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The quantum needle of the avian magnetic compass

  1. P. J. Horea,2
  1. aDepartment of Chemistry, Physical & Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom;
  2. bInstitut für Biologie und Umweltwissenschaften, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany;
  3. cResearch Centre for Neurosensory Sciences, University of Oldenburg, 26111 Oldenburg, Germany

  1. Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved March 1, 2016 (received for review January 8, 2016)

  1. Fig. 1.
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    Fig. 1.

    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).

  2. Fig. 2.
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    Fig. 2.

    Reaction yields of various radical pairs. (A) <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 for a [FAD•− TrpH•+] radical pair in which the transverse principal components of selected nitrogen hyperfine interactions (Axx and Ayy) were set to zero: for N5 (blue), N10 (red), and both N5 and N10 (green). <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 for the unmodified [FAD•− TrpH•+] is shown in black. In all cases, τ = 1 ms. For clarity, three of the traces have been offset vertically by 0.006 (green) and 0.003 (blue and red). (B) <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 for a [FAD•− Y•] radical pair in which radical Y• contains a single 14N nucleus with an axial hyperfine tensor with principal components (Axx, Ayy, Azz) = (0.0, 0.0, 1.0812) mT (modeled on N1 in TrpH•+). The radical pair lifetimes are as indicated (1–100 μs). The angle between the z axes of Y• and FAD•− was 45°; the intensity of the spike was found to decrease smoothly to zero as this angle was increased from 0° to 90°. For clarity, the five traces for τ < 100 μs have been offset vertically, from top to bottom, by 0.020, 0.016, 0.012, 0.008, and 0.004 respectively. (C) <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 for toy radical pairs, [X• Y•]. For the red, orange and green traces, X• contains a single 14N hyperfine tensor with principal components (Axx, Ayy, Azz) = (−0.0989, −0.0989, 1.7569) mT. For the blue and black traces, (Axx, Ayy, Azz) = (−0.2, −0.2, 1.7569) and (−0.4, −0.4, 1.7569) mT, respectively. In all five cases, Y• contains a single 14N nucleus with an axial hyperfine interaction: (Axx, Ayy, Azz) = (0.0, 0.0, 1.0812) mT. The two hyperfine tensors have parallel z axes. The radical pair lifetimes are as indicated (10, 33.3, 100 μs); ×2 and ×4 indicate the doubling and quadrupling of Axx and Ayy in X•. For clarity, three of the traces have been offset vertically by 0.03 (green) and 0.06 (orange and red).

  3. Fig. 3.
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    Fig. 3.

    Reaction yields of radical pairs with spin relaxation included. (A) The toy radical pair, [X• Y•]. X• has a single 14N nucleus with hyperfine components (Axx, Ayy, Azz) = (−0.2, −0.2, 1.7569) mT; Y• has a single 14N nucleus with hyperfine components (0.0, 0.0, 1.0812) mT. The two hyperfine tensors have parallel z axes. The radical pair lifetime is 10 μs. X• underwent 10° rotational jumps (i.e., β = 5°) around the y axis with rate constants kr between 3 × 1011 and 108 s−1, as indicated. (B) The [FAD•− Y•] radical pair. FAD•− has seven magnetic nuclei, as in Fig. 1. Y• has single 14N nucleus with hyperfine components (Axx, Ayy, Azz) = (0.0, 0.0, 1.0812) mT. The radical pair lifetime is 10 μs. FAD•− underwent 10° rotational jumps (i.e., β = 5°) around the y axis, with rate constants kr varying between 3 × 1011 and 109 s−1, as indicated. In A and B, the direction of the magnetic field (θ) is varied in the zx plane of the flavin ring system (Fig. 1A). Almost identical results were found for the zy plane.

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