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

Francesco Tacchino,Oliver Ebenhöh,Dario Gerace,Antonella Succurro

doi:10.1038/s41598-019-52842-x

Abstract

The Q-cycle mechanism entering the electron and proton transport chain in oxygenic photosynthesis is an example of how biological processes can be efficiently investigated with elementary microscopic models. Here we address the problem of energy transport across the cellular membrane from an open quantum system theoretical perspective. We model the cytochrome {b}_{6},f protein complex under cyclic electron flow conditions starting from a simplified kinetic model, which is hereby revisited in terms of a Markovian quantum master equation formulation and spin-boson Hamiltonian treatment. We apply this model to theoretically demonstrate an optimal thermodynamic efficiency of the Q-cycle around ambient and physiologically relevant temperature conditions. Furthermore, we determine the quantum yield of this complex biochemical process after setting the electrochemical potentials to values well established in the literature. The present work suggests that the theory of quantum open systems can successfully push forward our theoretical understanding of complex biological systems working close to the quantum/classical boundary.

Highlights

The Q-cycle mechanism entering the electron and proton transport chain in oxygenic photosynthesis is an example of how biological processes can be efficiently investigated with elementary microscopic models
After benchmarking our alternative model by calculating the so-called quantum yield and comparing our results to the original ones[17], we extend the original study and provide new predictions of biological relevance: in particular, we determine the thermodynamic efficiency of the Q-cycle as a function of the external temperature, and find optimal performances around ambient temperatures compatible with physiological conditions for living cells
The Q-cycle mechanism is a relevant energy conversion process entering the electron transport chain in oxygenic photosynthesis, but its complex biochemical nature, difficult to capture with theoretical approaches, has to date limited the development of analytic and numerical models

Summary

Introduction

The Q-cycle mechanism entering the electron and proton transport chain in oxygenic photosynthesis is an example of how biological processes can be efficiently investigated with elementary microscopic models. We model the cytochrome b6 f protein complex under cyclic electron flow conditions starting from a simplified kinetic model, which is hereby revisited in terms of a Markovian quantum master equation formulation and spin-boson Hamiltonian treatment We apply this model to theoretically demonstrate an optimal thermodynamic efficiency of the Q-cycle around ambient and physiologically relevant temperature conditions. Building on an OQS-based kinetic model originally proposed by Smirnov and Nori[17], here we develop a simple but accurate Markovian theory of the Q-cycle The latter is a remarkable www.nature.com/scientificreports biochemical mechanism that efficiently conserves energy stored in excited electrons to increase the number of protons per electron that are pumped against the concentration gradient across the cellular membrane. Complemented by alternative mathematical approaches[19,20], this theoretical work potentially provides a deeper and more complete understanding of many bioenergetic aspects at the molecular level

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