Conditions for EPR detection of chirality-induced spin selectivity in spin-polarized radical pairs in isotropic solution

Chiral molecules can act as spin filters, preferentially transmitting electrons with spins polarized along their direction of travel, an effect known as chirality-induced spin selectivity (CISS). In a typical experiment, injected electrons tunnel coherently through a layer of chiral material and emerge spin-polarized. It is also possible that spin polarization arises in radical pairs formed photochemically when electrons hop incoherently between donor and acceptor sites. Here we aim to identify the magnetic properties that would optimise the visibility of CISS polarization in time-resolved electron paramagnetic resonance (EPR) spectra of transient radical pairs without the need to orient or align their precursors. By simulating spectra of actual and model systems, we find that CISS contributions to the polarization should be most obvious when at least one of the radicals has small g-anisotropy and an inhomogeneous linewidth larger than the dipolar coupling of the two radicals. Under these conditions there is extensive cancellation of absorptive and emissive enhancements making the spectrum sensitive to small changes in the individual EPR line intensities. Although these cancellation effects are more pronounced at lower spectrometer frequencies, the spectral changes are easier to appreciate with the enhanced resolution afforded by high-frequency EPR. Consideration of published spectra of light-induced radical pairs in photosynthetic bacterial reaction centres reveals no significant CISS component in the polarization generated by the conventional spin-correlated radical pair mechanism.

Singlet-triplet dephasing in radical pairs in avian cryptochromes leads to time-dependent magnetic field effects

Cryptochrome 4a (Cry4a) has been proposed as the sensor at the heart of the magnetic compass in migratory songbirds. Blue-light excitation of this protein produces magnetically sensitive flavin-tryptophan radical pairs whose properties suggest that Cry4a could indeed be suitable as a magnetoreceptor. Here, we use cavity ring-down spectroscopy to measure magnetic field effects on the kinetics of these radical pairs in modified Cry4a proteins from the migratory European robin and from nonmigratory pigeon and chicken. B1/2, a parameter that characterizes the magnetic field-dependence of the reactions, was found to be larger than expected on the basis of hyperfine interactions and to increase with the delay between pump and probe laser pulses. Semiclassical spin dynamics simulations show that this behavior is consistent with a singlet-triplet dephasing (STD) relaxation mechanism. Analysis of the experimental data gives dephasing rate constants, rSTD, in the range 3-6 × 107 s-1. A simple "toy" model due to Maeda, Miura, and Arai [Mol. Phys. 104, 1779-1788 (2006)] is used to shed light on the origin of the time-dependence and the nature of the STD mechanism. Under the conditions of the experiments, STD results in an exponential approach to spin equilibrium at a rate considerably slower than rSTD. We attribute the loss of singlet-triplet coherence to electron hopping between the second and third tryptophans of the electron transfer chain and comment on whether this process could explain differences in the magnetic sensitivity of robin, chicken, and pigeon Cry4a's.

No evidence for magnetic field effects on the behaviour of Drosophila

Migratory songbirds have the remarkable ability to extract directional information from the Earth's magnetic field1,2. The exact mechanism of this light-dependent magnetic compass sense, however, is not fully understood. The most promising hypothesis focuses on the quantum spin dynamics of transient radical pairs formed in cryptochrome proteins in the retina3-5. Frustratingly, much of the supporting evidence for this theory is circumstantial, largely because of the extreme challenges posed by genetic modification of wild birds. Drosophila has therefore been recruited as a model organism, and several influential reports of cryptochrome-mediated magnetic field effects on fly behaviour have been widely interpreted as support for a radical pair-based mechanism in birds6-23. Here we report the results of an extensive study testing magnetic field effects on 97,658 flies moving in a two-arm maze and on 10,960 flies performing the spontaneous escape behaviour known as negative geotaxis. Under meticulously controlled conditions and with vast sample sizes, we have been unable to find evidence for magnetically sensitive behaviour in Drosophila. Moreover, after reassessment of the statistical approaches and sample sizes used in the studies that we tried to replicate, we suggest that many-if not all-of the original results were false positives. Our findings therefore cast considerable doubt on the existence of magnetic sensing in Drosophila and thus strongly suggest that night-migratory songbirds remain the organism of choice for elucidating the mechanism of light-dependent magnetoreception.

