Negative Cooperativity in the Interaction of Prostaglandin H Synthase-1 with the Competitive Inhibitor Naproxen Can Be Described as the Interaction of a Non-competitive Inhibitor with Heterogeneous Enzyme Preparation.

The kinetic mechanism of the interaction of nonsteroidal anti-inflammatory drugs (NSAIDs) with their main pharmacological target, prostaglandin H synthase (PGHS), has not yet been established. We showed that inhibition of PGHS-1 from sheep vesicular glands by naproxen (a representative of NSAIDs) demonstrates a non-competitive character with respect to arachidonic acid and cannot be described within a framework of the commonly used kinetic schemes. However, it can be described by taking into account the negative cooperativity of naproxen binding to the cyclooxygenase active sites of the PGHS-1 homodimer (the first naproxen molecule forms a more stable complex (K1 = 0.1 µM) with the enzyme than the second naproxen molecule (K2 = 9.2 µM)). An apparent non-competitive interaction of PGHS-1 with naproxen is due to slow dissociation of the enzyme-inhibitor complexes. The same experimental data could also be described using commonly accepted kinetic schemes, assuming that naproxen interacts was a mixture of two enzyme species with the inhibition constants Kα = 0.05 µM and Kß = 18.3 µM. Theoretical analysis and numerical calculations show that the phenomenon of kinetic convergence of these two models has a general nature: when K2 >> K1, the kinetic patterns (for transient kinetics and equilibrium state) generated by the cooperative model could be described by a scheme assuming the presence of two enzyme forms with the inhibition constants Kα = K1/2, Kß = 2·K2. When K2 << K1, the cooperative model can be presented as a scheme with two inhibitor molecules simultaneously binding to the enzyme with the observed inhibition constant K (K = K1·K2). The assumption on the heterogeneity of the enzyme preparation in relation to its affinity to the inhibitor can be used instead of the assumption on the negative cooperativity of the enzyme-inhibitor interactions for convenient and easy practical description of such phenomena in enzymology, biotechnology, pharmacology, and other fields of science.

[The accuracy of rapid equilibrium assumption in steady-state enzyme kinetics is the function of equilibrium segment structure and properties].

Quantitative evaluation of the accuracy of the rapid equilibrium assumption in the steady-state enzyme kinetics was obtained for an arbitrary mechanism of an enzyme-catalyzed reaction. This evaluation depends only on the structure and properties of the equilibrium segment, but doesn't depend on the structure and properties of the rest (stationary part) of the kinetic scheme. The smaller the values of the edges leaving equilibrium segment in relation to values of the edges within the equilibrium segment, the higher the accuracy of determination of intermediate concentrations and reaction velocity in a case of the rapid equilibrium assumption.

[New relations for steady-state enzyme kinetics and their application to rapid equilibrium assumption].

With the use of a graph theory new relations for steady-state enzyme kinetics are derived and strictly proved for the arbitrary mechanism of an enzyme-catalysed reaction containing a reversible segment. Using these relations, a general principle for rapid equilibrium assumption is formulated and proved: the reversible bound segment can be considered as an equilibrium segment only when the values of the base trees that are not proper to this segment can be neglected (within a prescribed accuracy) in relation to the values of the base trees that belong to this segment. In contrast with the foreign base trees the base trees that are proper to the segment have the following properties: the tree that is directed to the base within this segment does not contain the edges leaving this segment; and the tree that is directed to the base outside the segment contains only one edge leaving this segment. Equilibrium variations are assessed for steady-state intermediates concentrations of the equilibrium segment, numerical expressions are obtained for the accuracy of determination of the intermediates concentrations as well as for the accuracy of determination of the rate of enzyme-catalysed reaction in case of using rapid equilibrium assumption.

Quasi-equilibrium assumption for arbitrary mechanism of enzymatic reaction. Criteria for existence of equilibrium segments.

The possible application of the quasi-equilibrium assumption for an arbitrary mechanism of enzymatic reaction is considered. It is shown at what ratios of kinetic constants a segment consisting of two, three, and four intermediates may be considered as an equilibrium one. Expressions for evaluation of accuracy of distribution of intermediate concentrations inside the equilibrium segment and accuracy of determination of intermediate concentrations inside and outside the equilibrium segment as a function of the ratio of kinetic constants are derived. A method for determination of the limitations on the ratio of rate constants for an equilibrium segment of arbitrary structure is suggested.

Inhibition of cyclooxygenase activity of prostaglandin-H-synthase by excess substrate (molecular oxygen).

