The sensitivity of a radical pair compass magnetoreceptor can be significantly amplified by radical scavengers

Understanding the Red Shift in the Absorption Spectrum of the FAD Cofactor in ClCry4 Protein

It is still a puzzle that has not been entirely solved how migratory birds utilize the Earth's magnetic field for biannual migration. The most consistent explanation thus far is rooted in the modulation of the biological function of the cryptochrome 4 (Cry4) protein by an external magnetic field. This phenomenon is closely linked with the flavin adenine dinucleotide (FAD) cofactor that is noncovalently bound in the protein. Cry4 is activated by blue light, which is absorbed by the FAD cofactor. Subsequent electron and proton transfers trigger radical pair formation in the protein, which is sensitive to the external magnetic field. An important long-lasting redox state of the FAD cofactor is the signaling (FADH•) state, which is present after the transient electron transfer steps have been completed. Recent experimental efforts succeeded in crystallizing the Cry4 protein from Columbia livia (ClCry4) with all of the important residues needed for protein photoreduction. This specific crystallization of Cry4 protein so far is the only avian cryptochrome crystal structure available, which, however, has great similarity to the Cry4 proteins of night migratory birds. The previous experimental studies of the ClCry4 protein included the absorption properties of the protein in its different redox states. The absorption spectrum of the FADH• state demonstrated a peculiar red shift compared to the photoabsorption properties of the FAD cofactor in its FADH• state in other Cry proteins from other species. The aim of this study is to understand this red shift by employing the tools of computational microscopy and, in particular, a QM/MM approach that relies on the polarizable embedding approximation.

Therapeutic nuclear magnetic resonance and intermittent hypoxia trigger time dependent on/off effects in circadian clocks and confirm a central role of superoxide in cellular magnetic field effects

Cellular magnetic field effects are assumed to base on coherent singlet-triplet interconversion of radical pairs that are sensitive to applied radiofrequency (RF) and weak magnetic fields (WEMFs), known as radical pair mechanism (RPM). As a leading model, the RPM explains how quantum effects can influence biochemical and cellular signalling. Consequently, radical pairs generate reactive oxygen species (ROS) that link the RPM to redox processes, such as the response to hypoxia and the circadian clock. Therapeutic nuclear magnetic resonance (tNMR) occupies a unique position in the RPM paradigm because of the used frequencies, which are far below the range of 0.1-100 MHz postulated for the RPM to occur. Nonetheless, tNMR was shown to induce RPM like effects, such as increased extracellular H2O2 levels and altered cellular bioenergetics. In this study we compared the impact of tNMR and intermittent hypoxia on the circadian clock, as well as the role of superoxide in tNMR induced ROS partitioning. We show that both, tNMR and intermittent hypoxia, exert on/off effects on cellular clocks that are dependent on the time of application (day versus night). In addition, our data provide further evidence that superoxide plays a central role in magnetic signal transduction. tNMR used in combination with scavengers, such as Vitamin C, led to strong ROS product redistributions. This discovery might represent the first indication of radical triads in biological systems.

'Seeing' the electromagnetic spectrum: spotlight on the cryptochrome photocycle

Cryptochromes are widely dispersed flavoprotein photoreceptors that regulate numerous developmental responses to light in plants, as well as to stress and entrainment of the circadian clock in animals and humans. All cryptochromes are closely related to an ancient family of light-absorbing flavoenzymes known as photolyases, which use light as an energy source for DNA repair but themselves have no light sensing role. Here we review the means by which plant cryptochromes acquired a light sensing function. This transition involved subtle changes within the flavin binding pocket which gave rise to a visual photocycle consisting of light-inducible and dark-reversible flavin redox state transitions. In this photocycle, light first triggers flavin reduction from an initial dark-adapted resting state (FADox). The reduced state is the biologically active or 'lit' state, correlating with biological activity. Subsequently, the photoreduced flavin reoxidises back to the dark adapted or 'resting' state. Because the rate of reoxidation determines the lifetime of the signaling state, it significantly modulates biological activity. As a consequence of this redox photocycle Crys respond to both the wavelength and the intensity of light, but are in addition regulated by factors such as temperature, oxygen concentration, and cellular metabolites that alter rates of flavin reoxidation even independently of light. Mechanistically, flavin reduction is correlated with conformational change in the protein, which is thought to mediate biological activity through interaction with biological signaling partners. In addition, a second, entirely independent signaling mechanism arises from the cryptochrome photocycle in the form of reactive oxygen species (ROS). These are synthesized during flavin reoxidation, are known mediators of biotic and abiotic stress responses, and have been linked to Cry biological activity in plants and animals. Additional special properties arising from the cryptochrome photocycle include responsivity to electromagnetic fields and their applications in optogenetics. Finally, innovations in methodology such as the use of Nitrogen Vacancy (NV) diamond centers to follow cryptochrome magnetic field sensitivity in vivo are discussed, as well as the potential for a whole new technology of 'magneto-genetics' for future applications in synthetic biology and medicine.

