A theoretical analysis of rate constants and kinetic isotope effects corresponding to different reactant valleys in lactate dehydrogenase

Delineation of the complete reaction cycle of a natural Diels-Alderase

The Diels-Alder reaction is one of the most effective methods for the synthesis of substituted cyclohexenes. The development of protein catalysts for this reaction remains a major priority, affording new sustainable routes to high value target molecules. Whilst a small number of natural enzymes have been shown capable of catalysing [4 + 2] cycloadditions, there is a need for significant mechanistic understanding of how these prospective Diels-Alderases promote catalysis to underpin their development as biocatalysts for use in synthesis. Here we present a molecular description of the complete reaction cycle of the bona fide natural Diels-Alderase AbyU, which catalyses formation of the spirotetronate skeleton of the antibiotic abyssomicin C. This description is derived from X-ray crystallographic studies of AbyU in complex with a non-transformable synthetic substrate analogue, together with transient kinetic analyses of the AbyU catalysed reaction and computational reaction simulations. These studies reveal the mechanistic intricacies of this enzyme system and establish a foundation for the informed reengineering of AbyU and related biocatalysts.

Accounting for the instantaneous disorder in the enzyme-substrate Michaelis complex to calculate the Gibbs free energy barrier of an enzyme reaction

Many enzyme reactions present instantaneous disorder. These dynamic fluctuations in the enzyme-substrate Michaelis complexes generate a wide range of energy barriers that cannot be experimentally observed, but that determine the measured kinetics of the reaction. These individual energy barriers can be calculated using QM/MM methods, but then the problem is how to deal with this dispersion of energy barriers to provide kinetic information. So far, the most usual procedure has implied the so-called exponential average of the energy barriers. In this paper, we discuss the foundations of this method, and we use the free energy perturbation theory to derive an alternative equation to get the Gibbs free energy barrier of the enzyme reaction. In addition, we propose a practical way to implement it. We have chosen four enzyme reactions as examples. In particular, we have studied the hydrolysis of a glycosidic bond catalyzed by the enzyme Thermus thermophilus β-glycosidase, and the mutant Y284P Ttb-gly, and the hydrogen abstraction reactions from C13 and C7 of arachidonic acid catalyzed by the enzyme rabbit 15-lipoxygenase-1.

Convergence of theory and experiment on the role of preorganization, quantum tunneling and enzyme motions into flavoenzyme-catalyzed hydride transfer

Hydride transfer is one of the most common reactions catalyzed by enzymatic systems and it has become an object of study due to possible significant quantum tunneling effects. In the present work, we provide a combination of theoretical QM/MM simulations and experimental measurements of the rate constants and kinetic isotopic effects (KIEs) for the hydride transfer reaction catalyzed by morphinone reductase, MR. Quantum mechanical tunneling coefficients, computed in the framework of variational transition-state theory, play a significant role in this reaction, reaching values of 23.8 ± 5.5 for the lightest isotopologue; one of the largest values reported for enzymatic systems. This prediction is supported by the agreement between the theoretically predicted rate constants and the corresponding experimental values. Simulations indicate that the role of protein motions can be satisfactorily described as equilibrium fluctuations along the reaction coordinate, in line with a high degree of preorganization displayed by this enzyme.

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

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

Improving the Catalytic Power of the DszD Enzyme for the Biodesulfurization of Crude Oil and Derivatives

The enhancement of the catalytic power of enzymes is a subject of enormous interest both for science and for industry. The latter, in particular, due to the vast applications enzymes can have in industrial processes, for instance in the desulfurization of crude oil, which is mandatory by law in many developed countries and is currently performed using costly chemical processes. In this work we sought to enhance the turnover rate of DszD from Rhodococcus erythropolis, a NADH-FMN oxidoreductase responsible for supplying FMNH₂ to DszA and DszC in the biodesulfurization process of crude oil, the 4S pathway. For this purpose, we replaced the wild type spectator residue of the rate limiting step of the reduction of FMN to FMNH₂ , a process catalysed by DszD and known to play an important role in the reaction energy profile. As replacements, we used all the naturally occurring amino acids, one at a time, using computational methodologies, and repeated the above-mentioned reaction with each mutant. To calculate the different free energy profiles, one for each mutated model, we applied quantum mechanics/molecular mechanics (QM/MM) methods within an ONIOM scheme. The free energy barriers obtained varied between 15.1 and 29.9 kcal mol^-1 . Multiple factors contributed to the different ΔG values. The most relevant were electrostatic interactions and the induction of a favourable alignment between substrate and cofactor. These results confirm the great potential that chirurgic mutations have for increasing the catalytic power of DszD in relation to the wild type (wt) enzyme.