For the cyclooxygenase reaction of prostaglandin-H-synthase isolated from ram vesicular glands, dependences of the initial reaction rate, the maximal yield of the product, and the rate constant of enzyme inactivation in the course of reaction on oxygen concentration were studied in the absence and in the presence of electron donor in the reaction medium. It is shown that in the absence of electron donor the cyclooxygenase reaction is strictly governed by Michaelis-Menten kinetics over a wide range of oxygen concentrations (5-800 µM). In the presence of electron donor in the reaction medium it was found that cyclooxygenase reaction is inhibited by an excess of dissolved oxygen: the maximal values of the initial reaction rate and yield of the product are attained at oxygen concentration 50 µM, and its increase to 500 µM causes twofold decrease in the initial rate and maximal yield. The rate constant of enzyme inactivation in the course of reaction increases on increase in oxygen concentration both in the presence and in the absence of electron donor.

The quasi-equilibrium assumption for Bi-Bi ordered bisubstrate enzymatic reaction. How to discriminate the mechanism correctly.

Application of the quasi-equilibrium assumption for the steady-state kinetics of bisubstrate irreversible enzymatic reactions in the case of ordered binding of substrates (Bi-Bi ordered mechanism) is considered. The necessary and sufficient conditions for application of the quasi-equilibrium assumption have been found and accuracy of this assumption has been numerically evaluated. The limitations on application of the quasi-equilibrium assumption have been shown and errors of its application have been analyzed. It is shown that possible discrimination of substrate binding order using asymmetrical expressions grounded on the quasi-equilibrium assumption is inconsistent because such asymmetrical expressions arise from incorrect application of the quasi-equilibrium assumption. Moreover, it has been proved in the general case that mechanisms generating such substrate-asymmetrical expressions for the steady-state rate of enzymatic reaction do not exist. The error source when using graphical interpretation for discrimination of mechanisms of bisubstrate enzymatic reactions has been determined. The strategy to avoid such errors is pointed out.

Mutants of monomeric red fluorescent protein mRFP1 at residue 66: structure modeling by molecular dynamics and search for correlations with spectral properties.

To study the interrelation between the spectral and structural properties of fluorescent proteins, structures of mutants of monomeric red fluorescent protein mRFP1 with all possible point mutations of Glu66 (except replacement by Pro) were simulated by molecular dynamics. A global search for correlations between geometrical structure parameters and some spectral characteristics (absorption maximum wavelength, integral extinction coefficient at the absorption maximum, excitation maximum wavelength, emission maximum wavelength, and quantum yield) was performed for the chromophore and its 6 A environment in mRFP1, Q66A, Q66L, Q66S, Q66C, Q66H, and Q66N. The correlation coefficients (0.81-0.87) were maximal for torsion angles in phenolic and imidazolidine rings as well as for torsion angles in the regions of connection between these rings and chromophore attachment to beta-barrel. The data can be used to predict the spectral properties of fluorescent proteins based on their structures and to reveal promising positions for directed mutagenesis.

Quasi-equilibrium assumption in enzyme kinetics. Necessary and sufficient conditions and accuracy of its application for single-substrate reactions.

Steady-state kinetics of compulsory-ordered single-substrate irreversible and reversible enzyme reactions with two, three, and arbitrary number of intermediates were observed. Necessary and sufficient conditions for application of the quasi-equilibrium assumption and restrictions of this assumption were found in cases of two and three intermediates in the equilibrium segment. For all cases, accuracy of the quasi-equilibrium assumption was evaluated.

Kinetic models of cyclooxygenase and peroxidase inactivation of prostaglandin-H-synthase during catalysis.

Kinetic models of inactivation of cyclooxygenase and peroxidase activities of prostaglandin-H-synthase (PGHS) during cyclooxygenase and peroxidase reactions catalyzed by the enzyme and also on preincubation with H2O2 have been developed; these models account for data obtained by the authors as well as data from the literature. Being rather simple, these models simultaneously describe the processes of cyclooxygenase and peroxidase inactivation of PGHS, using the minimal set of experimental parameters.

Steady-state kinetics of bifunctional enzymes. Taking into account kinetic hierarchy of fast and slow catalytic cycles in a generalized model.

A steady-state approximation of the generalized two-dimensional model of a bifunctional enzyme catalyzing independent proceeding of two one-pathway reactions is considered in a case of mutual influence of the active sites. Coexistence of fast and slow catalytic cycles in the reaction mechanism is analyzed. Conditions when the hierarchy of fast and slow catalytic cycles allows simplification of a two-dimensional model and its reduction to the one-dimensional cyclic schemes were determined. Kinetic equations describing these simplified schemes are presented.

Molecular oxygen (a substrate of the cyclooxygenase reaction) in the kinetic mechanism of the bifunctional enzyme prostaglandin-H-synthase.

