Order, motion and relaxation in radical pair compass magnetoreception

Traditionally, biological systems are thought to be governed by classical, rather than quantum behaviour. In the warm, aqueous environment of a cell, the thermal energy kBT is much larger than the spacing of quantum energy levels and there are many processes, such as molecular motion, that can rapidly destroy delicate quantum coherences. An exception may be the remarkable ability of birds to navigate using the Earth's pervasive but extremely weak magnetic field; an ability that is thought to depend on the spin-selective reactions of photochemically-generated radical pair species. Despite substantial (although inconclusive) evidence pointing towards a radical pair mechanism of avian magnetoreception, whether, and how, spin coherence can be maintained long enough to produce a field-dependent compass signal remains a key question. It becomes even more critical in light of recent work, presented in this thesis, showing that coherence lifetimes > 10 microseconds reveal `spiky' features in the compass signal that could explain the astonishing precision of the avian compass and its sensitivity to radiofrequency noise. In the first half of this thesis, two different models are used to explore the resilience of the compass to restricted rotational motion of individual radicals, with a focus on the flavin and tryptophan radicals in the proposed magnetoreceptor, cryptochrome. Fast, highly constrained motion is found to be crucial for the flavin radical, whilst the tryptophan radical can be allowed greater motional freedom, in keeping with its position near the surface of the protein. However, even in an optimised system, very little compass information is likely to survive in the presence of realistic relaxation, suggesting that our current understanding of the radical-pair mechanism may be incomplete. Chapter 7 investigates how relaxation effects could be exploited to probe the function of cryptochrome. An experiment in which relaxation rates are locally enhanced by the presence of the biomimetic, superparamagnetic nanoparticle magnetoferritin is proposed and assessed. This experiment could provide much-needed evidence for the identity of the magnetoreceptor, allowing for more focused investigation of the compass mechanism. Finally, the requirements for highly restricted motion and long-range ordering of the magnetoreceptors make the radical pair compass inherently sensitive to polarized light. This is potentially problematic because natural variations in skylight polarization could compromise detection of the magnetic field. A combination of algebraic and biological arguments are used to demonstrate how unwanted information can be filtered out of the compass signal by taking the ratio of signals from two neighbouring cells related by a 180° rotation about their line-of-sight. The combination of magnetic field patterns from the two cells additionally helps to pinpoint a precise heading.