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

A large and growing body of research shows that weak magnetic fields can significantly influence various biological systems, including plants, animals, and humans. However, the underlying mechanisms behind these phenomena remain elusive. It is remarkable that the magnetic energies implicated in these effects are much smaller than thermal energies. Here we review these observations, of which there are now hundreds, and we suggest that a viable explanation is provided by the radical pair mechanism, which involves the quantum dynamics of the electron and nuclear spins of naturally occurring transient radical molecules. While the radical pair mechanism has been studied in detail in the context of avian magnetoreception, the studies reviewed here show that magnetosensitivity is widespread throughout biology. We review magnetic field effects on various physiological functions, organizing them based on the type of the applied magnetic fields, namely static, hypomagnetic, and oscillating magnetic fields, as well as isotope effects. We then review the radical pair mechanism as a potential unifying model for the described magnetic field effects, and we discuss plausible candidate molecules that might constitute the radical pairs. We review recent studies proposing that the quantum nature of the radical pairs provides promising explanations for xenon anesthesia, lithium effects on hyperactivity, magnetic field and lithium effects on the circadian clock, and hypomagnetic field effects on neurogenesis and microtubule assembly. We conclude by discussing future lines of investigation in this exciting new area of quantum biology related to weak magnetic field effects.


Introduction
Sensitivity to weak magnetic fields is abundant throughout biology, as discussed in numerous review articles  . Effects of either static or oscillating weak magnetic fields have been reported on the circadian clock, electron transfer in cryptochrome, stem cells, calcium concentration, the brain's functions such as action potentials, reactive oxygen species, development, neuronal activities, DNA, memory, anxiety, analgaesia, genetics, and many other functions (See Section 2). Despite the wealth of observations, thus far there is no clear explanation for the mechanism behind these phenomena. This is mainly due to the fact that the corresponding energies for such effects are far smaller than thermal energies.
However, there is a promising quantum physics (or spin chemistry) concept that can account for the effects of such weak fields, namely the radical pair mechanism 26, 27 . This mechanism, which is an example of the emerging field of quantum biology 28-32 , has been studied in significant detail in the comparatively narrow context of bird magnetoreception [33][34][35][36][37][38][39][40] , where it is accepted as one of the leading potential explanations for how birds sense magnetic fields, and in particular the Earth's magnetic field, for the purpose of navigation.
It involves magnetically sensitive intermediate molecules, so-called radical pairs 26, 41-46 . The key ingredient is the spin correlation between two unpaired electrons, one on the donor molecule and the other on the acceptor molecule. Depending on the initial spin configuration of the donor molecule, this initial spin correlation of the radical pair will be either a singlet (S) or a triplet (T) state, which are respectively spin-0 and spin-1 states (See Section 3.1 for further discussion). Due to the spin interactions with its environment (in particular with external magnetic fields and with nearby nuclear spins), the state of the radical pair will oscillate between S and T states 27,47 . Each spin state, S and T, can lead to different reaction products, providing an example of spin chemistry 48,49 . The energies induced by the above-mentioned magnetic fields are hundreds of thousands of times smaller than thermal energies, k B T (k B is Boltzmann constant and T is temperature), which are associated with motions, rotation, and vibrations in biological environments. In thermal equilibrium, the energies required to alter the rate or yield of a chemical transformation should be at least comparable to K B T . Due to this, the radical pair 2/72 mechanism was originally ignored in the context of physiology. However, the situation differs in systems far from thermal equilibrium, which is the case for radical pairs 44 . Sensitivity to weak magnetic fields is one of the key properties of radical pair reactions. Nowadays, many research labs study the role of radical pairs in (bio)chemical reactions 27, 49-53 .
Recent studies have proposed roles for radical pairs beyond avian magnetoreception, in particular in xenon-induced anesthesia 54 , lithium effects on mania 55 , magnetic field and lithium effects on the circadian clock 56 , and hypomagnetic field effects on microtubule reorganization 57 and neurogenesis 58 (where hypomagnetic fields are fields much weaker than that of the Earth). Here we suggest that the radical pair mechanism is in fact quite common in biology, and that it may provide an explanation for many of the weak magnetic field effects on physiological functions that have been observed.
This paper, which is part review and part perspective article, is organised as follows. Section 2 briefly surveys studies reporting effects of low-intensity magnetic fields on biological systems, including effects of static (Section 2.1), hypomagnetic (Section 2.2), and oscillating (Section 2.3) magnetic fields. We further survey studies on isotope effects in biology form a spin perspective. In Section 3, we discuss how the radical pair mechanism can account for static, hypomagnetic, and oscillating magnetic field effects. Section 3.4 reviews possible candidate molecules for radical pair formation in biological systems. In Section 4, we review the above-mentioned recent studies on the possible biological roles of radical pairs beyond avian magnetoreception. Section 5 discusses important directions for further investigation.

Magnetosensitivity in biology
There is a considerable amount of research investigating magnetic field effects on biological functions 23, 59-67 . In the following, we review the effects of low-intensity magnetic fields on biology. We organize this section based on the type of magnetic fields, namely static magnetic fields, hypomagnetic fields, and oscillating magnetic fields. Isotope effects in biology, which can be related to nuclear magnetic moments, are also discussed at the end of this section.

Cryptochrome
In the context of avian magnetoreception in animals, the canonical proteins are cryptochromes 44 71 . In addition, using a transgenic approach, Foley et al. showed that human cryptochrome-2 has the molecular capability to function as a light-sensitive magnetosensor 72 . Applying a 0.5 mT magnetic field, Ahmad and co-workers reported that cryptochrome responses were enhanced by the magnetic field, including darkstate processes following the cryptochrome photoreduction step 73,74 . Further, there have been extensive studies on the radical pair mechanism for cryptochrome(s) 43, 44 . Table 1 summarizes static magnetic field effects on various biological functions.

Genetics
It is known that exposure to magnetic fields has genetic consequences 75 Table 1).

Circadian clock
It has been shown that magnetic fields can modulate the circadian clock 78-80 . Yoshii et al. 81 showed that the effects of static magnetic fields affected the circadian clock of Drosophila and reported that exposure to these fields slowed down the clock rhythms in the presence of blue light, with a maximal change at 300 µT, and reduced effects at both lower and slightly higher field strengths. We discuss this observation further from the perspective of the radical pair mechanism in Section 4.3 (See Table 1).

Stem cells
Static magnetic field has been commonly used in medicine as a tool to increase wound healing, bone regeneration and as a component of magnetic resonance techniques. However, recent data shed light on deeper mechanism of Static magnetic field action on physiological properties of different cell populations, including stem cells. It is known that static magnetic fields can increase wound healing and bone regeneration 8 . Huizen et al. reported that weak magnetic fields (<1 mT) alter stem cell-mediated growth, where changes in ROS were implicated 82 . The authors suggested that the radical pair mechanism may be the potential explanation for their observations. Zheng et al. showed that static magnetic field of 1, 2, or 4 mT regulated proliferation, migration, and differentiation of human dental pulp stem cells 83 . It is also known that applied static magnetic fields (0.5-30 mT) affect stem cells in vitro 84-86 (See Table 1).

