Energetic photons applied to COVID-19 Coronavirus S2 subunit of spike glycoprotein for host cell entry inhabitation: An alternative approach for conventional vaccination


 We have investigated numerically the ability to inhibit spike protein from SARS-CoV-2 to attach and inter the host cell when exposed to energetic photons. The Geometric Progression fitting method have been adopted to calculate the equivalent atomic number for photon energy absorption (Zeq), exposure and absorption buildup factors in the energy range E∈ [15–300] keV for the S2-subunit in the spike protein. The buildup factors have shown a peak value at adsorption resonance energy between 36–60 eV per amino acid of the S2-subunit which depends on the mean free path of the photon within the protein structure and the type of mutation. The resonance energies (between UV and X-ray range) have been found to depend on the protein molecular composition. This opens the possibility of using energetic photons to break up the S2-subunit into small fragments. Our results may contribute to the continues racing for finding noninvasive technique for medical trials using radiotherapy treatment for the COVID-19 virus.


Introduction
During the last two decades several variants of coronaviruses have caused serious health threats to humanity [1][2][3][4][5][6][7]. Among them, severe acute respiratory syndrome coronavirus (SARS-CoV), in 2003 [1][2], Middle East respiratory syndrome coronavirus (MERS-CoV) in 2012 [3], porcine epidemic diarrhea coronavirus in 2013 [4], and nally the 2019novelcoronavirus, COVID-19, (o cially known as SARS-CoV-2). COVID-19 is a newly emerged human infectious coronavirus that was originated in Wuhan seafood market and quickly spread beyond China [5][6]. In general, coronaviruses cause widespread respiratory and central nervous system diseases in humans [7][8][9]. Coronaviruses can adapt to new environments through mutation and recombination with relative ease and hence are programmed to alter host range and tissue tropism e ciently [10][11]. The World Health Organization (WHO) has declared COVID-19as a pandemic in March 2020. Up to date over 105 million cases have been reported worldwide, and more than two million casualties. Very recently the U.S. Food and Drug Administration (FDA) has approved two antiviral vaccines against SARS-CoV-2. The rst one is due to the P zer and BioNTech, while the other one is due to Moderna. Both vaccines have shown a 95% e ciency against this pandemic virus [23].
Although many resent statistical surveys and clinical tests are being rushing on COVID-19 across the globe [12,13], yet no clue from the available clinical controlled tests has proven that it may enhances the therapy conclusions about the patients end results [14]. As the pandemic escalate s, it is an essential issue to discover a exceptional therapeutic for COVID-19, and vaccines pledge to different variants of SARS-CoV-2 proteins. This protein types are a family of a monostranded enveloped positive-sense RNA virus [15]. The entire RNA sequencing genome procedure revealed that such stranded-RNA is recognized by 29,881 bp while encoding 9860 amino acids (GeneBank no. MN908947) [16]. Moreover, these speci c coronavirus proteins via gene fragmentation method uncovers there structural and nonstructural secondary conformations. In particular, SARS-CoV-2 virus encompasses four distinct structural proteins: Spike, Nucleocapsid, Envelope and Membrane protein [17]. Amongst them, the Spike (S-) glycoprotein is a giant, transmembrane and multifunctional protein. This S-protein compete with other coronavirus proteins by mediating itself in an deadly and vital role with respect to host cell via viral attachment, fusion and entry into it [17,18]. The S-protein has two sub-domains namely, S1 and S2 [19,20], which are then ssure into various biologically active subunits. Of interest, the S1-subunit which runs the binding to the host cell receptor which nally fascinating the cell entry [19,20]. On the other hand, the whole virus initiation and fusion entry into the host cellular membrane is governed by the S2 portion of the spike protein. During this process the viral contains of the virus is being injected into the infected cell [21,22]. Furthermore, It has been recently concluded that the coronaviruses adapted the circumvention method to trick the host immune system of the infected host cells using conformational masking and glycan shielding of its own S-protein [22].
Several physical and chemical techniques [28,29] have been applied to inactivate the virus. Such techniques include heating, UV light and ionizing radiation methods. Each rout has its own drawback regarding epitopes damage and development during medical treatment. Gamma irradiation might be considered as a very safe and effective method as indicated in many recent research articles (for full review see [28] and the references therein). On the other hand, the electromagnetic (EM) spectrum between the UV (i.e., 10 18 Hz) and the X-ray radiation (i.e., 10 19 Hz) is very sensitive to molecular vibration between groups of atoms in macromolecules [30]. Since the resonance absorption energy depends on the protein backbone molecular structure of the amino acids, then each molecule produces its own vibration resonance frequency signature which may lead to the breaking up of the protein structure at speci c position along its backbone [31,32].
Many researchers have employed the ve-parameter geometric progression (G-P) tting method which is originally developed and pioneered by Berger and Hubbell [24] to determine both EABF and EBF for amino acids, single-chain fatty acids and carbohydrates and other non-biological compounds [25]. These studies have shown that G-P tting is a convenient method for estimating the energy absorption and exposure buildup factors (i.e., EABF and EBF) for many biological molecules. These two important factors may be used to pinpoint the resonance frequency or energy of the viral RNA or DNA strand.
Scanning the energy range from few keV up to hundreds of keV may enable the determination of the breaking-up energy of speci c sub-domains of the protein in the target.
Large volume of publications has appeared in literature as a consequence of the development of WinXCom software. Manohara and Hanagodimth [26] in couples of independent research reports have determined the effective atomic numbers and electron densities of some essential amino acids in a broad range of photon energies from a few keVup to 100 GeV. A progressive investigation has also been performed by Kurudireket al. [27] who investigated the effect of γ-ray energy on some important human tissues by calculating the absorption and exposure buildup factors. On further attempt of the same research group, Kurudirek and Onara [28] have detailed the γ-ray energy absorption (EABF) and exposure buildup factors (EBF) for different biological-related molecules in the energy range E∈  keV up to a 40 mfp. Most of these "in vitro" experiments have been performed to understand what is happing at sub-cellular level when X-or γ-ray interacts with proteins, tissues, or cell membrane [29].
In the present work, we are motivated by the current research work onCOVID-19 vaccination development around the globe using the conventional clinical treatment. The roles of the SARS-CoV-2 spike glycoprotein in receptor binding and membrane fusion make it an ideal target for vaccine and antiviral development. The development of SARS vaccines based on the spike protein has been summarized in [33][34][35][36][37]. Here, we propose a novel approach to inhabit the S-protein from entering the host cell by applying UV and X-ray irradiation. Thereby, we have investigated theoretically the effect of photon irradiation on the amino acids building blocks in the SARS-CoV-2 spike protein (see Schematic 1) for possible inhabitation of virus to enter and relocate itself into the host cell. This approach is based on the resonance energy for S2-subdomain of the spike protein to break it up into small fragments (see schematic 1) [18][19][20]. The molecular formula of the nucleotide bases of S2 protein from different coronaviruses mutations used in this study are summarized in Table 1.

