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Biothermodynamics of the BA.5.2 and BF.7 variants of SARS-CoV-2

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17 January 2023

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18 January 2023

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Abstract
SARS-CoV-2 resembles the ancient mythical creature Hydra. Just like with the Hydra, when one head is cut, it is followed by appearance of two more heads, suppression of one SARS-CoV-2 variant causes appearance of newer variants. Unlike Hydra that grows identical heads, newer SARS-CoV-2 variants are usually more infective, which can be observed as time evolution of the virus at hand, which occurs through acquisition of mutations during time. The appearance of new variants is followed by appearance of new COVID-19 pandemic waves. With the appearance of new pandemic waves and determining of sequences, in the scientific community and general public the question is always raised of whether the new variant will be more virulent and more pathogenic. The two variants characterized in this paper, BA.5.2 and BF.7, have caused a pandemic wave during the late 2022. This paper gives full chemical and thermodynamic characterization of the BA.5.2 and BF.7 variants of SARS-CoV-2. Having in mind that Gibbs energy of binding and biosynthesis represent the driving forces for the viral life cycle, based on the calculated thermodynamic properties we can conclude that the newer variants are more infective than earlier ones, but that their pathogenicity has not changed.
Keywords: 
COVID-19
;  
variant of concern
;  
infectivity
;  
pathogenicity
;  
evolution
;  
Gibbs energy
Subject: 
Biology and Life Sciences  -   Virology

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Introduction

Living organisms represent open thermodynamic systems, which during interactions with their animate and inanimate surroundings change their thermodynamic parameters [Boltzmann, 1974; von Bertalanffy, 1950, 1971; Balmer, 2010; Popovic, 2018a, 2018b; Prigogine and Wiame, 1946; Prigogine, 1977, 1947; Glansdorff and Prigogine, 1971; Morowitz et al., 2000, 1988; Morowitz, 1995, 1992, 1976, 1968, 1955; Schrödinger, 1944; Ozilgen and Sorgüven, 2017]. Even though they represent the simplest biological systems, viruses completely fit into von Bertalanffy’s theory of open systems in biology [von Bertalanffy, 1950, 1971].
Viruses are obligate intracellular parasites, which hijack metabolism and resources of their host cells, and use their host cell to perform basic biological functions [Popovic and Minceva, 2020a, 2020b]. Until 2019, the empirical formula was known only for the poliovirus [Wimmer, 2006; Molla et al., 1991]. Since the beginning of the COVID-19 pandemic, there has been an intense development of biothermodynamics of viruses. The next virus to be chemically and thermodynamically characterized was the Hu-1 variant of SARS-CoV-2 [Popovic, 2022a]. During the COVID-19 pandemic, SARS-CoV-2 has mutated many times on the genes encoding the spike glycoprotein and other viral proteins. The consequence of mutations was development of new variants. Chemical and thermodynamic characterization of new virus variants has been reported in the literature [Popovic and Popovic, 2022; Özilgen and Yilmaz, 2021; Yilmaz et al., 2020; Nadi and Özilgen, 2021; Şimşek et al., 2021; Degueldre, 2021; Popovic, 2022a, 2022b, 2022c, 2022d, 2022e, 2022f, 2022g, 2022h, 2022i, 2022j; Gale, 2022; Lucia, 2021, 2020a, 2020b; Kaniadakis et al., 2020; Popovic and Minceva, 2021a, 2020b; Istifli et al., 2022]. In that way, biothermodynamics has followed the reports on sequencing of nucleic acids and proteins of various variants. The atom counting method has been developed, which determines empirical formulas of viruses, based on their genetic and protein sequences [Popovic, 2022k].
Thermodynamic analysis and calorimetry have for a long time been used in research on viruses. The calorimetric methods include differential scanning calorimetry (DSC), isothermal titration calorimetry (ITC) and reaction calorimetry (isothermal microcalorimetry) [Privalov, 2012; Sarge et al., 2014]. Differential scanning calorimetry (DSC) has been applied to measure energetics of virus capsid self-assembly and denaturation [Krell et al., 2005; Yang et al., 2017], virus particle structure [Bauer et al., 2015, 2013], thermal stability [Yang et al., 2017; Makarov et al., 2013; Virudachalam et al., 1985a, 1985b], virus identification [Krell et al., 2005], virus denaturation [Toinon et al., 2015 ; Brouillette et al., 1982], entry into host cell [Banerjee et al., 2010; Nebel et al., 1995], capsid self-assembly [Sturtevant et al., 1981; Stauffer, 1970] and vaccine development [Deschuyteneer et al., 2010; Wang et al., 2015].
Isothermal titration calorimetry (ITC) was also applied to study a wide range of phenomena related to viruses, such as virus adsorption and disassembly [Yu et al., 2015], influence on metabolism and cell cycle [Javorsky et al., 2022; Prins et al., 2010], apoptosis inhibition [Anasir et al., 2017; Aladag et al., 2014], virus structure and entry into host cells [Liu et al., 2014], nucleocapsid self-assembly [Maassen et al., 2019], inactivation [Yang et al., 2020; Kawahara et al., 2018], immune response evasion [Gao et al., 2021], antiviral therapy development [Zhou et al., 2022; Noble et al., 2016; Sharma et al., 2016; Byrn et al., 2015] and vaccine development [Vorobieva et al., 2014].
Reaction calorimetry (isothermal microcalorimetry) has been applied to study virus multiplication inside host cells [Sigg et al., 2022; Tkhilaishvili et al., 2018a; Guosheng et al., 2003; Morais et al., 2014], phage action against bacterial biofilms [Tkhilaishvili et al., 2020a, 2020b, 2018a, 2018b, 2018c; Wang et al., 2020a, 2020b], phage-bacteria interactions [Fanaei Pirlar et al., 2022; Wang et al., 2020c], phage transition from lytic into lysogenic cycles [Maskow et al., 2010], antiviral therapy [Shadrick et al., 2013; Tkhilaishvili, 2022; Gelman et al., 2021], and influence on marine ecosystem metabolism [Djamali et al., 2012].
Working with SARS-CoV-2 requires a high biosafety level and few analytic and biothermodynamic laboratories fulfill such conditions. To overcome this obstacle, the atom counting method was developed [Popivic, 2022k], which proved itself useful in chemical and thermodynamic characterization of contagious viruses like SARS-CoV-2. During the last year, the atom counting method has proved itself useful in characterization of other viruses, including Ebola [Popovic, 2022j], Monkeypox [Popovic, 2022L], Herpes [Popovic, 2022m], HIV-1 [Popovic, 2022n] and bacteriophages [Popovic, 2022q], as well as viroids [Popovic, 2023].
Change in thermodynamic properties represents the driving force for most processes in nature [Demirel, 2014; Balmer, 2010; Atkins and de Paula, 2011, 2014; Ozilgen and Sorgüven, 2017]. The viral life cycle consists of several processes, which have their biological, chemical and thermodynamic nature [Popovic, 2022i, 2022p, Ridgway et al., 2022]. Replication of viral nucleic acid represents a chemical reaction of polymerization of nucleotides driven by Gibbs energy of biosynthesis [Dodd et al., 2020; Johansson and Dixon, 2013]. Transcription represents a polymerization reaction that produces mRNA [Pinheiro et al., 2008]. Translation represents a chemical reaction of polymerization of amino acids into proteins [Popovic, 2022i; Lee et al., 2020]. Virus binding represents a chemical reaction similar to protein ligand interaction, driven by Gibbs energy of binding [Gale, 2021, 2020, 2019, 2018]. Self-assembly of viral components represents a physical process, also led by changes in thermodynamic properties [Katen and Zlotnick, 2009; Maassen et al., 2019].
The goal of this paper is to perform a chemical and thermodynamic characterization of the BA.5.2 and BF.7 variants of SARS-CoV-2, to estimate their infectivity and pathogenicity, which depend on kinetic (e.g. biosynthesis rate and binding rate) and thermodynamic properties (e.g. enthalpy, entropy and Gibbs energy).

