Hydrogen tunneling in enzyme reactions

Heavy water inhibits DNA double-strand break repairs and disturbs cellular transcription, presumably via quantum-level mechanisms of kinetic isotope effects on hydrolytic enzyme reactions

Heavy water, containing the heavy hydrogen isotope, is toxic to cells, although the underlying mechanism remains incompletely understood. In addition, certain enzymatic proton transfer reactions exhibit kinetic isotope effects attributed to hydrogen isotopes and their temperature dependencies, indicative of quantum tunneling phenomena. However, the correlation between the biological effects of heavy water and the kinetic isotope effects mediated by hydrogen isotopes remains elusive. In this study, we elucidated the kinetic isotope effects arising from hydrogen isotopes of water and their temperature dependencies in vitro, focusing on deacetylation, DNA cleavage, and protein cleavage, which are crucial enzymatic reactions mediated by hydrolysis. Intriguingly, the intracellular isotope effects of heavy water, related to the in vitro kinetic isotope effects, significantly impeded multiple DNA double-strand break repair mechanisms crucial for cell survival. Additionally, heavy water exposure enhanced histone acetylation and associated transcriptional activation in cells, consistent with the in vitro kinetic isotope effects observed in histone deacetylation reactions. Moreover, as observed for the in vitro kinetic isotope effects, the cytotoxic effect on cell proliferation induced by heavy water exhibited temperature-dependency. These findings reveal the substantial impact of heavy water-induced isotope effects on cellular functions governed by hydrolytic enzymatic reactions, potentially mediated by quantum-level mechanisms underlying kinetic isotope effects.

Heavy-Atom Tunneling in Ring-Closure Reactions of Beryllium Ozonide Complexes

Quantum mechanical tunneling (QMT) has long been recognized as crucial for understanding chemical reaction mechanisms, particularly in reactions involving light atoms like hydrogen. However, recent findings have expanded this understanding to include heavy-atom tunneling reactions. In this report, we present the observation of two heavy-atom tunneling reactions involving the spontaneous conversions from end-on bonded beryllium ozonide complexes, OBeOOO (A) and BeOBeOOO (C), to their corresponding side-on bonded ozonide isomers, OBe(η2-O3) (B) and BeOBe(η2-O3) (D), respectively, in a cryogenic neon matrix. This discovery is supported by the weak temperature dependence of the rate constants and unusually large 16O/18O kinetic isotope effects. Quantum chemistry calculations reveal extremely low barriers (<1 kcal/mol) for both ring-closure reactions. Additionally, instanton theory calculations on both reactions unveil that the tunneling processes involve the concerted motion of all four oxygen atoms.

Nonadiabatic Hydrogen Tunneling Dynamics for Multiple Proton Transfer Processes with Generalized Nuclear-Electronic Orbital Multistate Density Functional Theory

Proton transfer and hydrogen tunneling play key roles in many processes of chemical and biological importance. The generalized nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) method was developed in order to capture hydrogen tunneling effects in systems involving the transfer and tunneling of one or more protons. The generalized NEO-MSDFT method treats the transferring protons quantum mechanically on the same level as the electrons and obtains the delocalized vibronic states associated with hydrogen tunneling by mixing localized NEO-DFT states in a nonorthogonal configuration interaction scheme. Herein, we present the derivation and implementation of analytical gradients for the generalized NEO-MSDFT vibronic state energies and the nonadiabatic coupling vectors between these vibronic states. We use this methodology to perform adiabatic and nonadiabatic dynamics simulations of the double proton transfer reactions in the formic acid dimer and the heterodimer of formamidine and formic acid. The generalized NEO-MSDFT method is shown to capture the strongly coupled synchronous or asynchronous tunneling of the two protons in these processes. Inclusion of vibronically nonadiabatic effects is found to significantly impact the double proton transfer dynamics. This work lays the foundation for a variety of nonadiabatic dynamics simulations of multiple proton transfer systems, such as proton relays and hydrogen-bonding networks.

Melanin: Nature's 4th bioorganic polymer

The pigments known as the melanins are widely recognized for their responsibility in the coloration of human skin, eyes, hair, and minimising the harmful effects of solar ultraviolet radiation. But specialists are aware that the melanins are present in all living kingdoms, barring viruses, and have functionality that extends beyond neutralizing ionising radiation. The ubiquitous presence of melanin in almost all human organs, recognized in recent years, as well as the presence of melanin in organisms that are evolutionarily distant from each other, indicate the fundamental importance of this class of material for all life forms. In this review, we argue for the need to accept melanins as the fourth primordial class of biological polymers, along with nucleic acids, proteins and polysaccharides. We consistently compare the properties of these canonical biological polymers with the properties of melanin and highlight key features that fundamentally distinguish melanins, their function and its mysteries.

Solvent isotope and mutagenesis studies on the proton relay system in yeast alcohol dehydrogenase 1

