A note on the kinetics of enzyme action: A decomposition that highlights thermodynamic effects

Michaelis and Menten’s mechanism for enzymatic catalysis is remarkable both in its simplicity and its wide applicability. The extension for reversible processes, as done by Haldane, makes it even more relevant as most enzymes catalyze reactions that are reversible in nature and carry in vivo flux in both directions. Here, we decompose the reversible Michaelis–Menten equation into three terms, each with a clear physical meaning: catalytic capacity, substrate saturation and thermodynamic driving force. This decomposition facilitates a better understanding of enzyme kinetics and highlights the relationship between thermodynamics and kinetics, a relationship which is often neglected. We further demonstrate how our separable rate law can be understood from different points of view, shedding light on factors shaping enzyme catalysis.     

Crystal structure and site-directed mutagenesis of a nitroalkane oxidase from Streptomyces ansochromogenes

Nitroalkane oxidase (NAO) catalyzes neutral nitroalkanes to their corresponding aldehydes or ketones, hydrogen peroxide and nitrite. The crystal structure of NAO from Streptomyces ansochromogenes was determined; it consists of two domains, a TIM barrel domain bound to FMN and C-terminal domain with a novel folding pattern. Site-directed mutagenesis of His¹⁷⁹, which is spatially adjacent to FMN, resulted in the loss of enzyme activity, demonstrating that this amino acid residue is important for catalysis. The crystal structure of mutant H179D-nitroethane was also analyzed. Interestingly, Sa-NAO shows the typical function as nitroalkane oxidase but its structure is similar to that of 2-nitropropane dioxygenase. Overall, these results suggest that Sa-NAO is a novel nitroalkane oxidase with TIM barrel structure.     

Michaelis and Menten and the long road to the discovery of cooperativity

This article sketches the road from the establishment of the principles of enzyme kinetics, at the beginning of the 20th century, to the discovery of regulatory mechanisms and the models to explain them, from the middle of the century onwards. A long gap in time separates the two periods, in which technological advances were made that allowed the discovery of feedback inhibition and cooperativity. In particular, these discoveries and the theory needed to explain them could not have been made without knowledge of the major metabolic pathways and the enzymes and metabolites involved in them.     

HPLC-based kinetics assay facilitates analysis of systems with multiple reaction products and thermal enzyme denaturation

Glucosinolates are plant secondary metabolites abundant in Brassica vegetables that are substrates for the enzyme myrosinase, a thioglucoside hydrolase. Enzyme-mediated hydrolysis of glucosinolates forms several organic products, including isothiocyanates (ITCs) that have been explored for their beneficial effects in humans. Myrosinase has been shown to be tolerant of non-natural glucosinolates, such as 2,2-diphenylethyl glucosinolate, and can facilitate their conversion to non-natural ITCs, some of which are leads for drug development. An HPLC-based method capable of analyzing this transformation for non-natural systems has been described. This current study describes (1) the Michaelis–Menten characterization of 2,2-diphenyethyl glucosinolate and (2) a parallel evaluation of this analogue and the natural analogue glucotropaeolin to evaluate effects of pH and temperature on rates of hydrolysis and product(s) formed. Methods described in this study provide the ability to simultaneously and independently analyze the kinetics of multiple reaction components. An unintended outcome of this work was the development of a modified Lambert W(x) which includes a parameter to account for the thermal denaturation of enzyme. The results of this study demonstrate that the action of Sinapis alba myrosinase on natural and non-natural glucosinolates is consistent under the explored range of experimental conditions and in relation to previous accounts.     

tRNA Binding,Positioning, and Modification by the Pseudouridine Synthase Pus10

Pus10 is the most recently identified pseudouridine synthase found in archaea and higher eukaryotes. It modifies uridine 55 in the TΨC arm of tRNAs. Here, we report the first quantitative biochemical analysis of tRNA binding and pseudouridine formation by Pyrococcus furiosus Pus10. The affinity of Pus10 for both substrate and product tRNA is high (K_d of 30 nM), and product formation occurs with a K_m of 400 nM and a k_cat of 0.9 s^− 1. Site-directed mutagenesis was used to demonstrate that the thumb loop in the catalytic domain is important for efficient catalysis; we propose that the thumb loop positions the tRNA within the active site. Furthermore, a new catalytic arginine residue was identified (arginine 208), which is likely responsible for triggering flipping of the target uridine into the active site of Pus10. Lastly, our data support the proposal that the THUMP-containing domain, found in the N-terminus of Pus10, contributes to binding of tRNA. Together, our findings are consistent with the hypothesis that tRNA binding by Pus10 occurs through an induced-fit mechanism, which is a prerequisite for efficient pseudouridine formation.     