Prostaglandin-H-synthase is a bifunctional enzyme catalyzing conversion of arachidonic acid into prostaglandin H2 as a result of cyclooxygenase and peroxidase reactions. The dependence of the rate of the cyclooxygenase reaction on oxygen concentration in the absence and in the presence of electron donor was determined. A two-dimensional kinetic scheme accounting for independent proceeding and mutual influence of the cyclooxygenase and peroxidase reactions and also for hierarchy of the rates of these reactions was used as a model. In the context of this model, it was shown that there are irreversible stages in the mechanism of the cyclooxygenase reaction between points of substrate donation (between donation of arachidonic acid and the first oxygen molecule and also between donation of two oxygen molecules).

Cyclooxygenase and peroxidase inactivation of prostaglandin-H-synthase during catalysis.

Prostaglandin-H-synthase (PGHS) is a bifunctional enzyme catalyzing cyclooxygenase and peroxidase reactions and undergoing irreversible inactivation during catalysis. A new method for kinetic studies of both PGHS activities in the course of cyclooxygenase as well as peroxidase reactions and also preincubation with hydroperoxides is suggested. It is shown that peroxidase activity is retained after complete cyclooxygenase inactivation and cyclooxygenase activity is retained after complete peroxidase inactivation. Two-stage cyclooxygenase inactivation occurs on preincubation of PGHS with hydrogen peroxide. Studies on inactivation under various conditions indicate that chemical mechanisms of cyclooxygenase and peroxidase inactivation are different. The data allow development of kinetic models.

Kinetic mechanism of the bifunctional enzyme prostaglandin-H-synthase. Effect of electron donors on the cyclooxygenase reaction.

Prostaglandin-H-synthase (PGHS, EC 1.14.99.1) catalyzes the first committed step in biosynthesis of all prostaglandins, thromboxanes, and prostacyclins by converting arachidonic acid to prostaglandin H(2) (PGH(2)). PGHS exhibits two enzymatic activities: cyclooxygenase activity converting arachidonic acid to prostaglandin G(2) (PGG(2)) and peroxidase activity reducing the hydroperoxide PGG(2) to the corresponding alcohol, PGH(2). Despite the many investigations of the kinetics of PGHS, many features such as the absence of competition and mutual activation between the cyclooxygenase and peroxidase activities cannot be explained in terms of existing schemes. In this work we have studied the influence of different electron donors (N,N,N ,N -tetramethyl-p-phenylenediamine, L-epinephrine, 2,2 -azinobis(3-ethylbenzthiazoline-6-sulfonic acid), potassium ferrocyanide) on the PGHS activities. The proposed scheme describes independent but interconnected cyclooxygenase and peroxidase activities of PGHS. It also explains the experimental data obtained in the present work and known from the literature.

Red fluorescent protein DsRed: parametrization of its chromophore as an amino acid residue for computer modeling in the OPLS-AA force field.

Topology of the neutral form of the DsRed fluorescent protein chromophore as a residue of [(4-cis)-2-[(1-cis)-4-amino-4-oxobutanimidoyl]-4-(4-hydroxybenzylidene)-5-oxo-4,5-dihydro-1H-imidazol-1-yl]acetic acid was calculated with OPLS-AA force field. Use of this topology and molecular dynamics simulation allows calculating the parameters of proteins that contain such residue in their polypeptide chains. The chromophore parameters were obtained by ab initio (RHF/6-31G**) quantum chemical calculations applying density functional theory (B3LYP). Using this chromophore, we have calculated the molecular dynamics trajectory of tetrameric fluorescent protein DsRed in solution at 300 K (4 nsec). Correctness of the chromophore parametrization was revealed by comparison of quantitative characteristics of the chromophore structure obtained from the molecular dynamic simulations of DsRed protein with the quantitative characteristics of the chromophore based on the crystallographic X-ray data of fluorescent protein DsRed (PDB ID: 1ZGO, 1G7K, and 1GGX), and also with the quantitative characteristics of the chromophore obtained by quantum chemical calculations. Inclusion of the neutral form of DsRed protein chromophore topology into the OPLS-AA force field yielded the extended force field OPLS-AA/DsRed. This force field can be used for molecular dynamics calculations of proteins containing the DsRed chromophore. The parameter set presented in this study can be applied for similar extension in any other force fields.

Kinetic analysis of maturation and denaturation of DsRed, a coral-derived red fluorescent protein.

