Nuclear quantum effects and kinetic isotope effects in enzyme reactions

Amber free energy tools: Interoperable software for free energy simulations using generalized quantum mechanical/molecular mechanical and machine learning potentials

We report the development and testing of new integrated cyberinfrastructure for performing free energy simulations with generalized hybrid quantum mechanical/molecular mechanical (QM/MM) and machine learning potentials (MLPs) in Amber. The Sander molecular dynamics program has been extended to leverage fast, density-functional tight-binding models implemented in the DFTB+ and xTB packages, and an interface to the DeePMD-kit software enables the use of MLPs. The software is integrated through application program interfaces that circumvent the need to perform "system calls" and enable the incorporation of long-range Ewald electrostatics into the external software's self-consistent field procedure. The infrastructure provides access to QM/MM models that may serve as the foundation for QM/MM-ΔMLP potentials, which supplement the semiempirical QM/MM model with a MLP correction trained to reproduce ab initio QM/MM energies and forces. Efficient optimization of minimum free energy pathways is enabled through a new surface-accelerated finite-temperature string method implemented in the FE-ToolKit package. Furthermore, we interfaced Sander with the i-PI software by implementing the socket communication protocol used in the i-PI client-server model. The new interface with i-PI allows for the treatment of nuclear quantum effects with semiempirical QM/MM-ΔMLP models. The modular interoperable software is demonstrated on proton transfer reactions in guanine-thymine mispairs in a B-form deoxyribonucleic acid helix. The current work represents a considerable advance in the development of modular software for performing free energy simulations of chemical reactions that are important in a wide range of applications.

Electronic and Nuclear Quantum Effects on Proton Transfer Reactions of Guanine-Thymine (G-T) Mispairs Using Combined Quantum Mechanical/Molecular Mechanical and Machine Learning Potentials

Rare tautomeric forms of nucleobases can lead to Watson-Crick-like (WC-like) mispairs in DNA, but the process of proton transfer is fast and difficult to detect experimentally. NMR studies show evidence for the existence of short-time WC-like guanine-thymine (G-T) mispairs; however, the mechanism of proton transfer and the degree to which nuclear quantum effects play a role are unclear. We use a B-DNA helix exhibiting a wGT mispair as a model system to study tautomerization reactions. We perform ab initio (PBE0/6-31G*) quantum mechanical/molecular mechanical (QM/MM) simulations to examine the free energy surface for tautomerization. We demonstrate that while the ab initio QM/MM simulations are accurate, considerable sampling is required to achieve high precision in the free energy barriers. To address this problem, we develop a QM/MM machine learning potential correction (QM/MM-ΔMLP) that is able to improve the computational efficiency, greatly extend the accessible time scales of the simulations, and enable practical application of path integral molecular dynamics to examine nuclear quantum effects. We find that the inclusion of nuclear quantum effects has only a modest effect on the mechanistic pathway but leads to a considerable lowering of the free energy barrier for the GT*⇌G*T equilibrium. Our results enable a rationalization of observed experimental data and the prediction of populations of rare tautomeric forms of nucleobases and rates of their interconversion in B-DNA.

Hydrogen Bonding Shuts Down Tunneling in Hydroxycarbenes: A Gas-Phase Study by Tandem-Mass Spectrometry, Infrared Ion Spectroscopy, and Theory

Hydroxycarbenes can be generated and structurally characterized in the gas phase by collision-induced decarboxylation of α-keto carboxylic acids, followed by infrared ion spectroscopy. Using this approach, we have shown earlier that quantum-mechanical hydrogen tunneling (QMHT) accounts for the isomerization of a charge-tagged phenylhydroxycarbene to the corresponding aldehyde in the gas phase and above room temperature. Herein, we report the results of our current study on aliphatic trialkylammonio-tagged systems. Quite unexpectedly, the flexible 3-(trimethylammonio)propylhydroxycarbene turned out to be stable─no H-shift to either aldehyde or enol occurred. As supported by density functional theory calculations, this novel QMHT inhibition is due to intramolecular H-bonding of a mildly acidic α-ammonio C-H bonds to the hydroxyl carbene's C-atom (C:···H-C). To further support this hypothesis, (4-quinuclidinyl)hydroxycarbenes were synthesized, whose rigid structure prevents this intramolecular H-bonding. The latter hydroxycarbenes underwent "regular" QMHT to the aldehyde at rates comparable to, e.g., methylhydroxycarbene studied by Schreiner et al. While QMHT has been shown for a number of biological H-shift processes, its inhibition by H-bonding disclosed here may serve for the stabilization of highly reactive intermediates such as carbenes, even as a mechanism for biasing intrinsic selectivity patterns.

