Thermodynamic insight into viral infections 2: empirical formulas, molecular compositions and thermodynamic properties of SARS, MERS and SARS-CoV-2 (COVID-19) viruses.

The current situation with the SARS-CoV-2 pandemic indicates the importance of new approaches in vaccine design. In order to design new attenuated vaccines, to decrease virulence of virus wild types, it is important to understand what allows a virus to hijack its host cell's metabolism, a property of all viruses. RNA and protein sequences obtained from databases were used to count the number of atoms of each element in the virions of SARS, MERS and SARS-CoV-2. The number of protein copies and carbohydrate composition were taken from the literature. The number of lipid molecules was estimated from the envelope surface area. Based on elemental composition, growth equations were balanced, and thermodynamic properties of the viruses were determined using Patel-Erickson and Battley equations. Elemental and molecular compositions of SARS, MERS and SARS-CoV-2 were found, as well as their standard thermodynamic properties of formation and growth. Standard Gibbs energy of growth of virus nucleocapsids was found to be significantly more negative than that of their host tissue. The ratio of Gibbs energies of growth of virus nucleocapsids and host cell is greater than unity. The more negative Gibbs energy of growth of viruses implies that virus multiplication has a greater driving force than synthesis of host cell components, giving a physical explanation of why viruses are able to hijack their host cell's metabolism. Knowing the mechanism of viral metabolism hijacking can open new paths for vaccine design. By manipulating chemical composition of viruses, virulence can be decreased by making the Gibbs energy of their growth less negative, resulting in decreased multiplication rate, while preserving antigenic properties.

Introduction

SARS, n class="Disease">MERSpan> aene">nd n class="Species">SARS-CoV-2 are three related RNA viruses, beloene">nging to the family n class="Species">Coronaviridae and sharing the same morphology (Figure 1) and similar (but not identical) chemical composition. The nucleic acid sequences of all three viruses, SARS (He et al., 2004), MERS (van Boheemen et al., 2012) and SARS-CoV-2 (Wu et al., 2020) have been determined. The lipid constituents of the viral envelopes of all three viruses are similar, since all three viruses attack the same host tissue and hence their envelopes are formed by budding from the same kind of cell membrane (Riedel et al., 2019). The protein components of the envelope differ between SARS, MERS and SARS-CoV-2 (Table 1). There are no data on capsid structure for the three viruses, except that they are of helical symmetry, since they are difficult to culture and therefore poorly characterized (Riedel et al., 2019).

Figure 1

Schematic representation of a virus from the family Coronaviridae. The yellow line represents RNA, orange – nucleoproteins lining the RNA (yellow and orange combined represent the nucleocapsid), grey – membrane proteins, light blue – lipids in the envelope, blue spikes – spike proteins.

Table 1

RNA and protein data for the viruses analyzed in this work. The number of protein copies per virion varies, even within a single species (Neuman et al., 2011, 2006). For example, the number of spike protein trimers can vary between 50 and 100 per virion. The average number is 74 trimers, giving 74 × 3 = 222 spike proteins in total (Neuman et al., 2011, 2006).

Virus	Name	Number of copies	ID number	Source
SARS	Genome	1	NC_004718.3	NCBI
	Nucleoprotein	2368	P59595	UniProt
	Membrane protein	1184	Q3S2C1	UniProt
	Spike protein	222	P59594	UniProt
MERS	Genome	1	NC_019843.3	NCBI
	Nucleoprotein	2368	R9UM87	UniProt
	Membrane protein	1184	QGW51926.1	NCBI
	Spike protein	222	A0A140AYZ5	UniProt
SARS-CoV-2	Genome	1	NC_045512.2	NCBI
	Nucleoprotein	2368	QIK50455.1	NCBI
	Membrane protein	1184	QHR63293.1	NCBI
	Spike protein	222	QHR63290.2	NCBI

Schematic ren class="Gene">prpan>esentationpan> of a virus from the family n class="Species">Coronaviridae. The yellow line represents RNA, oraene">nge – nucleon class="Gene">proteins lining the RNA (yellow and orange combined represent the nucleocapsid), grey – membrane proteins, light blue – lipids in the envelope, blue spikes – spike proteins.

Rn class="Gene">Npan>A aene">nd protein data for the viruses analyzed in this work. The number of protein copies per virioene">n varies, even within a single species (n class="Gene">Neuman et al., 2011, 2006). For example, the number of spike protein trimers can vary between 50 and 100 per virion. The average number is 74 trimers, giving 74 × 3 = 222 spike proteins in total (Neuman et al., 2011, 2006).

Empirical formulas of the three viruses allow calculation of thermodypan class="Gene">namic n class="Gene">properties (enthalpy, enpan>tropy, Gibbs energy) of formationpan> and growth of each of the three viruses. Gibbs energy allows estimationpan> of the sponpan>taneity of formationpan> of new virionpan>s and the rate of their multiplicationpan> (Popovic and Minpan>ceva 2020a).

Viral multiplication is fupan class="Gene">ndamentally a chemical n class="Gene">process that can be ren class="Gene">presented by a growth reaction (Von Stockar, 2014; Battley, 1998; Popovic and Minceva, 2020a). Gibbs energy of growth, through nonequilibrium thermodynamics, allows comparison of growth reaction rates of host cells and viruses (Popovic and Minceva, 2020a; Popovic and Minceva, 2020b). Knowledge of growth reaction rates allows us to gain insight into multiplication dynamics of the microorganisms (Westerhoff et al., 1982; Von Stockar, 2014). The multiplication dynamics can be of benefit to epidemiologists and infectologists, to estimate the maximal virus multiplication rate and to quantitatively estimate viral reservoir in a patient or a population. Thus, the knowledge of reservoir size and basic reproductive number can enable epidemiologists to estimate virus transmission dynamics (Kucharski et al., 2020; Fang et al., 2020).

Composition of viruses capan class="Gene">n be estimated, based on their nucleic acid and n class="Gene">proteinpan> sequences. Based onpan> nucleic acid compositionemical">pan>, n class="Gene">protein sequences aene">nd capsid structures, Jover et al. (2014) determined compositioene">ns of icosahedral aene">nd spherical Dn class="Gene">NA bacteriophages, and described their impact on oceanic cycling of the elements. Virus shapes were approximated by geometric figures, such as spheres and cylinders. A virus head was represented by a ball with a fraction of its internal volume filled by DNA. On the surface of the ball, a spherical shell with a uniform thickness was used to represent the capsid and estimate the quantity of proteins in the virion. When present, virus tails were approximated by hollow cylinders made of protein. The method gave accurate predictions for viruses of known composition (Jover et al., 2014).

Some aspects of life cycles of various virus species have already been apan class="Gene">nalyzed using thermodynamics. Katen and Zlotnick (2009) analyzed the thermodynamics of capsid assembly for several viruses, treating it as a polymerization reaction and n class="Gene">providinpan>g new inpan>sights inpan>to the assembly mechanisms of spherical virus capsids, as well as inpan>to the biology of the viral life cycle. Ceres and Zlotnick (2002) used thermodynpan>amics to analyze n class="Species">hepatitis B virus capsid assembly and found that it has a negative Gibbs energy change, implying that the process is thermodynamically spontaneous. Casasnovas and Springer (1995) studied the kinetics and thermodynamics of human rhinovirus interaction with its receptor, determining the enthalpy and Gibbs energy of their association, and analyzing their influence on virus disruption. Gale (2020) analyzed thermodynamics of virus binding to host cell receptors and proposed new directions for designing antiviral therapies. Mahmoudabadi et al. (2017) developed a quantitative description of viral infection energetics and they made predictions about viral evolution. In addition to studies of viral component synthesis and self-assembly, Tzlil et al. (2004) made a statistical thermodynamic description of viral budding and found that complete budding (full wrapping of nucleocapsids) can only take place if the adhesion energy exceeds a certain, critical, bending Gibbs energy. However, there is still insufficient quantitative understanding of infection energetics (Mahmoudabadi et al., 2017).

