Enzyme kinetic studies from progress curves

Measurement of Net Rate Constants from Enzyme Progress Curves without Curve Fitting

A method is described whereby net rate constants can be directly inferred from the progress curves of enzyme intermediates without the need for model specification, numerical analysis, curve fitting, or the steady-state approximation. Specifically, if an enzyme intermediate in an ultimately irreversible serial subsequence is perturbed from and returns back to its equilibrium state as the substrate is consumed, then its net rate constant is given by the ratio of the total substrate consumed and the area under the progress curve for the enzyme intermediate. A rigorous analysis demonstrates this result to hold independent of the complete enzymatic reaction in which the subsequence is embedded, making it broadly applicable to a very wide range of kinetic mechanisms, including those complicated by inhibition. As a theoretical consequence, it is shown that traditionally steady-state parameters such as k_cat, k_cat/K_M, and net rate constants can be expressed as limiting ratios of averages without requiring the steady-state hypothesis. Finally, a mock data set is generated for a system of contemporary interest that can serve as both an example of how the methodology would be used in practice and a proof of concept.

A COMPARISON BETWEEN THE INITIAL RATE EXPRESSIONS OBTAINED UNDER STRICT CONDITIONS AND THE RAPID EQUILIBRIUM ASSUMPTION USING, AS EXAMPLE, A FOUR SUBSTRATE ENZYME REACTION

The software WinStes, developed by our group, is used to derive the strict steady-state initial rate equation of the reaction mechanism of CTP:sn-glycerol-3-phosphate cytidylyltransferase [EC 2.7.7.39] from Bacillus subtilis. This enzyme catalyzes a reaction with two substrates and operates by a random ordered binding mechanism with two molecules of each substrate. The accuracy of the steady-state rate equation derived is checked by comparing the rate values it provides with those obtained from the simulated progress curves. To analyze the kinetics of this enzyme using the strict steady-state initial rate equation, several curves for different substrate concentrations and different rate constants are generated. A comparison of these curves with the curves obtained from the rapid equilibrium initial rate equation, with different substrate concentration values, serves to analyze how the strict steady-state rate equation values are closer to those of rapid equilibrium rate equations when rapid equilibrium conditions are fulfilled.

Sensitivity analysis and error structure of progress curves

Both the sensitivity of the monitored signal in progress curves to variations in enzyme concentration and the standard deviation of this signal were analyzed as a function of the proportion of transformed substrate. Three enzymes catalyzing essentially irreversible reactions were used as model systems: HIV-1 protease, glutathione reductase, and glutathione transferase. For all enzymes analyzed, the sensitivity was maximal when 60-80% of the substrate had been transformed. The standard deviation of reaction progress curve data replicates was also maximal at these substrate conversion levels, a result that was attributed to the influence of the sensitivity to random dispersion of the enzyme concentration. On this basis, we developed a model for the standard deviation of reaction progress curves that gave a good description of the experimental data and efficiently reduced the heteroscedasticity of residuals in a weighted fit of progress curves. This standard deviation model can be used for obtaining more efficient parameter estimates, to simulate noise in Monte Carlo procedures, and to delineate detection limits of enzyme inhibition. The transient increases in the sensitivity and in the standard deviation in progress curves are proposed to be features common to most enzymatic assays.

Use of a windows program for simulation of the progress curves of reactants and intermediates involved in enzyme-catalyzed reactions

A program that performs simulation of the kinetics of enzyme-catalyzed reactions with up to 32 species is described. The program is written in C++ for MS Windows 95/98/NT and uses a simple text file to define the kinetic model. The use of the program is illustrated with some examples. WES is available free of charge on request from the authors (e-mail: fgarcia@iele-ab.uclm.es).

The cluster-arranged cooperative model: a model that accounts for the kinetics of binding to A1 adenosine receptors

To explain the equilibrium binding and binding kinetics of ligands to membrane receptors, a number of models have been proposed, none of which is able to adequately describe the experimental findings, in particular the apparent negative cooperativity of ligand binding. In this paper, a new model, the cluster-arranged cooperative model, is presented whose main characteristic is that it explains the existence of negative cooperativity in the binding of ligands to the receptor molecule. The model is based on our findings of agonist binding to A1 adenosine receptors and of ligand-induced clustering of these receptors on the cell surface. The model assumes the existence of two conformational forms of the receptor in an equilibrium which depends on the concentration of the ligand. In this way, negative cooperativity is explained by the transmission of the information between receptor molecules through the structure of the membrane. The model is able to predict the thermodynamic binding and binding kinetics of [3H]-(R)-(phenylisopropyl)adenosine to A1 adenosine receptors in the presence and absence of guanylyl imidodiphosphate. In the presence of the guanine nucleotide analogue, the linear Scatchard plots obtained for [3H]-(R)-(phenylisopropyl)adenosine binding are explained by the disappearance of cooperativity, thus suggesting that G proteins are important for the existence of negative cooperativity in ligand binding. Among other predictions, the model justifies early events in homologous desensitization since high ligand concentrations would lead to the saturation of the receptor in a low-affinity conformation that does not signal. Our model can likely explain the behavior of a number of heptaspanning and tyrosine-kinase receptors exhibiting complex binding kinetics.