Upper bound for broadband radiofrequency field disruption of magnetic compass orientation in night-migratory songbirds

Night-migratory songbirds have a light-dependent magnetic compass sense, the mechanism of which is thought to depend on the photochemical formation of radical pairs in cryptochrome (Cry) proteins located in the retina. The finding that weak radiofrequency (RF) electromagnetic fields can prevent birds from orienting in the Earth's magnetic field has been regarded as a diagnostic test for this mechanism and as a potential source of information on the identities of the radicals. The maximum frequency that could cause such disorientation has been predicted to lie between 120 and 220 MHz for a flavin-tryptophan radical pair in Cry. Here we show that the magnetic orientation capabilities of Eurasian blackcaps (Sylvia atricapilla) are not affected by RF noise in the frequency bands 140 to 150 MHz and 235 to 245 MHz. From a consideration of its internal magnetic interactions, we argue that RF field effects on a flavin-containing radical-pair sensor should be approximately independent of frequency up to 116 MHz and that birds' sensitivity to RF disorientation should fall by about two orders of magnitude when the frequency exceeds 116 MHz. Taken together with our earlier finding that 75 to 85 MHz RF fields disrupt the magnetic orientation of blackcaps, these results provide compelling evidence that the magnetic compass of migratory birds operates by a radical pair mechanism.

Dimerization of European Robin Cryptochrome 4a

Homo-dimer formation is important for the function of many proteins. Although dimeric forms of cryptochromes (Cry) have been found by crystallography and were recently observed in vitro for European robin Cry4a, little is known about the dimerization of avian Crys and the role it could play in the mechanism of magnetic sensing in migratory birds. Here, we present a combined experimental and computational investigation of the dimerization of robin Cry4a resulting from covalent and non-covalent interactions. Experimental studies using native mass spectrometry, mass spectrometric analysis of disulfide bonds, chemical cross-linking, and photometric measurements show that disulfide-linked dimers are routinely formed, that their formation is promoted by exposure to blue light, and that the most likely cysteines are C317 and C412. Computational modeling and molecular dynamics simulations were used to generate and assess a number of possible dimer structures. The relevance of these findings to the proposed role of Cry4a in avian magnetoreception is discussed.

Modeling spin relaxation in complex radical systems using MolSpin

Spin relaxation is an important aspect of the spin dynamics of free radicals and can have a significant impact on the outcome of their spin-selective reactions. Examples range from the use of radicals as spin qubits in quantum information processing to the radical pair reactions in proteins that may allow migratory birds to sense the direction of the Earth's magnetic field. Accurate modeling of spin relaxation, however, is non-trivial. Bloch-Redfield-Wangsness theory derives a quantum mechanical master equation from system-bath interactions in the Markovian limit that provides a comprehensive framework for describing spin relaxation. Unfortunately, the construction of the master equation is system-specific and often resource-heavy. To address this challenge, we introduce a generalized and efficient implementation of BRW theory as a new feature of the spin dynamics toolkit MolSpin which offers an easy-to-use approach for studying systems of reacting radicals of varying complexity.

Isotope Substitution Effects on the Magnetic Compass Properties of Cryptochrome-Based Radical Pairs: A Computational Study

The biophysical mechanism of the magnetic compass sense of migratory songbirds is thought to rely on the photochemical reactions of flavin-containing radical pairs in cryptochrome proteins located in the birds' eyes. A consequence of this hypothesis is that the effect of the Earth's magnetic field on the quantum yields of reaction products should be sensitive to isotopic substitutions that modify the hyperfine interactions in the radicals. In this report, we use spin dynamics simulations to explore the effects of ¹H → ²H, ¹²C → ¹³C, and ¹⁴N → ¹⁵N isotopic substitutions on the functioning of cryptochrome 4a as a magnetic direction sensor. Two main conclusions emerge. (1) Uniform deuteration of the flavin chromophore appears to be the best way to boost the anisotropy of the magnetic field effect and to change its symmetry. (2) ¹³C substitution of three of the 12 flavin carbons, in particular C4, C4a, and C8α, seems to be the best recipe for attenuating the anisotropy. These predictions should give insight into the factors that control the magnetic sensitivity once spectroscopic techniques are available for measuring magnetic field effects on oriented protein samples.