The goal of this research is to determine the elemepan class="Gene">ntal and molecular composition of SARS, n class="Disease">MERS and n class="Species">SARS-CoV-2, and make thermodynamic characterization of the three viruses, by finding enthalpy, entropy and Gibbs energy of formation and growth of all three viruses.

Methods

Elemental apan class="Gene">nd molecular composition of the three viruses was determined by counting atoms coming from each of the four n class="Gene">prinpan>cipal molecular conpan>stituent of virionpan>s: nucleic acid, n class="Gene">proteins, lipids and non-nucleic acid carbohydrates (Knight, 1975). For this to be done, two pieces of information had to be known: (1) the number of atoms of each element in the molecular constituents and (2) the number of molecules of each constituent in the virion.

Virus elemental and molecular composition

The four main molecular comemical">popan class="Gene">nents of viruses are: nucleic acids, n class="Gene">proteinpan>s, n class="Chemical">lipids and non-nucleic acid carbohydrates (Knight, 1975). Since each of these molecular classes has a well-defined elemental composition, it was possible to find the elemental composition of virions. The calculations for SARS, MERS and SARS-CoV-2 were done using custom made software.

Nucleic acids

The number of atoms of each elemepan class="Gene">nt coming from nucleic acids was calculated using an atom counting method. n class="Gene">Nucleic acid sequences were obtainpan>ed from the n class="Gene">NCBI database (National Center for Biotechnology Information, 2020) and are listed in Table 1. Since the elemental composition of each nucleotide residue in the sequence is known, the number of atoms of each element in the nucleic acid was found by going along the sequence and adding atoms of each element coming from each residue. Coronaviruses contain only one copy of their single stranded RNA genomes.

The composition of viral pan class="Gene">nucleic acids was determined using an atom counting method. First, nucleic acid sequences were obtained from the n class="Gene">NCBI database (n class="Gene">National Center for Biotechnology Information, 2020) and are listed in Table 1. Since the elemental composition of each nucleotide residue in the sequence is known, the number of atoms of each element in the nucleic acid was found by going along the sequence and adding atoms of each element coming from each residue. The result of such a calculation is a nucleic acid formula of the form CNnaCHNnaHONnaONNnaNSNnaS, where N(NA), N(NA), N(NA), N(NA) and N(NA) are the number of C, H, O, N and S atoms in the nucleic acid. The molar mass of the nucleic acid, m (NA) can be calculated using the formulawhere N is Avogadro's number and A is the atomic mass of element J.

Proteins

The atom countipan class="Gene">ng method was also used to find the number of atoms coming from n class="Gene">proteinpan>s. Protein sequences were taken from the UniProt database (The UniProt Consortium, 2019) and the NCBI database (National Center for Biotechnology Information, 2020), and are listed in Table 1. Coronavirus particles consist of four kinds of proteins: nucleoproteins (N), membrane proteins (M), envelope proteins (E) and spike proteins (S) (Neuman and Buchmeier, 2016). Envelope proteins were not considered due to their low abundance in the virus (Neuman and Buchmeier, 2016). They improve, but are not required, for the functioning of the virus (Neuman and Buchmeier, 2016; DeDiego et al., 2007; Kuo and Masters, 2010). Thus, they do not have a significant influence on elemental composition and thermodynamic properties of the viruses. The number of protein copies in coronavirus particles was reported by Neuman et al. (2011, 2006) and is summarized in Table 1.

Similarly to nucleic acids, papan class="Gene">n class="Gene">proteinpan> compositioene">n was found by countinpan>g atoms cominpan>g from each aminpan>o acid residue. The protein sequences were taken from the UniProt database (The UniProt Consortium, 2019) and the NCBI database (National Center for Biotechnology Information, 2020), and are listed in Table 1. The result of such a calculation is a protein formula of the form CNn class="Gene">prCHNprHONprONNprNSNprS, where N, N, N, N and N are the number of C, H, O, N and S atoms in a single protein molecule (Table 2). From the formula, the protein's molar mass in Daltons, M, can be calculatedwhere N is the number of atoms of element J in the protein. M is converted into the mass of a single protein molecule, m, molecule by dividing it by Avogadro's number

Table 2

Calculated viral protein data.

Virus	Protein name	Number of copies	Mr (Da)	Atoms per protein molecule
				C	H	O	N	S
SARS-CoV-2	Nucleoprotein	2368	45624.58	1971	3137	629	607	7
	Membrane protein	1184	25146.01	1165	1823	301	303	8
	Spike protein	222	141175.1	6336	9770	1894	1656	54
MERS	Nucleoprotein	2368	45047.17	1965	3102	611	594	7
	Membrane protein	1184	24516.27	1128	1756	302	282	13
	Spike protein	222	149380.5	6681	10245	2029	1737	63
SARS	Nucleoprotein	2368	46023.9	1985	3150	633	618	7
	Membrane protein	1184	25059.92	1155	1809	300	303	10
	Spike protein	222	139121.8	6252	9593	1871	1609	59

Calculated viral n class="Gene">prpan>otein data.

However, unlike pan class="Gene">nucleic acids, structural proteinpan>s inpan> viruses are n class="Gene">present in multiple copies. Thus, the number of atoms in each capsid n class="Gene">protein was multiplied by the number of the protein copies present in the capsid.

n class="Semical">pecies">Coronaviridaepan> virioene">ns conpan>sitst of four proteins: spike proteins (S), envelope proteins (E), membrane proteins (M) and nucleoproteins (N) (Neumaene">n aene">nd Buchmeier, 2016) (Figure 1). The most distinctive feature of n class="Species">Coronaviridae are the spikes on the virion surface made of spike proteins (Neuman and Buchmeier, 2016). On the average, a coronavirus has 74 spikes, each consisting of a spike protein trimer, giving 222 spike proteins per virion (Neuman et al., 2011). The envelope protein is encoded by all known coronavirus genomes, but its role is still under debate (Neuman and Buchmeier, 2016). The envelope protein is probably best viewed as a multifunctional accessory protein that contributes to both virus growth and pathogenesis (Neuman and Buchmeier, 2016). Since the E protein is present in virions in small amounts (Neuman and Buchmeier, 2016), its contribution to virion chemical composition will be neglected. The most important role in coronavirus particle assembly is that of the membrane protein (Neuman and Buchmeier, 2016). The membrane proteins span through the viral envelope (Neuman et al., 2011). On the outer side, M proteins hold the spikes, while on the inside they bind the nucleoproteins, thus connecting the ribonucleoprotein core to the envelope (Neuman et al., 2011). For each S protein trimer, there are 8 M protein dimers (Neuman et al., 2011). Thus, in an average coronavirus there are 1184 copies of the M protein (Neuman et al., 2011). The nucleoprotein surrounds the viral RNA. Analysis of coronaviruses has shown that M and N proteins come in a fixed ratio, although the value differs between 1 and 3 in various studies (Neuman et al., 2011). In this work, the mean value of 2 N proteins per an M protein will be taken.