Radical pair model for magnetic field effects on NMDA receptor activity

The N-methyl-D-aspartate receptor is a prominent player in brain development and functioning. Perturbations to its functioning through external stimuli like magnetic fields can potentially affect the brain in numerous ways. Various studies have shown that magnetic fields of varying strengths affect these receptors. We propose that the radical pair mechanism, a quantum mechanical process, could explain some of these field effects. Radicals of the form [Formula: see text], where R is a protein residue that can be Serine or Tyrosine, are considered for this study. The variation in the singlet fractional yield of the radical pairs, as a function of magnetic field strength, is calculated to understand how the magnetic field affects the products of the radical pair reactions. Based on the results, the radical pair mechanism is a likely candidate for explaining the magnetic field effects observed on the receptor activity. The model predicts changes in the behaviour of the system as magnetic field strength is varied and also predicts certain isotope effects. The results further suggest that similar effects on radical pairs could be a plausible explanation for various magnetic field effects within the brain.

Cryptochrome and quantum biology: unraveling the mysteries of plant magnetoreception

Magnetoreception, the remarkable ability of organisms to perceive and respond to Earth's magnetic field, has captivated scientists for decades, particularly within the field of quantum biology. In the plant science, the exploration of the complicated interplay between quantum phenomena and classical biology in the context of plant magnetoreception has emerged as an attractive area of research. This comprehensive review investigates into three prominent theoretical models: the Radical Pair Mechanism (RPM), the Level Crossing Mechanism (LCM), and the Magnetite-based MagR theory in plants. While examining the advantages, limitations, and challenges associated with each model, this review places a particular weight on the RPM, highlighting its well-established role of cryptochromes and in-vivo experiments on light-independent plant magnetoreception. However, alternative mechanisms such as the LCM and the MagR theory are objectively presented as convincing perspectives that permit further investigation. To shed light on these theoretical frameworks, this review proposes experimental approaches including cutting-edge experimental techniques. By integrating these approaches, a comprehensive understanding of the complex mechanisms driving plant magnetoreception can be achieved, lending support to the fundamental principle in the RPM. In conclusion, this review provides a panoramic overview of plant magnetoreception, highlighting the exciting potential of quantum biology in unraveling the mysteries of magnetoreception. As researchers embark on this captivating scientific journey, the doors to deciphering the diverse mechanisms of magnetoreception in plants stand wide open, offering a profound exploration of nature's adaptations to environmental cues.

The Geomagnetic Field (GMF) Is Required for Lima Bean Photosynthesis and Reactive Oxygen Species Production

