Quantum effects in ultrafast electron transfers within cryptochromes

Cryptochromes and photolyases are flavoproteins that may undergo ultrafast charge separation upon electronic excitation of their flavin cofactors. Charge separation involves chains of three or four tryptophan residues depending on the protein of interest. The molecular mechanisms of these processes are not completely clear. In the present work we investigate the relevance of quantum effects like the occurrence of nuclear tunneling and of coherences upon charge transfer in Arabidopsis thaliana cryptochromes. The possible breakdown of the Condon approximation is also investigated. We have devised a simulation protocol based on the realization of molecular dynamics simulations on diabatic potential energy surfaces defined at the hybrid constrained density functional theory/molecular mechanics level. The outcomes of the simulations are analyzed through various dedicated kinetics schemes related to the Marcus theory that account for the aforementioned quantum effects. MD simulations also provide a basic material to define realistic model Hamiltonians for subsequent quantum dissipative dynamics. To carry out quantum simulations, we have implemented an algorithm based on the Hierarchical Equations of Motion. With this new tool in hand we have been able to model the electron transfer chain considering either two- or three-state models. Kinetic models and quantum simulations converge to the conclusion that quantum effects have a significant impact on the rate of charge separation. Nuclear tunneling involving atoms of the tryptophan redox cofactors as well as of the environment (protein atoms and water molecules) is significant. On the other hand non-Condon effects are negligible in most simulations. Taken together, the results of the present work provide new insights into the molecular mechanisms controlling charge separation in this family of flavoproteins.