Radical pairs may play a role in xenon-induced general anesthesia
Jordan Smith, Hadi Zadeh Haghighi, Dennis Salahub, Christoph Simon
CCould radical pairs play a role in xenon-inducedgeneral anesthesia?
Jordan Smith , Hadi ZADEH HAGHIGHI , and Christoph Simon Department of Physics and Astronomy, Institute for Quantum Science and Technology and Hotchkiss BrainInstitute, University of Calgary, Calgary, T2N 1N4, Canada * [email protected], [email protected] ABSTRACT
Understanding the mechanisms underlying anesthesia would be a key step towards understanding consciousness. Theprocess of xenon-induced general anesthesia has been shown to involve electron transfer, and the potency of xenon as ageneral anesthetic exhibits isotopic dependence. We propose that these observations can be explained by a mechanism inwhich the xenon nuclear spin influences the recombination dynamics of a naturally occurring radical pair of electrons. Wedevelop a simple model inspired by the body of work on the radical-pair mechanism in cryptochrome in the context of avianmagnetoreception, and we show that our model can reproduce the observed isotopic dependence of the general anestheticpotency of xenon in mice. Our results are consistent with the idea that radical pairs of electrons with entangled spins could beimportant for consciousness.
Understanding consciousness remains one of the big open questions in neuroscience , and in science in general. The study ofanesthesia is one of the key approaches to elucidating the processes underlying consciousness , but there are still significantopen questions regarding the physical mechanisms of anesthesia itself .One anesthetic agent that has been studied extensively is xenon. Xenon has been shown experimentally to produce astate of general anesthesia in several species, including Drosophila , mice , and humans . While the anesthetic properties ofxenon were discovered in 1939 , the exact underlying mechanism by which it produces anesthetic effects remains unclear evenafter decades of research . Our focus here is on this underlying physical mechanism, and there are important hints about themechanism provided by two recent publications.First, Turin et al. showed that when xenon acts anesthetically on Drosophila unpaired electron spin resonance takes place ,providing evidence of some form of electron transfer. Turin et al. proposed that the anesthetic action of xenon may be causedby the xenon atom(s) acting as an “electron bridge” , facilitating the electron transfer between a nearby electron donor andelectron acceptor. They supported their proposal by density-functional theory calculations showing the effect of xenon onnearby molecular orbitals. Second, Li et al. showed experimentally that isotopes of xenon with non-zero nuclear spin hadreduced anesthetic potency in mice compared with isotopes with no nuclear spin .If the process by which xenon produces anesthetic effects includes free-electron transfer as well as nuclear-spin dependence,a mechanistic framework proposed to explain xenon-induced anesthesia should possess these characteristics. Here we showthat a model involving a radical pair of electrons (RP) and the subsequent modulation of the RP spin dynamics by hyperfineinteractions is consistent with these assumptions.The radical pair mechanism (RPM) was first proposed more than 50 years ago . The rupture of a chemical bond can createa pair of electrons that are localized on two different molecular fragments, but whose spins are entangled in a singlet state .The magnetic dipole moment associated with electron spin can interact and couple with other magnetic dipoles, includinghyperfine interactions and Zeeman interactions . As a consequence of such interactions, the initial singlet state can evolveinto a more complex state that has both singlet and triplet components. Eventually, the coherent oscillation of the RP betweensinglet and triplet states ceases and the electrons may recombine (for the singlet component of the state) or diffuse apart to formvarious triplet products . In order for significant interconversion between singlet and triplet states to occur, the RP lifetimeand the RP spin-coherence lifetime should be comparable to the electron Larmor precession period, which in the case of thegeomagnetic field of the Earth ( B ≈ µ T) is approximately 700 ns . The coherent spin dynamics and spin-dependentreactivity of radical pairs allow magnetic interactions which are 6 orders of magnitude smaller than the thermal energy, k B T , tohave predictable and reproducible effects on chemical reaction yields .1 a r X i v : . [ phy s i c s . b i o - ph ] S e p he RPM has become a prominent concept in quantum biology . In particular, it has been studied in detail for thecryptochrome protein as a potential explanation for avian magnetoreception . In the present work we apply the principlesand methods used to investigate cryptochrome to xenon-induced anesthesia.General anesthetics produce widespread neurodepression in the central nervous system by enhancing inhibitory neuro-transmission