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.

The Effect of Spin Relaxation on Magnetic Compass Sensitivity in ErCry4a.

This study explores the impact of thermal motion on the magnetic compass mechanism in migratory birds, focusing on the radical pair mechanism within cryptochrome photoreceptors. The coherence of radical pairs, crucial for magnetic field inference, is curbed by spin relaxation induced by intra-protein motion. Molecular dynamics simulations, density-functional-theory-based calculations, and spin dynamics calculations were employed, utilizing Bloch-Redfield-Wangsness (BRW) relaxation theory, to investigate compass sensitivity. Previous research hypothesized that European robin's cryptochrome 4a (ErCry4a) optimized intra-protein motion to minimize spin relaxation, enhancing magnetic sensing compared to the plant Arabidopsis thaliana's cryptochrome 1 (AtCry1). Different correlation times of the nuclear hyperfine coupling constants in AtCry1 and ErCry4a were indeed found, leading to distinct radical pair yields in the two species, with ErCry4a showing optimized sensitivity. However, this optimization is likely negligible in realistic spin systems with numerous nuclear spins. Beyond insights in magnetic sensing, the study presents a detailed method employing molecular dynamics simulations to assess spin relaxation effects on chemical reactions with realistically modelled protein motion, relevant for studying radical pair reactions at finite temperature.

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.

Radical triads, not pairs, may explain effects of hypomagnetic fields on neurogenesis.

Adult hippocampal neurogenesis and hippocampus-dependent cognition in mice have been found to be adversely affected by hypomagnetic field exposure. The effect concurred with a reduction of reactive oxygen species in the absence of the geomagnetic field. A recent theoretical study suggests a mechanistic interpretation of this phenomenon in the framework of the Radical Pair Mechanism. According to this model, a flavin-superoxide radical pair, born in the singlet spin configuration, undergoes magnetic field-dependent spin dynamics such that the pair's recombination is enhanced as the applied magnetic field is reduced. This model has two ostensible weaknesses: a) the assumption of a singlet initial state is irreconcilable with known reaction pathways generating such radical pairs, and b) the model neglects the swift spin relaxation of free superoxide, which abolishes any magnetic sensitivity in geomagnetic/hypomagnetic fields. We here suggest that a model based on a radical triad and the assumption of a secondary radical scavenging reaction can, in principle, explain the phenomenon without unnatural assumptions, thus providing a coherent explanation of hypomagnetic field effects in biology.

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.

Ab initio derivation of flavin hyperfine interactions for the protein magnetosensor cryptochrome.

The radicals derived from flavin adenine dinucleotide (FAD) are a corner stone of recent hypotheses about magnetoreception, including the compass of migratory songbirds. These models attribute a magnetic sense to coherent spin dynamics in radical pairs within the flavo-protein cryptochrome. The primary determinant of sensitivity and directionality of this process are the hyperfine interactions of the involved radicals. Here, we present a comprehensive computational study of the hyperfine couplings in the protonated and unprotonated FAD radicals in cryptochrome 4 from C. livia. We combine long (800 ns) molecular dynamics trajectories to accurate quantum chemistry calculations. Hyperfine parameters are derived using auxiliary density functional theory applied to cluster and hybrid QM/MM (Quantum Mechanics/Molecular Mechanics) models comprising the FAD and its significant surrounding environment, as determined by a detailed sensitivity analysis. Thanks to this protocol we elucidate the sensitivity of the hyperfine interaction parameters to structural fluctuations and the polarisation effect of the protein environment. We find that the ensemble-averaged hyperfine interactions are predominantly governed by thermally induced geometric distortions of the flavin. We discuss our results in view of the expected performance of these radicals as part of a magnetoreceptor. Our data could be used to parametrize spin Hamiltonians including not only average values but also standard deviations.

Anisotropic magnetic field effects in the re-oxidation of cryptochrome in the presence of scavenger radicals.

The avian compass and many other of nature's magnetoreceptive traits are widely ascribed to the protein cryptochrome. There, magnetosensitivity is thought to emerge as the spin dynamics of radicals in the applied magnetic field enters in competition with their recombination. The first and dominant model makes use of a radical pair. However, recent studies have suggested that magnetosensitivity could be markedly enhanced for a radical triad, the primary radical pair of which undergoes a spin-selective recombination reaction with a third radical. Here, we test the practicality of this supposition for the reoxidation reaction of the reduced FAD cofactor in cryptochrome, which has been implicated with light-independent magnetoreception but appears irreconcilable with the classical radical pair mechanism (RPM). Based on the available realistic cryptochrome structures, we predict the magnetosensitivity of radical triad systems comprising the flavin semiquinone, the superoxide, and a tyrosine or ascorbyl scavenger radical. We consider many hyperfine-coupled nuclear spins, the relative orientation and placement of the radicals, their coupling by the electron-electron dipolar interaction, and spin relaxation in the superoxide radical in the limit of instantaneous decoherence, which have not been comprehensively considered before. We demonstrate that these systems can provide superior magnetosensitivity under realistic conditions, with implications for dark-state cryptochrome magnetoreception and other biological magneto- and isotope-sensitive radical recombination reactions.

