A priori evaluation of aqueous polarization effects through Monte Carlo QM-MM simulations

Accelerating QM/MM Free Energy Computations via Intramolecular Force Matching

The calculation of free energy differences between levels of theory has numerous potential pitfalls. Chief among them is the lack of overlap, i.e., ensembles generated at one level of theory (e.g., "low") not being good approximations of ensembles at the other (e.g., "high"). Numerous strategies have been devised to mitigate this issue. However, the most straightforward approach is to ensure that the "low" level ensemble more closely resembles that of the "high". Ideally, this is done without increasing computational cost. Herein, we demonstrate that by reparametrizing classical intramolecular potentials to reproduce high level forces (i.e., force matching) configurational overlap between a "low" (i.e., classical) and "high" (i.e., quantum) level can be significantly improved. This procedure is validated on two test cases and results in vastly improved convergence of free energy simulations.

A Multiscale Simulation Approach to Modeling Drug-Protein Binding Kinetics

Drug-target binding kinetics has recently emerged as a sometimes critical determinant of in vivo efficacy and toxicity. Its rational optimization to improve potency or reduce side effects of drugs is, however, extremely difficult. Molecular simulations can play a crucial role in identifying features and properties of small ligands and their protein targets affecting the binding kinetics, but significant challenges include the long time scales involved in (un)binding events and the limited accuracy of empirical atomistic force fields (lacking, e.g., changes in electronic polarization). In an effort to overcome these hurdles, we propose a method that combines state-of-the-art enhanced sampling simulations and quantum mechanics/molecular mechanics (QM/MM) calculations at the BLYP/VDZ level to compute association free energy profiles and characterize the binding kinetics in terms of structure and dynamics of the transition state ensemble. We test our combined approach on the binding of the anticancer drug Imatinib to Src kinase, a well-characterized target for cancer therapy with a complex binding mechanism involving significant conformational changes. The results indicate significant changes in polarization along the binding pathways, which affect the predicted binding kinetics. This is likely to be of widespread importance in binding of ligands to protein targets.

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.

Dual QM and MM Approach for Computing Equilibrium Isotope Fractionation Factor of Organic Species in Solution

A dual QM and MM approach for computing equilibrium isotope effects has been described. In the first partition, the potential energy surface is represented by a combined quantum mechanical and molecular mechanical (QM/MM) method, in which a solute molecule is treated quantum mechanically, and the remaining solvent molecules are approximated classically by molecular mechanics. In the second QM/MM partition, differential nuclear quantum effects responsible for the isotope effect are determined by a statistical mechanical double-averaging formalism, in which the nuclear centroid distribution is sampled classically by Newtonian molecular dynamics and the quantum mechanical spread of quantized particles about the centroid positions is treated using the path integral (PI) method. These partitions allow the potential energy surface to be properly represented such that the solute part is free of nuclear quantum effects for nuclear quantum mechanical simulations, and the double-averaging approach has the advantage of sampling efficiency for solvent configuration and for path integral convergence. Importantly, computational precision is achieved through free energy perturbation (FEP) theory to alchemically mutate one isotope into another. The PI-FEP approach is applied to model systems for the 18O enrichment found in cellulose of trees to determine the isotope enrichment factor of carbonyl compounds in water. The present method may be useful as a general tool for studying isotope fractionation in biological and geochemical systems.

Force matching as a stepping stone to QM/MM CB[8] host/guest binding free energies: a SAMPL6 cautionary tale