and reducing excitatory neurotransmission across synapses . Three ligand-gated ion-channels in particularhave emerged as likely molecular targets for a range of anesthetic agents : the inhibitory glycine receptor, the inhibitory γ -aminobutyric acid type-A (GABA A ) receptor, and the excitatory N-methyl-D-aspartate (NMDA) receptor . NMDA receptorsrequire both glycine and glutamate for excitatory activation , and it has been suggested that xenon’s anesthetic action is relatedto xenon atoms participating in competitive inhibition of the NMDA receptor in central-nervous-system neurons by binding atthe glycine binding site in the NMDA receptor . Armstrong et al. propose that the glycine binding site of the NMDAreceptor contains aromatic rings of similar chemical nature to those found in cryptochrome, which is consistent with thepossibility that the anesthetic action of xenon uses a spin-dependent process similar to the radical-pair mechanism (RPM)thought to occur in cryptochrome. Let us note that other targets have also been proposed for many anesthetics, e.g. tubulin .In the following we focus on the NMDA receptor to be specific, but our model is very general and could well apply to othertargets.We suggest that the electron transfer evidenced by Turin et al. could affect the recombination dynamics of a naturallyoccurring radical pair (based on the results of Armstrong et al. this RP may involve aromatic phenylalanine residues locatedin the binding site), and that an isotope of xenon with a non-zero nuclear spin could couple with the electron spins of such aradical pair, reducing the “electron bridge” effect that is proposed to correlate with anesthesia. Such a mechanism is consistentwith the experimental results of Li et al. that xenon isotopes with non-zero nuclear spin have reduced anesthetic potencycompared to isotopes with zero nuclear spin.We hypothesize that in the context of xenon-induced general anesthesia, xenon itself may not be involved in the creationof radical pairs, where the energy for radical-pair creation likely comes from another source such as local ROS. It has beensuggested that water (a source of oxygen) may be present in the NMDA receptor , and Aizenman et al. as well as Girouard et al. suggest that reactive oxygen species (ROS) may be located in the NMDA receptor. Further, Turin and Skoulakisfound that when a sample of xenon gas was administered to Drosophila without oxygen gas present in the sample no spinchanges were observed in the flies . Here we propose that ROS could be involved in the formation and existence of a naturallyoccurring RP in the NMDA receptor.Given that cryptochrome is one case in which the RPM has been studied extensively, we propose that by recognizingcommonalities in the biological and chemical environments in which magnetoreception and xenon-induced general anesthesiaare thought to take place, analytical and numerical techniques that have been used to study cryptochrome may be adapted andapplied to the case of xenon-induced anesthesia, potentially providing insight into general anesthetic mechanisms. We explorethe feasibility of such a mechanism by determining and analyzing the necessary parameters and conditions under which thespin-dependent RP product yields can explain the experimental isotope-dependent anesthetic effects reported by Li et al . Predicting Experimental Xenon Anesthesia Results using the RPM Model
Quantifying anesthetic potency
In the work of Li et al. , a metric referred to as the “loss of righting reflex ED50” (LRR-ED50) was defined using theconcentration of xenon administered to mice, in which the mice were no longer able to right themselves within 10 s of beingflipped onto their backs. The LRR-ED50 metric was reported to be correlated with consciousness in mice, and was measuredexperimentally for Xe,
Xe,
Xe, and
Xe to be 70(4)%, 72(5)%, 99(5)%, and 105(7)%, respectively .Here we defined the anesthetic potency as the inverse of the LRR-ED50 metric. In order to quantify the anesthetic potencyof the various xenon isotopes, the potency of Xe (with I =
0) was normalized to 1. The inverse of the LRR-ED50 valueof isotopes
Xe and
Xe were then divided by that of
Xe. The relative isotopic anesthetic potencies were quantified as
Pot = Pot / = . ( ) , and Pot / = . ( ) for Xe,
Xe, and
Xe, respectively, as shown in Table 1, where
Pot isthe relative potency of xenon with nuclear spin I =
0, and likewise for
Pot / and Pot / . RPM model
We have developed an RPM model to predict anesthetic potency by making a connection with the relative singlet yield fordifferent isotopes, as described in more detail below. The model that we have used here was developed using a hypotheticalxenon-NMDA receptor RP system based on the information about xenon action sites mentioned previously, involving xenonatoms surrounded by phenylalanine and tryptophan residues located in the glycine-binding site of the NMDA receptor, andalso modelled after the cryptochrome case as related to magnetoreception. A spin-correlated radical pair of electrons (termed able 1.
