Migratory birds have a light-dependent magnetic compass, the mechanism of which is thought to involve radical pairs formed photochemically in cryptochrome proteins in the retina. Theoretical descriptions of this compass have thus far been unable to account for the high precision with which birds are able to detect the direction of the Earth's magnetic field. Here we use coherent spin dynamics simulations to explore the behavior of realistic models of cryptochrome-based radical pairs. We show that when the spin coherence persists for longer than a few microseconds, the output of the sensor contains a sharp feature, referred to as a spike. The spike arises from avoided crossings of the quantum mechanical spin energy-levels of radicals formed in cryptochromes. Such a feature could deliver a heading precision sufficient to explain the navigational behavior of migratory birds in the wild. Our results (i) afford new insights into radical pair magnetoreception, (ii) suggest ways in which the performance of the compass could have been optimized by evolution, (iii) may provide the beginnings of an explanation for the magnetic disorientation of migratory birds exposed to anthropogenic electromagnetic noise, and (iv) suggest that radical pair magnetoreception may be more of a quantum biology phenomenon than previously realized. magnetic compass | magnetoreception | migratory birds | quantum biology | radical pair mechanism M igratory birds have a light-dependent magnetic compass (1-4). The primary sensory receptors are located in the eyes (2, 3, 5-7), and directional information is processed bilaterally in a small part of the forebrain accessed via the thalamofugal visual pathway. The evidence currently points to a chemical sensing mechanism based on photo-induced radical pairs in cryptochrome flavoproteins in the retina (8-18). Anisotropic magnetic interactions within the radicals are thought to give rise to intracellular levels of a cryptochrome signaling state that depend on the orientation of the bird's head in the Earth's magnetic field (8,9,19). In support of this proposal, the photochemistry of isolated cryptochromes in vitro has been found to respond to applied magnetic fields in a manner that is quantitatively consistent with the radical pair mechanism (15). Aspects of the radical pair hypothesis have also been explored in a number of theoretical studies, the majority of which have concentrated on the magnitude of the anisotropic magnetic field effect (9,10,16,17,(19)(20)(21)(22)(23)(24)(25)(26)(27). Very little attention has been devoted to the matter we address here: the precision of the compass bearing available from a radical pair sensor (28).To migrate successfully over large distances, it is not sufficient simply to distinguish north from south (or poleward from equatorward) (29). A bar-tailed godwit (Limosa lapponica baueri), for example, was tracked by satellite flying from Alaska to New Zealand in a single 11,000-km nonstop flight across the Pacific Ocean (30). A directional error of more than a few degre...

The radical-pair mechanism has been put forward as the basis of the magnetic compass sense of migratory birds. Some of the strongest supporting evidence has come from behavioral experiments in which birds exposed to weak time-dependent magnetic fields lose their ability to orient in the geomagnetic field. However, conflicting results and skepticism about the requirement for abnormally long quantum coherence lifetimes have cast a shroud of uncertainty over these potentially pivotal studies. Using a recently developed computational approach, we explore the effects of various radiofrequency magnetic fields on biologically plausible radicals within the theoretical framework of radical-pair magnetoreception. We conclude that the current model of radical-pair magnetoreception is unable to explain the findings of the reported behavioral experiments. Assuming that an unknown mechanism amplifies the predicted effects, we suggest experimental conditions that have the potential to distinguish convincingly between the two distinct families of radical pairs currently postulated as magnetic compass sensors. We end by making recommendations for experimental protocols that we hope will increase the chance that future experiments can be independently replicated.

Night-migratory songbirds appear to sense the direction of the Earth's magnetic field via radical pair intermediates formed photochemically in cryptochrome flavoproteins contained in photoreceptor cells in their retinas. It is an open question whether this light-dependent mechanism could be sufficiently sensitive given the low-light levels experienced by nocturnal migrants. The scarcity of available photons results in significant uncertainty in the signal generated by the magnetoreceptors distributed around the retina. Here we use results from Information Theory to obtain a lower bound estimate of the precision with which a bird could orient itself using only geomagnetic cues. Our approach bypasses the current lack of knowledge about magnetic signal transduction and processing in vivo by computing the best-case compass precision under conditions where photons are in short supply. We use this method to assess the performance of three plausible cryptochrome-derived flavin-containing radical pairs as potential magnetoreceptors.

According to the currently prevailing theory, the magnetic compass sense in night-migrating birds relies on a light-dependent radical-pair-based mechanism. It has been shown that radio waves at megahertz frequencies disrupt magnetic orientation in migratory birds, providing evidence for a quantum-mechanical origin of the magnetic compass. Still, many crucial properties, e.g. the lifetime of the proposed magnetically sensitive radical pair, remain unknown. The current study aims to estimate the spin coherence time of the radical pair, based on the behavioural responses of migratory birds to broadband electromagnetic fields covering the frequency band 0.1–100 kHz. A finding that the birds were unable to use their magnetic compass under these conditions would imply surprisingly long-lived (greater than 10 µs) spin coherence. However, we observed no effect of 0.1–100 kHz radiofrequency (RF) fields on the orientation of night-migratory Eurasian blackcaps ( Sylvia atricapilla ). This suggests that the lifetime of the spin coherence involved in magnetoreception is shorter than the period of the highest frequency RF fields used in this experiment (i.e. approx. 10 µs). This result, in combination with an earlier study showing that 20–450 kHz electromagnetic fields disrupt magnetic compass orientation, suggests that the spin coherence lifetime of the magnetically sensitive radical pair is in the range 2–10 µs.

We present a new method for calculating the product yield of a radical pair recombination reaction in the presence of a weak time-dependent magnetic field. This method successfully circumvents the computational difficulties presented by a direct solution of the Liouville-von Neumann equation for a long-lived radical pair containing many hyperfine-coupled nuclear spins. Using a modified formulation of Floquet theory, treating the time-dependent magnetic field as a perturbation, and exploiting the slow radical pair recombination, we show that one can obtain a good approximation to the product yield by considering only nearly degenerate sub-spaces of the Floquet space. Within a significant parameter range, the resulting method is found to give product yields in good agreement with exact quantum mechanical results for a variety of simple model radical pairs. Moreover it is considerably more efficient than the exact calculation, and it can be applied to radical pairs containing significantly more nuclear spins. This promises to open the door to realistic theoretical investigations of the effect of radiofrequency electromagnetic radiation on the photochemically induced radical pair recombination reactions in the avian retina which are believed to be responsible for the magnetic compass sense of migratory birds. Published by AIP Publishing. [http://dx