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

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

Structural Rearrangements of Pigeon Cryptochrome 4 Undergoing a Complete Redox Cycle.

Cryptochrome is currently the major contender of a protein to underpin magnetoreception, the ability to sense the Earth's magnetic field. Among various types of cryptochromes, cryptochrome 4 has been identified as the likely magnetoreceptor in migratory birds. All-atom molecular dynamics (MD) studies have offered first insights into the structural dynamics of cryptochrome but are limited to a short time scale due to large computational demands. Here, we employ coarse-grained MD simulations to investigate the emergence of long-lived states and conformational changes in pigeon cryptochrome 4. Our coarse-grained simulations complete the picture by permitting observation on a significantly longer time scale. We observe conformational transitions in the phosphate-binding loop of pigeon cryptochrome 4 upon activation and identify prominent motions in residues 440-460, suggesting a possible role as a signaling state of the protein or as a gated interaction site for forming protein complexes that might facilitate downstream processes. The findings highlight the importance of considering longer time scales in studying cryptochrome dynamics and magnetoreception. Coarse-grained MD simulations offer a valuable tool to unravel the complex behavior of cryptochrome proteins and shed new light on the mechanisms underlying their role in magnetoreception. Further exploration of these conformational changes and their functional implications may contribute to a deeper understanding of the molecular mechanisms of magnetoreception in birds.

Structure of the two-component S-layer of the archaeon Sulfolobus acidocaldarius.

Surface layers (S-layers) are resilient two-dimensional protein lattices that encapsulate many bacteria and most archaea. In archaea, S-layers usually form the only structural component of the cell wall and thus act as the final frontier between the cell and its environment. Therefore, S-layers are crucial for supporting microbial life. Notwithstanding their importance, little is known about archaeal S-layers at the atomic level. Here, we combined single-particle cryo electron microscopy, cryo electron tomography, and Alphafold2 predictions to generate an atomic model of the two-component S-layer of Sulfolobus acidocaldarius. The outer component of this S-layer (SlaA) is a flexible, highly glycosylated, and stable protein. Together with the inner and membrane-bound component (SlaB), they assemble into a porous and interwoven lattice. We hypothesise that jackknife-like conformational changes in SlaA play important roles in S-layer assembly.

Avian cryptochrome 4 binds superoxide.

Flavin-binding cryptochromes are blue-light sensitive photoreceptors that have been implicated with magnetoreception in some species. The photocycle involves an intra-protein photo-reduction of the flavin cofactor, generating a magnetosensitive radical pair, and its subsequent re-oxidation. Superoxide (O2•-) is generated in the re-oxidation with molecular oxygen. The resulting O2•--containing radical pairs have also been hypothesised to underpin various magnetosensitive traits, but due to fast spin relaxation when tumbling in solution would require immobilisation. We here describe our insights in the binding of superoxide to cryptochrome 4 from C. livia based on extensive all-atom molecular dynamics studies and density-functional theory calculations. The positively charged "crypt" region that leads to the flavin binding pocket transiently binds O2•- at 5 flexible binding sites centred on arginine residues. Typical binding times amounted to tens of nanoseconds, but exceptional binding events extended to several hundreds of nanoseconds and slowed the rotational diffusion, thereby realising rotational correlation times as large as 1 ns. The binding sites are particularly efficient in scavenging superoxide escaping from a putative generation site close to the flavin-cofactor, possibly implying a functional relevance. We discuss our findings in view of a potential magnetosensitivity of biological flavin semiquinone/superoxide radical pairs.

No evidence for magnetic field effects on the behaviour of Drosophila.

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

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.

The Biological Qubit: Calcium Phosphate Dimers, Not Trimers.

