Reaction yields of a [FAD•− TrpH•+] radical pair. (A) The axis system used in the simulations superimposed on the tricyclic flavin ring system. (B) The variation of <mml:math><mml:mrow><mml:msub><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub></mml:mrow></mml:math>ΦS with θ for radical pairs with lifetimes between 1 and 100 μs. For clarity, two of the traces have been offset vertically:
by −0.001 (light green) and −0.002 (red). θ specifies the direction of the magnetic field in the zx plane of the flavin. (C) The same data as in B (1- to 20-μs lifetimes) presented as 2D polar plots. In each case, only the anisotropic part of <mml:math><mml:mrow><mml:msub><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub></mml:mrow></mml:math>ΦS is shown, with red and blue indicating values, respectively, larger and smaller than the isotropic value. The five plots
are drawn on the same scale. The blue features at θ = ±90° (labeled <mml:math><mml:mo>∗</mml:mo></mml:math>∗ in the 20-μs plot) are the spikes. (D) The anisotropic part of <mml:math><mml:mrow><mml:msub><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub></mml:mrow></mml:math>ΦS (10-μs lifetime) presented as a 3D polar plot. A circle in the xy plane (θ = 90°) is included as a guide to the eye. The blue disk in the xy plane (labeled <mml:math><mml:mo>∗</mml:mo></mml:math>∗) gives rise to the spike. The smaller blue disk, labeled # (also in C), angled at ∼40° to the xy plane, comes principally from the N1 indole nitrogen of TrpH•+. Its tilt reflects the orientation of the indole group of the tryptophan relative to the flavin (42, 43). (E) Visual modulation patterns calculated from <mml:math><mml:mrow><mml:msub><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub></mml:mrow></mml:math>ΦS (1- to 20-μs lifetimes) representing the directional information available from an array of cryptochrome-containing magnetoreceptor
cells distributed around the retina. The bright spot in the lower half of the pattern arises from the spike. (F) 3D polar plot of <mml:math><mml:mrow><mml:msub><mml:mi mathvariant="normal">Φ</mml:mi><mml:mi mathvariant="normal">S</mml:mi></mml:msub></mml:mrow></mml:math>ΦS (10-μs lifetime) averaged over a 360° rotation around an axis in the xy plane. This object has been rotated by 90° relative to D and scaled up by a factor of 2.1. The patterns in E were calculated using the same averaging procedure (SI Appendix, Section S6).