Enhanced Rigidification within a Double Mutant of Soybean Lipoxygenase Provides Experimental Support for Vibronically Nonadiabatic Proton-Coupled Electron Transfer Models

Soybean lipoxygenase (SLO) is a prototype for nonadiabatic hydrogen tunneling reactions and, as such, has served as the subject of numerous theoretical studies. In this work, we report a nearly temperature-independent kinetic isotope effect (KIE) with an average KIE value of 661 ± 27 for a double mutant (DM) of SLO at six temperatures. The data are well-reproduced within a vibronically nonadiabatic proton-coupled electron transfer model in which the active site has become rigidified compared to wild-type enzyme and single-site mutants. A combined temperature-pressure perturbation further shows that temperature-dependent global motions within DM-SLO are more resistant to perturbation by elevated pressure. These findings provide strong experimental support for the model of hydrogen tunneling in SLO, where optimization of both local protein and ligand motions and distal conformational rearrangements is a prerequisite for effective proton vibrational wave function overlap between the substrate and the active-site iron cofactor.

Thermal activation of 'allosteric-like' large-scale motions in a eukaryotic Lactate Dehydrogenase

Conformational changes occurring during the enzymatic turnover are essential for the regulation of protein functionality. Individuating the protein regions involved in these changes and the associated mechanical modes is still a challenge at both experimental and theoretical levels. We present here a detailed investigation of the thermal activation of the functional modes and conformational changes in a eukaryotic Lactate Dehydrogenase enzyme (LDH). Neutron Spin Echo spectroscopy and Molecular Dynamics simulations were used to uncover the characteristic length- and timescales of the LDH nanoscale motions in the apo state. The modes involving the catalytic loop and the mobile region around the binding site are activated at room temperature, and match the allosteric reorganisation of bacterial LDHs. In a temperature window of about 15 degrees, these modes render the protein flexible enough and capable of reorganising the active site toward reactive configurations. On the other hand an excess of thermal excitation leads to the distortion of the protein matrix with a possible anti-catalytic effect. Thus, the temperature activates eukaryotic LDHs via the same conformational changes observed in the allosteric bacterial LDHs. Our investigation provides an extended molecular picture of eukaryotic LDH's conformational landscape that enriches the static view based on crystallographic studies alone.

Variational transition state theory: theoretical framework and recent developments

This article reviews the fundamentals of variational transition state theory (VTST), its recent theoretical development, and some modern applications.

Triple Isotope Effects Support Concerted Hydride and Proton Transfer and Promoting Vibrations in Human Heart Lactate Dehydrogenase

Transition path sampling simulations have proposed that human heart lactate dehydrogenase (LDH) employs protein promoting vibrations (PPVs) on the femtosecond (fs) to picosecond (ps) time scale to promote crossing of the chemical barrier. This chemical barrier involves both hydride and proton transfers to pyruvate to form l-lactate, using reduced nicotinamide adenine dinucleotide (NADH) as the cofactor. Here we report experimental evidence from three types of isotope effect experiments that support coupling of the promoting vibrations to barrier crossing and the coincidence of hydride and proton transfer. We prepared the native (light) LDH and a heavy LDH labeled with ¹³C, ¹⁵N, and nonexchangeable ²H (D) to perturb the predicted PPVs. Heavy LDH has slowed chemistry in single turnover experiments, supporting a contribution of PPVs to transition state formation. Both the [4-²H]NADH (NADD) kinetic isotope effect and the D₂O solvent isotope effect were increased in dual-label experiments combining both NADD and D₂O, a pattern maintained with both light and heavy LDHs. These isotope effects support concerted hydride and proton transfer for both light and heavy LDHs. Although the transition state barrier-crossing probability is reduced in heavy LDH, the concerted mechanism of the hydride-proton transfer reaction is not altered. This study takes advantage of triple isotope effects to resolve the chemical mechanism of LDH and establish the coupling of fs-ps protein dynamics to barrier crossing.

The influence of active site conformations on the hydride transfer step of the thymidylate synthase reaction mechanism

The hydride transfer from C6 of tetrahydrofolate to the reaction's exocyclic methylene-dUMP intermediate is the rate limiting step in thymidylate synthase (TSase) catalysis. This step has been studied by means of QM/MM molecular dynamics simulations to generate the corresponding free energy surfaces. The use of two different initial X-ray structures has allowed exploring different conformational spaces and the existence of chemical paths with not only different reactivities but also different reaction mechanisms. The results confirm that this chemical conversion takes place preferentially via a concerted mechanism where the hydride transfer is conjugated to thiol-elimination from the product. The findings also confirm the labile character of the substrate-enzyme covalent bond established between the C6 of the nucleotide substrate and a conserved cysteine residue. The calculations also reproduce and rationalize a normal H/T 2° kinetic isotope effect measured for that step. From a computational point of view, the results demonstrate that the use of an incomplete number of coordinates to describe the real reaction coordinate can render biased results.

