Biothermodynamic Analysis of Norovirus: Mechanistic Model of Virus–Host Interactions and Virus–Virus Competition Based on Gibbs Energy

Abstract

Norovirus is a leading cause of viral gastroenteritis worldwide and has been studied extensively from the perspective of life and biomedical sciences. However, no biothermodynamic analysis of Norovirus has been reported in the literature. Such an analysis would provide insights into the role of energetic constraints in the interactions between Norovirus and its host cells and other viruses. In this research, Norovirus was characterized from the aspect of chemistry and chemical thermodynamics, with the determination of its molecular formula, empirical formula, molar mass and thermodynamic properties (enthalpy, entropy, Gibbs energy) of formation. Based on these properties, biosynthesis reactions were formulated that show how Norovirus particles are synthetized inside host cells, and the thermodynamic properties of biosynthesis were determined. Moreover, the thermodynamic properties of the binding of Norovirus to its host cell receptor were determined. These were then used to develop a model of virus–host interactions at the cell membrane (antigen-receptor binding) and inside the cytoplasm (virus multiplication), with the phenomenological equations of nonequilibrium thermodynamics. Based on the model, an analysis of the virus–virus competition between Norovirus and Rotavirus was conducted.

1. Introduction

Norovirus is a major cause of viral gastroenteritis worldwide [1,2]. It belongs to Noroviruses (NoVs), which are emerging pathogens that represent a risk for human health [3]. Norovirus has been studied extensively from the perspective of life and biomedical sciences. However, in the literature, no study of Norovirus was reported from the perspective of biothermodynamics. The biothermodynamic approach has been applied to research on several viruses, which include SARS-CoV-2 [4,5,6,7,8], SARS-CoV [9], MERS-CoV [10], Ebola [11], Rhinovirus [12], Mpox [13], Rotavirus [14], HIV [15], Dengue virus [16], West Nile virus [17], Arboviruses [15,18,19], Coxsackievirus [20], etc. This research was able to explain interactions between viruses and their host organisms at the cell membrane (virus attachment and entry into host cells) [12,21,22] and in the cytoplasm (virus multiplication) [4,7,23]. Biothermodynamics was applied in studies of interactions between viruses and evolution of viruses [4,24,25]. Moreover, a biothermodynamic methodology was used to analyze the development of epidemics and pandemics [6,26]. This is why a biothermodynamic analysis could provide insights into the role of the metabolic energy requirements in interactions between Norovirus and its host cells and other viruses.

Viruses lack cellular metabolic machinery and must therefore hijack the metabolism of a host cell in order to multiply [27,28,29]. They have been studied extensively from the perspective of life and biomedical sciences [30,31,32]. With the development of biology and chemistry, the approach of molecular biology and biochemistry have contributed greatly to our understanding of viruses [33,34,35]. Genetic and protein sequences have been determined for many viruses [36,37,38]. Moreover, interactions of viruses with their host cells have been studied extensively at the molecular level in molecular virology [39,40,41].

Except for biological systems, viruses also represent macromolecular assemblies and can therefore be analyzed as chemical and thermodynamic systems [24,42,43]. Inside host cells, viruses establish metabolic processes [44,45,46]. These include replication, transcription, translation, and self-assembly processes [47,48,49]. All these processes represent chemical reactions [50,51,52]. These reactions can be analyzed with the methodology of chemical thermodynamics [53,54,55]. This approach can provide insight into energetic constraints on metabolic processes in biological systems [56,57,58].

Based on genetic and protein sequences, chemical and thermodynamic properties of viruses can be found [7,59,60]. The approach of chemical thermodynamics can be a useful tool in studies of virus–host interactions, which can complement the approaches of molecular biology and biochemistry [61,62,63,64,65]. Biothermodynamics was applied to study interactions between organisms [66,67] and evolution [68,69]. It has been applied in research on competition between the variants of SARS-CoV-2 [21,70,71]. Moreover, biothermodynamics was applied in studies on virus–host interactions [5,8,23] and epidemiology [6,26]. It has been applied in research on virus–virus competition [21,70]. The biothermodynamic approach can provide additional information about virus–host interactions, based on the results of molecular biology and biochemistry.