Methods

Data Sources

The genetic sequences of the BA.5.2 and BF.7 variants of SARS-CoV-2 were taken from GISAID, the global data science initiative [Khare et al., 2021; Elbe and Buckland-Merrett, 2017; Shu and McCauley, 2017]. The genetic sequence of the BA.5.2 isolate from Australia can be found under the accession ID: EPI_ISL_16342181. It was isolated in Sydney on December 18, 2022. The genetic sequence of the BA.5.2 isolate from Japan can be found under the accession ID: EPI_ISL_16374653. It was isolated in Fukuoka on December 3, 2022. The genetic sequence of the BA.5.2 isolate from USA can be found under the accession ID: EPI_ISL_16382809. It was isolated in New Hampshire on December 23, 2022. The genetic sequence of the BF.7 isolate from China can be found under the accession ID: EPI_ISL_16348517. It was isolated in Beijing on December 19, 2022. The genetic sequence of the BF.7 isolate from Greece can be found under the accession ID: EPI_ISL_16383259. It was isolated in Attica on November 17, 2022. The genetic sequence of the BF.7 isolate from Serbia can be found under the accession ID: EPI_ISL_16317088. It was isolated in Belgrade on November 21, 2022. Therefore, the findings of this study are based on metadata associated with 6 sequences available on GISAID up to January 7, 2023, and accessible at https://doi.org/10.55876/gis8.230107ef
The sequence of the nucleocapsid phosphoprotein of SARS-CoV-2 was obtained from the NCBI database [Sayers et al., 2022; National Center for Biotechnology Information, 2022], under the accession ID: UKQ14424.1. The number of copies of the nucleocapsid phosphoprotein in virus particle was taken from [Neuman and Buchmeier, 2016; Neuman et al., 2011; Neuman et al., 2006].
The dissociation equilibrium constant, Kd, of the spike glycoprotein of BF.7 variant of SARS-CoV-2 to the human ACE2 receptor was taken from [Wang et al., 2022]. Its value is Kd = 0.4 nM [Wang et al., 2022]. It was measured using surface plasmon resonance at 25°C [Wang et al., 2022].