Alcohol dehydrogenase catalyzes the reversible transfer of a hydride directly from an alcohol to the nicotinamide ring of NAD+ to form an aldehyde and NADH, and the proton from the alcohol probably is transferred through a hydrogen-bonded system to the imidazole of His-48. Studies of the pH dependencies, and solvent and substrate isotope effects on the wild-type and the enzyme with His-48 substituted with Gln-48 were used to demonstrate a role for the proton relay system. The H48Q substitution increases affinities for NAD+ and NADH by ∼2-fold, suggesting that the overall protein structure is maintained. In contrast, catalytic efficiencies (V/Km) on ethanol and acetaldehyde and affinity for 2,2,2-trifluoroethanol are decreased by about 10-fold. The pH dependencies for catalytic efficiencies on ethanol and acetaldehyde (log V/Km versus pH), show pK values of about 7.5 for wild-type enzyme, but ethanol oxidation by H48Q ADH is essentially linear over the pH range from 5.5 to 9.2 with a slope of 0.47. Steady-state kinetics and substrate isotope effects suggest that the kinetic mechanism of H48Q ADH has become partly random for oxidation of ethanol. Both wild-type and H48Q ADHs have pH-independent isotope effects for oxidation (V1/Kb) of 1-butanol/1-butanol-d9 of 4, suggesting that hydride transfer is a major rate-limiting step. The pH dependence for butanol oxidation by wild type ADH shows a wavy profile over the pH range from pH 6 to 10, with a ∼2.3-fold larger V1/Kb in D2O than in H2O, an "inverse" isotope effect. The substrate isotope effect of 4 is not altered by the solvent isotope effect, suggesting concerted proton/hydride transfer. The solvent isotope effect can be explained by a ground state with a water bound to the catalytic zinc in the enzyme-NAD+ complex, and a transition state that resembles a complex with NADH and aldehyde. In contrast, the H48Q enzyme has a diminished inverse solvent isotope effect of ∼1.3 and an essentially linear pH dependence with a slope of log V1/Kb against pH of 0.49 for oxidation of 1-butanol, which together are consistent with a transition state where hydroxide ion directly accepts a proton from the 2'-hydroxyl group of the nicotinamide ribose in the proton relay system in the enzyme-NAD+-alcohol complex. The results support a catalytic role for His-48 in the proton relay system.

Tunnelling of electrons via the neighboring atom

As compared to the intuitive process that the electron emits straight to the continuum from its parent ion, there is an alternative route that the electron may transfer to and be trapped by a neighboring ionic core before the eventual release. Here, we demonstrate that electron tunnelling via the neighboring atomic core is a pronounced process in light-induced tunnelling ionization of molecules by absorbing multiple near-infrared photons. We devised a site-resolved tunnelling experiment using an Ar-Kr+ ion as a prototype system to track the electron tunnelling dynamics from the Ar atom towards the neighboring Kr+ by monitoring its transverse momentum distribution, which is temporally captured into the resonant excited states of the Ar-Kr+ before its eventual releasing. The influence of the Coulomb potential of neighboring ionic cores promises new insights into the understanding and controlling of tunnelling dynamics in complex molecules or environment.

Toward Accurate Post-Born-Oppenheimer Molecular Simulations on Quantum Computers: An Adaptive Variational Eigensolver with Nuclear-Electronic Frozen Natural Orbitals

Nuclear quantum effects such as zero-point energy and hydrogen tunneling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei quantum mechanically on the same footing as electrons. On classical computers, the resources required for an exact solution of NEO-based models grow exponentially with system size. By contrast, quantum computers offer a means of solving this problem with polynomial scaling. However, due to the limitations of current quantum devices, NEO simulations are confined to the smallest systems described by minimal basis sets, whereas realistic simulations beyond the Born-Oppenheimer approximation require more sophisticated basis sets. For this purpose, we herein extend a hardware-efficient ADAPT-VQE method to the NEO framework in the frozen natural orbital (FNO) basis. We demonstrate on H2 and D2 molecules that the NEO-FNO-ADAPT-VQE method reduces the CNOT count by several orders of magnitude relative to the NEO unitary coupled cluster method with singles and doubles while maintaining the desired accuracy. This extreme reduction in the CNOT gate count is sufficient to permit practical computations employing the NEO method─an important step toward accurate simulations involving nonclassical nuclei and non-Born-Oppenheimer effects on near-term quantum devices. We further show that the method can capture isotope effects, and we demonstrate that inclusion of correlation energy systematically improves the prediction of difference in the zero-point energy (ΔZPE) between isotopes.

Nonadiabatic Nuclear-Electron Dynamics: A Quantum Computing Approach

Coupled quantum electron-nuclear dynamics is often associated with the Born-Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent representations of electrons and nuclei also exist, which do not rely on any a priori approximation. However, their implementation is hampered by prohibitive scaling. Consequently, quantum computers offer a unique opportunity for extending their use to larger systems. Here, we propose a quantum algorithm for simulating the time-evolution of molecular systems and apply it to proton transfer dynamics in malonaldehyde, described as a rigid scaffold. The proposed quantum algorithm can be easily generalized to include the explicit dynamics of the classically described molecular scaffold. We show how entanglement between electronic and nuclear degrees of freedom can persist over long times if electrons do not follow the nuclear displacement adiabatically. The proposed quantum algorithm may become a valid candidate for the study of such phenomena when sufficiently powerful quantum computers become available.

Generalized Nuclear-Electronic Orbital Multistate Density Functional Theory for Multiple Proton Transfer Processes

Proton transfer and hydrogen tunneling play pivotal roles in many chemical and biological processes. The nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) approach was developed to describe hydrogen tunneling systems within the multicomponent NEO framework, where the transferring proton is quantized and treated with molecular orbital techniques on the same level as the electrons. Herein, the NEO-MSDFT framework is generalized to an arbitrary number of quantum protons to allow applications to systems involving the transfer and tunneling of multiple protons. The generalized NEO-MSDFT approach is shown to produce delocalized, bilobal proton densities and accurate tunneling splittings for fixed geometries of the formic acid dimer and asymmetric substituted variants, as well as the porphycene molecule. Investigation of a protonated water chain highlights the applicability of this approach to proton relay systems. This work provides the foundation for nuclear-electronic quantum dynamics simulations of a wide range of multiple proton transfer processes.