Calcium
Fanelli et al. reported that magnetic fields allow the indefinite survival and replication of the cells hit by apoptogenic agents. The anti-apoptosis effect was found to be mediated by the ability of the fields to increase Ca 2+ influx from the extracellular medium. In that experiment, the geomagnetic field was not shielded. They found 0.6 mT to be the minimal intensity required to detect an anti-apoptotic effect 87 . Moreover, it has been shown that weak static magnetic fields can influence myosin phosphorylation in a cell-free preparation in a Ca 2+ -dependent manner 88 . Tenuzzo and colleagues observed that exposure to a 6 mT static magnetic field influenced Ca 2+ concentration and bcl-2, bax, p53 and hsp70 expression in freshly isolated and in vitro aged human lymphocytes 89 . Further, Chionna et al. showed that exposure to a static magnetic field of 6 mT of Hep G2 cells resulted in time dependent modifications in cell shape, cell surface, sugar residues, cytoskeleton, and apoptosis 90 . They reported that after 24 h exposure, the cells had a less flat shape due to partial detachment from the culture dishes. They further observed that microfilaments and microtubules were modified in a time dependent manner. They also suggested that the induced apoptosis was likely due to the increment of Ca 2+ during exposure. In another study, Tenuzzo and co-workers showed that cell viability, proliferation, intracellular Ca 2+ concentration and morphology in several primary cultures and cell lines can be influenced by a 6 mT magnetic field 91 (See Table 1).

Neurons and brain
Exposure to static magnetic fields can have impacts on various brain functions. McLean et al. reported that a static magnetic field in the 10 mT range blocked sensory neuron action potentials in the somata of adult mouse dorsal root ganglion neurons in monolayer dissociated cell culture 92 . It has also been shown that exposure to a transcranial static magnetic field over the supplementary motor area can modulate resting-state activity and motor behavior associated with modulation of both local and distant functionally-connected cortical circuits 93 . Static magnetic field exposure can also affect the production of melatonin 94-97 , the pineal gland 98,99 , and cause functional alterations in immature cultured rat hippocampal neurons 100  induce dopamine-dependent changes of cortical excitability in patients with Parkinson's disease 101 . In addition, neuron firing frequency can also be affected by static magnetic field intensity 102,103 . There exist a considerable number of studies indicating the effects of applied magnetic field on pain sensitivity (nociception) and pain inhibition (analgesia) 104 . Additionally, it has been known that a static magnetic field (50 mT) can influence symptomatic diabetic neuropathy 105 (See Table 1).

Reactive oxygen species
Reactive oxygen species (ROS) is the collection of derivatives of molecular oxygen that occur in biology, which can be categorized into two types, free radicals and non-radical species. The non-radical species are hydrogen peroxide (H 2 O 2 ), organic hydroperoxides (ROOH), singlet molecular oxygen ( 1 O 2 ), electronically excited carbonyl, ozone (O 3 ), hypochlorous acid (HOCl, and hypobromous acid HOBr). Free radical species are superoxide anion radical (O -2 ), hydroxyl radical (·OH), peroxyl radical (ROO·), and alkoxyl radical (RO·) 106 15,111,112 , which is "an imbalance between oxidants and antioxidants in favor of the oxidants, leading to a disruption of redox signaling and control and/or molecular damage." [113][114][115] . Studies found that exposure to static magnetic fields of 2.2 mT 116 and 31.7-232 mT 117 increased the intercellular ROS in human neuroblastoma cells. Furthermore, De Nicola et al. observed that the intracellular ROS level in human monocyte tumor cells was raised when exposed to a static magnetic field 118 . Further, Bekhite et al. reported that static magnetic field exposure (1-10 mT) increased the H 2 O 2 level in embryoid bodies 119 . Later, the same group found an induced increase of ROS in cardiac progenitor cells derived from mouse cells by 0.2-5 mT static magnetic field, where ROS was suggested to be generated by NADPH oxidase 120 . Sullivan et al. reported that 230-250 mT of a magnetic field elevated H 2 O 2 in diploid embryonic lung fibroblast cell 121 . Upon exposure to 45-60 µT, Marino and Castello observed an increase of H 2 O 2 in the human fibrosarcoma cancer cell, which can be suppressed by reducing the geomagnetic field's strength 122 . Further studies show that exposure to 60 mT magnetic field increased H 2 O 2 production of human peripheral blood neutrophils 123 . It has also been reported that the effects of an applied magnetic field of 10 mT on DOXO-induced toxicity and proliferation rate of cancer cells are correlated to ROS levels 124 . Furthermore, Carter et al. observed that a 3 mT static magnetic field can influence type 2 diabetes via regulating cellular ROS 125, 126 . Pooam et al. showed that applying low intensity static magnetic field modulated ROS generation in HEK293 cells. The authors suggested that the radical pair mechanism may explain that observation 127 . In a recent work, Sheu and co-workers reported that static low intensity magnetic field can regulate mitochondrial electron transport chain activity as thus enhance mitochondrial respiration. 128 . They observed that exposure to magnetic fields of 0-1.93 mT of mitochondria isolated from adult rat hearts produced a bell-shape increase in the respiratory control ratio with a maximum at 0.50 mT and a return to baseline at 1.50 mT. It was further observed that the magnetic field affected only the activity of the complexes 2, 3 and 5 but not 1 of the mitochondrial electron transport chain and several enzymes of the tricarboxylic acid cycle. The authors suggested that the low intensity magnetic field effects on the mitochondrial respiratory activity may be explained by the radical pair mechanism. Huizen and co-workers showed that weak magnetic fields (<1 mT) changed stem cell-mediated growth, where changes in ROS were implicated 82 .

Others
Ikeya et al. reported that exposure to magnetic field influenced autofluorescence in cells involving flavins 129 . Studies also showed that static magnetic fields can affect the photoactivation reaction of E.coli DNA photolyase 130 . Moreover, Giachello et al. observed that applying static magnetic fields on blue-light activated cryptochromes in Drosophila neurons resulted in an elevation of action potential firing 131 . Further, it is also known that the chemiluminescence intensity in Madin-Darby canine kidney cells is magnetic field dependent 132 , where ROS are implicated. In solutions, flavin adenine dinucleotide is the key cofactor of cryptochrome. Antill and co-workers showed that flavin adenine dinucleotide photochemistry in solution is magnetic field sensitive (<20 mT) even at physiological pH and higher 133 .
Buchachenko et al. reported that applying 80 mT static magnetic field affected enzymatic ATP production 134 . Recently, Ercan et al. showed that exposure to magnetic fields (20, 42, 125, and 250 mT) can affect the magnetic properties, germination, chlorophyll fluorescence, and nutrient content of barley (Hordeum vulgare L.) 135 . Further, it is observed that exposure to magnetic fields (10 and 30 mT) can deteriorate the antioxidant defense system of plant cells 136 . Hao et al. reported that exposure to a 8.8 mT static magnetic field can enhance the killing effect of adriamycin on K562 cells 137 . It is also observed that exposure to magnetic fields (2.9-4.6 mT) of soybean tissue culture enhances the regeneration and plant growth of shoot tips 138 . Teodori et al. showed that exposure of HL-60 cells to a 6 mT static magnetic field accelerated loss of integrity of plasma membrane during apoptosis 139 . It has been shown that exposure of human pro-monocytic U937 cells to a static magnetic field (6 mT) decreased the degree of macrophagic differentiation 140 . Buemi et al. report that exposure to a 0.5 mT magnetic field of renal cell cultures and cortical astrocyte cultures from rats influenced cell proliferation and cell death balance 141 . They concluded that such magnetic field effects were cell type-dependent. It has been shown that exposure to magnetic fields (1 mT) significantly affected growth and sporulation of phytopathogenic microscopic fungi 142 .
Surma et al. found that the application of weak static magnetic field with intensities only a few times that of the geomagnetic field can accelerate the development of skeletal muscle cells, resulting in the formation of multinuclear hypertrophied myotubes 143 . They further reported that these effects were accompanied by a 1.5-to 3.5-fold rise in the concentration of intracellular [Ca 2+ ] i .
It has also been suggested that the apparent cyclic of mass extinction on Earth 150 may be related to the geomagnetic field fluctuation 151 . Decades ago, first studies on the effects of hypomagnetic field on humans were conducted, motivated by the concerns around the health of astronauts in outer space [152][153][154][155] . These studies concluded that exposure to hypomagnetic fields had adverse effects on human health. Besides hypomagnetic field effects on animal and human cells and tissues, deprivation in geomagnetic field can influence the development of plants as well 148,149 . The geomagnetic field seems to play essential roles in living organisms, and diminishing or disappearing of it could result in adverse consequences.
It was shown that exposure to hypomagnetic fields decreased the size and number of Staphylococcus aureus Rosenbach 156 . Exposure to hypomagnetic fields can also influence early developmental processes of newt (Cynops pyrrhogaster) 157 , early embryogenesis 158,159 , development of Xenopus 160 , cryptochromerelated hypocotyl growth and flowering of Arabidopsis 161, 162 , development and reproduction of brown planthopper 163 , mortality 164 and anhydrobiotic abilities 165

