Electron spin relaxation in cryptochrome-based magnetoreception

Sensitivity enhancement of radical-pair magnetoreceptors as a result of spin decoherence

Electron spin relaxation is, on many occasions, considered an elephant in the room that challenges the idea of a radical-pair compass, a leading hypothesis for the navigation of migratory avian species. It has been widely recognized that an effective radical-pair magnetoreceptor requires a relaxation time that is long enough for an external magnetic field as weak as the geomagnetic field to significantly modify the coherent spin dynamics. However, previous studies proposed that certain spin relaxation, far quicker than the radical recombination reactions, could enhance, rather than degrade, the directional sensitivity of a radical-pair magnetoreceptor. Here, I investigate relaxation effects on the singlet-triplet interconversion of a model radical pair and find that the enhancement effect originates from population relaxation over a period of several microseconds as a result of efficient spin decoherence. Insights into the truncated spin systems shed light on the physics behind them. I further investigate the possibilities of such enhancement in cryptochrome-based magnetoreception, in which electron hopping takes place between tryptophan residues.

Hypomagnetic Conditions and Their Biological Action (Review)

The geomagnetic field plays an important role in the existence of life on Earth. The study of the biological effects of (hypomagnetic conditions) HMC is an important task in magnetobiology. The fundamental importance is expanding and clarifying knowledge about the mechanisms of magnetic field interaction with living systems. The applied significance is improving the training of astronauts for long-term space expeditions. This review describes the effects of HMC on animals and plants, manifested at the cellular and organismal levels. General information is given about the probable mechanisms of HMC and geomagnetic field action on living systems. The main experimental approaches are described. We attempted to systematize quantitative data from various studies and identify general dependencies of the magnetobiology effects' value on HMC characteristics (induction, exposure duration) and the biological parameter under study. The most pronounced effects were found at the cellular level compared to the organismal level. Gene expression and protein activity appeared to be the most sensitive to HMC among the molecular cellular processes. The nervous system was found to be the most sensitive in the case of the organism level. The review may be of interest to biologists, physicians, physicists, and specialists in interdisciplinary fields.

Expression of clMagR/clCry4 protein in mBMSCs provides T2-contrast enhancement of MRI

Here, we propose for the first time the evaluation of magnetosensitive clMagR/clCry4 as a magnetic resonance imaging (MRI) reporter gene that imparts sensitivity to endogenous contrast in eukaryotic organisms. Using a lentiviral vector, we introduced clMagR/clCry4 into C57BL/6 mice-derived bone marrow mesenchymal stem cells (mBMSCs), which could specifically bind with iron, significantly affected MRI transverse relaxation, and generated readily detectable contrast without adverse effects in vivo. Specifically, clMagR/clCry4 makes mBMSCs beneficial for enhancing the sensitivity of MRI-R2 for iron-bearing granules, in which cells recruit exogenous iron and convert these stores into an MRI-detectable contrast; this is not achievable with control cells. Additionally, Prussian blue staining was performed together with ultrathin cell slices to provide direct evidence of natural iron-bearing granules being detectable on MRI. Hence, it was inferred that the sensitivity of MRI detection should be correlated with clMagR/clCry4 and exogenous iron. Taken together, the clMagR/clCry4 has great potential as an MRI reporter gene. STATEMENT OF SIGNIFICANCE: In this study, we propose the evaluation of magnetosensitive clMagR/clCry4 as an MRI reporter gene, imparting detection sensitivity to eukaryotic mBMSCs for endogenous contrast. At this point, the clMagR and clCry4 were located within the cytoplasm and possibly influence each other. The clMagR/clCry4 makes mBMSCs beneficial for enhancing the sensitivity of MRI-R2 for iron-bearing granules, in which protein could specifically bind with iron and convert these stores into MRI-detectable contrast; this is not achieved by control cells. The viewpoint was speculated that the clMagR/clCry4 and exogenous iron were complementary to each other. Additionally, Prussian blue staining was performed together with TEM observations to provide direct evidence that the iron-bearing granules were sensitive to MRI.