Empirical Formulas and Biosynthesis Reactions

The genetic and protein sequences were used to find empirical formulas of nucleocapsids of the BA.5.2 and BF.7 variants of SARS-CoV-2. This was done using the atom counting method [Popovic, 2022k]. The atom counting method is implemented using a computer program [Popovic, 2022k]. The input are genetic and protein sequences of the virus of interest, as well as the number of copies of proteins in the virus particle and the virus particle size [Popovic, 2022k]. The program goes along the nucleic acid and protein sequences and adds atoms coming from each residue in the sequence, to find the number of atoms contributed by that macromolecule to the virus particle [Popovic, 2022k]. The contributions of viral proteins are multiplied by their copy numbers, since proteins are present in multiple copies in virus particles [Popovic, 2022k]. The output of the program is elemental composition of virus particles, in the form of empirical formulas, and molar masses of virus particles [Popovic, 2022k]. The advantage of the atom counting method is that it can provide the empirical formulas of virus particles, based on widely available data on genetic and protein sequences [Popovic, 2022k]. The atom counting method was shown to give results in good agreement with experimental results [Popovic, 2022k].
The empirical formulas of virus particles were used to construct biosynthesis reactions, summarizing conversion of nutrients into new live matter [von Stockar, 2013a, 2013b; Battley, 1998]. The biosynthesis reaction for virus particles has the general form
(Amino acid) + O2 + HPO42- + HCO3- → (Bio) + SO42- + H2O + H2CO3
where (Bio) represents new live matter, described by an empirical formula given by the atom counting method [Popovic, 2022b, 2022c, 2022f]. (Amino acid) represents a mixture of amino acids with the empirical formula CH1.798O0.4831N0.2247S0.022472 (expressed per mole of carbon), representing the source of energy, carbon, nitrogen and sulfur [Popovic, 2022b, 2022c, 2022f]. O2 is the electron acceptor [Popovic, 2022b, 2022c, 2022f]. HPO42- is the source of phosphorus [Popovic, 2022b, 2022c, 2022f]. HCO3- is a part of the bicarbonate buffer that takes excess H+ ions that are generated during biosynthesis [Popovic, 2022b, 2022c, 2022f]. SO42- is an additional metabolic product that takes excess sulfur atoms [Popovic, 2022b, 2022c, 2022f]. H2CO3 takes the oxidized carbon atoms and is also a part of the bicarbonate buffer [Popovic, 2022b, 2022c, 2022f].