Magnetic field effects on radical pair reactions: estimation of B1/2 for flavin-tryptophan radical pairs in cryptochromes

Magnetic field effects on the yields of radical pair reactions are often characterised by the "half-field" parameter, B_1/2, which encodes useful information on spin relaxation, radical recombination kinetics and electron-electron couplings as well as electron-nuclear hyperfine interactions. Here we use a variety of spin dynamics simulation methods to estimate the hyperfine-only values of B_1/2 for the flavin-tryptophan radical pair, [FAD˙^- TrpH˙⁺], thought to be the detector in the magnetic compass sense of migratory songbirds. The main findings are: (a) in the absence of fast recombination and spin relaxation, [FAD˙^- TrpH˙⁺] radical pairs in solution and in the putative magnetoreceptor protein, cryptochrome, have B_1/2 ≈ 1.89 mT and 2.46 mT, respectively. (b) The widely used expression for B_1/2 due to Weller et al. (Chem. Phys. Lett, 1983, 96, 24-27) is only applicable to small, short-lived (∼5 ns), rapidly tumbling radical pairs in solution, and is quantitatively unreliable in the context of magnetoreception. (c) In the absence of molecular tumbling, the low-field effect for [FAD˙^- TrpH˙⁺] is predicted to be abolished by the anisotropic components of the hyperfine interactions. Armed with the 2.46 mT "base value" for cryptochrome, measurements of B_1/2 can be used to understand the impact of spin relaxation on its performance as a magnetic compass sensor.

Radical quantum oscillations

[Figure: see text].

Cryptochrome magnetoreception: four tryptophans could be better than three

The biophysical mechanism of the magnetic compass sensor in migratory songbirds is thought to involve photo-induced radical pairs formed in cryptochrome (Cry) flavoproteins located in photoreceptor cells in the eyes. In Cry4a-the most likely of the six known avian Crys to have a magnetic sensing function-four radical pair states are formed sequentially by the stepwise transfer of an electron along a chain of four tryptophan residues to the photo-excited flavin. In purified Cry4a from the migratory European robin, the third of these flavin-tryptophan radical pairs is more magnetically sensitive than the fourth, consistent with the smaller separation of the radicals in the former. Here, we explore the idea that these two radical pair states of Cry4a could exist in rapid dynamic equilibrium such that the key magnetic and kinetic properties are weighted averages. Spin dynamics simulations suggest that the third radical pair is largely responsible for magnetic sensing while the fourth may be better placed to initiate magnetic signalling particularly if the terminal tryptophan radical can be reduced by a nearby tyrosine. Such an arrangement could have allowed independent optimization of the essential sensing and signalling functions of the protein. It might also rationalize why avian Cry4a has four tryptophans while Crys from plants have only three.

Nuclear polarization effects in cryptochrome-based magnetoreception

The mechanism of the magnetic compass sense of migratory songbirds is thought to involve magnetically sensitive chemical reactions of light-induced radical pairs in cryptochrome proteins located in the birds' eyes. However, it is not yet clear whether this mechanism would be sensitive enough to form the basis of a viable compass. In the present work, we report spin dynamics simulations of models of cryptochrome-based radical pairs to assess whether accumulation of nuclear spin polarization in multiple photocycles could lead to significant enhancements in the sensitivity with which the proteins respond to the direction of the geomagnetic field. Although buildup of nuclear polarization appears to offer sensitivity advantages in the more idealized model systems studied, we find that these enhancements do not carry over to conditions that more closely resemble the situation thought to exist in vivo. On the basis of these simulations, we conclude that buildup of nuclear polarization seems unlikely to be a source of significant improvements in the performance of cryptochrome-based radical pair magnetoreceptors.

Angular Precision of Radical Pair Compass Magnetoreceptors

The light-dependent magnetic compass sense of night-migratory songbirds is thought to rely on magnetically sensitive chemical reactions of radical pairs in cryptochrome proteins located in the birds' eyes. Recently, an information theory approach was developed that provides a strict lower bound on the precision with which a bird could estimate its head direction using only geomagnetic cues and a cryptochrome-based radical pair sensor. By means of this lower bound, we show here how the performance of the compass sense could be optimized by adjusting the orientation of cryptochrome molecules within photoreceptor cells, the distribution of cells around the retina, and the effects of the geomagnetic field on the photochemistry of the radical pair.