F-cluster: Reaction-induced spin correlation in multi-radical systems.

We provide a theoretical analysis of spin-selective recombination processes in clusters of n ≥ 3 radicals. Specifically, we discuss how spin correlation can ensue from random encounters of n radicals, i.e., "F-clusters" as a generalization of radical F-pairs, acting as precursors of spin-driven magnetic field effects. Survival probabilities and the spin correlation of the surviving radical population, as well as transients, are evaluated by expanding the spin density operator in an operator basis that is closed under application of the Haberkorn recombination operator and singlet-triplet dephasing. For the primary spin cluster, the steady-state density operator is found to be independent of the details of the recombination network, provided that it is irreducible; pairs of surviving radicals are triplet-polarized independent of whether they are actually reacting with each other. The steady state is independent of the singlet-triplet dephasing, but the kinetics and the population of sister clusters of smaller size can depend on the degree of dephasing. We also analyze reaction-induced singlet-triplet interconversion in radical pairs due to radical scavenging by initially uncorrelated radicals ("chemical Zeno effect"). We generalize previous treatments for radical triads by discussing the effect of spin-selective recombination in the original pair and extending the analysis to four radicals, i.e., radical pairs interacting with two radical scavengers.

How symmetry-breaking can amplify the magnetosensitivity of dipolarly coupled n-radical systems.

In systems of more than two reactive radicals, the radical recombination probability can be magnetosensitive due to the mere effect of the inter-radical electron-electron dipolar coupling. Here, we demonstrate that this principle, previously established for three-radical systems, generalizes to n-radical systems. We focus on radical systems in the plane and explore the effects of symmetry, in particular its absence, on the associated magnetic field effects of the recombination yield. We show, by considering regular configurations and slightly distorted geometries, that the breaking of geometric symmetry can lead to an enhancement of the magnetosensitivity of these structures. Furthermore, we demonstrate the presence of effects at low-field that are abolished in the highly symmetric case. This could be important to the understanding of the behavior of radicals in biological environments in the presence of weak magnetic fields comparable to the Earth's, as well as the construction of high-precision quantum sensing devices.

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.

Controlling Anomalous Diffusion in Lipid Membranes.

Diffusion in cell membranes is not just simple two-dimensional Brownian motion but typically depends on the timescale of the observation. The physical origins of this anomalous subdiffusion are unresolved, and model systems capable of quantitative and reproducible control of membrane diffusion have been recognized as a key experimental bottleneck. Here, we control anomalous diffusion using supported lipid bilayers containing lipids derivatized with polyethylene glycol (PEG) headgroups. Bilayers with specific excluded area fractions are formed by control of PEG lipid mole fraction. These bilayers exhibit a switch in diffusive behavior, becoming anomalous as bilayer continuity is disrupted. Using a combination of single-molecule fluorescence and interferometric imaging, we measure the anomalous behavior in this model over four orders of magnitude in time. Diffusion in these bilayers is well described by a power-law dependence of the mean-square displacement with observation time. Anomaleity in this system can be tailored by simply controlling the mole fraction of PEG lipid, producing bilayers with diffusion parameters similar to those observed for anomalous diffusion in biological membranes.

On the magnetosensitivity of lipid peroxidation: two- versus three-radical dynamics.

We present a theoretical analysis of the putative magnetosensitivity of lipid peroxidation. We focus on the widely accepted radical pair mechanism (RPM) and a recently suggested idea based on spin dynamics induced in three-radical systems by the mutual electron-electron dipolar coupling (D3M). We show that, contrary to claims in the literature, lipid peroxides, the dominant chain carriers of the autoxidation process, have associated non-zero hyperfine coupling interactions. This suggests that their recombination could, in principle, be magnetosensitive due to the RPM. While the RPM indeed goes a long way to explaining magnetosensitivity in these systems, we show that the simultaneous interaction of three peroxyl radicals via the D3M can achieve larger magnetic field effects (MFE), even if the third radical is remote from the recombining radical pair. For randomly oriented three-radical systems, the D3M induces a low-field effect comparable to that of the RPM. The mechanism furthermore immunizes the spin dynamics to the presence of large exchange coupling interactions in the recombining radical pair, thereby permitting much larger MFE at magnetic field intensities comparable to the geomagnetic field than would be expected for the RPM. Based on these characteristics, we suggest that the D3M could be particularly relevant for MFE at low fields, provided that the local radical concentration is sufficient to allow for three-spin radical correlations. Eventually, our observations suggest that MFEs could intricately depend on radical concentration and larger effects could ensue under conditions of oxidative stress.

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.

Magnetosensitivity in Dipolarly Coupled Three-Spin Systems.

