Application of the median method to the determination of kinetic constants for competitive enzyme inhibition

A procedure was developed to determine kinetic constants for competitive inhibition (Km, Ki, Vmax) by the median method. Simulated experiments were used to compare the accuracy and precision of kinetic constants determined by the median method with unweighted and weighted least-squares analysis. The median method was superior to unweighted least-squares analysis. The weighted least-squares method was superior to the median method when the error was normally distributed but the median method was superior when two or more outliers were present. The dependence of the accuracy and precision of kinetic constants obtained by the median method on several experimentally important parameters, including the number of experimental points, the number and range of substrate concentrations, and the number and range of inhibitor concentrations, was determined.     

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(?)     

The use of chromogenic reference substrates for the kinetic analysis of penicillin acylases.

Determination of kinetic parameters of penicillin acylases for phenylacetylated compounds is complicated due to the low K(m) values for these substrates, the lack of a spectroscopic signal, and the strong product inhibition by phenylacetic acid. To overcome these difficulties, a spectrophotometric method was developed, with which kinetic parameters could be determined by measuring the effects on the hydrolysis of the chromogenic reference substrate 2-nitro-5-[(phenylacetyl)amino]benzoic acid (NIPAB). To that end, spectrophotometric progress curves with NIPAB in the absence and presence of the phenylacetylated substrates and their products were measured and analyzed by numerical fitting to the appropriate equations for competing substrates with product inhibition. This analysis yielded kinetic constants for phenylacetylated substrates such as penicillin G, which are in close agreement with those obtained in independent initial velocity experiments. Using NIPAB analogs with lower k(cat)/K(m) values, kinetic parameters for the hydrolysis of cephalexin and penicillin V were determined. This method was suitable for determining the kinetic constants of penicillin acylases in periplasmic extracts from Escherichia coli, Alcaligenes faecalis, and Kluyvera citrophila. The use of chromogenic reference substrates thus appears to be a rapid and reliable method for determining kinetic constants with various substrates and enzymes.     

Convenient method for studying enzyme kinetics.

A convenient method for enzyme kinetic studies is introduced. The method includes identification of reaction mechanism and estimation of the associated kinetic constants with a minimum number of experiments. The application of the method is illustrated by using literature data. Factors limiting the application of this method are also discussed.     

Determination of rate constants of antigen-antibody reaction. A theory

A new method of determination of rate constants for antigen-antibody interactions is proposed. This method is based on a solid phase immunoenzymatic analysis of the dynamics of elution of immobilized antigen-bound antibodies in the presence of a free antigen. The kinetics of this process is described by a system of differential equations, whose solution results in expression defining the dynamics of antibody interaction with immobilized and free antigens. Simple formulas were derived for the calculation of the rate and equilibrium constants for the antibody-antigen reaction on the basis of experimental kinetic curves. The use of theoretical kinetic curves for antibody elution showed that these formulas reflect with a high degree of accuracy the kinetic properties of the reaction under study.     

Kinetic studies of a beta-lactamase by a computerized microacidimetric method.

On-line computerized treatment of enzyme kinetic data allows the precise measurement of Michaelis--Menten constants (Km and V) from a single progress curve. This method has been used to determine the kinetic constants of a beta-lactamase extracted from an Escherichia coli strain. In the profile of enzymatic activity there obtained, Km and V are a function of the pH. From these results some information is derived about the mechanism of the enzyme--substrate binding.     

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.     

区别滞后酶解离和聚合过程的动力学方法

分析了滞后酶解离-聚合的动力学过程,提出了区分解离和聚合机制的动力学方法。这一方法不仅可用于滞后酶本身的研究,确定滞后酶解离态和聚合态的动力学常数,也可以用于判别变性剂引起寡聚酶的失活过程是否由亚基的解离或聚合所致。     

Biosynthesis reaction mechanism and kinetics of deoxynucleoside triphosphates, dATP and dGTP