The Posner molecule (calcium phosphate trimer, Ca9(PO4)6) has been hypothesized to function as a biological quantum information processor due to its supposedly long-lived entangled 31P nuclear spin states. This hypothesis was challenged by our recent finding that the molecule lacks a well-defined rotational axis of symmetry─an essential assumption in the proposal for Posner-mediated neural processing─and exists as an asymmetric dynamical ensemble. Following up, we investigate here the spin dynamics of the molecule's entangled 31P nuclear spins within the asymmetric ensemble. Our simulations show that entanglement between two nuclear spins prepared in a Bell state in separate Posner molecules decays on a subsecond time scale─much faster than previously hypothesized, and not long enough for supercellular neuronal processing. Calcium phosphate dimers (Ca6(PO4)4) however, are found to be surprisingly resilient to decoherence and are able to preserve entangled nuclear spins for hundreds of seconds, suggesting that neural processing might occur through them instead.

Biological Effects of Radiofrequency Electromagnetic Fields above 100 MHz on Fauna and Flora: Workshop Report.

ABSTRACT: This report summarizes the effects of anthropogenic radiofrequency electromagnetic fields with frequencies above 100 MHz on flora and fauna presented at an international workshop held on 5-7 November 2019 in Munich, Germany. Anthropogenic radiofrequency electromagnetic fields at these frequencies are commonplace; e.g., originating from transmitters used for terrestrial radio and TV broadcasting, mobile communication, wireless internet networks, and radar technologies. The effects of these radiofrequency fields on flora, fauna, and ecosystems are not well studied. For high frequencies exceeding 100 MHz, the only scientifically established action mechanism in organisms is the conversion of electromagnetic into thermal energy. In accordance with that, no proven scientific evidence of adverse effects in animals or plants under realistic environmental conditions has yet been identified from exposure to low-level anthropogenic radiofrequency fields in this frequency range. Because appropriate field studies are scarce, further studies on plants and animals are recommended.

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

ABSTRACT: 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.

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

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

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.

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.

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.

High-Pressure ESR Spectroscopy: On the Rotational Motion of Spin Probes in Pressurized Ionic Liquids.

We report high-pressure (up to 50 MPa) ESR-spectroscopic investigations on the rotational correlation times of the nitroxide radicals 2,2,6,6-tetramethylpiperidine 1-oxyl (TEMPO), 4-hydroxy-2,2,6,6-tetramethylpiperidine 1-oxyl (TEMPOL), and 4-amino-2,2,6,6-tetramethylpiperidine 1-oxyl (ATEMPO) in the ionic liquids 1-ethyl-3-methylimidazolium tetrafluoroborate (emimBF4), 1-butyl-3-methylimidazolium hexafluorophosphate (bmimPF6), 1-butyl-3-methylimidazolium tetrafluoroborate (bmimBF4), 1-methyl-3-octylimidazolium tetrafluoroborate (omimBF4), and 1-methyl-3-octylimidazolium hexafluorophosphate (omimPF6). The activation volumes (38.5-56.6 Å3) determined from pressure dependent rotational diffusion coefficients agree well with the pressure dependent viscosities of the ionic liquids. Experimentally, the fractional exponent of the generalized Stokes-Einstein-Debye relation is found to be close to one.

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.

The Dynamical Ensemble of the Posner Molecule Is Not Symmetric.

The Posner molecule, Ca9(PO4)6, has long been recognized to have biochemical relevance in various physiological processes. It has found recent attention for its possible role as a biological quantum information processor, whereby the molecule purportedly maintains long-lived nuclear spin coherences among its 31P nuclei (presumed to be symmetrically arranged), allowing it to function as a room temperature qubit. The structure of the molecule has been of much dispute in the literature, although the S6 point group symmetry has often been assumed and exploited in calculations. Using a variety of simulation techniques (including ab initio molecular dynamics and structural relaxation), rigorous data analysis tools, and by exploring thousands of individual configurations, we establish that the molecule predominantly assumes low-symmetry structures (Cs and Ci) at room temperature, as opposed to the higher-symmetry configurations explored previously. Our findings have important implications for the viability of this molecule as a qubit.

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.