Theoretical And Computational Background
The buildup factor values and the G-P tting parameters of the S2-subdomian were calculated using the well-known method of logarithmic interpolation from the equivalent atomic number (Z eq ) [37,38]. The computational work has been conducted in three steps. The rst step concerns with the computation of the Z eq values for S2-subdomain. The second step deals with the calculations of G-P tting parameters and nally the computation of the buildup factor values are illustrated in step three.

Calculation of the equivalent atomic number Z eq
The Z eq of a particular material is de ned as the ratio R(μ/ρ) Compton /(μ/ρ) Total of that material at a speci c photon energy corresponding to the ratio of an element at the same photon energy. Thus, rstly the Compton partial mass attenuation coe cients, (μ/ρ) Compton and the total partial mass attenuation coe cients (μ/ρ) Total were obtained for elements of atomic number ZÎ . These two ratios were also calculated for the ve nucleotide bases for the incident photon energy E Î [15-300] keV using XCOM; Photon Cross Sections Database, Web Version 3.1 program [38,39]. The logarithmic interpolation of Z eq has been performed using the relation [40,41] where Z 1 and Z 2 are the atomic numbers of the elements corresponding to the ratios R 1 and R 2 respectively. The ratio R for a nucleotide base satis es the following inequality R 2 < R < R 1 at a speci c photon energy.

Calculation of the geometric progression (G-P) tting parameters
In the second step we used the standard reference database recently released by the American National Standards ANSI/ANS-3.1 [22] which provides the various buildup factor (or consequently G-P tting parameters) for 23 chemical elements, one compound (i.e., H 2 O) and two mixtures (i.e., air and concrete) in the energy range of E Î  keV. This database has covered the G-P tting parameters for penetration depths up to 40 mfp. Then, the G-P tting buildup factor coe cients of the ve nucleotide bases used in this study were then interpolated according to the following formula [22]: where P 1 and P 2 are the values of the G-P tting coe cients corresponding to elements of atomic numbers Z 1 and Z 2 respectively at a given photon energy; Z eq is the equivalent atomic number of S2subdomain. The effective atomic number (Z eff ) is related to s a and s e through the following relation [22,23] where s a is the effective atomic cross section and s e is the total electronic cross section [22].

