The sensitivity of enzyme electrodes can be increased substantially by incorporation of a substrate recycling scheme. One possible strategy to achieve this goal is based on amperometric enzyme electrodes involving during the transduction step an electrochemical recycling of enzyme substrate. In this kind of device, the shuttle analyte is not only measured once but is reconverted to be measured again leading to an amplification of the transduction signal. In this paper we present a theoretical analysis of this kind of device using the catechol-polyphenol oxidase model system immobilized as an enzyme layer at the surface of a rotating-disk electrode. For low concentrations of substrate, which correspond to practical conditions, we derive analytical expressions for the response of such a sensor. On the basis of the model, we;are able to quantify the respective influence of mass transport, partition coefficient, enzyme and electron transfer kinetics on the metrological characteristics of the bioelectrode. This is especially relevant when optimizing biosensor construction.