in tardigrades.
It was observed that the circadian clock in fiddler crabs and other organisms 166 , including human 167 , and birds 168 can be influenced by exposure to hypomagnetic fields.  Zhang et al. showed that long-term exposure to hypomagnetic fields adversely influenced adult hippocampal neurogenesis in mice 169 . They further observed that these effects were accompanied by reductions in ROS levels. Moreover, Wang et al. observed that exposure to hypomagnetic fields (10-100 nT) caused disorders in tubulin self-assembly 170 . They show that the absorbance for monitoring tubulin self-assembly was altered by exposure to hypomagnetic fields. We discuss both these observations from 7/72 the perspective of the radical pair mechanism in the following (See Sections 4.4 and 4.5). Furthermore, Baek et al. reported that exposure to hypomagnetic fields influenced DNA methylation in vitro in mouse embryonic stem cell (ESC) culture 171 . Upon exposure to a hypomagnetic field ESCs morphology remained undifferentiated while under exposure to the geomagnetic field, ESCs exhibited differentiation. Moreover, Ikenaga and co-workers reported that genetic mutation in Drosophila during space flight 172 . Further, Martino and co-workers reported that reducing the geomagnetic field to 6-13 µT resulted in significantly altered cell cycle rates for multiple cancer-derived cell lines 173 . Belyavskaya observed that hypomagnetic conditions included reduction of the meristem, disruption of protein synthesis and accumulation of lipids, reduction of the organelle's growth, the amount of phytoferritin in plastids and crista in mitochondria 174 . Further, the effects of zero magnetic field on human VH-10 fibroblasts and lymphocytes were observed by Belyaev et al. 175 . They concluded that exposure to hypomagnetic fields caused hypercondensation and decondensation of chromatin. Studies conducted by NASA revealed that exposure to hypomagnetic fields decreased enzyme activity in cells obtained from mice 176 .

6/72
Yan et al. show that reducing the magnetic field to <0.5 µT significantly lengthened larval and pupal development durations, increased male longevity, and reduced pupal weight, female reproduction, and the relative expression level of the vitellogenin (Vg) gene in Mythimna separata 177 . In addition, they observed that exposure to the hypomagnetic field had adverse effect on the mating ratio of M. separata adults. They further reported that the moths in the hypomagnetic conditions had less flight activity late in the night compared to the control group. They suggest that the latter may be related to the circadian rhythm of M. separata.
Sarimov et al. reported that hypomagnetic conditions influence human cognitive processes 178 . They concluded that exposure to hypomagnetic fields resulted in an increased number of errors and extension of the time required to complete the tasks compared to normal conditions. Wang and co-workers showed that exposure to hypomagnetic fields induced cell proliferation of SH-SY5Y cells in a glucose-dependent manner 179 . They suggested that lactate dehydrogenase was a direct response to cell proliferation under hypomagnetic conditions. The authors further proposed that the up-regulation of anaerobic glycolysis and repression of oxidative stress shifted cellular metabolism more towards the Warburg effect commonly observed in cancer metabolism. Table 2 summarizes hypomagnetic field effects observed on various physiological functions.

Low-frequency
The effects of oscillating magnetic fields on biological functions are abundant [204][205][206][207][208][209][210][211][212] , and are often correlated with modulation of ROS levels [213][214][215] . In this section, we review several studies on extremely low-frequency (< 3 kHz) magnetic fields on various biological functions. Sherrard and co-workers showed that exposure of the cerebellum to low-intensity repetitive transcranial magnetic stimulation (LI-rTMS) (10 mT) modulated behaviour and Purkinje cell morphology 216,217 . Recently, the same group reported that LI-rTMS (2 mT) induced axon growth and synapse formation providing olivocerebellar reinnervation in the cerebellum 218 . The authors concluded that cryptochrome was required for the magnetosensitivity of the neurons, which was consistent with ROS production by activated cryptochrome 219 . In a recent study, the team showed that LI-rTMS (10 mT and 10 Hz) evoked neuronal firing during the stimulation period and induced durable attenuation of synaptic activity and spontaneous firing in cortical neurons of rats in vivo 220 .
Contalbrigo et al. showed that magnetic fields (< 1 mT, 50 Hz) influenced some haematochemical parameters of circadian rhythms in Sprague-Dawley rats 221 . Further, Fedele et al. reported that a 300 µT magnetic field (3-50 Hz) induced changes in two locomotor phenotypes, circadian period and activity levels via modulating cryptochrome in Drosophila 222 . Moreover, it has been shown that exposure to a magnetic field of a 0.1 mT and 50 Hz alters clock gene expressions 223 .
Manikonda et al. applied magnetic fields (50 and 100 µT, 50 Hz) to cerebellum, hippocampus, and cortex of rat's brain. They observed that H 2 O 2 increased in the descending order of cerebellum, hippocampus, and cortex. In that work, 100 µT induced more oxidative stress compared to 50 µT 224 . Furthermore, Özgün et al. reported that exposure to a magnetic field (1 mT, 50 Hz) in vitro induced human neuronal differentiation through N-methyl-d-aspartate (NMDA) receptor activation 225 . They observed that magnetic field enhanced intracellular Ca 2+ levels. The authors concluded that NMDA receptors are essential for magnetosensitivity in such phenomena. It is also known that a combination of static (27-37 µT) and time varying (13/114 µT, 7/72 Hz) magnetic fields directly interact with the Ca 2+ channel protein in the cell membrane 226 . It has also been reported that exposure to >5 mT (50 Hz) magnetic fields may promote X-ray-induced mutations in hamster ovary K1 cells 227 . Koyama et al. showed that exposure to a magnetic field of 5 mT (60 Hz) promoted damage induced by H 2 O 2 , resulting in an increase in the number of mutations in plasmids in Escherichia coli 228 . Studies of extremely low-frequency magnetic field effects (< 1000 Hz) on various biological functions are shown in Tables 3 and 4.