QM/MM study of the mechanism of reduction of 3-hydroxy-3-methylglutaryl coenzyme A catalyzed by human HMG-CoA reductase

Detailing with atomistic resolution the reaction mechanism of human HMG-CoA reductase (HMG-CoA-R) might provide valuable insights for the development of new cholesterol-lowering drugs.

The importance of ensemble averaging in enzyme kinetics

The active site of an enzyme is surrounded by a fluctuating environment of protein and solvent conformational states, and a realistic calculation of chemical reaction rates and kinetic isotope effects of enzyme-catalyzed reactions must take account of this environmental diversity. Ensemble-averaged variational transition state theory with multidimensional tunneling (EA-VTST/MT) was developed as a way to carry out such calculations. This theory incorporates ensemble averaging, quantized vibrational energies, energy, tunneling, and recrossing of transition state dividing surfaces in a systematic way. It has been applied successfully to a number of hydrogen-, proton-, and hydride-transfer reactions. The theory also exposes the set of effects that should be considered in reliable rate constants calculations.

We first review the basic theory and the steps in the calculation. A key role is played by the generalized free energy of activation profile, which is obtained by quantizing the classical potential of mean force as a function of a reaction coordinate because the one-way flux through the transition state dividing surface can be written in terms of the generalized free energy of activation. A recrossing transmission coefficient accounts for the difference between the one-way flux through the chosen transition state dividing surface and the net flux, and a tunneling transmission coefficient converts classical motion along the reaction coordinate to quantum mechanical motion. The tunneling calculation is multidimensional, accounting for the change in vibrational frequencies along the tunneling path and shortening of the tunneling path with respect to the minimum energy path (MEP), as promoted by reaction-path curvature. The generalized free energy of activation and the transmission coefficients both involve averaging over an ensemble of reaction paths and conformations, and this includes the coupling of protein motions to the rearrangement of chemical bonds in a statistical mechanically correct way. The standard deviations of the transmissions coefficients provide information on the diversity of the distribution of reaction paths, barriers, and protein conformations along the members of an ensemble of reaction paths passing through the transition state.

We first illustrate the theory by discussing the application to both wild-type and mutant Escherichia coli dihydrofolate reductase and hyperthermophilic Thermotoga maritima dihydrofolate reductase (DHFR); DHFR is of special interest because the protein conformational changes have been widely studied. Then we present shorter discussions of several other applications of EA-VTST/MT to transfer of protons, hydrogen atoms, and hydride ions and their deuterated analogs. Systems discussed include hydride transfer in alcohol dehydrogenase, xylose isomerase, and thymidylate synthase, proton transfer in methylamine dehydrogenase, hydrogen atom transfer in methylmalonyl-CoA mutase, and nucleophilic substitution in haloalkane dehalogenase and two-dimensional potentials of mean force for potentially coupled proton and hydride transfer in the β-oxidation of butyryl-coenzyme A catalyzed by short-chain acyl-CoA dehydrogenase and in the pyruvate to lactate transformation catalyzed by lactate dehydrogenase.

Protein Conformational Landscapes and Catalysis. Influence of Active Site Conformations in the Reaction Catalyzed by L-Lactate Dehydrogenase

In the last decade L-Lactate Dehydrogenase (LDH) has become an extremely useful marker in both clinical diagnosis and in monitoring the course of many human diseases. It has been assumed from the 80s that the full catalytic process of LDH starts with the binding of the cofactor and the substrate followed by the enclosure of the active site by a mobile loop of the protein before the reaction to take place. In this paper we show that the chemical step of the LDH catalyzed reaction can proceed within the open loop conformation, and the different reactivity of the different protein conformations would be in agreement with the broad range of rate constants measured in single molecule spectrometry studies. Starting from a recently solved X-ray diffraction structure that presented an open loop conformation in two of the four chains of the tetramer, QM/MM free energy surfaces have been obtained at different levels of theory. Depending on the level of theory used to describe the electronic structure, the free energy barrier for the transformation of pyruvate into lactate with the open conformation of the protein varies between 12.9 and 16.3 kcal/mol, after quantizing the vibrations and adding the contributions of recrossing and tunneling effects. These values are very close to the experimentally deduced one (14.2 kcal·mol^-1) and ~2 kcal·mol^-1 smaller than the ones obtained with the closed loop conformer. Calculation of primary KIEs and IR spectra in both protein conformations are also consistent with our hypothesis and in agreement with experimental data. Our calculations suggest that the closure of the active site is mainly required for the inverse process; the oxidation of lactate to pyruvate. According to this hypothesis H4 type LDH enzyme molecules, where it has been propose that lactate is transformed into pyruvate, should have a better ability to close the mobile loop than the M4 type LDH molecules.

