Mathematical Algorithm behind the Protein-Film Voltammetry of a Surface EC’ Catalytic Mechanism under Butler–Volmer Kinetics

Protein-film voltammetry is a simple and powerful electrochemical methodology designed to provide direct access to electron-transfer reactions of redox-active proteins immobilized at the electrode surface. In such systems, the reacting redox centers are confined to the interfacial region and no diffusional transport of the protein from the bulk solution toward the electrode is involved. Consequently, the voltammetric response is governed by the amount of electroactive material adsorbed at the electrode, by the heterogeneous electron-transfer kinetics, and by possible chemical reactions coupled to the electrode process. The surface EC’ mechanism considered here is a regenerative catalytic mechanism. In this mechanism, the reduced form of the adsorbed protein undergoes a one-electron oxidation at the electrode surface, whereas the oxidized form is regenerated chemically back to the reduced form by reaction with another adsorbed or interracially available species, denoted as Y(ads). Such mechanisms are highly relevant in protein-film voltammetry, because many redox proteins and enzymes operate through catalytic cycles in which the electrochemically generated state is rapidly converted back to the initial redox form by a chemical reaction. This type of regeneration is particularly important for redox enzymes, metalloproteins, and surface-confined catalytic systems, where electron transfer and chemical turnover are strongly coupled.