Use of quantum mechanical/molecular mechanical (QM/MM) methods in binding free energy calculations, particularly in the SAMPL challenge, often fail to achieve improvement over standard additive (MM) force fields. Frequently, the implementation is through use of reference potentials, or the so-called "indirect approach", and inherently relies on sufficient overlap existing between MM and QM/MM configurational spaces. This overlap is generally poor, particularly for the use of free energy perturbation to perform the MM to QM/MM free energy correction at the end states of interest (e.g., bound and unbound states). However, by utilizing MM parameters that best reproduce forces obtained at the desired QM level of theory, it is possible to lessen the configurational disparity between MM and QM/MM. To this end, we sought to use force matching to generate MM parameters for the SAMPL6 CB[8] host-guest binding challenge, classically compute binding free energies, and apply energetic end state corrections to obtain QM/MM binding free energy differences. For the standard set of 11 molecules and the bonus set (including three additional challenge molecules), error statistics, such as the root mean square deviation (RMSE) were moderately poor (5.5 and 5.4 kcal/mol). Correlation statistics, however, were in the top two for both standard and bonus set submissions ([Formula: see text] of 0.42 and 0.26, [Formula: see text] of 0.64 and 0.47 respectively). High RMSE and moderate correlation strongly indicated the presence of systematic error. Identifiable issues were ameliorated for two of the guest molecules, resulting in a reduction of error and pointing to strong prospects for the future use of this methodology.

Representation of the QM Subsystem for Long-Range Electrostatic Interaction in Non-Periodic Ab Initio QM/MM Calculations

In QM/MM calculations, it is essential to handle electrostatic interactions between the QM and MM subsystems accurately and efficiently. To achieve maximal efficiency, it is convenient to adopt a hybrid scheme, where the QM electron density is used explicitly in the evaluation of short-range QM/MM electrostatic interactions, while a multipolar representation for the QM electron density is employed to account for the long-range QM/MM electrostatic interactions. In order to avoid energy discontinuity at the cutoffs, which separate the short- and long-range QM/MM electrostatic interactions, a switching function should be utilized to ensure a smooth potential energy surface. In this study, we benchmarked the accuracy of such hybrid embedding schemes for QM/MM electrostatic interactions using different multipolar representations, switching functions and cutoff distances. For test systems (neutral and anionic oxyluciferin in MM (aqueous and enzyme) environments), the best accuracy was acquired with a combination of QM electrostatic potential (ESP) charges and dipoles and two switching functions (long-range electrostatic corrections (LREC) and Switch) in the treatment of long-range QM/MM electrostatics. It allowed us to apply a 10Å distance cutoff and still obtain QM/MM electrostatics/polarization energies within 0.1 kcal/mol and time-dependent density functional theory (TDDFT)/MM vertical excitation energies within 10-3 eV from theoretical reference values.

Efficient Computation of Free Energy Surfaces of Diels⁻Alder Reactions in Explicit Solvent at Ab Initio QM/MM Level

For Diels–Alder (DA) reactions in solution, an accurate and converged free energy (FE) surface at ab initio (ai) quantum mechanical/molecular mechanical (QM/MM) level is imperative for the understanding of reaction mechanism. However, this computation is still far too expensive. In a previous work, we proposed a new method termed MBAR+wTP, with which the computation of the ai FE profile can be accelerated by several orders of magnitude via a three-step procedure: (I) an umbrella sampling (US) using a semi-empirical (SE) QM/MM Hamiltonian is performed; (II) the FE profile is generated using the Multistate Bennett Acceptance Ratio (MBAR) analysis; and (III) a weighted Thermodynamic Perturbation (wTP) from the SE Hamiltonian to the ai Hamiltonian is performed to obtain the ai QM/MM FE profile using weight factors from the MBAR analysis. In this work, this method is extended to the calculations of two-dimensional FE surfaces of two Diels–Alder reactions of cyclopentadiene with either acrylonitrile or 1-4-naphthoquinone at ai QM/MM level. The accurate activation free energies at the ai QM/MM level, which are much closer to the experimental measurements than those calculated by other methods, indicate that this MBAR+wTP method can be applied in the studies of complex reactions in condensed phase with much-enhanced efficiency.

