Tunneling and Nonadiabatic Effects on a Proton-Coupled Electron Transfer Model for the Q Site in Cytochrome bc₁

Cytochrome bc₁ is a fundamental enzyme for cellular respiration and photosynthesis. This dimeric protein complex catalyzes a proton-coupled electron transfer (PCET) from the reduced coenzyme-Q substrate (Q) to a bimetallic iron-sulfur cluster in the Q active site. Herein, we combine molecular dynamics simulations of the complete cytochrome bc₁ protein with electronic-structure calculations of truncated models and a semiclassical tunneling theory to investigate the electron-proton adiabaticity of the initial reaction catalyzed in the Q site. After sampling possible orientations between the Q substrate and a histidine side chain that functions as hydrogen acceptor, we find that a truncated model composed by ubiquinol-methyl and imidazole-iron(III)-sulfide captures the expected changes in oxidation and spin states of the electron donor and acceptor. Diabatic electronic surfaces obtained for this model with multiconfigurational wave function calculations demonstrate that this reaction is electronic nonadiabatic, and proton tunneling is faster than mixing of electronic configurations. These results indicate the formalism that should be used to calculate vibronic couplings and kinetic parameters for the initial reaction in the Q site of cytochrome bc₁. This framework for molecular simulation may also be applied to investigate other PCET reactions in the Q-cycle or in various metalloproteins that catalyze proton translocation coupled to redox processes.