On the Steady-State Assumption and Its Application to the Rotating Disk Voltammetry of Adsorbed Enzymes

Relaxation and Simplex mathematical algorithms applied to the study of steady-state electrochemical responses of immobilized enzyme biosensors: Comparison with experiments

A description of the implementation of the relaxation method with automatic mesh point allocation for immobilized enzyme electrodes is presented. The advantages of this method for the solution of coupled reaction-diffusion problems are discussed. The relaxation numerical simulation technique is combined with the Simplex fitting algorithm to extract kinetic parameters from experimental data. The results of the simulations are compared to experimental data from self-assembled multilayered electrodes comprised of glucose oxidase (GOx) and an Os modified redox mediator and found to be in excellent agreement.

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).

Electron Flow in Multicenter Enzymes: Theory, Applications, and Consequences on the Natural Design of Redox Chains

In protein film voltammetry, a redox enzyme is directly connected to an electrode; in the presence of substrate and when the driving force provided by the electrode is appropriate, a current flow reveals the steady-state turnover. We show that, in the case of a multicenter enzyme, this signal reports on the energetics and kinetics of electron transfer (ET) along the redox chain that wires the active site to the electrode, and this provides a new strategy for studying intramolecular ET. We propose a model which takes into account all the enzyme's redox microstates, and we prove it useful to interpret data for various enzymes. Several general ideas emerge from this analysis. Considering the reversibility of ET is a requirement: the usual picture, where ET is depicted as a series of irreversible steps, is oversimplified and lacks the important features that we emphasize. We give justification to the concept of apparent reduction potential on the time scale of turnover and we explain how the value of this potential relates to the thermodynamic and kinetic properties of the system. When intramolecular ET does not limit turnover, the redox chain merely mediates the driving force provided by the electrode or the soluble redox partner, whereas when intramolecular ET is slow, the enzyme behaves as if its active active site had apparent redox properties which depend on the reduction potentials of the relays. This suggests an alternative to the idea that redox chains are optimized in terms of speed: evolutionary pressure may have resulted in slowing down intramolecular ET in order to tune the enzyme's "operating potential".