QM/MM Molecular Dynamics Investigations of the Substrate Binding of Leucotriene A4 Hydrolase: Implication for the Catalytic Mechanism

LTA4H is a monozinc bifunctional enzyme which exhibits both aminopeptidase and epoxide hydrolase activities. Its dual functions in anti- and pro-inflammatory roles have attracted wide attention to the inhibitor design. In this work, we tried to construct Michaelis complexes of LTA4H with both a native peptide substrate and LTA4 molecule using combined quantum mechanics and molecular mechanics molecular dynamics simulations. First of all, the zinc ion is coordinated by H295, H299, and E318. For its aminopeptidase activity, similar to conventional peptidases, the fourth ligand to the zinc ion is suggested to be an active site water, which is further hydrogen bonded with a downstream glutamic acid, E296. For the epoxide hydrolase activity, the fourth ligand to the zinc ion is found to be an epoxy oxygen atom. The potential of mean force calculation indicates about an 8.5 kcal/mol activation barrier height for the ring-opening reaction, which will generate a metastable carbenium intermediate. Subsequent frontier molecular orbital analyses suggest that the next step would be the nucleophilic attacking reaction at the C12 atom by a water molecule activated by D375. Our simulations also analyzed functions of several important residues like R563, K565, E271, Y383, and Y378 in the binding of peptide and LTA4.

Revisiting the catalytic mechanism of Mo-Cu carbon monoxide dehydrogenase using QM/MM and DFT calculations

Previous density functional theory (DFT) studies have shown that the release of the produced carbon dioxide (CO2) from an active-site cluster is a thermodynamically or kinetically difficult step in the enzymatic carbon monoxide (CO) oxidation catalyzed by Mo-Cu carbon monoxide dehydrogenase (Mo-Cu CODH). To better understand the effect of the protein environment on this difficult CO2 release step as well as other reaction steps, we applied hybrid quantum mechanics and molecular mechanics (QM/MM) calculations to the Mo-Cu CODH enzyme. The results show that in the first step, the equatorial Mo[double bond, length as m-dash]O group in the active-site cluster attacks the nearby CO molecule bound to the Cu site. Afterward, a stable thiocarbonate intermediate is formed in which the CO2 molecule is embedded and the copper-S(μ-sulfido) bond is broken. A free CO2 molecule, i.e., the final product, is then released from the active-site cluster, not directly from the thiocarbonate intermediate but via a previously formed intermediate that also contains CO2 but retains the Cu-S(μ-sulfido) bond. In contrast to the previous DFT results, the calculated barrier for this process was low in our QM/MM calculations. An additional QM/MM analysis of the barrier height showed that the effect of the protein environment on this barrier lowering is not very large. We found that the reason for the low barrier obtained by QM/MM is that the barrier for CO2 release is already not high at the DFT level. These results allow us to conclude that the CO oxidation reaction passes through the formation of a thiocarbonate intermediate, and that the subsequent CO2 release is kinetically not difficult. Nevertheless, the protein environment has an important role to play in making the latter process thermodynamically favored. No low-barrier pathway for the product release could be obtained for the reaction of n-butylisocyanide, which is consistent with the experimental fact that n-butylisocyanide inhibits Mo-Cu CODH.

The importance of nuclear quantum effects in spectral line broadening of optical spectra and electrostatic properties in aromatic chromophores

In this work, we examine the importance of nuclear quantum effects on capturing the line broadening and vibronic structure of optical spectra. We determine the absorption spectra of three aromatic molecules indole, pyridine, and benzene using time dependent density functional theory with several molecular dynamics sampling protocols: force-field based empirical potentials, ab initio simulations, and finally path-integrals for the inclusion of nuclear quantum effects. We show that the absorption spectrum for all these chromophores are similarly broadened in the presence of nuclear quantum effects regardless of the presence of hydrogen bond donor or acceptor groups. We also show that simulations incorporating nuclear quantum effects are able to reproduce the heterogeneous broadening of the absorption spectra even with empirical force fields. The spectral broadening associated with nuclear quantum effects can be accounted for by the broadened distribution of chromophore size as revealed by a particle in the box model. We also highlight the role that nuclear quantum effects have on the underlying electronic structure of aromatic molecules as probed by various electrostatic properties.

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.