Thermodynamic Properties of Live Matter and Biosynthesis

Empirical formulas of virus nucleocapsids were used to find standard thermodynamic properties of their live matter, using predictive biothermodynamic models: the Patel-Erickson and Battley equations [Patel and Erickson, 1981; Battley, 1999, 1998, 1992]. The Patel-Erickson equation was used to find enthalpy of live matter, based on its elemental composition. The Patel-Erickson equation gives standard enthalpy of combustion, ΔCH⁰, of live matter
∆ C H 0 b i o = − 111.14 k J C − m o l · E  
where E is number of electrons transferred to oxygen during combustion [Patel and Erickson, 1981; Battley, 1998, 1992]. E can be calculated from the empirical formula of live matter
E = 4 n C + n H − 2 n O − 0   n N + 5 n P + 6 n S  
where nC, nH, nO, nN, nP and nS represent the numbers of C, H, O, N, P and S atoms in the live matter empirical formula, respectively [Patel and Erickson, 1981; Battley, 1998, 1992]. Once calculated using the Patel-Erickson equation, ΔCH⁰ can be converted into standard enthalpy of formation, ΔfH⁰, of live matter. ΔCH⁰ is the enthalpy change of the reaction of complete combustion of live matter.
CnCHnHOnONnNPnPSnS + (nC + ¼ nH + 1¼ nP + 1½ nS - ½ nO) O2 → nC CO2 + ½ nH H2O +
½ nN N2 + ¼ nP P4O10 + nS SO3
This means that ΔCH⁰ can be used to find ΔfH⁰ of live matter using the equation [Popovic, 2022b, 2022c, 2022f; Atkins and de Paula, 2011, 2014]
∆ f H 0 b i o = n C   ∆ f H 0 C O 2 + n H 2   ∆ f H 0 H 2 O + n P 4   ∆ f H 0 P 4 O 10 + n S   ∆ f H 0 S O 3 − ∆ C H 0  
The Battley equation gives standard molar entropy of live matter, S⁰m, based on its empirical formula
S m 0 b i o = 0.187   ∑ J S m 0 ( J ) a J n J
where nJ is the number of atoms of element J in the empirical formula of live matter [Battley, 1999; Battley and Stone, 2000]. S⁰m and aJ are standard molar entropy and number of atoms per formula unit of element J in its standard state elemental form [Battley, 1999; Battley and Stone, 2000]. The Battley equation can be modified to give standard entropy of formation, ΔfS⁰, of live matter [Battley, 1999; Battley and Stone, 2000]
S m 0 b i o = − 0.813   ∑ J S m 0 ( J ) a J n J
Finally, ΔfH⁰ and ΔfS⁰ are combined to give standard Gibbs energy of formation of live matter, ΔfG⁰.
∆ f G 0 b i o = ∆ f H 0 b i o − T ∆ f S 0 b i o
Once live matter is characterized by finding its ΔfH⁰, S⁰m and ΔfG⁰, these properties can be combined with biosynthesis reactions to find standard thermodynamic properties of biosynthesis. Standard thermodynamic properties of biosynthesis include standard enthalpy of biosynthesis, ΔbsH⁰, standard entropy of biosynthesis, ΔbsS⁰, and standard Gibbs energy of biosynthesis, ΔbsG⁰. These properties are found by applying the Hess’s law to biosynthesis reactions
∆ b s H 0 = ∑ p r o d u c t s ν   ∆ f H 0 − ∑ r e a c t a n t s ν   ∆ f H 0
∆ b s S 0 = ∑ p r o d u c t s ν   S m o − ∑ r e a c t a n t s ν     S m o
∆ b s G 0 = ∑ p r o d u c t s ν   ∆ f G 0 − ∑ r e a c t a n t s ν   ∆ f G 0
where ν represents a stoichiometric coefficient [Popovic, 2022b, 2022c, 2022f; Atkins and de Paula, 2011, 2014; von Stockar, 2013a, 2013b; Battley, 1998]. The most important of these three properties is standard Gibbs energy of biosynthesis, which represents the thermodynamic driving force for growth of all organisms [von Stockar, 2013a, 2013b; von Stockar and Liu, 1999], including viruses [Popovic, 2022b, 2022c, 2022f, 2022i].

Thermodynamic Properties of Antigen-Receptor Binding

In order to multiply inside the cytoplasm, a virus must first enter its host cell. The first step in this process is binding of the virus antigen to the host cell receptor. The antigen of SARS-CoV-2 is the spike glycoprotein trimer (SGP) [Duan et al., 2020], while the host cell receptor is angiotensin-converting enzyme 2 (ACE2) [Scialo et al., 2020]. The process of antigen-receptor binding is, in its essence, a chemical reaction, similar to protein-ligand interactions [Du et al., 2016; Popovic and Popovic, 2022]. Thus, the binding of SGP to ACE2 can be described through the chemical reaction
(An) + (Re) = (An-Re)
where (An) represents the virus antigen (SGP in the case of SARS-CoV-2), (Re) represents the host cell receptor (ACE2 for SARS-CoV-2), while (An-Re) represents the antigen-receptor complex [Du et al., 2016; Popovic and Popovic, 2022].
Like for all other chemical reactions, laws of chemical thermodynamics apply and the process of antigen-receptor binding can be described through several thermodynamic parameters. The dissociation equilibrium constant, Kd, is defined as
K d = A n R e A n − R e
where [An] is the concentration of the virus antigen, [Re] the concentration of the host receptor and [An-Re] the concentration of the antigen-receptor complex [Du et al., 2016; Popovic and Popovic, 2022]. The reciprocal of Kd is the binding equilibrium constant, KB, [Du et al., 2016; Popovic and Popovic, 2022]
K B = 1 K d
The binding equilibrium constant can be used to find standard Gibbs energy of binding, ΔBG⁰, through the equation
∆ B G 0 = − R T ln ⁡ K B
Where T is temperature and R is the universal gas constant [Du et al., 2016; Popovic and Popovic, 2022].

