Influence of inter- and intramolecular hydrogen bonding on kemp decarboxylations from QM/MM simulations

Influence of water content on the [2σ+2σ+2π] cycloaddition of dimethyl azodicarboxylate with quadricyclane in mixed methanol-water solvents from QM/MM Monte Carlo simulations

Mixed quantum mechanics/molecular mechanics Monte Carlo (QM/MM/MC) simulations combined with the free energy perturbation (FEP) theory have been performed to investigate the mechanism and solvent effect of the [2σ+2σ+2π] cycloaddition reaction between dimethyl azodicarboxylate and quadricyclanes in the binary mixture solvents of methanol and water by varying the water content from 0 to 100 vol%. The two-dimensional potentials of mean force (2D PMF) calculations demonstrated that the mechanism of the reaction is a collaborative asynchronous procedure. The transition structures do not show large variation among different solvents. The calculated free energies of activation indicated that the QM/MM/MC method reproduced well the tendency of rate enhancement from pure methanol to methanol-water mixtures to "on water" with the water content increasing obtained in the experimental observation. The analyses of the energy pair distribution and radial distribution functions illustrated that hydrogen bonding plays an indispensable role in the stabilization of the transition structures. According to the results in methanol-water mixtures at different volume ratios, it is clear that the site-specific hydrogen bond effects are the central reason which leads to fast rate increases in progressing from a methanol-water volume ratio of 3 : 1 to 1 : 1. This work provides a new insight into the solvent effect for the [2σ+2σ+2π] cycloaddition reaction.

Supramolecular kinetic effects by pillararenes: the synergism between spatiotemporal and preorganization concepts in decarboxylation reactions

Spatiotemporal and preorganization factors were both responsible for the catalytic and inhibitory supramolecular effects in decarboxylation reactions.

Potential of Mean Force Calculations for an SN2 Fluorination Reaction in Five Different Imidazolium Ionic Liquid Solvents Using Quantum Mechanics/Molecular Mechanics Molecular Dynamics Simulations

The use of ionic liquids (ILs) as both catalysts and solvents in a wide range of chemical reactions has received considerable attention over the last few years due to their positive effects in enhancing reaction rates and selectivities. In this work, hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations were carried out in conjunction with umbrella-sampling techniques to study the bimolecular nucleophilic substitution (S_N2) fluorination reaction between propyl-mesylate and potassium fluoride using five ILs as solvents, specifically, 1-butyl-3-methylimidazolium mesylate ([C₄mim][OMs]), 1-butyl-3-methylimidazolium tetrafluoroborate ([C₄mim][BF₄]), 1-butyl-3-methylimidazolium trifluoroacetate ([C₄mim][CF₃COO]), 1-butyl-3-methylimidazolium bromide ([C₄mim][Br]), and 1-butyl-3-methylimidazolium chloride ([C₄mim][Cl]) at 373.15 K. The QM region (reactive part) in all QM/MM systems was simulated using the Parametric Method 6 (PM6) semiempirical methods, and for the MM region (IL solvent), classical force fields (FF) were employed, with the FF developed within the group. The calculated activation free energy barriers (ΔG^‡) for the S_N2 reaction in the presence of [C₄mim][OMs] and [C₄mim][BF₄] ILs were in agreement with the experimental values reported in the literature. On the other hand, only predicted values were obtained for the activation energies for the [C₄mim][CF₃COO], [C₄mim][Br], and [C₄mim][Cl] ILs. These activation energies indicated that the S_N2 reaction would be more facile to proceed using the [C₄mim][Cl] and [C₄mim][OMs] ILs, in contrast with the use of [C₄mim][Br] IL, which presented the highest activation energy. Energy-pair distributions, radial distribution functions, and noncovalent interactions (NCI) were also calculated to elucidate the molecular interactions between the reactive QM region and the solvents or reaction media. From these calculations, it was found that not only the reactivity can be enhanced by selecting a specific anion to increase the K-F separation but also the cation plays a relevant role, producing a synergetic effect by forming hydrogen bonds with the fluorine atom from KF and with the oxygen atoms within the mesylate leaving group. Three interactions are significant for the IL catalytic behavior, F_QM-HX, K_QM-anion, and O_QM-HX interactions, where the F_QM and K_QM labels correspond to fluorine and potassium atoms from the KF salt, O_QM corresponds to oxygen atoms within the mesylate leaving group (reactant), and HX refers to hydrogen atoms within the IL cation. The NCI analysis revealed that K_QM-anion interactions are of weak type, indicating the importance of hydrogen bond interactions from the cation such as F_QM-HX and O_QM-HX for the catalytic behavior of ILs.

