Simultaneous interaction of enzymes with two modifiers: Reappraisal of kinetic models and new paradigms

Enzyme activity can be modulated by the concurrent action of two modifiers, either activators or inhibitors. The kinetic mechanisms for the interaction of the individual modifiers with the target enzyme can change considerably when two modifiers bind simultaneously. We illustrate a general equation for this kind of interactions, which can unambiguously describe the behavior of activators and inhibitors acting by any combination of classical kinetic mechanisms. The flexibility of this model is exemplified by combinations of activators and/or inhibitors, which can be competitive, uncompetitive or mixed-type, bind the target enzyme in either compulsory or random order, and are able to drive or not enzyme activity to zero at saturation. The model shows that the effects of zero-interaction and synergy between simultaneously acting enzyme modifiers are common events. Yet, in disagreement with previous theories, this model shows that antagonism between enzyme modifiers is a rare effect, which can be predicted only under very particular circumstances.     

非稳态酶活化动力学的布尔函数图论分析

以非稳态酶动力学的布尔函数图形方法研究非稳态酶活化动力学问题,推导出此类反应的非稳态酶动力学方程,并对此动力学方程进行了讨论,分析了酶活化反应体系的非稳态酶动力学过程．     

Isothermal titration calorimetry determination of individual rate constants of trypsin catalytic activity

Determination of individual rate constants for enzyme-catalyzed reactions is central to the understanding of their mechanism of action and is commonly obtained by stopped-flow kinetic experiments. However, most natural substrates either do not fluoresce/absorb or lack a significant change in their spectra while reacting and, therefore, are frequently chemically modified to render adequate molecules for their spectroscopic detection. Here, isothermal titration calorimetry (ITC) was used to obtain Michaelis–Menten plots for the trypsin-catalyzed hydrolysis of several substrates at different temperatures (278–318 K): four spectrophotometrically blind lysine and arginine N-free esters, one N-substituted arginine ester, and one amide. A global fitting of these data provided the individual rate constants and activation energies for the acylation and deacylation reactions, and the ratio of the formation and dissociation rates of the enzyme–substrate complex, leading also to the corresponding free energies of activation. The results indicate that for lysine and arginine N-free esters deacylation is the rate-limiting step, but for the N-substituted ester and the amide acylation is the slowest step. It is shown that ITC is able to produce quality kinetic data and is particularly well suited for those enzymatic reactions that cannot be measured by absorption or fluorescence spectroscopy.     

Applicability of fluorescence-based sensors to the determination of kinetic parameters for O2 in oxygenases

Optical methods for O₂ determination based on dynamic fluorescence quenching have been applied to measure oxygen uptake rates in cell culture and to determine intracellular oxygen levels. Here we demonstrate the applicability of fluorescence-based probes in determining kinetic parameters for O₂ using as an example catalysis by a cofactor-independent oxygenase (DpgC). Fluorescence-based sensors provide a direct assessment of enzyme-catalyzed O₂ consumption using commercially available, low-cost instrumentation that is easily customizable and, thus, constitutes a convenient alternative to the widely used Clark-type electrode, especially in cases where chemical interference is expected to be problematic.     

Inhibition of cathepsin G by 2-amino-3,1-benzoxazin-4-ones: kinetic investigations and docking studies

A series of benzoxazinones was used to investigate the interaction of human cathepsin G with acyl-enzyme inhibitors. With respect to the primary specificity of cathepsin G, inhibitors with hydrophobic or basic residues at position 2 were included in the study. Parameters of the enzyme acylation and deacylation were determined by slow-binding kinetics in the presence of a chromogenic substrate. For selected inhibitors, the time course of the enzyme-catalyzed conversion of the inhibitors was followed. This approach was suitable to elucidate a rate-determining deacylation step. Docking simulations of the noncovalent enzyme-inhibitor complexes were performed and several clusters were analyzed for each inhibitor. The amino acids of the active site that participate in the binding of the inhibitors were determined. The arrangements in several clusters of an inhibitor were not uniform with respect to the orientation by which the inhibitor was bound in the S(1) pocket. Docking of the basic piperazino derivatives 6 and 10 indicated an interaction with Glu 226 at the bottom of the S(1) specificity pocket. The (N-methyl)benzylamino derivative 1 showed the strongest acylation rate (k(on)=1200 M(-1) s(-1)), which was attributed to a high extent of pseudo-productive orientations of the noncovalent preassociation complex.     