Norovirus, also known as Norwalk virus, belongs to the Calciviridae family [72,73]. In humans, it causes acute gastroenteritis known as the winter vomiting disease [74,75]. Norovirus is primarily transmitted by the fecal–oral route, which includes direct person-to-person contact, contact with contaminated surfaces, ingestion of contaminated water or food and aerosol transmission [76,77]. Norovirus can cause infection with a very small infective inoculum, which means that only a very small number of virions are required for infection [78,79]. This makes Norovirus highly contagious [80,81] and its epidemics difficult to control [82,83]. The incubation period is 12 to 48 h [84,85]. The symptoms include diarrhea, vomiting, nausea, stomach pain, and sometimes fever, headache and body aches [84,85].

Norovirus has an unsegmented single-stranded positive-sense RNA genome [86,87,88,89]. Norovirus particles are non-enveloped [90,91,92,93]. Most Norovirus virions are of T = 3 icosahedral symmetry [94,95,96,97]. They are composed of the RNA genome and 180 copies of the VP1 capsid protein [98,99,100,101]. The VP1 capsid proteins are arranged as 90 dimers [102,103,104,105]. The VP1 capsid protein contains the shell (S) and protruding (P) domains [106,107]. The S domain forms the interior shell of the capsid [108,109]. The P domain consists of the P1 and P2 subdomains [110,111]. The P2 subdomain represents the viral antigen that binds to the host cell receptor [112,113,114,115]. After antigen-receptor binding, the virus enters the cell by endocytosis [116,117,118,119].

The goal of this paper is to perform a chemical and thermodynamic analysis of Norovirus. This was carried out by determining its molecular formula, empirical formula, thermodynamic properties (enthalpy, entropy, and Gibbs energy) of formation, biosynthesis reactions, and thermodynamic properties of biosynthesis. These properties were used to develop a mechanistic model of virus–host interaction of Norovirus with its host enterocytes. Based on the model, virus–virus interactions between Norovirus and Rotavirus were discussed.

2. Methods

2.1. Data Sources

The genetic sequence and sequence of the VP1 capsid protein of the Norovirus strain GII was taken from the NCBI database [120,121]. The genetic sequence can be found under the accession number NC_044932.1 [122] and is reported by [123]. The sequence of the VP1 capsid protein can be found under the accession number AIV43156.2 [124] and is reported by [125]. The Norovirus capsid exhibits T = 3 icosahedral symmetry and consists of 180 copies of the VP1 capsid protein [126,127].

Dissociation equilibrium constant, K_d, data for the binding of the VP1 protruding (P) domain of Murine norovirus (MNoV) to the CD300lf receptor were taken from [128,129]. They were measured through surface plasmon resonance (SPR) and isothermal titration calorimetry (ITC) at 25 °C [128]. The dissociation equilibrium constant for the binding of Norovirus VP1 P domain to the CD300lf receptor in absence of Ca²⁺, Mg²⁺ and GCDCA (glycochenodeoxycholic acid) is K_d = 219 µM [128,129]. The dissociation equilibrium constant for the binding of the Norovirus VP1 P domain to the CD300lf receptor in the presence of Ca²⁺ ions is K_d = 24.51 µM [128]. The dissociation equilibrium constant for the binding of Norovirus VP1 P domain to the CD300lf receptor in the presence of Mg²⁺ ions and EGTA (ethylene glycol-bis(β-aminoethyl ether)-N,N,N′,N′-tetraacetic acid) is K_d = 24.29 µM [128]. The dissociation equilibrium constant for binding of Norovirus VP1 P domain to the CD300lf receptor in the presence of Ca²⁺ ions and GCDCA is K_d = 12.04 µM [128].