Xenon isotopic nuclear spin, LRR-ED50, and
Pot values for xenon isotopes
Xe,
Xe,
Xe, and
Xe.LRR-ED50 values as reported in the work of Li et al. Isotope Nuclear Spin, I LRR-ED50 (%)
Pot
Xe 0 70(4) 1
Xe 0 72(5) -
Xe 3/2 99(5) 0.71(8)
Xe 1/2 105(7) 0.67(8)
Figure 1.
Aromatic residues are important for the binding of xenon and glycine at the glycine binding site of the NMDAreceptor. The image shows the predicted position of xenon atoms (red spheres) in the glycine site together with the aromaticresidues phenylalanine 758, phenylalanine 484, and tryptophan 731. electrons A and B), most likely found in chemically excited phenylalanine residues , couple to xenon nuclei with non-zeronuclear spin, as shown in Fig. 1.The number of xenon atoms located in the active site when anesthetic action takes place is not yet completely clear,and the work of Dickinson et al. suggests that the number of xenon atoms simultaneously present in the active site rangesprobabilistically between zero and three .Here we show that the simplest case of a single xenon atom occupying the active site already allows us to explain theanesthetic potency ratios derived from the experimental results of Li et al. . The additional degrees of freedom implicit inmore complex Hilbert spaces, such as the cases of two and three-xenon occupation states, only aid the model in explainingthe experimental results of Li et al. . Further, when our model is optimized in order to reproduce the experimental results, thetwo-xenon occupation state essentially reduces to the single-xenon occupation state, in which one hyperfine interaction betweena xenon nucleus and one of the radical electrons is dominant. We therefore focus our analysis on the single atom case, but thetwo and three-xenon occupation states are discussed in the Supplementary Information.The Hamiltonian of the RPM in the case of xenon-induced anesthesia depends not only upon the number of xenon atomspresent in the glycine binding site of the NMDA receptor, but also upon the assumed hyperfine interactions. In the simulationinvolving a single xenon atom occupying the active site it was assumed that the xenon nucleus may couple to both radicalelectrons, and the Hamiltonian is given asˆ H = ω (cid:0) ˆ S Az + ˆ S Bz (cid:1) + a ˆ S A · ˆ I + a ˆ S B · ˆ I , (1)where ˆ S A and ˆ S B are the spin operators of radical electrons A and B, respectively, ˆ I i is the nuclear spin operator of xenonnucleus i , a j is a hyperfine coupling constant where a j = γ e a (cid:48) j , and ω is the Larmor precession frequency of the electronsabout an external magnetic field . The Larmor precession frequency is defined as ω = γ e B , where γ e is the gyromagneticratio of an electron and B is the external magnetic field strength. It should be pointed out that we focus here on the hyperfineinteractions between the radical electrons and xenon atoms, and that interactions between the two electron spins, as well aspotential interactions between the electron spins and other nuclei are neglected. This is justifiable for our purposes, since weare primarily interested in the differential effect of the xenon nuclear spin. etermination of Singlet Yield Ratios The eigenvalues and eigenvectors of the Hamiltonian can be used to determine the ultimate singlet yield ( Φ S ) for all timesmuch greater than the radical-pair lifetime ( t (cid:29) τ ): Φ S = − k ( k + r ) + M M ∑ m = M ∑ n = (cid:12)(cid:12) (cid:104) m | ˆ P S | n (cid:105) (cid:12)(cid:12) k ( k + r )( k + r ) + ( ω m − ω n ) , (2)where, following the methodology used by Hore in the context of cryptochrome, M is the total number of nuclear spinconfigurations, ˆ P S is the singlet projection operator, | m (cid:105) and | n (cid:105) are eigenstates of ˆ H with corresponding energies of ω m = (cid:104) m | ˆ H | m (cid:105) and ω n = (cid:104) n | ˆ H | n (cid:105) , respectively, k = τ − is inverse of the RP lifetime, and r = τ − c is the inverse of the RPspin-coherence lifetime.The spin-dependent RP singlet yield was calculated for each xenon isotope under consideration. The singlet yield ratio ( SR )for each nuclear spin value was then calculated by dividing the singlet yield obtained using the given spin value by the singletyield obtained using spin I =
0, resulting in the ratio of spin-1/2 singlet yield to spin-0 singlet yield being expressed as SR / ,and the ratio of spin-3/2 singlet yield to spin-0 singlet yield expressed as SR / , with the singlet yield ratio of spin-0 beingnormalized to SR =
1. The calculated singlet yield ratios were compared with the xenon potency ratios (
Pot ) derived using thedata reported by Li et al. as described above.We investigated the sensitivity of the singlet yield ratios to changes in the hyperfine interactions ( a (cid:48) and a (cid:48) ), RP reaction rate( k ), external magnetic field strength ( B ), and RP spin-coherence relaxation rate ( r ). The dependence of the quantity | Pot − SR | on a (cid:48) and a (cid:48) is shown in Figs. 2/3, while the dependence of | Pot − SR | on the relationship between r and k is shown in Figs.4/5. The relationship between SR and B can be seen in Fig. 6. The same dependencies for the two-xenon occupation state canbe seen in Supplementary Figs. S1/S2, S3/S4, and S5, respectively. Our goal was to find regions in parameter space such thatthe spin-dependent singlet yield ratios match the anesthetic isotopic potency ratios, i.e., the quantities | Pot / − SR / | and | Pot / − SR / | should be smaller than the experimental uncertainties on the anesthetic potency.In the case of single-xenon occupation the optimized parameter values were found to be a (cid:48) = µ T, a (cid:48) = µ T, B = µ T, k = r = . × s − , resulting in SR / = .