Results

Based on the dissociation equilibrium constant reported in the literature [Wang et al., 2022], standard Gibbs energy of binding of the BF.7 variant of SARS-CoV-2 was found to be -53.64 kJ/mol, at 25°C.
Based on genetic and protein sequences, elemental composition was determined for nucleocapsids of the BA.5.2 and BF.7 variants of SARS-CoV-2. It is reported in the form of empirical formulas, which are given in Table 1, together with their molar masses. The empirical formula of the BA.5.2 nucleocapsid isolated in Australia is CH1.573784O0.342390N0.312321P0.005956S0.003361, with a molar mass of 23.7419 g/mol. The molar mass of the entire nucleocapsid of the BA.5.2 sample from Australia is 117.0958 MDa. The empirical formula of the BA.5.2 nucleocapsid isolated in Japan is CH1.573557O0.342676N0.312372P0.006022S0.003359, with a molar mass of 23.7489 g/mol. The molar mass of the entire nucleocapsid of the BA.5.2 sample from Japan is 117.2088 MDa. The empirical formula of the BA.5.2 nucleocapsid isolated in USA is CH1.573566O0.342668N0.312369P0.00602S0.003359, with a molar mass of 23.7487 g/mol. The molar mass of the entire nucleocapsid of the BA.5.2 sample from USA is 117.2050 MDa. The empirical formula of the BF.7 nucleocapsid isolated in China is CH1.573531O0.342715N0.312374P0.006031S0.003358, with a molar mass of 23.7498 g/mol. The molar mass of the entire nucleocapsid of the BF.7 sample from China is 117.2227 MDa. The empirical formula of the BF.7 nucleocapsid isolated in Greece is CH1.573511O0.342740N0.312379P0.006036S0.003358, with a molar mass of 23.7504 g/mol. The molar mass of the entire nucleocapsid of the BF.7 sample from Greece is 117.2326 MDa. The empirical formula of the BF.7 nucleocapsid isolated in Serbia is CH1.573528O0.342718N0.312375P0.006031S0.003358, with a molar mass of 23.7499 g/mol. The molar mass of the entire nucleocapsid of the BF.7 sample from Serbia is 117.2241 MDa. Based on the empirical formulas, biosynthesis reactions were formulated and reported in Table 2.
Table 3 gives standard thermodynamic properties of live matter of nucleocapsids of the BA.5.2 and BF.7 variants of SARS-CoV-2. These include standard enthalpy of formation, ΔfH⁰, standard molar entropy, S⁰m, and standard Gibbs energy of formation, ΔfG⁰. For the nucleocapsid of the BA.5.2 isolate from Australia, standard enthalpy of formation is -75.32 kJ/C-mol, standard molar entropy is 32.49 J/C-mol K, and standard Gibbs energy of formation is -33.21 kJ/C-mol. For the nucleocapsid of the BA.5.2 isolate from Japan, standard enthalpy of formation is -75.39 kJ/C-mol, standard molar entropy is 32.49 J/C-mol K, and standard Gibbs energy of formation is -33.27 kJ/C-mol. For the nucleocapsid of the BA.5.2 isolate from USA, standard enthalpy of formation is -75.39 kJ/C-mol, standard molar entropy is 32.49 J/C-mol K, and standard Gibbs energy of formation is -33.27 kJ/C-mol. For the nucleocapsid of the BF.7 isolate from China, standard enthalpy of formation is -75.40 kJ/C-mol, standard molar entropy is 32.49 J/C-mol K, and standard Gibbs energy of formation is -33.28 kJ/C-mol. For the nucleocapsid of the BF.7 isolate from Greece, standard enthalpy of formation is -75.41 kJ/C-mol, standard molar entropy is 32.49 J/C-mol K, and standard Gibbs energy of formation is -33.29 kJ/C-mol. For the nucleocapsid of the BF.7 isolate from Serbia, standard enthalpy of formation is -75.40 kJ/C-mol, standard molar entropy is 32.49 J/C-mol K, and standard Gibbs energy of formation is -33.28 kJ/C-mol.
Table 4 gives standard thermodynamic properties of biosynthesis of nucleocapsids of the BA.5.2 and BF.7 variants of SARS-CoV-2. These include standard enthalpy of biosynthesis, ΔbsH⁰, standard entropy of biosynthesis, ΔbsS⁰, and standard Gibbs energy of biosynthesis, ΔbsG⁰. For the nucleocapsid of the BA.5.2 isolate from Australia, standard enthalpy of biosynthesis is -232.14 kJ/C-mol, standard entropy of biosynthesis is -37.29 J/C-mol K, and standard Gibbs energy of biosynthesis is -221.06 kJ/C-mol. For the nucleocapsid of the BA.5.2 isolate from Japan, standard enthalpy of biosynthesis is -232.32 kJ/C-mol, standard entropy of biosynthesis is -37.34 J/C-mol K, and standard Gibbs energy of biosynthesis is -221.23 kJ/C-mol. For the nucleocapsid of the BA.5.2 isolate from USA, standard enthalpy of biosynthesis is -232.31 kJ/C-mol, standard entropy of biosynthesis is -37.34 J/C-mol K, and standard Gibbs energy of biosynthesis is -221.22 kJ/C-mol. For the nucleocapsid of the BF.7 isolate from China, standard enthalpy of biosynthesis is -232.33 kJ/C-mol, standard entropy of biosynthesis is -37.34 J/C-mol K, and standard Gibbs energy of biosynthesis is -221.24 kJ/C-mol. For the nucleocapsid of the BF.7 isolate from Greece, standard enthalpy of biosynthesis is -232.35 kJ/C-mol, standard entropy of biosynthesis is -37.35 J/C-mol K, and standard Gibbs energy of biosynthesis is -221.25 kJ/C-mol. For the nucleocapsid of the BF.7 isolate from Serbia, standard enthalpy of biosynthesis is -232.33 kJ/C-mol, standard entropy of biosynthesis is -37.34 J/C-mol K, and standard Gibbs energy of biosynthesis is -221.24 kJ/C-mol.