2.2. Atom Counting Method

Molecular formulas, empirical formulas, molar masses, and macromolecular composition of Norovirus particles, genomic RNA and VP1 capsid protein were determined, based on genetic and protein sequences and virus morphology, using the atom counting method, as described in [59,130,131]. The atom counting method is a computational method for the calculation of chemical properties of macromolecules and macromolecular assemblies, based on genomic and proteomic data [59,130,132]. The input of the program are genetic sequences, protein sequences and, in case of macromolecular assemblies, morphology [59,130]. Biological macromolecules consist of residues of monomers, like nucleotides and amino acids [59,130]. All the residues have a well-defined elemental composition [59,130]. The program goes along sequences of macromolecules and adds atoms coming from each residue [59,130]. In the case of macromolecular assemblies, the atoms coming from every kind of macromolecule are multiplied by the number of copies of that macromolecule in the particle [59,130]. Adding atoms of all elements in a particle gives its molecular formula [59,130]. To obtain the empirical formula, the numbers of atoms of all constituent elements are divided by the number of carbon atoms [59,130]. Finally, to calculate the macromolecular composition, the molar mass of a macromolecule is multiplied with its number of copies to find the total mass of that macromolecule in the macromolecular assembly. After that, the macromolecules are sorted into types (DNA, RNA, proteins, lipids and carbohydrates) and mass fractions of every type are calculated.

2.3. Patel–Erickson Model

Standard enthalpies of the formation of Norovirus particles, genomic RNA, and VP1 capsid protein were calculated based on empirical formulas with the Patel–Erickson model, as described in [133,134,135]. The Patel–Erickson model gives enthalpy of live matter based on its elemental composition [133,134,136,137]. Based on the empirical formula, the degree of reduction, E, is calculated with the equation

$$E=4n_C+n_H-2n_O-0n_N+5n_P+6n_S$$

(1)

where n_C, n_H, n_O, n_N, n_P, and n_S are numbers of C, H, O, N, P, and S atoms in the empirical formula, respectively [133,134,138]. Then, the degree of reduction is used to find standard enthalpy of combustion, Δ_CH⁰, of live matter with the equation [133,134]

$${∆}_C{H}^0\left(bio\right)=-111.14{\displaystyle \frac{kJ}{C-mol}}·E$$

(2)

After that, Δ_CH⁰ is used to find the standard enthalpy of formation, Δ_fH⁰, of live matter, with Hess’s law [134,139,140].

$${∆}_f{H}^0\left(bio\right)=n_C{∆}_f{H}^0\left(C{O}_2\right)+{\displaystyle \frac{n_H}{2}}{∆}_f{H}^0\left(H_{2}O\right)+{\displaystyle \frac{n_P}{4}}{∆}_f{H}^0\left(P_4{O}_{10}\right)+n_S{∆}_f{H}^0\left(S{O}_3\right)-{∆}_C{H}^0$$

(3)

The Patel–Erickson model is sometimes called Thornton’s rule, since it is based on Thornton’s theory of combustion [141]. Thornton found that the energy released by combustion comes from acceptance of electrons by oxygen [141]. This is why it is proportional to the number of electrons transferred to oxygen during the process, which is represented by E [133,134].

2.4. Battley Model

Standard molar entropies of Norovirus particles, genomic RNA and VP1 capsid protein were calculated, based on empirical formulas, with the Battley model, as described in [142,143]. The Battley model gives entropy of live matter, based on its elemental composition [142,143]. Standard molar entropy is calculated from the empirical formula with the equation

$$S_m^0\left(bio\right)=0.187{\sum }_J{\displaystyle \frac{S_m^0\left(J\right)}{a_J}}{n}_J$$

(4)

where S⁰_m(J) is standard molar entropy of element J in its standard state elemental (pure) form, a_J number of atoms of element J in its standard state elemental form, and n_J the number of atoms of element J in the empirical formula of live matter [142,143]. Standard entropy of formation, Δ_fS⁰, can be found from the following equation [142,143]:

$${∆}_f{S}^0\left(bio\right)=-0.813{\sum }_J{\displaystyle \frac{S_m^0\left(J\right)}{a_J}}{n}_J$$

(5)

The Battley model comes from the additivity property of entropy. Entropy of a complex system is a sum of contributions of its parts. If live matter consists of different elements, then its entropy is proportional to the sum of entropies of the constituent elements (the sum term). The sum term is multiplied by a constant (0.187 or −0.813) to take into account the changed environment of the elements (live matter vs. pure form).