72 and SR / = .
63. It should be noted here that while | Pot / − SR / | is greaterthan | Pot / − SR / | for these optimized parameter values, both SR / and SR / are consistent with the experimental results ofLi et al. , within their uncertainties. Further experiments with smaller uncertainty about the relative anesthetic potencies ofspin-3/2 and spin-1/2 xenon isotopes would be of interest. The optimized parameter values for a single xenon atom suggest strong coupling only between the xenon nucleus and oneof the two RP electrons, while having weak interactions with the other, see Figs. 2 and 3. To gain a deeper understandingof this coupling, it would be of interest to perform molecular modelling of the electron transfer between xenon and trypto-phan/phenylalanine residues using Marcus Theory. Such modelling could be expanded on by exploring the molecular dynamicsof the binding site using quantum mechanics/molecular mechanics (QM/MM) simulation techniques, similar to those used inthe case of cryptochrome , to determine which aromatic rings are most likely to contain a radical pair, and therefore whichmolecules the xenon nuclei are most likely to couple with. Further, rather than determining the hyperfine coupling constants byfitting parameters to a model, it could be useful to perform density functional theory (DFT) modelling to determine theoreticalhyperfine coupling constants, accounting for the quantity and relative positioning of the xenon atoms within the NMDA receptorglycine binding site.The sensitivity analysis of the relationship between the RP spin-coherence relaxation rate ( r ) and the RP first-order reactionrate ( k ) shown in Figs. 4 and 5 is promising, in that the RP lifetime requirements are within an order of magnitude of the resultsreported by Hore in the cryptochrome case . The calculated range for the RP lifetime, τ , is comparable to the spin-coherencelifetime, τ c , and also to the electron Larmor precession period. It is interesting to note that the r and k parameter spaces forwhich SR and Pot agree indicate that for spin I = / k ) should be at least as fast as the RP spin-coherencerelaxation rate ( r ), while in the spin I = / of r = k = . × s − , SR and Pot diverge.Relaxation rates much greater than these values result in the RP not having sufficient time to coherently oscillate betweensinglet and triplet states such that the singlet yield ratios and the derived anesthetic potency ratios are in agreement. As withthe cryptochrome case, as the RP lifetime becomes much greater than the RP spin-coherence lifetime, the RP exponentiallydecays toward the equilibrium state of Φ S = .