The number of atoms of elemepan class="Gene">nt J coming from the all viral n class="Gene">proteinpan>s isc(X) the number of copies of emical">pan> class="Gene">protein X in the virion and N(X) is the number of atoms of element J in a single molecule of X. Here, X represents S, M and N proteins. The total mass of all proteins in the virion is

Lipids

n class="Chemical">Liemical">pidspan> are located in the viral envelope. Sinpan>ce enveloped viruses bud off their host cells, their n class="Chemical">lipid composition resembles that of the host cell membrane. Thus, the lipid composition of the viral envelopes was represented with that of the human cell membrane: 17% phosphatidylcholine, 6% n class="Chemical">phosphatidylserine, 16% phosphatidylethanolamine, 17% sphingomyelin, 2% glycolipids and 45% cholesterol (mole fractions) (Cooper, 2000). More information on the lipid constituents can be found in Table 3. The number of lipid molecules was determined from the envelope surface area and the average surface area taken by a single lipid molecule, taken from Ingólfsson et al. (2014). The envelope surface area was calculated from virus particle diameter, reported by Neuman and Buchmeier (2016). A correction was made for the envelope surface area taken by membrane proteins, using the average protein density (Serdyuk et al., 2007; Jover et al., 2014) and viral envelope thickness (Neuman and Buchmeier, 2016).

Table 3

Virus lipid representative molecules, their chemical formulas and abundances. The abundances are mole fractions of the total lipid content and were taken from (Cooper, 2000).

Class	Representative name	Formula	Mole fraction
Phosphatidylcholine	1-Oleoyl-2-palmitoylphosphatidylcholine	C42H82O8NP	17%
Phosphatidylserine	Phosphatidylserine (18:0/18:1) (PubChem CID: 9547087)	C42H79O10NP	6%
Phosphatidylethanolamine	Phophatidylethanolamine(15:0/20:0) (ChemSpider ID: 394115)	C40H80O8NP	16%
Sphingomyelin	C18 Sphingomyelin	C41H85O6N2P	17%
Glycolipids	Stearoyl-glucose	C24H46O7	2%
Cholesterol	Cholesterol	C27H46O	45%

Virus n class="Chemical">liemical">pidpan> ren class="Gene">presentative molecules, their chemical formulas aene">nd abuene">ndaene">nces. The abuene">ndaene">nces are mole fractioene">ns of the total n class="Chemical">lipid content and were taken from (Cooper, 2000).

The total number of papan class="Gene">n class="Chemical">lipid molecules inpan> the envelope was calculated from its surface area (Figure 2). The total area of the envelope, A, is equal to the sum of the envelope inpan>ner, A, and outer surface area, A

Figure 2

Schematic representation of the viral envelope. The envelope is a lipid bilayer membrane of thickness d, consisting of lipids and membrane (M) proteins. It has two surface areas: one facing outside the virion, A, and one inside the virion, A. The total area taken by M proteins, on both sides of the membrane, is A. The average area covered by a lipid molecule is α.

Schematic ren class="Gene">prpan>esentationpan> of the viral envelope. The envelope is a n class="Chemical">lipid bilayer membrane of thickness d, consisting of lipids and membrane (M) proteins. It has two surface areas: one facing outside the virion, A, and one inside the virion, A. The total area taken by M proteins, on both sides of the membrane, is A. The average area covered by a lipid molecule is α.

The outer surface area is the surface area of a sphere with a radius equal to the radius of the virus, r,

Radii of n class="Semical">pecies">coronavirusespan> vary, even withinpan> a sinpan>gle species, but an average n class="Species">coronavirus has a radius of r = 45 nm (Neuman and Buchmeier, 2016). The inner surface area is the area of the inner surface of the viral envelope, which has a thickness of d = 8 nm (Neuman and Buchmeier, 2016). Thus,

The virus surface area, A, is covered with M n class="Gene">prpan>oteins and n class="Chemical">lipids. The surface area covered by M proteins, A, can be determined from their mass and the average protein density, ρ = 1.36986 ∙ 10−21 g/nm3, reported in (Serdyuk et al., 2007; Jover et al., 2014).

In the equatiopan class="Gene">n above the molar mass of M, M(M), was divided with the Avogadro's number, n class="Gene">N, to finpan>d the mass of a sinpan>gle M emical">pan> class="Gene">protein molecule. This mass was then multiplied with the number of M proteins in the envelope, c(M), to find the total mass of M proteins in the envelope. The total mass of M proteins in the envelope was then divided by the average protein density, ρ, to find the volume taken by M proteins in the envelope, and then divided by the envelope thickness, d, to find the surface area. Multiplication with 2 is due to the fact that the proteins take an area on both the inner and outer surfaces of the envelope.

The area covered by the M n class="Gene">prpan>oteins, A, was then subtracted from the total enpan>velope area, A, to find the area of the enpan>velope covered by n class="Chemical">lipids, A.

When A is divided by the average area per papan class="Gene">n class="Chemical">lipid molecule, α = 0.533 npan>m2 (Ingólfsson et al., 2014), the result is the total number of n class="Chemical">lipid molecules in the envelope, c (Lip).

Finally, the pan class="Gene">number of molecules of n class="Chemical">lipid conpan>stituenpan>t X, c(X), was determined by multiplyinpan>g c (n class="Gene">Lip) with the mole fraction of that lipid, x(X),

The number of atoms of elemepan class="Gene">nt J in all n class="Chemical">lipids n class="Gene">present, N (Lip), was determined from the equationwhere N(X) is the number of atoms of element J in a single molecule of X. Here X represents the lipid components: phosphatidylcholine, phosphatidylserine, phosphatidylethanolamine, sphingomyelin, glycolipids and cholesterol. The properties of the considered lipid constituents are given in Table 3. The total mass of lipids in the virion was calculated using the equationwhere Mr(X) is the molar mass of lipid constituent X.

Non-nucleic acid carbohydrates

n class="Gene">Npan>oene">n-nucleic n class="Chemical">acid carbohydrates are present in virions bound in glycolipids aene">nd glycon class="Gene">proteins, as parts of viral envelopes. Glycolipids were represented by stearoyl-glucose, C24H46O7, the glucose residue of which belongs to non-nucleic acid carbohydrates. Glycoproteins were represented by attaching oligosaccharide molecules onto spike proteins. Oligosaccharide composition was set to be equal to that of Orthomyxoviridae: for each spike protein molecule, 14 000 Da of oligosaccharides was added, composed of mannose and 2 N-acetyglucosamine residues in a ratio of 5:2 (Kuroda et al., 1990).

n class="Gene">Npan>oene">n-nucleic n class="Chemical">acid carbohydrates are present in glycolipids aene">nd glycon class="Gene">proteins, as parts of viral envelopes. Glycolipids were represented by stearoyl-glucose, C24H46O7, the glucose residue of which, C6H10O5 (molar mass 162 Da) belongs to non-nucleic acid carbohydrates. Thus, for each glycolipid molecule (2% of the envelope lipids), 6 C, 10 H and 5 O atoms were added to the virion composition. Glycoproteins were represented by attaching oligosaccharide molecules onto spike proteins (S). Oligosaccharide composition was set to be equal to that of Orthomyxoviridae: for each spike protein molecule (S), 14 000 Da of oligosaccharides was added, composed of mannose and N-acetyglucosamine residues in a ratio of 5:2 (C46H76O35N2, molar mass 1217 Da) (Kuroda et al., 1990).where N (CH) is the number of atoms of element J in the virion coming from non-nucleic acid carbohydrates. The total mass of non-nucleic acid carbohydrates in the virion was found using the equation

Complete virus composition

The total number of atoms ipan class="Gene">n the virion is the sum of contributions from the four classes of molecules

The results are n class="Gene">prpan>esented inpan> Table 4. The empirical formula or UCF of the virus has the form CHnpan>HOnpan>On class="Gene">NnNPnPSnS, where n is the number of moles of element J in the virus UCF and can be found using the equation

Table 4

Total number of atoms constituting viruses, obtained by the atom counting method. For each virus, the number of atoms is given for the entire virion (nucleocapsid + envelope) and the nucleocapsid. The last column presents the molar mass of entire virions, in Daltons. The molar masses of all three viruses are similar.