On the contribution of the positively charged headgroup of choline to substrate binding and catalysis in the reaction catalyzed by choline oxidase

Recent kinetic studies established that the positive charge on the trimethylammonium group of choline plays an important role in substrate binding and specificity in the reaction catalyzed by choline oxidase. In the present study, pH and solvent viscosity effects with the isosteric analogue of choline 3,3-dimethyl-butan-1-ol have been used to further dissect the contribution of the substrate positive charge to substrate binding and catalysis in the reaction catalyzed by choline oxidase. Both the kcat and kcat/Km values with 3,3-dimethyl-butan-1-ol increased to limiting values that were approximately 3- and approximately 400-times lower than those observed with choline, defining pKa values that were similar to the thermodynamic pKa value of approximately 7.5 previously determined. No effects of increased solvent viscosity were observed on the kcat and kcat/Km values with the substrate analogue at pH 8, suggesting that the chemical step of substrate oxidation is fully rate-limiting for the overall turnover and the reductive half-reaction in which the alcohol substrate is oxidized to the aldehyde. The kcat/Km value for oxygen determined with the substrate analogue was pH-independent in the pH range from 6 to 10, with an average value that was approximately 75-times lower than that previously determined with choline as substrate. These data are consistent with the positive charge headgroup of choline playing important roles for substrate binding and flavin oxidation, with minimal contribution to substrate oxidation.     

The effect of pH on the oxygen kinetics of cytochrome c oxidase proteoliposomes

The effect of pH on the oxygen kinetics of cytochrome c oxidase incorporated into phospholipid vesicles is studied. The pH profiles of the oxygen kinetics of energized and deenergized oxidase vesicles are similar. An effect of pH on the slope of the reciprocal plot of rate against oxygen concentration is observed, and this may indicate that protons are involved in the rate limiting step of the reaction between oxygen and reduced oxidase. In contrast to the pH dependence of the oxygen kinetics, the binding of CO to the oxidase is not pH dependent.     

Solvent isotope effects and the pH dependence of laccase activity under steady-state conditions

Solvent isotope effects and the pH dependence of laccase catalysis under steady-state conditions were examined with a rapid reductant to assess the potential roles of protein protic groups and the catalytic mechanism. The pH dependence of both reductant-dependent and reductant-independent steps showed bell-shaped profiles implicating at least two protic groups in each case. The apparent pKa values were: for the reductant-independent step(s), pK alpha 1 = 8.98 +/- 0.02 and pK alpha 2 = 5.91 +/- 0.03; for the reductant-dependent step(s), pK' alpha 1 = 7.55 +/- 0.12, pK' alpha 2 = 8.40 +/- 0.23. No solvent isotope effect on reductant-dependent steps was detected other than a standard shift effect. However, a significant solvent isotope effect on a reductant-independent step(s) was observed; kH/kD = 2.12 at the pH optimum of 7.5. The concentration dependence of the D2O effect indicated that a single proton was involved. Simulations of the p(H,D) data suggested that the solvent isotope effect was associated with the protein protic group required in its undissociated form (pK alpha 2). The pH effects on reductant-dependent steps are apparently associated with reductant-dependent steps that occur between O2 binding and water formation in the catalytic reaction sequence.     

Solvent isotope effects on the refolding kinetics of hen egg-white lysozyme.

Solvent isotope effects have been observed on the in vitro refolding kinetics of a protein, hen lysozyme. The rates of two distinct phases of refolding resolved by intrinsic fluorescence have been found to be altered, to differing extents, in D2O compared with H2O, and experiments have been conducted aimed at assessing the contributions to these effects from various possible sources. The rates were found to be essentially independent of whether backbone amide nitrogens were protiated or deuterated, indicating that making and breaking of their hydrogen bonding interactions is not associated with a substantial isotope effect. Neither were the rates significantly affected by adding moderate concentrations of sucrose or glycerol to the refolding buffer, suggesting that viscosity differences between H2O and D2O are also unlikely to explain the isotope effects. The data suggest that different factors, acting in opposing directions, may be dominant under different conditions. Thus, the isotope effect on the rate-determining step was found to be qualitatively reversed on going to low pH, suggesting that one component is probably associated with changes in the environments of carboxylate groups in forming the folding transition state. This term disappears at low pH as these groups are protonated and an opposing effect then dominates. It was not possible to identify this other effect on the basis of the present data, but a dependence of the hydrophobic interaction on solvent isotopic composition is a likely candidate.     