25 for all nuclear spin values. These results emphasizes the importance of the RPspin-coherence lifetime ( τ c ) being comparable to the electron Larmor precession period ( τ L = π / ω ) and also to the requisiteRP lifetime ( τ ). hen considering the sensitivity of the single-xenon model to changes in external magnetic field as shown in Fig. 6,the range of B values that produce agreement between SR and Pot ratios is given as B ∈ [ , ] µ T, and approximates thegeomagnetic field at different geographic locations (25 to 65 µ T) . This result indicates that for a single-xenon occupationstate external field values vastly stronger than the geomagnetic field may result in the anesthetic potency of xenon being reducedsignificantly. Further, at geographic locations on the Earth where the geomagnetic field is larger than 51 µ T, anesthetic potencymay be reduced compared to locations where B earth ≤ µ T. It is also seen in Fig. 6 that the isotope of xenon with spin I = B . It would be ofinterest to investigate the experimental effects of the external magnetic field strength on xenon-induced general anesthesia invivo . For example, such an experiment could involve the measurement of anesthetic potency of xenon isotopes with variousnuclear spin values, including both zero spin and non-zero spin, in an environment with controllable external magnetic field.In this study the RPM model in the context of cryptochrome was adapted to the case of xenon in the glycine binding siteof the N-methyl-D-aspartate receptor, and the experimental isotope-dependent anesthetic potency ratios derived from the resultsof Li et al. were reproduced theoretically using the RPM model in which a single xenon atom occupies the active site of theNMDA receptor. The RP lifetime and hyperfine coupling parameters were optimized to reproduce the experimental results ofLi et al. , and the sensitivity of the model to changes in hyperfine coupling constants, RP reaction rate, external magnetic fieldstrength, and RP spin-coherence relaxation rate was explored. The optimized model parameter values and parameter spacesfound here seem physiologically feasible, and indicate that the RPM may provide a reasonable explanation for the generalanesthetic action of xenon in vivo .Our results thus suggest that xenon-induced general anesthesia may fall within the realm of quantum biology, and be similarin nature to the proposed mechanism of magnetoreception involving the cryptochrome protein .This also raises the question whether other anesthetic agents use the same mechanism as xenon to induce general anesthesia.It could prove interesting to explore isotopic nuclear-spin effects as well as magnetic field effects in experiments with othergeneral anesthetic agents that are thought to function similarly to xenon, such as nitrous oxide and ketamine .General anesthesia is clearly related to consciousness, and it has been proposed that consciousness (and other aspects ofcognition) could be related to large-scale entanglement . Radical pairs are entangled and could be a key element in thecreation of such large-scale entanglement, especially when combined with the suggested ability of axons to serve as waveguidesfor photons . Viewed in this - admittedly highly speculative - context, the results of the present study are consistent with theidea that general anesthetic agents, such as xenon, could interfere with this large-scale entanglement process, and thus withconsciousness. Data Availability
The datasets generated and analysed during the current study are available from the corresponding author on reasonable request.
References Koch, C., Massimini, M., Boly, M. & Tononi, G. Neural correlates of consciousness: progress and problems.
Nat. Rev.Neurosci. , 307–321 (2016). Alkire, M. T., Hudetz, A. G. & Tononi, G. Consciousness and anesthesia.
Science , 876–880 (2008). Mashour, G. A. Integrating the science of consciousness and anesthesia.
Anesth. & Analg. , 975–982 (2006). Franks, N. P. General anaesthesia: from molecular targets to neuronal pathways of sleep and arousal.
Nat. Rev. Neurosci. , 370–386 (2008). Turin, L., Skoulakis, E. M. & Horsfield, A. P. Electron spin changes during general anesthesia in drosophila.
Proc. Natl.Acad. Sci. , E3524–E3533 (2014). Li, N. et al.
Nuclear spin attenuates the anesthetic potency of xenon isotopes in miceimplications for the mechanisms ofanesthesia and consciousness.
Anesthesiol. The J. Am. Soc. Anesthesiol. , 271–277 (2018). Rex, S. et al.
Positron emission tomography study of regional cerebral metabolism during general anesthesia with xenon inhumans.
Anesthesiol. The J. Am. Soc. Anesthesiol. , 936–943 (2006). Jordan, B. D. & Wright, E. L. Xenon as an anesthetic agent.
AANA J , 387–392 (2010). Liu, L. T., Xu, Y. & Tang, P. Mechanistic insights into xenon inhibition of nmda receptors from md simulations.
The J.Phys. Chem. B , 9010–9016 (2010).
Closs, G. L. Mechanism explaining nuclear spin polarizations in radical combination reactions.
J. Am. Chem. Soc. ,4552–4554 (1969). Bagryansky, V. A., Borovkov, V. I. & Molin, Y. N. Quantum beats in radical pairs.
Russ. Chem. Rev. , 493 (2007). Steiner, U. E. & Ulrich, T. Magnetic field effects in chemical kinetics and related phenomena.
Chem. Rev. , 51–147(1989). Timmel, C. R., Till, U., Brocklehurst, B., Mclauchlan, K. A. & Hore, P. J. Effects of weak magnetic fields on free radicalrecombination reactions.
Mol. Phys. , 71–89 (1998). Hore, P. J. Upper bound on the biological effects of 50/60 hz magnetic fields mediated by radical pairs.
Elife , e44179(2019). Rodgers, C. T. & Hore, P. J. Chemical magnetoreception in birds: the radical pair mechanism.
Proc. Natl. Acad. Sci. ,353–360 (2009).