Name	Total atoms per virion
	C	H	O	N	P	S	Total	Molar mass (Da)
SARS-CoV-2: Entire virus	1.010E+07	1.656E+07	2.881E+06	2.325E+06	6.523E+04	3.804E+04	3.197E+07	2.200E+08
SARS-CoV-2: Nucleocapsid	4.951E+06	7.778E+06	1.709E+06	1.547E+06	2.990E+04	1.658E+04	1.603E+07	1.178E+08
MERS: Entire virus	1.014E+07	1.654E+07	2.875E+06	2.287E+06	6.569E+04	4.595E+04	3.195E+07	2.200E+08
MERS: Nucleocapsid	4.938E+06	7.697E+06	1.669E+06	1.516E+06	3.012E+04	1.658E+04	1.587E+07	1.165E+08
SARS: Entire virus	1.011E+07	1.654E+07	2.883E+06	2.340E+06	6.511E+04	4.151E+04	3.198E+07	2.203E+08
SARS: Nucleocapsid	4.983E+06	7.807E+06	1.717E+06	1.573E+06	2.975E+04	1.658E+04	1.613E+07	1.187E+08

Total number of atoms copan class="Gene">nstituting viruses, obtained by the atom counting method. For each virus, the number of atoms is given for the entire virion (n class="Gene">nucleocapsid + envelope) and the n class="Gene">nucleocapsid. The last column presents the molar mass of entire virions, in Daltons. The molar masses of all three viruses are similar.

The total mass of the virion is similarly calculated as

The mass fractions of each of the molecular copan class="Gene">nstituents are calculated using the equations

Similarly, the total number of atoms elemepan class="Gene">nt J in the n class="Gene">nucleocapsid is the sum of atoms of J cominpan>g from the nucleic acid, emical">pan> class="Gene">N (NA), and all the nucleoproteins (N), N(N).

The coefficients ipan class="Gene">n the n class="Gene">nucleocapsid UCF, n, canemical">pan> be fouene">nd from the equationpan>

The total mass of the n class="Gene">nucleocapsidpan> is

The mass fractions of pan class="Gene">nucleic acid, w (n class="Gene">NA), and emical">pan> class="Gene">proteins in the nucleocapsid, w (Prot), are

The molecular mass of the virus is determined by addipan class="Gene">ng the masses of each element in the viruswhere n class="Gene">N is the number of atoms of element J and A is the molar mass of elemenpan>t J.

Thermodynamic properties of live matter

Based on the determipan class="Gene">ned elemental composition, standard thermodynamic n class="Gene">properties of SARS, n class="Disease">MERS and SARS-CoV-2 were determined (the standard state is defined as dry virus particles at a temperature of 298.15 K and pressure of 101.3 kPa). The main product of growth of any organism are biological molecules and structures, which are contained in the organism's dry matter. Thus, organism dry matter is the main constituent of an organism and will in the further text be denoted as live matter. There are two ways to determine standard thermodynamic properties of live matter: Battley and Roels methods. In the Battley method, standard enthalpy of formation and standard molar entropy are determined using the Patel-Erickson and Battley equations, respectively. These are then combined to determine standard Gibbs energy of formation. In the Roels method, Gibbs energy is determined directly, using the Roels equation. Thermodynamic properties of SARS, MERS and SARS-CoV-2 were determined using both methods. Since the Battley method is more accurate (Von Stockar and Liu, 1999), all the presented results (Sections 3.1, 3.2 and 3.3.1) are based on it. The Roels method was used to see whether changing the method of estimating thermodynamic properties has influence on the conclusions (Section 3.3.2). The uncertainties in determining thermodynamic properties are 5.36% for Patel-Erickson (Popovic, 2019) and 19.7% for Battley equation (Battley, 1999; Popovic, 2019).

Battley method

Standard epan class="Gene">nthalpy of formation of live matter, ΔH⁰(bio), was calculated from its standard molar enthalpy of combustion, ΔH⁰,where n is the number of atoms of element J in the live matter empirical formula, bio denotes live matter, and ΔH⁰(X) is standard enthalpy of formation of substance X (Patel and Erickson, 1981; Battley, 1998). ΔH⁰ was calculated from the Patel-Erickson equationwhere the term in the parentheses ren class="Gene">presents the number of electronpan>s transferred to n class="Chemical">oxygen during complete combustion of live matter (Patel and Erickson, 1981; Battley, 1998). Next, standard molar entropy, S⁰ (bio), of live matter was calculated using the Battley equation (Battley, 1999)where n is the number of atoms of element J in the empirical formula of the live matter, S⁰(J) is standard molar entropy of element J and a is the number of atoms per molecule of element J in its standard state elemental form. Standard molar entropy of formation of live matter, ΔS⁰(bio), was calculated using the equation (Battley, 1999)

Finally, stapan class="Gene">ndard Gibbs energy of formation of live matter, ΔG⁰(bio), was found through the equationwhere T is temperature.

Roels method

Gibbs energy of live matter capan class="Gene">n be determined directly using the Roels equation. The Roels equation is analogous to the Patel-Erickson equation, giving standard Gibbs energy of combustion, ΔG⁰, of live matterwhere E is the number of electrons transferred to n class="Chemical">oxygen durinpan>g combustionpan> to n class="Chemical">CO2(g), H2O(l), N2(g), P4O10(s) and SO3(g) (Roels, 1983; Von Stockar and Liu, 1999). ΔG⁰ is then converted into standard Gibbs energy of formation of live matter, ΔG⁰(bio), using an equation analogous to Eq. (26).

The Roels Battley methods are complementary ways of fipan class="Gene">nding Gibbs energy of formation of live matter. However, the Battley equation was calibrated on a better dataset than the Roels equation, making it more n class="Gene">precise (Vonpan> Stockar and Liu, 1999). Thus, all results n class="Gene">presented in Tables 5 and 6, are based on the Battley method. The Roels method was used to make a parallel calculation of ΔG⁰(bio), to determine whether the conclusions of this research are dependent on the method used to find live matter thermodynamic properties.

Table 5

Standard thermodynamic properties of formation and growth of SARS, MERS and SARS-CoV-2. The thermodynamic properties of formation of Lung – parenchyma were taken from (Popovic and Minceva, 2020b) and [Woodard and White, 1986], respectively.

Name	Formation			Growth
	ΔfH⁰bio (kJ/C-mol)	S⁰m,bio (J/C-mol K)	ΔfG⁰bio (kJ/C-mol)	ΔrH⁰ (kJ/C-mol)	ΔrS⁰ (J/C-mol K)	ΔrG⁰ (kJ/C-mol)
SARS-CoV-2: Entire virus	-64.7 ± 30.5	30.7 ± 6.1	-24.8 ± 32.3	-4.8 ± 60.1	6.9 ± 13.2	-6.9 ± 64.0
SARS-CoV-2: Nucleocapsid	-75.9 ± 29.4	32.5 ± 6.4	-33.7 ± 31.3	-233.4 ± 59.0	-37.7 ± 13.6	-222.2 ± 63.0
MERS: Entire virus	-63.8 ± 30.5	30.5 ± 6.0	-24.3 ± 32.3	-5.2 ± 60.1	7.7 ± 13.2	-7.5 ± 64.0
MERS: Nucleocapsid	-73.9 ± 29.4	32.1 ± 6.3	-32.3 ± 31.3	-218.8 ± 59.0	-34.8 ± 13.5	-208.5 ± 63.0
SARS-1: Entire virus	-64.5 ± 30.5	30.7 ± 6.1	-24.7 ± 32.3	-4.5 ± 60.1	6.6 ± 13.2	-6.5 ± 64.0
SARS-1: Nucleocapsid	-75.6 ± 29.4	32.5 ± 6.4	-33.5 ± 31.3	-242.0 ± 58.9	-39.2 ± 13.6	-230.3 ± 63.0
Lung - parenchyma	-65.6 ± 30.7	31.4 ± 6.2	-24.9 ± 32.6	-50.5 ± 60.3	-2.8 ± 13.4	-49.8 ± 64.3

Table 6

The influence of uncertainty on the conclusions of this research. The column “Worst-case ΔrG⁰” contains uncertainty combinations that are the most unfavorable for the conclusions of this research: the Gibbs energies of growth of viruses was increased by the error, making them less negative, while that of the host tissue was decreased to make it more negative.

