Impact of enzyme concentration and residence time on apparent activity recovery in jump dilution analysis

Jump dilution analysis is commonly used to evaluate the reversibility of inhibition and to quantify the residence time of the inhibitor–enzyme complex. During hit and lead characterization, one sometimes observes apparently linear progress curves after jump dilution that display activity recoveries that are intermediate between those expected for fully reversible and irreversible inhibition. Computer simulations of progress curves after jump dilution indicate that seemingly linear progress curves can result when dealing with tight-binding inhibitors if substoichiometric concentrations of inhibitor are preincubated with enzyme. In this situation, the activity recovered is comparable to that expected for instantaneously reversible inhibitors. In addition, simulations demonstrate that intermediate values of activity recovery may be observed for compounds with modestly slow dissociation rates (i.e., residence times >0 min but ?20 min) when the attending curvature of the data is not accounted for. The observation of intermediate values of recovery can, thus, serve as an indication of either modest residence time or a contaminating inactivator within an inhibitor sample, in either case prompting greater scrutiny of the test compound.     

Kinetic analysis of multisite phosphorylation using analytic solutions to Michaelis-Menten equations

Phosphorylation-induced expression or modulation of a functional protein is a common signal in living cells. Many functional proteins are phosphorylated at multiple sites and it is frequently observed that phosphorylation at one site enhances or suppresses phosphorylation at another site. Therefore, characterizing such cooperative phosphorylation is important. In this study, we determine a temporal progress curve of multisite phosphorylation by analytically integrating the Michaelis-Menten equations in time. Using this theoretical progress curve, we derive the useful criterion that an intersection of two progress curves implies the presence of cooperativity. Experiments generally yield noisy progress curves. We fit the theoretical progress curves to noisy progress curves containing 4% Gaussian noise in order to determine the kinetics of the phosphorylation. This fitting correctly identifies the sites involved in cooperative phosphorylation.     

Fibrin assembly in human plasma and fibrinogen/albumin mixtures

Magnetic birefringence is used to monitor the kinetics of thrombin-catalyzed fibrin polymerization in model systems of increasing complexity (i.e., fibrinogen solutions, fibrinogen/albumin mixtures, and plasma anticoagulated with citrate) and in plasma containing free calcium which is the physiological condition. The introduction of albumin into fibrinogen solutions shortens the lag period and enhances fiber thickness. The polymerization progress curves are sigmoidal at zero or low albumin concentrations, but at physiological and higher concentrations, they become hyperbola-like from the end of the lag period. High albumin concentration has thus induced a change in the assembly kinetics. The progress curves from plasma in which the cascade is dormant are also hyperbola-like although they round off more quickly because of antithrombin activity. In plasma containing free calcium, thrombin is endogenously produced, and the progress curves are nearly linear; hence, the assembly kinetics are very different from those of the model systems. The curves are not influenced by calcium-dependent cross-linking involving factor XIIIa. The progress curves are also linear when polymerization is induced with Russell's viper venom, which by directly activating factor X circumvents earlier steps in the cascade. This implies that linear polymerization is caused by events posterior to factor X activation and are thus likely to be largely dependent on the functioning of the prothrombinase complex. Addition of thrombin to plasma containing free calcium reduces the lag period. At low exogenous thrombin levels, the polymerization rate is increased, and the progress curves remain linear. However, at higher levels, the curves become more complicated and, paradoxically, full polymerization takes longer.(ABSTRACT TRUNCATED AT 250 WORDS)     

Kinetics of sickle hemoglobin polymerization. III. Nucleation rates determined from stochastic fluctuations in polymerization progress curves

The polymerization kinetics of sickle cell hemoglobin are found to exhibit stochastic variations when observed in very small volumes (approximately 10(-10) cm3). The distribution of progress curves has been measured at several temperatures for a 4.50 mM-hemoglobin S sample using a laser-photolysis, light-scattering technique. The progress curves at a given temperature are superimposable when translated along the time axis, showing that the variability of the kinetic progress curves results primarily from fluctuations in the time at which polymerization is initiated. The shapes of the initial part of the progress curves are well-fitted using the functional form I(t) = Io + As exp (Bt), derived from a dual nucleation model. When the distribution of the measured tenth times is broad, the rate of homogeneous nucleation can be obtained by fitting the exponential tail of the distribution. As the distribution sharpen, the rate of homogeneous nucleation can be estimated by modelling the width of the distribution function using a simple Monte-Carlo simulation of the polymerization kinetics. Using the rates of homogeneous nucleation obtained from the distributions, the rates of heterogeneous nucleation and polymer growth can be obtained from the experimental parameters As and B. The resulting nucleation rates are roughly 1000 times greater than those obtained from an analysis of bulk kinetic data. The results provide strong support for the dual-nucleation mechanism and show that the distribution of progress curves provides a powerful independent method for measuring the rate of homogeneous nucleation and thereby obtaining values for the other principal rates of the mechanism.     