Solvent Effects on the Shape of a Tetramer

Abstract

The solvent effect on the shape of a tetramer with increasing temperature is analyzed. For this purpose models of an isolated chain and a chain immersed in a solvent have been simulated by Molecular Dynamics. A solvent model represented by stochastic forces has been tested against molecular dynamics results. The behaviour of the mean-square end-to-end distance 〈R ²〉 and 〈l ₁ ³ S ²〉 with increasing temperature are shown. where l ₁ is the longest eigenvalue of the moment of inertia tensor and S is the radius of gyration. All the chain models studied show different behaviour of these quantities at low temperature compared to high temperature where the shape of the tetramer is temperature insensitive. The main solvent effect is to pospone the transition to higher temperature. The stochastic solvent model qualitatively agrees with molecular dynamics results.     

FTIR spectroelectrochemical study of the activation and inactivation processes of [NiFe] hydrogenases: effects of solvent isotope replacement and site-directed mutagenesis

The kinetics of the activation and anaerobic inactivation processes of Desulfovibrio gigas hydrogenase have been measured in D₂O by FTIR spectroelectrochemistry. A primary kinetic solvent isotope effect was observed for the inactivation process but not for the activation step. The kinetics of these processes have been also measured after replacement of a glutamic residue placed near the active site of an analogous [NiFe] hydrogenase from Desulfovibrio fructosovorans. Its replacement by a glutamine affected greatly the kinetics of the inactivation process but only slightly the activation process. The interpretation of the experimental results is that the rate-limiting step for anaerobic inactivation is the formation from water of a -OH^– bridge at the hydrogenase active site, and that Glu25 has a role in this step.Electronic Supplementary Material Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00775-004-0559-7     

The concept of high- and low-affinity reactions in bovine cytochrome c oxidase steady-state kinetics

(1) Analysis of the data from steady-state kinetic studies shows that two reactions between cytochrome c and cytochrome c oxidase sufficed to describe the concave Eadie-Hofstee plots ($\text{K}{}_{\mathrm{<mtext>m</mtext>}}\text{? 1 · 10}{}^{\mathrm{?8}}\text{M}$ and $\text{K}{}_{\mathrm{<mtext>m</mtext>}}\text{? 2 · 10}{}^{\mathrm{?5}}\text{M}$). It is not necessary to postulate a third reaction of $\text{K}{}_{\mathrm{<mtext>m</mtext>}}\text{? 10}{}^{\mathrm{?6}}\text{M}$. (2) Change of temperature, type of detergent and type of cytochrome c affected both reactions to the same extent. The presence of only a single catalytic cytochrome c interaction site on the oxidase could explain the kinetic data. (3) Our experiments support the notion that, at least under our conditions (pH 7.8, low-ionic strength), the dissociation of ferricytochrome c from cytochrome c oxidase is the rate-limiting step in the steady-state kinetics. (4) A series of models, proposed to describe the observed steady-state kinetics, is discussed.     

Interpretation of V/K isotope effects for enzymatic reactions exhibiting multiple isotopically sensitive steps

Formulations of an enzyme mechanism where only a single step is presumed to be isotopically sensitive can be written in terms of forward and reverse commitments to catalysis. These commitments provide a natural and intuitive way of interpreting the observed isotope effects. Unfortunately, when multiple isotopically sensitive steps are present in the mechanism, including effects associated with pre-equilibria of the unbound substrate, the observed V/K kinetic isotope effect is expressed as a complicated expression of the intrinsic rate constants for each step, the interpretation of which is not always immediately obvious. We show here that V/K isotope effects from unbranched or rapid-equilibrium random Michaelis-Menten systems containing multiple isotopically sensitive steps can be written as a weighted average of the intrinsic isotope effects on each step, where this intrinsic isotope effect from each step is the product of the equilibrium isotope effect on the formation of the reacting intermediate for that step and the intrinsic kinetic effect on the forward rate constant for that step, and the weighting factors are simply the reciprocal sum of the forward and reverse commitments for each step i plus unity, 1/(C(fi)+C(ri)+1), equivalent to the sensitivity index [Ray, W.J., 1983.     