Viability of superoxide-containing radical pairs as magnetoreceptors

The ability of night-migratory songbirds to sense the direction of the Earth's magnetic field is increasingly attributed to a photochemical mechanism in which the magnetic field acts on transient radical pairs in cryptochrome flavoproteins located in the birds' eyes. The magnetically sensitive species is commonly assumed to be [FAD^•- TrpH^•+], formed by sequential light-induced intraprotein electron transfers from a chain of tryptophan residues to the flavin adenine dinucleotide chromophore. However, some evidence points to superoxide, O₂ ^•-, as an alternative partner for the flavin radical. The absence of hyperfine interactions in O₂ ^•- could lead to a more sensitive magnetic compass, but only if the electron spin relaxation of the O₂ ^•- radical is much slower than normally expected for a small mobile radical with an orbitally degenerate electronic ground state. In this study we use spin dynamics simulations to model the sensitivity of a flavin-superoxide radical pair to the direction of a 50 μT magnetic field. By varying parameters that characterize the local environment and molecular dynamics of the radicals, we identify the highly restrictive conditions under which a O₂ ^•--containing radical pair could form the basis of a geomagnetic compass sensor. We conclude that the involvement of superoxide in compass magnetoreception must remain highly speculative until further experimental evidence is forthcoming.

How quantum is radical pair magnetoreception?

Semiclassical methods cannot accurately simulate magnetic field effects relevant to avian magnetoreception, which may therefore deserve the label “quantum biology”.

Electromagnetic 0.1-100 kHz noise does not disrupt orientation in a night-migrating songbird implying a spin coherence lifetime of less than 10 µs

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.

Chemical compass behaviour at microtesla magnetic fields strengthens the radical pair hypothesis of avian magnetoreception

The fact that many animals, including migratory birds, use the Earth's magnetic field for orientation and compass-navigation is fascinating and puzzling in equal measure. The physical origin of these phenomena has not yet been fully understood, but arguably the most likely hypothesis is based on the radical pair mechanism (RPM). Whilst the theoretical framework of the RPM is well-established, most experimental investigations have been conducted at fields several orders of magnitude stronger than the Earth's. Here we use transient absorption spectroscopy to demonstrate a pronounced orientation-dependence of the magnetic field response of a molecular triad system in the field region relevant to avian magnetoreception. The chemical compass response exhibits the properties of an inclination compass as found in migratory birds. The results underline the feasibility of a radical pair based avian compass and also provide further guidelines for the design and operation of exploitable chemical compass systems.

Ultrafast flavin/tryptophan radical pair kinetics in a magnetically sensitive artificial protein

Radical pair formation and decay are implicated in a wide range of biological processes including avian magnetoreception. However, studying such biological radical pairs is complicated by both the complexity and relative fragility of natural systems. To resolve open questions about how natural flavin-amino acid radical pair systems are engineered, and to create new systems with novel properties, we developed a stable and highly adaptable de novo artificial protein system. These protein maquettes are designed with intentional simplicity and transparency to tolerate aggressive manipulations that are impractical or impossible in natural proteins. Here we characterize the ultrafast dynamics of a series of maquettes with differing electron-transfer distance between a covalently ligated flavin and a tryptophan in an environment free of other potential radical centers. We resolve the spectral signatures of the cysteine-ligated flavin singlet and triplet states and reveal the picosecond formation and recombination of singlet-born radical pairs. Magnetic field-sensitive triplet-born radical pair formation and recombination occurs at longer timescales. These results suggest that both triplet- and singlet-born radical pairs could be exploited as biological magnetic sensors.

Magnetocarcinogenesis: is there a mechanism for carcinogenic effects of weak magnetic fields?

Extremely low-frequency (ELF) magnetic fields have been classified as possibly carcinogenic, mainly based on rather consistent epidemiological findings suggesting a link between childhood leukaemia and 50-60 Hz magnetic fields from power lines. However, causality is not the only possible explanation for the epidemiological associations, as animal and in vitro experiments have provided only limited support for carcinogenic effects of ELF magnetic fields. Importantly, there is no generally accepted biophysical mechanism that could explain such effects. In this review, we discuss the possibility that carcinogenic effects are based on the radical pair mechanism (RPM), which seems to be involved in magnetoreception in birds and certain other animals, allowing navigation in the geomagnetic field. We review the current understanding of the RPM in magnetoreception, and discuss cryptochromes as the putative magnetosensitive molecules and their possible links to cancer-relevant biological processes. We then propose a hypothesis for explaining the link between ELF fields and childhood leukaemia, discuss the strengths and weaknesses of the current evidence, and make proposals for further research.