A procedure for analysis of stopped-flow transients for protein-ligand association

A method for extracting kinetic and optical parameters from progress curves for protein-ligand association, obtained by stopped-flow experiments, is described. The method is limited to one-step and two-step association kinetics, but it allows concentration of protein and offset of the signals to be adjustable parameters during an interactive non-linear least-squares fitting procedure. The method is tested on simulated pseudo-experimental data and applied to progress curves obtained in a stopped-flow spectrofluorimeter, for association of the translation initiation factor eIF4E with 7-methyl-GDP, an analog of 5'-end of mRNA.     

利用酶催化反应过程曲线确定动力学参数的新方法

本文提出了一个利用过程曲线确定酶催化反应动力学参数的新方法.利用这一方法,仅仅根据两条实验曲线就可以确定单底物酶催化反应的全部动力学参数,并且所有的图形都是(?)     

Activation of human prothrombin by human prothrombinase. Influence of factor Va on the reaction mechanism

The kinetics of the activation of human prothrombin catalyzed by human prothrombinase was studied using the fluorescent alpha-thrombin inhibitor dansylarginine-N-(3-ethyl-1,5-pentanediyl)amide (DAPA). Prothrombinase proteolytically activates prothrombin to alpha-thrombin by cleavages at Arg273-Thr274 (bond A) and Arg322-Ile323 (bond B). The differential fluorescence properties of DAPA complexed with the intermediates and products of human prothrombin activation were exploited to study the kinetics of the individual bond cleavages in the zymogen. When the catalyst was composed of prothrombinase (human factor Xa, human factor Va, synthetic phospholipid vesicles, and calcium ion), initial velocity studies of alpha-thrombin formation indicated that the kinetic constants for the cleavage of bonds A or B were similar to the constants that were obtained for the overall reaction (bonds A + B). The progress of the reaction was also monitored by polyacrylamide gel electrophoresis in the presence of sodium dodecyl sulfate. The results indicated that the activation of human prothrombin catalyzed by prothrombinase proceeded exclusively via the formation of meizothrombin (bond B-cleaved) as an intermediate. Kinetic studies of the cofactor dependence of the rates of cleavage of the individual bonds indicated that, in the absence of the cofactor, cleavage at bond B would constitute the rate-limiting step in prothrombin activation. Progress curves for prothrombin activation catalyzed by prothrombinase and monitored using the fluorophore DAPA were typified by the appearance of a transient maximum, indicating the formation of meizothrombin as an intermediate. When factor Xa alone was the catalyst, progress curves were characterized by an initial burst phase, suggesting the rapid production of prethrombin 2 (bond A-cleaved) followed by its slow conversion to alpha-thrombin. Gel electrophoresis followed by autoradiography was used to confirm these results. Collectively, the results indicate that the activation of human prothrombin via the formation of meizothrombin as an intermediate is a consequence of the association of the cofactor, human factor Va, with the enzyme, human factor Xa, on the phospholipid surface.     

Deacylation of penicilloylated penicillin-binding proteins from Micrococcus luteus: kinetic study of thiol-promoted release of the bound penicilloyl moiety

The stability of covalent complexes obtained by labelling penicillin-binding proteins 1-6 from Micrococcus luteus with a radioactive derivative of ampicillin has been examined in the presence of thiols. When the incubation medium contained only 1 mM 2-mercaptoethanol, the complexes were almost unaffected for at least 1 h. If 20 mM dithiothreitol was also included in the medium, the amount of bound radioactivity decreased throughout the incubation period. The breakdown of the complexes derived from penicillin-binding proteins 4 and 5 proceeded very slowly, following an apparent first-order kinetics, whereas the kinetics of deacylation of other penicillin-binding proteins exhibited a biphasic pattern with an initial fast phase followed by a slow one, each of which could be approximated by an apparent first-order reaction. This behavior is explained adequately by a two-step mechanism: the penicilloylated penicillin-binding proteins are first deacylated in a reversible exchange with the added thiol, giving rise to an intermediate thioester; once formed, this intermediate is hydrolysed irreversibly. A simple graphical method has been devised to deduce rate constants from the time course of the reaction. Theoretical curves have been constructed, and they fit experimental data satisfactorily. The results point out that added thiols may effectively interfere with the quantitation of penicillin-binding proteins; therefore, the stability of penicilloylated penicillin-binding proteins should be checked carefully when these protecting agents are included in membrane extracts or incubation media.     

