Kinetic analysis of a model for double substrate cycling: highly amplified ADP (and/or ATP) quantification.

A mathematical description has been made of an enzyme amplification mechanism involving the coupling of two substrate cycles. In this amplification system one of the noncycling products of a first substrate cycle acts as a trigger molecule that continuously feeds a second substrate cycle. Time-concentration equations describing the evolution of the species involved in the system have been obtained. The model is illustrated by the quantification of nanomolar levels of ADP (and/or ATP) in a continuous assay involving the enzymes L-lactate dehydrogenase and L-lactate oxidase to cycle the pyruvate accumulated in a first enzymatic cycle constituted by the enzymes pyruvate kinase and hexokinase. Progress curves were seen to be parabolic, and, according to the kinetic equations obtained, followed second-order polynomials of the reaction time. Mathematical equations for minimizing the cost of the assays are also given. The model is applicable to the amplified analytical determination of low levels of a metabolite or an enzyme activity, and its amplification capacity, together with the simplicity of determining kinetic parameters, enable it to be employed in enzyme immunoassays to increase the magnitude of the measured response.