A century of enzyme kinetic analysis, 1913 to 2013

This review traces the history and logical progression of methods for quantitative analysis of enzyme kinetics from the 1913 Michaelis and Menten paper to the application of modern computational methods today. Following a brief review of methods for fitting steady state kinetic data, modern methods are highlighted for fitting full progress curve kinetics based upon numerical integration of rate equations, including a re-analysis of the original Michaelis–Menten full time course kinetic data. Finally, several illustrations of modern transient state kinetic methods of analysis are shown which enable the elucidation of reactions occurring at the active sites of enzymes in order to relate structure and function.     

An algebraic model to determine substrate kinetic parameters by global nonlinear fit of progress curves

We propose that the time course of an enzyme reaction following the Michaelis-Menten reaction mechanism can be conveniently described by a newly derived algebraic equation, which includes the Lambert Omega function. Following Northrop's ideas [Anal. Biochem.321, 457–461, 1983], the integrated rate equation contains the Michaelis constant (K_M) and the specificity number (k_S≡k_cat/K_M$k_{\text{S}}\equiv k_{\text{cat}}/K_{\text{M}}$) as adjustable parameters, but not the turnover number k_cat. A modification of the usual global-fit approach involves a combinatorial treatment of nominal substrate concentrations being treated as fixed or alternately optimized model parameters. The newly proposed method is compared with the standard approach based on the “initial linear region” of the reaction progress curves, followed by nonlinear fit of initial rates to the hyperbolic Michaelis-Menten equation. A representative set of three chelation-enhanced fluorescence EGFR kinase substrates is used for experimental illustration. In one case, both data analysis methods (linear and nonlinear) produced identical results. However, in another test case, the standard method incorrectly reported a finite (50–70 μM) K_M value, whereas the more rigorous global nonlinear fit shows that the K_M is immeasurably high.     

A kinetic model for surfactant inhibition of pentachlorophenol biodegradation

A kinetic model is used to describe the effect of the nonionic surfactant Tergitol NP-10 (TNP10) on pentachlorophenol (PCP) biodegradation by Sphingomonas chlorophenolica sp. strain RA2. Different initial biomass to initial substrate ratios ranging from 13 to 418 were tested with 23 TNP10 concentrations ranging from 0 to 1500 mg/L. Tests were also conducted at 10 degrees C and 20 degrees C. No PCP biodegradation inhibition was observed at concentrations below the critical micelle concentration (CMC) of 50 mg/L. TNP10 concentrations above 100 to 200 mg/L were increasingly inhibitory to PCP biodegradation rates. This inhibition was best described by the Monod kinetic equation wherein the effect of TNP10 inhibition is reflected in the half-saturation constant (Ks). The value of the Ks increased from between 1.5 and 13.5 mg/L with no surfactant present to 44 to 131 mg/L at 1000 mg/L TNP10. Using a standard competitive inhibition approach, the inhibition constant for TNP10 was approximately 100 mg/L at both 10 degrees C and 20 degrees C.     