A study of the kinetics of iron and copper binding to hen ovotransferrin.

The kinetics of iron and copper binding to hen's-egg apo-ovotransferrin were studied by using citrate chelates of these metals at pH9.3 in borate buffer in the presence of bicarbonate. The kinetics of the absorbance change associated with the formation of the final product show a fast process, which is pseudo-first-order, where the reagents are in excess with respect to the protein, and the citrate concentration is higher than 25mM. At lower citrate concentration, the progress curves are clearly biphasic. There is marked dependence of the rate of the reaction on bicarbonate concentration, which may be interpreted as a displacement reaction of the ligand-metal-protein ternary complex. The kinetics have been interpreted in the framework of a reaction scheme which involves bimolecular reaction of a metal chelate to the protein and subsequent colour development by displacement of the chelator by bicarbonate. The pH-dependence of this reaction supports the belief that tyrosine residues are involved in the process of iron-binding. The overall similarity of kinetics for iron and copper binding, notwithstanding their different co-ordination preferences, suggests that the process of metal-binding or chromophore development for the two metal complexes must be similar.     

Reaction kinetics of some important site-specific endonucleases.

Reaction kinetics of the site-specific endonucleases BamHI, BgIII, C1aI, EcoRI, HpaII, PstI, SaII, SmaI, and XorII were investigated employing some frequently used substrates. Six of these enzymes could be analyzed under steady-state conditions. Kinetic data were obtained from progress curves applying an integrated Michaelis-Menten equation. KM ranged from 4 x 10(-9) M to 4 x 10(-11) M. Activities also spanned two orders of magnitude. In the case of C1aI the analysis of the pre-steady-state kinetics ("burst reaction") allowed the assessment of several rate constants. The rate-limiting step is the very slow dissociation of the enzyme-product complex (0.22 min(-1)). This complex is formed from the enzyme-bound nicked intermediate at a rate of 1.7 min(-1). The introduction of the first cut is again faster by a factor of about 6. SmaI and XorII resembled C1aI in their kinetics. The burst reaction can be used for the easy and unambiguous determination of molar concentrations of site-specific endonucleases in any preparation, which is free of non-specific DNases.     

Dipole cooperative model of ion channels of excitable biomembranes. Conductance of ion channels

An analysis of ionic channel conductance is presented in terms of dipole cooperative model. The dependence of conductance on displaced charge is found to be an S-shaped function. Basing on this function and kinetics of gating currents, the kinetic curves for the conductance are calculated. These curves are compared with Hodgkin--Huxley results on sodium channel. A good agreement may be observed for the case of positive jumps of the potential. Less accurate coincidence takes place for negative jumps of the potential.     

Kinetics of ligand binding to receptor immobilized in a polymer matrix, as detected with an evanescent wave biosensor. I. A computer simulation of the influence of mass transport.

The influence of mass transport on ligand binding to receptor immobilized in a polymer matrix, as detected with an evanescent wave biosensor, was investigated. A one-dimensional computer model for the mass transport of ligand between the bulk solution and the polymer gel and within the gel was employed, and the influence of the diffusion coefficient, the partition coefficient, the thickness of the matrix, and the distribution of immobilized receptor were studied for a variety of conditions. Under conditions that may apply to many published experimental studies, diffusion within the matrix was found to decrease the overall ligand transport significantly. For relatively slow reactions, small spatial gradients of free and bound ligand in the gel are found, whereas for relatively rapid reactions strong inhomogeneities of ligand within the gel occur before establishment of equilibrium. Several types of deviations from ideal pseudo-first-order binding progress curves are described that resemble those of published experimental data. Extremely transport limited reactions can in some cases be fitted with apparently ideal binding progress curves, although with apparent reaction rates that are much lower than the true reaction rates. Nevertheless, the ratio of the apparent rate constants can be semiquantitatively consistent with the true equilibrium constant. Apparently "cooperative" binding can result from high chemical on rates at high receptor saturation. Dissociation in the presence of transport limitation was found to be well described empirically by a single or a double exponential, with both apparent rate constants considerably lower than the intrinsic chemical rate constant. Transport limitations in the gel can introduce many generally unknown factors into the binding progress curve. The simulations suggest that unexpected deviations from ideal binding progress curves may be due to highly transport influenced binding kinetics. The use of a thinner polymer matrix could significantly increase the range of detectable rate constants.     