Medium/High-frequency
In this section, we review several studies on medium/high-frequency (> 3kHz) magnetic field effects on various physiological functions. Usselman et al. reported that oscillating magnetic fields at Zeeman resonance (1.4 MHz and 50 µT) influenced relative yields of cellular O -2 and H 2 O 2 products in human umbilical vein endothelial cells 337 . Considering a radical pair in [FADH ..O -2 ] form, the authors suggested that coherent electron spin dynamics may explain their observation. Moreover, Friedman et al. observed that a 875 MHz magnetic field increased ROS production, which was mediated by membrane-associated Nox in HeLa cells and rat 338 . Castello and colleagues showed that exposure of fibrosarcoma HT1080 cells to weak radio frequency (5/10 MHz) combined with a 45 µT static magnetic field modulated the number of cells and significantly increased H 2 O 2 production 339 . Martino and Castello showed that exposure of cultured yeast and isolated mitochondria to magnetic fields (150 µT; 45 µT and a parallel 10 MHz RF; 45 µT and a perpendicular 10 MHz RF) modulated the production of extracellular, intracellular, and mitochondrial O -2 and H 2 O 2 340 . They concluded that complex I of the electron transport chain is involved in the H 2 O 2 production. Table 6 summarizes a few medium/high-frequency magnetic field effects observed 10/72 Table 3. Extremely low-frequency (< 3 kHz) magnetic field effects on memory, stress, pain, dopamine, serotonin, melatonine, genetics, and calcium flux. in various experiments.

Isotope effects
Atomic nuclei contain protons and neutrons. The number of protons determines the element (e.g. carbon, oxygen, etc.), and the number of neutrons determines the isotope of the desired element. Some isotopes are  Inheriting quantum properties, not only do different isotopes of an element have different masses, but they can also have different spins. For that reason, isotope effects in (bio)chemical reactions can be regarded from two distinct points of view: mass-dependency and spin-dependency. Thiemens et al. observed massindependent isotope effects as a deviation of isotopic distribution in reaction products [366][367][368][369][370] . Furthermore, in 1976 Buchachenko and colleagues by applying magnetic fields detected the first mass-independent isotope effect, which chemically discriminated isotopes by their nuclear spins and nuclear magnetic moments 371 . Since then, the term "magnetic isotope effect" was dubbed for such phenomena as they are controlled by electron-nuclear hyperfine coupling in the paramagnetic species. Moreover, isotope effects have been observed for a great variety of chemical and biochemical reactions involving oxygen, silicon, 12/72   sulfur, germanium, tin, mercury, magnesium, calcium, zinc, and uranium 62, 364,365,[372][373][374][375][376][377][378] . In this review, we focus on isotope effects from spin perspective, see Table 7.
In 1986 Sechzer and co-workers reported that lithium administration results in different parenting behaviors and potentially delayed offspring development in rats 379 . Their findings weren't quantitative; however, it was observed that different lithium isotopes exhibited different impacts. Moreover, in 2020, Ettenberg et al. 380 conducted an experiment demonstrating an isotope effect of lithium on rat's hyperactivity. Lithium has two stable isotopes, 6 Li and 7 Li, possessing different nuclear spin angular 13/72 momentum, I 6 = 1 and I 7 = 3/2, respectively. In that work, the mania phase was induced by sub-anesthetic doses of ketamine. The authors reported that 6 Li produced a longer suppression of hyperactivity in an animal model of mania compared to 7 Li. We further discuss this phenomenon from the point of view of the radical pair mechanism in Section 4.2.
Li and co-workers reported that xenon (Xe)-induced anesthesia in mice is isotope-dependent. They used four different Xe isotopes, 129 Xe, 131 Xe, 132 Xe, and 134 Xe with nuclear spins of 1/2, 3/2, 0, and 0, respectively 381 . The results fell into two groups, isotopes with spin and isotopes without spin, such that isotopes of xenon with non-zero nuclear spin had lower anesthetic potency than isotopes with no nuclear spin. The results of this work are discussed from the perspective of the radical pair mechanism in Section 4.1.
Buchachenko et al. observed that magnesium-25 ( 25 Mg) controlled phosphoglycerate kinase (PGK) 382 . 25 Mg has a nuclear spin of 5/2, while 24 Mg is spin-less. The authors reported that ATP production was more than twofold in the presence of 25 Mg compared to 24 Mg. They suggested that the nuclear spin of Mg was the key factor for such an observation. In another study, the same group reported that 25 Mg reduced enzymatic activity compared to 25 Mg in polymerases β . They concluded that DNA synthesis is magnetic-dependent 383,384 . In the same system, they further observed that if Mg 2+ ion is replaced by stable isotopes of calcium ion, 40 Ca 2+ and 43 Ca 2+ (with nuclear spins of 0, 7/2, respectively), the enzyme catalytic reactions will be isotope-dependent, such that 43 Ca 2+ promoted enzyme hyper-suppression leading to a residual synthesis of shorted DNA fragments compared to 40 Ca 2+385 . They repeated the same experiment but his time instead of Mg 2+ ion stable isotopes of zinc, 64 Zn 2+ and 67 Zn 2+ (with nuclear spins of 0, 5/2, respectively) were used. The authors reported that 67 Zn 2+ suppressed DNA synthesis a few times more than 64 Zn 2+386 . 3 The radical pair mechanism

Spin and radical pairs
Spin is an inherently quantum property that emerges from Dirac's relativistic quantum mechanics 387, 388 , and is described by two numbers, S and m s , respectively, the spin quantum number and the spin projection quantum number. Electrons, protons, and neutrons have spins of S = 1 2 . Having an angular momentum characteristic, spin can be coupled not only with external magnetic fields but also with other spin in its vicinity. For instance, coupling of two electrons spins, S A and S B , results in a total spin of S T , which has a quantum number of either S = 1 or S = 0. The latter case is called a singlet state, with m s = 0, and the former is called a triplet state, with m s = 0, ±1 389 .

14/72
where ⊗ is the tensor product. Radicals are molecules with an odd number of electrons in the outer shell 390,391 . A pair of radicals can be formed by breaking a chemical bond or electron transfer between two molecules. It is important to notice that in reactions of organic molecules, spin is usually a conserved quantity, which is essential for magnetic field effect in biochemical reactions. For example, a radical pair can be created if a bond between a pair of molecules [A...D] breaks or an electron is transferred from D to A, [A -...D + ] (D and A denote donor and acceptor molecules). A radical pair may be in a superposition of singlet and triplet states, depending on the parent molecule's spin configuration. Assuming that the initial state of the electron pairs before separation was a singlet (triplet), the recombination of unpaired electrons can only happen if they stayed in a singlet (triplet) 392 .
If the radical pairs are formed in singlet (triplet) states, the initial spin density matrix reads as follows: whereP S andP T are the singlet and triplet projection operators, respectively, M is the nuclear spin multiplicity, I i is the spin angular momentum of i-th nucleus, and1 is the identity matrix. S is entangled. The T projector is not entangled, even though T0 is an entangled state.