Unraveling the role of protein dynamics in dihydrofolate reductase catalysis

Protein dynamics have controversially been proposed to be at the heart of enzyme catalysis, but identification and analysis of dynamical effects in enzyme-catalyzed reactions have proved very challenging. Here, we tackle this question by comparing an enzyme with its heavy ((15)N, (13)C, (2)H substituted) counterpart, providing a subtle probe of dynamics. The crucial hydride transfer step of the reaction (the chemical step) occurs more slowly in the heavy enzyme. A combination of experimental results, quantum mechanics/molecular mechanics simulations, and theoretical analyses identify the origins of the observed differences in reactivity. The generally slightly slower reaction in the heavy enzyme reflects differences in environmental coupling to the hydride transfer step. Importantly, the barrier and contribution of quantum tunneling are not affected, indicating no significant role for "promoting motions" in driving tunneling or modulating the barrier. The chemical step is slower in the heavy enzyme because protein motions coupled to the reaction coordinate are slower. The fact that the heavy enzyme is only slightly less active than its light counterpart shows that protein dynamics have a small, but measurable, effect on the chemical reaction rate.

A Benchmark Test Suite for Proton Transfer Energies and its Use to Test Electronic Structure Model Chemistries

We present benchmark calculations of nine selected points on potential energy surfaces describing proton transfer process in three model systems, H(5)O(2) (+), CH(3)OH…H(+)…OH(2), and CH(3)COOH…OH(2). The calculated relative energies of these geometries are compared to those calculated by various wave function and density functional methods, including the polarized molecular orbital (PMO) model recently developed in our research group and other semiempirical molecular orbital methods. We found that the SCC-DFTB and PMO methods (the latter available so far only for molecules consisting of only O and H and therefore only for the first of the three model systems) give results that are, on average, within 2 kcal/mol of the benchmark results. Other semiempirical molecular orbital methods have mean unsigned errors (MUEs) of 3 to 8 kcal/mol, local density functionals have MUEs in the range 0.7 to 3.7 kcal/mol, and hybrid density functionals have MUEs of only 0.3 to 1.0 kcal/mol, with the best density functional performance obtained by hybrid meta-GGAs, especially M06 and PW6B95.

A hybrid elastic band string algorithm for studies of enzymatic reactions

A common challenge in theoretical biophysics is the identification of a minimum energy path (MEP) for the rearrangement of a group of atoms from one stable configuration to another. The structure with maximum energy along the MEP approximates the transition state for the process and the energy profile itself permits estimation of the transition rates. In this work we describe a computationally efficient algorithm for the identification of minimum energy paths in complicated biosystems. The algorithm is a hybrid of the nudged elastic band (NEB) and string methods. It has been implemented in the pDynamo simulation program and tested by examining elementary steps in the reaction mechanisms of three enzymes: citrate synthase, RasGAP, and lactate dehydrogenase. Good agreement is found for the energies and geometries of the species along the reaction profiles calculated using the new algorithm and previous versions of the NEB and string techniques, and also those obtained by the common method of adiabatic exploration of the potential energy surface as a function of predefined reaction coordinates. Precisely refined structures of the saddle points along the paths may be subsequently obtained with the climbing image variant of the NEB algorithm. Directions in which the utility of the methods that we have implemented can be further improved are discussed.

Direct quantification of the attempt frequency determining the mechanical unfolding of ubiquitin protein

Understanding protein dynamics requires a comprehensive knowledge of the underlying potential energy surface that governs the motion of each individual protein molecule. Single molecule mechanical studies have provided the unprecedented opportunity to study the individual unfolding pathways along a well defined coordinate, the end-to-end length of the protein. In these experiments, unfolding requires surmounting an energy barrier that separates the native from the extended state. The calculation of the absolute value of the barrier height has traditionally relied on the assumption of an attempt frequency, υ(‡). Here we used single molecule force-clamp spectroscopy to directly determine the value of υ(‡) for mechanical unfolding by measuring the unfolding rate of the small protein ubiquitin at varying temperatures. Our experiments demonstrate a significant effect of the temperature on the mechanical rate of unfolding. By extrapolating the unfolding rate in the absence of force for different temperatures, varying within the range spanning from 5 to 45 °C, we measured a value for the activation barrier of ΔG(‡) = 71 ± 5 kJ/mol and an exponential prefactor υ(‡) ∼4 × 10(9) s(-1). Although the measured prefactor value is 3 orders of magnitude smaller than the value predicted by the transition state theory (∼6 × 10(12) s(-1)), it is 400-fold higher than that encountered in analogous experiments studying the effect of temperature on the reactivity of a protein-embedded disulfide bond (∼10(7) M(-1) s(-1)). This approach will allow quantitative characterization of the complete energy landscape of a folding polypeptide from highly extended states, of capital importance for proteins with elastic function.