Magnetic Stimulation as a Therapeutic Approach for Brain Modulation and Repair: Underlying Molecular and Cellular Mechanisms

Neurological and psychiatric diseases generally have no cure, so innovative non-pharmacological treatments, including non-invasive brain stimulation, are interesting therapeutic tools as they aim to trigger intrinsic neural repair mechanisms. A common brain stimulation technique involves the application of pulsed magnetic fields to affected brain regions. However, investigations of magnetic brain stimulation are complicated by the use of many different stimulation parameters. Magnetic brain stimulation is usually divided into two poorly connected approaches: (1) clinically used high-intensity stimulation (0.5-2 Tesla, T) and (2) experimental or epidemiologically studied low-intensity stimulation (μT-mT). Human tests of both approaches are reported to have beneficial outcomes, but the underlying biology is unclear, and thus optimal stimulation parameters remain ill defined. Here, we aim to bring together what is known about the biology of magnetic brain stimulation from human, animal, and in vitro studies. We identify the common effects of different stimulation protocols; show how different types of pulsed magnetic fields interact with nervous tissue; and describe cellular mechanisms underlying their effects-from intracellular signalling cascades, through synaptic plasticity and the modulation of network activity, to long-term structural changes in neural circuits. Recent advances in magneto-biology show clear mechanisms that may explain low-intensity stimulation effects in the brain. With its large breadth of stimulation parameters, not available to high-intensity stimulation, low-intensity focal magnetic stimulation becomes a potentially powerful treatment tool for human application.

Long-Time Oxygen and Superoxide Localization in Arabidopsis thaliana Cryptochrome

Cryptochromes are proteins that are highly conserved across species and in many instances bind the flavin adenine dinucleotide (FAD) cofactor within their photolyase-homology region (PHR) domain. The FAD cofactor has multiple redox states that help catalyze reactions, and absorbs photons at about 450 nm, a feature linked to the light-related functions of cryptochrome proteins. Reactive oxygen species (ROS) are produced from redox reactions involving molecular oxygen and are involved in a myriad of biological processes. Superoxide O2•- is an exemplary ROS that may be formed through electron transfer from FAD to O2, generating an electron radical pair. Although the formation of a superoxide-FAD radical pair has been speculated, it is still unclear if the required process steps could be realized in cryptochrome. Here, we present results from molecular dynamics (MD) simulations of oxygen interacting with the PHR domain of Arabidopsis thaliana cryptochrome 1 (AtCRY1). Using MD simulation trajectories, oxygen binding locations are characterized through both the O2-FAD intermolecular distance and the local protein environment. Oxygen unbinding times are characterized through replica simulations of the bound oxygen. Simulations reveal that oxygen molecules can localize at certain sites within the cryptochrome protein for tens of nanoseconds, and superoxide molecules can localize for significantly longer. This relatively long-duration molecule binding suggests the possibility of an electron-transfer reaction leading to superoxide formation. Estimates of electron-transfer rates using the Marcus theory are performed for the identified potential binding sites. Molecular oxygen binding results are compared with recent results demonstrating long-time oxygen binding within the electron-transfer flavoprotein (ETF), another FAD binding protein.

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.

On the anisotropic weak magnetic field effect in radical-pair reactions

For more than 60 years, scientists have been fascinated by the fact that magnetic fields even weaker than internal hyperfine fields can markedly affect spin-selective radical-pair reactions. This weak magnetic field effect has been found to arise from the removal of degeneracies in the zero-field spin Hamiltonian. Here, I investigated the anisotropic effect of a weak magnetic field on a model radical pair with an axially symmetric hyperfine interaction. I found that S-T± and T0-T± interconversions driven by the smaller x and y-components of the hyperfine interaction can be hindered or enhanced by a weak external magnetic field, depending on its direction. Additional isotropically hyperfine-coupled nuclear spins preserve this conclusion, although the S → T± and T0 → T± transitions become asymmetric. These results are supported by simulating reaction yields of a more biologically plausible, flavin-based radical pair.

Spin Dynamics of Flavoproteins

This short review reports the surprising phenomenon of nuclear hyperpolarization occurring in chemical reactions, which is called CIDNP (chemically induced dynamic nuclear polarization) or photo-CIDNP if the chemical reaction is light-driven. The phenomenon occurs in both liquid and solid-state, and electron transfer systems, often carrying flavins as electron acceptors, are involved. Here, we explain the physical and chemical properties of flavins, their occurrence in spin-correlated radical pairs (SCRP) and the possible involvement of flavin-carrying SCRPs in animal magneto-reception at earth's magnetic field.

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.