Kemp Elimination Reaction Catalyzed by Electric Fields

The Kemp elimination reaction is the most widely used in the de novo design of new enzymes. The effect of two different kinds of electric fields in the reactions of acetate as a base with benzisoxazole and 5-nitrobenzisoxazole as substrates have been theoretically studied. The effect of the solvent reaction field has been calculated using the SMD continuum model for several solvents; we have shown that solvents inhibit both reactions, the decrease of the reaction rate being larger as far as the dielectric constant is increased. The diminution of the reaction rate is especially remarkable between aprotic organic solvents and protic solvents as water, the electrostatic term of the hydrogen bonds being the main factor for the large inhibitory effect of water. The presence of an external electric field oriented in the direction of the charge transfer (z axis) increases it and, so, the reaction rate. In the reaction of the nitro compound, if the electric field is oriented in an orthogonal direction (x axis) the charge transfer to the NO₂ group is favored and there is a subsequent increase of the reaction rate. However, this increase is smaller than the one produced by the field in the z axis. It is worthwhile mentioning that one of the main effects of external electric fields of intermediate intensity is the reorientation of the reactants. Finally, the implications of our results in the de novo design of enzymes are discussed.

Effects of solvents on the DACBO-catalyzed vinylogous Henry reaction of isatin with 3,5-dimethyl-4-nitroisoxazole "on-water" and in solution from QM/MM MC simulations

The mechanism of the DABCO-catalyzed vinylogous Henry reaction of isatin with 3,5-dimethyl-4-nitroisoxazole and solvent effects on it have been investigated using density functional theory (DFT) methods and QM/MM Monte Carlo (MC) simulation under "on-water" conditions as well as in methanol and THF solutions. The DFT calculations concluded that Path A, in which DABCO directly catalyzes the reaction of isatin 1a with 3,5-dimethyl-4-nitroisoxazole 2 in water, is the most favorable and the first step, the proton transfer process, is the rate-determining step for the reaction. For the roles of solvents in the reaction, QM/MM MC simulations using free energy perturbation theory and PDDG/PM3 as the QM method have been utilized to predict the free energy profiles. The results indicated that the QM/MM method reproduced well the large rate increases on-water. Solute-solvent energy pair distribution and radial distribution functions were also analyzed and illustrated that hydrogen bonding plays a significant role in stabilizing the transition structures. This work reveals the feasible reaction mechanisms and provides new insight into solvent effects for the DACBO-catalyzed vinylogous Henry reaction.

The Role of Water in the Catalyst-Free Aldol Reaction of Water-Insoluble N-Methyl-2,4-thiazolidinedione with N-Methylisatin from QM/MM Monte Carlo Simulations

The role of water in the uncatalyzed aldol reaction of N-methyl-2,4-thiazolidinedione with N-methylisatin is investigated through Monte Carlo statistical mechanics simulations that utilize free energy perturbation theory and the mixed quantum mechanics and molecular mechanics (QM/MM) model with PDDG/PM3 for the QM method in "on-water" and DMSO environments. There are several conceivable orientations between thiazolidinedione and isatin in the process of C-C bond formation. However, the formation of the C-C bond takes place between the re face of isatin and the si face of (E)-enol of the thiazolidinedione to form the preferred anti-type product, which results from enhanced hydrogen-bonding interactions between water molecules and the oxygen atoms undergoing bond breakage and bond formation during the reaction. Novel insights into the effect of water on the aldol reaction are presented herein.

Computation of Accurate Activation Barriers for Methyl-Transfer Reactions of Sulfonium and Ammonium Salts in Aqueous Solution

The energetics of methyl-transfer reactions from dimethylammonium, tetramethylammonium, and trimethylsulfonium to dimethylamine were computed with density functional theory, MP2, CBS-QB3, and quantum mechanics/molecular mechanics (QM/MM) Monte Carlo methods. At the CBS-QB3 level, the gas-phase activation enthalpies are computed to be 9.9, 15.3, and 7.9 kcal/mol, respectively. MP2/6-31+G(d,p) activation enthalpies are in best agreement with the CBS-QB3 results. The effects of aqueous solvation on these reactions were studied with polarizable continuum model, generalized Born/surface area (GB/SA), and QM/MM Monte Carlo simulations utilizing free-energy perturbation theory in which the PDDG/PM3 semiempirical Hamiltonian for the QM and explicit TIP4P water molecules in the MM region were used. In the aqueous phase, all of these reactions proceed more slowly when compared to the gas phase, since the charged reactants are stabilized more than the transition structure geometries with delocalized positive charges. In order to obtain the aqueous-phase activation free energies, the gas-phase activation free energies were corrected with the solvation free energies obtained from single-point conductor-like polarizable continuum model and GB/SA calculations for the stationary points along the reaction coordinate.

An Integrated Path Integral and Free-Energy Perturbation-Umbrella Sampling Method for Computing Kinetic Isotope Effects of Chemical Reactions in Solution and in Enzymes

An integrated centroid path integral and free-energy perturbation-umbrella sampling (PI-FEP/UM) method for computing kinetic isotope effects (KIEs) for chemical reactions in solution and in enzymes is presented. The method is based on the bisection sampling in centroid path integral simulations to include nuclear quantum effects to the classical potential of mean force. The required accuracy for computing kinetic isotope effects is achieved by coupled free-energy perturbation and umbrella sampling for reactions involving different isotopes. The use of FEP with respect to different masses results in relatively small statistical uncertainties, whereas if KIEs are computed directly by the difference in free energies obtained from the quantum mechanical potentials of mean force for different isotopes, the statistical errors are significantly greater. The PI-FEP/UM method is illustrated in two applications. The first reaction is the decarboxylation of N-methyl picolinate in water, for which the primary (13)C and secondary (15)N KIEs have been determined. The second reaction is the proton-transfer reaction between nitroethane and an acetate ion in water. In both cases, the computational results are in accord with experimental data, and the findings provide further insight into the mechanism of these reactions in water.