A quantum mechanical computational method for modeling electrostatic and solvation effects of protein

An efficient computational approach for modeling protein electrostatic is developed according to static point-charge model distributions based on the linear-scaling EE-GMFCC (electrostatically embedded generalized molecular fractionation with conjugate caps) quantum mechanical (QM) method. In this approach, the Electrostatic-Potential atomic charges are obtained from ab initio calculation of protein, both polarization and charge transfer effect are taken into consideration. This approach shows a significant improvement in the description of electrostatic potential and solvation energy of proteins comparing with current popular molecular mechanics (MM) force fields. Therefore, it has gorgeous prospect in many applications, including accurate calculations of electric field or vibrational Stark spectroscopy in proteins and predicting protein-ligand binding affinity. It can also be applied in QM/MM calculations or electronic embedding method of ONIOM to provide a better electrostatic environment.

Oxygen binding isotope effects of triazole-based HIV-1 reverse transcriptase inhibitors indicate the actual binding site

Binding isotope effects (BIEs) associated with binding of four triazole-based ligands to HIV-1 reverse transcriptase have been calculated at the QM/MM MD level of theory. Two main binding sites: allosteric cavity and RNase H active site, as well as three other sites reported in the literature (the Knuckles, the NNRTI Adjacent, and Incoming Nucleotide Binding) have been considered. The interactions between inhibitors and these protein sites have been quantified by binding free energies obtained from free energy perturbation (FEP) calculations, supported by interaction energy analysis. It has been shown that binding in the allosteric cavity can be distinguished from binding to other sites based on BIEs as it is associated with normal ¹⁸O-BIEs of the carbonyl oxygen atom while binding to RNase H active site is characterized by inverse binding isotope effect (¹⁸O-BIE < 1). For other sites ¹⁸O-BIEs close to unity are predicted. This information points to oxygen binding isotope effects of carbonyl group as indicative of the actual binding site of studied inhibitors.

Electronic structure and absorption spectra of fluorescent nucleoside analogues

This work presents a systematic investigation of the electronic and conformational properties of five new fluorescent nucleobases belonging to the alphabet based on the isothiazole[4,3-d]pyrimidine molecule, very recently synthesized. This is of particular importance in the characterization of the main electronic aspects of these fluorescent nucleosides. The solvent effects of 1,4-dioxane and water were included combining the Sequential Monte Carlo/CASPT2 and the Free Energy Gradient (FEG) methods. For comparison, the Polarizable Continuum method was also used. The geometries of all compounds were optimized in solvent with the largest effects observed in water using the average solvent electrostatic configuration (ASEC) and the FEG approaches. Statistical analysis of the solute-solvent hydrogen bonds is performed and their effect on the absorption spectra analyzed. The dipole moments were calculated and the value obtained from the ASEC-FEG method in water follows the same trend as the natural canonical bases (adenine → uracil → guanine → cytosine). The theoretical results for the absorption spectra obtained from CASPT2(18,13) calculations using the geometries obtained with the ASEC-FEG procedure are in very good agreement with the experimental data. A detailed elucidation of the main aspects of the absorption spectra of the five new fluorescent nucleoside analogues is successfully attempted.

Comment on "Substrate Folding Modes in Trichodiene Synthase: A Determinant of Chemo- and Stereoselectivity"

Wang et al. recently reported an in silico study of the trichodiene synthase (TDS) conversion of farnesyl diphosphate (FPP) to trichodiene (TD) (Wang et al., ACS Catal. 2017, 7, 5841-5846). Although the methods and level of theory used in that work are nearly identical to our own recent work on this system (Dixit et al., ACS Catal. 2017, 7, 812-818), Wang et al. reach rather different conclusions. The authors claimed to obtain a "very credible" mechanism for the biosynthesis of TD and optimized the optimal folding mode of FPP in the 1,6-ring closure in TDS. However, the folding mode of the FPP substrate that was presented contradicts well-established NMR and mass spectrometry data. Moreover, the authors make numerous incorrect statements regarding our earlier work.