Fay, T. P., Lindoy, L. P., Manolopoulos, D. E. & Hore, P. How quantum is radical pair magnetoreception?
Faraday Discuss. , 77–91 (2019).
Lambert, N. et al.
Quantum biology.
Nat. Phys. , 10–18 (2013). Hore, P. J. & Mouritsen, H. The radical-pair mechanism of magnetoreception.
Annu. review biophysics , 299–344(2016). Hiscock, H. G. et al.
The quantum needle of the avian magnetic compass.
Proc. Natl. Acad. Sci. , 4634–4639 (2016).
Solov’yov, I. A., Chandler, D. E. & Schulten, K. Magnetic field effects in arabidopsis thaliana cryptochrome-1.
Biophys.journal , 2711–2726 (2007). Ball, P. Physics of life: The dawn of quantum biology.
Nature , 272 (2011).
Lee, A. A. et al.
Alternative radical pairs for cryptochrome-based magnetoreception.
J. The Royal Soc. Interface ,20131063 (2014). Schulten, K., Swenberg, C. E. & Weller, A. A biomagnetic sensory mechanism based on magnetic field modulated coherentelectron spin motion.
Z. Phys. Chem , 1–5 (1978).
Son, Y. Molecular mechanisms of general anesthesia.
Korean journal anesthesiology , 3 (2010). Furukawa, H., Singh, S. K., Mancusso, R. & Gouaux, E. Subunit arrangement and function in nmda receptors.
Nature ,185–192 (2005).
Dickinson, R. et al.
Competitive inhibition at the glycine site of the n-methyl-d-aspartate receptor by the anesthetics xenonand isoflurane: Evidence from molecular modeling and electrophysiology.
Anesthesiol. The J. Am. Soc. Anesthesiol. ,756–767 (2007).
Franks, N., Dickinson, R., De Sousa, S., Hall, n. A. & Lieb, W. How does xenon produce anaesthesia?
Nature ,324–324 (1998).
Furukawa, H. & Gouaux, E. Mechanisms of activation, inhibition and specificity: crystal structures of the nmda receptornr1 ligand-binding core.
The EMBO journal , 2873–2885 (2003). Armstrong, S. P. et al.
Identification of two mutations (f758w and f758y) in the n-methyl-d-aspartate receptor glycine-binding site that selectively prevent competitive inhibition by xenon without affecting glycine binding.
Anesthesiol. The J.Am. Soc. Anesthesiol. , 38–47 (2012).
Esencan, E. et al.
Xenon in medical area: emphasis on neuroprotection in hypoxia and anesthesia.
Med. gas research , 4(2013). Craddock, T. J. et al.
Anesthetic alterations of collective terahertz oscillations in tubulin correlate with clinical potency:Implications for anesthetic action and post-operative cognitive dysfunction.
Sci. reports , 1–12 (2017). Aizenman, E., Hartnett, K. A. & Reynoldst, I. J. Oxygen free radicals regulate nmda receptor function via a redoxmodulatory site.
Neuron , 841–846 (1990). Girouard, H. et al.
Nmda receptor activation increases free radical production through nitric oxide and nox2.
J. Neurosci. , 2545–2552 (2009). Turin, L. & Skoulakis, E. M. Electron spin resonance (epr) in drosophila and general anesthesia. In
Methods in enzymology ,vol. 603, 115–128 (Elsevier, 2018).
Mendive-Tapia, D. et al.
Multidimensional quantum mechanical modeling of electron transfer and electronic coherence inplant cryptochromes: The role of initial bath conditions.
The J. Phys. Chem. B , 126–136 (2018). Finlay, C. C. et al.
International geomagnetic reference field: the eleventh generation.
Geophys. J. Int. , 1216–1230(2010).
Yamakura, T. & Harris, R. A. Effects of gaseous anesthetics nitrous oxide and xenon on ligand-gated ion channelscompari-son with isoflurane and ethanol.
Anesthesiol. The J. Am. Soc. Anesthesiol. , 1095–1101 (2000). Nagele, P., Metz, L. B. & Crowder, C. M. Xenon acts by inhibition of non–n-methyl-d-aspartate receptor–mediatedglutamatergic neurotransmission in caenorhabditis elegans.
Anesthesiol. The J. Am. Soc. Anesthesiol. , 508–513 (2005).
Adams, B. & Petruccione, F. Quantum effects in the brain: A review.
AVS Quantum Sci. , 022901 (2020). Fisher, M. P. Quantum cognition: The possibility of processing with nuclear spins in the brain.
