Curve Crossing Formulation for Proton Transfer Reactions in Solution

Comparison of rates and kinetic isotope effects using PEG-modified variants and glycoforms of glucose oxidase: the relationship of modification of the protein envelope to C-H activation and tunneling

An earlier investigation of the temperature dependencies of rates and kinetic isotope effects (KIEs) in glucose oxidase (GO) used variants that differed in the extent of glycosylation at the surface of the protein. Kohen et al. [Kohen, A., Jonsson, T., and Klinman, J. P. (1997) Biochemistry 36, 2603-2611] presented evidence that the KIE on the Arrhenius prefactor varied as a function of protein modification, concluding that the degree of hydrogen tunneling at the active site was dependent on changes in mass at the surface. We now examine GO proteins containing polyethylene glycol (PEG) at their surface and a more extensively glycosylated form of GO, to distinguish simple mass effects from other sources of altered catalytic behavior. One PEG variant was created by modifying deglycosylated GO with short PEG chains (average of 350 Da each), while another contained a smaller number of long PEG chains (average of 5000 Da each). The light (146 kDa) and heavy (211 kDa) PEG variants and the hyperglycosylated variant display isotope effects on the Arrhenius prefactor that are similar (A(D)/A(T) = 0.55-0.62), while the unperturbed wild-type GO (WT-GO) is found to have an A(D)/A(T) that is reassessed as being close to unity. It appears that any modification of the protein surface away from that of the wild type gives rise to altered behavior for hydrogen transfer in the active site. We have also compared the effect of enthalpies of activation on both k(cat)/K(M) and k(cat) for the variants, introducing a new method to extract the k(cat)/K(M) rate constant and enthalpy of activation for the tritiated substrate from competitive KIE experiments. We find similar trends in Delta H(++) for both competitive and noncompetitive parameters and a smaller trend in k(cat) than reported earlier. Correlations are observed between A(D)/A(T) and both the enthalpies of activation and the thermal melt temperatures (T(M)) of the GO isoforms. In addition to the present study, there are now a number of examples where a perturbation of enzyme structure away from that of the wild type causes the observed KIE to become more temperature-dependent. The implications of these findings are discussed in the context of hydrogen tunneling and the relationship of protein structure and dynamics to this process.

Environmentally coupled hydrogen tunneling. Linking catalysis to dynamics

Many biological C-H activation reactions exhibit nonclassical kinetic isotope effects (KIEs). These nonclassical KIEs are too large (kH/kD > 7) and/or exhibit unusual temperature dependence such that the Arrhenius prefactor KIEs (AH/AD) fall outside of the semiclassical range near unity. The focus of this minireview is to discuss such KIEs within the context of the environmentally coupled hydrogen tunneling model. Full tunneling models of hydrogen transfer assume that protein or solvent fluctuations generate a reactive configuration along the classical, heavy-atom coordinate, from which the hydrogen transfers via nuclear tunneling. Environmentally coupled tunneling also invokes an environmental vibration (gating) that modulates the tunneling barrier, leading to a temperature-dependent KIE. These properties directly link enzyme fluctuations to the reaction coordinate for hydrogen transfer, making a quantum view of hydrogen transfer necessarily a dynamic view of catalysis. The environmentally coupled hydrogen tunneling model leads to a range of magnitudes of KIEs, which reflect the tunneling barrier, and a range of AH/AD values, which reflect the extent to which gating modulates hydrogen transfer. Gating is the primary determinant of the temperature dependence of the KIE within this model, providing insight into the importance of this motion in modulating the reaction coordinate. The potential use of variable temperature KIEs as a direct probe of coupling between environmental dynamics and the reaction coordinate is described. The evolution from application of a tunneling correction to a full tunneling model in enzymatic H transfer reactions is discussed in the context of a thermophilic alcohol dehydrogenase and soybean lipoxygenase-1.