Methylglyoxal as substrate and inhibitor of human aldehyde dehydrogenase: Comparison of kinetic properties among the three isozymes

Methylglyoxal was demonstrated to be a substrate for the isozymes E1, E2 and E3 of human aldehyde dehydrogenase. Pyruvate was the product from the oxidation of methylglyoxal by the three isozymes. At pH 7.4 and 25^oC, the major and minor components of the E3 isozyme catalyzed the reaction with V_max of 1.1 and 0.8 μmol NADH min⁻¹ mg⁻¹ protein, respectively, compared to 0.067 and 0.060 μmol NADH min⁻¹ mg⁻¹ protein for the E1 and E2 isozymes, respectively. The E2 isozyme had a K_m for methylglyoxal of 8.6 μM, the lowest compared to 46 μM for E1 and 586 and 552 μM for the major and minor components of the E3 isozyme, respectively. Both components of the E3 isozyme showed substrate inhibition by methylglyoxal, with K_i values of 2.0 mM for the major component and 12 mM for the minor component at pH 9.0. Substrate inhibition by methylglyoxal was not observed with the E1 and E2 isozymes. Methylglyoxal strongly inhibited the glycolaldehyde activity of the E1 and E2 isozymes. Mixed-type models of inhibition were employed as an approach to calculate the inhibition constants, 44 and 10.6 μM for E1 and E2 isozymes, respectively.     

Determination of kinetic parameters of enzyme-catalyzed reactions with a minimum number of velocity measurements

Duggleby [Duggleby, R.G., 1979. Experimental designs for estimating kinetic parameters for enzyme-catalyzed reactions. J. Theor. Biol. 81, 672-684] discussed the “design of several replicate measurements of the velocity at as many experimental conditions as there are parameters to be estimated.” He discussed the application of this method to A→products, without and with competitive inhibition, and commented briefly on A+B→products. The availability of computer applications that can solve large sets of simultaneous equations makes it possible to use this method to calculate kinetic parameters for more complicated enzyme mechanisms. This article is concerned with rapid-equilibrium rate equations, but this method can also be used with steady-state rate equations. Computer programs are provided for the calculation of the three kinetic parameters for ordered A+B→products from three velocity measurements and for the calculation of the four kinetic parameters for random A+B→products from four velocity measurements. Computer programs are also provided for competitive inhibition, uncompetitive inhibition, and mixed inhibition of ordered A+B→products.     

Mass spectrometry assay for studying kinetic properties of dipeptidases: characterization of human and yeast dipeptidases

Chemical modifications of substrate peptides are often necessary to monitor the hydrolysis of small bioactive peptides. We developed an electrospray ionization mass spectrometry (ESI–MS) assay for studying substrate distributions in reaction mixtures and determined steady-state kinetic parameters, the Michaelis–Menten constant (K_m), and catalytic turnover rate (V_max/[E]_t) for three metallodipeptidases: two carnosinases (CN1 and CN2) from human and Dug1p from yeast. The turnover rate (V_max/[E]_t) of CN1 and CN2 determined at pH 8.0 (112.3 and 19.5 s⁻¹, respectively) suggested that CN1 is approximately 6-fold more efficient. The turnover rate of Dug1p for Cys-Gly dipeptide at pH 8.0 was found to be slightly lower (73.8 s⁻¹). In addition, we determined kinetic parameters of CN2 at pH 9.2 and found that the turnover rate was increased by 4-fold with no significant change in the K_m. Kinetic parameters obtained by the ESI–MS method are consistent with results of a reverse-phase high-performance liquid chromatography (RP–HPLC)-based assay. Furthermore, we used tandem MS (MS/MS) analyses to characterize carnosine and measured its levels in CHO cell lines in a time-dependent manner. The ESI–MS method developed here obviates the need for substrate modification and provides a less laborious, accurate, and rapid assay for studying kinetic properties of dipeptidases in vitro as well as in vivo.     

Inhibition of Thrombin Formation by Active Site Mutated (S360A) Activated Protein C