Measurement and Prediction of Chlorine Kinetic Isotope Effects in Enzymatic Systems

Approaches to determine chlorine kinetic isotope effects (Cl-KIEs) on enzymatic dehalogenations are discussed and illustrated by representative examples. Three aspects are considered. First methodology for experimental measurement of Cl-KIEs, with stress being on FAB-IRMS technique developed in our laboratory, is described. Subsequently, we concentrate our discussion on the consequences of reaction complexity in the interpretation of experimental values, a problem especially important in cases of polychlorinated reactants. The most fruitful studies of enzymatic dehalogenations by Cl-KIEs require their theoretical evaluation, hence the computational focus of the second part of this chapter.

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.

Drastic Compensation of Electronic and Solvation Effects on ATP Hydrolysis Revealed through Large-Scale QM/MM Simulations Combined with a Theory of Solutions

Hydrolysis of adenosine triphosphate (ATP) is the "energy source" for a variety of biochemical processes. In the present work, we address key features of ATP hydrolysis: the relatively moderate value (about -10 kcal/mol) of the standard free energy, ΔG_hyd, of reaction and the insensitivity of ΔG_hyd to the number of excess electrons on ATP. We conducted quantum mechanical/molecular mechanical simulation combined with the energy-representation theory of solutions to analyze the electronic-state and solvation contributions to ΔG_hyd. It was revealed that the electronic-state contribution in ΔG_hyd is largely negative (favorable) upon hydrolysis, due to the reduction of electrostatic repulsion accompanying the breakage of the P-O bond. In contrast, the solvation effect was found to be strongly more favorable on the reactant side. Thus, we showed that a drastic compensation of the two opposite effects takes place, leading to the modest value of ΔG_hyd at each number of excess electrons examined. The computational analyses were also conducted for pyrophosphate ions (PPi), and the parallelism between the ATP and PPi hydrolyses was confirmed. Classical molecular dynamics simulation was further carried out to discuss the effect of the solvent environment; the insensitivity of ΔG_hyd to the number of excess electrons was seen to hold in solvent water and ethanol.

An averaged polarizable potential for multiscale modeling in phospholipid membranes

A set of average atom-centered charges and polarizabilities has been developed for three types of phospholipids for use in polarizable embedding calculations. The lipids investigated are 1,2-dimyristoyl-sn-glycero-3-phosphocholine, 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine, and 1-palmitoyl-2-oleoyl-sn-glycerol-3-phospho-L-serine given their common use both in experimental and computational studies. The charges, and to a lesser extent the polarizabilities, are found to depend strongly on the molecular conformation of the lipids. Furthermore, the importance of explicit polarization is underlined for the description of larger assemblies of lipids, that is, membranes. In conclusion, we find that specially developed polarizable parameters are needed for embedding calculations in membranes, while common non-polarizable point-charge force fields usually perform well enough for structural and dynamical studies. © 2017 Wiley Periodicals, Inc.

An Estimation of Hybrid Quantum Mechanical Molecular Mechanical Polarization Energies for Small Molecules Using Polarizable Force-Field Approaches

In this work, we report two polarizable molecular mechanics (polMM) force field models for estimating the polarization energy in hybrid quantum mechanical molecular mechanical (QM/MM) calculations. These two models, named the potential of atomic charges (PAC) and potential of atomic dipoles (PAD), are formulated from the ab initio quantum mechanical (QM) response kernels for the prediction of the QM density response to an external molecular mechanical (MM) environment (as described by external point charges). The PAC model is similar to fluctuating charge (FQ) models because the energy depends on external electrostatic potential values at QM atomic sites; the PAD energy depends on external electrostatic field values at QM atomic sites, resembling induced dipole (ID) models. To demonstrate their uses, we apply the PAC and PAD models to 12 small molecules, which are solvated by TIP3P water. The PAC model reproduces the QM/MM polarization energy with a R² value of 0.71 for aniline (in 10,000 TIP3P water configurations) and 0.87 or higher for other 11 solute molecules, while the PAD model has a much better performance with R² values of 0.98 or higher. The PAC model reproduces reference QM/MM hydration free energies for 12 solute molecules with a RMSD of 0.59 kcal/mol. The PAD model is even more accurate, with a much smaller RMSD of 0.12 kcal/mol, with respect to the reference. This suggests that polarization effects, including both local charge distortion and intramolecular charge transfer, can be well captured by induced dipole type models with proper parametrization.