Zeeman interaction
The interaction between the unpaired electron spins on each radical and the external magnetic field is essential for generating MFEs. This interaction is called the Zeeman effect 393 . The nuclear spins of radical molecules also experience applied magnetic fields; however, as nuclear magnetogyric ratios are much smaller than that of the electrons, these interactions are negligible. The Zeeman interaction is defined in the following form:Ĥ where µ B ,Ŝ, g-tensor, and B are the Bohr magneton, the spin operators of electron, the interaction coupling, and applied magnetic field, respectively. Here, we focus on magnetic field interactions with relatively low field strengths. In such cases, it is possible to assume that the g-tensor equals to g e of free electron, and hence,Ĥ where γ e is the electron magnetogyric ratio.

Hyperfine interaction
Similar to electron-electron spin coupling, electron spins can couple to the nuclear spins, called hyperfine interactions 394 . This interaction consists of two contributions, isotropic and anisotropic interactions. The former is also called Fermi contact term, which results from the magnetic interaction of the electron and nuclear spins when the electron is within the nucleus. The overall hyperfine interaction can be defined as follows:Ĥ where a i andÎ i are the hyperfine coupling tensor and nuclear spin of i-th nucleus. The anisotropic components of the hyperfine interactions are only relevant when the radicals are immobilised and aligned 26 .
Neglecting the anisotropic component of the hyperfine interaction, the hyperfine Hamiltonian has the following form:Ĥ where a i is the isotropic hyperfine coupling constant and can be calculated as: µ 0 is the vacuum permeability, γ n is the nuclear magnetogyric ratio, and |Ψ(0)| 2 is the electron probability density at the nucleus 395 .

Exchange interaction
The electrons on radicals are identical in quantum calculations. This indistinguishability of electrons on radical pairs can be introduced via the exchange interaction 396 . It is generally assumed to weaken exponentially with increasing radical pair separation. The exchange interaction can prevent singlet-triplet interconversion, as discussed later. However, recent studies show that this term is negligible 397 in the magnetic field effects on pigeon cryptochrome 398 .

Dipolar interaction
As spins are magnetic moments, the radical pairs also influence each other by a dipolar interaction 399 . This interaction can suppress singlet-triplet interconversion in the radical pair dynamics. However, studies on avian magnetoreception suggest that under certain conditions exchange and dipolar interactions can be neglected 44, 400-403 .

Other contributions
It is thought that after a first re-encounter, radicals either react or diffuse apart forever 404 . In the context of brids' magnetoreception, for this contribution, an exponential model is used 44, 405 . High electron density on an atom of a radical can lead to have a higher anisotropic g-value compared to the case with lower electron density, called spin-orbit effect, which results in the non-radiative transition between two electronic states with different spin multiplicity (e.g. singlet and triplet)-intersystem crossing, which can play important roles in chemical reactions [406][407][408][409] .

Spin dynamics of radical pairs
The sensitivity of certain reactions to weak magnetic fields relies on the oscillations between singlet and triplet states of radical pairs, also known as "quantum beats" 27 . If the radicals are spatially enough separated, having the same energies, singlet and triplet will undergo a coherent interconversion process, 16/72 quantum beating. The interconversion is tuned by the magnetic fields experienced by the electrons, including Zeeman and hyperfine interactions. At low magnetic fields, the main drive for S-T interconversion is due to the hyperfine interactions. Obeying selection rules, the singlet and triplet yields will follow different chemical pathways, which depend on the timing of the coherent spin dynamics 410 . These quantum beats have just recently been observed directly 411 .
The fractional singlet yield resulting from the radical pair mechanism throughout the reaction can be normally defined by using the Liouville-von Neumann equation 47 : whereρ(t) andĤ are the spin density and Hamiltonian operators, respectively. [·,·] denotes the commutator.

Figure 1.
A simple schematic presentation of donor (D)-acceptor (A) radical pair reaction undergoing intersystem crossing between singlet (S) and triplet (T) states. Each state takes different chemical pathways via distinct reaction rates to produces S and T products with k S and k T , respectively, for S and T states.
For instance, the probability of finding the radical pairs in singlet states at some later time is determined by Hamiltonian using Eq. 15: where Tr is trace. The probability P S (t) depends on other contributions, including kinetic reactions, spin relaxation, vibration and rotation of radical pairs, which can be introduced to Eq. 15.

Static magnetic field
Static magnetic field effects have been extensively studied in the context of birds' magnetosensitivity 42, 45 . However, the applications of these models can extended to other magnetic field effects reviewed in Section 17/72 2.1. Assuming that the spin of the radical pairs start off from a singlet state, Eq. 16 can be rewritten as: where |m and |n are eigenstates ofĤ with corresponding eigenenergies of ω m and ω n , respectively. Spin relaxation can be introduced phenomenologically 405, 412 such that: where r denotes the spin relaxation rate. Following the work of Timmel et al. 47 , the chemical fate of the radical pair can be modelled separating spin-selective reactions of the singlet and triplet pairs, as shown in Figure 1. For simplicity it is assumed that k = k S = k T , where k S and k T are the singlet and triplet reaction rates, respectively. The final singlet yield, Φ S , for periods much greater than the radical pair lifetime reads as follows: where the fractional triplet yield can be calculated as In Section 4, we briefly review recent studies that suggest the radical pair mechanism may explain xenon-induced anesthesia, lithium effects on hyperactivity, magnetic field and lithium effects on circadian clock, and hypomagnetic field effects on neurogenesis and microtubule reorganization (See Section 4). In these studies, for simplicity, only Zeeman and isotropic hyperfine interactions are considered. For a pair of radicals, the Hamiltonian reads: whereŜ A andŜ D are the spin operators of radical electrons on Aand D + , respectively,Î A andÎ D are the nuclear spin operators on the acceptor and donor radical molecule, a A and a B are the isotropic hyperfine coupling constants, N A and N D are the number of nuclei coupled to electron A and D, respectively, and ω is the Larmor precession frequency of the electrons due to the Zeeman effect.

Hypomagnetic field
Although hypomagnetic fields belong to the static magnetic field category, the effects due to extremely low magnetic field are often particularly significant compared to other magnetic field effects. Using Eq. 19, it can be shown that for different relaxation and reactions rates, the hypomagnetic field effects are significant, as show in Fig. 2.

Extremely low-frequency magnetic field
Given the short lifetime of radical pairs compared to the low frequency of applied magnetic field, in general, the extremely low-frequency magnetic field can be treated as static during the lifetime of a radical pair 405,413 . Depending on the phase of oscillation, α ∈ (0, π), each radical pair therefore experiences a different, effectively static, magnetic field whose field strength is B. The net effect of the oscillating field is an average over α, such that: where B 0 and B 1 indicate the static magnetic field and the amplitude of the oscillating magnetic field, receptively. Such theoretical model can be applied to the magnetic field effects reviewed in Section 2.3.1.

