key: cord-0669594-vl8l76vd
authors: Adams, Betony; Sinayskiy, Ilya; Grondelle, Rienk van; Petruccione, Francesco
title: Bad vibrations: Quantum tunnelling in the context of SARS-CoV-2 infection
date: 2021-11-17
journal: nan
DOI: nan
sha: a6a08736521c3fb4c1343dac941a1bc50c4141a9
doc_id: 669594
cord_uid: vl8l76vd

The SARS-CoV-2 pandemic has added new urgency to the study of viral mechanisms of infection. But while vaccines offer a measure of protection against this specific outbreak, a new era of pandemics has been predicted. In addition to this, COVID-19 has drawn attention to post-viral syndromes and the healthcare burden they entail. It seems integral that knowledge of viral mechanisms is increased through as wide a research field as possible. To this end we propose that quantum biology might offer essential new insights into the problem, especially with regards to the important first step of virus-host invasion. Research in quantum biology often centres around energy or charge transfer. While this is predominantly in the context of photosynthesis there has also been some suggestion that cellular receptors such as olfactory or neural receptors might employ vibration assisted electron tunnelling to augment the lock-and-key mechanism. Quantum tunnelling has also been observed in enzyme function. Enzymes are implicated in the invasion of host cells by the SARS-CoV-2 virus. Receptors such as olfactory receptors also appear to be disrupted by COVID-19. Building on these observations we investigate the evidence that quantum tunnelling might be important in the context of infection with SARS-CoV-2. We illustrate this with a simple model relating the vibronic mode of, for example, a viral spike protein to the likelihood of charge transfer in an idealised receptor. Our results show a distinct parameter regime in which the vibronic mode of the spike protein enhances electron transfer. With this in mind, novel therapeutics to prevent SARS-CoV-2 transmission could potentially be identified by their vibrational spectra.

Quantum biology is almost as old as quantum mechanics itself 1 . Where quantum mechanics is often preoccupied with the interaction of light and matter, photosynthesis, that backbone of biology, is the interaction of light with living matter. Bohr himself delivered a lecture which he titled 'Light and Life' 2 . Schrödinger, for his part, wrote What is Life? The Physical Aspect of the Living Cell, which served as inspiration for the discovery of DNA 1,3 .

In a discussion of life, viruses offer a novel case study, straddling, as they do, the properties of both living and non-living systems 4 . As such, they might also offer a novel application for quantum biology. There has been some research into investigating how quantum mechanics and viruses intersect. For example, Park et al. engineered a virus to obtain enhanced energy transport in excitonic networks 5 . Quantum dots have been used to label viral proteins in an attempt to enhance live imaging of virus-host interactions 6, 7 . They have also been suggested to have antiviral properties 8-10 . There has even been an attempt to simulate the life cycle of a virus using quantum gates 11 . Meanwhile, the new coronavirus SARS-CoV-2 has fundamentally changed the world we find ourselves in. While SARS-CoV-2 vaccine development has been integral, there is some suggestion that we have entered a new era of pandemics 12 . It seems imperative that research into understanding viral mechanisms is accelerated. One way in which this might be achieved is to look at how research outside of established disciplines might allow new insights into physiological mechanisms. Quantum biology, which looks at how non-trivial quantum effects, such as coherence, tunnelling and entanglement, might play a role in biological systems, is one such field of research [13] [14] [15] . The phenomenon of charge transfer is central to much of the research emerging in this field.