Reaction pathways and free energy profiles for cholinesterase-catalyzed hydrolysis of 6-monoacetylmorphine

As the most active metabolite of heroin, 6-monoacetylmorphine (6-MAM) can penetrate into the brain for the rapid onset of heroin effects. The primary enzymes responsible for the metabolism of 6-MAM to the less potent morphine in humans are acetylcholinesterase (AChE) and butyrylcholinesterase (BChE). The detailed reaction pathways for AChE- and BChE-catalyzed hydrolysis of 6-MAM to morphine have been explored, for the first time, in the present study by performing first-principles quantum mechanical/molecular mechanical free energy calculations. It has been demonstrated that the two enzymatic reaction processes follow similar catalytic reaction mechanisms, and the whole catalytic reaction pathway for each enzyme consists of four reaction steps. According to the calculated results, the second reaction step associated with the transition state TS2(a)/TS2(b) should be rate-determining for the AChE/BChE-catalyzed hydrolysis, and the free energy barrier calculated for the AChE-catalyzed hydrolysis (18.3 kcal mol(-1)) is 2.5 kcal mol(-1) lower than that for the BChE-catalyzed hydrolysis (20.8 kcal mol(-1)). The free energy barriers calculated for the AChE- and BChE-catalyzed reactions are in good agreement with the experimentally derived activation free energies (17.5 and 20.7 kcal mol(-1) for the AChE- and BChE-catalyzed reactions, respectively). Further structural analysis reveals that the aromatic residues Phe295 and Phe297 in the acyl pocket of AChE (corresponding to Leu286 and Val288 in BChE) contribute to the lower energy of TS2(a) relative to TS2(b). The obtained structural and mechanistic insights could be valuable for use in future rational design of a novel therapeutic treatment of heroin abuse.

Quantum and Molecular Mechanical (QM/MM) Monte Carlo Techniques for Modeling Condensed-Phase Reactions

A recent review (Acc. Chem. Res. 2010, 43:142-151) examined our use and development of a combined quantum and molecular mechanical (QM/MM) technique for modelling organic and enzymatic reactions. Advances included the PDDG/PM3 semiempirical QM (SQM) method, computation of multi-dimensional potentials of mean force (PMF), incorporation of on-the-fly QM in Monte Carlo simulations, and a polynomial quadrature method for rapidly treating proton-transfer reactions. The current article serves as a follow up on our progress. Highlights include new reactions, alternative SQM methods, a polarizable OPLS force field, and novel solvent environments, e.g., "on water" and room temperature ionic liquids. The methodology is strikingly accurate across a wide range of condensed-phase and antibody-catalyzed reactions including substitution, decarboxylation, elimination, isomerization, and pericyclic classes. Comparisons are made to systems treated with continuum-based solvents and ab initio or density functional theory (DFT) methods. Overall, the QM/MM methodology provides detailed characterization of reaction paths, proper configurational sampling, several advantages over implicit solvent models, and a reasonable computational cost.

QM/MM investigations of organic chemistry oriented questions

About 35 years after its first suggestion, QM/MM became the standard theoretical approach to investigate enzymatic structures and processes. The success is due to the ability of QM/MM to provide an accurate atomistic picture of enzymes and related processes. This picture can even be turned into a movie if nuclei-dynamics is taken into account to describe enzymatic processes. In the field of organic chemistry, QM/MM methods are used to a much lesser extent although almost all relevant processes happen in condensed matter or are influenced by complicated interactions between substrate and catalyst. There is less importance for theoretical organic chemistry since the influence of nonpolar solvents is rather weak and the effect of polar solvents can often be accurately described by continuum approaches. Catalytic processes (homogeneous and heterogeneous) can often be reduced to truncated model systems, which are so small that pure quantum-mechanical approaches can be employed. However, since QM/MM becomes more and more efficient due to the success in software and hardware developments, it is more and more used in theoretical organic chemistry to study effects which result from the molecular nature of the environment. It is shown by many examples discussed in this review that the influence can be tremendous, even for nonpolar reactions. The importance of environmental effects in theoretical spectroscopy was already known. Due to its benefits, QM/MM can be expected to experience ongoing growth for the next decade.In the present chapter we give an overview of QM/MM developments and their importance in theoretical organic chemistry, and review applications which give impressions of the possibilities and the importance of the relevant effects. Since there is already a bunch of excellent reviews dealing with QM/MM, we will discuss fundamental ingredients and developments of QM/MM very briefly with a focus on very recent progress. For the applications we follow a similar strategy.