Annals Phys. , 593–602(2015).
Hameroff, S. & Penrose, R. Consciousness in the universe: A review of the ‘orch or’ theory.
Phys. life reviews , 39–78(2014). Simon, C. Can quantum physics help solve the hard problem of consciousness?
J. Conscious. Stud. , 204–218 (2019). Kumar, S., Boone, K., Tuszy´nski, J., Barclay, P. & Simon, C. Possible existence of optical communication channels in thebrain.
Sci. reports , 1–13 (2016). Acknowledgements
The authors would like to thank Peter Hore, Robert Dickinson, Dennis Salahub, Sourabh Kumar, Parisa Zarkeshian, SumitGoswami, Faezeh Kimiaee Asadi, Stephen Wein, Jiawei Ji, Yufeng Wu, and Kenneth Sharman for their input, comments, andinsights on this topic. C.S. particularly thanks Stuart Hameroff for bringing the results of Li et al. to his attention. This workwas supported by the Natural Sciences and Engineering Research Council of Canada. Author Contributions Statement
J.S. performed the calculations with help from H.Z.H. and C.S.; J.S. and C.S. wrote the paper with feedback from H.Z.H.; C.S.conceived and supervised the project.
Competing Interests
The authors declare no competing interests.
In contrast to the case of the cryptochrome model, in which the nuclear spins are permitted to take on different isotopic spinvalues leading to various permutations of nuclear spins, in the experimental case of xenon each isotope was supplied separatelyby Li et al. , so here all xenon nuclei in the RPM model were constrained to have the same simultaneous isotopic nuclear spin ( I = I = I ∈ { , / , / } ) .In the case of two xenon nuclei occupying the active site the assumption was made that each xenon nucleus couplesexclusively to a unique electron in the RP, motivated by the proximity of the xenon nuclei to each phenylalenine residue, and byextension to each radical electron, in the work of Dickinson et al . The Hamiltonian describing this case, where each of the twonuclei couples solely to a unique radical electron, can be expressed asˆ H = ω (cid:0) ˆ S Az + ˆ S Bz (cid:1) + a ˆ S A · ˆ I + a ˆ S B · ˆ I . (3)The optimized parameter values using the two-xenon occupation state were found to be a (cid:48) = µ T, a (cid:48) = µ T, B = µ T, k = . × s − , and r = . × s − , resulting in SR / = .
73 and SR / = .
71. Similar to the single-xenon case, thetwo-xenon model produced results indicating that the RPM can explain experimental anesthetic potency results most closelyin the case that one xenon nucleus couples with its respective radical electron very strongly, while the other xenon nucleusinteracts with its corresponding electron relatively weakly, which essentially renders the two cases equivalent; one radicalelectron couples strongly with one xenon atom, while the other electron only couples weakly. In the two-xenon case, however,the hyperfine parameter space for which SR is within uncertainty of Pot is relatively large compared with the single-xenoncase, as seen in Supplementary Figures S1 and S2. Similar optimized RP lifetime values are seen in this case as in the case ofsingle-xenon occupation, see Supplementary Figs. S3 and S4, but the range of agreeable values extends to somewhat longer RP ifetimes than in the single-xenon case, where both cases are within an order of magnitude of the value suggested by Hore inthe cryptochrome context.The results of the B -sensitivity analysis of the two-xenon occupation model show that for external fields with either verysmall ( < µ T) or extremely large ( > µ T) magnitudes, SR and Pot values may diverge, see Supplementary Fig. S5.Considering the three-xenon occupation state in which three xenon atoms occupy the glycine binding site in the NMDAreceptor, based on the geometric modelling done by Armstrong et al. it was assumed that radical electron A couples with twoxenon nuclei ( I and I ) and radical electron B couples only to the third xenon nucleus ( I ). In this case the Hamiltonian can bemodelled asˆ H = ω (cid:0) ˆ S Az + ˆ S Bz (cid:1) + a ˆ S A · ˆ I + a ˆ S A · ˆ I + a ˆ S B · ˆ I , (4)The optimized parameter values using the three-xenon occupation state were found to be a (cid:48) = µ T, a (cid:48) = µ T, a (cid:48) = µ T, B = µ T, k = . × s − , and r = . × s − , resulting in SR / = .
72 and SR / = .