Upper bound on the biological effects of 50/60 Hz magnetic fields mediated by radical pairs

Prolonged exposure to weak (~1 μT) extremely-low-frequency (ELF, 50/60 Hz) magnetic fields has been associated with an increased risk of childhood leukaemia. One of the few biophysical mechanisms that might account for this link involves short-lived chemical reaction intermediates known as radical pairs. In this report, we use spin dynamics simulations to derive an upper bound of 10 parts per million on the effect of a 1 μT ELF magnetic field on the yield of a radical pair reaction. By comparing this figure with the corresponding effects of changes in the strength of the Earth’s magnetic field, we conclude that if exposure to such weak 50/60 Hz magnetic fields has any effect on human biology, and results from a radical pair mechanism, then the risk should be no greater than travelling a few kilometres towards or away from the geomagnetic north or south pole.

Posner qubits: spin dynamics of entangled Ca9(PO4)6 molecules and their role in neural processing

It has been suggested that 31P nuclear spins in Ca9(PO4)6 molecules could form the basis of a quantum mechanism for neural processing in the brain. A fundamental requirement of this proposal is that spins in different Ca9(PO4)6 molecules can become entangled and remain so for periods (estimated at many hours) that hugely exceed typical 31P spin relaxation times. Here, we consider the coherent and incoherent spin dynamics of Ca9(PO4)6 arising from dipolar and scalar spin-spin interactions and derive an upper bound of 37 min on the entanglement lifetime under idealized physiological conditions. We argue that the spin relaxation in Ca9(PO4)6 is likely to be much faster than this estimate.

Proposal to use superparamagnetic nanoparticles to test the role of cryptochrome in magnetoreception

Evidence is accumulating to support the hypothesis that some animals use light-induced radical pairs to detect the direction of the Earth's magnetic field. Cryptochrome proteins seem to be involved in the sensory pathway but it is not yet clear if they are the magnetic sensors: they could, instead, play a non-magnetic role as signal transducers downstream of the primary sensor. Here we propose an experiment with the potential to distinguish these functions. The principle is to use superparamagnetic nanoparticles to disable any magnetic sensing role by enhancing the electron spin relaxation of the radicals so as to destroy their spin correlation. We use spin dynamics simulations to show that magnetoferritin, a synthetic, protein-based nanoparticle, has the required properties. If cryptochrome is the primary sensor, then it should be inactivated by a magnetoferritin particle placed 12-16 nm away. This would prevent a bird from using its magnetic compass in behavioural tests and abolish magnetically sensitive neuronal firing in the retina. The key advantage of such an experiment is that any signal transduction role should be completely unaffected by the tiny magnetic interactions (≪kBT) required to enhance the spin relaxation of the radical pair.

Ascorbic acid may not be involved in cryptochrome-based magnetoreception

Seventeen years after it was originally suggested, the photoreceptor protein cryptochrome remains the most probable host for the radical pair intermediates that are thought to be the sensors in the avian magnetic compass. Although evidence in favour of this hypothesis is accumulating, the intracellular interaction partners of the sensory protein are still unknown. It has been suggested that ascorbate ions could interact with surface-exposed tryptophan radicals in photoactivated cryptochromes, and so lead to the formation of a radical pair comprised of the reduced form of the flavin adenine dinucleotide cofactor, FAD^•-, and the ascorbate radical, Asc^•- This species could provide a more sensitive compass than a FAD-tryptophan radical pair. In this study of Drosophila melanogaster cryptochrome and Erithacus rubecula (European robin) cryptochrome 1a, we use molecular dynamics simulations to characterize the transient encounters of ascorbate ions with tryptophan radicals in cryptochrome in order to assess the likelihood of the [FAD^•- Asc^•-]-pathway. It is shown that ascorbate ions are expected to bind near the tryptophan radicals for periods of a few nanoseconds. The rate at which these encounters happen is low, and it is therefore concluded that ascorbate ions are unlikely to be involved in magnetoreception if the ascorbate concentration is only of the order of 1 mM or less.

