The cryptochrome protein located in the retina of migratory song birds, currently thought to be the source of the avian magnetic compass, is not a stationary or frozen structure; it is expected to be anchored inside the cells of the birds such that overall translational and rotational motion is limited, but the protein continually undergoes thermal motion which causes small fluctuations in the overall structure of the protein. Such thermal motion induces so-called spin relaxation in the radical pair, once a radical pair has been generated in cryptochrome.
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Coherence and spin relaxation
Once a radical pair is generated within cryptochrome, it will be generated in an entangled quantum state, such as the singlet state. Entangled states are characterized by a large coherence between the two involved electrons: one electron cannot be described without describing the other electron at the same time, i.e. the two electrons are not independent of each other but must be considered part of the same physical entity. Such coherence between particles is a quantum mechanical phenomenon without any macroscopic analogue.
Coherent states are highly non-equilibrium states, and as such they will tend to relax towards an equilibrium state where the two electrons can again be considered two completely independent particles, i.e. a state without any coherence. The physical process that makes the system - the radical pair quantum state - tend towards thermal equilibrium is spin relaxation, thus it is an effect of the thermal motions in the protein. Since spin relaxation is a process that removes coherences from the radical pair, it is also often referred to as decoherence which is the more generally used term when considering interactions between arbitrary quantum systems and their interactions with their environment (so-call open quantum systems).
Spin relaxation in Arabidopsis thaliana cryptochrome
The thermal motion in a protein can be investigated through molecular dynamics simulations, provided that a three-dimensional structure of the protein is available. Such a structure is available for cryptochrome1 from the plant Arabidopsis thaliana, and therefore this specific cryptochrome was simulated. The thermal motion of the FAD and tryptophan radicals in this cryptochrome were obtained from the simulation, and this information was used in spin dynamics calculations. The conclusion of most of those calculations was that spin relaxation processes - thermal motion of cryptochrome - decreases the sensivity of a radical pair-based compass sensor.
This conclusion was mainly seen for modulation of the hyperfine interactions (between electronic spin and the spin of magnetic atomic nuclei) by thermal motion, but the inter-radical interactions, the exchange and magnetic dipole-dipole interactions, may actually enhance the sensitivity of a radical pair-based magnetosensor in some special cases due to modulation of the interactions by thermal motion. Thus spin relaxation is not exclusively a mechanism that diminishes compass sensitivity, and it is possible that nature has taken advantage of this fact throughout evolution of the avian magnetic compass.
Theoretical treatment of spin relaxation
The effect of thermal motion is that certain interactions become time-dependent; for example the hyperfine interactions between the spin of the unpaired electron in a radical and the magnetic moments of nearby magnetic atomic nuclei could change over time as the atoms move around. Solving equations such as the Liouville-von Neumann equation with interactions possessing a complex time-dependence becomes too computationally expensive when the effect of a realistic amount of magnetic nuclei are to be accounted for. Thus it is common to use so-called Redfield theory to describe the effects of fluctuating interactions, as it removes the explicit time-dependence from the equations.