Influence of specific intermolecular interactions on the thermal and dielectric properties of bulk polymers: atomistic molecular dynamics simulations of Nylon 6

Specific intermolecular interactions, in particular H-bonding, have a strong influence on the structural, thermal and relaxation characteristics of polymers. We report here the results of molecular dynamics simulations of Nylon 6 which provides an excellent example for the investigation of such an influence. To demonstrate the effect of proper accounting for H-bonding on bulk polymer properties, the AMBER99sb force field is used with two different parametrization approaches leading to two different sets of partial atomic charges. The simulations allowed the study of the thermal and dielectric properties in a wide range of temperatures and cooling rates. The feasibility of the use of the three methods for the estimation of the glass transition temperature not only from the temperature dependence of structural characteristics such as density, but also by using the electrostatic energy and dielectric constant is demonstrated. The values of glass transition temperatures obtained at different cooling rates are practically the same for the three methods. By proper accounting for partial charges in the simulations, a reasonable agreement between the results of our simulations and experimental data for the density, thermal expansion coefficient, static dielectric constant and activation energy of γ and β relaxations is obtained demonstrating the validity of the modeling approach reported.

The mechanism of an asymmetric ring-opening reaction of epoxide with amine catalyzed by a metal–organic framework: insights from combined quantum mechanics and molecular mechanics calculations

QM/MM computations suggest that the asymmetric ring-opening reaction of epoxide with amine is controlled by CH–π interactions between aniline and a naphthol moiety.

Computational tools for the evaluation of laboratory-engineered biocatalysts

Biocatalysis is based on the application of natural catalysts for new purposes, for which enzymes were not designed. Although the first examples of biocatalysis were reported more than a century ago, biocatalysis was revolutionized after the discovery of an in vitro version of Darwinian evolution called Directed Evolution (DE). Despite the recent advances in the field, major challenges remain to be addressed. Currently, the best experimental approach consists of creating multiple mutations simultaneously while limiting the choices using statistical methods. Still, tens of thousands of variants need to be tested experimentally, and little information is available on how these mutations lead to enhanced enzyme proficiency. This review aims to provide a brief description of the available computational techniques to unveil the molecular basis of improved catalysis achieved by DE. An overview of the strengths and weaknesses of current computational strategies is explored with some recent representative examples. The understanding of how this powerful technique is able to obtain highly active variants is important for the future development of more robust computational methods to predict amino-acid changes needed for activity.

Toward polarizable AMOEBA thermodynamics at fixed charge efficiency using a dual force field approach: application to organic crystals

First principles prediction of the structure, thermodynamics and solubility of organic molecular crystals, which play a central role in chemical, material, pharmaceutical and engineering sciences, challenges both potential energy functions and sampling methodologies. Here we calculate absolute crystal deposition thermodynamics using a novel dual force field approach whose goal is to maintain the accuracy of advanced multipole force fields (e.g. the polarizable AMOEBA model) while performing more than 95% of the sampling in an inexpensive fixed charge (FC) force field (e.g. OPLS-AA). Absolute crystal sublimation/deposition phase transition free energies were determined using an alchemical path that grows the crystalline state from a vapor reference state based on sampling with the OPLS-AA force field, followed by dual force field thermodynamic corrections to change between FC and AMOEBA resolutions at both end states (we denote the three step path as AMOEBA/FC). Importantly, whereas the phase transition requires on the order of 200 ns of sampling per compound, only 5 ns of sampling was needed for the dual force field thermodynamic corrections to reach a mean statistical uncertainty of 0.05 kcal mol-1. For five organic compounds, the mean unsigned error between direct use of AMOEBA and the AMOEBA/FC dual force field path was only 0.2 kcal mol-1 and not statistically significant. Compared to experimental deposition thermodynamics, the mean unsigned error for AMOEBA/FC (1.4 kcal mol-1) was more than a factor of two smaller than uncorrected OPLS-AA (3.2 kcal mol-1). Overall, the dual force field thermodynamic corrections reduced condensed phase sampling in the expensive force field by a factor of 40, and may prove useful for protein stability or binding thermodynamics in the future.