Magnetically Sensitive Radical Photochemistry of Non-natural Flavoproteins

It is a remarkable fact that ∼50 μT magnetic fields can alter the rates and yields of certain free-radical reactions and that such effects might be the basis of the light-dependent ability of migratory birds to sense the direction of the Earth's magnetic field. The most likely sensory molecule at the heart of this chemical compass is cryptochrome, a flavin-containing protein that undergoes intramolecular, blue-light-induced electron transfer to produce magnetically sensitive radical pairs. To learn more about the factors that control the magnetic sensitivity of cryptochromes, we have used a set of de novo designed protein maquettes that self-assemble as four-α-helical proteins incorporating a single tryptophan residue as an electron donor placed approximately 0.6, 1.1, or 1.7 nm away from a covalently attached riboflavin as chromophore and electron acceptor. Using a specifically developed form of cavity ring-down spectroscopy, we have characterized the photochemistry of these designed flavoprotein maquettes to determine the identities and kinetics of the transient radicals responsible for the magnetic field effects. Given the gross structural and dynamic differences from the natural proteins, it is remarkable that the maquettes show magnetic field effects that are so similar to those observed for cryptochromes.

A light-dependent magnetoreception mechanism insensitive to light intensity and polarization

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.

Disruption of Magnetic Compass Orientation in Migratory Birds by Radiofrequency Electromagnetic Fields

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.

Millitesla magnetic field effects on the photocycle of an animal cryptochrome

Drosophila have been used as model organisms to explore both the biophysical mechanisms of animal magnetoreception and the possibility that weak, low-frequency anthropogenic electromagnetic fields may have biological consequences. In both cases, the presumed receptor is cryptochrome, a protein thought to be responsible for magnetic compass sensing in migratory birds and a variety of magnetic behavioural responses in insects. Here, we demonstrate that photo-induced electron transfer reactions in Drosophila melanogaster cryptochrome are indeed influenced by magnetic fields of a few millitesla. The form of the protein containing flavin and tryptophan radicals shows kinetics that differ markedly from those of closely related members of the cryptochrome-photolyase family. These differences and the magnetic sensitivity of Drosophila cryptochrome are interpreted in terms of the radical pair mechanism and a photocycle involving the recently discovered fourth tryptophan electron donor.

Engineering an Artificial Flavoprotein Magnetosensor

Migratory birds use the Earth's magnetic field as a source of navigational information. This light-dependent magnetic compass is thought to be mediated by cryptochrome proteins in the retina. Upon light activation, electron transfer between the flavin adenine dinucleotide cofactor and tryptophan residues leads to the formation of a spin-correlated radical pair, whose subsequent fate is sensitive to external magnetic fields. To learn more about the functional requirements of this complex chemical compass, we have created a family of simplified, adaptable proteins-maquettes-that contain a single tryptophan residue at different distances from a covalently bound flavin. Despite the complete absence of structural resemblance to the native cryptochrome fold or sequence, the maquettes exhibit a strong magnetic field effect that rivals those observed in the natural proteins in vitro. These novel maquette designs offer unprecedented flexibility to explore the basic requirements for magnetic sensing in a protein environment.

The quantum needle of the avian magnetic compass

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.

Sensitive fluorescence-based detection of magnetic field effects in photoreactions of flavins

Magnetic field effect studies have been conducted on a variety of flavin-based radical pair systems chosen to model the magnetosensitivity of the photoinduced radical pairs found in cryptochrome flavoproteins. Cryptochromes are blue-light photoreceptor proteins which are thought to mediate avian magnetoreception, an hypothesis supported by recent in vitro observations of magnetic field-dependent reaction kinetics for a light-induced radical pair in a cryptochrome from the plant Arabidopsis thaliana. Many cryptochromes are difficult to express in large quantities or high concentrations and are easily photodegraded. Magnetic field effects are typically measured by spectroscopic detection of the transient radical (pair) concentrations. Due to its low sensitivity, single-pass transient absorption spectroscopy can be of limited use in such experiments and much recent work has involved development of other methodologies offering improved sensitivity. Here we explore the use of flavin fluorescence as the magnetosensitive probe and demonstrate the exceptional sensitivity of this technique which allows the detection of magnetic field effects in flavin samples at sub-nanomolar concentrations and in cryptochromes.