Fundamental reaction pathway for peptide metabolism by proteasome: insights from first-principles quantum mechanical/molecular mechanical free energy calculations

Proteasome is the major component of the crucial non-lysosomal protein degradation pathway in the cells, but the detailed reaction pathway is unclear. In this study, first-principles quantum mechanical/molecular mechanical free energy calculations have been performed to explore, for the first time, possible reaction pathways for proteasomal proteolysis/hydrolysis of a representative peptide, succinyl-leucyl-leucyl-valyl-tyrosyl-7-amino-4-methylcoumarin (Suc-LLVY-AMC). The computational results reveal that the most favorable reaction pathway consists of six steps. The first is a water-assisted proton transfer within proteasome, activating Thr1-O(γ). The second is a nucleophilic attack on the carbonyl carbon of a Tyr residue of substrate by the negatively charged Thr1-O(γ), followed by the dissociation of the amine AMC (third step). The fourth step is a nucleophilic attack on the carbonyl carbon of the Tyr residue of substrate by a water molecule, accompanied by a proton transfer from the water molecule to Thr1-N(z). Then, Suc-LLVY is dissociated (fifth step), and Thr1 is regenerated via a direct proton transfer from Thr1-N(z) to Thr1-O(γ). According to the calculated energetic results, the overall reaction energy barrier of the proteasomal hydrolysis is associated with the transition state (TS3(b)) for the third step involving a water-assisted proton transfer. The determined most favorable reaction pathway and the rate-determining step have provided a reasonable interpretation of the reported experimental observations concerning the substituent and isotopic effects on the kinetics. The calculated overall free energy barrier of 18.2 kcal/mol is close to the experimentally derived activation free energy of ∼18.3-19.4 kcal/mol, suggesting that the computational results are reasonable.

Fundamental reaction pathway and free energy profile for butyrylcholinesterase-catalyzed hydrolysis of heroin

The pharmacological function of heroin requires an activation process that transforms heroin into 6-monoacetylmorphine (6-MAM), which is the most active form. The primary enzyme responsible for this activation process in human plasma is butyrylcholinesterase (BChE). The detailed reaction pathway of the activation process via BChE-catalyzed hydrolysis has been explored computationally, for the first time, in this study via molecular dynamics simulation and first-principles quantum mechanical/molecular mechanical free energy calculations. It has been demonstrated that the whole reaction process includes acylation and deacylation stages. The acylation consists of two reaction steps, i.e., the nucleophilic attack on the carbonyl carbon of the 3-acetyl group of heroin by the hydroxyl oxygen of the Ser198 side chain and the dissociation of 6-MAM. The deacylation also consists of two reaction steps, i.e., the nucleophilic attack on the carbonyl carbon of the acyl-enzyme intermediate by a water molecule and the dissociation of the acetic acid from Ser198. The calculated free energy profile reveals that the second transition state (TS2) should be rate-determining. The structural analysis reveals that the oxyanion hole of BChE plays an important role in the stabilization of rate-determining TS2. The free energy barrier (15.9 ± 0.2 or 16.1 ± 0.2 kcal/mol) calculated for the rate-determining step is in good agreement with the experimentally derived activation free energy (~16.2 kcal/mol), suggesting that the mechanistic insights obtained from this computational study are reliable. The obtained structural and mechanistic insights could be valuable for use in the future rational design of a novel therapeutic treatment of heroin abuse.

QM/MM investigation on 1,3-dipolar cycloadditions of the phthalazinium dicyanomethanide with three different dipolarophiles on water and in solution

An "on water" environment, describing the reactions with insoluble reactants in water, has been reported to give high yields of products compared to organic solvents. The 1,3-dipolar cycloadditions of phthalazinium dicyanomethanide 1 with three different dipolarophiles, methyl vinyl ketone (MVK), methyl acrylate (MAC), and styrene (STY), have been investigated using QM/MM calculations in water, acetonitrile, and acetonitrile-water solvent mixtures, as well as at the vacuum-water interface. Monte Carlo statistical mechanics simulations utilizing the free-energy perturbation theory and PDDG/PM3 for the QM method have been used. The transition structures for all three reactions do not show large variations among different solvents. However, the calculated free energies of activation at the interface are found to be higher than those calculated in bulk water. Computed energy pair distributions and radial distribution functions reveal a uniform loss of hydrogen bonds for the reactants and transitions states in progressing from bulk water to the vacuum-water interface. The hydrophobic effects in the reactions of 1 with MVK and MAC are similar for both, and weaker than the effect in the reaction with STY. According to the results in water-acetonitrile mixtures at different molar ratios, it is clear that the special hydrogen bonding effects are the main reason which leads to the rapid rate enhancement in progressing from a water-acetonitrile molar ratio of 0.9 : 0.1 to pure water. New insights into solvent effects for 1,3-dipolar cycloadditions are presented herein.