Name	ΔrG⁰ (kJ/C-mol)	Worst-case ΔrG⁰ (kJ/C-mol)
SARS-CoV-2: Entire virus	-6.9 ± 64.0	57.2
SARS-CoV-2: Nucleocapsid	-222.2 ± 63.0	-159.2
MERS: Entire virus	-7.5 ± 64.0	56.5
MERS: Nucleocapsid	-208.5 ± 63.0	-145.5
SARS-1: Entire virus	-6.5 ± 64.0	57.5
SARS-1: Nucleocapsid	-230.3 ± 63.0	-167.4
Lung - parenchyma	-49.8 ± 64.3	-114.1

Standard thermodypan class="Gene">namic n class="Gene">properties of formationpan> anemical">pan>d growth of SARS, n class="Disease">MERS aene">nd n class="Species">SARS-CoV-2. The thermodynamic properties of formation of Lung – parenchyma were taken from (Popovic and Minceva, 2020b) and [Woodard and White, 1986], respectively.

The influepan class="Gene">nce of uncertainty on the conclusions of this research. The column “Worst-case ΔrG⁰” contains uncertainty combinations that are the most unfavorable for the conclusions of this research: the Gibbs energies of growth of viruses was increased by the error, making them less negative, while that of the host tissue was decreased to make it more negative.

Growth stoichiometry and thermodynamics

In this research, a growth medium was chosepan class="Gene">n that resembles n class="Species">human blood. The mainpan> source of emical">pan> class="Gene">N and S, and partly C is an equimolar mixture of amino acids, with the empirical formula CH1.7978O0.4831N0.2247S0.0225. The remaining C comes from carbohydrates with the empirical formula CH2O. The source of P is the hydrogen phosphate ion HPO42-, while the sources of inorganic ions are Na+, K+, Mg2+, Ca2+ and Cl−. Since S in amino acids come in a quantity greater than needed for growth, the excess S is removed as the SO42- ion. The pH of the growth mixture is regulated by the bicarbonate buffer. Thus, the general unbalanced growth reaction has the formwhere Bio denotes live matter. The stoichiometric coefficients are given in Table 7.

Table 7

Growth stoichiometries of SARS, MERS and SARS-CoV-2 viruses, and their host tissue. The coefficients given in this table are for reaction (1). (Bio) represents the UCF of live matter, the composition of which is given in Table 3.

Name	Reactants								→	Products
	Amino acid	CH2O	O2	HPO42-	HCO3-	Na+	K+	Cl-		Bio	SO42-	H2O	H2CO3
SARS-CoV-2: Entire virus	1.0238	0.0098	0.0000	0.0065	0.0256	0.0000	0.0000	0.0000	→	1	0.0192	0.0674	0.0591
SARS-CoV-2: Nucleoprotein	1.3905	0.0000	0.4937	0.0060	0.0437	0.0000	0.0000	0.0000	→	1	0.0279	0.0551	0.4342
MERS: Entire virus	1.0035	0.0349	0.0000	0.0065	0.0231	0.0000	0.0000	0.0000	→	1	0.0180	0.0748	0.0615
MERS: Nucleoprotein	1.3657	0.0000	0.4623	0.0061	0.0425	0.0000	0.0000	0.0000	→	1	0.0273	0.0644	0.4081
SARS-1: Entire virus	1.0302	0.0016	0.0000	0.0064	0.0252	0.0000	0.0000	0.0000	→	1	0.0190	0.0683	0.0570
SARS-1: Nucleoprotein	1.4047	0.0000	0.5121	0.0060	0.0445	0.0000	0.0000	0.0000	→	1	0.0282	0.0553	0.4492
Lung - parenchyma	1.1266	0.0000	0.1070	0.0074	0.0206	0.0100	0.0059	0.0097	→	1	0.0146	0.0661	0.1472

Growth stoichiometries of SARS, n class="Disease">MERSpan> aene">nd n class="Species">SARS-CoV-2 viruses, and their host tissue. The coefficients given in this table are for reaction (1). (Bio) represents the UCF of live matter, the compositioene">n of which is given in Table 3.

The term live matter refers to viruses and their host cells. Growth reactiopan class="Gene">n thermodynamic parameters, including standard enthalpy of growth, ΔH⁰, standard entropy of growth, ΔS⁰, and standard Gibbs energy of growth, ΔG⁰, were calculated using the n class="Gene">prinpan>ciples of thermochemistry [Atkinpan>s and de Paula, 2014, 2011]. Growth reactionpan> thermodynpan>amic parameters were calculated usinpan>g the equationpan>swhere ν′s are stoichiometric coefficients of species participatinpan>g the reactionpan> (Atkinpan>s and de Paula, 2014, 2011).

Uncertainties

Thermodynamic papan class="Gene">n class="Gene">properties (ΔH⁰(bio), S⁰ (bio) anemical">pan>d ΔG⁰(bio)) were determined from elemental compositionpan> usinpan>g empirical relationpan>s and thus have some uncertainpan>ty. ΔH⁰ was found usinpan>g the Patel-Ericksonpan> equationpan>, the uncertainpan>ty of which is 5.36% (Popovic, 2019). The determinpan>ed ΔH⁰ values were then subtracted from standard enthalpies of formationpan> of n class="Chemical">oxides (Eq. (26)) to find ΔH⁰(bio). Since standard enthalpies of formation of oxides were precisely determined by experiment (more details in (Chase, 1998)), they have a negligible error compared to that in ΔH⁰. Thus, the uncertainty in standard enthalpy of formation of live matter, δ(ΔH⁰(bio)), is equal to the error in ΔH⁰.

S⁰ (bio) was determined usipan class="Gene">ng the Battley equation, which was calibrated on a wide range of organic molecule and live matter data (Battley, 1999). The uncertainty in estimation of entropy using the Battley equation is 2% for n class="Disease">dry matter and 19.7% for hydrated matter (Battley, 1999). Therefore, the uncertainpan>ty inpan> standard molar entropy of live matter, δ(S⁰ (bio)), is

ΔS⁰(bio) is the entropy of the reactiopan class="Gene">n

and is defipan class="Gene">ned as the difference in S⁰ (bio) and standard molar entropies of the elements, which have been determined with great accuracy by experiment (Chase, 1998). Thus, the uncertainty in ΔS⁰(bio) is equal to that in S⁰ (bio) (Popovic, 2019).