Temperature dependence of the kinetic isotope effects in thymidylate synthase. A theoretical study

In recent years, the temperature dependence of primary kinetic isotope effects (KIE) has been used as indicator for the physical nature of enzyme-catalyzed H-transfer reactions. An interactive study where experimental data and calculations examine the same chemical transformation is a critical means to interpret more properly temperature dependence of KIEs. Here, the rate-limiting step of the thymidylate synthase-catalyzed reaction has been studied by means of hybrid quantum mechanics/molecular mechanics (QM/MM) simulations in the theoretical framework of the ensemble-averaged variational transition-state theory with multidimensional tunneling (EA-VTST/MT) combined with Grote-Hynes theory. The KIEs were calculated across the same temperature range examined experimentally, revealing a temperature independent behavior, in agreement with experimental findings. The calculations show that the H-transfer proceeds with ∼91% by tunneling in the case of protium and ∼80% when the transferred protium is replaced by tritium. Dynamic recrossing coefficients are almost invariant with temperature and in all cases far from unity, showing significant coupling between protein motions and the reaction coordinate. In particular, the relative movement of a conserved arginine (Arg166 in Escherichia coli ) promotes the departure of a conserved cysteine (Cys146 in E. coli ) from the dUMP by polarizing the thioether bond thus facilitating this bond breaking that takes place concomitantly with the hydride transfer. These promoting vibrations of the enzyme, which represent some of the dimensions of the real reaction coordinate, would limit the search through configurational space to efficiently find those decreasing both barrier height and width, thereby enhancing the probability of H-transfer by either tunneling (through barrier) or classical (over-the-barrier) mechanisms. In other words, the thermal fluctuations that are coupled to the reaction coordinate, together with transition-state geometries and tunneling, are the same in different bath temperatures (within the limited experimental range examined). All these terms contribute to the observed temperature independent KIEs in thymidylate synthase.

Binding ligands and cofactor to L-lactate dehydrogenase from human skeletal and heart muscles

Binding affinities of cofactor and ligands to the active site of two different isoforms of lactate dehydrogenase (LDH), heart and skeletal muscles (H4 and M4, respectively), can be used for medical and biological applications. Herein, a hybrid QM/MM computational approach based on free energy perturbation methods has been carried out to estimate binding affinities and binding isotope effects (BIEs) for NADH/NAD(+) and oxamate, pyruvate, L-lactate, and D-lactate ligands to the M4 and H4 isoforms of L-LDH. Here, we show that determining how cofactor and ligands interact with the active site of LDH isoforms advanced the still open discussion on the intracellular lactate shuttle hypothesis. In our discussion we deny the key concept of this hypothesis showing, based on interaction energy values, that there is no evidence that the M4 type of LDH in the skeletal muscles cells served as a catalyst of the conversion of lactate to pyruvate. Additionally, theoretical determination of BIEs for H4 and M4 types of LDH shows that there is a way of using the BIEs as a tool capable to distinguish these isoforms, and for this purpose D-lactate labeled with deuterium in positions 11 or 7, 8, 9 ([11-2H]-BIE and [7,8,9-2H3]-BIE) or L-lactate labeled only in position 11 ([11-2H]-BIE) could be used. We propose the BIEs as a useful tool which can be applied in order to experimentally determine the types of LDH.

Contrasting the individual reactive pathways in protein unfolding and disulfide bond reduction observed within a single protein

Identifying the dynamics of individual molecules along their reactive pathways remains a major goal of modern chemistry. For simple chemical reactions, the transition state position is thought to be highly localized. Conversely, in the case of more complex reactions involving proteins, the potential energy surfaces become rougher, resulting in heterogeneous reaction pathways with multiple transition state structures. Force-clamp spectroscopy experimentally probes the individual reaction pathways sampled by a single protein under the effect of a constant stretching force. Herein, we examine the distribution of conformations that populate the transition state of two different reactions; the unfolding of a single protein and the reduction of a single disulfide bond, both occurring within the same single protein. By applying the recently developed static disorder theory, we quantify the variance of the barrier heights, σ(2), governing each distinct reaction. We demonstrate that the unfolding of the I27 protein follows a nonexponential kinetics, consistent with a high value of σ(2) ∼ 18 (pN nm)(2). Interestingly, shortening of the protein upon introduction of a rigid disulfide bond significantly modulates the disorder degree, spanning from σ(2) ∼ 8 to ∼21 (pN nm)(2). These results are in sharp contrast with the exponential distribution of times measured for an S(N)2 chemical reaction, implying the absence of static disorder σ(2) ∼ 0 (pN nm)(2). Our results demonstrate the high sensitivity of the force-clamp technique to capture the signatures of disorder in the individual pathways that define two distinct force-induced reactions, occurring within the core of a single protein.