There is some evidence that coherent energy and charge transfer play a role in photosynthetic networks 13,16-18 . This is perhaps the best known application of quantum effects in the biological context. Charge transfer, however, is also important in the context of tunnelling in enzymes, which was first observed a number of decades ago 19 . Electron tunnelling has also been proposed to be the mechanism, or one of the mechanisms, by which olfactants activate olfactory receptors 20,21 . Olfactory receptors are a class of rhodopsin-like receptors known as G-protein coupled receptors, or GPCRs 22,23 . These receptors are implicated in numerous important physiological phenomena from the regulation of inflammation to the binding of neurotransmitters, the latter of which is currently emerging as a new applica-rhodopsin 22,23 . Rhodopsin is a retinal photoreceptor protein which consists of the lightsensitive chromophore retinal in an opsin protein 36 . Chromophores are a central theme with respect to quantum effects in photosynthesis, where it has been suggested that quantum coherence might play a role in energy and charge transfer [16] [17] [18] . This is perhaps less a unique feature of photosynthesis than it is due to the more general arrangement of chromophores in a protein 37 . Chromophores, then, would appear to be important to redox activity in biological materials. There is also a growing focus on the role that the protein scaffold might play in enhancing energy or charge transfer. Far from the warm, wet, decoherent environment that is often cited as an argument against quantum effects in biology, the vibrational or spin states of proteins might be coupled to electronic states in a favourable way 38,39 . Interaction with proteins can fundamentally change the properties of a chromophore. Rhodopsin and related opsins, for instance, absorb across a range of frequencies even though they share the same chromophore: retinal. What differs is the opsin protein, which tunes the chromophore's absorption frequency 40 . This coupling of vibrational to electronic states is most often imagined with respect to the proteins in which the chromophore is embedded, but it might be re-imagined in terms of protein-receptor bonding. While it is still debatable that GPCRs, being related to rhodopsins, operate through a mechanism related to electron transfer, both olfaction and neurotransmitter binding have been of interest in the context of quantum biology. Olfaction has conventionally been described as operating through the recognisable shapes of olfactants 21 . However, this model has to some extent failed at fully describing the intricacies of our olfactory apparatus. This has given rise to an alternative vibrational theory of olfaction. In this theory, the vibrational spectrum of a ligand rather than its shape is responsible for receptor activation by facilitating electron tunnelling 20,41 .

While there is some evidence to support the differentiation of deuterated odorants in various species 24,42-44 , there remains some scepticism with regards to the theory 45 . The suggestion has been made that the mechanism of olfaction might be closer to a swipe card model, with various different factors contributing 46 . More recently, attempts have been made to apply the vibrational theory of olfaction in a different physiological context: the binding of neurotransmitters. Neurotransmitters are integral to the process of neural signal transmission. Signals travelling along the axon of a nerve cell are communicated to adjacent nerve cells by the release of neurotransmitters across the synaptic cleft between cells 47 . These neurotransmitters bind to membrane receptors which facilitate the opening of ion channels and thus initiate the activation of nerve cells 47 . Theoretical research suggests that the action of specific neurotransmitters such as serotonin and related ligands is correlated to their vibrational spectra 24,48 . Similar theoretical effects have been suggested for the binding of histamine 26 and adenosine 25,49 although experimental verification is still lacking. What we would like to highlight, however, is the fact that charge transfer is a well established topic in quantum biology. More specifically, the biological context of this transfer is very often that of membrane-embedded proteins. Within this research much attention is paid to how the biological environment might assist transfer processes, through, for example the vibrations of the protein scaffold or the vibrations of a binding ligand. It is thus potentially informative to consider this in the context of infection by the SARS-CoV-2 virus, which utilises membrane-embedded proteins to invade host cells. Another enzyme, cathepsin L, has been linked to spike protein cleavage and enhanced viral entry into host cells 61, 63 . Given the importance of enzymes in viral activity and given the fact that quantum tunnelling plays a role in enzyme activity it seems a closer look at quantum effects in the context of viruses might prove fruitful. More generally, a closer look at receptor mechanisms might offer some insights. Criticism of the vibration assisted tunnelling theory of olfaction often points to the fact that there isn't evidence for electron transfer in olfactory receptors, which are GPCRs 64 . However, a recent, as yet to be reviewed, paper suggests that there is the potential for electron transfer in certain types of GPCRs. Various possibilities for the specific site of this electron transfer are explored in detail in the paper 64 . In the context of SARS-CoV-2, one of these is of particular interest: the disulfide bridge. ACE2 is not a G-protein coupled receptor. Evidence does suggest, however, that its interaction with the spike protein might involve redox activity [65] [66] [67] . This redox status is also suggested to involve a disulfide bridge. Both spike protein and ACE2 are rich in cysteine residues, which are implicated in intramolecular disulfide bonds 65 . Indeed, the infectivity of SARS-CoV-2 appears to depend on the disulfide redox potential with resistant animals lacking a redoxactive disulfide 65, 66 . Binding affinity has also been demonstrated to be significantly impaired when the disulfide bonds of ACE2 and SARS-CoV-2 spike proteins are reduced 67 Hamiltonians (H) that mathematically describe the system and environment as well as the interaction between the two. Biological systems interact with their environments and thus are often modelled using an open systems approach. This involves modelling the system and environment as a closed system, the environment is then traced out to arrive at the reduced system dynamics.

