Cryptochromes and photolyases are flavoproteins that undergo cascades of electron/hole transfers after excitation of the flavin cofactor. It was recently discovered that animal (6-4) photolyases, as well as animal cryptochromes, feature a chain of four tryptophan residues, while other members of the family contain merely a tryptophan triad. Transient absorption spectroscopy measurements on Xenopus laevis (6-4) photolyase have shown that the fourth residue is effectively involved in photoreduction but at the same time could not unequivocally ascertain the final redox state of this residue. In this article, polarizable molecular dynamics simulations and constrained density functional theory calculations are carried out to reveal the energetics of charge migration along the tryptophan tetrad. Migration toward the fourth tryptophan is found to be thermodynamically favorable. Electron transfer mechanisms are sought either through an incoherent hopping mechanism or through a multiple sites tunneling process. The Jortner-Bixon formulation of electron transfer (ET) theory is employed to characterize the hopping mechanism. The interplay between electron transfer and relaxation of protein and solvent is analyzed in detail. Our simulations confirm that ET in (6-4) photolyase proceeds out of equilibrium. Multiple site tunneling is modeled with the recently proposed flickering resonance mechanism. Given the position of energy levels and the distribution of electronic coupling values, tunneling over three tryptophan residues may become competitive in some cases, although a hopping mechanism is likely to be the dominant channel. For both reactive channels, computed rates are very sensitive to the starting protein configuration, suggesting that both can take place and eventually be mixed, depending on the state of the system when photoexcitation takes place.