Standard Gibbs energy of formation, Δ_fG⁰, of live matter is found from Δ_fH⁰ and Δ_fS⁰, with the equation

$${∆}_f{G}^0\left(bio\right)={∆}_f{H}^0\left(bio\right)-T{∆}_f{S}^0\left(bio\right)$$

(6)

where T is temperature [144,145,146].

2.5. Biosynthesis Reactions

Biosynthesis reactions of Norovirus particles, genomic RNA and VP1 capsid protein were calculated, based on their empirical formulas, with the rules of stoichiometry [147,148]. Biosynthesis reactions are macrochemical equations that explain conversion of nutrients into new live matter in metabolism [53,139,149,150,151,152]. The general biosynthesis reaction of viruses has the form [153,154,155]

(Amino acid) + O₂ + HPO₄²⁻ + HCO₃⁻ → (Bio) + SO₄²⁻ + H₂O + HCO₃⁻ + H₂CO₃

(7)

The nutrients for biosynthesis of virus live matter include amino acids with the empirical formula CH_1.798O_0.4831N_0.2247S_0.022472 (source of energy, carbon, nitrogen and sulfur), O₂ (electron acceptor) and HPO₄²⁻ (source of phosphorus) [153,154,155]. Main products of biosynthesis are new live matter (bio) with the empirical formula CH_nHO_nON_nNP_nPS_nS, SO₄²⁻ (excess sulfur removal) and H₂CO₃ (oxidized carbon removal) [153,154,155]. Moreover, the H⁺ ions produced during biosynthesis are absorbed by the bicarbonate buffer made of HCO₃⁻ and H₂CO₃ [153,154,155].

2.6. Thermodynamic Properties of Biosynthesis

Thermodynamic properties of biosynthesis were calculated with Hess’s law [144,145,156,157]. They were calculated by application of Hess’s law to biosynthesis reactions and thermodynamic properties of live matter. Thermodynamic properties of biosynthesis include standard enthalpy of biosynthesis, Δ_bsH⁰, standard entropy of biosynthesis, Δ_bsS⁰, and standard Gibbs energy of biosynthesis, Δ_bsG⁰ [53,150,158,159]. They were found with the following equations

$${∆}_{bs}{H}^0={\sum }_{products}\nu {∆}_f{H}^0-{\sum }_{reactants}\nu {∆}_f{H}^0$$

(8)

$${∆}_{bs}{S}^0={\sum }_{products}\nu S_m^o-{\sum }_{reactants}\nu S_m^o$$

(9)

$${∆}_{bs}{G}^0={\sum }_{products}\nu {∆}_f{G}^0-{\sum }_{reactants}\nu {∆}_f{G}^0$$

(10)

where Δ_fH⁰ is standard enthalpy of formation, S_m⁰ standard molar entropy, Δ_fG⁰ standard Gibbs energy of formation and ν represents a stoichiometric coefficient [53,134,139,150,153,154,155,160].

2.7. Thermodynamic Properties of Binding

The interaction of a virus with its host cell begins at the host cell membrane [161]. There, the virus antigen binds to the host cell receptor [161]. Antigen-receptor binding is a chemical process similar to protein ligand binding [21,162]. Antigen-receptor binding can be represented with the chemical reaction

(An) + (Re) ⇄ (An-Re)

(11)

where (An) is the free virus antigen, (Re) free host receptor and (An-Re) the antigen-receptor complex [21,162]. This reaction can, like all other chemical reactions, be analyzed with the laws of chemical thermodynamics and is characterized with thermodynamic properties. The dissociation equilibrium constant, K_d, is given by the equation

$$K_d={\displaystyle \frac{\left[An\right]\left[Re\right]}{\left[An-Re\right]}}$$