71. Note that ourthree-xenon model includes the two-xenon model as a special case, so it is not surprising that the three-xenon model can alsoexplain the experimental anesthetic potency of xenon reported by Li et al . igure 2. The dependence of the single-xenon RPM model on changes in the hyperfine coupling constants a (cid:48) and a (cid:48) for a (cid:48) , a (cid:48) ∈ [ , ] µ T, using r = . × s − , B = µ T, and τ = . × − s. The model can explain the experimentallyderived relative anesthetic potency of xenon for values of r and k where | Pot / − SR / | , | Pot / − SR / | ≤ . (a) Theabsolute difference between
Pot / and SR / . (b) The absolute difference between
Pot / and SR / . igure 3. The dependence of the single-xenon RPM model on changes in the hyperfine coupling constants a (cid:48) and a (cid:48) for a (cid:48) , a (cid:48) ∈ [ , ] µ T, using r = . × s − , B = µ T, and τ = . × − s. The model can explain the experimentallyderived relative anesthetic potency of xenon where | Pot / − SR / | ≤ .
080 and | Pot / − SR / | ≤ .
08 intersect. igure 4.
The dependence of the single-xenon RPM model on the relationship between r and k for r , k ∈ [ . × , . × ] s − , using a (cid:48) = µ T, a (cid:48) = µ T, and B = µ T. The model can explain the experimentallyderived relative anesthetic potency of xenon for values of r and k where | Pot / − SR / | , | Pot / − SR / | ≤ . (a) Theabsolute difference between
Pot / and SR / . (b) The absolute difference between
Pot / and SR / . igure 5. The dependence of the single-xenon RPM model on the relationship between r and k for r , k ∈ [ . × , . × ] s − , using a (cid:48) = µ T, a (cid:48) = µ T, and B = µ T. The model can explain the experimentallyderived relative anesthetic potency of xenon where | Pot / − SR / | ≤ .
080 and | Pot / − SR / | ≤ .
08 intersect. igure 6.
The external field-dependence of the single-xenon RPM model with B ∈ [ , ] µ T, τ = . × − s, r = . × s − , and hyperfine constants of a (cid:48) = µ T, a (cid:48) = µ T. (a) The absolute singlet yield using xenon isotopicnuclear spin values of I ∈ { , / , / } . (b) The relative singlet yield ratios SR / and SR / with the singlet yield of spin I = SR =
1. Values of SR and Pot agree for B ∈ [ , ] µ T. upplementary Figure S1. The dependence of the two-xenon RPM model on changes in the hyperfine coupling constants a (cid:48) and a (cid:48) for a (cid:48) , a (cid:48) ∈ [ , ] µ T, using r = . × s − , B = µ T, and τ = . × − s. The model can explain theexperimentally derived relative anesthetic potency of xenon for values of r and k where | Pot / − SR / | , | Pot / − SR / | ≤ . (a) The absolute difference between
Pot / and SR / . (b) The absolute differencebetween
Pot / and SR / . upplementary Figure S2. The dependence of the two-xenon RPM model on changes in the hyperfine coupling constants a (cid:48) and a (cid:48) for a (cid:48) , a (cid:48) ∈ [ , ] µ T, using r = . × s − , B = µ T, and τ = . × − s. The model can explain theexperimentally derived relative anesthetic potency of xenon where | Pot / − SR / | ≤ .
080 and | Pot / − SR / | ≤ . upplementary Figure S3. The dependence of the two-xenon RPM model on the relationship between r and k for r , k ∈ [ . × , . × ] s − , using a (cid:48) = µ T, a (cid:48) = µ T, and B = µ T. The model can explain the experimentallyderived relative anesthetic potency of xenon for values of r and k where | Pot / − SR / | , | Pot / − SR / | ≤ . (a) Theabsolute difference between
Pot / and SR / . (b) The absolute difference between
Pot / and SR / . upplementary Figure S4. The dependence of the two-xenon RPM model on the relationship between r and k for r , k ∈ [ . × , . × ] s − , using a (cid:48) = µ T, a (cid:48) = µ T, and B = µ T. The model can explain the experimentallyderived relative anesthetic potency of xenon where | Pot / − SR / | ≤ .
080 and | Pot / − SR / | ≤ .
08 intersect. upplementary Figure S5.
The external field-dependence of the two-xenon RPM model with B ∈ [ , ] µ T, τ = . × − s, r = . × s − , and hyperfine constants of a (cid:48) = µ T, a (cid:48) = µ T. (a) The absolute singlet yield usingxenon isotopic nuclear spin values of I ∈ { , / , / } . (b) The relative singlet yield ratios SR / and SR / with the singletyield of spin I = SR =