On the optimal relative orientation of radicals in the cryptochrome magnetic compass

Abstract

Birds appear to be equipped with an innate magnetic compass. One biophysical model of this sense relies on spin dynamics in photogenerated radical pairs in the protein cryptochrome. This study employs a systematic approach to predict the dependence of the compass sensitivity on the relative orientation of the constituent radicals for spin systems comprising up to 21 hyperfine interactions. Evaluating measures of compass sensitivity (anisotropy) and precision (optimality) derived from the singlet yield, we find the ideal relative orientations for the radical pairs consisting of the flavin anion (F•-) coupled with a tryptophan cation (W•+) or tyrosine radical (Y•). For the geomagnetic field, the two measures are found to be anticorrelated in [F•- W•+]. The angle spanned by the normals to the aromatic planes of the radicals is the decisive parameter determining the compass sensitivity. The third tryptophan of the tryptophan triad/tetrad, which has been implicated with magnetosensitive responses, exhibits a comparably large anisotropy, but unfavorable optimality. Its anisotropy could be boosted by an additional ∼50% by optimizing the relative orientation of the radicals. For a coherent lifetime of 1 μs, the maximal relative anisotropy of [F•- W•+] is 0.27%. [F•- Y•] radical pairs outperform [F•- W•+] for most relative orientations. Furthermore, anisotropy and optimality can be simultaneously maximized. The entanglement decays rapidly, implicating it as a situational by-product rather than a fundamental driver within the avian compass. In magnetic fields of higher intensity, the relative orientation of radicals in [F•- W•+] is less important than for the geomagnetic field.