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, B1/2, 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 B1/2 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 B1/2 ≈ 1.89 mT and 2.46 mT, respectively. (b) The widely used expression for B1/2 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 B1/2 can be used to understand the impact of spin relaxation on its performance as a magnetic compass sensor.

Effects of Dynamical Degrees of Freedom on Magnetic Compass Sensitivity: A Comparison of Plant and Avian Cryptochromes.

The magnetic compass of migratory birds is thought to rely on a radical pair reaction inside the blue-light photoreceptor protein cryptochrome. The sensitivity of such a sensor to weak external magnetic fields is determined by a variety of magnetic interactions, including electron-nuclear hyperfine interactions. Here, we investigate the implications of thermal motion, focusing on fluctuations in the dihedral and librational angles of flavin adenine dinucleotide (FAD) and tryptophan (Trp) radicals in cryptochrome 4a from European robin (Erithacus rubecula, ErCry4a) and pigeon (Columba livia, ClCry4a) and cryptochrome 1 from the plant Arabidopsis thaliana (AtCry1). Molecular dynamics simulations and density functional theory-derived hyperfine interactions are used to calculate the quantum yield of radical pair recombination dependent on the direction of the geomagnetic field. This quantity and various dynamical parameters are compared for [FAD•- Trp•+] in ErCry4a, ClCry4a, and AtCry1, with TrpC or TrpD being the third and fourth components of the tryptophan triad/tetrad in the respective proteins. We find that (i) differences in the average dihedral angles in the radical pairs are small, (ii) the librational motions of TrpC•+ in the avian cryptochromes are appreciably smaller than in AtCry1, (iii) the rapid vibrational motions of the radicals leading to strong fluctuations in the hyperfine couplings affect the spin dynamics depending on the usage of instantaneous or time-averaged interactions. Future investigations of radical pair compass sensitivity should therefore not be based on single snapshots of the protein structure but should include the ensemble properties of the hyperfine interactions.

Broadband 75-85 MHz radiofrequency fields disrupt magnetic compass orientation in night-migratory songbirds consistent with a flavin-based radical pair magnetoreceptor.

The light-dependent magnetic compass sense of night-migratory songbirds can be disrupted by weak radiofrequency fields. This finding supports a quantum mechanical, radical-pair-based mechanism of magnetoreception as observed for isolated cryptochrome 4, a protein found in birds' retinas. The exact identity of the magnetically sensitive radicals in cryptochrome is uncertain in vivo, but their formation seems to require a bound flavin adenine dinucleotide chromophore and a chain of four tryptophan residues within the protein. Resulting from the hyperfine interactions of nuclear spins with the unpaired electrons, the sensitivity of the radicals to radiofrequency magnetic fields depends strongly on the number of magnetic nuclei (hydrogen and nitrogen atoms) they contain. Quantum-chemical calculations suggested that electromagnetic noise in the frequency range 75-85 MHz could give information about the identity of the radicals involved. Here, we show that broadband 75-85 MHz radiofrequency fields prevent a night-migratory songbird from using its magnetic compass in behavioural experiments. These results indicate that at least one of the components of the radical pair involved in the sensory process of avian magnetoreception must contain a substantial number of strong hyperfine interactions as would be the case if a flavin-tryptophan radical pair were the magnetic sensor.

Radical quantum oscillations.

Laser spectroscopy reveals spin quantum beats in electron transfer reactions.

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.

Magnetic sensitivity of cryptochrome 4 from a migratory songbird.

Night-migratory songbirds are remarkably proficient navigators1. Flying alone and often over great distances, they use various directional cues including, crucially, a light-dependent magnetic compass2,3. The mechanism of this compass has been suggested to rely on the quantum spin dynamics of photoinduced radical pairs in cryptochrome flavoproteins located in the retinas of the birds4-7. Here we show that the photochemistry of cryptochrome 4 (CRY4) from the night-migratory European robin (Erithacus rubecula) is magnetically sensitive in vitro, and more so than CRY4 from two non-migratory bird species, chicken (Gallus gallus) and pigeon (Columba livia). Site-specific mutations of ErCRY4 reveal the roles of four successive flavin-tryptophan radical pairs in generating magnetic field effects and in stabilizing potential signalling states in a way that could enable sensing and signalling functions to be independently optimized in night-migratory birds.

Amplification of weak magnetic field effects on oscillating reactions.

We explore the possibility that chemical feedback and autocatalysis in oscillating chemical reactions could amplify weak magnetic field effects on the rate constant of one of the constituent reactions, assumed to proceed via a radical pair mechanism. Using the Brusselator model oscillator, we find that the amplitude of limit cycle oscillations in the concentrations of reaction intermediates can be extraordinarily sensitive to minute changes in the rate constant of the initiation step. The relevance of such amplification to biological effects of 50/60 Hz electromagnetic fields is discussed.

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.

Source of magnetic field effects on the electrocatalytic reduction of CO2.

We present an analysis of reported magnetic field effects (MFEs) on the yield of formic acid produced by electrocatalytic reduction of carbon dioxide at a nanoparticle tin electrode [H. P. Pan et al., J. Phys. Chem. Lett. 11, 48-53 (2020)]. Radical pair spin dynamics simulations are used to show that (1) the Δg mechanism favored by Pan et al. is not sufficient to explain the observed magneto-current, (2) field-dependent spin relaxation, resulting from the anisotropy of the g-tensor of CO2 •-, combined with the coherent singlet-triplet interconversion arising from isotropic hyperfine and Zeeman interactions, can quantitatively account for the observed MFE, and (3) modification of hyperfine interactions by isotopic substitution (1H → 2H and/or 12C → 13C) could be used to test both the proposed reaction mechanism and the interpretation presented here.

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.

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.