Experimental and Computational Study of Aryl-thiosemicarbazones Inhibiting Cruzain Reveals Reversible Inhibition and a Stepwise Mechanism

Trypanosoma cruzi is a parasite that infects about 6-7 million people worldwide, mostly in Latin America, causing Chagas disease. Cruzain, the main cysteine protease of T. cruzi, is a validated target for developing drug candidates for Chagas disease. Thiosemicarbazones are one of the most relevant warheads used in covalent inhibitors targeting cruzain. Despite its relevance, the mechanism of inhibition of cruzain by thiosemicarbazones is unknown. Here, we combined experiments and simulations to unveil the covalent inhibition mechanism of cruzain by a thiosemicarbazone-based inhibitor (compound 1). Additionally, we studied a semicarbazone (compound 2), which is structurally similar to compound 1 but does not inhibit cruzain. Assays confirmed the reversibility of inhibition by compound 1 and suggested a two-step mechanism of inhibition. The K_i was estimated to be 36.3 μM and K_i* to be 11.5 μM, suggesting the pre-covalent complex to be relevant for inhibition. Molecular dynamics simulations of compounds 1 and 2 with cruzain were used to propose putative binding modes for the ligands. One-dimensional (1D) quantum mechanics/molecular mechanics (QM/MM) potential of mean force (PMF) and gas-phase energies showed that the attack of Cys25-S^- on the C═S or C═O bond yields a more stable intermediate than the attack on the C═N bond of the thiosemicarbazone/semicarbazone. Two-dimensional (2D) QM/MM PMF revealed a putative reaction mechanism for compound 1, involving the proton transfer to the ligand, followed by the Cys25-S^- attack at C═S. The ΔG and energy barrier were estimated to be -1.4 and 11.7 kcal/mol, respectively. Overall, our results shed light on the inhibition mechanism of cruzain by thiosemicarbazones.

Highly selective catalytic transfer hydrodeuteration of cyclic alkenes

Selective deuterium installation into small molecules is becoming increasingly desirable not only for the elucidation of mechanistic pathways and studying biological processes but also because of deuterium's ability to favorably adjust the pharmacokinetic parameters of bioactive molecules. Fused bicyclic moieties, especially those containing heteroatoms, are prevalent in drug discovery and pharmaceuticals. Herein, we report a copper-catalyzed transfer hydrodeuteration of cyclic and heterocyclic alkenes, which enables the synthesis of chromans, quinolinones, and tetrahydronaphthalenes that are precisely deuterated at the benzylic position. We also demonstrate the ability to place one deuterium atom at the homobenzylic site of these scaffolds with high regioselectivity by swapping transfer reagents for their isotopic analogs. Furthermore, examples of chemoselective transfer hydrogenation and transfer deuteration are disclosed, allowing for the simultaneous incorporation of two vicinal hydrogen or deuterium atoms into a double bond.

Dynamical activation of function in metalloenzymes

Formulations of hydrogen tunneling in enzyme-catalysed C-H activation reactions indicate enthalpic barriers to reaction that are independent of chemical steps and dependent on the protein scaffold. A tool to identify catalytically relevant site-specific protein thermal networks has emerged from temperature-dependent hydrogen deuterium exchange (TDHDX). Focusing on mutant enzyme forms with altered activation energies for catalysis, TDHDX provides a comparative analysis of the impact of mutation on Ea for local protein unfolding. Identified thermal networks appear unrelated to protein scaffold conservation and track to the dictates of the catalysed reaction, including sites for metal binding. The positions of thermal networks provide a framework for further understanding of time-dependent, functionally relevant protein motions. Measurement of nanosecond Stokes shifts at the surface of the thermal network in soybean lipoxygenase yields activation energies that are identical to Ea values measured for kcat . This finding identifies a rapid (> nanosecond), long-range and cooperative structural reorganization as the thermal barrier to catalysis. A model for protein dynamics is put forward that integrates broadly distributed protein conformational sampling with protein embedded thermal networks.

Nonadiabatic Dynamics of Hydrogen Tunneling with Nuclear-Electronic Orbital Multistate Density Functional Theory

Proton transfer reactions play a critical role in many chemical and biological processes. The development of computationally efficient approaches to describe the quantum dynamics of proton transfer, which often involves hydrogen tunneling, is challenging. Herein, the nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) method is combined with both Ehrenfest and surface hopping nonadiabatic dynamics methods to describe hydrogen tunneling. The NEO-MSDFT method treats the transferring hydrogen nucleus quantum mechanically on the same level as the electrons and incorporates both static and dynamical correlation by mixing localized NEO-DFT solutions with a nonorthogonal configuration interaction scheme. The other nuclei are propagated on the NEO-MSDFT vibronic surfaces during the Ehrenfest or surface hopping dynamics. These methods are applied to proton transfer in malonaldehyde as a prototypical hydrogen tunneling system. The inclusion of vibronically nonadiabatic effects is found to significantly impact the proton transfer time and tunneling dynamics. This approach is applicable to a wide range of other proton transfer reactions.

Solvent Effects on the Temperature Dependence of Hydride Kinetic Isotope Effects: Correlation to the Donor-Acceptor Distances

Protein structural effects on the temperature (T) dependence of kinetic isotope effects (KIEs) in H-tunneling reactions have recently been used to discuss about the role of enzyme thermal motions in catalysis. Frequently observed nearly T-independent KIEs in the wild-type enzymes and T-dependent KIEs in variants suggest that H-tunneling in the former is assisted by the naturally evolved protein constructive vibrations that help sample short donor-acceptor distances (DADs) needed. This explanation that correlates the T-dependence of KIEs with DAD sampling has been highly debated as simulations following other H-tunneling models sometimes gave alternative explanations. In this paper, solvent effects on the T-dependence of KIEs of two hydride tunneling reactions of NADH/NAD⁺ analogues (represented by ΔE_a = E_aD - E_aH) were determined in attempts to replicate the observations in enzymes and test the protein vibration-assisted DAD sampling concept. Effects of selected aprotic solvents on the DAD_PRC's of the productive reactant complexes (PRCs) and the DAD_TRS's of the activated tunneling ready states (TRSs) were obtained through computations and analyses of the kinetic data, including 2° KIEs, respectively. A weaker T-dependence of KIEs (i.e., smaller ΔE_a) was found in a more polar aprotic solvent in which the system has a shorter average DAD_PRC and DAD_TRS. Further results show that a charge-transfer (CT) complexation made of a stronger donor/acceptor gives rise to a smaller ΔE_a. Overall, the shorter and less broadly distributed DADs resulting from the stronger CT complexation vibrations give rise to a smaller ΔE_a. Our results appear to support the explanation that links the T-dependence of KIEs to the donor-acceptor rigidity in enzymes.