is integral to viral infection. As a common factor to enzyme function, receptor binding, olfactory symptoms and immune response, it deserves closer scrutiny through as many lenses as possible. 

where D and A are the energy levels of the donor (D) and acceptor (A) levels and J describes the coupling between levels and the likelihood of transition. For a dimer isolated from external interaction, the maximum probability of a transition from donor to acceptor is given by

where ∆ = ( A − D )/2. When the energy of the donor and the acceptor are equal then the probability of transfer [P D→A (t 0 )] = 1 at time t 0 = π/2J 76 . For a dimer that is not isolated the total Hamiltonian is given by:

The receptor is represented by the dimer with Hamiltonian, H R . The ligand, in this case the spike protein, is represented as a harmonic oscillator with frequencies associated with the spike protein. This has been incorporated into H R−P , the interaction between the receptor and the protein, given by:

The sum runs over the interaction of the protein with both the donor and the acceptor; the latter is presumed to be zero in the numerical solution. The coupling strength between ligand protein and receptor is given by γ and a and a † are the creation and annihilation operators associated with the spike protein vibrations, with associated frequency ω. The

Hamiltonians H R and H R−P represent the system in our model of SARS-CoV-2 receptor tunnelling. The membrane environment H E and its interaction with the receptor H R−E is similarly approximated as:

where γ E represents the coupling between the receptor and its membrane environment. This coupling is taken to be weaker than the spike protein coupling to the receptor. 

where ρ is the reduced density matrix describing the dynamics of the system, κ D and κ A denote respective coupling of donor and acceptor to the external environments. We assume that the initial state of the dimer is at the donor site, and the vibronic mode is initially in the thermal state (T = 300K). Using numerical simulation, we would like to understand if coupling to a vibronic mode could enhance the transition probability in the dimer system: from donor to acceptor. To this end, we will measure the usefulness of the vibronic mode coupling by considering the following difference:

where Max[P D→A (t)] vibronic mode denotes the maximum probability of the transition in the dimer system calculated from the numerical integration of Equation (6), while Max[P D→A (t)]

represents the maximum probability of transition without vibronic mode coupling, given by Equation (2). 

Parameter ranges 500 − 1700cm transfer probability in distinct regions, especially for higher frequencies of the vibronic mode (see Figure 7 ).

A better understanding of the various ways in which viruses and host cells interact through molecular recognition and binding might also lead to novel treatments for COVID-19. It has already been suggested that treatment with ACE2 inhibitors might have an effect on What makes this more interesting in the context of COVID-19 is that antidepressants known as selective serotonin reuptake inhibitors (SSRIs) have been shown to be somewhat effective against the SARS-CoV-2 virus [93] [94] [95] . While the studies are far from being conclusive this isn't the first time that these antidepressants have been investigated as antivirals, although the mechanism of action appears to be less to do with serotonin modulation than viral replication 96, 97 . Recent studies also suggest that SSRIs are not alone in their poten-tial as a COVID-19 therapeutic. Other antidepressants, including venlafaxine, appear to improve the prognosis of patients hospitalised with COVID-19 94 . Venlafaxine targets both serotonin and norepinephrine, both of which bind to GPCRs to activate ion channels 98, 99 .

Other GPCR agonists have also been reported to have some effect in mitigating COVID-19

infection. Histamine, which plays a role in neuromodulation and transmission in addition to mediating immune and allergy responses, is an agonist that binds to a number of GPCRs 100 .