ΔH⁰(bio) and ΔS⁰(bio) are used to fipan class="Gene">nd ΔG⁰(bio). Therefore, the uncertainty in the standard Gibbs energy of formation of live matter, δ(ΔG⁰(bio)), is (Popovic, 2019)

Finally, the upan class="Gene">ncertainty in ΔG⁰(bio) is equal to that in ΔG⁰, since it is the greatest source of uncertainty in its determination. ΔG⁰ is determined using Eq. (36), as the difference of ΔG⁰ values of reactants and n class="Gene">products. The ΔG⁰ values of all reactionpan> n class="Species">participants, except for live matter have been determined with great accuracy by experiment (Chase, 1998). Thus, uncertainty in Gibbs energy of growth, δ(ΔG⁰), is equal to δ(ΔG⁰(bio)). Similarly, δ(ΔH⁰) and δ(ΔS⁰) are equal to δ(ΔH⁰(bio)) and S⁰ (bio), respectively.

Results and discussion

Elemental composition and thermodynamic properties of SARS, MERS and SARS-CoV-2

Wimmer (2006) persuasively portrays viruses as chemicals. Using the methodology described above, elemepan class="Gene">ntal and molecular composition of SARS, n class="Disease">MERS and n class="Species">SARS-CoV-2 were calculated and are given in Table 8. The empirical formulas of entire virions are SARS CH1.6362O0.2852N0.2315P0.0064S0.0041, MERS CH1.6308O0.2835N0.2255P0.0065S0.0045, and SARS-CoV-2 CH1.6390O0.2851N0.2301P0.0065S0.0038. The empirical formulas of nucleocapsids only are SARS CH1.5668O0.3446N0.3157P0.0060S0.0033, MERS CH1.5586O0.3380N0.3069P0.0061S0.0034 and SARS-CoV-2 CH1.5708O0.3452N0.3125P0.0060S0.0033. Thus, there is a difference in empirical formulas of both the nucleocapsids and entire viruses between SARS, MERS and SARS-CoV-2. For comparison, the empirical formulas of other classes of organisms are: bacteria CH1.7O0.4N0.2, fungi CH1.7O0.5N0.1, algae CH1.7O0.5N0.1 (Popovic, 2019) and human soft tissue average CH1.7296O0.2591N0.1112P0.0134S0.0030Na0.0027K0.0031Ca0.0173Cl0.0018 (Popovic and Minceva, 2020a). The empirical formulas are similar to those of other classes of organisms.

Table 8

Elemental and molecular compositions per C-mole of SARS, MERS and SARS-CoV-2. The general unit carbon formula (UCF) has the form CHnHOnONnNPnPSnS, where nH, nO, nN, nP and nS are coefficients given in this table. The elemental and molecular composition of Lung – parenchyma were taken from (Popovic and Minceva, 2020b) and (Woodard and White, 1986), respectively.

Name	Elemental composition					Molecular composition
	nH	nO	nN	nP	nS	Nucleic acid	Proteins	Lipids	Non-RNA carbohydrates
SARS-CoV-2: Entire virus	1.6390	0.2851	0.2301	0.0065	0.0038	4%	77%	17%	2%
SARS-CoV-2: Nucleocapsid	1.5708	0.3452	0.3125	0.0060	0.0033	8%	92%	0%	0%
MERS: Entire virus	1.6308	0.2835	0.2255	0.0065	0.0045	4%	77%	17%	2%
MERS: Nucleocapsid	1.5586	0.3380	0.3069	0.0061	0.0034	8%	92%	0%	0%
SARS-1: Entire virus	1.6362	0.2852	0.2315	0.0064	0.0041	4%	77%	17%	2%
SARS-1: Nucleocapsid	1.5668	0.3446	0.3157	0.0060	0.0033	8%	92%	0%	0%
Lung - parenchyma	1.6268	0.2836	0.2532	0.0074	0.0107	<5%	88.1%	6.7%	<5%

Elemental apan class="Gene">nd molecular compositions per C-mole of SARS, n class="Disease">MERS and n class="Species">SARS-CoV-2. The general unit carbon formula (UCF) has the form CHnHOnONnNPnPSnS, where nH, nO, nN, nP and nS are coefficients given in this table. The elemental and molecular composition of Lung – parenchyma were taken from (Popovic and Minceva, 2020b) and (Woodard and White, 1986), respectively.

Based on the calculated elemepan class="Gene">ntal compositions, growth stoichiometry and standard thermodynamic n class="Gene">properties of formationpan> of the three viruses were determinpan>ed, which are given inpan> Tables 5 and 7, respectively. Moreover, these were used to finpan>d staene">ndard thermodynpan>amic n class="Gene">properties of growth, which are given in Table 5.

Standard molar epan class="Gene">ntropies of live matter are around 30 J/C-mol K (Table 5), laying between that of n class="Chemical">graphite, 5.740 J/mol K, and n class="Chemical">carbon in gaseous state, 158.10 J/mol K (Atkins and de Paula, 2014). This indicates that the mobility of C atoms in live matter is greater than in graphite, but lower than in the gaseous state.

Thermodynamic properties and virus multiplication

SARS, n class="Disease">MERSpan> aene">nd n class="Species">SARS-CoV-2 cause respiratory infections. As all other viruses, they are obligatory intracellular parasites. The n class="Gene">processes of replication, transcription and translation of viruses compete with metabolic processes of the host cell. Thus, it is necessary to know Gibbs energies of growth of the host tissue. The Gibbs energies of formation and growth of lung parenchymal tissue (Popovic and Minceva, 2020a) is given in Table 5. It can be seen that the Gibbs energy of growth of nucleocapsids of all three viruses is significantly more negative than Gibbs energy of growth of the host tissue. Due to this, the viruses are able to hijack cellular metabolism and their components are synthesized at a greater rate than those of the host. Notice that the highly negative Gibbs energies of growth indicate a great driving force for viral multiplication.

Multiplication rate of a virus is apan class="Gene">nalogous to its growth reaction rate, r, which is n class="Gene">proportionpan>al to the Gibbs energy of growth, ΔG, the Gibbs enpan>ergy chaene">nge of reactionpan> (33)where L is a conpan>stant (phenomenological coefficient) and T is temperature (Demirel, 2014, p. 149), a relationpan>ship that has been applied to multiplicationpan> of microorganisms (Vonpan> Stockar, 2014, p. 416; Demirel, 2014, p. 407; Westerhoff et al., 1982; Hellinpan>gwerf et al., 1982), inpan>cludinpan>g viruses (Popovic and Minpan>ceva, 2020a). The exponpan>ential dependence of reactionpan> rate onpan> temperature is conpan>tainpan>ed inpan> L (Demirel, 2014). However, physiological n class="Gene">processes occur in a very narrow temperature range. Thus, physiological temperature of a species can be assumed to be constant. The L constant also includes the influence of various kinetic factors, such as enzymes that lower activation energies.

Gibbs energy of growth, ΔG, is the Gibbs epan class="Gene">nergy change when live matter is formed from nutrients, as in reaction (33). ΔG should not be confused with Gibbs energy of formation of live matter, ΔG, the change in Gibbs energy when live matter is formed from elements. The elements here are just a reference state, which is used because there is no way of knowing the absolute Gibbs energies of substances (Atkins and de Paula, 2011). Thus, ΔG is a n class="Gene">property of live matter, inpan>dependent of the environpan>ment inpan> which it grows, while ΔG is a property of the growth process.