Simultaneous Optimization of Nuclear-Electronic Orbitals

Accurate modeling of important nuclear quantum effects, such as nuclear delocalization, zero-point energy, and tunneling, as well as non-Born-Oppenheimer effects, requires treatment of both nuclei and electrons quantum mechanically. The nuclear-electronic orbital (NEO) method provides an elegant framework to treat specified nuclei, typically protons, on the same level as the electrons. In conventional electronic structure theory, finding a converged ground state can be a computationally demanding task; converging NEO wavefunctions, due to their coupled electronic and nuclear nature, is even more demanding. Herein, we present an efficient simultaneous optimization method that uses the direct inversion in the iterative subspace method to simultaneously converge wavefunctions for both the electrons and quantum nuclei. Benchmark studies show that the simultaneous optimization method can significantly reduce the computational cost compared to the conventional stepwise method for optimizing NEO wavefunctions for multicomponent systems.

Dependence of crystallographic atomic displacement parameters on temperature (25-150 K) for complexes of horse liver alcohol dehydrogenase

Enzymes catalyze reactions by binding and orienting substrates with dynamic interactions. Horse liver alcohol dehydrogenase catalyzes hydrogen transfer with quantum-mechanical tunneling that involves fast motions in the active site. The structures and B factors of ternary complexes of the enzyme with NAD+ and 2,3,4,5,6-pentafluorobenzyl alcohol or NAD+ and 2,2,2-trifluoroethanol were determined to 1.1-1.3 Å resolution below the `glassy transition' in order to extract information about the temperature-dependent harmonic motions, which are reflected in the crystallographic B factors. The refinement statistics and structures are essentially the same for each structure at all temperatures. The B factors were corrected for a small amount of radiation decay. The overall B factors for the complexes are similar (13-16 Å2) over the range 25-100 K, but increase somewhat at 150 K. Applying TLS refinement to remove the contribution of pseudo-rigid-body displacements of coenzyme binding and catalytic domains provided residual B factors of 7-10 Å2 for the overall complexes and of 5-10 Å2 for C4N of NAD+ and the methylene carbon of the alcohols. These residual B factors have a very small dependence on temperature and include local harmonic motions and apparently contributions from other sources. Structures at 100 K show complexes that are poised for hydrogen transfer, which involves atomic displacements of ∼0.3 Å and is compatible with the motions estimated from the residual B factors and molecular-dynamics simulations. At 298 K local conformational changes are also involved in catalysis, as enzymes with substitutions of amino acids in the substrate-binding site have similar positions of NAD+ and pentafluorobenzyl alcohol and similar residual B factors, but differ by tenfold in the rate constants for hydride transfer.

Analytical gradients for nuclear–electronic orbital multistate density functional theory: Geometry optimizations and reaction paths

Hydrogen tunneling plays a critical role in many biologically and chemically important processes. The nuclear–electronic orbital multistate density functional theory (NEO-MSDFT) method was developed to describe hydrogen transfer systems. In this approach, the transferring proton is treated quantum mechanically on the same level as the electrons within multicomponent DFT, and a nonorthogonal configuration interaction scheme is used to produce delocalized vibronic states from localized vibronic states. The NEO-MSDFT method has been shown to provide accurate hydrogen tunneling splittings for fixed molecular systems. Herein, the NEO-MSDFT analytical gradients for both ground and excited vibronic states are derived and implemented. The analytical gradients and semi-numerical Hessians are used to optimize and characterize equilibrium and transition state geometries and to generate minimum energy paths (MEPs), for proton transfer in the deprotonated acetylene dimer and malonaldehyde. The barriers along the resulting MEPs are lower when the transferring proton is quantized because the NEO-MSDFT method inherently includes the zero-point energy of the transferring proton. Analysis of the proton densities along the MEPs illustrates that the proton density can exhibit symmetric or asymmetric bilobal character associated with symmetric or slightly asymmetric double-well potential energy surfaces and hydrogen tunneling. Analysis of the contributions to the intrinsic reaction coordinate reveals that changes in the C–O bond lengths drive proton transfer in malonaldehyde. This work provides the foundation for future reaction path studies and direct nonadiabatic dynamics simulations of a wide range of hydrogen transfer reactions.

Conditional Wave Function Theory: A Unified Treatment of Molecular Structure and Nonadiabatic Dynamics

We demonstrate that a conditional wave function theory enables a unified and efficient treatment of the equilibrium structure and nonadiabatic dynamics of correlated electron-ion systems. The conditional decomposition of the many-body wave function formally recasts the full interacting wave function of a closed system as a set of lower-dimensional (conditional) coupled "slices". We formulate a variational wave function ansatz based on a set of conditional wave function slices and demonstrate its accuracy by determining the structural and time-dependent response properties of the hydrogen molecule. We then extend this approach to include time-dependent conditional wave functions and address paradigmatic nonequilibrium processes including strong-field molecular ionization, laser-driven proton transfer, and nuclear quantum effects induced by a conical intersection. This work paves the road for the application of conditional wave function theory in equilibrium and out-of-equilibrium ab initio molecular simulations of finite and extended systems.

Artificial Neural Networks as Propagators in Quantum Dynamics

The utilization of artificial neural networks (ANNs) provides strategies for accelerating molecular simulations. Herein, ANNs are implemented as propagators of the time-dependent Schrödinger equation to simulate the quantum dynamics of systems with time-dependent potentials. These ANN propagators are trained to map nonstationary wavepackets from a given time to a future time within the discrete variable representation. Each propagator is trained for a specified time step, and iterative application of the propagator enables the propagation of wavepackets over long time scales. Such ANN propagators are developed and applied to one- and two-dimensional proton transfer systems, which exhibit nuclear quantum effects such as hydrogen tunneling. These ANN propagators are trained for either a specific time-independent potential or general potentials that can be time-dependent. Hierarchical, multiple time step algorithms enable parallelization, and the extension to higher dimensions is straightforward. This strategy is applicable to quantum dynamical simulations of diverse chemical and biological processes.