Calculation of energy and exposure buildup factors
Finally, the computed G-P tting parameters {P 1 , P 2 } were then used to generate the energy buildup factors (i.e., absorption and exposure) for the ve nucleotide bases at selected incident photon energies in the range 15<E<300 keV up to 40 mfp penetration depths. This was performed using the G-P tting formula according to the following piecewise function [22,23] The function K(E, x) which represents the photon dose multiplication factor is rather a complicated tangent hyperbolic function and is given by: where E is the incident photon energy and x is the penetration depth in units of mfp. The letters {a, b, c, d, x k } are the G-P tting parameters. The parameter b represents the value of the buildup factor at 1mfp.
These parameters are usually obtained by the least-square tting procedure. The dose function K(E, x) strongly depends on the incident photon energy E and the penetration depth x.

Results And Discussion
The molecular formulae of SARS-CoV-2 spike glycoprotein mutations spanning the S2-subdomain investigated in this study are presented in Table 2. The composition of each mutation will be correlated with the EBF and EABF in the subsequent discussion (see below). In addition, the change in the effective atomic number (Z eq ) as a function of the incident photon energy for each mutation is shown in Table 3 and the supplementary materials provided with this report. Moreover, the change in the equivalent atomic number with incident photon energy (Z eq ) for S2-subdomain along with the G-P tting parameters for the various mutations in the energy range EÎ  keV are shown.
It is clear from Table 3 that the only atomic weight fraction between the S2-subdomain constituents that may satisfy this proportion is the H-atom number. Therefore, we infer that the variation of Z eq between the S2-subdomains for the various mutations can be correlated with the number of hydrogen atoms presented in each compound. Meanwhile, other atomic weight fractions cannot satisfy the observed behavior of Z eq of the S2-subdomain for all mutations used in this study. The energy exposure (EBF) and absorption (EABF) buildup factors for S2-subdomain are shown in Fig. 1 and Fig. 2 as a function of the incident photon energy for mean free path (mfp) values mfp Î [1,40]. Information extracted from these two gures are then used to compare the effect on S2-subdomain in different mutations as a function of the incident photon energy at speci c mfp values.  Figure. The general conclusions drawn from this gure can be summarized as 1) the calculated values of EBF start to decline with increasing the mfp value nearly in the same energy range regardless of the mutation used in this study, 2) the Figure also shows that EBF globally having a Gaussian-like distribution with skews to the left indicating the domination of the lower than higher photon energy when living matter interacts with radiation. and 3) the distribution peak shifts to the right as the mfp is increased where one of the three well-known scattering processes would dominate the others (will be commented on later). The energy peak shift might be correlated with the resonance energy or frequency of the S2-subunite that may lead to breaking up the bonds along the backbone of this part of the spike protein. This also may involve the different bonding energies between all the S2-subunite molecular constitutes such as Carbon, Oxygen, Hydrogen and Nitrogen that might be the exact resonance energy between any of these atoms. For low mpf values, the resonance energy is estimated to be about 60 keV per S2 subunit (equivalent to 36 eV per amino acid residue) [28]. This energy corresponds to 9´10 18 Hz (or l= 0.344 Å) which lies between the UV and X-ray region in the electromagnetic radiation spectrum. For the other mpf values, this resonance frequency depends on the value of mpf. Many theoretical predictions of the resonance absorption spectra of biological macromolecules are in the UV-X-ray range [28][29][30]. Thus the EM waves offer multiple resonance frequencies that may excite the low-frequency part of the internal molecular structure of the S2-protein. These internal vibrations include atoms within the amino acid molecules linked via weak bonds (e.g. van der Walls and hydrogen bonds) [41,42].