Fundamental reaction pathway and free energy profile for inhibition of proteasome by Epoxomicin

First-principles quantum mechanical/molecular mechanical free energy calculations have been performed to provide the first detailed computational study on the possible mechanisms for reaction of proteasome with a representative peptide inhibitor, Epoxomicin (EPX). The calculated results reveal that the most favorable reaction pathway consists of five steps. The first is a proton transfer process, activating Thr1-O(γ) directly by Thr1-N(z) to form a zwitterionic intermediate. The next step is nucleophilic attack on the carbonyl carbon of EPX by the negatively charged Thr1-O(γ) atom, followed by a proton transfer from Thr1-N(z) to the carbonyl oxygen of EPX (third step). Then, Thr1-N(z) attacks on the carbon of the epoxide group of EPX, accompanied by the epoxide ring-opening (S(N)2 nucleophilic substitution) such that a zwitterionic morpholino ring is formed between residue Thr1 and EPX. Finally, the product of morpholino ring is generated via another proton transfer. Noteworthy, Thr1-O(γ) can be activated directly by Thr1-N(z) to form the zwitterionic intermediate (with a free energy barrier of only 9.9 kcal/mol), and water cannot assist the rate-determining step, which is remarkably different from the previous perception that a water molecule should mediate the activation process. The fourth reaction step has the highest free energy barrier (23.6 kcal/mol) which is reasonably close to the activation free energy (∼21-22 kcal/mol) derived from experimental kinetic data. The obtained novel mechanistic insights should be valuable for not only future rational design of more efficient proteasome inhibitors but also understanding the general reaction mechanism of proteasome with a peptide or protein.

On the mechanism and rate of spontaneous decomposition of amino acids

Spontaneous decarboxylation of amino acids is among the slowest known reactions; it is much less facile than the cleavage of amide bonds in polypeptides. Establishment of the kinetics and mechanisms for this fundamental reaction is important for gauging the proficiency of enzymes. In the present study, multiple mechanisms for glycine decomposition in water are explored using QM/MM Monte Carlo simulations and free energy perturbation theory. Simple CO(2) detachment emerges as the preferred pathway for decarboxylation; it is followed by water-assisted proton transfer to yield the products: CO(2) and methylamine. The computed free energy of activation of 45 kcal/mol, and the resulting rate-constant of 1 × 10(-21) s(-1), can be compared with an extrapolated experimental rate constant of ~2 × 10(-17) s(-1) at 25 °C. The half-life for the reaction is more than 1 billion years. Furthermore, examination of deamination finds simple NH(3)-detachment yielding α-lactone to be the favored route, though it is less facile than decarboxylation by 6 kcal/mol. Ab initio and DFT calculations with the CPCM hydration model were also carried out for the reactions; the computed free energies of activation for glycine decarboxylation agree with the QM/MM result, whereas deamination is predicted to be more favorable. QM/MM calculations were also performed for decarboxylation of alanine; the computed barrier is 2 kcal/mol higher than for glycine in qualitative accord with experiment.

Thorpe-Ingold acceleration of oxirane formation is mostly a solvent effect

The Thorpe-Ingold hypothesis for the gem-dimethyl effect in the cyclization reactions of 2-chloroethoxide derivatives has been investigated computationally in the gas phase and in aqueous solution. Ab initio MP2/6-311+G(d,p) and CBS-Q calculations reveal little intrinsic difference in reactivity with increasing alpha-methylation for the series of reactants 1-3. However, inclusion of continuum hydration or of explicit hydration through mixed quantum and statistical mechanics (MC/FEP) simulations does reproduce the substantial, experimentally observed rate increases with increasing alpha-methylation. Analysis of the MC/FEP results provides clear evidence that the rate increases stem primarily from increased steric hindrance to hydration of the nucleophilic oxygen atom with increasing alpha-methylation. Thus, the gem-dimethyl acceleration of oxirane formation for 1-3 is found to be predominantly a solvent effect.

Role of water in the multifaceted catalytic antibody 4B2 for allylic isomerization and Kemp elimination reactions

Specificity toward a single reaction is a well-known characteristic of catalytic antibodies. However, contrary to convention, catalytic antibody 4B2 possesses the ability to efficiently catalyze two unrelated reactions: a Kemp elimination and an allylic isomerization of a beta,gamma-unsaturated ketone. To elucidate how this multifaceted antibody operates, mixed quantum and molecular mechanics calculations coupled to Monte Carlo simulations were carried out. The antibody was determined to derive its adaptability for the mechanistically different reactions through the rearrangement of water molecules in the active site into advantageous geometric orientations for enhanced electrostatic stabilization. In the case of the Kemp elimination, a general base, Glu L34, carried out the proton abstraction from the isoxazole ring of 5-nitro-benzisoxazole while water molecules delivered specific stabilization at the transition state. The role of water was found to be more pronounced in the allylic isomerization because the solvent actively participated in the stepwise mechanism. A rate-limiting abstraction of the alpha-proton from the beta,gamma-unsaturated ketone via Glu L34 led to the formation of a neutral dienol intermediate, which was rapidly reprotonated at the gamma-position via a solvent hydronium ion. Preferential channeling of H(3)O(+) in the active site ensured a stereoselective proton exchange from the alpha- to the gamma-position, in good agreement with deuterium exchange NMR and HPLC experiments. Ideas for improved water-mediated catalytic antibody designs are presented. In a technical advancement, improvements to a recent polynomial fitting and integration technique utilizing free energy perturbation theory delivered greater accuracy and speed gains.