Solvent effects on the distribution of conformational substates in native and azide reacted Cu, Zn superoxide dismutase

Native and azide reacted Cu, Zn superoxide dismutase in aqueous and mixed water-glycerol solution have been investigated by EPR spectroscopy at low temperature. An accurate computer simulation, based on a well established theoretical model which has been reformulated for rhombic symmetry, has shown that the EPR spectrum of the copper ion in the native protein shows a significant g and A strain in the parallel region. The strain arises from a distribution of the ligand field strengths onto the metal ion and this could be traced back to the existence of a multiplicity of conformational states in the protein molecule. The strain is reduced in the presence of azide which is known to bind directly to the copper atom and to give rise to a more relaxed configuration corresponding to a square pyramidal geometry in which the apical ligand occupies an elongated position. In both samples, addition of glycerol further reduces the strain, indicating that the solvent is directly coupled to the protein matrix, thereby modulating the structural heterogeneity displayed by the protein molecule. Received: 6 June 1996 / Accepted: 9 April 1997     

Probing the chemical steps of nitroalkane oxidation catalyzed by 2-nitropropane dioxygenase with solvent viscosity, pH, and substrate kinetic isotope effects

Among the enzymes that catalyze the oxidative denitrification of nitroalkanes to carbonyl compounds, 2-nitropropane dioxygenase is the only one known to effectively utilize both the neutral and anionic (nitronate) forms of the substrate. A recent study has established that the catalytic pathway is common to both types of substrates, except for the initial removal of a proton from the carbon of the neutral substrates [Francis, K., Russell, B., and Gadda, G. (2005) J. Biol. Chem. 280, 5195-5204]. In the present study, the mechanistic properties of the enzyme have been investigated with solvent viscosity, pH, and kinetic isotope effects. With nitroethane or ethylnitronate, the kcat/Km and kcat values were independent of solvent viscosity, consistent with the substrate and product binding to the enzyme in rapid equilibrium. The abstraction of the proton from the alpha carbon of neutral substrates was investigated by measuring the pH dependence of the D(kcat/KNE) value with 1,1-[2H2]-nitroethane. The formation of the enzyme-bound flavosemiquinone formed during catalysis was examined by determining the pH dependence of the kcat/Km values with ethylnitronate and nitroethane and the inhibition by m-nitrobenzoate. Finally, alpha-secondary kinetic isotope effects with 1-[2H]-ethylnitronate were used to propose a non-oxidative tautomerization pathway, in which the enzyme catalyzes the interconversion of nitroalkanes between their anionic and neutral forms. The data presented suggest that enzymatic turnover of 2-nitropropane dioxygenase with neutral substrates is limited by the cleavage of the substrate CH bond at low pH, whereas that with anionic substrates is limited by the non-oxidative tautomerization of ethylnitroante to nitroethane at high pH.     

Solvent effects on fluorescence properties of protochlorophyll and its derivatives with various porphyrin side chains

Fluorescence spectra and fluorescence lifetimes of protochlorophyll (Pchl) were measured in organic solvents having different physical and chemical properties and were analyzed taking into account the nonspecific (dependent on bulk solvent parameters), and specific (e.g. H bonds, Mg coordination) solvent–solute interactions. The energy of the fluorescence emission band decreased, while the Stokes shift increased for increasing solvent orientation polarizability, which is a function of both the dielectric constant (ε) and the refractive index (n). The extent of the dependence of the Stokes shift on solvent orientation polarizability was higher in protic (i.e. those able to form hydrogen-binding) than in aprotic solvents. High value of the Stokes shift was also observed in pyridine and methanol, i.e. in solvents hexacoordinating the central Mg atom. The fluorescence decay of Pchl was monoexponential in all of the investigated solvents. The fluorescence lifetime decreased for increasing solvent orientation polarizability from 5.5 ± 0.1 ns in 1,4-dioxane to 3.3 ± 0.1 ns in methanol. Longer lifetime values were observed in the case of aprotic solvents than in protic solvents. The hexacoordination of Mg had no effect on the fluorescence lifetime. The present data are discussed with respect to results found for protochlorophyllide (Pchlide) (My?liwa-Kurdziel et al. in Photochem Photobiol 79:62–67, 2004), and they indicate that the presence of phytol chain in the porphyrin ring influences the spectral properties of the whole chromophore. This is the first complex analysis comparing the fluorescence emission and fluorescence lifetimes of purified Pchl and Pchlide.     