Barrier passage and protein dynamics in enzymatically catalyzed reactions

This review describes studies of particular enzymatically catalyzed reactions to investigate the possibility that catalysis is mediated by protein dynamics. That is, evolution has crafted the protein backbone of the enzyme to direct vibrations in such a fashion to speed reaction. The review presents the theoretical approach we have used to investigate this problem, but it is designed for the nonspecialist. The results show that in alcohol dehydrogenase, dynamic protein motion is in fact strongly coupled to chemical reaction in such a way as to promote catalysis. This result is in concert with both experimental data and interpretations for this and other enzyme systems studied in the laboratories of the two other investigators who have published reviews in this issue.

Temperature-dependent isotope effects in soybean lipoxygenase-1: correlating hydrogen tunneling with protein dynamics

The hydrogen-atom transfer in soybean lipoxygenase-1 (SLO) exhibits a large kinetic isotope effect on k(cat) (KIE = 81) near room temperature and a very weak temperature dependence (E(act) = 2.1 kcal/mol). These properties are consistent with H small middle dot transfer that occurs entirely by a tunneling event. Mutants of SLO were prepared, and the temperature dependence of the KIE was measured, to test for alterations in the tunneling behavior. All mutants studied exhibit KIEs of similar, large magnitude at 30 degrees C, despite an up to 3 orders of magnitude change in k(cat). E(act) for two of the mutants (Leu(754) --> Ala, Leu(546) --> Ala) is larger than for wild-type (WT), and the KIE becomes slightly more temperature dependent. In contrast, Ile(553) --> Ala exhibits k(cat) and E(act) parameters similar to wild-type soybean lipoxygenase-1 (WT-SLO) for protiated substrate; however, the KIE is markedly temperature dependent. The behavior of the former two mutants could reflect increased reorganization energies (lambda), but the behavior of the latter mutant is inconsistent with this description. We have invoked a full H* tunneling model (Kuznetsov, A. M.; Ulstrup, J. Can. J. Chem. 1999, 77, 1085-1096) to explain the temperature dependence of the KIE, which is indicative of the extent to which distance sampling (gating) modulates hydrogen transfer. WT-SLO exhibits a very small E(act) and a nearly temperature-independent KIE, which was modeled as arising from a compressed hydrogen transfer distance with little modulation of the hydrogen transfer distance. The observations on the Leu(754) --> Ala and Leu(546) --> Ala mutants were modeled as arising from a slightly less compressed active site with greater modulation of the hydrogen transfer distance by environmental dynamics. Finally, the observed behavior of the Ile(553) --> Ala mutant indicates a relaxed active site with extensive involvement of gating to facilitate hydrogen transfer. We conclude that WT-SLO has an active site structure that is well organized to support hydrogen tunneling and that mutations perturb structural elements that support hydrogen tunneling. Modest alterations in active site residues increase lambda and/or increase the hydrogen transfer distance, thereby affecting the probability that tunneling can occur. These studies allow the detection and characterization of a protein-gating mode in catalysis.

Identification of a protein-promoting vibration in the reaction catalyzed by horse liver alcohol dehydrogenase

In this article we present computational studies of horse liver alcohol dehydrogenase (HLADH). The computations identify a rate-promoting vibration that is symmetrically coupled to the reaction coordinate. In HLADH a bulky amino acid (Val203) is positioned at the face of the nicotinamide adenine dinucleotide (NAD(+)) cofactor distal to alcohol substrate to restrict the separation of reactants and control the stereochemistry. Molecular dynamics simulations were performed on the dimeric HLADH, including the NAD cofactor, the substrate, and the crystallographic waters, for three different configurations, reactants, products, and transition state. From the spectral density for the substrate-NAD relative motion, and that for the NAD-Val203 relative motion, we find that the two motions are in resonance. By computing the associated spectrum, we find that the reaction coordinate is coupled with the substrate-NAD motion, and from the fact that the coupling vanishes at or near the transition state (demonstrated by the disappearance of strong features in the spectral density), we conclude that the substrate-NAD motion plays the role of a promoting vibration symmetrically coupled to the reaction coordinate.