Effective Fully Polarizable QM/MM Approach To Model Vibrational Circular Dichroism Spectra of Systems in Aqueous Solution

We propose a methodology, based on the combination of classical Molecular Dynamics (MD) simulations with a fully polarizable Quantum Mechanical (QM)/Molecular Mechanics (MM)/Polarizable Continuum Model (PCM) Hamiltonian, to calculate Vibrational Circular Dichroism (VCD) spectra of chiral systems in aqueous solution. Polarization effects are included in the MM force field by exploiting an approach based on Fluctuating Charges (FQ). By performing the MD, the description of the solvating environment is enriched by taking into account the dynamical aspects of the solute-solvent interactions. On the other hand, the QM/FQ/PCM calculation of the VCD spectrum ensures an accurate description of the electronic density of the solute and a proper account for the specific interactions in solution. The application of our approach to (R)-methyloxirane and (l)-alanine in aqueous solution gives calculated spectra in remarkable agreement with their experimental counterparts and a substantial improvement with respect to the same spectra calculated with the PCM.

Role of the Molecular Environment in Flavoprotein Color and Redox Tuning: QM Cluster versus QM/MM Modeling

We investigate the origin of the excitation energy shifts induced by the apoprotein in the active site of the bacterial photoreceptor BLUF (Blue Light sensor Using Flavin adenine dinucleotide). In order to compute the vertical excitation energies of three low-lying electronic states, including two π-π* states of flavin (S1 and S2) and a π-π* tyrosine-flavin electron-transfer state (ET), with respect to the energy of the closed-shell ground state (S0), we prepared alternative quantum mechanical (QM) cluster and quantum mechanics/molecular mechanics (QM/MM) models. We found that the excitation energies computed with both types of models correlate with the magnitude of the charge transfer character of the excitation. Accordingly, we conclude that the small charge transfer character of the light absorbing S0-S1 transition and the substantial charge transfer character of the nonabsorbing but redox active S0-ET transition explain the small color changes but substantial redox tuning in BLUF and also in other flavoproteins. Further analysis showed that redox tuning is governed by the electrostatic interaction in the QM/MM model and transfer of charge between the active site and its environment in the QM cluster. Moreover, the wave function polarization of the QM subsystem by the MM subsystem influences the magnitude of the charge transfer, resulting in the QM/MM and QM excitation energies that are not entirely consistent.

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.

An efficient protocol for obtaining accurate hydration free energies using quantum chemistry and reweighting from molecular dynamics simulations

The non-Boltzmann Bennett (NBB) free energy estimator method is applied to 21 molecules from the blind subset of the SAMPL4 challenge. When NBB is applied with the SMD implicit solvent model, and the OLYP/DZP level of quantum chemistry, highly accurate hydration free energy calculations are obtained with respect to experiment (RMSD=0.89kcal·mol^-1). Other quantum chemical methods are also tested, and the effects of solvent model, density functional, basis set are explored in this benchmarking study, providing a framework for improvements in calculating hydration free energies. We provide a practical guide for using the best QM-NBB protocols that are consistently more accurate than either pure QM or pure MM alone. In situations where high accuracy hydration free energy predictions are needed, the QM-NBB method with SMD implicit solvent should be the first choice of quantum chemists.

Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory

Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects.