Estimation of frequency factors for the calculation of kinetic isotope effects from classical and path integral free energy simulations

We use the modified Bigeleisen-Mayer equation to compute kinetic isotope effect values for non-enzymatic phosphoryl transfer reactions from classical and path integral molecular dynamics umbrella sampling. The modified form of the Bigeleisen-Mayer equation consists of a ratio of imaginary mode vibrational frequencies and a contribution arising from the isotopic substitution's effect on the activation free energy, which can be computed from path integral simulation. In the present study, we describe a practical method for estimating the frequency ratio correction directly from umbrella sampling in a manner that does not require normal mode analysis of many geometry optimized structures. Instead, the method relates the frequency ratio to the change in the mass weighted coordinate representation of the minimum free energy path at the transition state induced by isotopic substitution. The method is applied to the calculation of 16/18O and 32/34S primary kinetic isotope effect values for six non-enzymatic phosphoryl transfer reactions. We demonstrate that the results are consistent with the analysis of geometry optimized transition state ensembles using the traditional Bigeleisen-Mayer equation. The method thus presents a new practical tool to enable facile calculation of kinetic isotope effect values for complex chemical reactions in the condensed phase.

Temperature-Dependent Kinetic Isotope Effects in R67 Dihydrofolate Reductase from Path-Integral Simulations

Calculation of temperature-dependent kinetic isotope effects (KIE) in enzymes presents a significant theoretical challenge. Additionally, it is not trivial to identify enzymes with available experimental accurate intrinsic KIEs in a range of temperatures. In the current work, we present a theoretical study of KIEs in the primitive R67 dihydrofolate reductase (DHFR) enzyme and compare with experimental work. The advantage of R67 DHFR is its significantly lower kinetic complexity compared to more evolved DHFR isoforms. We employ mass-perturbation-based path-integral simulations in conjunction with umbrella sampling and a hybrid quantum mechanics-molecular mechanics Hamiltonian. We obtain temperature-dependent KIEs in good agreement with experiments and ascribe the temperature-dependent KIEs primarily to zero-point energy effects. The active site in the primitive enzyme is found to be poorly preorganized, which allows excessive water access to the active site and results in loosely bound reacting ligands.

Bovine Serum Albumin Catalysed Hydrogen and Deuterium Evolution at Mercury Electrodes

The hydrogen evolution reaction (HER), catalysed by proteins at mercury electrodes and reflected in chronopotentiometric stripping peak H, provides a label-free and reagentless analytical technique that is sensitive to protein structure. Here we show how the kinetic isotope effect affected the HER catalysed by the protein bovine serum albumin (BSA). We found that the deuteron bond, which is stronger than that of a proton, contributed to less effective transport of deuterons mediated by BSA at the Hg|D₂ O interface, and enhanced structural stability of the surface-attached native BSA in D₂ O solution. A structural transition was also observed in the surface-attached urea-denatured BSA, and is probably due to the destabilisation of some secondary structural remnants retained by the 17 SS-bonds. Because the catalytically active groups involved in proton or deuteron transfer in native proteins are often exposed towards solutions and their protons exchange almost instantly, no signs of H/D exchange were observed in native BSA using peak H under the given conditions.

Role of Microsolvation and Quantum Effects in the Accurate Prediction of Kinetic Isotope Effects: The Case of Hydrogen Atom Abstraction in Ethanol by Atomic Hydrogen in Aqueous Solution

Hydrogen abstraction from ethanol by atomic hydrogen in aqueous solution is studied using two theoretical approaches: the multipath variational transition state theory (MP-VTST) and a path-integral formalism in combination with free-energy perturbation and umbrella sampling (PI-FEP/UM). The performance of the models is compared to experimental values of H kinetic isotope effects (KIE). Solvation models used in this study ranged from purely implicit, via mixed–microsolvation treated quantum mechanically via the density functional theory (DFT) to fully explicit representation of the solvent, which was incorporated using a combined quantum mechanical-molecular mechanical (QM/MM) potential. The effects of the transition state conformation and the position of microsolvating water molecules interacting with the solute on the KIE are discussed. The KIEs are in good agreement with experiment when MP-VTST is used together with a model that includes microsolvation of the polar part of ethanol by five or six water molecules, emphasizing the importance of explicit solvation in KIE calculations. Both, MP-VTST and PI-FEP/UM enable detailed characterization of nuclear quantum effects accompanying the hydrogen atom transfer reaction in aqueous solution.

Chemoenzymatic Assembly of Isotopically Labeled Folates

Pterin-containing natural products have diverse functions in life, but an efficient and easy scheme for their in vitro synthesis is not available. Here we report a chemoenzymatic 14-step, one-pot synthesis that can be used to generate ¹³C- and ¹⁵N-labeled dihydrofolates (H₂F) from glucose, guanine, and p-aminobenzoyl-l-glutamic acid. This synthesis stands out from previous approaches to produce H₂F in that the average yield of each step is >91% and it requires only a single purification step. The use of a one-pot reaction allowed us to overcome potential problems with individual steps during the synthesis. The availability of labeled dihydrofolates allowed the measurement of heavy-atom isotope effects for the reaction catalyzed by the drug target dihydrofolate reductase and established that protonation at N5 of H₂F and hydride transfer to C6 occur in a stepwise mechanism. This chemoenzymatic pterin synthesis can be applied to the efficient production of other folates and a range of other natural compounds with applications in nutritional, medical, and cell-biological research.