Application of the Marcus cross relation to hydrogen atom transfer reactions

The transfer of a hydrogen atom-a proton and an electron-is a fundamental process in chemistry and biology. A variety of hydrogen atom transfer reactions, involving iron complexes, phenols, hydroxylamines, tBuOOH, toluene, and related radicals, are shown to follow the Marcus cross relation. Thus, the Marcus theory formalism based on ground-state energetics and self-exchange rates, originally developed for electron transfer processes, is also valuable for hydrogen atom transfer. Compounds that undergo slow proton transfer (C-H bonds) or slow electron transfer (cobalt complexes) also undergo slow hydrogen atom transfer. Limitations of this approach are also discussed.

Effect of para substituents on the rate of bond shift in arylcyclooctatetraenes

The rate constants for bond shift (k(BS)) in phenylcyclooctatetraene (1b) and its p-nitro and p-methoxy analogues (1a and 1c, respectively) in THF-d(8) were determined by dynamic NMR spectrometry to be identical, but k(BS) is eight times greater at 280 K relative to 1b when the para substituent is cyclooctatetraenyldipotassium (2(2-)/2K(+)). These results are discussed in the context of (a) possible intrinsically small substituent effects (as determined by (13)C chemical shifts in the ground state (GS)) for 1a-c and (b) differences in steric interactions and resonance stabilization between the ground and BS transition state (TS). The latter factor was modeled by employing HF/3-21G(*) ab initio molecular orbital calculations of the GS and ring inversion TS. It is concluded that k(BS) is unchanged in 1a-c because the potentially greater pi interaction in the BS TS is counterbalanced by a greater degree of twist between the aryl and COT rings resulting from increased steric hindrance relative to the GS. However, pi interaction assumes a greater importance in the TS of 2(2-)/2K(+) owing to a decreased HOMO-LUMO energy gap compared to 1a-c, particularly when the counterions are solvated. This causes a decrease in the inter-ring twist angle and, together, these changes are responsible for the observed increase in k(BS) in 2(2-)/2K(+). The effect of substituents on a possible contribution of heavy atom tunneling to the reaction mechanism is also discussed.

Deuterium isotope effect on the intramolecular electron transfer in Pseudomonas aeruginosa azurin

Intramolecular electron transfer in azurin in water and deuterium oxide has been studied over a broad temperature range. The kinetic deuterium isotope effect, k(H)/k(D), is smaller than unity (0.7 at 298 K), primarily caused by the different activation entropies in water (-56.5 J K(-1) mol(-1)) and in deuterium oxide (-35.7 J K(-1) mol(-1)). This difference suggests a role for distinct protein solvation in the two media, which is supported by the results of voltammetric measurements: the reduction potential (E(0')) of Cu(2+/+) at 298 K is 10 mV more positive in D(2)O than in H(2)O. The temperature dependence of E(0') is also different, yielding entropy changes of -57 J K(-1) mol(-1) in water and -84 J K(-1) mol(-1) in deuterium oxide. The driving force difference of 10 mV is in keeping with the kinetic isotope effect, but the contribution to DeltaS from the temperature dependence of E(0') is positive rather than negative. Isotope effects are, however, also inherent in the nuclear reorganization Gibbs free energy and in the tunneling factor for the electron transfer process. A slightly larger thermal protein expansion in H(2)O than in D(2)O (0.001 nm K(-1)) is sufficient both to account for the activation entropy difference and to compensate for the different temperature dependencies of E(0'). Thus, differences in driving force and thermal expansion appear as the most straightforward rationale for the observed isotope effect.