Nonclinical research areas of future importance for clinical therapies: Exploring the concepts of nonlinearity in dentistry

Linear system analysis has been dominating medical and dental research, and most of the research achievements in these fields have come from applying a reductionist view of nature. However, biologic systems are fundamentally nonlinear with highly composite dynamics made up of numerous interacting elements and feedback loops, therefore studying them as linear models may not result in an accurate representation of their true features. The authors reviewed and utilized some of the principles of chaos and nonlinearity and extended them to clinical dentistry, from cracked tooth and flare-up after root canal procedures to the outcome of clinical treatments. Utilization of the concepts of chaos and sensitive dependence on initial conditions, and the concepts of self-organization, stigmergy, and fractals may help us to understand some of the puzzles that have not been solved by conventional linear models. The goal of this paper is to present some areas within nonclinical research that we believe will have important roles in the development of future clinical examination methods and therapies.

Transition States for Psychrophilic and Mesophilic (R)-3-Hydroxybutyrate Dehydrogenase-Catalyzed Hydride Transfer at Sub-zero Temperatures

(R)-3-Hydroxybutyrate dehydrogenase (HBDH) catalyzes the NADH-dependent reduction of 3-oxocarboxylates to (R)-3-hydroxycarboxylates. The active sites of a pair of cold- and warm-adapted HBDHs are identical except for a single residue, yet kinetics evaluated at -5, 0, and 5 °C show a much higher steady-state rate constant (k_cat) for the cold-adapted than for the warm-adapted HBDH. Intriguingly, single-turnover rate constants (k_STO) are strikingly similar between the two orthologues. Psychrophilic HBDH primary deuterium kinetic isotope effects on k_cat (^Dk_cat) and k_STO (^Dk_STO) decrease at lower temperatures, suggesting more efficient hydride transfer relative to other steps as the temperature decreases. However, mesophilic HBDH ^Dk_cat and ^Dk_STO are generally temperature-independent. The ^Dk_STO data allowed calculation of intrinsic primary deuterium kinetic isotope effects. Intrinsic isotope effects of 4.2 and 3.9 for cold- and warm-adapted HBDH, respectively, at 5 °C, supported by quantum mechanics/molecular mechanics calculations, point to a late transition state for both orthologues. Conversely, intrinsic isotope effects of 5.7 and 3.1 for cold- and warm-adapted HBDH, respectively, at -5 °C indicate the transition state becomes nearly symmetric for the psychrophilic enzyme, but more asymmetric for the mesophilic enzyme. His-to-Asn and Asn-to-His mutations in the psychrophilic and mesophilic HBDH active sites, respectively, swap the single active-site position where these orthologues diverge. At 5 °C, the His-to-Asn mutation in psychrophilic HBDH decreases ^Dk_cat to 3.1, suggesting a decrease in transition-state symmetry, while the His-to-Asn mutation in mesophilic HBDH increases ^Dk_cat to 4.4, indicating an increase in transition-state symmetry. Hence, temperature adaptation and a single divergent active-site residue may influence transition-state geometry in HBDHs.

Electron flow between the worlds of Marcus and Warburg

Living organisms are characterized by the ability to process energy (all release heat). Redox reactions play a central role in biology, from energy transduction (photosynthesis, respiratory chains) to highly selective catalyzed transformations of complex molecules. Distance and scale are important: electrons transfer on a 1 nm scale, hydrogen nuclei transfer between molecules on a 0.1 nm scale, and extended catalytic processes (cascades) operate most efficiently when the different enzymes are under nanoconfinement (10 nm-100 nm scale). Dynamic electrochemistry experiments (defined broadly within the term "protein film electrochemistry," PFE) reveal details that are usually hidden in conventional kinetic experiments. In PFE, the enzyme is attached to an electrode, often in an innovative way, and electron-transfer reactions, individual or within steady-state catalytic flow, can be analyzed in terms of precise potentials, proton coupling, cooperativity, driving-force dependence of rates, and reversibility (a mark of efficiency). The electrochemical experiments reveal subtle factors that would have played an essential role in molecular evolution. This article describes how PFE is used to visualize and analyze different aspects of biological redox chemistry, from long-range directional electron transfer to electron/hydride (NADPH) interconversion by a flavoenzyme and finally to NADPH recycling in a nanoconfined enzyme cascade.

Artificial Neural Networks as Mappings between Proton Potentials, Wave Functions, Densities, and Energy Levels

Artificial neural networks (ANNs) have become important in quantum chemistry. Herein, applications to nuclear quantum effects, such as zero-point energy, vibrationally excited states, and hydrogen tunneling, are explored. ANNs are used to solve the time-independent Schrödinger equation for single- and double-well potentials representing hydrogen-bonded molecular systems capable of proton transfer. ANN mappings are trained to predict the lowest five proton vibrational energies, wave functions, and densities from the proton potentials and to predict the excited state proton vibrational energies and densities from the proton ground state density. For the inverse problem, ANN mappings are trained to predict the proton potential from the proton vibrational energy levels or the proton ground state density. This latter mapping is theoretically justified by the first Hohenberg-Kohn theorem establishing a one-to-one correspondence between the external potential and the ground state density. ANNs for two- and three-dimensional systems are also presented to illustrate the straightforward extension to higher dimensions.

Towards practical applications in quantum computational biology

Fascinating progress in understanding our world at the smallest scales moves us to the border of a new technological revolution governed by quantum physics. By taking advantage of quantum phenomena, quantum computing devices allow a speedup in solving diverse tasks. In this Perspective, we discuss the potential impact of quantum computing on computational biology. Bearing in mind the limitations of existing quantum computing devices, we attempt to indicate promising directions for further research in the emerging area of quantum computational biology.