Plants evolved in the presence of the Earth's magnetic field (or geomagnetic field, GMF). Variations in MF intensity and inclination are perceived by plants as an abiotic stress condition with responses at the genomic and metabolic level, with changes in growth and developmental processes. The reduction of GMF to near null magnetic field (NNMF) values by the use of a triaxial Helmholtz coils system was used to evaluate the requirement of the GMF for Lima bean (Phaseolus lunatus L.) photosynthesis and reactive oxygen species (ROS) production. The leaf area, stomatal density, chloroplast ultrastructure and some biochemical parameters including leaf carbohydrate, total carbon, protein content and δ¹³C were affected by NNMF conditions, as were the chlorophyll and carotenoid levels. RubisCO activity and content were also reduced in NNMF. The GMF was required for the reaction center's efficiency and for the reduction of quinones. NNMF conditions downregulated the expression of the MagR homologs PlIScA2 and PlcpIScA, implying a connection between magnetoreception and photosynthetic efficiency. Finally, we showed that the GMF induced a higher expression of genes involved in ROS production, with increased contents of both H₂O₂ and other peroxides. Our results show that, in Lima bean, the GMF is required for photosynthesis and that PlIScA2 and PlcpIScA may play a role in the modulation of MF-dependent responses of photosynthesis and plant oxidative stress.

Effects of inter-radical interactions and scavenging radicals on magnetosensitivity: spin dynamics simulations of proposed radical pairs

Although the magnetosensitivity to weak magnetic fields, such as the geomagnetic field, which was exhibited by radical pairs that are potentially responsible for avian navigation, has been previously investigated by spin dynamics simulations, understanding this behavior for proposed radical pairs in other species is limited. These include, for example, radical pairs formed in the single-cell green alga Chlamydomonas reinhardtii (CraCRY) and in Columba livia (ClCRY4). In addition, the radical pair of FADH^• with the one-electron reduced cyclobutane thymine dimer that was shown to be sensitive to weak magnetic fields has been of interest. In this work, we investigated the directional magnetosensitivity of these radical pairs to a weak magnetic field by spin dynamics simulations. We find significant reduction in the magnetosensitivity by inclusion of dipolar and exchange interactions, which can be mitigated by a scavenging radical, as demonstrated for the [FAD^•- TyrD^•] radical pair in CraCRY, but not for the [FADH^• T□T^•-] radical pair because of the large exchange coupling. The directional magnetosensitivity of the ClCRY4 [FAD^•- TyrE^•] radical pair can survive this adverse effect even without the scavenging reaction, possibly motivating further experimental exploration.

Biological Effects of Electric, Magnetic, and Electromagnetic Fields from 0 to 100 MHz on Fauna and Flora: Workshop Report

This report summarizes effects of anthropogenic electric, magnetic, and electromagnetic fields in the frequency range from 0 to 100 MHz on flora and fauna, as presented at an international workshop held on 5-7 November in 2019 in Munich, Germany. Such fields may originate from overhead powerlines, earth or sea cables, and from wireless charging systems. Animals and plants react differentially to anthropogenic fields; the mechanisms underlying these responses are still researched actively. Radical pairs and magnetite are discussed mechanisms of magnetoreception in insects, birds, and mammals. Moreover, several insects as well as marine species possess specialized electroreceptors, and behavioral reactions to anthropogenic fields have been reported. Plants react to experimental modifications of their magnetic environment by growth changes. Strong adverse effects of anthropogenic fields have not been described, but knowledge gaps were identified; further studies, aiming at the identification of the interaction mechanisms and the ecological consequences, are recommended.

Driven Radical Motion Enhances Cryptochrome Magnetoreception: Toward Live Quantum Sensing

The mechanism underlying magnetoreception has long eluded explanation. A popular hypothesis attributes this sense to the quantum coherent spin dynamics and spin-selective recombination reactions of radical pairs in the protein cryptochrome. However, concerns about the validity of the hypothesis have been raised because unavoidable inter-radical interactions, such as the strong electron-electron dipolar coupling, appear to suppress its sensitivity. We demonstrate that sensitivity can be restored by driving the spin system through a modulation of the inter-radical distance. It is shown that this dynamical process markedly enhances geomagnetic field sensitivity in strongly coupled radical pairs via Landau-Zener-Stückelberg-Majorana transitions between singlet and triplet states. These findings suggest that a "live" harmonically driven magnetoreceptor can be more sensitive than its "dead" static counterpart.

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.