Discussion

The story about SARS-CoV-2 is reminiscent of the ancient legend of the Hydra of Lerna, a mythical creature that possessed many heads. Just like the Hydra, SARS-CoV-2 has many poisonous heads (variants). Every time humanity cuts off one head, one variant that has caused a pandemic wave, in its place appears a new one. Unfortunately, Heracles has not yet appeared on the scene. Thus, we need a modern Heracles in form of a vaccine. Starting from 2019, several dozen variants of SARS-CoV-2 appeared, some of which have caused pandemic waves. Globally, as of 5:09pm CET, 4 January 2023, there have been 655,689,115 confirmed cases of COVID-19, including 6,671,624 deaths, reported to WHO [2022]. These data make SARS-CoV-2 a modern equivalent of the Hydra of Lerna and Medusa Gorgo, the ancient monsters.
The research on SARS-CoV-2 was started in 2020, with a chemical and thermodynamic characterization of the Hu-1 variant (wild type) [Popovic and Minceva, 2020b]. SARS-CoV-2 has since then mutated several dozen times. In that way, several dozen major variants of SARS-CoV-2 virus appeared, some of which caused pandemic waves. Chemical and thermodynamic characterization of more important known variants of SARS-CoV-2 has been made in the literature [Popovic and Popovic, 2022; Özilgen and Yilmaz, 2021; Yilmaz et al., 2020; Nadi and Özilgen, 2021; Şimşek et al., 2021; Degueldre, 2021; Popovic, 2022a, 2022b, 2022c, 2022d, 2022e, 2022f, 2022g, 2022h, 2022i, 2022j; Gale, 2022; Lucia, 2021, 2020a, 2020b; Kaniadakis et al., 2020; Popovic and Minceva, 2021a, 2020b]. Thus, obviously, great efforts have been made by researchers in the field of biothermodynamics to reveal the thermodynamic background of SARS-CoV-2 particles, their life cycle, as well as interactions performed with various host tissues and other viruses.
Virus-host interactions occur at the host cell membrane and in its cytoplasm [Popovic, 2022b, 2022i]. Both interactions represent chemical processes. The interaction at the membrane is similar to protein-ligand interactions [Popovic and Popovic, 2022; Du et al., 2016]. The interaction in the cytoplasm represents a polymerization reaction of nucleotides and amino acids into nucleic acids and proteins, respectively [Pinheiro et al., 2008; Lee et al., 2020; Dodd et al., 2020; Johansson and Dixon, 2013]. These reactions are competitive. The competition is performed between the virus and its host cell. The driving force for the antigen-receptor binding at the membrane and the polymerization of nucleotides into nucleic acids and synthesis of proteins is Gibbs energy [von Stockar, 2013a, 2013b; von Stockar and Liu, 1999; Demirel, 2014, Balmer, 2010; Berg et al., 2002]. Mutations of SARS-CoV-2 that appeared during time have led to change in empirical formula of new variants [Popovic, 2022i]. Changes in empirical formula have led to change in thermodynamic properties of binding and biosynthesis [Popovic, 2022f, 2022g, 2022i]. Changes in thermodynamic properties caused changes in kinetic parameters, including antigen-receptor binding rate and rate of biosynthesis of viral components, according to the phenomenological equations [Popovic, 2022f, 2022g, 2022i]. Changes in the kinetics have led to changes in infectivity and pathogenicity [Popovic, 2022e, 2022i].
Every time a new variant appears, a question is raised about its infectivity and pathogenicity. Thus, with appearance of new BA.5.2 and BF.7 variants, the question was raised of whether they will be able to cause a new pandemic wave. The new variants compete with the old variants, if they appear at the same time in the same place. In that competition, one variant will win and suppress and weaker one. To predict the outcome of the competition, it is necessary to know the Gibbs energy of binding and Gibbs energy of biosynthesis. In this paper, for the first time, standard Gibbs energy of binding was determined for the BF.7 variant. It is -53.64 kJ/C-mol, at 25°C. Figure 1 shows Gibbs energies of binding of various variants of SARS-CoV-2. From Figure 1, it is possible to see the trend of evolution of SARS-CoV-2 towards more negative Gibbs energy of binding. More negative Gibbs energy of binding leads to greater antigen-receptor binding rate, which in turn leads to increased infectivity [Popovic, 2022g].
Figure 2 shows Gibbs energies of biosynthesis through evolution of SARS-CoV-2 variants from Hu-1 to Omicron BA.5.2 and BF.7. All the Omicron variants are characterized by very similar Gibbs energies of biosynthesis. Gibbs energies of biosynthesis of all Omicron variants are slightly less negative than that of the Hu-1 variant. According to the phenomenological equations, this indicates a slightly slower multiplication of new variants compared to Hu-1. The slower multiplication leads to lesser range of damage to host tissues. This coincides with the fact that the number of more severe cases in any of the Omicron variants is lower than that of Hu-1. From this we can conclude that during evolution, mutations in the part of the SARS-CoV-2 genome that encodes proteins other than the spike glycoprotein have led to a decrease in pathogenicity. Indeed, from the evolutionary perspective, the favored mutations are those that lead to increase in infectivity and maintenance or slight decrease in pathogenicity [Popovic, 2022e]. Thus, in the wave that is currently hitting China and is dominated by the BF.7 variant, it is possible to expect an increased number of newly infected cases, due to an increase in infectivity, but without an increase in the number of severe cases, having in mind that pathogenicity has not significantly changed compared to the earlier variants. However, it is obvious that due to the significant difference in Gibbs energy of binding, BF.7 should be able to suppress other Omicron variants that are in circulation.