Do dynamic effects play a significant role in enzymatic catalysis? A theoretical analysis of formate dehydrogenase

A theoretical study of the protein dynamic effects on the hydride transfer between the formate anion and nicotinamide adenine dinucleotide (NAD(+)), catalyzed by formate dehydrogenase (FDH), is presented in this paper. The analysis of free downhill molecular dynamic trajectories, performed in the enzyme and compared with the reaction in aqueous solution, has allowed the study of the dynamic coupling between the reacting fragments and the protein or the solvent water molecules, as well as an estimation of the dynamic effect contribution to the catalytic effect from calculation of the transmission coefficient in the enzyme and in solution. The obtained transmission coefficients for the enzyme and in solution were 0.46±0.04 and 0.20±0.03, respectively. These values represent a contribution to catalysis of 0.5 kcal mol(-1), which, although small, is not negligible keeping in mind the low efficiency of FDH. The analysis of the reactive trajectories also reveals how the relative movements of some amino acids, mainly His332 and Arg284, precede and promote the chemical reaction. In spite of these movements, the time-dependent evolution of the electric field created by the enzyme on the key atoms of the reaction reveals a permanent field, which reduces the work required to reach the transition state, with a concomitant polarization of the cofactor. Finally, application of Grote-Hynes theory has allowed the identification of the modes responsible for the substrate-environment coupling, showing how some protein motions take place simultaneously with the reaction. Thus, the equilibrium approach would provide, in this case, an overestimation of the catalyzed rate constant.

A QM/MM study of the phosphoryl transfer to the Kemptide substrate catalyzed by protein kinase A. The effect of the phosphorylation state of the protein on the mechanism

We present here a theoretical study of the phosphoryl transfer catalytic mechanism of protein kinase A, which is the best known member of the large protein kinase family. We have built different theoretical models of the complete PKA-Mg(2)-ATP-substrate system to explore the two most accepted reaction pathways, using for the first time in a reaction mechanism theoretical study, the heptapeptide substrate Kemptide, which is relevant for its high efficiency and small size. The effect of the protein configuration, as modeled by two different X-ray structures with different phosphorylation states and degrees of flexibility, has been analyzed. The results indicate that the environmental conditions can influence the availability of the pathways and thus the choice of the mechanism to be followed. In addition, the roles of the two active site conserved residues, Asp166 and Lys168, have been analyzed for each reaction mechanism.

Comparison studies of the human heart and Bacillus stearothermophilus lactate dehydrogreanse by transition path sampling

Transition path sampling is a well-known technique that generates reactive paths ensembles. Due to the atomic detail of these reactive paths, information about chemical mechanisms can be obtained. We present here a comparative study of Bacillus stearothermophilus and human heart homologues of lactate dehydrogenase (LDH). A comparison of the transition path ensemble of both enzymes revealed that small differences in the active site reverses the order of the particle transfer of the chemical step. Whereas the hydride transfer preceded the proton transfer in the human heart LDH, the order is reversed in the Bacillus stearothermophilis homologue (in the direction of pyruvate to lactate). In addition, transition state analysis revealed that the dividing region that separates reactants and products, the separatrix, is likely wider for B. stearothermophilis LDH as compared to human heart LDH. This would indicate a more variable transition process in the Bacillus enzyme.

On the Origin of the Chemical Barrier and Tunneling in Enzymes

This paper presents both a review of some recent results from our group and experimental groups, and some new theoretical results all of which are helping to form a more physically rigorous picture of the process of enzymatic catalysis. A common classical picture of enzymatic catalysis is the transition state tight binding model. Schwartz and Schramm1 have recently argued from both theoretical and experimental results that this picture is incorrect. We now investigate what the nature of barriers might be in enzymatic reactions, and what this viewpoint might imply for tunneling in a hydrogen transfer enzyme. For lactate dehydrogenase we conclude that the enzymes role in catalysis is at least partially to hunt through configuration space for those configurations that minimize chemical free energy barriers. Those configurations do not seem to be stable basins on the free energy surface, and in fact the overall free energy barrier to reaction may well largely be due to this stochastic hunt - both probabilistically and energetically. We suggest further computations to test this hypothesis.

Parallel pathways and free-energy landscapes for enzymatic hydride transfer probed by hydrostatic pressure

