Mathematical model for the determination of enzyme activity based on enzymatic amplification by substrate cycling

A mathematical description of an enzyme amplification mechanism involving the coupling of the enzymatic reaction which is to be measured to a specific substrate cycle is presented, obtaining equations that allow the system to become linear in the steady-state. The amplification approach has been applied to the continuous measurement of pyruvate kinase activity. The enzymes l-lactate dehydrogenase and l-lactate oxidase are used to cycle the pyruvate product of pyruvate kinase catalytic activity to l-lactate, with the concomitant disappearance of one molecule of β-NADH in each turn of the cycle, which is monitored spectrophotometrically at 340 nm. A comparison is made with the standard linear coupled assay. This shows that any improvement obtained is dependent on the activity of the coupling enzymes, increasing with time. The model is simple and it can be applied to the amplified measurement of any enzyme whose catalytic reaction product may be recycled.