Isotope effects on radical pair performance in cryptochrome: A new hypothesis for the evolution of animal migration: The quantum biology of migration

Mechanisms occurring at the atomic level are now known to drive processes essential for life, as revealed by quantum effects on biochemical reactions. Some macroscopic characteristics of organisms may thus show an atomic imprint, which may be transferred across organisms and affect their evolution. This possibility is considered here for the first time, with the aim of elucidating the appearance of an animal innovation with an unclear evolutionary origin: migratory behaviour. This trait may be mediated by a radical pair (RP) mechanism in the retinal flavoprotein cryptochrome, providing essential magnetic orientation for migration. Isotopes may affect the performance of quantum processes through their nuclear spin. Here, we consider a simple model and then apply the standard open quantum system approach to the spin dynamics of cryptochrome RP. We changed the spin quantum number (I) and g-factor of hydrogen and nitrogen isotopes to investigate their effect on RP's yield and magnetic sensitivity. Strong differences arose between isotopes with I = 1 and I = 1/2 in their contribution to cryptochrome magnetic sensitivity, particularly regarding Earth's magnetic field strengths (25-65 µT). In most cases, isotopic substitution improved RP's magnetic sensitivity. Migratory behaviour may thus have been favoured in animals with certain isotopic compositions of cryptochrome.

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.

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.

Role of chiral-induced spin selectivity in the radical pair mechanism of avian magnetoreception

In this paper, we investigate the effect of chiral-induced spin selectivity (CISS) on the radical pair mechanism of avian magnetoreception. We examine the impact of spin selectivity on the avian compass sensitivity. In this analysis, we also consider the dipolar and exchange interactions and observe their interplay with CISS. We find that CISS results in a multifold increase in avian compass sensitivity. Interestingly, we also observe that CISS can counter the deleterious effect of dipolar interaction and increase system sensitivity. The analysis has been performed for the toy model (only one nucleus) and a more general case where we consider up to six nuclei from the cryptochrome radical pair system. We observe that the CISS allows the radical pair model to have more realistic recombination rates with good sensitivity. We also do an analysis of the functional window of the avian compass reported in behavioral experiments in the functional window. We could not find a parameter set where a functional window can be observed along with CISS. We also show the effect of spin relaxation on the system and show that under relaxation, CISS shows increased compass sensitivity compared to no CISS case.

Non-Separability of Physical Systems as a Foundation of Consciousness

A hypothesis is presented that non-separability of degrees of freedom is the fundamental property underlying consciousness in physical systems. The amount of consciousness in a system is determined by the extent of non-separability and the number of degrees of freedom involved. Non-interacting and feedforward systems have zero consciousness, whereas most systems of interacting particles appear to have low non-separability and consciousness. By contrast, brain circuits exhibit high complexity and weak but tightly coordinated interactions, which appear to support high non-separability and therefore high amount of consciousness. The hypothesis applies to both classical and quantum cases, and we highlight the formalism employing the Wigner function (which in the classical limit becomes the Liouville density function) as a potentially fruitful framework for characterizing non-separability and, thus, the amount of consciousness in a system. The hypothesis appears to be consistent with both the Integrated Information Theory and the Orchestrated Objective Reduction Theory and may help reconcile the two. It offers a natural explanation for the physical properties underlying the amount of consciousness and points to methods of estimating the amount of non-separability as promising ways of characterizing the amount of consciousness.

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.

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.

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.

Quantum Entanglement from Classical Trajectories

A long-standing challenge in mixed quantum-classical trajectory simulations is the treatment of entanglement between the classical and quantal degrees of freedom. We present a novel approach that describes the emergence of entangled states entirely in terms of independent and deterministic Ehrenfest-like classical trajectories. For a two-level quantum system in a classical environment, this is derived by mapping the quantum system onto a path-integral representation of a spin 1/2. We demonstrate that the method correctly accounts for coherence and decoherence and thus reproduces the splitting of a wave packet in a nonadiabatic scattering problem. This discovery opens up a new class of simulations as an alternative to stochastic surface-hopping, coupled-trajectory, or semiclassical approaches.

Radical quantum oscillations

[Figure: see text].

The avian compass can be sensitive even without sustained electron spin coherence

Theoretical studies indicating the presence of long-lived coherence in the radical pair system have engendered questions about its utilitarian role in the avian compass. In this paper, we investigate the role of electron spin coherence in a multinuclear radical pair system including its impact on compass sensitivity. We find that sustenance of long-lived electron spin coherence is unlikely in a multinuclear hyperfine environment. After probing the role of the hyperfine interactions in the compass, we affirm the hyperfine anisotropy to be an essential parameter for the necessary sensitivity required for the compass action. Thereby, we identify a parameter regime where the compass would exhibit good sensitivity even without sustained electron spin coherence.

Radical pairs may play a role in xenon-induced general anesthesia

Understanding the mechanisms underlying general anesthesia would be a key step towards understanding consciousness. The process of xenon-induced general anesthesia has been shown to involve electron transfer, and the potency of xenon as a general anesthetic exhibits isotopic dependence. We propose that these observations can be explained by a mechanism in which the xenon nuclear spin influences the recombination dynamics of a naturally occurring radical pair of electrons. We develop a simple model inspired by the body of work on the radical-pair mechanism in cryptochrome in the context of avian magnetoreception, and we show that our model can reproduce the observed isotopic dependence of the general anesthetic potency of xenon in mice. Our results are consistent with the idea that radical pairs of electrons with entangled spins could be important for consciousness.

Spin relaxation in radical pairs from the stochastic Schrödinger equation

We show that the stochastic Schrödinger equation (SSE) provides an ideal way to simulate the quantum mechanical spin dynamics of radical pairs. Electron spin relaxation effects arising from fluctuations in the spin Hamiltonian are straightforward to include in this approach, and their treatment can be combined with a highly efficient stochastic evaluation of the trace over nuclear spin states that is required to compute experimental observables. These features are illustrated in example applications to a flavin-tryptophan radical pair of interest in avian magnetoreception and to a problem involving spin-selective radical pair recombination along a molecular wire. In the first of these examples, the SSE is shown to be both more efficient and more widely applicable than a recent stochastic implementation of the Lindblad equation, which only provides a valid treatment of relaxation in the extreme-narrowing limit. In the second, the exact SSE results are used to assess the accuracy of a recently proposed combination of Nakajima-Zwanzig theory for the spin relaxation and Schulten-Wolynes theory for the spin dynamics, which is applicable to radical pairs with many more nuclear spins. We also analyze the efficiency of trace sampling in some detail, highlighting the particular advantages of sampling with SU(N) coherent states.

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.