Low-Frequency Protein Motions Coupled to Catalytic Sites

This review examines low-frequency vibrational modes of proteins and their coupling to enzyme catalytic sites. That protein motions are critical to enzyme function is clear, but the kinds of motions present in proteins and how they are involved in function remain unclear. Several models of enzyme-catalyzed reaction suggest that protein dynamics may be involved in the chemical step of the catalyzed reaction, but the evidence in support of such models is indirect. Spectroscopic studies of low-frequency protein vibrations consistently show that there are underdamped modes of the protein with frequencies in the tens of wavenumbers where overdamped behavior would be expected. Recent studies even show that such underdamped vibrations modulate enzyme active sites. These observations suggest that increasingly sophisticated spectroscopic methods will be able to unravel the link between low-frequency protein vibrations and enzyme function.

Isotope Effects in Plasmonic Photosynthesis

The photoexcitation of plasmonic nanoparticles has been shown to drive multistep, multicarrier transformations, such as the conversion of CO₂ into hydrocarbons. But for such plasmon-driven chemistry to be precisely understood and modeled, the critical photoinitiation step in the reaction cascade must be identified. We meet this goal by measuring H/D and ¹² C/¹³ C kinetic isotope effects (KIEs) in plasmonic photosynthesis. In particular, we found that the substitution of H₂ O with D₂ O slows hydrocarbon production by a factor of 5-8. This primary H/D KIE leads to the inference that hole-driven scission of the O-H bond in H₂ O is a critical, limiting step in plasmonic photosynthesis. This study advances mechanistic understanding of light-driven chemical reactions on plasmonic nanoparticles.

Nuclear-Electronic Orbital Multistate Density Functional Theory

Hydrogen tunneling is essential for a wide range of chemical and biological processes. The description of hydrogen tunneling with multicomponent quantum chemistry approaches, where the transferring hydrogen nucleus is treated on the same level as the electrons, is challenging due to the importance of both static and dynamical electron-proton correlation. Herein the nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) method is presented as a strategy to include both types of correlation. In this approach, two localized nuclear-electronic wave functions obtained with the NEO-DFT method are combined with a nonorthogonal configurational interaction approach to produce bilobal, delocalized ground and excited vibronic states. By including a correction function, the NEO-MSDFT approach can produce quantitatively accurate hydrogen tunneling splittings for fixed geometries of systems such as malonaldehyde and acetoacetaldehyde. This approach is computationally efficient and can be combined with methods such as vibronic coupling theory to describe tunneling dynamics and to compute vibronic couplings in many types of systems.

Biological concepts for catalysis and reactivity: empowering bioinspiration

Biological systems provide attractive reactivity blueprints for the design of challenging chemical transformations. Emulating the operating mode of natural systems may however not be so easy and direct translation of structural observations does not always afford the anticipated efficiency. Metalloenzymes rely on earth-abundant metals to perform an incredibly wide range of chemical transformations. To do so, enzymes in general have evolved tools and tricks to enable control of such reactivity. The underlying concepts related to these tools are usually well-known to enzymologists and bio(inorganic) chemists but may be a little less familiar to organometallic chemists. So far, the field of bioinspired catalysis has greatly focused on the coordination sphere and electronic effects for the design of functional enzyme models but might benefit from a paradigm shift related to recent findings in biological systems. The goal of this review is to bring these fields closer together as this could likely result in the development of a new generation of highly efficient bioinspired systems. This contribution covers the fields of redox-active ligands, entatic state reactivity, energy conservation through electron bifurcation, and quantum tunneling for C-H activation.

Development of nuclear basis sets for multicomponent quantum chemistry methods

The nuclear-electronic orbital (NEO) framework provides a practical approach for directly incorporating nuclear quantum effects and non-Born-Oppenheimer effects of specified nuclei, typically protons, into quantum chemistry calculations. Multicomponent wave function based methods, such as NEO coupled cluster singles and doubles, and multicomponent density functional theory (DFT), such as NEO-DFT, require the appropriate selection of electronic and nuclear basis sets. Although a wide array of electronic basis sets are available, systematically developed nuclear basis sets that balance accuracy and efficiency have been lacking. Herein, a series of nuclear basis sets are developed and shown to be accurate and efficient for describing both ground and excited state properties of multicomponent systems in which electrons and specified protons are treated quantum mechanically. Three series of Gaussian-type nuclear basis sets, denoted PB4, PB5, and PB6, are developed with varying levels of angular momentum. A machine-learning optimization procedure relying on the Gaussian process regression method is utilized to accelerate the optimization process. The basis sets are validated in terms of predictions of ground state energies, proton densities, proton affinities, and proton vibrational excitation energies, allowing the user to select the desired balance between accuracy and efficiency for the properties of interest. These nuclear basis sets will enhance the tractability of NEO methods for applications to a wide range of chemical systems.

Temperature, Dynamics, and Enzyme-Catalyzed Reaction Rates

We review the adaptations of enzyme activity to different temperatures. Psychrophilic (cold-adapted) enzymes show significantly different activation parameters (lower activation enthalpies and entropies) from their mesophilic counterparts. Furthermore, there is increasing evidence that the temperature dependence of many enzyme-catalyzed reactions is more complex than is widely believed. Many enzymes show curvature in plots of activity versus temperature that is not accounted for by denaturation or unfolding. This is explained by macromolecular rate theory: A negative activation heat capacity for the rate-limiting chemical step leads directly to predictions of temperature optima; both entropy and enthalpy are temperature dependent. Fluctuations in the transition state ensemble are reduced compared to the ground state. We show how investigations combining experiment with molecular simulation are revealing fundamental details of enzyme thermoadaptation that are relevant for understanding aspects of enzyme evolution. Simulations can calculate relevant thermodynamic properties (such as activation enthalpies, entropies, and heat capacities) and reveal the molecular mechanisms underlying experimentally observed behavior.

