Effects of Slow Substrate Binding and Release in Redox Enzymes:  Theory and Application to Periplasmic Nitrate Reductase

For redox enzymes, the technique called protein film voltammetry makes it possible to determine the entire profile of activity against driving force by having the enzyme exchanging directly electrons with the rotating-disc electrode onto which it is adsorbed. Both the potential location of the catalytic response and its detailed shape report on the sequence of catalytic events, electron transfers and chemical steps, but the models that have been used so far to decipher this signal lack generality. For example, it was often proposed that substrate binding to multiple redox states of the active site may explain that turnover is greater in a certain window of electrode potential, but no fully analytical treatment has been given. Here, we derive (i) the general current equation for the case of reversible substrate binding to any redox states of a two-electron active site (as exemplified by flavins and Mo cofactors), (ii) the quantitative conditions for an extremum in activity to occur, and (iii) the expressions from which the substrate-concentration dependence of the catalytic potential can be interpreted to learn about the kinetics of substrate binding and how this affects the reduction potential of the active site. Not only does slow substrate binding and release make the catalytic wave shape highly complex, but we also show that it can have important consequences which will escape detection in traditional experiments:  the position of the wave (this is the driving force that is required to elicit catalysis) departs from the reduction potential of the active site even at the lowest substrate concentration, and this deviation may be large if substrate binding is irreversible. This occurs in the reductive half-cycle of periplasmic nitrate reductase where irreversibility lowers the driving force required to reduce the active site under turnover conditions and favors intramolecular electron transfer from the proximal [4Fe4S]⁺ cluster to the active site Mo^V.