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.