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 photo-generated 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 anti-correlated 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 byproduct 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.

The avian compass can be sensitive even without sustained electron spin coherence

“…Our results indicate that coherent electron spin dynamics is unlikely to be sustained in more realistic scenarios [36,39] but the avian compass could still be sensitive. We suggest that the actual compass parameters need to be deduced from more in vivo or in vitro experiments on migratory avian species; comparison with the parameters presented here could help to fully clarify the role In addition, in this work, while we are able to capture the essential electron spin coherence dynamics of a multinuclear radical pair system, our conclusions would bear verification by calculations on the full cryptochrome-based system.…”

“…Or have its parameters evolved over millennia just to make the radical pair spin dynamics most sensitive to the field inclination? Our results indicate that coherent electron spin dynamics is unlikely to be sustained in more realistic scenarios [36,39] but the avian compass could still be sensitive. We suggest that the actual compass parameters need to be deduced from more in vivo or in vitro experiments on migratory avian species; comparison with the parameters presented here could help to fully clarify the role of electron spin coherence and the physical origin of the needle-like sensitivity characteristic.…”

“…The actual scenario would be different in nature but the conclusions of the analysis would hold. As a complementary work, a recent study has investigated the role of the relative orientation between the radical pair molecules [39]. We would also like to state that noise due to various sources in radical pair system also needs to be investigated thoroughly both experimentally and numerically.…”

“…Most of the radical pair studies have considered either one or two nuclei for hyperfine interaction [4,5,17,24,[29][30][31][32]. Radical pair studies with realistic number of nuclei in the hyperfine environment are limited [27,[33][34][35][36][37][38][39]. Moreover, the exact role of electron spin coherence and possible interplay between coherence and compass parameters in a multinuclei radical pair system is still unclear.…”

Cryptochrome magnetoreception: four tryptophans could be better than three

“…Hyperfine tensors, calculated by density functional methods [ 47 ], were rotated to match the relative orientations of FAD, Trp C and Trp D in the crystal structure of Cl Cry4a [ 37 , 48 ]. As the computational resources required for the simulations scale steeply with the number of spins, only a subset of the hyperfine interactions in the flavin and tryptophan radicals could be included.…”