Radiation buildup factors of the S2-subdomain
The variation of energy absorption exposure buildup (EABF) factor versus the incident photon energy at selected penetration depths for all S2-subdomain is depicted in Fig. 2a-2e. Obviously, all S2-subdomain consistently show the same general trend of variations of EABF with the incident photon energy. The variations in the buildup factors as a function of the incident photon energy show three distinct regions depending on the interaction process between the incident photon with matter.
The buildup factors show a rapid increase in the low energy region, reaching a maximum then decrease at a much lower rate when the incident photon energy is increased further. It is worth noting that the buildup factors for S2-subdomain coincide in the low energy region and deviate at higher energy regardless of the mutation or the mfp values. The observed variations can be easily explained by adopting the three well-known processes of photon interaction with matter. The photoelectric effect is the dominant process at the low energy side of the spectrum and operates for a short period of time resulting in small buildup factor values. On the other hand, Compton scattering is the dominant process in the energy region (100-300 keV) and lasts for longer time. The probability of Compton scattering decreases as the photon energy increases. In the intermediate region around the peak maximum the two processes compete with each other. Compton scattering can maximally enhance both buildup factors by multiple photon scattering inside the S2-subdomain intermolecular structure. For example, the largest EBF and EABF values occur around 60 keV (or 36 eV per amino acid) at 1 mfp, and around 100 keV (or 60 eV per amino acid) at 40 mfp [28]. The third process in which the incident photon interacts with matter is the pair production. This process was excluded as the maximum photon energy used in this study is 300 keV which is well below the threshold energy (1.02 MeV) for pair production to occur. The energy of peak maximum (peak of the buildup factors vs energy) may be considered as a resonance energy that the macromolecule may adsorb before it breaks up into small fragments (see the discussion below).
Our results show that the buildup factors depend on the chemical composition of S2-subdomain for the entire energy region studied here. In addition, it is also observed that the buildup factors attain their largest values for penetration depth of 40 mfp, which is the limit of our calculations. In fact, for mfp > 40 another mathematical and theoretical formalism must be adopted to gain insight about their variations with energy or mfp [22]. The equivalent atomic number Z eq takes the values between 6.04 and 4.44 for all mutations and steadily decrease with the incident photon energy.
The above results can be discussed in view of the vibrational adsorption frequencies exhibited within the molecular structure of the S2-subunite [28,41,42]. It is know that the function and conformational kinetics of proteins and peptides are governed by the intermolecular forces hidden in the hydrogen bonding like amide and carbonyl C=O groups and other functional groups present in the protein backbone. The presence of multiple hydrogen bonds in the secondary structure of the protein under study results in stabilizing and strengthen the molecular strands of the S2 subunit. This in part may explain the anticipated higher binding energy calculated in this report which came collective from all hydrogen and non-hydrogen bonds present within the protein structure. These bonds together determine the expected 3D-molecluer structure, vibrational resonance frequencies along with the conformational changes in the S2-subunit when exposed to a unique environment that affect its molecular structure [40,41]. Obviously, each protein or peptide possesses a unique resonance absorption energy that can be used to identify the breaking frequency of the various mutations in the S-protein based on such spectroscopic theoretical calculations. Our data clearly demonstrate that the molecular structure of the studied S2-subdomain is a crucial factor for possible radiation treatment of COVID-19 using energetic photons that lie in the UV-X-ray region of the EM spectrum. The data presented here for exposure and adsorption buildup factors for the S-protein opens the possibility to break up this molecule into small fragments by using photons with speci c energy [42,43].
Along these lines of nding and of particular interest is the treatment of COVID-19 with X-ray therapy which dated back to 1939 [43][44][45]. The recent studies using modern technology recommended a single dose of 0.5-1.0 Gy and a whole doses of 3.0-6.0 Gy in 2 or 3 fractions /week [44]. In fact, high X-ray radiation doses may initiate or lead to DNA and RND damage resulting in a cell death. Since the majority of death cases of COVID-19 is due to a failure in the cardiopulmonary dysfunction, it becomes necessary to recommend low-dose radiotherapy to patients with COVID-19 as it reduces endothelial-leukocyte interaction. This process may activate T-cells and change the polarization of macrophage in response to X-ray treatment [45]. Feldman et. al. [Am J. 2019, 46] have applied gamma irradiation for a possible inactivation of the emergent vial pathogen namely COVID-19. They used 60 Co source to inactivate infectious diseases by destructing multiple replicates of the nucleic acid either directly or by radiocleavage of the genetic materials of SARS-Cov-2 proteins. They have tested the inactivation of selected viral pathogens in liquid medium containing T-proteins from different members of virus families and infectious agents in different mixtures. Their conclusion require a de ned peak of the absorbed gamma ray doses to fully inactivate these enveloped protein within these viruses. They also found that this peak depends on different factors such as virus susceptibility to gamma irradiation, genome size and virus type and composition [46].

Conclusions
Valuable information have been gathered about the equivalent atomic number of S2-subdomain at different energies and mfp. Moreover, the photon buildup factors (i.e., EBF and EABF) have been numerically calculated for this life-essential molecules in the energy range EÎ  keV up to ultimate penetration depths of 40 mfp. For medical trails applications, we observed, within the energy range studied in this report, the existence of different energy resonance frequencies for the S2-subdomain in various mutations. This adsorption resonance energy may be used to break up this type of S-proteins and prevents it entry to the host cell. The calculated resonance frequencies depend on the molecular structure, the environmental conditions and the type of mutation in the Spike protein. The calculated resonance energy values are in the range of 36-60 eV per amino acid. The current study showed that the presence of the S2-subdomain within the structure of SARS-CoV-2 virus plays a vital role in their response to external stimuli and breaking the S2-subunit into small fragments when exposed radiation (see Schematic 1). Tables Table 1: Some modifications of the RSFIEDLLFNKV motif in SARS-CoV-2 of mammalian hosts along with their GeneBank code  Figure 1 Variation of energy exposure buildup factors with photon energy for S2 subsequence of SARS-COV-2 Spike protein for the various mutations used in this study with photon energy at selected values of mfp as indicated in the gure. The resonance peak depends on the type of mutation of SARS-COV-2 Spike protein.