Progress curves analysis as an alternative for exploration of activation-inhibition phenomena in cholinesterases

The kinetic behaviour of insect acetylcholinesterases deviates from the Michaelis-Menten pattern. These deviations are known as activation or inhibition at various substrate concentrations and can be more or less observable depending on mutations around the active site of the enzyme. Most kinetic studies on these enzymes still rely on initial rate measurements. It is demonstrated here that according to this method one of the deviations can be overlooked. We attempt to point out that in such cases a detailed step-by-step progress curves analysis is successful. The study is focused on two different methods of analysing progress curves: (i) the first one is based on an integrated initial rate equation which can sufficiently fit truncated progress curves under corresponding conditions; and (ii) the other one precludes the algebraic formulae, but uses numerical integration for searching a non analytical solution of ordinary differential equations describing a kinetic model. All methods are tested on three different acetylcholinesterase mutants from Drosophila melanogaster. The results indicate that kinetic parameters for the E107K mutant with highly expressive activation and inhibition can be well evaluated applying any analysis method. It is quite different for E107W and E107Y mutants where latent activation is present, but discovered only using one or the other progress curves analysis methods.     

Redesign of MST enzymes to target lyase activity instead promotes mutase and dehydratase activities

The isochorismate and salicylate synthases are members of the MST family of enzymes. The isochorismate synthases establish an equilibrium for the conversion chorismate to isochorismate and the reverse reaction. The salicylate synthases convert chorismate to salicylate with an isochorismate intermediate; therefore, the salicylate synthases perform isochorismate synthase and isochorismate-pyruvate lyase activities sequentially. While the active site residues are highly conserved, there are two sites that show trends for lyase-activity and lyase-deficiency. Using steady state kinetics and HPLC progress curves, we tested the “interchange” hypothesis that interconversion of the amino acids at these sites would promote lyase activity in the isochorismate synthases and remove lyase activity from the salicylate synthases. An alternative, “permute” hypothesis, that chorismate-utilizing enzymes are designed to permute the substrate into a variety of products and tampering with the active site may lead to identification of adventitious activities, is tested by more sensitive NMR time course experiments. The latter hypothesis held true. The variant enzymes predominantly catalyzed chorismate mutase–prephenate dehydratase activities, sequentially generating prephenate and phenylpyruvate, augmenting previously debated (mutase) or undocumented (dehydratase) adventitious activities.     

Progress Curves Analysis as an Alternative for Exploration of Activation-inhibition Phenomena in Cholinesterases

The kinetic behaviour of insect acetylcholinesterases deviates from the Michaelis-Menten pattern. These deviations are known as activation or inhibition at various substrate concentrations and can be more or less observable depending on mutations around the active site of the enzyme. Most kinetic studies on these enzymes still rely on initial rate measurements. It is demonstrated here that according to this method one of the deviations can be overlooked. We attempt to point out that in such cases a detailed step-by-step progress curves analysis is successful. The study is focused on two different methods of analysing progress curves: (i) the first one is based on an integrated initial rate equation which can sufficiently fit truncated progress curves under corresponding conditions; and (ii) the other one precludes the algebraic formulae, but uses numerical integration for searching a non analytical solution of ordinary differential equations describing a kinetic model. All methods are tested on three different acetylcholinesterase mutants from Drosophila melanogaster. The results indicate that kinetic parameters for the E107K mutant with highly expressive activation and inhibition can be well evaluated applying any analysis method. It is quite different for E107W and E107Y mutants where latent activation is present, but discovered only using one or the other progress curves analysis methods.     

Alternative algebraic rate‐integration approach for progress‐curve analysis of enzyme kinetics

A recent article of Zavrel et al. in this journal (Eng. Life Sci. 2010, 10, 191–200) described a comparison of several computer programs for progress‐curve analysis with respect to different computational approaches for parameter estimation. The authors applied both algebraic and dynamic parameter estimations, although they omitted time‐course analysis through the integrated rate equation. Recently, it was demonstrated that progress‐curve analysis through the integrated rate equation can be considered a simple and useful alternative for enzymes that obey the generalized Michaelis–Menten reaction mechanism. To complete this gap, the time‐dependent solution of the generalized Michaelis–Menten equation is here fitted to the progress curves from the Zavrel et al. reference article. This alternative rate‐integration approach for determining the kinetics parameters of Michaelis–Menten‐type enzymes yields the values with the greatest accuracy, as compared with the results obtained by other (algebraic or dynamic) parameter estimations.     