Electron spin relaxation in cryptochrome-based magnetoreception

The magnetic compass sense of migratory birds is thought to rely on magnetically sensitive radical pairs formed photochemically in cryptochrome proteins in the retina. An important requirement of this hypothesis is that electron spin relaxation is slow enough for the Earth's magnetic field to have a significant effect on the coherent spin dynamics of the radicals. It is generally assumed that evolutionary pressure has led to protection of the electron spins from irreversible loss of coherence in order that the underlying quantum dynamics can survive in a noisy biological environment. Here, we address this question for a structurally characterized model cryptochrome expected to share many properties with the putative avian receptor protein. To this end we combine all-atom molecular dynamics simulations, Bloch-Redfield relaxation theory and spin dynamics calculations to assess the effects of spin relaxation on the performance of the protein as a compass sensor. Both flavin-tryptophan and flavin-Z˙ radical pairs are studied (Z˙ is a radical with no hyperfine interactions). Relaxation is considered to arise from modulation of hyperfine interactions by librational motions of the radicals and fluctuations in certain dihedral angles. For Arabidopsis thaliana cryptochrome 1 (AtCry1) we find that spin relaxation implies optimal radical pair lifetimes of the order of microseconds, and that flavin-Z˙ pairs are less affected by relaxation than flavin-tryptophan pairs. Our results also demonstrate that spin relaxation in isolated AtCry1 is incompatible with the long coherence times that have been postulated to explain the disruption of the avian magnetic compass sense by weak radiofrequency magnetic fields. We conclude that a cryptochrome sensor in vivo would have to differ dynamically, if not structurally, from isolated AtCry1. Our results clearly mark the limits of the current hypothesis and lead to a better understanding of the operation of radical pair magnetic sensors in noisy biological environments.

Weak Broadband Electromagnetic Fields are More Disruptive to Magnetic Compass Orientation in a Night-Migratory Songbird (Erithacus rubecula) than Strong Narrow-Band Fields

Magnetic compass orientation in night-migratory songbirds is embedded in the visual system and seems to be based on a light-dependent radical pair mechanism. Recent findings suggest that both broadband electromagnetic fields ranging from ~2 kHz to ~9 MHz and narrow-band fields at the so-called Larmor frequency for a free electron in the Earth's magnetic field can disrupt this mechanism. However, due to local magnetic fields generated by nuclear spins, effects specific to the Larmor frequency are difficult to understand considering that the primary sensory molecule should be organic and probably a protein. We therefore constructed a purpose-built laboratory and tested the orientation capabilities of European robins in an electromagnetically silent environment, under the specific influence of four different oscillating narrow-band electromagnetic fields, at the Larmor frequency, double the Larmor frequency, 1.315 MHz or 50 Hz, and in the presence of broadband electromagnetic noise covering the range from ~2 kHz to ~9 MHz. Our results indicated that the magnetic compass orientation of European robins could not be disrupted by any of the relatively strong narrow-band electromagnetic fields employed here, but that the weak broadband field very efficiently disrupted their orientation.

Chemical amplification of magnetic field effects relevant to avian magnetoreception

Magnetic fields as weak as the Earth's can change the yields of radical pair reactions even though the energies involved are orders of magnitude smaller than the thermal energy, kBT, at room temperature. Proposed as the source of the light-dependent magnetic compass in migratory birds, the radical pair mechanism is thought to operate in cryptochrome flavoproteins in the retina. Here we demonstrate that the primary magnetic field effect on flavin photoreactions can be amplified chemically by slow radical termination reactions under conditions of continuous photoexcitation. The nature and origin of the amplification are revealed by studies of the intermolecular flavin-tryptophan and flavin-ascorbic acid photocycles and the closely related intramolecular flavin-tryptophan radical pair in cryptochrome. Amplification factors of up to 5.6 were observed for magnetic fields weaker than 1 mT. Substantial chemical amplification could have a significant impact on the viability of a cryptochrome-based magnetic compass sensor.

