It is still a puzzle that has not been entirely solved how migratory birds utilize the Earth's magnetic field for biannual migration.The most consistent explanation thus far is rooted in the modulation of the biological function of the cryptochrome 4 (Cry4) protein by an external magnetic field. This phenomenon is closely linked with the flavin adenine dinucleotide (FAD) cofactor that is noncovalently bound in the protein. Cry4 is activated by blue light, which is absorbed by the FAD cofactor. Subsequent electron and proton transfers trigger radical pair formation in the protein, which is sensitive to the external magnetic field. An important long-lasting redox state of the FAD cofactor is the signaling (FADH^•) state, which is present after the transient electron transfer steps have been completed. Recent experimental efforts succeeded in crystallizing the Cry4 protein from Columbia livia (ClCry4) with all of the important residues needed for protein photoreduction. This specific crystallization of Cry4 protein so far is the only avian cryptochrome crystal structure available, which, however, has great similarity to the Cry4 proteins of night migratory birds. The previous experimental studies of the ClCry4 protein included the absorption properties of the protein in its different redox states. The absorption spectrum of the FADH^• state demonstrated a peculiar red shift compared to the photoabsorption properties of the FAD cofactor in its FADH^• state in other Cry proteins from other species. The aim of this study is to understand this red shift by employing the tools of computational microscopy and, in particular, a QM/MM approach that relies on the polarizable embedding approximation.