The hippocampal region of the brain plays a major role in learning and memory functionality. In male mice, shielding of the Earth’s magnetic field was found to decrease hippocampal neurogenesis, i.e. the formation of new neurons, following from a decrease in levels of reactive oxygen species. In this study, we suggest an explanation in terms of spin dynamics of a three radical system composed of flavin-semiquinone, superoxide and ascorbyl radical. This model agrees with the experimental data whilst retaining realistic parameters for a biological system, unlike the Radical Pair Mechanism.

Magnetic field effects in biology from the perspective of the radical pair mechanism

Hundreds of studies have found that weak magnetic fields can significantly influence various biological systems. However, the underlying mechanisms behind these phenomena remain elusive. Remarkably, the magnetic energies implicated in these effects are much smaller than thermal energies. Here, we review these observations, and we suggest an explanation based on the radical pair mechanism, which involves the quantum dynamics of the electron and nuclear spins of transient radical molecules. While the radical pair mechanism has been studied in detail in the context of avian magnetoreception, the studies reviewed here show that magnetosensitivity is widespread throughout biology. We review magnetic field effects on various physiological functions, discussing static, hypomagnetic and oscillating magnetic fields, as well as isotope effects. We then review the radical pair mechanism as a potential unifying model for the described magnetic field effects, and we discuss plausible candidate molecules for the radical pairs. We review recent studies proposing that the radical pair mechanism provides explanations for isotope effects in xenon anaesthesia and lithium treatment of hyperactivity, magnetic field effects on the circadian clock, and hypomagnetic field effects on neurogenesis and microtubule assembly. We conclude by discussing future lines of investigation in this exciting new area of quantum biology.

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.

Radical pairs may explain reactive oxygen species-mediated effects of hypomagnetic field on neurogenesis

Exposures to a hypomagnetic field can affect biological processes. Recently, it has been observed that hypomagnetic field exposure can adversely affect adult hippocampal neurogenesis and hippocampus-dependent cognition in mice. In the same study, the role of reactive oxygen species (ROS) in hypomagnetic field effects has been demonstrated. However, the mechanistic reasons behind this effect are not clear. This study proposes a radical pair mechanism based on a flavin-superoxide radical pair to explain the modulation of ROS production and the attenuation of adult hippocampal neurogenesis in a hypomagnetic field. The results of our calculations favor a singlet-born radical pair over a triplet-born radical pair. Our model predicts hypomagnetic field effects on the triplet/singlet yield of comparable strength as the effects observed in experimental studies on adult hippocampal neurogenesis. Our predictions are in qualitative agreement with experimental results on superoxide concentration and other observed ROS effects. We also predict the effects of applied magnetic fields and oxygen isotopic substitution on adult hippocampal neurogenesis.

Exposure to magnetic fields influences many neurobiological processes. The formation of new neurons (neurogenesis) in the hippocampal region of the adult brain plays a crucial role in learning and memory. It can be adversely affected by shielding the earth’s magnetic field, and this effect is intimately related to ROS concentration. In this study, we have developed a quantum mechanical model to explain this magnetic field dependence of adult hippocampal neurogenesis. Our model is also consistent with the observed ROS effects.

Radical pairs may play a role in microtubule reorganization

The exact mechanism behind general anesthesia remains an open question in neuroscience. It has been proposed that anesthetics selectively prevent consciousness and memory via acting on microtubules (MTs). It is known that the magnetic field modulates MT organization. A recent study shows that a radical pair model can explain the isotope effect in xenon-induced anesthesia and predicts magnetic field effects on anesthetic potency. Further, reactive oxygen species are also implicated in MT stability and anesthesia. Based on a simple radical pair mechanism model and a simple mathematical model of MT organization, we show that magnetic fields can modulate spin dynamics of naturally occurring radical pairs in MT. We propose that the spin dynamics influence a rate in the reaction cycle, which translates into a change in the MT density. We can reproduce magnetic field effects on the MT concentration that have been observed. Our model also predicts additional effects at slightly higher fields. Our model further predicts that the effect of zinc on the MT density exhibits isotopic dependence. The findings of this work make a connection between microtubule-based and radical pair-based quantum theories of consciousness.

