Resolving Double Regenerative Catalytic Pathways in Redox Protein Films via Cyclic Voltammetry

Redox protein films immobilized on electrode surfaces often exhibit complex catalytic behavior arising from coupled electron-transfer and chemical regeneration steps. In this work, we present a comprehensive theoretical model describing double regenerative catalytic pathways in surface-confined redox protein systems, resolved for the first time through numerical simulations implemented in Mathcad. The model is based on a sequential EC′EC″-type mechanism, in which an initial interfacial electron transfer is followed by two kinetically coupled chemical regeneration steps that sustain catalytic turnover. The system of governing differential equations, incorporating surface confinement, finite electron-transfer kinetics, and regenerative chemical reactions, was solved under cyclic voltammetric conditions. Systematic simulations were performed to evaluate the influence of key dimensionless parameters, including kinetic rate constants, on the shape, position, and magnitude of voltammetric responses. The results reveal distinct voltammetric signatures characteristic of double regenerative catalysis, including amplified peak currents, asymmetric peak profiles, and the emergence of quasi-steady-state regimes at high catalytic efficiencies. Importantly, the analysis identifies critical parameter domains in which the two catalytic pathways interact synergistically or competitively, thereby governing the overall electrochemical response. A generalized scaling relationship between peak current and the composite kinetic parameter is proposed, providing a unified framework for interpreting complex protein-film voltammetry. This study establishes a robust theoretical platform for understanding multi-step catalytic mechanisms in redox protein films and demonstrates the power of Mathcad-based modeling in resolving intricate electrochemical systems. The findings are expected to facilitate the rational design and interpretation of bioelectrochemical experiments involving enzymatic and protein-modified electrodes.