Separation of L-Pro-DL-boroPro into its component diastereomers and kinetic analysis of their inhibition of dipeptidyl peptidase IV. A new method for the analysis of slow, tight-binding inhibition

The potent dipeptidyl peptidase IV (DP IV) inhibitor [1-(2-pyrrolidinylcarbonyl)-2-pyrrolidinyl]boronic acid (L-Pro-DL-boroPro) [Flentke, G. R., Munoz, E., Huber, B. T., Plaut, A. G., Kettner, C. A., & Bachovchin, W. W. (1991) Proc. Natl. Acad. Sci. U.S.A. 88, 1556-1559] was fractionated into its component L-L and L-D diastereomers by C18 HPLC, and the binding of the purified diastereomers to DP IV was analyzed. Inhibition kinetics confirms that the L-L diastereomer is a potent inhibitor of DP IV, having a Ki of 16 pM. The L-D isomer binds at least 1000-fold more weakly than the L-L, if it binds at all, as the approximately 200-fold weaker inhibition observed for the purified L-D isomer is shown here to be due entirely to the presence of a small amount (0.59%) of the L-L diastereomer contaminating the L-D preparation. The instability of Pro-boroPro, together with its very high affinity for DP IV and the time dependence of the inhibition, makes a rigorous kinetic analysis of its binding to DP IV difficult. Here we have developed a method which takes advantage of the slow rate at which the inhibitor dissociates from the enzyme. The method involves preincubating the enzyme and the inhibitor without substrate and then assaying the free enzyme by the addition of substrate and following its hydrolysis for a period of time which is short relative to the dissociation rate of the inhibitor.(ABSTRACT TRUNCATED AT 250 WORDS)

Fitting integrated enzyme rate equations to progress curves with the use of a weighting matrix

A method is presented for fitting the pairs of values product formed-time taken from progress curves to the integrated rate equation. The procedure is applied to the estimation of the kinetic parameters of the adenosine deaminase system. Simulation studies demonstrate the capabilities of this strategy. A copy of the FORTRAN77 program used can be obtained from the authors by request.

Analysis of progress curves by simulations generated by numerical integration

A highly flexible computer program written in FORTRAN is presented which fits computer-generated simulations to experimental progress-curve data by an iterative non-linear weighted least-squares procedure. This fitting procedure allows kinetic rate constants to be determined from the experimental progress curves. Although the numerical integration of the rate equations by a previously described method [Barshop, Wrenn & Frieden (1983) Anal. Biochem. 130, 134-145] is used here to generate predicted curves, any routine capable of the integration of a set of differential equations can be used. The fitting program described is designed to be widely applicable, easy to learn and convenient to use. The use, behaviour and power of the program is explored by using simulated test data.

Mechanism and binding specificity of beta-glucosidase-catalyzed hydrolysis of cellobiose analogues studied by competition enzyme kinetics monitored by 1H-NMR spectroscopy

The application of high-resolution 1H-NMR spectroscopy to monitor substrate and product time dependencies in progress curve enzyme kinetics is described with beta-glucosidase-catalyzed hydrolyses of cellobiose analogues as examples. It is demonstrated that inhibition patterns, relative binding specificities and catalytic rates can be inferred from competition experiments with two or more substrates. It could be concluded from competition experiments that substrates which form less stable enzyme-substrate complexes than methyl beta-cellobioside are hydrolyzed faster than this reference substrate when they are the sole substrate, due to a lower activation energy in the catalytic step, but that they are hydrolyzed slower than the reference compound in direct competition, due to the formation of the less stable enzyme-substrate complex in the binding step.

The analysis of enzyme progress curves by numerical differentiation, including competitive product inhibition and enzyme reactivation

A new method for analyzing steady-state enzyme kinetic data is presented. The technique, which is based on the numerical differentiation of the complete reaction curve, has several advantages over initial velocity and integrated Michaelis-Menten equation methods. The differentiated data are fit to the differential equation describing the appropriate kinetic scheme. This approach is particularly valuable in cases of strong competitive product inhibition and of changing concentrations of active enzyme. The method assumes a reversible reaction and is applicable to a very wide variety of steady-state kinetic schemes. A particular advantage of this approach over integrated methods is that it is independent of [S0] and hence of errors in [S0]. The combination of complete progress curve and computer analysis makes this approach very efficient with respect to both time and materials. Running on an IBM PC XT or equivalent microcomputer with an 8087 coprocessor, the analyses are very fast, the complete process usually being complete in a minute or two. The utility of the technique is demonstrated by application to both simulated and real data. We show that the differentiation of the progress curve for the ribonuclease-catalyzed hydrolysis of 2',3'-cyclic cytidine monophosphate reveals strong product inhibition by 3'-CMP, and this product inhibition accounts for the large discrepancies reported in the literature for the value of Km for this substrate. The method was also applied to determine the rate of reactivation of beta-lactamase which had been reversibly inactivated by cloxacillin. Since large numbers of data points are required for the numerical differentiation the method has become practical only with the advent of computer-acquired data systems.