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The Q-cycle mechanism entering the electron and proton transport chain inoxygenic photosynthesis is an example of how biological processes can beefficiently investigated with elementary microscopic models. Here we addressthe problem of energy transport across the cellular membrane from an openquantum system theoretical perspective. We model the cytochrome $b_6f$ proteincomplex under cyclic electron flow conditions starting from a simplifiedkinetic model, which is hereby revisited in terms of a quantum master equationformulation and spin-boson Hamiltonian treatment. We apply this model totheoretically demonstrate an optimal thermodynamic efficiency of the Q-cyclearound ambient and physiologically relevant temperature conditions.Furthermore, we determine the quantum yield of this complex biochemical processafter setting the electrochemical potentials to values well established in theliterature. The present work suggests that the theory of quantum open systemscan successfully push forward our theoretical understanding of complexbiological systems working close to the quantum/classical boundary.

Optimal efficiency of the Q-cycle mechanism around physiological temperatures from an open quantum systems approach