Statistical Amplification of the Effects of Weak Magnetic Fields in Cellular Translation

We assume that the enzymatic processes of recognition of amino acids and their addition to the synthesized molecule in cellular translation include the formation of intermediate pairs of radicals with spin-correlated electrons. The mathematical model presented describes the changes in the probability of incorrectly synthesized molecules in response to a change in the external weak magnetic field. A relatively high chance of errors has been shown to arise from the statistical enhancement of the low probability of local incorporation errors. This statistical mechanism does not require a long thermal relaxation time of electron spins of about 1 μs-a conjecture often used to match theoretical models of magnetoreception with experiments. The statistical mechanism allows for experimental verification by testing the usual Radical Pair Mechanism properties. In addition, this mechanism localizes the site where magnetic effects originate, the ribosome, which makes it possible to verify it by biochemical methods. This mechanism predicts a random nature of the nonspecific effects caused by weak and hypomagnetic fields and agrees with the diversity of biological responses to a weak magnetic field.

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.

Quantum-mechanical insights into the anisotropic response of the cryptochrome radical pair to a weak magnetic field

Cryptochrome photoreceptors contain a photochemically generated radical pair, which is thought to mediate sensing of the geomagnetic field direction in many living organisms. To gain insight into the response of the cryptochrome to a weak magnetic field, we have studied the quantum-mechanical hyperfine spin states of the radical pair. We identify quantum states responsible for the precise detection of the magnetic field direction, taking into account the strongly axial hyperfine interactions of each radical in the radical pair. The contribution of these states to the formation of the cryptochrome signaling state sharply increases when the magnetic field becomes orthogonal to the hyperfine axis of either radical. Due to such a response, the radical pair may be able to detect the particular field direction normal to the plane containing the hyperfine axes of the radicals.

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

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

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

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

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.

Long-Time Oxygen Localization in Electron Transfer Flavoprotein

Reactive oxygen species (ROS) exert a wide range of biological effects from beneficial regulatory function to deleterious oxidative stress. The electron transfer flavoprotein (ETF) is ubiquitous to life and is associated with aerobic metabolism and ROS production due to its location in the mitochondria. Quantifying oxygen localization within the ETF complex is critical for understanding the potential for electron transfer and radical pair formation between flavin adenine dinucleotide (FAD) cofactor and superoxide during ROS formation. Our study employed all-atom molecular dynamics simulations and identified several novel, long-lived oxygen binding sites within the ETF complex that appear near the FAD cofactor. Site locations, the local electrostatic environment, and characteristic oxygen binding times for each site were evaluated to establish factors that may lead to possible charge transfer reactions and superoxide formation within the ETF complex. The study revealed that some oxygen binding sites are naturally linked to protein domain features, suggesting opportunities to engineer and control ROS production and subsequent dynamics.

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.

Double cones in the avian retina form an oriented mosaic which might facilitate magnetoreception and/or polarized light sensing

To navigate between breeding and wintering grounds, night-migratory songbirds are aided by a light-dependent magnetic compass sense and maybe also by polarized light vision. Although the underlying mechanisms for magnetoreception and polarized light sensing remain unclear, double cone photoreceptors in the avian retina have been suggested to represent the primary sensory cells. To use these senses, birds must be able to separate the directional information from the Earth's magnetic field and/or light polarization from variations in light intensity. Theoretical considerations suggest that this could be best achieved if neighbouring double cones were oriented in an ordered pattern. Therefore, we investigate the orientation patterns of double cones in European robins (Erithacus rubecula) and domestic chickens (Gallus gallus domesticus). We used whole-mounted retinas labelled with double cone markers to quantify the orientations of individual double cones in relation to their nearest neighbours. In both species, our data show that the double cone array is highly ordered: the angles between neighbouring double cones were more likely to be 90°/-90° in the central retina and 180°/0° in the peripheral retina, respectively. The observed regularity in double cone orientation could aid the cells' putative function in light-dependent magnetoreception and/or polarized light sensing.

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.

Theoretical Concepts in Magnetobiology after 40 Years of Research

This review contains information on the development of magnetic biology, one of the multidisciplinary areas of biophysics. The main historical facts are presented and the general observed properties of magnetobiological phenomena are listed. The unavoidable presence of nonspecific magnetobiological effects in the everyday life of a person and society is shown. Particular attention is paid to the formation of theoretical concepts in magnetobiology and the state of the art in this area of research. Some details are provided on the molecular mechanisms of the nonspecific action of a magnetic field on organisms. The prospects of magnetobiology for the near and distant future are discussed.

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.

