Noise-assisted quantum electron transfer in photosynthetic complexes

Electron transfer (ET) between primary electron donor and acceptor is modeled in the photosynthetic complexes. Our model includes (i) two discrete energy levels associated with donor and acceptor, which are directly interacting and (ii) two continuum manifolds of electron energy levels (“sinks”), each interacting with the donor and acceptor. We also introduce external (classical) noise which acts on both donor and acceptor. We derive a closed system of integro-differential equations which describes the non-Markovian quantum dynamics of the ET. A region of parameters is found in which the ET dynamics can be simplified, and described by coupled ordinary differential equations. Using these simplified equations, both cases of sharp and flat redox potentials are analyzed. We analytically and numerically obtain the characteristic parameters that optimize the ET rates and efficiency in this system. In particular, we demonstrate that even for flat redox potential a simultaneous influence of sink and noise can significantly increase the efficiency of the ET. We discuss a relation between our approach and the Marcus theory of ET.