The radical pair mechanism is a canonical model for the magnetosensitivity of chemical reaction processes. The key ingredient of this model is the hyperfine interaction that induces a coherent mixing of singlet and triplet electron spin states in pairs of radicals, thereby facilitating magnetic field effects (MFEs) on reaction yields through spin-selective reaction channels. We show that the hyperfine interaction is not a categorical requirement to realize the sensitivity of radical reactions to weak magnetic fields. We propose that, in systems comprising three instead of two radicals, dipolar interactions provide an alternative pathway for MFEs. By considering the role of symmetries and energy level crossings, we present a model that demonstrates a directional sensitivity to fields weaker than the geomagnetic field and remarkable spikes in the reaction yield as a function of the magnetic field intensity; these effects can moreover be tuned by the exchange interaction. Our results further the current understanding of the effects of weak magnetic fields on chemical reactions, could pave the way to a clearer understanding of the mysteries of magnetoreception and other biological MFEs and motivate the design of quantum sensors. Further still, this phenomenon will affect spin systems used in quantum information processing in the solid state and may also be applicable to spintronics.

Substitutions mimicking deimination and phosphorylation of 18.5-kDa myelin basic protein exert local structural effects that subtly influence its global folding.

Intrinsically-disordered proteins (IDPs) present a complex interplay of conformational variability and multifunctionality, modulated by environment and post-translational modifications. The 18.5-kDa myelin basic protein (MBP) is essential to the formation of the myelin sheath of the central nervous system and is exemplary in this regard. We have recently demonstrated that the unmodified MBP-C1 component undergoes co-operative global conformational changes in increasing concentrations of trifluoroethanol, emulating the decreasing dielectric environment that the protein encounters upon adsorption to the oligodendrocyte membrane [K.A. Vassall et al., Journal of Molecular Biology, 427, 1977-1992, 2015]. Here, we extended this study to the pseudo-deiminated MBP-C8 charge component, one found in greater proportion in developing myelin and in multiple sclerosis. A similar tri-conformational distribution as for MBP-C1 was observed with slight differences in Gibbs free energy. A more dramatic difference was observed by cathepsin D digestion of the protein in both aqueous and membrane environments, which showed significantly greater accessibility of the F42-F43 cut site of MBP-C8, indicative of a global conformational change. In contrast, this modification caused little change in the protein's density of packing on myelin-mimetic membranes as ascertained by double electron-electron resonance spectroscopy [D.R. Kattnig et al., Biochimica et Biophysica Acta (Biomembranes), 1818, 2636-2647, 2012], or in its affinity for Ca(2+)-CaM. Site-specific threonyl pseudo-phosphorylation at residues T92 and/or T95 did not appreciably affect any of the thermodynamic mechanisms of conformational transitions, susceptibility to cathepsin D, or affinity for Ca(2+)-CaM, despite previously having been shown to affect local structure and disposition on the membrane surface.

Hole Transfer Processes in meta- and para-Conjugated Mixed Valence Compounds: Unforeseen Effects of Bridge Substituents and Solvent Dynamics.

To address the question whether donor substituents can be utilized to accelerate the hole transfer (HT) between redox sites attached in para- or in meta-positions to a central benzene bridge, we investigated three series of mixed valence compounds based on triarylamine redox centers that are connected to a benzene bridge via alkyne spacers at para- and meta-positions. The electron density at the bridge was tuned by substituents with different electron donating or accepting character. By analyzing optical spectra and by DFT computations we show that the HT properties are independent of bridge substituents for one of the meta-series, while donor substituents can strongly decrease the intrinsic barrier in the case of the para-series. In stark contrast, temperature-dependent ESR measurements demonstrate a dramatic increase of both the apparent barrier and the rate of HT for strong donor substituents in the para-cases. This is caused by an unprecedented substituent-dependent change of the HT mechanism from that described by transition state theory to a regime controlled by solvent dynamics. For solvents with slow longitudinal relaxation (PhNO2, oDCB), this adds an additional contribution to the intrinsic barrier via the dielectric relaxation process. Attaching the donor substituents to the bridge at positions where the molecular orbital coefficients are large accelerates the HT rate for meta-conjugated compounds just as for the para-series. This effect demonstrates that the para-meta paradigm no longer holds if appropriate substituents and substitution patterns are chosen, thereby considerably broadening the applicability of meta-topologies for optoelectronic applications.

Influence of the excitation light intensity on the rate of fluorescence quenching reactions: pulsed experiments.

The effect of multiple light excitation events on bimolecular photo-induced electron transfer reactions in liquid solution is studied experimentally. It is found that the decay of fluorescence can be up to 25% faster if a second photon is absorbed after a first cycle of quenching and recombination. A theoretical model is presented which ascribes this effect to the enrichment of the concentration of quenchers in the immediate vicinity of fluorophores that have been previously excited. Despite its simplicity, the model delivers a qualitative agreement with the observed experimental trends. The original theory by Burshtein and Igoshin (J. Chem. Phys., 2000, 112, 10930-10940) was created for continuous light excitation though. A qualitative extrapolation from the here presented pulse experiments to the continuous excitation conditions lead us to conclude that in the latter the order of magnitude of the increase of the quenching efficiency upon increasing the light intensity of excitation, must also be on the order of tens of percent. These results mean that the rate constant for photo-induced bimolecular reactions depends not only on the usual known factors, such as temperature, viscosity and other properties of the medium, but also on the intensity of the excitation light.

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.

Spin relaxation of radicals in cryptochrome and its role in avian magnetoreception.

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.