(12)

where [An] is the concentration of the free virus antigen, [Re] the concentration of the free host receptor and [An − Re] the concentration of the antigen-receptor complex [21,162]. K_d for antigen-receptor binding can be measured experimentally with surface plasmon resonance [163] or non-competitive ELISA approach [164]. From K_d, the binding equilibrium constant, K_B, can be determined from the equation [21,162]

$$K_B={\displaystyle \frac{\left[An-Re\right]}{\left[An\right]\left[Re\right]}}={\displaystyle \frac{1}{K_d}}$$

(13)

Based on K_B, it is possible to find standard Gibbs energy of binding, Δ_BG⁰, with the equation [21,162]

$${∆}_B{G}^0=-RT\ln K_B$$

(14)

3. Results

Table 1. Molecular formulas of the Norovirus particle, genomic RNA and VP1 capsid protein. The molecular formulas have the general form C_mCH_mHO_mON_mNP_mPS_mS, where m_C, m_H, m_O, m_N, m_P and m_S are the numbers of C, H, O, N, P and S atoms in the molecular formula, respectively, which are given in this table. The table also shows molar masses of entire molecules/structures, Mr (tot).

Name	mC	mH	mO	mN	mP	mS	Mr (kDa)
Norovirus particle	548,504	817,571	193,862	157,282	7525	3060	13,048
Norovirus RNA	71,684	88,571	52,202	28,762	7525	0	2421.4
Norovirus VP1	2649	4050	787	714	0	17	59.035

presents molecular formulas and molar masses of the Norovirus particle, genomic RNA and VP1 capsid protein. Molecular formulas show the total numbers of atoms of all constituent elements in a molecule or macromolecular assembly (e.g., virus particle). The molecular formulas and molar masses were calculated with the atom counting method, based on genetic and protein sequences and virus morphology, as described in [59,130]. The molecular formula of the Norovirus particle is C₅₄₈₅₀₄H₈₁₇₅₇₁O₁₉₃₈₆₂N₁₅₇₂₈₂P₇₅₂₅S₃₀₆₀, with a molar mass of 13,048 kDa. The molecular formula of the Norovirus genomic RNA is C₇₁₆₈₄H₈₈₅₇₁O₅₂₂₀₂N₂₈₇₆₂P₇₅₂₅, with a molar mass of 2421.4 kDa. The molecular formula of the Norovirus VP1 capsid protein is C₂₆₄₉H₄₀₅₀O₇₈₇N₇₁₄S₁₇, with a molar mass of 59.035 kDa.

Table 2. Macromolecular composition of the Norovirus particle.

Name	Content (%-Mass)
RNA	18.6
Proteins	81.4

gives the macromolecular composition of the Norovirus particle. The macromolecular composition was calculated with the atom counting method, based on genetic and protein sequences and virus morphology, as described in [59,130] The norovirus particle consists of 18.6% RNA and 81.4% proteins (by mass).

Table 3. Empirical formulas of the Norovirus particle, genomic RNA, and VP1 capsid protein. Empirical formulas show the number of atoms of each element present per carbon atom. The empirical formulas have the general form CH_nHO_nON_nNP_nPS_nS, where n_H, n_O, n_N, n_P and n_S are the numbers of H, O, N, P and S atoms in the empirical formula, respectively, which are given in this table. The table also gives molar masses of empirical formulas, Mr.

Name	nH	nO	nN	nP	nS	Mr (g/C-mol)
Norovirus particle	1.4905	0.3534	0.2867	0.013719	0.005579	23.79
Norovirus RNA	1.2356	0.7282	0.4012	0.104975	0.000000	33.78
Norovirus VP1	1.5289	0.2971	0.2695	0.000000	0.006418	22.29

shows the empirical formulas of the Norovirus particle, genomic RNA and VP1 capsid protein. Empirical formulas show the numbers of atoms of constituent elements in a molecule or macromolecular assembly (e.g., virus particle) per carbon atom. The empirical formulas and their molar masses were calculated with the atom counting method, based on genetic and protein sequences and virus morphology, as described in [59,130]. The empirical formula of the Norovirus particle is CH_1.4905O_0.3534N_0.2867P_0.013719S_0.005579, with a molar mass of 23.79 g/C-mol. The empirical formula of the Norovirus genomic RNA is CH_1.2356O_0.7282N_0.4012P_0.104975, with a molar mass of 33.78 g/C-mol. The empirical formula of the Norovirus VP1 capsid protein is CH_1.5289O_0.2971N_0.2695S_0.006418, with a molar mass of 22.29 g/C-mol.

