The arrangement of anisotropic spin couplings can optimize sensitivity of the cryptochrome radical pair to the direction of geomagnetic field

Sensing of the geomagnetic field direction by many living organisms is commonly thought to involve radical pairs, such as those formed photochemically between the flavin and tryptophan radicals in the cryptochrome proteins. Previous theoretical studies have shown that strongly axial hyperfine couplings in the cryptochrome radicals greatly enhance the formation of a signaling state of the protein when the magnetic field is directed perpendicular to the hyperfine axis of either of the radicals. However, further analysis led to the conclusion that sharpness of detecting those magnetic directions is strongly suppressed by the inter-radical electron spin coupling. Here, we perform theoretical simulations of the compass function for a set of arrangements of the intra- and inter-radical spin couplings in the idealized cryptochrome radical pair, and find certain arrangements that preserve the sharpness in detecting the direction of the geomagnetic field. One particular arrangement, with the hyperfine axes of the radicals orthogonal to the symmetry axis of inter-radical coupling, provides even sharper field-direction sensitivity than that contributed solely by the anisotropy of the hyperfine coupling.