Conclusions

Gibbs energy of antigen-receptor binding of Omicron BF.7 is more negative than that of the other variants. Thus, the rate of antigen-receptor binding of Omicron BF.7 is greater than that of other variants present in the population. This leads to an increased infectivity of BF.7 and probable domination in the next wave of the COVID-19 pandemic.
Gibbs energy of biosynthesis of BA.5.2 and BF.7 is not significantly different than the Gibbs energy of biosynthesis of other Omicron variants. The rate of biosynthesis of BF.7 and BA.5.2 is approximately equal to the biosynthesis rate of other Omicron variants. The pathogenicity of BF.7 and BA.5.2 variants should not be greater than those of other Omicron variants.

Acknowledgements

The author gratefully acknowledges all data contributors, i.e., the Authors and their Originating laboratories responsible for obtaining the specimens, and their Submitting laboratories for generating the genetic sequence and metadata and sharing via the GISAID Initiative, on which this research is based.

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Figure 1. Gibbs energies of binding through evolution of SARS-CoV-2. This graph shows standard Gibbs energies of binding, ΔBG⁰, of SARS-CoV-2 variants during their evolution. The graph starts from the Hu-1 variant (Wild type) that appeared in late 2019 and ends with the newest BF.7 variant. The blue dots represent Gibbs energies of binding of the SARS-CoV-2 variants. The blue dashed line represents the direction of evolution of the ΔBG⁰ values.
Figure 1. Gibbs energies of binding through evolution of SARS-CoV-2. This graph shows standard Gibbs energies of binding, ΔBG⁰, of SARS-CoV-2 variants during their evolution. The graph starts from the Hu-1 variant (Wild type) that appeared in late 2019 and ends with the newest BF.7 variant. The blue dots represent Gibbs energies of binding of the SARS-CoV-2 variants. The blue dashed line represents the direction of evolution of the ΔBG⁰ values.
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Figure 2. Gibbs energy of biosynthesis through evolution of SARS-CoV-2. This graph shows standard Gibbs energies of biosynthesis, ΔbsG⁰, of SARS-CoV-2 variants during their evolution. The graph starts from the Hu-1 variant (Wild type) that appeared in late 2019 and ends with the newest BA.5.2 and BF.7 variants. The orange dots represent Gibbs energies of binding of the SARS-CoV-2 variants. The orange dashed line represents the direction of evolution of the ΔbsG⁰ values.
Figure 2. Gibbs energy of biosynthesis through evolution of SARS-CoV-2. This graph shows standard Gibbs energies of biosynthesis, ΔbsG⁰, of SARS-CoV-2 variants during their evolution. The graph starts from the Hu-1 variant (Wild type) that appeared in late 2019 and ends with the newest BA.5.2 and BF.7 variants. The orange dots represent Gibbs energies of binding of the SARS-CoV-2 variants. The orange dashed line represents the direction of evolution of the ΔbsG⁰ values.
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Table 1. Empirical formulas of nucleocapsids of BA.5.2 and BF.7 variants of SARS-CoV-2 isolated in various countries. The empirical formula of live matter has the general form CnCHnHOnONnNPnPSnS. In addition, molar masses were reported for the empirical formulas, Mr, and for entire nucleocapsids, Mr(nc).
Table 1. Empirical formulas of nucleocapsids of BA.5.2 and BF.7 variants of SARS-CoV-2 isolated in various countries. The empirical formula of live matter has the general form CnCHnHOnONnNPnPSnS. In addition, molar masses were reported for the empirical formulas, Mr, and for entire nucleocapsids, Mr(nc).
Variant C H O N P S Mr (g/mol) Mr(nc) (MDa)
