial issues including the iron-binding site, the optimal reaction path, the substrate porphyrin distortion, and the presence of the sitting-atop (SAT) complex. Our results reveal that the ferrous iron is probably at the binding site coordinating with Met76, and His263 plays the role of proton acceptor. The rate-determining step is either the first proton removed by His263 or the proton transition within the porphyrin with an energy barrier of 14.99 or 14.87 kcal/mol by the quantum mechanical thermodynamic cycle perturbation (QTCP) calculations, respectively. The fast deprotonation step with the conservative residues rather than porphyrin deformation found in solution provides the driving force for biochelation. The SAT complex is not a necessity for the catalysis though it induces a modest distortion on the porphyrin ring.

Calculating distribution coefficients based on multi-scale free energy simulations: an evaluation of MM and QM/MM explicit solvent simulations of water-cyclohexane transfer in the SAMPL5 challenge

One of the central aspects of biomolecular recognition is the hydrophobic effect, which is experimentally evaluated by measuring the distribution coefficients of compounds between polar and apolar phases. We use our predictions of the distribution coefficients between water and cyclohexane from the SAMPL5 challenge to estimate the hydrophobicity of different explicit solvent simulation techniques. Based on molecular dynamics trajectories with the CHARMM General Force Field, we compare pure molecular mechanics (MM) with quantum-mechanical (QM) calculations based on QM/MM schemes that treat the solvent at the MM level. We perform QM/MM with both density functional theory (BLYP) and semi-empirical methods (OM1, OM2, OM3, PM3). The calculations also serve to test the sensitivity of partition coefficients to solute polarizability as well as the interplay of the quantum-mechanical region with the fixed-charge molecular mechanics environment. Our results indicate that QM/MM with both BLYP and OM2 outperforms pure MM. However, this observation is limited to a subset of cases where convergence of the free energy can be achieved.

Computational Investigation of the Interplay of Substrate Positioning and Reactivity in Catechol O-Methyltransferase

Catechol O-methyltransferase (COMT) is a SAM- and Mg2+-dependent methyltransferase that regulates neurotransmitters through methylation. Simulations and experiments have identified divergent catecholamine substrate orientations in the COMT active site: molecular dynamics simulations have favored a monodentate coordination of catecholate substrates to the active site Mg2+, and crystal structures instead preserve bidentate coordination along with short (2.65 Å) methyl donor-acceptor distances. We carry out longer dynamics (up to 350 ns) to quantify interconversion between bidentate and monodentate binding poses. We provide a systematic determination of the relative free energy of the monodentate and bidentate structures in order to identify whether structural differences alter the nature of the methyl transfer mechanism and source of enzymatic rate enhancement. We demonstrate that the bidentate and monodentate binding modes are close in energy but separated by a 7 kcal/mol free energy barrier. Analysis of interactions in the two binding modes reveals that the driving force for monodentate catecholate orientations in classical molecular dynamics simulations is derived from stronger electrostatic stabilization afforded by alternate Mg2+ coordination with strongly charged active site carboxylates. Mixed semi-empirical-classical (SQM/MM) substrate C-O distances (2.7 Å) for the bidentate case are in excellent agreement with COMT X-ray crystal structures, as long as charge transfer between the substrates, Mg2+, and surrounding ligands is permitted. SQM/MM free energy barriers for methyl transfer from bidentate and monodentate catecholate configurations are comparable at around 21-22 kcal/mol, in good agreement with experiment (18-19 kcal/mol). Overall, the work suggests that both binding poses are viable for methyl transfer, and accurate descriptions of charge transfer and electrostatics are needed to provide balanced relative barriers when multiple binding poses are accessible, for example in other transferases.

QM/MM free energy simulations: recent progress and challenges

Due to the higher computational cost relative to pure molecular mechanical (MM) simulations, hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations particularly require a careful consideration of balancing computational cost and accuracy. Here we review several recent developments in free energy methods most relevant to QM/MM simulations and discuss several topics motivated by these developments using simple but informative examples that involve processes in water. For chemical reactions, we highlight the value of invoking enhanced sampling technique (e.g., replica-exchange) in umbrella sampling calculations and the value of including collective environmental variables (e.g., hydration level) in metadynamics simulations; we also illustrate the sensitivity of string calculations, especially free energy along the path, to various parameters in the computation. Alchemical free energy simulations with a specific thermodynamic cycle are used to probe the effect of including the first solvation shell into the QM region when computing solvation free energies. For cases where high-level QM/MM potential functions are needed, we analyze two different approaches: the QM/MM-MFEP method of Yang and co-workers and perturbative correction to low-level QM/MM free energy results. For the examples analyzed here, both approaches seem productive although care needs to be exercised when analyzing the perturbative corrections.