Recombination of S-peptide with S-protein during folding of ribonuclease S. I. Folding pathways of the slow-folding and fast-folding classes of unfolded S-protein.

The refolding kinetics of ribonuclease S have been measured by tyrosine absorbance, by tyrosine fluorescence emission, and by rapid binding of the specific inhibitor 2′CMP ² to folded RNAase S. The S-protein is first unfolded at pH 1.7 and then either mixed with S-peptide as refolding is initiated by a stopped-flow pH jump to pH 6.8, or the same results are obtained if S-protein and S-peptide are present together before refolding is initiated. The refolding kinetics of RNAase S have been measured as a function of temperature (10 to 40 °C) and of protein concentration (10 to 120 μm). The results are compared to the folding kinetics of S-protein alone and to earlier studies of RNAase A. A thermal folding transition of S-protein has been found below 30 °C at pH 1.7; its effects on the refolding kinetics are described in the following paper (Labhardt &; Baldwin, 1979).In this paper we characterize the refolding kinetics of unfolded S-protein, as it is found above 30 °C at pH 1.7, together with the kinetics of combination between S-peptide and S-protein during folding at pH 6.8. Two classes of unfolded S-protein molecules are found, fast-folding and slow-folding molecules, in a 20: 80 ratio. This is the same result as that found earlier for RNAase A; it is expected if the slow-folding molecules are produced by the slow cis-trans isomerization of proline residues after unfolding, since S-protein contains all four proline residues of RNAase A.The refolding kinetics of the fast-folding molecules show clearly that combination between S-peptide and S-protein occurs before folding of S-protein is complete. If combination occurred only after complete folding, then the kinetics of formation of RNAase S should be rather slow (5 s and 100 s at 30 °C) and nearly independent of protein concentration, as shown by separate measurements of the folding kinetics of S-protein, and of the combination between S-peptide and folded S-protein. The observed folding kinetics are faster than predicted by this model and also the folding rate increases strongly with protein concentration (apparent 1.6 order kinetics). The fact that RNAase S is formed more rapidly than S-protein alone is sufficient by itself to show that combination with S-peptide precedes complete folding of S-protein. Computer simulation of a simple, parallel-pathway scheme is able to reproduce the folding kinetics of the fast-folding molecules. All three probes give the same folding kinetics.These results exclude the model for protein folding in which the rate-limiting step is an initial diffusion of the polypeptide chain into a restricted range of three-dimensional configurations (“nueleation”) followed by rapid folding (“propagation”). If this model were valid, one would expect comparable rates of folding for RNAase A and for S-protein and one would also expect to find no populated folding intermediates, so that combination between S-peptide and S-protein should occur after folding is complete. Instead, RNAase A folds 60 times more rapidly than S-protein and also combination with S-peptide occurs before folding of S-protein is complete. The results demonstrate that the folding rate of S-protein increases after the formation, or stabilization, of an intermediate which results from combination with S-peptide. They support a sequential model for protein folding in which the rates of successive steps in folding depend on the stabilities of preceding intermediates.The refolding kinetics of the slow-folding molecules are complex. Two results demonstrate the presence of folding intermediates: (1) the three probes show different kinetic progress curves, and (2) the folding kinetics are concentration-dependent, in contrast to the results expected if complete folding of S-protein precedes combination with S-peptide. A faster phase of the slow-refolding reaction is detected both by tyrosine absorbance and fluorescence emission but not by 2′CMP binding, indicating that native RNAase S is not formed in this phase. Comparison of the kinetic progress curves measured by different probes is made with the use of the kinetic ratio test, which is defined here.     

Prediction of X-ray induced mitotic delay and recovery of G2 cells

A mathematical model is presented that predicts the delay of mitosis caused by X-irradiation of an asynchronous, exponentially growing cell culture (data of Schneiderman & Schneiderman, 1984). In the model, based on Gompertz kinetics, the driving function to generate the curves is a simple exponential decay expression. For the delayed mitotic progress curves, this function characterizes the distribution of the time required for cells to enter mitosis.     

Prediction of X-ray induced mitotic delay and recovery of G2 cells

Abstract. A mathematical model is presented that predicts the delay of mitosis caused by X-irradiation of an asynchronous, exponentially growing cell culture (data of Schneiderman & Schneiderman, 1984). In the model, based on Gompertz kinetics, the driving function to generate the curves is a simple exponential decay expression. For the delayed mitotic progress curves, this function characterizes the distribution of the time required for cells to enter mitosis.