Activated protein C (APC) down-regulates thrombin formation through proteolytic inactivation of factor Va (FVa) by cleavage at Arg⁵⁰⁶ and Arg³⁰⁶ and of factor VIIIa (FVIIIa) by cleavage at Arg³³⁶ and Arg⁵⁶². To study substrate recognition by APC, active site-mutated APC (APC(S360A)) was used, which lacks proteolytic activity but exhibits anticoagulant activity. Experiments in model systems and in plasma show that APC(S360A), and not its zymogen protein C(S360A), expresses anticoagulant activities by competing with activated coagulation factors X and IX for binding to FVa and FVIIIa, respectively. APC(S360A) bound to FVa with a K_D of 0.11 ± 0.05 nm and competed with active site-labeled Oregon Green activated coagulation factor X for binding to FVa. The binding of APC(S360A) to FVa was not affected by protein S but was inhibited by prothrombin. APC(S360A) binding to FVa was critically dependent upon the presence of Arg⁵⁰⁶ and not Arg³⁰⁶ and additionally required an active site accessible to substrates. Inhibition of FVIIIa activity by APC(S360A) was >100-fold less efficient than inhibition of FVa. Our results show that despite exosite interactions near the Arg⁵⁰⁶ cleavage site, binding of APC(S360A) to FVa is almost completely dependent on Arg⁵⁰⁶ interacting with APC(S360A) to form a nonproductive Michaelis complex. Because docking of APC to FVa and FVIIIa constitutes the first step in the inactivation of the cofactors, we hypothesize that the observed anticoagulant activity may be important for in vivo regulation of thrombin formation.     

A kinetic model structure for delayed fluorescence from plants

In this research, we demonstrated that the plastoquinone-related electron-transport kinetics in photosynthesis could be sufficiently described with as few as three state variables, Q(A)(-), Q(B)(-), and Q(B)(2-). A third-order kinetic model structure was developed with delayed fluorescence as the measurable output. Delayed fluorescence emissions from drought-stressed, DCMU [3-(3,4-dichlorophenyl)-1,1-dimethylurea] treated, or healthy plants were measured with a photon-counting system and used to verify the model structure through nonlinear least-squares optimization. While there were no visible differences between the healthy and the stressed plants, the model showed an obvious decrease of Q(A) reduction rate in the drought-stressed samples and a clear decline of functional Q(A)Q(B) pairs in the DCMU-treated samples. The changes were consistent with the known mechanisms by which water and DCMU affect electron transport in photosynthetic plants. The results proved that the three-state formulation was a compact and practically useful model structure for describing delayed fluorescence from plants.     

Engineering and kinetic characterisation of two glucosyltransferases from Arabidopsis thaliana

This study describes the characterisation of a chimeric mutant derived from two arabidopsis glucosyltransferases, 71C1 and 71C3. A chimera, N1C3, was constructed to contain the N-terminal domain of 71C1 and the C-terminal domain of 71C3. The chimera and the wild-type GTs displayed a similar Km towards the acceptor scopoletin. However, N1C3 had a Km near identical to 71C3 towards UDP-glucose, but was three-fold lower than that of 71C1. The results suggest that the acceptor and sugar donor are recognised independently by the N- and C-terminal domain of the GTs respectively, and provide a foundation for the future design of glucosyltransferase biocatalysts through assembling domains with different affinity towards the acceptor and donor.     

A kinetic comparison between E2P and the E2P-like state induced by a beryllium fluoride complex in the Na,K-ATPase. Interactions with Rb+

Metal-fluoride complexes have been used to induce E2P-like states with the aim of studying the events that occur during E2P hydrolysis in P-type ATPases. In the present work, we compared the E2P-like state induced by a beryllium fluoride complex (BeF_x) with the actual E2P state formed through backdoor phosphorylation of the Na,K-ATPase. Formation of E2P and E2P-like states were investigated employing the styryl dye RH421. We found that BeF_x is the only fluorinated phosphate analog that, like Pi, increases the RH421 fluorescence. The observed rate constant, k_obs, for the formation of E2P decreases with [Pi] whereas that of E2BeF_x increases with [BeF_x]. This might wrongly be taken as evidence of a mechanism where the binding of BeF_x induces a conformational transition. Here, we rather propose that, like for Pi, binding of BeF_x follows a conformational-selection mechanism, i.e. it binds to the E2 conformer forming a complex that is much more stable than E2P, as seen from its impaired capacity to return to E1 upon addition of Na⁺. Although E2P and E2BeF_x are able to form states with 2 occluded Rb⁺, both enzyme complexes differ in that the affinity for the binding and occlusion of the second Rb⁺ is much lower in E2BeF_x than in E2P. The higher rates of Rb⁺ occlusion and deocclusion observed for E2BeF_x, as compared to those observed for other E2P-like transition and product states suggest a more open access to the cation transport sites, supporting the idea that E2BeF_x mimics the E2P ground state.     