Advances in quantum and molecular mechanical (QM/MM) simulations for organic and enzymatic reactions

Application of combined quantum and molecular mechanical (QM/MM) methods focuses on predicting activation barriers and the structures of stationary points for organic and enzymatic reactions. Characterization of the factors that stabilize transition structures in solution and in enzyme active sites provides a basis for design and optimization of catalysts. Continued technological advances allowed for expansion from prototypical cases to mechanistic studies featuring detailed enzyme and condensed-phase environments with full integration of the QM calculations and configurational sampling. This required improved algorithms featuring fast QM methods, advances in computing changes in free energies including free-energy perturbation (FEP) calculations, and enhanced configurational sampling. In particular, the present Account highlights development of the PDDG/PM3 semi-empirical QM method, computation of multi-dimensional potentials of mean force (PMF), incorporation of on-the-fly QM in Monte Carlo (MC) simulations, and a polynomial quadrature method for efficient modeling of proton-transfer reactions. The utility of this QM/MM/MC/FEP methodology is illustrated for a variety of organic reactions including substitution, decarboxylation, elimination, and pericyclic reactions. A comparison to experimental kinetic results on medium effects has verified the accuracy of the QM/MM approach in the full range of solvents from hydrocarbons to water to ionic liquids. Corresponding results from ab initio and density functional theory (DFT) methods with continuum-based treatments of solvation reveal deficiencies, particularly for protic solvents. Also summarized in this Account are three specific QM/MM applications to biomolecular systems: (1) a recent study that clarified the mechanism for the reaction of 2-pyrone derivatives catalyzed by macrophomate synthase as a tandem Michael-aldol sequence rather than a Diels-Alder reaction, (2) elucidation of the mechanism of action of fatty acid amide hydrolase (FAAH), an unusual Ser-Ser-Lys proteolytic enzyme, and (3) the construction of enzymes for Kemp elimination of 5-nitrobenzisoxazole that highlights the utility of QM/MM in the design of artificial enzymes.

Catalytic mechanism and performance of computationally designed enzymes for Kemp elimination

A series of enzymes for Kemp elimination of 5-nitrobenzisoxazole has been recently designed and tested. In conjunction with the design process, extensive computational analyses were carried out to evaluate the potential performance of four of the designs, as presented here. The enzyme-catalyzed reactions were modeled using mixed quantum and molecular mechanics (QM/MM) calculations in the context of Monte Carlo (MC) statistical mechanics simulations. Free-energy perturbation (FEP) calculations were used to characterize the free-energy surfaces for the catalyzed reactions as well as for reference processes in water. The simulations yielded detailed information about the catalytic mechanisms, activation barriers, and structural evolution of the active sites over the course of the reactions. The catalytic mechanism for the designed enzymes KE07, KE10(V131N), and KE15 was found to be concerted with proton transfer, generally more advanced in the transition state than breaking of the isoxazolyl N-O bond. On the basis of the free-energy results, all three enzymes were anticipated to be active. Ideas for further improvement of the enzyme designs also emerged. On the technical side, the synergy of parallel QM/MM and experimental efforts in the design of artificial enzymes is well illustrated.

Origin of the activity drop with the E50D variant of catalytic antibody 34E4 for Kemp elimination

In enzymes, multiple structural effects cooperatively lead to the high catalytic activity, while individually these effects can be small. The design of artificial enzymes requires the understanding and ability to manipulate such subtle effects. The 34E4 catalytic antibody, catalyzing Kemp elimination of 5-nitrobenzisoxazole, and its Glu50Asp (E50D) variant are the subject of the present investigation. This removal of only a methylene group yields an approximately 30-fold reduction in the rate for the catalyzed Kemp elimination. Here, the aim is to understand this difference in the catalytic performance. The mechanism of Kemp elimination catalyzed by 34E4 and the E50D mutant is elucidated using QM/MM Monte Carlo simulations and free energy perturbation theory. In both proteins, the reaction is shown to follow a single-step, concerted mechanism. In the mutant, the activation barrier rises by 2.4 kcal/mol, which corresponds to a 62-fold rate deceleration, which is in good agreement with the experimental data. The positions and functionality of the residues in the active site are monitored throughout the reaction. It is concluded that the looser contact with the base, shorter base-Asn58 contact, less favorable pi-stacking with Trp91 in the transition state of the reaction, and different solvation pattern all contribute to the reduction of the reaction rate in the E50D variant of 34E4.

Charge-dependent model for many-body polarization, exchange, and dispersion interactions in hybrid quantum mechanical/molecular mechanical calculations

This work explores a new charge-dependent energy model consisting of van der Waals and polarization interactions between the quantum mechanical (QM) and molecular mechanical (MM) regions in a combined QMMM calculation. van der Waals interactions are commonly treated using empirical Lennard-Jones potentials, whose parameters are often chosen based on the QM atom type (e.g., based on hybridization or specific covalent bonding environment). This strategy for determination of QMMM nonbonding interactions becomes tedious to parametrize and lacks robust transferability. Problems occur in the study of chemical reactions where the "atom type" is a complex function of the reaction coordinate. This is particularly problematic for reactions, where atoms or localized functional groups undergo changes in charge state and hybridization. In the present work we propose a new model for nonelectrostatic nonbonded interactions in QMMM calculations that overcomes many of these problems. The model is based on a scaled overlap model for repulsive exchange and attractive dispersion interactions that is a function of atomic charge. The model is chemically significant since it properly correlates atomic size, softness, polarizability, and dispersion terms with minimal one-body parameters that are functions of the atomic charge. Tests of the model are examined for rare-gas interactions with neutral and charged atoms in order to demonstrate improved transferability. The present work provides a new framework for modeling QMMM interactions with improved accuracy and transferability.

