Effects of Dynamical Degrees of Freedom on Magnetic Compass Sensitivity: A Comparison of Plant and Avian Cryptochromes

The magnetic compass of migratory birds is thought to rely on a radical pair reaction inside the blue-light photoreceptor protein cryptochrome. The sensitivity of such a sensor to weak external magnetic fields is determined by a variety of magnetic interactions, including electron-nuclear hyperfine interactions. Here, we investigate the implications of thermal motion, focusing on fluctuations in the dihedral and librational angles of flavin adenine dinucleotide (FAD) and tryptophan (Trp) radicals in cryptochrome 4a from European robin (Erithacus rubecula, ErCry4a) and pigeon (Columba livia, ClCry4a) and cryptochrome 1 from the plant Arabidopsis thaliana (AtCry1). Molecular dynamics simulations and density functional theory-derived hyperfine interactions are used to calculate the quantum yield of radical pair recombination dependent on the direction of the geomagnetic field. This quantity and various dynamical parameters are compared for [FAD center dot- Trp center dot+] in ErCry4a, ClCry4a, and AtCry1, with TrpC or TrpD being the third and fourth components of the tryptophan triad/tetrad in the respective proteins. We find that (i) differences in the average dihedral angles in the radical pairs are small, (ii) the librational motions of TrpC center dot+ in the avian cryptochromes are appreciably smaller than in AtCry1, (iii) the rapid vibrational motions of the radicals leading to strong fluctuations in the hyperfine couplings affect the spin dynamics depending on the usage of instantaneous or time-averaged interactions. Future investigations of radical pair compass sensitivity should therefore not be based on single snapshots of the protein structure but should include the ensemble properties of the hyperfine interactions.