Exploring Post-activation Conformational Changes in Pigeon Cryptochrome 4

A widespread hypothesis ascribes the ability of migratory birds to navigate over large distances to an inclination compass realized by the protein cryptochrome in the birds' retinae. Cryptochromes are activated by blue light, which induces a radical pair state, the spin dynamics of which may become sensitive to earth's weak magnetic fields. The magnetic information is encoded and passed on to downstream processes by structural rearrangements of the protein, the details of which remain vague. We utilize extensive all-atom molecular dynamics simulations to probe the conformational changes of pigeon cryptochrome 4 upon light activation. The structural dynamics are analyzed based on principal component analysis and with the help of distance matrices, which reveal significant changes in selected inter-residue distances. The results are evaluated and discussed with reference to the protein structure and its putative function as a magnetoreceptor. It is suggested that the phosphate-binding loop could act as a gate controlling the access to the flavin adenine dinucleotide cofactor depending on the redox state of the protein.

Alzheimer's and Consciousness: How Much Subjectivity Is Objective?

Does Alzheimer Disease show a decline in cognitive functions that relate to the awareness of external reality? In this paper, we will propose a perspective that patients with increasing symptoms of AD show a change in the awareness of subjective versus objective representative axis of reality thus consequently move to a more internal like perception of reality. This paradigm shift suggests that new insights into the dynamicity of the conscious representation of reality in the AD brain may give us new clues to the very early signs of memory and self-awareness impairment that originates from, in our view the microtubules. Dialog between Adso and William, in Umberto Eco's The Name of the Rose, Third Day: Vespers. "But how does it happen," I said with admiration, "that you were able to solve the mystery of the library looking at it from the outside, and you were unable to solve it when you were inside?" "Thus, God knows the world, because He conceived it in His mind, as if it was from the outside, before it was created, and we do not know its rule, because we live inside it, having found it already made."

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 compass^2,3. 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 birds^4-7. 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.

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.

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.

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.

Electron transfer and spin dynamics of the radical-pair in the cryptochrome from Chlamydomonas reinhardtii by computational analysis

In an effort to elucidate the origin of avian magnetoreception, it was postulated that a radical-pair formed in a cryptochrome upon light activation provided the basis for the mechanism that enables an inclination compass sensitive to the geomagnetic field. Photoreduction in this case involves formation of a flavin adenine dinucleotide (FAD)-tryptophan (TRP) radical-pair, following electron transfer within a conserved TRP triad in the cryptochrome. Recently, an animal-like cryptochrome from Chlamydomonas reinhardtii (CraCRY) was analyzed, demonstrating the role of a fourth aromatic residue, which serves as a terminal electron donor in the photoreduction pathway, resulting in the creation of a more distal radical-pair and exhibiting fast electron transfer. In this work, we investigated the electron transfer in CraCRY with a combination of free energy molecular dynamics (MD) simulations, frozen density functional theory, and QM/MM MD simulations, supporting the suggestion of a proton coupled electron transfer mechanism. Spin dynamics simulations discerned details on the dependence of the singlet yield on the direction of the external magnetic field for the [FAD^•- TYRH^•+] and [FAD^•- TYR^•] radical-pairs in CraCRY, in comparison with the previously modeled [FAD^•- TRPH^•+] radical-pair.

The reference-probe model for a robust and optimal radical-pair-based magnetic compass sensor

Radical-pair reactions have been suggested to be sensitive to the direction of weak magnetic fields, thereby providing a mechanism for the magnetic compass in animals. Discovering the general principles that make radical pairs particularly sensitive to the direction of weak magnetic fields will be essential for designing bioinspired compass sensors and for advancing our understanding of the spin physics behind directional effects. The reference-probe model is a conceptual model introduced as a guide to identify radical-pair parameters for optimal directional effects. Radical pairs with probe character have been extensively shown to enhance directional sensitivity to weak magnetic fields, but investigations on the role of the reference radical are lacking. Here, we evaluate whether a radical has reference character and then study its relevance for optimal directional effects. We investigate a simple radical-pair model with one axially anisotropic hyperfine interaction using both analytical and numerical calculations. Analytical calculations result in a general expression of the radical-pair reaction yield, which in turn provides useful insights into directional effects. We further investigate the relevance of the reference character to robustness against variations of earth-strength magnetic fields and find that the reference character captures robust features as well. Extending this study to radical pairs with more hyperfine interactions, we discuss the interplay between reference character and optimal and robust directional effects in such more complex radical pairs.

