Kinetics of an autocatalytic zymogen reaction in the presence of an inhibitor coupled to a monitoring reaction

Kinetic analysis of a general model of activation of aspartic proteinase zymogens involving a reversible inhibitor. II. Contribution of the uni- and bimolecular activation routes

From the kinetic study carried out in part I of this series (preceding article) an analysis quantifying the relative contribution to the global process of the uni- and bimolecular routes has been carried out. This analysis suggests a way to predict the time course of the relative contribution as well as the effect on this relative weight of the initial zymogen, inhibitor and activating enzyme concentrations.

Competitive and uncompetitive inhibitors simultaneously acting on an autocatalytic zymogen activation reaction

The time course of the residual enzyme activity of a general model consisting of an autocatalytic zymogen activation process inhibited by an irreversible competitive inhibitor and an irreversible uncompetitive inhibitor has been studied. Approached analytical expressions which furnish the time course of the residual enzyme activity from the onset of the reaction depending on the rate constants and initial concentration have been obtained. The goodness and limitations of the analytical equations were checked by comparing with the results obtained from the numerical integration, i.e. with the simulated progress curves. A dimensionless parameter giving the relative contributions of both the activation and the inhibitions routes is suggested, so that the value of this parameter determines whether the activation or the inhibitions routes prevail or if both processes are balanced during the time for which the analytical expressions are valid. The effects of the initial zymogen, free enzyme and inhibitors concentrations are analysed. Finally an experimental design and kinetic data analysis is proposed to evaluate simultaneously the kinetic parameters involved and to discriminate between different zymogen activation processes which can be considered particular cases of the general model.

Kinetic analysis of a general model of activation of aspartic proteinase zymogens

Starting from a simple general reaction mechanism of activation of aspartic proteinase zymogens involving an uni- and a bimolecular simultaneous route, the time course equation of the concentration of the zymogen and of the activated enzyme have been derived. From these equations, an analysis quantifying the relative contribution to the global process of the two routes has been carried out for the first time. This analysis suggests a way to predict the time course of the relative contribution as well as the effect of the initial zymogen and activating enzyme concentrations, on the relative weight. An experimental design and kinetic data analysis is suggested to estimate the kinetic parameters involved in the reaction mechanism proposed. Finally, we apply some of our results to experimental data obtained by other authors in experimental studies of the activation of some aspartic proteinase zymogens.

Kinetics of autocatalytic zymogen activation measured by a coupled reaction: pepsinogen autoactivation

A kinetic study was performed of a model for an autocatalytic zymogen activation process involving both intra- and intermolecular routes, to which a chromogenic reaction in which the active enzyme acts upon one of its substrates was coupled to continuously monitor the reaction. Kinetic equations describing the evolution of species involved in the system with time were obtained. These equations are valid for any zymogen autocatalytic activation process under the same initial conditions. Experimental design and kinetic data analysis procedures to evaluate the kinetic parameters, based on the derived kinetic equations, are suggested. In addition, a dimensionless distribution coefficient was defined, which shows mathematically whether the intra- or the intermolecular route prevails once the kinetic parameters involved in the system are known. The validity of the results obtained was checked using simulated curves for the species involved. As an example of application of the method, the system is experimentally illustrated by the continuous monitoring of pepsinogen transformation to pepsin.

Kinetics of intra- and intermolecular zymogen activation with formation of an enzyme-zymogen complex

A mathematical description was made of an autocatalytic zymogen activation mechanism involving both intra- and intermolecular routes. The reversible formation of an active intermediary enzyme-zymogen complex was included in the intermolecular activation route, thus allowing a Michaelis-Menten constant to be defined for the activation of the zymogen towards the active enzyme. Time-concentration equations describing the evolution of the species involved in the system were obtained. In addition, we have derived the corresponding kinetic equations for particular cases of the general model studied. Experimental design and kinetic data analysis procedures to evaluate the kinetic parameters, based on the derived kinetic equations, are suggested. The validity of the results obtained were checked by using simulated progress curves of the species involved. The model is generally good enough to be applied to the experimental kinetic study of the activation of different zymogens of physiological interest. The system is illustrated by following the transformation kinetics of pepsinogen into pepsin.