The red fluorescent protein DsRed recently cloned from Discosoma coral, with its significantly red-shifted excitation and emission maxima (558 and 583 nm, respectively), has attracted great interest because of its spectral complementation to other fluorescent proteins, including the green fluorescent protein and its enhanced mutant EGFP. We demonstrated that the much slower DsRed fluorescence development could be described by a three-step kinetic model, in contrast to the fast EGFP maturation, which was fitted by a one-step model. At pH below 5.0 DsRed fluorescence gradually decreased, and the rate and degree of this fluorescence inactivation depended on the pH value. The kinetics of fluorescence inactivation under acidic conditions was fitted by a two-exponential function where the initial inactivation rate was proportional to the fourth power of proton concentration. Subsequent DsRed alkalization resulted in partial fluorescence recovery, and the rate and degree of such recovery depended on the incubation time in the acid. Recovery kinetics had a lag-time and was fitted minimally by three exponential functions. The DsRed absorbance and circular dichroism spectra revealed that the fluorescence loss was accompanied by protein denaturation. We developed a kinetic mechanism for DsRed denaturation that includes consecutive conversion of the initial state of the protein, protonated by four hydrogen ions, to the denatured one through three intermediates. The first intermediate still emits fluorescence, and the last one is subjected to irreversible inactivation. Because of tight DsRed tetramerization we have suggested that obligatory protonation of each monomer results in the fluorescence inactivation of the whole tetramer.

Denaturation and partial renaturation of a tightly tetramerized DsRed protein under mildly acidic conditions.

The red fluorescent protein, DsRed, recently cloned from coral Discosoma sp. has one of the longest fluorescence waves and one of the most complex absorbance spectra among the family of fluorescent proteins. In this work we found that with time DsRed fluorescence decreases under mildly acidic conditions (pH 4.0-4.8) in a pH-dependent manner, and this fluorescence inactivation could be partially recovered by subsequent re-alkalization. The DsRed absorbance and circular dichroism spectra under these conditions revealed that the fluorescence changes were caused by denaturation followed by partial renaturation of the protein. Further, analytical ultracentrifugation determined that native DsRed formed a tight tetramer under various native conditions. Quantitative analysis of the data showed that several distinct states of protein exist during the fluorescence inactivation and recovery, and the inactivation of fluorescence can be caused by protonation of a single ionogenic group in each monomer of DsRed tetramer.

[Integral kinetics of multisubstrate enzyme reactions. Criteria of kinetic behavior and characteristic coordinates for solution of direct and reverse problems]. / Integral'naia kinetika mnogosubstratnykh fermentativnykh reaktsii. Kriterii kineticheskogo povedeniia i kharakteristicheskie koordinaty dlia resheniia priamoi i obratnoi zadach.

General schemes of unbranched multisubstrate enzyme reactions associated with enzyme inactivation during catalysis are analyzed. Equations of integral kinetics at constant substrate concentrations and at depletion in one of the substrate are presented. Experimental dose-response curve characterized by additivity of some enzyme intermediates (absorption spectra, fluorescence, EPR, etc.) are theoretically analyzed. Also rapid equilibrium at certain stages of enzyme reaction is considered. The interrelationship of enzyme intermediates is a criterion of the kinetic behavior of enzyme reaction mechanism. New coordinates are suggested for the analysis of the integral kinetics of self-inactivating enzymes. Results of the analysis are used for interpretation of the data on arachidonic cascade enzymes.

[Synthesis of new platelet aggregation inhibitors substituted with pyridylisoxazoles and their 4,5-dihydroanalogs]. / Sintez novykh ingibitorov agregatsii trombotsitov--zameshchennykh piridilizoksazolov i ikh 4,5-digidroanalogov.

A number of substituted pyridylisoxazoles and their 4,5-dihydro analogs were synthesized by 1,3-dipolar cycloaddition of substituted nitrile oxides to either alkenes or alkynes. The synthesized compounds inhibit arachidonic acid-induced aggregation of human thrombocytes at concentrations of 10(-6) to 10(-3) M. Due to low toxicity, these compounds can be regarded as potential antithrombosis medicines.

Supercooperativity in platelet aggregation: substituted pyridyl isoxazoles, a new class of supercooperative platelet aggregation inhibitors.

The phenomenon of supercooperativity in platelet aggregation is manifested by the occurrence of clear-cut thresholds in dose-response relationships; in such cases the Hill coefficient has unusually high values. Approximation, by the Hill equation, of the relationship of the rate of arachidonate-induced platelet aggregation to the concentrations of either the inducer or inhibitors such as substituted pyridyl isoxazoles (synthesized by us), indomethacin, and pinane thromboxane A2, demonstrated that the Hill coefficients ranged from 30 to 100. 3-(3-Pyridyl)-5-phenylisoxazole, which exhibited maximal anti-aggregatory activity among the synthesized compounds, inhibited neither cyclooxygenase nor thromboxane synthase. The compounds affected the signal transduction pathway at/or posterior to the stage of thromboxane A2 reception.