Asymmetric recombination and electron spin relaxation in the semiclassical theory of radical pair reactions

We describe how the semiclassical theory of radical pair recombination reactions recently introduced by two of us [D. E. Manolopoulos and P. J. Hore, J. Chem. Phys. 139, 124106 (2013)] can be generalised to allow for different singlet and triplet recombination rates. This is a non-trivial generalisation because when the recombination rates are different the recombination process is dynamically coupled to the coherent electron spin dynamics of the radical pair. Furthermore, because the recombination operator is a two-electron operator, it is no longer sufficient simply to consider the two electrons as classical vectors: one has to consider the complete set of 16 two-electron spin operators as independent classical variables. The resulting semiclassical theory is first validated by comparison with exact quantum mechanical results for a model radical pair containing 12 nuclear spins. It is then used to shed light on the spin dynamics of a carotenoid-porphyrin-fullerene triad containing considerably more nuclear spins which has recently been used to establish a "proof of principle" for the operation of a chemical compass [K. Maeda, K. B. Henbest, F. Cintolesi, I. Kuprov, C. T. Rodgers, P. A. Liddell, D. Gust, C. R. Timmel, and P. J. Hore, Nature (London) 453, 387 (2008)]. We find in particular that the intriguing biphasic behaviour that has been observed in the effect of an Earth-strength magnetic field on the time-dependent survival probability of the photo-excited C(·+)PF(·-) radical pair arises from a delicate balance between its asymmetric recombination and the relaxation of the electron spin in the carotenoid radical.

Fluorescence-detected magnetic field effects on radical pair reactions from femtolitre volumes

We show that the effects of applied magnetic fields on radical pair reactions can be sensitively measured from sample volumes as low as ∼100 femtolitres using total internal reflection fluorescence microscopy. Development of a fluorescence-based microscope method is likely to be a key step in further miniaturisation that will allow detection of magnetic field effects on single molecules.

Probing a chemical compass: novel variants of low-frequency reaction yield detected magnetic resonance

We present a study of a carotenoid-porphyrin-fullerene triad previously shown to function as a chemical compass: the photogenerated carotenoid-fullerene radical pair recombines at a rate sensitive to the orientation of an applied magnetic field. To characterize the system we develop a time-resolved Low-Frequency Reaction Yield Detected Magnetic Resonance (tr-LF-RYDMR) technique; the effect of varying the relative orientation of applied static and 36 MHz oscillating magnetic fields is shown to be strongly dependent on the strength of the oscillating magnetic field. RYDMR is a diagnostic test for involvement of the radical pair mechanism in the magnetic field sensitivity of reaction rates or yields, and has previously been applied in animal behavioural experiments to verify the involvement of radical-pair-based intermediates in the magnetic compass sense of migratory birds. The spectroscopic selection rules governing RYDMR are well understood at microwave frequencies for which the so-called 'high-field approximation' is valid, but at lower frequencies different models are required. For example, the breakdown of the rotating frame approximation has recently been investigated, but less attention has so far been given to orientation effects. Here we gain physical insights into the interplay of the different magnetic interactions affecting low-frequency RYDMR experiments performed in the challenging regime in which static and oscillating applied magnetic fields as well as internal electron-nuclear hyperfine interactions are of comparable magnitude. Our observations aid the interpretation of existing RYDMR-based animal behavioural studies and will inform future applications of the technique to verify and characterize further the biological receptors involved in avian magnetoreception.

Alternative radical pairs for cryptochrome-based magnetoreception

There is growing evidence that the remarkable ability of animals, in particular birds, to sense the direction of the Earth's magnetic field relies on magnetically sensitive photochemical reactions of the protein cryptochrome. It is generally assumed that the magnetic field acts on the radical pair [FAD•- TrpH•+] formed by the transfer of an electron from a group of three tryptophan residues to the photo-excited flavin adenine dinucleotide cofactor within the protein. Here, we examine the suitability of an [FAD•- Z•] radical pair as a compass magnetoreceptor, where Z• is a radical in which the electron spin has no hyperfine interactions with magnetic nuclei, such as hydrogen and nitrogen. Quantum spin dynamics simulations of the reactivity of [FAD•- Z•] show that it is two orders of magnitude more sensitive to the direction of the geomagnetic field than is [FAD•- TrpH•+] under the same conditions (50 µT magnetic field, 1 µs radical lifetime). The favourable magnetic properties of [FAD•- Z•] arise from the asymmetric distribution of hyperfine interactions among the two radicals and the near-optimal magnetic properties of the flavin radical. We close by discussing the identity of Z• and possible routes for its formation as part of a spin-correlated radical pair with an FAD radical in cryptochrome.