Nitroalkane oxidase: Structure and mechanism

The flavoprotein nitroalkane oxidase catalyzes the oxidation of neutral nitroalkanes to the corresponding aldehydes or ketones, releasing nitrite and transferring electrons to O₂ to form H₂O₂. A combination of solution and structural analyses have provided a detailed understanding of the mechanism of this enzyme.

Mechanistic Studies of an Amine Oxidase Derived from d-Amino Acid Oxidase

The flavoprotein d-amino acid oxidase has long served as a paradigm for understanding the mechanism of oxidation of amino acids by flavoproteins. Recently, a mutant d-amino acid oxidase (Y228L/R283G) that catalyzed the oxidation of amines rather than amino acids was described [Yasukawa, K., et al. (2014) Angew. Chem., Int. Ed. 53, 4428-4431]. We describe here the use of pH and kinetic isotope effects with (R)-α-methylbenzylamine as a substrate to determine whether the mutant enzyme utilizes the same catalytic mechanism as the wild-type enzyme. The effects of pH on the steady-state and rapid-reaction kinetics establish that the neutral amine is the substrate, while an active-site residue, likely Tyr224, must be uncharged for productive binding. There is no solvent isotope effect on the k_cat/K_m value for the amine, consistent with the neutral amine being the substrate. The deuterium isotope effect on the k_cat/K_m value is pH-independent, with an average value of 5.3, similar to values found with amino acids as substrates for the wild-type enzyme and establishing that there is no commitment to catalysis with this substrate. The k_cat/K_O2 value is similar to that seen with amino acids as the substrate, consistent with the oxidative half-reaction being unperturbed by the mutation and with flavin oxidation preceding product release. All of the data are consistent with the mutant enzyme utilizing the same mechanism as the wild-type enzyme, transfer of hydride from the neutral amine to the flavin.

Comparison of classical reaction paths and tunneling paths studied with the semiclassical instanton theory

Comparison of classical reaction paths and semiclassical instanton paths for a proton transfer reaction mechanism.

13C kinetic isotope effects on the reaction of a flavin amine oxidase determined from whole molecule isotope effects

A large number of flavoproteins catalyze the oxidation of amines. Because of the importance of these enzymes in metabolism, their mechanisms have previously been studied using deuterium, nitrogen, and solvent isotope effects. While these results have been valuable for computational studies to distinguish among proposed mechanisms, a measure of the change at the reacting carbon has been lacking. We describe here the measurement of a 13C kinetic isotope effect for a representative amine oxidase, polyamine oxidase. The isotope effect was determined by analysis of the isotopic composition of the unlabeled substrate, N, N'-dibenzyl-1,4-diaminopropane, to obtain a pH-independent value of 1.025. The availability of a 13C isotope effect for flavoprotein-catalyzed amine oxidation provides the first measure of the change in bond order at the carbon involved in this carbon-hydrogen bond cleavage and will be of value to understanding the transition state structure for this class of enzymes.

Improved Sugar Puckering Profiles for Nicotinamide Ribonucleoside for Hybrid QM/MM Simulations

The coenzyme nicotinamide adenine dinucleotide (NAD⁺) and its reduced form (NADH) play ubiquitous roles as oxidizing and reducing agents in nature. The binding, and possibly the chemical redox step, of NAD⁺/NADH may be influenced by the cofactor conformational distribution and, in particular, by the ribose puckering of its nicotinamide-ribonucleoside (NR) moiety. In many hybrid quantum mechanics-molecular mechanics (QM/MM) studies of NAD⁺/NADH dependent enzymes, the QM region is treated by semiempirical (SE) methods. Recent work suggests that SE methods do not adequately describe the ring puckering in sugar molecules. In the present work we adopt an efficient and practical strategy to correct for this deficiency for NAD⁺/NADH. We have implemented a cost-effective correction to a SE Hamiltonian by adding a correction potential, which is defined as the difference between an accurate benchmark density functional theory (DFT) potential energy surface (PES) and the SE PES. In practice, this is implemented via a B-spline interpolation scheme for the grid-based potential energy difference surface. We find that the puckering population distributions obtained from free energy QM(SE)/MM simulations are in good agreement with DFT and in fair accord with experimental results. The corrected PES should facilitate a more accurate description of the ribose puckering in the NAD⁺/NADH cofactor in simulations of biological systems.