Antihistamines, on the other hand, bind to histamine GPCRs and act as blockers or reverse

agonists. There is some evidence that certain antihistamines protect against SARS-CoV-2 infection by disrupting the way in which the virus binds to its host cell 101 . There is still some doubt as to whether nicotinic receptors act, as least in part, as GPCRs 102 . These receptors, which bind the neurotransmitter acetylcholine as well as the agonist nicotine, do however open ion channels 103,104 . Whereas there is little debate that smoking itself offers any protection against COVID-19, surprising statistics around the hospitalisation of smokers and non-smokers with COVID-19 has led to some speculation that nicotine might be a potentially therapeutic intervention against severe disease. It remains unclear, however, whether the effects of nicotine are helpful or harmful 105,106 . The generalisation of the vibrational theory of olfaction to the binding of neurotransmitters has led to some suggestion that the agonist and antagonist action of certain ligands might be classified according to their vibrational spectra 25,26,49 . In the context of SARS-CoV-2, new therapeutics might be discovered by screening and selecting related ligands through, for example, their Raman spectra. The different vibrational spectra of mutated spike proteins might also allow some prediction of the infectivity of new variants of SARS-CoV-2. This paper has focused on the SARS-CoV-2 spike protein binding to ACE2 receptors and its possible interaction with G-protein coupled receptors. In particular it has looked at at how the spike protein vibronic mode might alter electron transfer in certain receptors. What many of these receptors potentially have in common is a disulfide bridge and the potential for redox activity 64, 65 . Targeting the disulfide bonds has been shown to modulate host cell invasion 66 . This interest in the redox activity of the SARS-CoV-2 virus might also be extended beyond host cell invasion to offer insights on other aspects of COVID-19. ACE2 is a regulator of oxidative stress and it has been suggested that increased vulnerability to COVID-19 is related to increased oxidative stress, through factors such as increased age or underlying health issues 65,107-109 . Redox reactions proliferate in the body, not least in the electron transport chains within mitochondria. The spike protein has also been shown to directly modulate mitochondrial activity, most probably through ACE2 signalling 110 . Whether or not the spike protein is involved, a growing body of research suggests that mitochondria are implicated in COVID-19 and as such might inform novel therapeutic options 107, 111, 112 .

.

While redox considerations, receptor binding mechanisms and the involvement of GPCRs in SARS-CoV-2 infection might lead to possible novel treatments for the disease, it might also offer insights into the post-viral condition referred to as 'long COVID' 113 . Research into this condition is still in the very early stages, and much of it is focused on the urgent need for more research to be undertaken, due to the large number of people who appear to experience long term symptoms relating to COVID-19 [113] [114] [115] . Long COVID is not necessarily correlated with the severity of the active infection, with some patients reporting mild symptoms during the initial, acute stage of the disease before going on to experience lingering sequelae 113, 116 . Some of the long-term effects may be due to damage wrought by COVID-19 to organs such as the lungs and heart [116] [117] [118] . However, an appreciable portion of those reporting long term effects show no obvious biomarkers to account for their disorienting collection of symptoms, ranging from fatigue and joint pain to brain fog, memory problems, mood swings and mental illness 116, 117 . In its lack of defining mechanism and broad range of symptoms, long COVID resembles the condition that is sometimes called myalgic encephalomyelitis (ME) or chronic fatigue syndrome (CFS) 113, 117 . It is well known that viral infections can cause a range of long term effects 119, 120 . Despite this, the condition remains under-researched, and, due to its various psychological manifestations often prompts suggestions that the syndrome is psychosomatic 121, 122 . There is some research, however, that points to the involvement of GPCRs in both ME and CFS, in particular the disruption of GPCR function by autoantibodies [123] [124] [125] . GPC receptors control a wide range of essential functions and bind to a broad spectrum of different ligands, which makes them an excellent target for drug development. However this also means that specific ligands might interact with receptors other than their primary receptor, contributing, for example, to the side-effects of a GPCR-targeting drug 87 . Whether long COVID involves GPCR disruption remains to be seen. But if ACE2 can bind both the SARS-CoV-2 virus as well as molecules such as angiotensin, then perhaps the virus can mimic, at least partially, the way in which angiotensin binds to GPCRs, either through specific viral proteins or through autoantibodies. GPCR disruption would also potentially explain the wide-ranging array of symptoms reported by long COVID sufferers, as GPCRs are implicated in many different physiological processes 22 .