Moving Through Barriers in Science and Life

This first serious attempt at an autobiographical accounting has forced me to sit still long enough to compile my thoughts about a long personal and scientific journey. I especially hope that my trajectory will be of interest and perhaps beneficial to much younger women who are just getting started in their careers. To paraphrase from Virginia Woolf's writings in A Room of One's Own at the beginning of the 20th century, "for most of history Anonymous was a Woman." However, Ms. Woolf is also quoted as saying "nothing has really happened until it has been described," a harbinger of the enormous historical changes that were about to be enacted and recorded by women in the sciences and other disciplines. The progress in my chosen field of study-the chemical basis of enzyme action-has also been remarkable, from the first description of an enzyme's 3D structure to a growing and deep understanding of the origins of enzyme catalysis.

The Soybean Lipoxygenase-Substrate Complex: Correlation between the Properties of Tunneling-Ready States and ENDOR-Detected Structures of Ground States

Hydrogen tunneling in enzymatic C-H activation requires a dynamical sampling among ground-state enzyme-substrate (E-S) conformations, which transiently generates a tunneling-ready state (TRS). The TRS is characterized by a hydrogen donor-acceptor distance (DAD) of 2.7 Å, ∼0.5 Å shorter than the dominant DAD of optimized ground states. Recently, a high-resolution, 13C electron-nuclear double-resonance (ENDOR) approach was developed to characterize the ground-state structure of the complex of the linoleic acid (LA) substrate with soybean lipoxygenase (SLO). The resulting enzyme-substrate model revealed two ground-state conformers with different distances between the target C11 of LA and the catalytically active cofactor [Fe(III)-OH]: the active conformer "a", with a van der Waals DAD of 3.1 Å between C11 and metal-bound hydroxide, and an inactive conformer "b", with a distance that is almost 1 Å longer. Herein, the structure of the E-S complex is examined for a series of six variants in which subtle structural modifications of SLO have been introduced either at a hydrophobic side chain near the bound substrate or at a remote residue within a protein network whose flexibility influences hydrogen transfer. A remarkable correlation is found between the ENDOR-derived population of the active ground-state conformer a and the kinetically derived differential enthalpic barrier for D versus H transfer, ΔEa, with the latter increasing as the fraction of conformer a decreases. As proposed, ΔEa provides a "ruler" for the DAD within the TRS. ENDOR measurements further corroborate the previous identification of a dynamical network coupling the buried active site of SLO to the surface. This study shows that subtle imperfections within the initial ground-state structures of E-S complexes are accompanied by compromised geometries at the TRS.

Substitutions of Amino Acid Residues in the Substrate Binding Site of Horse Liver Alcohol Dehydrogenase Have Small Effects on the Structures but Significantly Affect Catalysis of Hydrogen Transfer

Previous studies showed that the L57F and F93W alcohol dehydrogenases catalyze the oxidation of benzyl alcohol with some quantum mechanical hydrogen tunneling, whereas the V203A enzyme has diminished tunneling. Here, steady-state kinetics for the L57F and F93W enzymes were studied, and microscopic rate constants for the ordered bi-bi mechanism were estimated from simulations of transient kinetics for the S48T, F93A, S48T/F93A, F93W, and L57F enzymes. Catalytic efficiencies for benzyl alcohol oxidation (V₁/E_tK_b) vary over a range of ∼100-fold for the less active enzymes up to the L57F enzyme and are mostly associated with the binding of alcohol rather than the rate constants for hydride transfer. In contrast, catalytic efficiencies for benzaldehyde reduction (V₂/E_tK_p) are ∼500-fold higher for the L57F enzyme than for the less active enzymes and are mostly associated with the rate constants for hydride transfer. Atomic-resolution structures (1.1 Å) for the F93W and L57F enzymes complexed with NAD⁺ and 2,3,4,5,6-pentafluorobenzyl alcohol or 2,2,2-trifluoroethanol are almost identical to previous structures for the wild-type, S48T, and V203A enzymes. Least-squares refinement with SHELXL shows that the nicotinamide ring is slightly strained in all complexes and that the apparent donor-acceptor distances from C4N of NAD to C7 of pentafluorobenzyl alcohol range from 3.28 to 3.49 Å (±0.02 Å) and are not correlated with the rate constants for hydride transfer or hydrogen tunneling. How the substitutions affect the dynamics of reorganization during hydrogen transfer and the extent of tunneling remain to be determined.

Quantum electrocatalysts: theoretical picture, electrochemical kinetic isotope effect analysis, and conjecture to understand microscopic mechanisms

The fundamental aspects of quantum electrocatalysts are discussed together with the newly developed electrochemical kinetic isotope effect (EC-KIE) approach.

Advances and challenges for experiment and theory for multi-electron multi-proton transfer at electrified solid–liquid interfaces

Understanding microscopic mechanism of multi-electron multi-proton transfer reactions at complexed systems is important for advancing electrochemistry-oriented science in the 21st century.

Transient proton transfer of base pair hydrogen bonds induced by intense terahertz radiation

Intense terahertz radiation was applied to trigger transient proton transfer in DNA base pairs through quantum simulation.

Quantum proton tunneling in multi-electron/-proton transfer electrode processes

Quantum proton tunneling in multi-electron/-proton transfer electrode processes were investigated in order to understand their possible microscopic mechanisms.

What are the signatures of tunnelling in enzyme-catalysed reactions?

Computed tunnelling contributions and correlations between apparent activation enthalpy and entropy are explored for the interpretation of enzyme-catalysed H-transfer reactions.