Quantitative computer simulations of biomolecules: A snapshot

A recent workshop titled "Quantitative Computational Biophysics" at Florida State University provided an overview of the state of the art in quantitative modeling of biomolecular systems. The presentations covered a wide range of interrelated topics, including the development and validation of force fields, the modeling of protein-protein interactions, the sampling of conformational space, and the assessment of equilibration and statistical errors. Substantial progress in all these areas was reported.

Medium effects on the decarboxylation of a biotin model in pure and mixed solvents from QM/MM simulations

The decarboxylation of imidazolidin-2-one-1-carboxylate anion 2 has been investigated via combined quantum and statistical mechanics methodology. Monte Carlo statistical mechanics simulations utilizing free-energy perturbation theory and PDDG/PM3 for the QM method yielded free-energy profiles for the reaction in water, methanol, acetonitrile, and mixed solvents. The results for free energies of activation are uniformly in close accord with experimental data and reflect large rate accelerations in progressing from protic to dipolar aprotic media. Structural and energetic analyses confirm that the rate retardation in protic solvents comes from loss of hydrogen bonding in progressing from the carboxylate anion 2 to the more charge-delocalized transition state (TS). The structure of the TS is found to be significantly affected by the reaction medium; it occurs at a 0.2-A shorter C-N separation in protic solvents than in acetonitrile. Characterization of the hydrogen bonding for 2 and the TS also provided insights for design of decarboxylase catalysts, namely, it is desirable to have three hydrogen-bond donating groups positioned to interact with the ureido oxygen along with two hydrogen-bond donors positioned to interact with the ureido nitrogen of the breaking C-N bond.

Why urea eliminates ammonia rather than hydrolyzes in aqueous solution

A joint QM/MM and ab initio study on the decomposition of urea in the gas phase and in aqueous solution is reported. Numerous possible mechanisms of intramolecular decomposition and hydrolysis have been explored; intramolecular NH3 elimination assisted by a water molecule is found to have the lowest activation energy. The solvent effects were elucidated using the TIP4P explicit water model with free energy perturbation calculations in conjunction with QM/MM Monte Carlo simulations. The explicit representation of the solvent was found to be essential for detailed resolution of the mechanism, identification of the rate-determining step, and evaluation of the barrier. The assisting water molecule acts as a hydrogen shuttle for the first step of the elimination reaction. The forming zwitterionic intermediate, H3NCONH, participates in 8-9 hydrogen bonds with water molecules. Its decomposition is found to be the rate-limiting step, and the overall free energy of activation for the decomposition of urea in water is computed to be approximately 37 kcal/mol; the barrier for hydrolysis by an addition/elimination mechanism is found to be approximately 40 kcal/mol. The differences in the electronic structure of the transition states of the NH3 elimination and hydrolysis were examined via natural bond order analysis. Destruction of urea's resonance stabilization during hydrolysis via an addition/elimination mechanism and its preservation in the rearrangement to the H3NCONH intermediate were identified as important factors in determining the preferred reaction route.

The origins of femtomolar protein-ligand binding: hydrogen-bond cooperativity and desolvation energetics in the biotin-(strept)avidin binding site

The unusually strong reversible binding of biotin by avidin and streptavidin has been investigated by density functional and MP2 ab initio quantum mechanical methods. The solvation of biotin by water has also been studied through QM/MM/MC calculations. The ureido moiety of biotin in the bound state hydrogen bonds to five residues, three to the carbonyl oxygen and one for each--NH group. These five hydrogen bonds act cooperatively, leading to stabilization that is larger than the sum of individual hydrogen-bonding energies. The charged aspartate is the key residue that provides the driving force for cooperativity in the hydrogen-bonding network for both avidin and streptavidin by greatly polarizing the urea of biotin. If the residue is removed, the network is disrupted, and the attenuation of the energetic contributions from the neighboring residues results in significant reduction of cooperative interactions. Aspartate is directly hydrogen-bonded with biotin in streptavidin and is one residue removed in avidin. The hydrogen-bonding groups in streptavidin are computed to give larger cooperative hydrogen-bonding effects than avidin. However, the net gain in electrostatic binding energy is predicted to favor the avidin-bicyclic urea complex due to the relatively large penalty for desolvation of the streptavidin binding site (specifically expulsion of bound water molecules). QM/MM/MC calculations involving biotin and the ureido moiety in aqueous solution, featuring PDDG/PM3, show that water interactions with the bicyclic urea are much weaker than (strept)avidin interactions due to relatively low polarization of the urea group in water.