Gibbs energy of growth deemical">pepan class="Gene">nds on the chemical nature of the organism and the growth medium. However, it is also influenced by conditions in the medium, in particular on temperature, reactant and n class="Gene">product conpan>centrationpan>s, and inpan>termolecular forces between reactionpan> n class="Species">participants. The dependence is given by the equationwhere ΔG⁰ is the standard Gibbs energy of growth, R the universal gas constant, while Q is the reaction quotient (Atkins and de Paula, 2014). The first term, ΔG⁰, describes the chemical properties of the organism and the growth medium (Atkins and de Paula, 2014). The second term on the right hand side describes the influence of the conditions in the medium through the reaction quotient, Q, which is defined aswhere C, γ and ν are concentration, activity coefficient and stoichiometric coefficient of substance i, respectively (Atkins and de Paula, 2014). However, the focus of this research is comparison of driving forces of growth of viruses and their host cells. Viruses and their host cells are subjected to the same environment, but they differ in chemical composition. Thus, the principal difference in Gibbs energies of growth of viruses and their host cells comes from the difference in their chemical composition, which is quantified by ΔG⁰. Thus, in this work ΔG in Eq. (41) can be approximated with ΔG⁰ values of viruses and their host cells (Von Stockar, 2014),

By comparing growth reactiopan class="Gene">n rates of viruses and their host tissues, their ratio, R, is greater than one (Popovic and Minceva, 2020a)

Since viruses apan class="Gene">nd their host perform transcription, translation and replication at the same temperature and using the same cellular machinery, T and L are the same for both. Viruses do not possess their own multiplication machinery and must use that of their host. The n class="Gene">process of transcriptionpan>, translationpan> and replicationpan> is identical inpan> a virus and its host. Therefore, virus and its host cell share the same phenomenological coefficient L. R inpan>dicates the ratio between the growth (multiplicationpan>) rate of the virus anemical">pan>d growth rate of the host cell (Popovic aene">nd Minpan>ceva, 2020a). The fact that R > 1 leads to the conpan>clusionpan> that inpan> the competitionpan> of metabolic n class="Gene">processes of viruses and their hosts, the virus will dominate (Popovic and Minceva, 2020a). Thus, viral multiplication will dominate over the metabolism of the infected tissue.

By performing its life cycle, a virus performs several chemical papan class="Gene">n class="Gene">processes: binpan>ding of the virus to the receptor onpan> the cell surface, transcriptionpan>, replicationpan>, translationpan> and self-assembly (Popovic and Minpan>ceva 2020a). Withinpan> self-assembly, new virionpan>s are formed from replicated Rn class="Gene">NA and synthesized nucleoproteins. However, the envelope originates from the host cell membrane. The rate of each of the mentioned chemical processes depends on their Gibbs energy, because the host cell and virus use the same metabolic machinery and are at the same temperature (Popovic and Minceva, 2020a). Since the envelope originates from the host cell, during self-assembly, the virus passively takes it from the host cell. Thus, the model suggested here focuses on determination of Gibbs energy of the nucleocapsid, since it is formed in self-assembly processes from components coded in the viral nucleic acid. However, Gibbs energies of formation and growth were determined both for the nucleocapsid and the entire virion. Based on the data in Table 5, the R-values for nucleocapsids were found to be 4.6 for SARS, 4.2 for MERS and 4.5 for SARS-CoV-2. The nucleocapsids of all three viruses have similar R-values.

The R-values were calculated comparing Gibbs epan class="Gene">nergies of growth of n class="Gene">nucleocapsids and host cells, because onemical">pan>ly n class="Gene">nucleocapsids are formed in a chemical n class="Gene">process, involving polymerization and self-assembly. On the other hand, entire virions are formed in the physical process of budding, from the already present nucleocapsid and cell membrane. The cell membrane is not synthesized during budding. It is already there, synthesized by the host cell, and is taken by the virion. R relates to the synthesis process and is thus not directly related to budding.

The influence of assumptions on the results

The discussion above rests opan class="Gene">n two assumptions: the Battley method for estimating thermodynamic n class="Gene">properties of live matter and approximating Gibbs energy of growth with standard Gibbs energy of growth. The influence of these assumptions on the results is considered in this section. The discussion begins with the uncertainty in thermodynamic properties. Then, it is considered whether the results are dependent on the method used to find thermodynamic properties. Finally, the influence of approximating ΔG with ΔG⁰ is considered.

The influence of uncertainties

Uncertaipan class="Gene">nties in the determined Gibbs energies of growth were calculated as described in Section 2.4. and are n class="Gene">presented inpan> Table 5. Their inpan>fluence onpan> the results of this research is analyzed inpan> Table 6. The most unemical">pan>favorable combinationpan> of uncertainpan>ties was conpan>sidered. The Gibbs energies of growth of the viruses were inpan>creased by the uncertainpan>ty, makinpan>g them less negative. Onpan> the other hand, the Gibbs energy of growth of the host tissue was decreased by the uncertainpan>ty, makinpan>g it more negative. As can be seen, Gibbs energy of growth of the host tissue remainpan>s more negative that of the virus n class="Gene">nucleocapsids.

The trend ipan class="Gene">n the R-values is also n class="Gene">preserved. To repeat, the originpan>al R-values were founemical">pan>d to be 4.6 for SARS, 4.2 for n class="Disease">MERS aene">nd 4.5 for n class="Species">SARS-CoV-2, while those of entire virions are 0.13 for SARS, 0.15 for MERS and 0.14 SARS-CoV-2. The worst-case R-values for virus nucleocapsids are 1.5 for SARS, 1.3 for MERS and 1.4 for SARS-CoV-2. The worst-case R-values for entire virions are -0.50 for SARS, -0.50 for MERS and -0.50 for SARS-CoV-2. The R-values of entire virions are negative, because their ΔG⁰ is only slightly negative and adding maximum uncertainty makes them positive, while that of the host tissue remain negative. However, this does not represent a problem for virus multiplication. The R-values of the nucleocapsids are greater than unity. Thus, virus nucleocapsid synthesis in the cytoplasm dominates over that of host cell components. Once a nucleocapsid is formed, it takes a part of the already existing cell membrane as its envelope, during the budding process, and leaves the cell. Since virions are constantly leaving the cell by budding, the process is shifted towards the products – budding of new virions.

The influence of thermodynamic property models

Gibbs energy of formatiopan class="Gene">n and growth of the three viruses and their host tissue have been calculated using the Battley and Roels methods (Section 2.2.), to see whether changing the thermodynamic n class="Gene">properties model will have inpan>fluence of the conpan>clusionpan>s. The results are n class="Gene">presented in Table 9 and Figure 3. As can be seen from Figure 3a, both models give very similar Gibbs energies of formation for both the viruses and their host tissue. Figure 3b shows a comparison of Gibbs energies of growth based on the two models. For higher values of ΔG⁰ the results are very similar, a slight discrepancy appears at lower ΔrG⁰ values, due to subtraction of large numbers. However, Table 9 shows that for both models, ΔrG⁰ of virus nucleocapsids is more negative than that of the host tissue. Thus, changing the thermodynamic property model has no influence on the results of this research.

Table 9

Comparison of Gibbs energies of formation and growth calculated using the Battley and Roels methods.

Name	Formation			Growth
	ΔfG⁰Battley (kJ/C-mol)	ΔfG⁰Roels (kJ/C-mol)	Relative deviation	ΔrG⁰Battley (kJ/C-mol)	ΔrG⁰Roels (kJ/C-mol)	Relative deviation
SARS-CoV-2: Entire virus	-24.84	-24.17	-2.7%	-6.9	-6.2	-9.7%
SARS-CoV-2: Nucleocapsid	-33.73	-33.85	0.4%	-222.2	-222.4	0.1%
MERS: Entire virus	-24.28	-23.52	-3.1%	-7.5	-6.7	-10.2%
MERS: Nucleocapsid	-32.26	-32.22	-0.1%	-208.5	-208.4	0.0%
SARS-1: Entire virus	-24.68	-24.05	-2.5%	-6.5	-5.9	-9.6%
SARS-1: Nucleocapsid	-33.46	-33.64	0.5%	-230.3	-230.5	0.1%
Lung - parenchyma	-24.94	-25.37	1.7%	-49.8	-50.2	0.9%

Figure 3

Comparison of Gibbs energies of (a) formation and (b) growth, calculated using the Battley and Roels methods.