Methods for Efficiently and Accurately Computing Quantum Mechanical Free Energies for Enzyme Catalysis

Enzyme activity is inherently linked to free energies of transition states, ligand binding, protonation/deprotonation, etc.; these free energies, and thus enzyme function, can be affected by residue mutations, allosterically induced conformational changes, and much more. Therefore, being able to predict free energies associated with enzymatic processes is critical to understanding and predicting their function. Free energy simulation (FES) has historically been a computational challenge as it requires both the accurate description of inter- and intramolecular interactions and adequate sampling of all relevant conformational degrees of freedom. The hybrid quantum mechanical molecular mechanical (QM/MM) framework is the current tool of choice when accurate computations of macromolecular systems are essential. Unfortunately, robust and efficient approaches that employ the high levels of computational theory needed to accurately describe many reactive processes (ie, ab initio, DFT), while also including explicit solvation effects and accounting for extensive conformational sampling are essentially nonexistent. In this chapter, we will give a brief overview of two recently developed methods that mitigate several major challenges associated with QM/MM FES: the QM non-Boltzmann Bennett's acceptance ratio method and the QM nonequilibrium work method. We will also describe usage of these methods to calculate free energies associated with (1) relative properties and (2) along reaction paths, using simple test cases with relevance to enzymes examples.

QM/MM Analysis of Transition States and Transition State Analogues in Metalloenzymes

Enzymology is approaching an era where many problems can benefit from computational studies. While ample challenges remain in quantitatively predicting behavior for many enzyme systems, the insights that often come from computations are an important asset for the enzymology community. Here we provide a primer for enzymologists on the types of calculations that are most useful for mechanistic problems in enzymology. In particular, we emphasize the integration of models that range from small active-site motifs to fully solvated enzyme systems for cross-validation and dissection of specific contributions from the enzyme environment. We then use a case study of the enzyme alkaline phosphatase to illustrate specific application of the methods. The case study involves examination of the binding modes of putative transition state analogues (tungstate and vanadate) to the enzyme. The computations predict covalent binding of these ions to the enzymatic nucleophile and that they adopt the trigonal bipyramidal geometry of the expected transition state. By comparing these structures with transition states found through free energy simulations, we assess the degree to which the transition state analogues mimic the true transition states. Technical issues worth treating with care as well as several remaining challenges to quantitative analysis of metalloenzymes are also highlighted during the discussion.

A General Boundary Potential for Hybrid QM/MM Simulations of Solvated Biomolecular Systems

We present a general boundary potential for the efficient and accurate evaluation of electrostatic interactions in hybrid quantum mechanical/molecular mechanical (QM/MM) approaches called solvated macromolecule boundary potential (SMBP), which is designed for QM/MM calculations with any kind of QM method. The SMBP targets QM/MM single-point energy calculations and geometry optimizations. In the SMBP scheme, the outer solvent and macromolecule region is described by a boundary potential obtained with the use of Poisson-Boltzmann calculations (treating the bulk solvent as a dielectric continuum). In the QM calculations, the SMBP is represented by virtual point charges on a surface enclosing the explicitly treated inner region. These charges and their interactions with the QM density are determined through a self-consistent reaction field procedure. The accuracy of the SMBP is evaluated on three diverse test systems: the intramolecular proton transfer of glycine in water, the hydroxylation reaction in p-hydroxybenzoate hydroxylase, and the spin state energy splittings in the pentacoordinated ferric complex of cytochrome P450cam. In the case of solvated glycine, application of the SMBP turns out to be problematic since analogous QM/MM/SMBP and full QM/MM geometry optimizations lead to different close-lying local minima. In both enzymes, the SMBP performs very well and closely reproduces the results from full QM/MM optimizations of these more rigid test systems. Starting from optimized QM/MM/SMBP structures along a reaction path, one can apply the previously implemented generalized solvent boundary potential (GSBP) to sample over MM phase space in QM/MM free energy calculations within the framework of free energy perturbation theory. This reduces the overall computational costs of sampling by 1 order of magnitude while maintaining good accuracy. The combined use of SMBP and GSBP thus allows for efficient QM/MM free energy studies of enzymes.