Comparative kinetic isotope effects on first- and second-order rate constants of soybean lipoxygenase variants uncover a substrate-binding network

Lipoxygenases are widespread enzymes found in virtually all eukaryotes, including fungi, and, more recently, in prokaryotes. These enzymes act on long-chain polyunsaturated fatty acid substrates (C18 to C20), raising questions regarding how the substrate threads its way from solvent to the active site. Herein, we report a comparison of the temperature dependence of isotope effects on first- and second-order rate constants among single-site variants of the prototypic plant enzyme soybean lipoxygenase-1 substituted at amino acid residues inferred to impact substrate binding. We created 10 protein variants including four amino acid positions, Val-750, Ile-552, Ile-839, and Trp-500, located within a previously proposed substrate portal. The conversion of these bulky hydrophobic side chains to smaller side chains is concluded to increase the mobility of flanking helices, giving rise to increased off rates for substrate dissociation from the enzyme. In this manner, we identified a specific "binding network" that can regulate movement of the substrate from the solvent to the active site. Taken together with our previous findings on C-H and O2 activation of soybean lipoxygenase-1, these results support the emergence of multiple complementary networks within a single protein scaffold that modulate different steps along the enzymatic reaction coordinate.

Temperature-Independent Kinetic Isotope Effects as Evidence for a Marcus-like Model of Hydride Tunneling in Phosphite Dehydrogenase

Phosphite dehydrogenase catalyzes the transfer of a hydride from phosphite to NAD⁺, producing phosphate and NADH. We have evaluated the role of hydride tunneling in a thermostable variant of this enzyme (17X-PTDH) by measuring the temperature dependence of the primary ²H kinetic isotope effects (KIEs) between 5 and 45 °C. Pre-steady-state kinetic measurements were used to demonstrate that the hydride transfer is rate-determining across this temperature range and that the observed KIEs are equal to the intrinsic isotope effect on the chemical step. The KIEs on the pre-exponential factor (A_H/A_D) and the activation energy (ΔE_a) were 1.6 ± 0.1 and 0.21 ± 0.05 kcal/mol, respectively, suggesting that 17X-PTDH facilitates extensive tunneling of both isotopes via a Marcus-like model. Site-directed mutagenesis was used to evaluate the role of an active site threonine (Thr104) found on the back face of the nicotinamide in promoting the close packing of the substrates. In mutants with reduced steric bulk at this position, values of A_H/A_D and ΔE_a fall within the range describing semiclassical "over the barrier" reactivity, suggesting that Thr104 acts as a steric backstop to promote tunneling in 17X-PTDH. Whereas hydrogen tunneling is now a widely appreciated feature of C-H activating enzymes, these observations with a P-H activating system are consistent with the proposal that tunneling is likely to be a common feature on all enzymes that catalyze hydrogen transfers.

Replication of the Enzymatic Temperature Dependency of the Primary Hydride Kinetic Isotope Effects in Solution: Caused by the Protein-Controlled Rigidity of the Donor-Acceptor Centers?

The change from the temperature independence of the primary (1°) H/D kinetic isotope effects (KIEs) in wild-type enzyme-catalyzed H-transfer reactions (ΔE_a = E_aD - E_aH ∼ 0) to a strong temperature dependence with the mutated enzymes (ΔE_a ≫ 0) has recently been frequently observed. This has prompted some enzymologists to develop new H-tunneling models to correlate ΔE_a with the donor-acceptor distance (DAD) at the tunneling-ready state (TRS) as well as the protein thermal motions/dynamics that sample the short DAD_TRS's for H-tunneling to occur. While extensive evidence supporting or disproving the thermally activated DAD sampling concept has emerged, a comparable study of the simpler bimolecular H-tunneling reactions in solution has not been carried out. In particular, small ΔE_a's (∼0) have not been found. In this paper, we report a study of the hydride-transfer reactions from four NADH models to the same hydride acceptor in acetonitrile. The ΔE_a's were determined: 0.37 (small), 0.60, 0.99, and 1.53 kcal/mol (large). The α-secondary (2°) KIEs on the acceptor that serve as a ruler for the rigidity of reaction centers were previously reported or determined. All possible productive reactant complex (PRC) configurations were computed to provide insight into the structures of the TRS's. Relationships among structures, 2° KIEs, DAD_PRC's, and ΔE_a's were discussed. The more rigid system with more suppressed 2° C-H vibrations at the TRS and more narrowly distributed DAD_PRC's in PRCs gave a smaller ΔE_a. The results replicated the trend observed in enzymes versus mutated enzymes and appeared to support the concepts of different thermally activated DAD_TRS sampling processes in response to the rigid versus flexible donor-acceptor centers.

Universality of fold-encoded localized vibrations in enzymes

Enzymes speed up biochemical reactions at the core of life by as much as 15 orders of magnitude. Yet, despite considerable advances, the fine dynamical determinants at the microscopic level of their catalytic proficiency are still elusive. In this work, we use a powerful mathematical approach to show that rate-promoting vibrations in the picosecond range, specifically encoded in the 3D protein structure, are localized vibrations optimally coupled to the chemical reaction coordinates at the active site. Remarkably, our theory also exposes an hithertho unknown deep connection between the unique localization fingerprint and a distinct partition of the 3D fold into independent, foldspanning subdomains that govern long-range communication. The universality of these features is demonstrated on a pool of more than 900 enzyme structures, comprising a total of more than 10,000 experimentally annotated catalytic sites. Our theory provides a unified microscopic rationale for the subtle structure-dynamics-function link in proteins.

Quantum Tunneling Mediated Interfacial Synthesis of a Benzofuran Derivative

Reaction pathways involving quantum tunneling of protons are fundamental to chemistry and biology. They are responsible for essential aspects of interstellar synthesis, the degradation and isomerization of compounds, enzymatic activity, and protein dynamics. On-surface conditions have been demonstrated to open alternative routes for organic synthesis, often with intricate transformations not accessible in solution. Here, we investigate a hydroalkoxylation reaction of a molecular species adsorbed on a Ag(111) surface by scanning tunneling microscopy complemented by X-ray electron spectroscopy and density functional theory. The closure of the furan ring proceeds at low temperature (down to 150 K) and without detectable side reactions. We unravel a proton-tunneling-mediated pathway theoretically and confirm experimentally its dominant contribution through the kinetic isotope effect with the deuterated derivative.