Medium/high-frequency magnetic field
For the cases of medium/high frequency magnetic fields, a general approach is to integrate Eq. 15, using, for example, a 4th order Runge-Kutta scheme. It is shown that high-frequency magnetic effects can be accounted for by the radical pair mechanism [414][415][416] . For instance, if the magnetic field has the following form: the corresponding Hamiltonian can be transformed into a rotating reference frame where it becomes a time-independent Hamiltonian 417 . To do so, one could use a unitary transformation matrix: such that: Where H is the time-independent Hamiltonian andṪ (t) is the time derivative of T (t). After some algebra, one can obtain: 19/72

Candidate radical pairs
It is now well known that in biology electron-transfer reactions can take place at reasonable rates even when the reactants are separated far beyond "collisional" distances 418,419 . A radical pair can be formed by breaking a chemical bond or electron-transfer between two molecules. Electron transfer between proteins is facilitated by formation of a complex of the reacting proteins, which may be accompanied by conformational changes in the proteins. For that, the reactants must reach each other to build up the coupling of their electronic orbitals. The most used approach to rationalize and predict the rate of electron transfer processes is Marcus Electron Transfer theory 420 . Determining realistic radical pair candidates for the magnetosensitivity of physiological function, however, is still an interesting challenge. Here, we briefly review a few plausible radical pairs that maybe be relevant for the magnetosensitivity in biology.

Cryptochrome-based radical pairs
In the context of songbird avian magnetoreception, the cryptochrome proteins are the canonical magnetosensitive agent 45, 421,422 . It is thought that, in cryptochromes and photolyases, photoreduction of FAD is through three consecutive electron transfers along a conserved triad of tryptophan (Trp) residues to give FADand TrpH + approximately 2 nm distant from each other [423][424][425][426] . In cryptochrome-4a, sequentially four radical pair states are formed by the progressive transfer of an electron along a chain of four tryptophan residues to the photo-excited flavin. In a recent study, Hore and co-workers suggest that, based on spin dynamics, while the third radical pair is mainly responsible for magnetic sensing, the fourth could enhance initiation of magnetic signalling particularly if the terminal tryptophan radical can be reduced by a nearby tyrosine (Tyr) 427 . They concluded that this arrangement may play an essential role in sensing and signalling functions of the protein. It is also suggested that tyrosine can be the donor instead of the fourth Trp 424 . It is also found based on spin dynamics analysis that a radical pair in the form form of [FADand Tyr ] can provide sensitivity to the direction of the magnetic field 428 .
There is also a consensus that there exist alternative radical pairs beyond [FAD -...TrpH + ]. In 2009, Ritz and Schulten showed that exposure to low-intensity oscillating magnetic fields disoriented European robins 429 . Interestingly the frequency of the applied magnetic field in that experiment was equal to the Larmor frequency (∼ 1.4 MHz) of a free electron spin in the geomagnetic field. Magnetic fields with the same amplitude but different frequencies had much less impacts on the birds' magnetic compass. Theoretical analysis suggests that such phenomenon may be explained if one of the radicals were free from internal magnetic interactions [430][431][432][433] , which implies that such an observation is not compatible with the radical pair model based on [FAD -...TrpH + ]. A lot of evidence suggests that the superoxide radical is the most plausible radical under such circumstances 429,430,[434][435][436][437][438] . This is also consistent with animal magnetoreception in dark [439][440][441] , as it was suggested that during the backreaction, a radical pair is formed between flavin and an O 2 and that the radical pair reaction responds significantly to reorientation in the geomagnetic field 433,434,[442][443][444]

Beyond cryptochrome-based radical pairs
Flavin-dependent enzymes are ubiquitous in biology. The isoalloxazine ring of the flavin cofactor can undergo thermally driven redox chemistry, as shown in Figure 3. The different redox states of flavin play essential roles in various electron transfer processes and consequently are crucial for a variety of important biological functions, including energy production, oxidation, DNA repair, RNA methylation, apoptosis, protein folding, cytoskeleton dynamics, detoxification, neural development, biosynthesis, the circadian clock, photosynthesis, light emission and biodegradation 419,[448][449][450][451][452][453][454][455][456][457][458][459] [460][461][462] . Although cryptochrome is the main protein for the avian magnetoreception, there exist many observation challenges for the canonical cryptochrome-centric radical pair mechanism. In a recent work, Bradlaugh and co-workers observed that the FAD binding domain and the Trp chain in cryptochrome are not required for magnetic field responses at single neuron and organismal level. They further reported that increase in FAD intracellular concentration enhanced neuronal sensitivity to blue light in the presence of a magnetic field. The authors concluded that the magnetosensitivity in cells may be well explained based on non-cryptochrome-dependent radical pair models 80 .
It is known that near the tetrodotoxin binding site in Na + channels there are tryptophan residues. Similarly, in the pore-forming region of voltage-sensitive Na + channels, tyrosine and tryptophan residues are located. It is suggested that gating these channel proteins may depend on the electron transfer between these residues, and hence formation of radicals 464 . This form of electron transfer is also proposed to play a key role in DNA photolyase 465 .
Many physiological and pathological processes involve protein oxidation 466 , icluding important residues such as Trp, Tyr, histidine (His), and proline (Pro). It is known that a radical pair in the form of [TyrO ...O -2 ] can be created 467 . The superoxide radical can also be formed in a spin correlated manner with other partners, including tetrahydrobiopterin [468][469][470] . In addition, it was shown that an electron transfer process can occur between Trp and superoxide 471,472 . It was also suggested that in phosphoglycerate kinase phosphorylation a radical pair [RO ...Mg(H 2 O)n + ] complex can be formed 382 .

Studies of the potential role of radical pairs in the brain
In this section, we briefly review recent studies that suggest that the radical pair mechanism may explain isotope effects in xenon-induced anesthesia, and lithium effects on hyperactivity, magnetic field and lithium effects on the circadian clock, and hypomagnetic field effects on neurogenesis and microtubule reorganization.

Xenon anesthesia
Xenon is a well-known general anesthetic used for several species, including Drosophila, mice, and humans 473 . Despite its simple structure (a single atom), the exact underlying mechanism by which it exerts its anesthetic effects remains unclear. Turin et al. showed that when xenon acts anesthetically on Drosophila, specific electron spin resonance (ESR) signals can be observed 474 . The same authors proposed that the anesthetic action of xenon may involve some form of electron transfer. Moreover, Li et al. showed experimentally that isotopes of xenon with non-zero nuclear spin had reduced anesthetic potency in mice compared with isotopes with no nuclear spin 381 . These findings are consistent with the hypothesis of radical pair creation in xenon-induced anesthesia.
Franks and co-workers identified NMDA subtype of glutamate receptor 475 as a target for xenon anesthesia 473,476 . They further showed that xenon exerted its effects by inhibiting NMDA receptors (NMDARs) by competing with the coagonist glycine at the glycine-binding site on the GluN1 subunit 477 . Subsequently, the same group identified that xenon interacts with a small number of amino acids at the predicted binding site of the NMDAR 478 . Using Grand Canonical Monte Carlo method, they showed that xenon at the binding site can interact with tryptophan and phenylalanine, as shown in Fig.4a. However, due to redox inactivity, it is highly unlikely that phenylalanine can be involved in the electron transfer process 479,480 . Meanwhile, tryptophan is redox active and hence can feasibly be involved in electron transfer and hence the formation of radical pairs, as seen in the context of cryptochrome magnetoreception 44