Comparison of Gibbs epan class="Gene">nergies of formation and growth calculated using the Battley and Roels methods.

Comparison of Gibbs epan class="Gene">nergies of (a) formation and (b) growth, calculated using the Battley and Roels methods.

The influence of reaction quotient Q

In the discussiopan class="Gene">n above ΔG was approximated with ΔG⁰, simplifyinpan>g Eqs. (41), (42), (43), anemical">pan>d (44). To find the inpan>fluence of this approximation, ΔG was calculated using Eqs. (42) and (43), and compared to ΔG⁰. The concentrations of substances in reaction (33) were taken from the literature (Fuggle, 2018; Blinn et al., 2006): amino acids 2.76 mol/dm3 (total blood protein 70 g/l, molar mass 25.39 g/C-mol), CH2O 0.036 mol/dm3 (blood glucose 6 mmol/l), O2 14 kPa, n class="Chemical">HPO42- 0.0012 mol/dm3, HCO3- 0.025 mol/dm3, Na+ 0.14 mol/dm3, K+ 0.0042 mol/dm3, Cl− 0.1 mol/dm3, SO42- 3.2 ∙ 10−5 mol/dm3, and CO2 5 kPa. The stoichiometric coefficients were taken from Table 7, while the activity coefficients were assumed to be 1 (activity coefficients make a correction for Q, which is itself a correction for ΔG⁰). The results are summarized in Table 10.

Table 10

Influence of the reaction quotient on Gibbs energy of growth. The table compares the influences of standard Gibbs energy of growth, ΔG⁰, and the reaction quotient Q on Gibbs energy of growth, ΔG. The last column %Q contains the relative size of the correction to ΔG made by Q, calculated as (%Q) = [ RT ln(Q) ]/ΔG. Also, notice that the size of the correction RT ln(Q) is in all cases lower than the uncertainty in ΔG⁰ (Table 5).

Name	Q	ΔrG⁰ (kJ/C-mol)	RgT ln(Q) (kJ/C-mol)	ΔrG (kJ/C-mol)	%Q
SARS-CoV-2: Entire virus	0.289	-6.890	-3.077	-9.967	31%
SARS-CoV-2: Nucleocapsid	0.169	-222.236	-4.413	-226.648	2%
MERS: Entire virus	0.320	-7.491	-2.827	-10.318	27%
MERS: Nucleocapsid	0.176	-208.466	-4.313	-212.779	2%
SARS-1: Entire virus	0.281	-6.545	-3.143	-9.688	32%
SARS-1: Nucleocapsid	0.165	-230.342	-4.468	-234.810	2%
Lung - parenchyma	0.269	-49.758	-3.252	-53.009	6%

Influepan class="Gene">nce of the reaction quotient on Gibbs energy of growth. The table compares the influences of standard Gibbs energy of growth, ΔG⁰, and the reaction quotient Q on Gibbs energy of growth, ΔG. The last column %Q contains the relative size of the correction to ΔG made by Q, calculated as (%Q) = [ RT ln(Q) ]/ΔG. Also, notice that the size of the correction RT ln(Q) is in all cases lower than the uncertainty in ΔG⁰ (Table 5).

From the data in Table 10, it capan class="Gene">n be seen that approximatinpan>g ΔG with ΔG⁰ does not inpan>fluence the mainpan> conpan>clusionpan>s of this research. The correctionpan> made by the Q-term inpan> Eq. (42) is 2% for the n class="Gene">nucleocapsids and 6% for the host tissue, while for entire virions it goes up to 32%, due to their small ΔG value. However, the trend in the ΔG values is preserved: nucleocapsids have a much more negative Gibbs energy of growth than the host tissue. Moreover, the absolute size of the RT ln(Q) terms is much lower than the uncertainty in ΔG⁰ (Table 5). Therefore, approximating Eq. (41) with Eq. (44) seems to be a reasonable assumption.

Outlook

Pathogenicity (capacity of a microbe to cause damage opan class="Gene">n affected cell/tissue) of viruses is a consequence of more efficient multiplication of a virus compared to its host cell. Multiplication of viruses leads to cell and tissue damage (Albrecht et al., 1996). Decrease in multiplication rate leads to decreased n class="Gene">productionpan> and accumulationpan>, as well as less cell and tissue damage. This leaves the organism enough time to develop an immune responpan>se, with less tissue damage anemical">pan>d milder clinical symptoms. Examples are the BCG (artificially designed) and Jenner (designed by nature) vaccinpan>e, attenuated vaccinpan>es capable of makinpan>g local inpan>flammatory changes followed by a general development of immune responpan>se. Moreover, n class="Species">Human diploid cell rabies vaccines are made using the attenuated Pitman-Moore L503 strain of the virus, while the purified Vero cell rabies vaccine uses the attenuated Wistar strain of the rabies virus (WHO, 2018).

Virulence repapan class="Gene">n class="Gene">presenpan>ts a pathogen's or microbe's ability to inpan>fect or damage a host. Virulence factors allow a virus to enter its host, replicate, modify host defenses (inpan> multicellular host organisms) and sn class="Gene">pread within a multicellular host (Flint et al., 2009). Entrance into a host and replication capability (ability to replicate more efficiently than the host cell) are chemical reactions governed by change in thermodynamic properties, i.e. Gibbs energy. Thus, if Gibbs energy of growth of an attenuated virus strain is made less negative, it is possible to decrease its rate of binding to the specific receptor or its replication rate. Thus, the result of Gibbs energy increase is the decrease in virulence of the attenuated virus. If the Gibbs energy of growth of the virus is less negative than that of its host tissue, then the virus loses its virulence. If the attenuated virus strain loses its virulence and keeps its antigenic properties, it can become an attenuated vaccine. Since the attenuated strain has a lower multiplication rate, it is not capable of destroying the host cell. Thus, during vaccine design, an attempt should be made to increase the Gibbs energy of growth of the nucleocapsid, by changing the chemical composition of the wild-type virus. In this way, R would be made equal to or lower than unity.

Conclusions

n class="Semical">pecies">SARS-CoV-2pan> (n class="Disease">COVID-19), in additioene">n to being a medical n class="Gene">problem, is also a biological and biothermodynamic phenomenon. Biothermodynamics attempts to find the driving forces and mechanisms that lead to biological phenomena. All processes in nature are a consequence of interactions between various systems. Organisms represent thermodynamic systems, while their life cycles are processes that appear as interactions with the environment. If the environment, as in the case of viruses, is another organism (human), then the interaction is infection. The driving force for all processes in nature is Gibbs energy. In this paper, Gibbs energies of growth of SARS, MERS and SARS-CoV-2 were compared to those of their host. The comparison implies a great spontaneity of virus multiplication, leading to high virus multiplication rate. High multiplication rate leads to formation of a great reservoir of viruses, which enables extensive transmission through the population.

Declarations

Author contribution statement

Marko Popovic: Conceived apan class="Gene">nd designed the experiments; Performed the experiments; Analyzed and intern class="Gene">preted the data; Wrote the paper.

Mirjana Mipan class="Gene">nceva: Analyzed and intern class="Gene">preted the data; Wrote the paper.

Funding statement

This research did not receive apan class="Gene">ny specific grant from funding agencies in the public, commercial, or not-for-n class="Gene">profit sectors.

Competing interest statement

The authors declare no copan class="Gene">nflict of interest.

Additional information

n class="Gene">Npan>o additional information is available for this paper.