Table 4. Thermodynamic properties of Norovirus particles, genomic RNA, and VP1 capsid protein: standard enthalpy of formation, Δ_fH⁰, standard molar entropy, S_m⁰, and standard Gibbs energy of formation, Δ_fG⁰.

Name	ΔfH0 (kJ/C-mol)	Sm0 (J/C-mol K)	ΔfG0 (kJ/C-mol)
Norovirus particle	−76.06	31.30	−35.49
Norovirus RNA	−170.69	38.09	−121.32
Norovirus VP1	−61.83	30.28	−22.58

gives thermodynamic properties of live matter of Norovirus particles, genomic RNA and VP1 capsid protein. These include standard enthalpy of formation, Δ_fH⁰, standard molar entropy, S_m⁰, and standard Gibbs energy of formation, Δ_fG⁰. They were calculated with the Patel–Erickson model [133,134] and Battley model [142,143], based on the empirical formulas from Table 3. Like the empirical formulas, the thermodynamic properties of live matter (Δ_fH⁰, S_m⁰ and Δ_fG⁰) are inherent properties of live matter and do not depend on the way that live matter produced by organisms (biosynthesis reactions). For the Norovirus particle, standard enthalpy of formation is −76.06 kJ/C-mol, standard molar entropy is 31.30 kJ/C-mol and standard Gibbs energy of formation is −35.49 kJ/C-mol. For the Norovirus genomic RNA, standard enthalpy of formation is −170.69 kJ/C-mol, standard molar entropy is 38.09 kJ/C-mol and standard Gibbs energy of formation is −121.32 kJ/C-mol. For the Norovirus VP1 capsid protein, standard enthalpy of formation is −61.83 kJ/C-mol, standard molar entropy is 30.28 kJ/C-mol and standard Gibbs energy of formation is −22.58 kJ/C-mol.

Table 5. Biosynthesis stoichiometries of Norovirus particles, genomic RNA and VP1 capsid protein. The general biosynthesis reaction has the following form: (Amino acid) + O₂ + HPO₄²⁻ + HCO₃⁻ → (Bio) + SO₂²⁻ + H₂O + HCO₃⁻ + H₂CO₃. “Amino acid” represents amino acids with the empirical formula CH_1.798O_0.4831N_0.2247S_0.022472. “Bio” represents the empirical formula of live matter from Table 1.

Name	Reactants				→	Products
	Amino acid	O2	HPO42−	HCO3−		Bio	SO42−	H2O	HCO3−	H2CO3
Norovirus particle	1.2760	0.3628	0.0137	0.0188	→	1	0.0231	0.1232	0.0000	0.2948
Norovirus RNA	1.7855	1.1408	0.1050	0.0000	→	1	0.0401	0.3190	0.1297	0.6558
Norovirus VP1	1.1994	0.2459	0.0000	0.0411	→	1	0.0205	0.0937	0.0000	0.2405

presents stoichiometric coefficients for the biosynthesis reactions of the Norovirus particles, genomic RNA and VP1 capsid protein. They were calculated with stoichiometry, based on the empirical formulas from Table 3. Biosynthesis reactions show how new live matter is produced by organisms from nutrients. The biosynthesis reaction of the Norovirus has the general form (Amino acid) + O₂ + HPO₄²⁻ + HCO₃⁻ → (Bio) + SO₂²⁻ + H₂O + HCO₃⁻ + H₂CO₃, where (Amino acid) represents amino acids with the empirical formula CH_1.798O_0.4831N_0.2247S_0.022472 and (Bio) represents the empirical formula of live matter.