The human tyrosine kinase Kit and its gatekeeper mutant T670I,show different kinetic properties: Implications for drug design

The tyrosine kinase Kit, a receptor for Stem Cell Factor, is involved, among others, in processes associated to cell survival, proliferation and migration. Upon physiological conditions, the activity of Kit is tightly regulated. However, primary mutations that lead to its constitutive activation are the causal oncogenic driver of gastrointestinal stromal tumours (GISTs). GISTs are known to be refractory to conventional therapies but the introduction of Imatinib, a selective inhibitor of tyrosine kinases Abl and Kit, significantly ameliorated the treatment options of GISTs patients. However, the acquisition of secondary mutations renders Kit resistant towards all available drugs. Mutation involving gatekeeper residues (such as V654a and T670I) influence both the structure and the catalytic activity of the enzyme. Therefore, detailed knowledge of the enzymatic properties of the mutant forms, in comparison with the wild type enzyme, is an important pre-requisite for the rational development of specific inhibitors. In this paper we report a thorough kinetic analysis of the reaction catalyzed by the Kit kinase and its gatekeeper mutated form T670I. Our results revealed the different mechanisms of action of these two enzymes and may open a new avenue for the future design of specific Kit inhibitors.     

The use of reaction timecourses to determine the level of minor contaminants in enzyme preparations

Enzyme mutagenesis is a commonly used tool to investigate the structure and activity of enzymes. However, even minute contamination of a weakly active mutant enzyme by a considerably more active wild-type enzyme can partially or completely obscure the activity of the mutant enzyme. In this work, we propose a theoretical approach using reaction timecourses and initial velocity measurements to determine the actual contamination level of an undesired wild-type enzyme. To test this method, we applied it to a batch of the Q215A/R235A double mutant of orotidine 5′-monophosphate decarboxylase (OMPDC) from Saccharomyces cerevisiae that was inadvertently contaminated by the more active wild-type OMPDC from Escherichia coli. The enzyme preparation showed significant deviations from the expected kinetic behavior at contamination levels as low as 0.093 mol%. We then confirmed the origin of the unexpected kinetic behavior by deliberately contaminating a sample of the mutant OMPDC from yeast that was known to be pure, with 0.015% wild-type OMPDC from E. coli and reproducing the same hybrid kinetic behavior.     

Apparent charge of binding site in ion-translocating enzymes: kinetic impact

Recently, we presented a general scope for the nonlinear electrical properties of enzymes E which catalyze translocation of a substrate S with charge number z_S through lipid membranes (Boyd et al. J. Membr. Biol. 195:1–12, 2003). In this study, the voltage sensitivity of the enzymatic reaction cycle has been assigned to one predominant reversible reaction step, i.e. the reorientation of either E or ES in the electric field, leaving the reorientation of the alternate state (ES or E) electroneutral, respectively. With this simplification, the steady-state current–voltage relationships (IV) assumed saturation kinetics like in Michaelis–Menten systems. Here, we introduce an apparent charge number z_E of the unoccupied binding site of the enzyme, which accounts for the impact of all charged residues in the vicinity of the physical binding site. With this more realistic concept, the occupied binding site assumes an apparent charge of , and IV does not saturate any more in general, but exponentially approaches infinite or zero current for large voltage displacements from equilibrium. These nonlinear characteristics are presented here explicitly. They are qualtitatively explained in a mechanistic way, and are illustrated by simple examples. We also demonstrate that the correct determination of the model parameters from experimental data is still possible after incorporating z_E and its corollaries into the previous model of enzyme-mediated ion translocation.