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it is known that tryptophan residues of the NMDAR play key roles in channel gating 481,482 . Moreover, exposure to low-intensity magnetic fields activates the NMDAR 225,242,268 . It is also known that reactive oxygen species are implicated in the activation of the NMDARs 477, 483-487 . Moreover, Turin and Skoulakis 488 reported that oxygen gas was necessary for observing spin changes during xenon-induced anesthesia in Drosophila. Motivated by these observations, the authors 54 suggested that the electron transfer related to xenon's anesthetic action that is evidenced by Turin et al. 474 plays a role in the recombination dynamics of a naturally occurring [Trp + ...O -2 ] radical pair (See Section 3.4 for further discussion). Using Eqs. 19 and 20, they showed that for isotopes of xenon with a non-zero nuclear spin, this nuclear spin couples with (at least one of) the electron spins of such a radical pair, affecting the reaction yields of the radical pair and hence xenon's anesthetic action. The radical pair was assumed to start off from a singlet state. Such a mechanism is consistent with the experimental results of Li et al. 381 that xenon isotopes with non-zero nuclear spin have reduced anesthetic potency compared to isotopes with zero nuclear spin. The authors also provide an experimental test for the validity of their model. It predicts that under a static magnetic field the anesthetic potency of xenon may be significantly different than that observed by Li et al. 381 , as shown in Fig.4c.
Bipolar disorder is also correlated with irregularities in circadian rhythms [509][510][511][512] . In addition, it is well known that Li influences the circadian rhythms that are disrupted in patients with bipolar disorders [513][514][515][516][517][518][519][520][521][522][523][524][525][526] . Further, Osland et al. reported that Li significantly enhanced the expression of Per2 and Cry1, while Per3, Cry2, Bmal1, E4BP4 and Rev-Erb-α expression was decreased 527 . However, the exact mechanisms and pathways behind this therapy are incompletely known. It has been shown that Li can exert it effects via a direct action on the suprachiasmatic nucleus (SCN), a circadian pacemaker in the brain [528][529][530][531] . Cryptochromes are key proteins for the circadian clock 532 and SCN's intercellular networks development, which subserves coherent rhythm expression 533 . Furthermore, it is also shown that cryptochrome is associated with bipolar disorder disease [534][535][536][537] . In the context of animal magnetoreception, cryptochromes are the canonical magnetic sensing proteins (See Section 3.4) 44 , with flavin radicals playing a key role. Moreover, it has been shown that circadian rhythms are susceptible to magnetic fields at low intensities 78-80, 166-168, 221, 223, 350 , where cryptochromes 81, 222 are implicated. It has also been observed that cryptochromes play key roles in alteration of ROS levels through exposure to magnetic fields 73, 127, 219, 538 . Based on these facts, a new study suggests 56 that Li's nuclear spin influences the recombination dynamics of S-T interconversion in the naturally occurring [FADH ..O -2 ] radical pairs (Fig.5a). These pairs are initially in singlet states, and due to the different nuclear spins, each isotope of Li alters these dynamics differently. Using Eqs. 19 and 20, the authors showed that a radical pair model could provide results consistent with the experimental finding of Ettenberg and colleagues 380 . In that work, it was assumed that the fractional triplet yield of the radical pairs is correlated with lithium potency. They further predict a magnetic-field dependence of the effectiveness of lithium, which provides one potential experimental test of their hypothesis, as shown in Fig.5c. Furthermore, the authors suggested that the proposed mechanism for Li effects is also plausible via different pathways. Li may exert it effect via competing with magnesium in inhibiting glycogen synthase kinase-3 (GSK-3) 539-541 , which is regulated by phosphorylation of inhibitory serine residues [542][543][544]

Magnetic field and lithium effects on circadian clock
The circadian clock is essential for the regulation of a variety of physiological and behavioral processes in nearly all organisms, including Neurospora 555 , Arabidopsis 556 , Drosophila 557 , mouse 558 , and humans [559][560][561] . It is known that the disruption of the circadian clock can be detrimental for many physiological functions, including depression 562, 563 , metabolic and cardiovascular diseases 564 , and cancer 565,566 .
It is also known that the circadian clock controls physiological processes such as brain metabolism, reactive oxygen species homeostasis, hormone secretion, autophagy and stem cell proliferation, which are correlated to ageing, memory formation, neurodegenerative and sleep disorders [567][568][569][570][571] . In Drosophila, the circadian clock regulates the timing of eclosion, courtship, rest, activity, and feeding; it also influences daytime color 572 and temperature preference 573 . Regardless of the differences in the molecular components of the circadian clocks, their organization, features, and the molecular mechanism that give rise to rhythmicity are very alike across organisms 574 . Environmental zeitgebers such as light, food, and temperature can influence the circadian clock's rhythmicity 575 578 . They showed that the period was altered significantly depending on the strength of the magnetic field, with a maximum change at 300 µT. In that work, the geomagnetic field was shielded, and arrhythmic flies were excluded from the analysis. As discussed in Section 4.2, the disruption of the circadian clock is associated with bipolar disorders, for which Li is the first line treatment. Li's effects on bipolar disorder are isotope-dependent. Dokucu et al. 579 reported that Li lengthened the period of Drosophila's circadian clock. However, the exact mechanism behind these phenomena is still mostly unknown. Further, reactive oxygen species homeostasis is correlated to the circadian rhythms [580][581][582][583][584][585][586] .
A recent study suggests that a radical pair model based on [FADH ...O -2 ], similar to Section 4.2, may explain the magnetic field and lithium effects on Drosophila's circadian clock 56 . Following the work of Tyson et al. 587 , the authors used a simple mathematical model for Drosophila's circadian clock, as shown in Fig.6a (For more detailed models see Ref 588 ). Similar to the work of Player et al. 589 , they introduced the effects of applied magnetic fields and hyperfine interactions on the circadian clock process by modifying the corresponding rate representing the role of cryptochrome's light activation and, hence, proteolysis of protein. Based on these models and using Eqs. 19 and 20, they reproduced the experimental findings of magnetic field 578 and lithium effects 579 on Drosophila's circadian clock, as shown in Figs.6c and 6d. The proposed model in that work predicts that lithium influences the clock in an isotope-dependent manner and magnetic fields and hyperfine interactions modulate oxidative stress in the circadian clock.

Hypomagnetic field effects on microtubule reorganization
Single-cell organisms perform cognitive activities predominantly by cytoskeletal microtubules and are inhibited by anesthetic gases even in the absence of synapses or networks 590 . Linganna and colleagues showed that modulation of microtubule stability is a mechanism of action for these anesthetics 591 . Bernard reported that anesthetics act directly on cytoplasm, depending on cytoskeletal proteins' dynamics comprising actin filaments and microtubules 592 . Further, Eckenhoff and co-workers found that anesthetics bind to actin and tubulin 593,594 . In another study, they show that microtubules play key roles in the The dependence of the agreement between the total traveled distance ratio, T D r , and the triple yield ratio, TY r of 7 Li over 6 Li on the radical pair reaction rate, k, and the radical pair spin-coherence relaxation rate, r. The green line indicates the ranges smaller than the experimental uncertainty. (c) The dependence of the triplet yield (Red, 6 Li; Blue, 7 Li) and triplet yield ratio 7 Li/ 6 Li (Green) on an external magnetic field, calculated based on the radical pair model 55 .