Elucidation of Hydrolysis Mechanisms for Fatty Acid Amide Hydrolase and Its Lys142Ala Variant via QM/MM Simulations

Fatty acid amide hydrolase (FAAH) is a serine hydrolase that degrades anandamide, an endocannabinoid, and oleamide, a sleep-inducing lipid, and has potential applications as a therapeutic target for neurological disorders. Remarkably, FAAH hydrolyzes amides and esters with similar rates; however, the normal preference for esters reemerges when Lys142 is mutated to alanine. To elucidate the hydrolysis mechanisms and the causes behind this variation of selectivity, mixed quantum and molecular mechanics (QM/MM) calculations were carried out to obtain free-energy profiles for alternative mechanisms for the enzymatic hydrolyses. The methodology features free-energy perturbation calculations in Monte Carlo simulations with PDDG/PM3 as the QM method. For wild-type FAAH, the results support a mechanism, which features proton transfer from Ser217 to Lys142, simultaneous proton transfer from Ser241 to Ser217, and attack of Ser241 on the substrate's carbonyl carbon to yield a tetrahedral intermediate, which subsequently undergoes elimination with simultaneous protonation of the leaving group by a Lys142-Ser217 proton shuttle. For the Lys142Ala mutant, a striking multistep sequence is proposed with simultaneous proton transfer from Ser241 to Ser217, attack of Ser241 on the carbonyl carbon of the substrate, and elimination of the leaving group and its protonation by Ser217. Support comes from the free-energy results, which well reproduce the observation that the Lys142Ala mutation in FAAH decreases the rate of hydrolysis for oleamide significantly more than for methyl oleate.

Cope Elimination: Elucidation of Solvent Effects from QM/MM Simulations

The Cope elimination reactions for threo- and erythro-N,N-dimethyl-3-phenyl-2-butylamine oxide have been investigated using QM/MM calculations in water, THF, and DMSO. The aprotic solvents provide up to million-fold rate accelerations. The effects of solvation on the reactants, transition structures, and rates of reaction are elucidated here using two-dimensional potentials of mean force (PMF) derived from free-energy perturbation calculations in Monte Carlo simulations (MC/FEP). The resultant free energies of activation in solution are in close agreement with experiment. Ab initio calculations at the MP2/6-311+G-(2d,p) level using the PCM continuum solvent model were also carried out; however, only the QM/MM methodology was able to reproduce the large rate increases in proceeding from water to the dipolar aprotic solvents. Solute-solvent interaction energies and radial distribution functions are also analyzed and show that poorer solvation of the reactant in the aprotic solvents is primarily responsible for the observed rate enhancements. It is found that the amine oxide oxygen is the acceptor of three hydrogen bonds from water molecules for the reactant but only one to two weaker ones at the transition state. The overall quantitative success of the computations supports the present QM/MM/MC approach, featuring PDDG/PM3 as the QM method.

Combined valence bond-molecular mechanics potential-energy surface and direct dynamics study of rate constants and kinetic isotope effects for the H+C2H6 reaction

This article presents a multifaceted study of the reaction H+C(2)H(6)-->H(2)+C(2)H(5) and three of its deuterium-substituted isotopologs. First we present high-level electronic structure calculations by the W1, G3SX, MCG3-MPWB, CBS-APNO, and MC-QCISD/3 methods that lead to a best estimate of the barrier height of 11.8+/-0.5 kcal/mol. Then we obtain a specific reaction parameter for the MPW density functional in order that it reproduces the best estimate of the barrier height; this yields the MPW54 functional. The MPW54 functional, as well as the MPW60 functional that was previously parametrized for the H+CH(4) reaction, is used with canonical variational theory with small-curvature tunneling to calculate the rate constants for all four ethane reactions from 200 to 2000 K. The final MPW54 calculations are based on curvilinear-coordinate generalized-normal-mode analysis along the reaction path, and they include scaled frequencies and an anharmonic C-C bond torsion. They agree with experiment within 31% for 467-826 K except for a 38% deviation at 748 K; the results for the isotopologs are predictions since these rate constants have never been measured. The kinetic isotope effects (KIEs) are analyzed to reveal the contributions from subsets of vibrational partition functions and from tunneling, which conspire to yield a nonmonotonic temperature dependence for one of the KIEs. The stationary points and reaction-path potential of the MPW54 potential-energy surface are then used to parametrize a new kind of analytical potential-energy surface that combines a semiempirical valence bond formalism for the reactive part of the molecule with a standard molecular mechanics force field for the rest; this may be considered to be either an extension of molecular mechanics to treat a reactive potential-energy surface or a new kind of combined quantum-mechanical/molecular mechanical (QM/MM) method in which the QM part is semiempirical valence bond theory; that is, the new potential-energy surface is a combined valence bond molecular mechanics (CVBMM) surface. Rate constants calculated with the CVBMM surface agree with the MPW54 rate constants within 12% for 534-2000 K and within 23% for 200-491 K. The full CVBMM potential-energy surface is now available for use in variety of dynamics calculations, and it provides a prototype for developing CVBMM potential-energy surfaces for other reactions.

Molecular modeling of organic and biomolecular systems using BOSS and MCPRO

An overview is provided of the capabilities for the current versions of the BOSS and MCPRO programs for molecular modeling of organic and biomolecular systems. Recent applications are noted, particularly for QM/MM studies of organic and enzymatic reactions and for protein-ligand binding.