The enzyme reaction mechanism and kinetics for biosyntheses of deoxyadenosine triphosphate (dATP) and deoxyguanosine triphosphate (dGTP) from the corresponding deoxyadenosine diphosphate (dADP) and deoxyguanosine diphosphate (dGDP) catalyzed by pyruvate kinase were studied. A kinetic model for this synthetic reaction was developed based on a Bi-Bi random rapid equilibrium mechanism. Kinetic constants involved in this pyruvate kinase catalyzed phosphorylation reactions of deoxynucleoside diphosphates including the maximum reaction velocity, Michaelis-Menten constants, and inhibition constants for dATP and dGTP biosyntheses were experimentally determined. These kinetic constants for dATP and dGTP biosyntheses are of the same order of magnitude but significantly different between the two reactions. Kinetic constants involved in ATP and GTP biosyntheses as reported in literature are about one order of magnitude different from those involved in dATP and dGTP biosyntheses. This enzyme reaction requires Mg2+ ion and the optimal Mg2+ concentration was also determined. The experimental results showed a very good agreement with the simulation results obtained from the kinetic model developed. This kinetic model can be applied to the practical application of a pyruvate kinase reaction system for production of dATP and dGTP. There is a significant advantage of using enzymatic biosyntheses of dATP and dGTP as compared to the chemical method that has been in commercial use.     

A spectrophotometric assay for determining the rate constants of acetylcholinesterase inhibitions.

A spectrophotometric assay procedure has been developed for determining the rate constants for the inhibition of acetylcholinesterase by carbamates and phosphates. The method permits the investigation of inhibitors over a large range in the value of the phosphorylation or carbamylation rate constants without involving the kinetic parameters of the assay substrate in the calculations.     

Rapid determination of kinetic constants by competitive spectrophotometry

The use of competitive spectrophotometry to measure kinetic constants for enzyme-catalyzed reactions is described. The equation for the progress curve characterizing the kinetic behavior of an enzyme acting simultaneously on two alternative substrates is derived. By the addition of a competition term to the integrated Michaelis-Menten equation, the kinetic constants of an alternative substrate can be evaluated by measuring the competition with a substrate of known kinetic constants in a single experiment. Studies are presented involving the enzymes leucine aminopeptidase (LAP) and carboxypeptidase A (CPA). The results obtained with LAP and CPA showed that the kinetic constants determined using competitive spectrophotometry were in agreement with values cited in the literature or with values determined by single substrate enzyme kinetics.     

Secondary structure of chondroitin sulphate in dimethyl sulphoxide

The transient phase of histone H1 phosphorylation was studied by the quenched-flow method. A 'minimal' kinetic scheme of the above process was proposed. A formal kinetic analysis was given to a four-step mechanism of the reaction. Computer simulation of the transient-phase kinetics of H1 phosphorylation and the steady-state kinetics of phosphate transfer from the enzyme phosphoform to histone permitted us to estimate all kinetic constants of the proposed mechanism.     

Efficient maximum likelihood estimation of kinetic rate constants from macroscopic currents

A new method is described that accurately estimates kinetic constants, conductance and number of ion channels from macroscopic currents. The method uses both the time course and the strength of correlations between different time points of macroscopic currents and utilizes the property of semiseparability of covariance matrix for computationally efficient estimation of current likelihood and its gradient. The number of calculation steps scales linearly with the number of channel states as opposed to the cubic dependence in a previously described method. Together with the likelihood gradient evaluation, which is almost independent of the number of model parameters, the new approach allows evaluation of kinetic models with very complex topologies. We demonstrate applicability of the method to analysis of synaptic currents by estimating accurately rate constants of a 7-state model used to simulate GABAergic macroscopic currents.     

Application of mobilities in electromagnetic fields to the determination of kinetic parameters

Changes in electrophoretic and/or electromagnetophoretic mobilities during the course of biochemical reactions are related to first order rate constants of those reactions. By linearization of the mobility/reaction-coordinate relations, a method for the determination of rate constants is suggested, an assessment being made of some likely advantages and limitations of this approach to kinetic problems.     

Progress curve analysis of adenosine deaminase-catalyzed reactions

The kinetic constants of the adenosine deaminase-catalyzed conversion of adenosine to inosine were found to be readily obtainable by analyzing the progress curve of a single reaction. A novel inhibitor, 9-(1-hydroxymethyl-3-methylbutyl)adenine, was studied to test the validity of the progress curve method with this enzyme. Estimates of kinetic constants determined by this method were compared to those determined by the conventional initial velocity analysis. The Km and Vmax values for adenosine and the Ki value for the inhibitor were estimated to be 26.1 microM, 1.27 mumol/min/unit of enzyme, and 0.48 microM, respectively, by the initial velocity method, and 29.3 microM, 1.27 mumol/min/unit of enzyme, and 0.52 microM, respectively, by the progress curve analysis. The inhibitor was shown to act competitively with substrate by both methods of analysis. The progress curve experiments were very simple to perform and the constants were calculated (with an interfaced microcomputer) within a few minutes of the completion of each assay.     