Studies on the specificity toward aldehyde substrates and steady-state kinetics of xanthine oxidase

The aldehyde specificity of xanthine oxidase (xanthine:oxygen oxidoreductase, EC 1.2.3.2) has been reinvestigated. The biogenic aldehydes and succinate semialdehyde are reasonable substrates for xanthine oxidase. Pyrophosphate, which binds to xanthine oxidase, does not seem to affect significantly the enzyme's catalytic activity. The steady-state parameters for the oxidation of several substrates by xanthine oxidase and oxygen have been determined. Formaldehyde differs from xanthine and other aldehydes in phi 2, the parameter describing the reaction with oxygen. Substrate inhibition has been studied at high concentrations of xanthine with oxygen as the electron acceptor. The inhibition is hyperbolic and uncompetitive with respect to oxygen. This is possibly due to rate-limiting product release from molybdenum(IV) being slower than from molybdenum(VI).     

Kinetic and regulatory aspects of the function of the alternative oxidase in plant respiration

The kinetic modelling of the respiratory network in plant mitochondria is discussed, with emphasis on the importance of the choice of boundary conditions, and of modelling of both quinol-oxidising and quinone-reducing pathways. This allows quantitative understanding of the interplay between the different pathways, and of the functioning of the plant respiratory network in terms of the kinetic properties of its component parts. The effects of activation of especially succinate dehydrogenase and the cyanide-insensitive alternative oxidase are discussed. Phenomena, such as respiratory control ratios depending on the substrate, shortcomings of the Bahr and Bonner model for electron distribution between the oxidases and reversed respiratory control, are explained. The relation to metabolic control analysis of the respiratory network is discussed in terms of top-down analysis.     

The effects of suspending medium viscosity on erythrocyte deformation and haemolysis in vitro

Fresh adult human erythrocytes were suspended in isotonic pH adjusted solutions containing various concentrations of Dextran T.500. The cells were subjected to uniform hydrodynamic shear stress in a Ferranti Shirley Cone and Plate Viscosimeter. The amount of lysis incurred at any given combination of explosure parameters was markedly affected by the viscosity of the suspending medium. Optical diffraction patterns obtained whilst the cells were undergoing shear demonstrated that cellular deformation was also a function of viscosity. Consequently, the distorted shape of the stressed cell must play a crucial role in the haemolytic process.     

Solvent effects on ouabain binding to the (Na+,K+)-ATPase of rat brain

The effects of the solvents deuterated water (²H₂O) and dimethyl sulfoxide (Me₂SO) on [³H]ouabain binding to (Na⁺,K⁺)-ATPase under different ligand conditions were examined. These solvents inhibited the type I ouabain binding to the enzyme (i.e., in the presence of Mg²⁺+ATP+Na⁺). In contrast, both solvents stimulated type II (i.e., Mg²⁺+P_i-, or Mn²⁺-dependent) binding of the drug. The solvent effects were not due to pH changes in the reaction. However, pH did influence ouabain binding in a differential manner, depending on the ligands present. For example, changes in pH from 7.05 to 7.86 caused a drop in the rate of binding by about 15% in the presence of Mg²⁺+Na⁺+ATP, 75% in the Mg²⁺+P_i system, and in the presence of Mn²⁺ an increase by 24% under similar conditions. Inhibitory or stimulatory effects of solvents were modified as various ligands, and their order of addition, were altered. Thus, ²H₂O inhibition of type I ouabain binding was dependent on Na⁺ concentration in the reaction and was reduced as Na⁺ was elevated. Contact of the enzyme with Me₂SO, prior to ligands for type I binding, resulted in a greater inhibition of ouabain binding than that when enzyme was exposed to Na⁺+ATP first and then to Me₂SO. Likewise, the stimulation of type II binding was greater when appropriate ligands acted on enzyme prior to addition of the solvent. Since Me₂SO and ²H₂O inhibit type I ouabain binding, it is proposed that this reaction is favored under conditions which promote loss of H₂O, and E₁ enzyme conformation; the stimulation of type II ouabain binding in the presence of the solvents suggests that this type of binding is favored under conditions which promote the presence of H₂O at the active enzyme center and E₂ enzyme conformation. This postulation of a role of H₂O in modulating enzyme conformations and ouabain interaction with them is in concordance with previous observations.