Observations about utilitarian coherence in the avian compass

It is hypothesised that the avian compass relies on spin dynamics in a recombining radical pair. Quantum coherence has been suggested as a resource to this process that nature may utilise to achieve increased compass sensitivity. To date, the true functional role of coherence in these natural systems has remained speculative, lacking insights from sufficiently complex models. Here, we investigate realistically large radical pair models with up to 21 nuclear spins, inspired by the putative magnetosensory protein cryptochrome. By varying relative radical orientations, we reveal correlations of several coherence measures with compass fidelity. Whilst electronic coherence is found to be an ineffective predictor of compass sensitivity, a robust correlation of compass sensitivity and a global coherence measure is established. The results demonstrate the importance of realistic models, and appropriate choice of coherence measure, in elucidating the quantum nature of the avian compass.

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.

Radical pairs can explain magnetic field and lithium effects on the circadian clock

Drosophila's circadian clock can be perturbed by magnetic fields, as well as by lithium administration. Cryptochromes are critical for the circadian clock. Further, the radical pairs in cryptochrome also can explain magnetoreception in animals. Based on a simple radical pair mechanism model of the animal magnetic compass, we show that both magnetic fields and lithium can influence the spin dynamics of the naturally occurring radical pairs and hence modulate the circadian clock's rhythms. Using a simple chemical oscillator model for the circadian clock, we show that the spin dynamics influence a rate in the chemical oscillator model, which translates into a change in the circadian period. Our model can reproduce the results of two independent experiments, magnetic field and lithium effects on the circadian clock. Our model predicts that stronger magnetic fields would shorten the clock's period. We also predict that lithium influences the clock in an isotope-dependent manner. Furthermore, our model also predicts that magnetic fields and hyperfine interactions modulate oxidative stress. The findings of this work suggest that the quantum nature of radical pairs might play roles in the brain, as another piece of evidence in addition to recent results on xenon anesthesia and lithium effects on hyperactivity.

Radical Scavenging Could Answer the Challenge Posed by Electron-Electron Dipolar Interactions in the Cryptochrome Compass Model

Many birds are endowed with a visual magnetic sense that may exploit magnetosensitive radical recombination processes in the protein cryptochrome. In this widely accepted but unproven model, geomagnetic sensitivity is suggested to arise from variations in the recombination rate of a pair of radicals, whose unpaired electron spins undergo coherent singlet-triplet interconversion in the geomagnetic field by coupling to nuclear spins via hyperfine interactions. However, simulations of this conventional radical pair mechanism (RPM) predicted only tiny magnetosensitivities for realistic conditions because the RPM's directional sensitivity is strongly suppressed by the intrinsic electron-electron dipolar (EED) interactions, casting doubt on its viability as a magnetic sensor. We show how this RPM-suppression problem is overcome in a three-radical system in which a third "scavenger" radical reacts with one member of the primary pair. We use this finding to predict substantial magnetic field effects that exceed those of the RPM in the presence of EED interactions in animal cryptochromes.

Entangled radicals may explain lithium effects on hyperactivity

It is known that bipolar disorder and its lithium treatment involve the modulation of oxidative stress. Moreover, it has been observed that lithium's effects are isotope-dependent. Based on these findings, here we propose that lithium exerts its effects by influencing the recombination dynamics of a naturally occurring radical pair involving oxygen. We develop a simple model inspired by the radical-pair mechanism in cryptochrome in the context of avian magnetoreception and xenon-induced anesthesia. Our model reproduces the observed isotopic dependence in the lithium treatment of hyperactivity in rats. It predicts a magnetic-field dependence of the effectiveness of lithium, which provides one potential experimental test of our hypothesis. Our findings show that Nature might harness quantum entanglement for the brain's cognitive processes.

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.