GPCR involvement in ion channel action might also prove an avenue of research for potential therapeutics. Viruses or the virome play an important, as yet not fully understood, role in the body 126 . It is thus conceivable that long COVID is a manifestation of some aspect of the SARS-CoV-2 virus being incorporated into host cells even beyond the infected stage. Viroporins, for instance are viral proteins that can oligomerise in host cell membranes to form ion channels of their own 127, 128 . The physiological mechanisms behind both ME and CFS have been suggested to involve ion channels 129 . It might thus be interesting to investigate this in the context of long COVID, particularly as the envelope protein found in the SARS-CoV-2 virus has been shown to have viroporin capabilities 130, 131 . Ion channels are instrumental in maintaining membrane potential. While it is more common knowledge that membrane potential is integral to the activation and efficient function of nerve cells, all cells have an associated membrane potential. It is also becoming clearer that this membrane potential plays an important role in disease, not least cancer 132, 133 . Membrane potential is also integral to mitochondrial function, where it is coupled to energy and charge transfer in metabolic processes. Both ME and CFS have been suggested to involve metabolic processes 134, 135 . It has recently been suggested that long COVID resembles ME and CFS in redox imbalance, inflammation, an impaired ability to generate adenosine triphosphate (ATP), and general hypometabolic state, all of which implicate mitochondria in the process 107, 112 . There is some evidence that supporting redox processes, through co-enzymes for instance, may help with metabolic illnesses 136, 137 . There is even some evidence that the ingestion of chlorophyll, the chromophore central to photosynthesis, might alter mitochondrial ATP production 138 . It is thus perhaps not too much of a stretch to suggest that elements of the SARS-CoV-2 virus might be incorporated into the redox function of mitochondria.

This paper has been structured around two related assertions. The first of these builds on the possibility that the lock-and-key or shape-based mechanism used to describe a number of biological phenomena might be replaced or augmented by a quantum tunnelling mechanism. As such, quantum tunnelling is worth investigating in a variety of contexts where molecular recognition and reception play a role; in particular, in this paper, in the context of membrane-receptor binding of SARS-CoV-2. The second assertion addresses this specific context and the way in which quantum tunnelling might be implicated in the receptor binding of the SARS-CoV-2 spike protein, either through the role of enzymes or the involvement of GPCRs. In the event of the latter, the degeneracy that no doubt allows biological systems their flexibility, also allows for the wide range of symptoms attributed to COVID-19 and long COVID. If GPCR-targeting pharmaceuticals can target more than the specific receptor they are aimed at, causing a variety of side-effects, then perhaps the spike protein behaves in a similar manner. And perhaps a better understanding of receptor recognition might contribute to better medical intervention. Regardless of whether these assertions prove to be true, the point remains that questions of interest in quantum biology, such as tunnelling in the context of enzymes and GPC receptors, intersect with some of the open questions in SARS-CoV-2 research. As such, quantum biology can add to the store of knowledge that will offer protection against the SARS-CoV-2 virus as well as novel future viruses. Techniques used in quantum biology, such as the comparison of vibrational spectra to predict GPCR agonist potency 24 , might also inform approaches to virus research. The vibrational characteristics of the SARS-CoV-2 spike protein have already been used to gain insight into its structure by translating the protein into music 139 . More prosaically, SARS-CoV-2 infection has also been investigated using Raman spectroscopy 140, 141 . This might be extended to comparing the spectra of mutated spike proteins and whether this correlates with how infectious the mutated versions are 142 . Quantum biology might also offer some insights into the long term debilitating effects of COVID-19 and shape possible treatments. While the focus in this paper has been on quantum tunnelling in enzymes and GPC receptors, other related mechanisms of interest in quantum biology offer further avenues of research. ACE2, for example, is a regulator of oxidative stress 65 . Reactive oxygen species (ROS) have also been implicated in GPCR activity 143 . ROS are important signalling molecules but are also implicated in cellular inflammation and damage 144 . The production of ROS has been demonstrated to be sensitive to magnetic fields, a fact that has been attributed to the involvement of radical pairs, one of the primary topics of interest in quantum biology 145 . Inflammation is a contributing factor in both acute infection with the SARS-CoV-2 virus as well as in long COVID 146,147 . Recently it has been shown that the application of electromagnetic fields can significantly ameliorate the inflammation associated with COVID-19 148 . Progress made in quantum biology may thus have even more to offer the study of viruses than the preliminary ideas laid out in this paper. 

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The authors declare no competing interests.