Gaps in Knowledge Relevant to the "Guidelines for Limiting Exposure to Time-Varying Electric and Magnetic Fields (1 Hz-100 kHz)"

Sources of low-frequency fields are widely found in modern society. All wires or devices carrying or using electricity generate extremely low frequency (ELF) electric fields (EFs) and magnetic fields (MFs), but they decline rapidly with distance to the source. High magnetic flux densities are usually found in the vicinity of power lines and close to equipment using strong electrical currents, but can also be found in buildings with unbalanced return currents, or indoor transformer stations. For decades, epidemiological as well as experimental studies have addressed possible health effects of exposure to ELF-MFs. The main goal of ICNIRP is to protect people and the environment from detrimental exposure to all forms of non-ionizing radiation (NIR). To this end, ICNIRP provides advice and guidance by developing and disseminating exposure guidelines based on the available scientific research. Research in the low-frequency range began more than 40 years ago, and there is now a large body of literature available on which ICNIRP set its protection guidelines. A review of the literature has been carried out to identify possible relevant knowledge gaps, and the aim of this statement is to describe data gaps in research that would, if addressed, assist ICNIRP in further developing guidelines and setting revised recommendations on limiting exposure to electric and magnetic fields. It is articulated in two parts: the main document, which reviews the science related to LF data gaps, and the annex, which explains the methodology used to identify the data gaps.

Viability of superoxide-containing radical pairs as magnetoreceptors

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

How quantum is radical pair magnetoreception?

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

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

According to the currently prevailing theory, the magnetic compass sense in night-migrating birds relies on a light-dependent radical-pair-based mechanism. It has been shown that radio waves at megahertz frequencies disrupt magnetic orientation in migratory birds, providing evidence for a quantum-mechanical origin of the magnetic compass. Still, many crucial properties, e.g. the lifetime of the proposed magnetically sensitive radical pair, remain unknown. The current study aims to estimate the spin coherence time of the radical pair, based on the behavioural responses of migratory birds to broadband electromagnetic fields covering the frequency band 0.1-100 kHz. A finding that the birds were unable to use their magnetic compass under these conditions would imply surprisingly long-lived (greater than 10 µs) spin coherence. However, we observed no effect of 0.1-100 kHz radiofrequency (RF) fields on the orientation of night-migratory Eurasian blackcaps (Sylvia atricapilla). This suggests that the lifetime of the spin coherence involved in magnetoreception is shorter than the period of the highest frequency RF fields used in this experiment (i.e. approx. 10 µs). This result, in combination with an earlier study showing that 20-450 kHz electromagnetic fields disrupt magnetic compass orientation, suggests that the spin coherence lifetime of the magnetically sensitive radical pair is in the range 2-10 µs.

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

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

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.

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

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

Towards predicting intracellular radiofrequency radiation effects

Recent experiments have reported an effect of weak radiofrequency magnetic fields in the MHz-range on the concentrations of reactive oxygen species (ROS) in living cells. Since the energy that could possibly be deposited by the radiation is orders of magnitude smaller than the energy of molecular thermal motion, it was suggested that the effect was caused by the interaction of RF magnetic fields with transient radical pairs within the cells, affecting the ROS formation rates through the radical pair mechanism. It is, however, at present not entirely clear how to predict RF magnetic field effects at certain field frequency and intensity in nanoscale biomolecular systems. We suggest a possible recipe for interpreting the radiofrequency effects in cells by presenting a general workflow for calculation of the reactive perturbations inside a cell as a function of RF magnetic field strength and frequency. To justify the workflow, we discuss the effects of radiofrequency magnetic fields on generic spin systems to particularly illustrate how the reactive radicals could be affected by specific parameters of the experiment. We finally argue that the suggested workflow can be used to predict effects of radiofrequency magnetic fields on radical pairs in biological cells, which is specially important for wireless recharging technologies where one has to know of any harmful effects that exposure to such radiation might cause.

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.

Modeling MesoBioNano systems with MBN Studio made easy

This paper introduces MesoBioNano (MBN) Studio - a graphical user interface for a popular multiscale simulation package MBN Explorer. MBN Studio has been developed to facilitate setting up and starting MBN Explorer calculations, monitoring their progress and examining the calculation results. It is tailored for any calculations that are supported by MBN Explorer, such as for example the single-point energy calculations, structure optimization, molecular dynamics, and kinetic Monte Carlo simulations. Apart from that MBN Studio has built-in tools allowing the calculation and analysis of specific characteristics that are determined by the output of the simulations, such as the diffusion coefficients of molecular species, melting temperatures and associated heat capacities, radial distribution function; a dedicated modeling plug-in allows constructing molecular systems in a quick and efficient manner. Employing this plug-in, one can easily construct molecular systems of different geometries (e.g., spherical or ellipsoidal nanoparticles, cubic crystalline samples) with various atomic composition. The paper presents the first public release of MBN Studio and provides an overview of its significant capabilities, as well as the reference point for further extensions.

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

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

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.