The mechanism of the proton transfer: an outline

A brief summary of the principal notions of the quantum-mechanical theory of the charge transfer reactions has been presented. In the framework of this theory, the mechanism of the proton transfer consists in the classical medium reorganization that equalizes the proton energy levels in the initial and final states, and a consequent proton transfer via a quantum-mechanical underbarrier transition. On the basis of this mechanism, factors influencing the proton transfer probability, and hence kinetic isotope effect, have been discussed; among them are the optimum tunneling distance, the involvement of the excited vibrational states, etc. Semi-classical and quantum-mechanical treatments of the Swain-Schaad relations have been compared. Some applications to enzymatic proton-transfer reactions have been described.

Enzymology takes a quantum leap forward

Enzymes are biological molecules that accelerate chemical reactions. They are central to the existence of life. Since the discovery of enzymes just over a century ago, we have witnessed an explosion in our understanding of enzyme catalysis, leading to a more detailed appreciation of how they work. A key breakthrough came from understanding how enzymes surmount the potential-energy barrier that separates reactants from products. The genetic engineering revolution has provided tools for dissecting enzyme structure and enabling design of novel function. Despite the huge efforts to redesign enzyme molecules for specific applications, progress in this area has been generally disappointing. This stems from our limited understanding of the subtleties by which enzymes enhance reaction rates. Based on current dogma, the vast majority of studies have concentrated on understanding how enzymes facilitate passage of the reaction over a static potential-energy barrier. However, recent studies have revealed that passage through, rather than over, the barrier can occur. These studies reveal that quantum mechanical phenomena, driven by protein dynamics, can play a pivotal role in enzyme action. The new millennium will witness a flurry of activity directed at understanding the role of quantum mechanics and protein motion in enzyme action. We discuss these new developments and how they will guide enzymology into the new millennium.

New insights into enzyme catalysis. Ground state tunnelling driven by protein dynamics

The wave-particle duality of matter suggests that quantum tunnelling may have a prominent role in enzymatic H-transfer. However, unlike for electron tunnelling, evidence for H-tunnelling in enzyme molecules is extremely limited. The theoretical development, and verification by experiment, of a role for protein dynamics in driving enzymatic H-tunnelling is presented. Dynamic theories of H-tunnelling suggest that the kinetic isotope effect, during rupture of a C-H/C-D bond, for example, can assume values interpreted previously as indicating classical transfer. Vibrationally enhanced ground state tunnelling has been demonstrated for enzymes that cleave stable C-H bonds. This is an attractive mechanism as large activation energies make it energetically unfavourable for a classical, over-the-barrier mode of cleavage. Furthermore, it may be a general strategy used by enzymes for catalysing these 'difficult' transformations.

Article

We discuss a broad theoretical frame for hydrogen transfer in chemical and biological systems. Hydrogen tunnelling, coupling between the tunnel modes and the environment, and fluctuational barrier preparation for hydrogen tunnelling are in focus and given precise analytical forms. Specific rate constants are provided for three limits, i.e., the fully diabatic, the partially adiabatic, and the fully adiabatic limits. These limits are all likely to represent real chemical or biological hydrogen transfer systems. The rate constants are referred particularly to the driving force and temperature dependence of the kinetic isotope effect (KIE). The origin of these correlations is different in the three limits. It is rooted in the tunnel factor and weak excitation of the heavier isotopes in the former two limits, giving a maximum for thermoneutral processes. A new observation is that the adiabatic limit also accords with a KIE maximum for thermoneutral processes but the KIE is here reflected solely in the activation Gibbs free energy differences, in this case rooted in the low-frequency environmental nuclear dynamics. Three systems of biological hydrogen tunnelling, viz. lipoxygenase, yeast alcohol dehydrogenase, and bovine serum amine oxygenase, offer unusual new cases for analysis and have been analysed using the theoretical frames. All the systems show large KIEs and strong indications of hydrogen tunnelling. They also represent different degrees of fluctuational barrier preparation, with lipoxygenase as the most rigid and bovine serum amine oxygenase as the softest system.Key words: generalized Born-Oppenheimer scheme, kinetic isotope effect, gated proton transfer, partially adiabatic proton transfer, proton tunnelling in enzyme catalysis.