Table 6. Thermodynamic properties of biosynthesis of Norovirus particles, genomic RNA and VP1 capsid protein: standard enthalpy of biosynthesis, Δ_bsH⁰, standard entropy of biosynthesis, Δ_bsS⁰, and standard Gibbs energy of biosynthesis, Δ_bsG⁰. Thermodynamic properties of biosynthesis are changes in thermodynamic properties brought about by biosynthesis reactions.

Name	ΔbsH0 (kJ/C-mol)	ΔbsS0 (J/C-mol K)	ΔbsG0 (kJ/C-mol)
Norovirus particle	−170.79	−27.12	−162.85
Norovirus RNA	−519.57	−104.02	−489.79
Norovirus VP1	−118.35	−15.56	−113.70

gives thermodynamic properties of biosynthesis of Norovirus particles, genomic RNA and VP1 capsid protein. They were calculated with Hess’s law [144,145], based on the biosynthesis reactions (from Table 5) and empirical formulas (from Table 3). Thermodynamic properties of biosynthesis are changes in thermodynamic properties during biosynthesis reactions. They are thermodynamic properties of the biosynthesis process and show how thermodynamic properties change during biosynthesis in organisms. They include standard enthalpy of biosynthesis, Δ_bsH⁰, standard entropy of biosynthesis, Δ_bsS⁰, and standard Gibbs energy of biosynthesis, Δ_bsG⁰. For the Norovirus particle, standard enthalpy of biosynthesis is −170.79 kJ/C-mol, standard entropy of biosynthesis −27.12 J/C-mol K and standard Gibbs energy of biosynthesis is −162.85 kJ/C-mol. For the Norovirus genomic RNA, standard enthalpy of biosynthesis is −519.57 kJ/C-mol, standard entropy of biosynthesis −104.02 J/C-mol K and standard Gibbs energy of biosynthesis is −489.79 kJ/C-mol. For the Norovirus VP1 capsid protein, standard enthalpy of biosynthesis is −118.35 kJ/C-mol, standard entropy of biosynthesis −15.56 J/C-mol K and standard Gibbs energy of biosynthesis is −113.70 kJ/C-mol.

Table 7. Thermodynamic properties of antigen-receptor binding of Murine norovirus (MNoV): dissociation equilibrium constant, K_d; binding equilibrium constant, K_B; and standard Gibbs energy of binding, Δ_BG⁰. EGTA denotes ethylene glycol-bis(β-aminoethyl ether)-N,N,N′,N′-tetraacetic acid, while GCDCA denotes glycochenodeoxycholic acid. The K_d values were taken from [128,129].

Interaction	Conditions	Kd (M)	KB (M−1)	ΔBG0 (kJ/mol)
VP1 protruding (P) domain with CD300lf receptor	Alone	2.19 × 10−4	4.57 × 103	−20.89
	Ca2+	2.45 × 10−5	4.08 × 104	−26.32
	Mg2+ and EGTA	2.43 × 10−5	4.12 × 104	−26.34
	Ca2+ and GCDCA	1.20 × 10−5	8.31 × 104	−28.08

shows thermodynamic properties of antigen-receptor binding of the Norovirus. They were calculated with chemical thermodynamics [144,145], based on literature K_d values [128,129]. Thermodynamic properties of binding are changes in thermodynamic properties during the process of binding of the virus antigen to the host cell receptor. For binding of the Norovirus VP1 protruding domain to the CD300lf receptor alone (in the absence of Ca²⁺, Mg²⁺ and GCDCA), the binding equilibrium constant is 4.57 × 10³ M⁻¹ and standard Gibbs energy of binding is −20.89 kJ/mol. For binding of the Norovirus VP1 protruding domain to the CD300lf receptor in the presence of Ca²⁺ ions, the binding equilibrium constant is 4.08 × 10⁴ M⁻¹ and standard Gibbs energy of binding is −26.32 kJ/mol. For binding of the Norovirus VP1 protruding domain to the CD300lf receptor in the presence of Mg²⁺ and EGTA, the binding equilibrium constant is 4.12 × 10⁴ M⁻¹ and standard Gibbs energy of binding is −26.34 kJ/mol. For binding of the Norovirus VP1 protruding domain to the CD300lf receptor in the presence of Ca²⁺ and GCDCA, the binding equilibrium constant is 8.31 × 10⁴ M⁻¹ and standard Gibbs energy of binding is −28.08 kJ/mol.