The MOD-QM/MM Method: Applications to Studies of Photosystem II and DNA G-Quadruplexes

Quantum mechanics/molecular mechanics (QM/MM) hybrid methods are currently the most powerful computational tools for studies of structure/function relations and catalytic sites embedded in macrobiomolecules (eg, proteins and nucleic acids). QM/MM methodologies are highly efficient since they implement quantum chemistry methods for modeling only the portion of the system involving bond-breaking/forming processes (QM layer), as influenced by the surrounding molecular environment described in terms of molecular mechanics force fields (MM layer). Some of the limitations of QM/MM methods when polarization effects are not explicitly considered include the approximate treatment of electrostatic interactions between QM and MM layers. Here, we review recent advances in the development of computational protocols that allow for rigorous modeling of electrostatic interactions in biomacromolecules and structural refinement, beyond the common limitations of QM/MM hybrid methods. We focus on photosystem II (PSII) with emphasis on the description of the oxygen-evolving complex (OEC) and its high-resolution extended X-ray absorption fine structure spectra (EXAFS) in conjunction with Monte Carlo structural refinement. Furthermore, we review QM/MM structural refinement studies of DNA G4 quadruplexes with embedded monovalent cations and direct comparisons to NMR data.

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.

Why is Benzene Soluble in Water? Role of OH/π Interaction in Solvation

The XH/π interaction (X = C, N, or O) plays an essential role in a variety of fundamental processes in condensed phase, and it attracts broad interests in the fields of chemistry and biochemistry in recent years. This issue has a direct relevance to an intriguing phenomenon that a benzene molecule exhibits a negative solvation free energy of -0.87 kcal/mol in ambient water though it is a typical nonpolar organic solute. In this work, we developed a novel method to analyze the free energy δμ due to the electron density fluctuation of a solute in solution to clarify the mechanism responsible for the affinity of benzene to bulk water. Explicitly, the free energy δμ is decomposed into contributions from σ and π electrons in π-conjugated systems on the basis of the QM/MM method combined with a theory of solutions. With our analyses, the free energy δμ(π) arising from the fluctuation of π electrons in benzene was obtained as -0.94 kcal/mol and found to be the major source of the affinity of benzene to water. Thus, the role of π electrons in hydration is quantified for the first time with our analyses. Our method was applied to phenyl methyl ether (PME) in water solution to examine the substituent effects of the electron donating group (EDG) on the hydration of a π-conjugated system. The delocalization effect of the π electrons on hydration was also investigated performing the decomposition analyses for ethene and 1,3-butadiene molecules in water solutions. It was revealed that the stabilization due to δμ(π) for butadiene (-0.76 kcal/mol) is about three times as large as that for ethene (-0.26 kcal/mol), which suggests the importance of the delocalization effect of the π electrons in mediating the affinity to polar solvent.

Comparison of Methods To Reweight from Classical Molecular Simulations to QM/MM Potentials

We examine methods to reweight classical molecular mechanics solvation calculations to more expensive QM/MM energy functions. We first consider the solvation free energy difference between ethane and methanol in a QM/MM Hamiltonian from configurations generated in a cheaper MM potential. The solute molecules in the QM/MM Hamiltonian are treated with B3LYP/6-31G*, and the solvent water molecules are treated classically. The free energy difference in the QM/MM Hamiltonian is estimated using Boltzmann reweighting with both the non-Boltzmann Bennett method (NBB) and the multistate Bennett acceptance ratio (MBAR), and the variance of each method is directly compared for an identical data set. For this system, MBAR-derived methods are found to produce smaller overall uncertainties than NBB-based methods. Additionally, we show that to reduce the variance in the overall free energy difference estimate in this system for a fixed amount of QM/MM calculations, the energy re-evaluations in the Boltzmann reweighting step should be concentrated on the physical MM states with the highest overlap to the QM/MM states, rather than allocated equally over all sampled MM states. We also show that reallocating the QM/MM re-evaluations can be used to diagnose poor overlap between the sampled and target state. The solvation free energies for molecules in the SAMPL4 solvation data set are also calculated in the QM/MM Hamiltonian with NBB and MBAR, and the variances are marginally smaller for MBAR. Overall, NBB and MBAR produce similar variances for systems with poor sampling efficiency, and MBAR provides smaller variances than NBB in systems with high sampling efficiency. Both NBB and MBAR converge to identical solvation free energy estimates in the QM/MM Hamiltonian, and the RMSD to experimental values for molecules in the SAMPL4 solvation data set decreases by approximately 28% when switching from the MM Hamiltonian to the QM/MM Hamiltonian.