Making sense of the kinetics of reactions of unstable modifiers with enzymes

Experimental approach to the kinetic study of unstable site-directed irreversible inhibitors: kinetic origin of the apparent positive co-operativity arising from inactivation of trypsin by p-amidinophenylmethanesulphonyl fluoride

Experimental characterization of enzyme inactivation by unstable irreversible inhibitors has only previously been carried out by using discontinuous methods involving preincubation, removal of samples and further residual activity assays. A continuous method for the kinetic study of these inhibitors in the presence of an auxiliary substrate was recently proposed in a theoretical study. This method was based on approximate expressions for the evolution of the product concentration, which contained series expansions with five or more exponential terms, seriously complicating their use in practice. In the present paper, a new experimental method has been developed for the kinetic study of unstable and site-directed irreversible inhibitors, considering two different ranges of inhibitor concentration. Thus at low inhibitor concentrations, the system evolves from an initial to a final steady state, the rates of which are described by exact analytical equations. At high inhibitor concentrations, however, the product accumulation can be described by an exact uniexponential equation. This simple and efficient method has been applied to the kinetic study of trypsin inactivation by p-amidinophenylmethanesulphonyl fluoride, near the optimum pH of the enzyme. The dependence of the final steady-state rate on the substrate concentration shows apparent positive co-operativity which has not previously been reported. The kinetic origin of this type of co-operativity is predicted by one of the exact analytical equations derived here. The instability of new protein and non-protein irreversible inhibitors has to be carefully characterized to prevent true unstable irreversible inhibitors being wrongly described as allosteric reversible inhibitors.