BA.5.2 nucleocapsid - Australia 1 1.573784 0.342390 0.312321 0.005956 0.003361 23.7419 117.0958
BA.5.2 nucleocapsid - Japan 1 1.573557 0.342676 0.312372 0.006022 0.003359 23.7489 117.2088
BA.5.2 nucleocapsid - USA 1 1.573566 0.342668 0.312369 0.00602 0.003359 23.7487 117.2050
BF.7 nucleocapsid - China 1 1.573531 0.342715 0.312374 0.006031 0.003358 23.7498 117.2227
BF.7 nucleocapsid - Greece 1 1.573511 0.342740 0.312379 0.006036 0.003358 23.7504 117.2326
BF.7 nucleocapsid - Serbia 1 1.573528 0.342718 0.312375 0.006031 0.003358 23.7499 117.2241
Table 2. Biosynthesis reactions for the nucleocapsids of the BA.5.2 and BF.7 variants of SARS-CoV-2. The general biosynthesis reaction has the form: (Amino acids) + O2 + HPO42- + HCO3- → (Bio) + SO42- + H2O + H2CO3, where (Bio) denotes the empirical formula of live matter from Table 1. The stoichiometric coefficients for the biosynthesis reactions are given in this table. .
Table 2. Biosynthesis reactions for the nucleocapsids of the BA.5.2 and BF.7 variants of SARS-CoV-2. The general biosynthesis reaction has the form: (Amino acids) + O2 + HPO42- + HCO3- → (Bio) + SO42- + H2O + H2CO3, where (Bio) denotes the empirical formula of live matter from Table 1. The stoichiometric coefficients for the biosynthesis reactions are given in this table. .
Variant Reactants → Products
Amino acid O2 HPO42- HCO3- Bio SO42- H2O H2CO3
BA.5.2 nucleocapsid - Australia 1.3898 0.4908 0.0060 0.0438 → 1 0.0279 0.0536 0.4337
BA.5.2 nucleocapsid - Japan 1.3901 0.4912 0.0060 0.0437 → 1 0.0279 0.0538 0.4338
BA.5.2 nucleocapsid - USA 1.3900 0.4912 0.0060 0.0437 → 1 0.0279 0.0538 0.4338
BF.7 nucleocapsid - China 1.3901 0.4913 0.0060 0.0437 → 1 0.0279 0.0538 0.4338
BF.7 nucleocapsid - Greece 1.3901 0.4913 0.0060 0.0437 → 1 0.0279 0.0538 0.4338
BF.7 nucleocapsid - Serbia 1.3901 0.4913 0.0060 0.0437 → 1 0.0279 0.0538 0.4338
Table 3. Standard thermodynamic properties of live matter of nucleocapsids of the BA.5.2 and BF.7 variants of SARS-CoV-2. This table gives data on standard enthalpies of formation, ΔfH⁰, standard molar entropies, S⁰m, and standard Gibbs energies of formation, ΔfG⁰.
Table 3. Standard thermodynamic properties of live matter of nucleocapsids of the BA.5.2 and BF.7 variants of SARS-CoV-2. This table gives data on standard enthalpies of formation, ΔfH⁰, standard molar entropies, S⁰m, and standard Gibbs energies of formation, ΔfG⁰.
Variant ΔfH⁰ (kJ/C-mol) S⁰m (J/C-mol K) ΔfG⁰ (kJ/C-mol)
BA.5.2 nucleocapsid - Australia -75.32 32.49 -33.21
BA.5.2 nucleocapsid - Japan -75.39 32.49 -33.27
BA.5.2 nucleocapsid - USA -75.39 32.49 -33.27
BF.7 nucleocapsid - China -75.40 32.49 -33.28
BF.7 nucleocapsid - Greece -75.41 32.49 -33.29
BF.7 nucleocapsid - Serbia -75.40 32.49 -33.28
Table 4. Standard thermodynamic properties of biosynthesis of nucleocapsids of the BA.5.2 and BF.7 variants of SARS-CoV-2. This table gives data on standard enthalpies of biosynthesis, ΔbsH⁰, standard entropies of biosynthesis, ΔbsS⁰, and standard Gibbs energies of biosynthesis, ΔbsG⁰.
Table 4. Standard thermodynamic properties of biosynthesis of nucleocapsids of the BA.5.2 and BF.7 variants of SARS-CoV-2. This table gives data on standard enthalpies of biosynthesis, ΔbsH⁰, standard entropies of biosynthesis, ΔbsS⁰, and standard Gibbs energies of biosynthesis, ΔbsG⁰.
Variant ΔbsH⁰ (kJ/C-mol) ΔbsS⁰ (J/C-mol K) ΔbsG⁰ (kJ/C-mol)
BA.5.2 nucleocapsid - Australia -232.14 -37.29 -221.06
BA.5.2 nucleocapsid - Japan -232.32 -37.34 -221.23
BA.5.2 nucleocapsid - USA -232.31 -37.34 -221.22
BF.7 nucleocapsid - China -232.33 -37.34 -221.24
BF.7 nucleocapsid - Greece -232.35 -37.35 -221.25
BF.7 nucleocapsid - Serbia -232.33 -37.34 -221.24
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