Spin relaxation of radicals in cryptochrome and its role in avian magnetoreception

Long-lived spin coherence and rotationally ordered radical pairs have previously been identified as key requirements for the radical pair mechanism of the avian magnetic compass sense. Both criteria are hard to meet in a biological environment, where thermal motion of the radicals creates dynamic disorder and drives efficient spin relaxation. This has long been cited as a major stumbling block of the radical pair hypothesis. Here we combine Redfield relaxation theory with analytical solutions to a rotational diffusion equation to assess the impact of restricted rotational motion of the radicals on the operation of the compass. The effects of such motions are first investigated generally in small, model systems and are then critically examined in the magnetically sensitive flavin-tryptophan radical pair that is formed photochemically in the proposed magnetoreceptor protein, cryptochrome. We conclude that relaxation is slowest when rotational motion of the radicals within the protein is fast and highly constrained; that in a regime of slow relaxation, the motional averaging of hyperfine interactions has the potential to improve the sensitivity of the compass; and that consideration of motional effects can significantly alter the design criteria for an optimal compass. In addition, we demonstrate that motion of the flavin radical is likely to be compatible with its role as a component of a functioning radical-pair compass, whereas the motion of the tryptophan radical is less ideal, unless it is particularly fast