Two-electron transfer reactions in proteins: Bridge-mediated and proton-assisted processes

Nonadiabatic two-electron transfer (TET) reactions through donor-bridge-acceptor (DBA) systems is investigated within the approximation of fast vibrational relaxation. For TET reactions in which the population of bridging states remains small (less than ${10}^{\ensuremath{-}2})$ it is demonstrated that a multiexponential transition process reduces to three-state kinetics. The transfer starts at the state with two excess electrons at the D center $({\mathrm{D}}^{2\ensuremath{-}}\mathrm{BA}),$ goes through the intermediate (transient) state with one electron at the $\mathrm{D}$ center and one at the $\mathrm{A}$ center $({\mathrm{D}}^{\ensuremath{-}}{\mathrm{BA}}^{\ensuremath{-}}),$ and ends up with the two electrons at the A center $({\mathrm{DBA}}^{2\ensuremath{-}}).$ Furthermore, if the population of the intermediate state becomes also small the two-exponential kinetics can be transformed with high accuracy to single-exponential D-A TET kinetics. The related overall transfer rate contains contributions from stepwise and from concerted TET. The latter process is determined by a specific two-electron superexchange coupling incorporating the bridging states $({\mathrm{D}}^{\ensuremath{-}}{\mathrm{B}}^{\ensuremath{-}}\mathrm{A}$ and $\mathrm{D}{\mathrm{B}}^{\ensuremath{-}}{\mathrm{A}}^{\ensuremath{-}})$ as well as the intermediate state $({\mathrm{D}}^{\ensuremath{-}}\mathrm{B}{\mathrm{A}}^{\ensuremath{-}}).$ As an example, the reduction of micothione reductase by nicotinamide adenine dinucleotide phosphate is analyzed. Existing experimental data can be explained if one assumes that the proton-assisted reduction of the enzyme is realized by the concerted TET mechanism.