Mutation of an active-site residue in morphinone reductase leads to a conformationally rich landscape that enhances the rate of hydride transfer from NADH to FMN at standard pressure (1 bar). Increasing the pressure causes interconversion between different conformational substates in the mutant enzyme. While high pressure reduces the donor-acceptor distance in the wild-type enzyme, increased conformational freedom "dampens" its effect in the mutant.We show that hydride transfer from NADH to FMN catalysed by the N189A mutant of morphinone reductase occurs along parallel "chemical" pathways in a conformationally rich free-energy landscape. We have developed experimental kinetic and spectroscopic tools by using hydrostatic pressure to explore this free-energy landscape. The crystal structure of the N189A mutant enzyme in complex with the unreactive coenzyme analogue NADH(4) indicates that the nicotinamide moiety of the analogue is conformationally less restrained than the corresponding structure of the wild-type NADH(4) complex. This increased degree of conformational freedom in the N189A enzyme gives rise to the concept of multiple reactive configurations (MRCs), and we show that the relative population of these states across the free-energy landscape can be perturbed experimentally as a function of pressure. Specifically, the amplitudes of individual kinetic phases that were observed in stopped-flow studies of the hydride transfer reaction are sensitive to pressure; this indicates that pressure drives an altered distribution across the energy landscape. We show by absorbance spectroscopy that the loss of charge-transfer character of the enzyme-coenzyme complex is attributed to the altered population of MRCs on the landscape. The existence of a conformationally rich landscape in the N189A mutant is supported by molecular dynamics simulations at low and high pressure. The work provides firm experimental and computational support for the existence of parallel pathways arising from multiple conformational states of the enzyme-coenzyme complex. Hydrostatic pressure is a powerful and general probe of multidimensional energy landscapes that can be used to analyse experimentally parallel pathways for enzyme-catalysed reactions. We suggest that this is especially the case following directed mutation of a protein, which can lead to increased population of reactant states that are essentially inaccessible in the free-energy landscape of wild-type enzyme.

Critical role of substrate conformational change in the proton transfer process catalyzed by 4-oxalocrotonate tautomerase

4-Oxalocrotonate tautomerase enzyme (4-OT) catalyzes the isomerization of 2-oxo-4-hexenedioate to 2-oxo-3-hexenedioate. The chemical process involves two proton transfers, one from a carbon of the substrate to the nitrogen of Pro1 and another from this nitrogen atom to a different carbon of the substrate. In this paper the isomerization has been studied using the combined quantum mechanical and molecular mechanical method with a dual-level treatment of the quantum subsystem employing the MPW1BK density functional as the higher level. Exploration of the potential energy surface shows that the process is stepwise, with a stable intermediate state corresponding to the deprotonated substrate and a protonated proline. The rate constant of the overall process has been evaluated using ensemble-averaged variational transition state theory, including the quantized vibrational motion of a primary zone of active-site atoms and a transmission coefficient based on an ensemble of optimized reaction coordinates to account for recrossing trajectories and optimized multidimensional tunneling. The two proton-transfer steps have similar free energy barriers, but the transition state associated with the first proton transfer is found to be higher in energy. The calculations show that reaction progress is coupled to a conformational change of the substrate, so it is important that the simulation allows this flexibility. The coupled conformational change is promoted by changes in the electron distribution of the substrate that take place as the proton transfers occur.

Theoretical site-directed mutagenesis: Asp168Ala mutant of lactate dehydrogenase

Molecular simulations based on the use of hybrid quantum mechanics/molecular mechanics methods are able to provide detailed information about the complex enzymatic reactions and the consequences of specific mutations on the activity of the enzyme. In this work, the reduction of pyruvate to lactate catalysed by wild-type and Asp168Ala mutant lactate dehydrogenase (LDH) has been studied by means of simulations using a very flexible molecular model consisting of the full tetramer of the enzyme, together with the cofactor NADH, the substrate and solvent water molecules. Our results indicate that the Asp168Ala mutation provokes a shift in the pKa value of Glu199 that becomes unprotonated at neutral pH in the mutant enzyme. This change compensates the loss of the negative charge of Asp168, rendering a still active enzyme. Thus, our methodology gives a calculated barrier height for the Asp168Ala mutant 3 kcal mol-1 higher than that for wild-type LDH, which is in very good agreement with the experiment. The computed potential energy surfaces reveal the reaction pathways and transition structures for the wild-type and mutant enzymes. Hydride transfer is less advanced and the proton transfer is more advanced in the Asp168Ala mutant than in the wild type. This approach provides a very powerful tool for the analysis of the roles of key active-site residues.

A theoretical study of the catalytic mechanism of formate dehydrogenase

A theoretical study of the hydride transfer between formate anion and nicotinamide adenine dinucleotide (NAD(+)) catalyzed by the enzyme formate dehydrogenase (FDH) has been carried out by a combination of two hybrid quantum mechanics/molecular mechanics techniques: statistical simulation methods and internal energy minimizations. Free energy profiles, obtained for the reaction in the enzyme active site and in solution, allow obtaining a comparative analysis of the behavior of both condensed media. Moreover, calculations of the reaction in aqueous media can be used to probe the dramatic differences between reactants state in the enzyme active site and in solution. The results suggest that the enzyme compresses the substrate and the cofactor into a conformation close to the transition structure by means of favorable interactions with the amino acid residues of the active site, thus facilitating the relative orientation of donor and acceptor atoms to favor the hydride transfer. Moreover, a permanent field created by the protein reduces the work required to reach the transition state (TS) with a concomitant polarization of the cofactor that would favor the hydride transfer. In contrast, in water the TS is destabilized with respect to the reactant species because the polarity of the solute diminishes as the reaction proceeds, and consequently the reaction field, which is created as a response to the change in the solute polarity, is also decreased. Therefore protein structure is responsible of both effects; substrate preorganization and TS stabilization thus diminishing the activation barrier. Because of the electrostatic features of the catalyzed reaction, both media preferentially stabilize the ground-state, thus explaining the small rate constant enhancement of this enzyme, but FDH does so to a much lower extent than aqueous solution. Finally, a good agreement between experimental and theoretical kinetic isotope effects is found, thus giving some credit to our results.