Magnetically modulated photochemical reaction pathways in anthraquinone molecules and aggregates

The chemical reactions involving excited-state radical pairs (RPs) of parallel/anti-parallel spin configurations are sensitive to magnetic field, leading to the possibilities of magnetically controlled synthesis of chemical compounds. Here we show that the reaction of anthraquinone (AQ) in sodium dodecyl sulfate (SDS) micellar solution under UV excitation is significantly influenced by applying external field. The steady state and time-resolved spectroscopies reveal that the reaction intermediate (pairs of AQH-SDS radicals) can undergo two distinct pathways depending on whether it is spin singlet or triplet, and the field is beneficial to the conversion between spin configurations of RPs. The applied field not only affects the reaction rate constant but also changes the final products. Besides, the aggregation of AQ molecules would change the population of singlets and triplets and thus enhance magnetic field effect. This work represents a promising way of controlling chemical reaction and improving reaction selectivity via magnetic field methods.

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.

Simple rules for resolved level-crossing spectra in magnetic field effects on reaction yields

In this work we derive conditions under which a level-crossing line in a magnetic field effect curve for a recombining radical pair will be equivalent to the electron spin resonance (ESR) spectrum and discuss three simple rules for qualitative prediction of the level-crossing spectra.

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.

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.

Electron-Electron Dipolar Interaction Poses a Challenge to the Radical Pair Mechanism of Magnetoreception

A visual magnetic sense in migratory birds has been hypothesized to rely on a radical pair reaction in the protein cryptochrome. In this model, magnetic sensitivity originates from coherent spin dynamics, as the radicals couple to magnetic nuclei via hyperfine interactions. Prior studies have often neglected the electron-electron dipolar (EED) coupling from this hypothesis. We show that EED interactions suppress the anisotropic response to the geomagnetic field by the radical pair mechanism in cryptochrome and that this attenuation is unlikely to be mitigated by mutual cancellation of the EED and electronic exchange coupling, as previously suggested. We then demonstrate that this limitation may be overcome by extending the conventional model to include a third, nonreacting radical. We predict that hyperfine effects could work in concert with three-radical dipolar interactions to tailor a superior magnetic response, thereby providing a new principle for magnetosensitivity with applications for sensing, navigation, and the assessment of biological magnetic field effects.

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”.

Theoretical insights into the formation and stability of radical oxygen species in cryptochromes

Cryptochrome is a blue-light absorbing flavoprotein containing a flavin adenine dinucleotide (FAD) cofactor. FAD can accept up to two electrons and two protons, which can be subsequently transferred to substrates present in the binding pocket. It is well known that reactive oxygen species are generated when triplet molecular oxygen is present in the cavity. Here, we investigate the formation and stability of radical oxygen species in Drosophila melanogaster cryptochrome using molecular dynamics simulations and electronic structure calculations. We find that the superoxide and hydroxyl radicals in doublet spin states are stabilized in the pocket due to the attractive electrostatic interactions and hydrogen bonding with partially reduced FAD. These findings validate from a molecular dynamics perspective that [FAD˙--HO2˙] or [FADH˙-O2˙-] can be alternative radical pairs at the origin of magnetoreception.

Navigating at night: fundamental limits on the sensitivity of radical pair magnetoreception under dim light

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

Melatonin Levels and Low-Frequency Magnetic Fields in Humans and Rats: New Insights From a Bayesian Logistic Regression

The present analysis revisits the impact of extremely low-frequency magnetic fields (ELF-MF) on melatonin (MLT) levels in human and rat subjects using both a parametric and non-parametric approach. In this analysis, we use 62 studies from review articles. The parametric approach consists of a Bayesian logistic regression (LR) analysis and the non-parametric approach consists of a Support Vector analysis, both of which are robust against spurious/false results. Both approaches reveal a unique well-ordered pattern, and show that human and rat studies are consistent with each other once the MF strength is restricted to cover the same range (with B ≲ 50 μT). In addition, the data reveal that chronic exposure (longer than ∼22 days) to ELF-MF appears to decrease MLT levels only when the MF strength is below a threshold of ~30 μT ( log B thr [ μ T ] = 1 . 4 - 0 . 4 + 0 . 7 ), i.e., when the man-made ELF-MF intensity is below that of the static geomagnetic field. Studies reporting an association between ELF-MF and changes to MLT levels and the opposite (no association with ELF-MF) can be reconciled under a single framework. Bioelectromagnetics. 2019;40:539-552. © 2019 Bioelectromagnetics Society.

