The Kinetic Basis of a General Method for the Investigation of Active Site Content of Enzymes and Catalytic Antibodies: First-Order Behaviour under Single-turnover and Cycling Conditions

The theoretical foundation has been laid for the investigation of catalytic systems using first-order kinetics and for a general kinetic method of investigation of the active site content, Ea, of enzymes, catalytic antibodies, and other enzyme-like catalysts. The method involves a combination of steady-state and single-turnover kinetics to provide Vmaxand Kmandklimobs and Kappm, respectively. The validity of the method is shown to remain valid for two extensions of the simple two-step enzyme catalysis model (a) when the catalyst preparation contains molecules (Eb) that bind substrate but fail to catalyse product formation and (b) when the catalyst itself binds substrate non-productively as well as productively. The former is a particularly serious complication for polyclonal catalytic antibodies and the latter a potential complication for all catalysts. For the simple model and for (b) Vmax/klimobsprovides the value of [Ea]Tand for (a) its upper limit. This can be refined by consideration of the relative values of Kmand the equilibrium dissociation constant of EbS. For the polyclonal catalytic antibody preparation investigated, the fact thatKappm >Kmdemonstrates for the first time the presence of a substrate-binding but non-catalytic component in a polyclonal preparation. First-order behaviour in catalytic systems occurs not only with a large excess of catalyst over substrate but also with lower catalyst/substrate ratios, including the equimolar condition, when Kappm⪢[S]O, a phenomenon that is not widely appreciated.