Theoretical study of catalytic efficiency of a Diels-Alderase catalytic antibody: an indirect effect produced during the maturation process

The Diels-Alder reaction is one of the most important and versatile transformations available to organic chemists for the construction of complex natural products, therapeutics agents, and synthetic materials. Given the lack of efficient enzymes capable of catalyzing this kind of reaction, it is of interest to ask whether a biological catalyst could be designed from an antibody-combining site. In the present work, a theoretical study of the different behavior of a germline catalytic antibody (CA) and its matured form, 39 A-11, that catalyze a Diels-Alder reaction has been carried out. A free-energy perturbation technique based on a hybrid quantum-mechanics/molecular-mechanics scheme, together with internal energy minimizations, has allowed free-energy profiles to be obtained for both CAs. The profiles show a smaller barrier for the matured form, which is in agreement with the experimental observation. Free-energy profiles were obtained with this methodology, thereby avoiding the much more demanding two-dimensional calculations of the energy surfaces that are normally required to study this kind of reaction. Structural analysis and energy evaluations of substrate-protein interactions have been performed from averaged structures, which allows understanding of how the single mutations carried out during the maturation process can be responsible for the observed fourfold enhancement of the catalytic rate constant. The conclusion is that the mutation effect in this studied germline CA produces a complex indirect effect through coupled movements of the backbone of the protein and the substrate.

Direct electrochemistry of lactate dehydrogenase immobilized on silica sol–gel modified gold electrode and its application

The direct electrochemistry of lactate dehydrogenase (LDH) immobilized in silica sol-gel film on gold electrode was investigated, and an obvious cathodic peak at about -200 mV (versus SCE) was found for the first time. The LDH-modified electrode showed a surface controlled irreversible electrode process involving a one electron transfer reaction with the charge-transfer coefficient (alpha) of 0.79 and the apparent heterogeneous electron transfer rate constant (K(s)) of 3.2 s(-1). The activated voltammetric response and decreased charge-transfer resistance of Ru(NH(3))(6)(2+/3+) on the LDH-modified electrode provided further evidence. The surface morphologies of silica sol-gel and the LDH embedded in silica sol-gel film were characterized by SEM. A potential application of the LDH-modified electrode as a biosensor for determination of lactic acid was also investigated. The calibration range of lactic acid was from 2.0 x 10(-6) to 3.0 x 10(-5) mol L(-1) and the detection limit was 8.0 x 10(-7) mol L(-1) at a signal-to-noise ratio of 3. Finally, the effect of environmental pollutant resorcinol on the direct electrochemical behavior of LDH was studied. The experimental results of voltammetry indicated that the conformation of LDH molecule was altered by the interaction between LDH and resorcinol. The modified electrode can be applied as a biomarker to study the pollution effect in the environment.

Mutagenesis of morphinone reductase induces multiple reactive configurations and identifies potential ambiguity in kinetic analysis of enzyme tunneling mechanisms

We have identified multiple reactive configurations (MRCs) of an enzyme-coenzyme complex that have measurably different kinetic properties. In the complex formed between morphinone reductase (MR) and the NADH analogue 1,4,5,6-tetrahydro-NADH (NADH4) the nicotinamide moiety is restrained close to the FMN isoalloxazine ring by hydrogen bonds from Asn-189 and His-186 as determined from the X-ray crystal structure. Molecular dynamic simulations indicate that removal of one of these hydrogen bonds in the N189A MR mutant allows the nicotinamide moiety to occupy a region of configurational space not accessible in wild-type enzyme. Using stopped-flow spectroscopy, we show that reduction of the FMN cofactor by NADH in N189A MR is multiphasic, identifying at least four different reactive configurations of the MR-NADH complex. This contrasts with wild-type MR in which hydride transfer occurs by environmentally coupled tunneling in a single kinetic phase [Pudney et al. J. Am. Chem. Soc. 2006, 128, 14053-14058]. Values for primary and alpha-secondary kinetic isotope effects, and their temperature dependence, for three of the kinetic phases in the N189A MR are consistent with hydride transfer by tunneling. Our analysis enables derivation of mechanistic information concerning different reactive configurations of the same enzyme-coenzyme complex using ensemble stopped-flow methods. Implications for the interpretation from kinetic data of tunneling mechanisms in enzymes are discussed.