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.

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.

Magnetic sensitivity mediated by the Arabidopsis blue-light receptor cryptochrome occurs during flavin reoxidation in the dark

Arabidopsis cryptochrome mediates responses to magnetic fields that have been applied in the absence of light, consistent with flavin reoxidation as the primary detection mechanism. Cryptochromes are highly conserved blue-light-absorbing flavoproteins which have been linked to the perception of electromagnetic stimuli in numerous organisms. These include sensing the direction of the earth's magnetic field in migratory birds and the intensity of magnetic fields in insects and plants. When exposed to light, cryptochromes undergo flavin reduction/reoxidation redox cycles leading to biological activation which generate radical pairs thought to be the basis for magnetic sensitivity. However, the nature of the magnetically sensitive radical pairs and the steps at which they act during the cryptochrome redox cycle are currently a matter of debate. Here, we investigate the response of Arabidopsis cryptochrome-1 in vivo to a static magnetic field of 500 μT (10 × earth's field) using both plant growth and light-dependent phosphorylation as an assay. Cryptochrome responses to light were enhanced by the magnetic field, as indicated by increased inhibition of hypocotyl elongation and increased cryptochrome phosphorylation. However, when light and dark intervals were given intermittently, a plant response to the magnetic field was observed even when the magnetic field was given exclusively during the dark intervals between light exposures. This indicates that the magnetically sensitive reaction step in the cryptochrome photocycle must occur during flavin reoxidation, and likely involves the formation of reactive oxygen species.

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.

Atomistic Insights into Cryptochrome Interprotein Interactions

It is striking that the mechanism by which birds sense geomagnetic fields during the biannual migration seasons is not entirely understood. A protein believed to be responsible for avian magnetoreception is the flavoprotein cryptochrome (CRY), which fulfills many of the criteria for a magnetic field sensor. Some experiments, however, indicate that magnetoreception in birds may be disturbed by extremely weak radio frequency fields, an effect that likely cannot be described by an isolated CRY protein. An explanation can possibly be delivered if CRY binds to another protein inside a cell that would possess certain biochemical properties, and it is, therefore, important to identify possible intracellular CRY interaction partners. The goal of this study is to investigate a possible interaction between CRY4 and the iron-sulfur-containing assembly protein (ISCA1) from Erithacus rubecula (European robin), which has recently been proposed to be relevant for magnetic field sensing. The interaction between the proteins is established through classical molecular dynamics simulations for several possible protein-docking modes. The analysis of these simulations concludes that the ISCA1 complex and CRY4 are capable of binding; however, the peculiarities of this binding argue strongly against ISCA1 as relevant for magnetoreception.

Low-Light Dependence of the Magnetic Field Effect on Cryptochromes: Possible Relevance to Plant Ecology

Various responses to static magnetic fields (MF) have been reported in plants, and it has been suggested that the geomagnetic field influences plant physiology. Accordingly, diverse mechanisms have been proposed to mediate MF effects in plants. The currently most probable sensor candidates are cryptochromes (Cry) which are sensitive to submillitesla MF. Here, we propose a quantitative approach of the MF effect on Cry depending on light intensity, and try to link it to a possible functional role for magnetic sensitivity in plants. Based on a theoretical evaluation and on a review of relevant data on Arabidopsis thaliana Cry 1, we point out that the MF effect on the signaling state of Cry, as well as the possible consequences of that effect on certain phenotypes (growth in particular) show parallel dependences on light intensity, being most prominent at low light levels. Based on these findings, we propose that Cry magnetosensitivity in plants could represent an ecological adaptation which regulates the amount of Cry signaling state under low light conditions. That hypothesis would preferentially be tested by studying sensitive and specific endpoints, such as the expression of clock proteins that are downregulated by Cry, but under light intensities lower than those used so far. Finally, we highlight that the low-light dependence of the MF effect described here could also apply to light-dependent functions of animal Cry, in particular magnetoreception which, from the present evaluation, would be based on the magnetic sensitivity of the photoreduction reaction, like in plants.