Microcomputer simulation of steady-state enzyme kinetics for educational purposes

A BASIC program to assist the instruction of steady-state enzymekinetics has been developed for the IBM PC microcomputer. Itspurpose is to simulate laboratory experiments in order to minimizethe time required to obtain kinetic data from which studentsdeduce kinetic mechanisms and determine kinetic constants ofenzyme-catalyzed reactions. The program randomly selects a kineticscheme from various sequential, ping pong, and iso reactionsequences as well as values for the kinetic constants. The schemeand kinetic constants are unknown to the student at this time;the only thing he or she knows is the stoichiometry of the catalyzedreaction which can have two or three substrates and products.The student is prompted to enter values for concentrations ofsubstrates and products; several different concentrations foreach substrate and product can be entered in a single experiment.The program then calculates, displays and prints (if desired)the corresponding initial steadystate velocities. The studentcan perform as many experiments as desired until enough informationis obtained to determine the kinetic mechanism and to calculatevalues for the kinetic constants. Received on March 10, 1986; accepted on May 6, 1986     

Analyzing a kinetic titration series using affinity biosensors

The classical method of measuring binding constants with affinity-based biosensors involves testing several analyte concentrations over the same ligand surface and regenerating the surface between binding cycles. Here we describe an alternative approach to collecting kinetic binding data, which we call "kinetic titration." This method involves sequentially injecting an analyte concentration series without any regeneration steps. Through a combination of simulation and experimentation, we show that this method can be as robust as the classical method of analysis. In addition, kinetic titrations can be more efficient than the conventional data collection method and allow us to fully characterize analyte binding to ligand surfaces that are difficult to regenerate.     

Diffusion-controlled association of a dye, 1-anilinonaphthalene-8-sulfonic acid, to a protein, bovine serum albumin, using a fast-flow microsecond mixer and stopped-flow

The kinetic constants of the two fastest reactions of 1-anilinonaphthalene-8-sulfonic acid binding to bovine serum albumin are derived from the results of experiments with a microsecond fast-flow mixing technique and a stopped-flow method. The experiments are interpreted in terms of rapid bimolecular diffusion-controlled associations to two independent regions on the protein surface; this reaction mechanism contrasts with previous kinetic studies of ligand binding to bovine serum albumin which have not demonstrated the fastest kinetic processes.     

一种新的纤溶酶原激活反应动力学研究方法

 在溶栓研究中 ,纤溶酶原激活剂 (plasminogen activator,PA)激活纤溶酶原 (plasminogen,Plg)反应的动力学常数的测定占有重要地位 .在前人的研究中 ,虽然进行了这项实验 ,但是并未给出一个方便、快捷的测定方法 .所以建立一种更准确 ,更适合一般的实验室条件的 PA分子激活 Plg反应动力学常数的测定方法是必要的 .在对该反应进行数学分析的基础上 ,得到由可测量表示的纤溶酶 (plasmin,Plm)生成速度 (v(Plm) )的计算公式 ,由 v(Plm)及相应已知量可进一步推导出 Km、kcat的表达式 ,最终测得相应动力学常数 .用这种方法测定的由甲醇酵母 (pichia pastoris)表达的人单链尿激酶型纤溶酶原激活剂 (human single chain urokinase- PA,scu- PA)激活 Plg的反应的 Km=0 .648μmol·L-1,kcat=0 .0 62 6s-1,与文献报导相符 (Km=0 .4～ 1 .1 μmol· L-1,kcat=0 .0 2～ 0 .0 93) s-1,说明此方法是可靠的 .又因该法只需相应底物及酶标仪且为连续测定 ,所以十分简便 .     

A general method for the analysis of random bisubstrate enzyme mechanisms

In the present communication, a general method for the kinetic analysis of random bisubstrate mechanisms is described. The method comprises a stepwise application of the following kinetic and ligand-binding experiments: determination of steady-state kinetic constants, product inhibition patterns, maximum rate relationships, application of alternate substrates, application of dead-end inhibitors, direct binding of substrates, kinetic isotope effects, and isotope exchange studies. This general method was applied to a practical example: a yeast alcohol dehydrogenase-catalyzed oxidation of 2-propanol by NAD⁺ at pH 7.0, 25°C. It was found that this fully reversible reaction proceeds by a steady-state random Bi-Bi mechanism, whereby both dead-end complexes are formed.