Quantum Thermodynamics of Electron Transport along Chains of Redox Centers

Intramolecular electron transport in biological systems is typically described as a diffusive hopping process, according to the semi-classical rate theories of Marcus and Hopfield combined with classical Pauli-type master equations. However, the possibility that non-trivial quantum mechanical effects could play a functional role in the transport dynamics in certain biomolecular processes has attracted increasing attention. Here, we extend the quantum mechanical model of open system dynamics by the Lindblad equation to a key biological component, the long chains of redox centers based on iron-sulfur clusters or heme groups that are widespread in many biological organisms, where they realize the cellular respiration. This approach allows to explore a wide range of physical parameters, showing key features of electron transport in these multi-domain protein structures. We pay particular attention to heat and entropy transfer between the electrons and the protein bath, which constitutes a benchmark of physical realism for the models. Electron currents, average transfer times and relative efficiency of the transport process are also explicitly characterized.