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...

Billions of migratory birds navigate thousands of kilometres every year aided by a magnetic compass sense, the biophysical mechanism of which is unclear. One leading hypothesis is that absorption of light by specialized photoreceptors in the retina produces short-lived chemical intermediates known as radical pairs whose chemistry is sensitive to tiny magnetic interactions. A potentially serious but largely ignored obstacle to this theory is how directional information derived from the Earth's magnetic field can be separated from the much stronger variations in the intensity and polarization of the incident light. Here we propose a simple solution in which these extraneous effects are cancelled by taking the ratio of the signals from two neighbouring populations of magnetoreceptors. Geometric and biological arguments are used to derive a set of conditions that make this possible. We argue that one likely location of the magnetoreceptor molecules would be in association with ordered opsin dimers in the membrane discs of the outer segments of double-cone photoreceptor cells.

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.

Photosynthetic organisms use networks of chromophores to absorb and deliver solar energy to reaction centres. We present a detailed model of the light-harvesting complexes in purple bacteria, including explicit interaction with sunlight; radiative and non-radiative energy loss; and dephasing and thermalizing effects of coupling to a vibrational bath. We capture the effect of slow vibrations by introducing time-dependent disorder. Our model describes the experimentally observed high efficiency of light harvesting, despite the absence of long-range quantum coherence. The one-exciton part of the quantum state fluctuates continuously, but remains highly mixed at all times.These results suggest a relatively minor role for structure in determining efficiency. We build hypothetical models with randomly arranged chromophores, but still observe high efficiency when nearest-neighbour distances are comparable to those in nature. This helps explain the high transport efficiency in organisms with widely differing antenna structures, and suggests new design criteria for artificial light-harvesting devices.

Delta-self-consistent field theory (∆SCF) is a conceptually simple and computationally inexpensive method for finding excited states. Using the maximum overlap method to guide optimization of the excited state, ∆SCF has been shown to predict excitation energies with a level of accuracy that is competitive with, and sometimes better than, that of TDDFT. Here we benchmark ∆SCF on a larger set of molecules than has previously been considered, and, in particular, we examine the performance of ∆SCF in predicting transition dipole moments, the essential quantity for spectral intensities. A potential downfall for ∆SCF transition dipoles is origin dependence induced by the nonorthogonality of ∆SCF ground and excited states. We propose and test the simplest correction for this problem, based on symmetric orthogonalization of the states, and demonstrate its use on bacteriochlorophyll structures sampled from the photosynthetic antenna in purple bacteria.