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action of anesthetics on protein reaction networks involved in neuronal growth, proliferation, division, and communication 595 . Despite the low binding affinity of anesthetics to tubulin compared to membrane protein, the abundance of tubulin is much more than membrane protein sites. It thus seems plausible that our conscious state of mind is intertwined with microtubules and their dynamics. In recent decades, it has been proposed that quantum physics may explain the mystery of consciousness. In particular the holistic character of quantum entanglement might shed more light on the binding problem 596 . Penrose and Hameroff proposed that quantum computations in microtubules may be the basis for consciousness [597][598][599] . It was suggested that electron resonance transfer among tryptophan residues in tubulin in a quantum electronic process could play a role in consciousness 600 . Computational models show that anesthetic molecules might bind in the same regions and hence result in loss of consciousness 601 . In a recent work, Zhang and co-workers observed a connection between electronic states and vibrational states in tubulin and microtubules 602 . However, quantum electronic coherence beyond ultrafast timescales has been recently challenged experimentally 31 . In contrast, the coherence of quantum spins can be preserved for much longer timescales 603 . Similarly, Fisher has proposed that phosphorus nuclear spins could be entangled in networks of Posner molecules which could form the basis of a quantum mechanism for neural processing in the brain 604 ; however, this sort of spin-based model also demands more supporting evidence 605 .
A considerable amount of evidence indicates that magnetic fields can influence microtubules 91, 606-612 . Wang and colleagues showed that shielding the geomagnetic field caused tubulin assembly disorder 170 . All these observations point to the magnetosensitivity of microtubules for wide ranges of magnetic field strengths. Further, studies suggest that oxidative stress plays important roles in regulating actin and microtubule dynamics 613 . Microtubule contain tryptophan, tyrosine, and phenylalanine residues which are susceptible to oxidation. Further, it is also known that the stability of polymerized microtubules is susceptible to changes in zinc ion concentration in neurons 614 .
Magnetosensitivty of chemical reactions often involve radical molecules 42 (See also Section 3.1). Using Eqs. 19 and 20 and a simple kinetic model 614 170 . They further predict that the effect of zinc on the microtubule density exhibits isotopic dependence, as shown in Fig. 7.

Hypomagnetic field effects on neurogenesis
In a recent work, Zhang and co-workers showed that shielding the geomagnetic field for a long-term (several weeks) decreased neurogenesis in the hippocampal region in mice 169 . They observed that the neurogenesis impairment was through decreasing adult neuronal stem cell proliferation, altering cell lineages in critical development stages of neurogenesis, impeding dendritic development of newborn neurons in the adult hippocampus, and resulting in impaired cognition. Using transcriptome analysis and endogenous reactive oxygen species in situ labeling via hydroethidine, they reported that the hypomagnetic fields reduced levels of reactive oxygen species 106 . The authors further revealed that such reduction of reactive oxygen species can be compensated by pharmacological inhibition of reactive oxygen species removal via diethyldithiocarbamate, which rescued defective adult hippocampal neurogenesis in hypomagnetic field-exposed mice.
Moreover, it is known that the cellular production of reactive oxygen species is susceptible to the magnetic field exposure 112,224,[615][616][617][618][619][620][621][622][623][624][625][626][627][628][629][630][631][632] . Reactive oxygen species play vital roles in biology. The mitochondrial electron transport chain and an enzyme family termed NADPH oxidase are two main cellular sources of reactive oxygen species 106  . Based on these findings, a recent study 58 suggests that a radical pair model may explain the modulation of reactive oxygen species production and the attenuation of adult hippocampal neurogenesis in a hypomagnetic field, observed by Zhang and colleagues 169

Conclusion and outlook
The effects of weak magnetic fields in biology are abundant, including in plants, fungi, animals, and humans. The corresponding energies for such effects are far below thermal energies. So far, there is no explanation for such phenomena. However, quantum biology provides a promising explanation for these effects, namely the radical pair mechanism. Here, we have reviewed numerous studies on the biological effects of weak magnetic fields (static and oscillating), as well as related isotope effects. We then reviewed the radical pair mechanism and proposed that it can provide a unified model for weak magnetic field and isotope effects on biology. We discussed candidate radical pairs that may be formed in biological environments. We reviewed recent studies that propose that the radical pair mechanism may explain xenon-induced anesthesia, lithium effects on mania, magnetic field and lithium effects on the circadian clock, and hypomagnetic field effects on neurogenesis and microtubule reorganization. These recent studies provide avenues for testing the proposed models. For instance, it is proposed that, in xenon anesthesia, applying magnetic fields > 1mT will increase the anesthetic potency difference between 129 Xe and 129 Xe 54 . Similarly, it is predicted that for mania treatment by 6 Li and 7 Li 55 exposure to hypomagnetic and magnetic fields >3 mT will magnify the difference in the potency of these two isotopes. Moreover, it is predicted that exposure of the circadian clock to magnetic fields >mT will shorten the period of the clock 56 . Another study suggests that exposure to magnetic fields greater than the geomagnetic field will reduce microtubule assembly 57 . Further, it is also predicted that hippocampal neurogenesis 58 , the circadian clock 56 , and microtubule reorganization 57 will be isotope-dependent using different isotopes of oxygen, lithium, and zinc, respectively.
Going beyond these already published proposals, it would be of interest to investigate the roles of radical pairs to help explain magnetic field effects on a large variety of physiological functions, including NMDAR activation 225,242 , DNA/RNA methylation 171 , dopamine dynamics 248,249 , flavin autofluorescence 129 , epigenetics 257,258 , and many others. As discussed earlier in this review, for each of these systems there are naturally occurring radical pairs that can conceivably act as magnetosensitive agents. However, in all of the mentioned systems it remains a major open challenge to definitively identify the magnetic sensitive radical pairs as well as the relevant chemical reactions and corresponding kinetic rates. This challenge will require multi-disciplinary collaborations including biologists, chemists, and quantum physicists.
A considerable amount of evidence indicates that shielding the geomagnetic field has direct biological consequences, which in some cases could be detrimental. This could also be pertinent for the quest of life on other planets without a magnetic field, including Mars 634,635 . In a similar vein, nowadays almost all species are exposed to magnetic fields at different intensities and frequencies originated by manufactured devices 67, 351, 636-640 . The effects of magnetic fields on physiological functions are inevitable and could be detrimental. Thus this review and perspective is pertinent to the debate on the putative adverse health effects of environmental magnetic fields. Understanding the underlying mechanism should help to clarify many of these issues. The dependence of the triplet yield of the radical pair model for singlet-born radical pair on external magnetic field 58 . (c) Triplet yield ratio (geomagnetic field to hypomagnetic field) for singlet-born radical pair in the plan of reaction rate (k) and relaxation rate (r). The region between the solid black lines is in agreement with the experimental range for the ratio of the numbers of BrdU+ cells after an 8 week, observed in Ref. 169 .

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From a quantum perspective, it would also be of interest to explore the relevance of quantum entanglement 641 in the radical pair models for various magnetic field effects on biological functions [642][643][644] . This could be particularly interesting in the context of neuroscience, where it has been suggested that the brain might use quantum effects such as entanglement for information processing purposes 600,604,645 .
Studying magnetic field and isotope effects in biology is a rich and important interdisciplinary field. The potential essential involvement of quantum effects related to the radical pair mechanism provides an exciting new avenue for further investigation, with the promise of revealing a common underlying mechanism for many of these effects.