4. Discussion

Norovirus is a major cause of viral gastroenteritis worldwide [1,2] and represents an emerging pathogen that poses a risk for human health [3]. Norovirus, like other viruses, lacks cellular metabolic machinery and performs its lifecycle in host cells [165,166,167,168]. Viruses hijack their host cell metabolic machinery to perform their own metabolic processes and multiply [169,170,171,172]. Virus–host interactions are processes performed by organisms, which are greatly dependent on energetic constraints and can therefore be analyzed with the methodology of biothermodynamics [15,22,70,173,174].

Organisms represent open thermodynamic systems with the property of growth [53,154,175,176]. These systems consist of live matter, which is separated from the environment [177,178,179]. They perform biological processes, like metabolism and multiplication [60]. To analyze biological processes from the perspective of biothermodynamics, it is necessary to find empirical formulas and thermodynamic properties of live matter [180,181,182]. Therefore, the biothermodynamic analysis of the Norovirus lifecycle begins with determination of its molecular formula, empirical formula and thermodynamic properties of live matter. Based on these, a model of multiplication of Norovirus inside its host cells will be developed, based on biosynthesis reactions and thermodynamic properties of biosynthesis. Moreover, thermodynamic properties of antigen-receptor binding will be determined. The thermodynamic properties of binding and biosynthesis will be used to analyze the interaction of the Norovirus with its host cells, as well as with the Rotavirus, based on nonequilibrium thermodynamics.

4.1. Chemical and Thermodynamic Properties of the Norovirus

The molecular formula of the Norovirus particle is C₅₄₈₅₀₄H₈₁₇₅₇₁O₁₉₃₈₆₂N₁₅₇₂₈₂P₇₅₂₅S₃₀₆₀ (Table 1). The molecular formulas of the constituents of the Norovirus particle are: C₇₁₆₈₄H₈₈₅₇₁O₅₂₂₀₂N₂₈₇₆₂P₇₅₂₅ for the genomic RNA and C₂₆₄₉H₄₀₅₀O₇₈₇N₇₁₄S₁₇ for the VP1 capsid protein (Table 1). The molar mass of the entire norovirus particle is 13 MDa. The molar mass of the VP1 capsid protein was found to be 59 kDa (Table 1). This is in good agreement with the experimental value of 58–60 kDa [183,184].

Molecular formulas of other viruses have been reported in the literature. The molecular formula of the Poliovirus particle is C₃₃₂₆₅₂H₄₉₂₃₈₈N₉₈₂₄₅O₁₃₁₁₉₆P₇₅₀₁S₂₃₄₀ [42,185]. The Poliovirus particle has a diameter of 25 to 30 nm [186]. The molecular formula of the Rotavirus particle is C_4589530H_7046535O_1530010N_1249723P₃₇₁₂₄S₃₄₅₆₀ [14], which has a molar mass of 106.47 MDa [14] and diameter of 70 nm [187]. The molecular formula of the West Nile virus is C_{1.54 × 10⁶}H_{2.71 × 10⁶}O_{4.01 × 10⁵}N_2.26×10⁵P_3.03×10⁴S_5.76×10³ [154], which has a molar mass of 31.91 MDa [154] and a diameter of 50 nm [188]. The molecular formula of the virus particle of the JN.1 variant of SARS-CoV-2 is C_1.01×10⁷H_1.66×10⁷O_2.87×10⁶N_2.32×10⁶P_6.51×10⁴S_3.80×10⁴ [24], which has a molar mass of 219.7 MDa [24] and a diameter of 60–140 nm [189]. On the other hand, the molecular formula of the Norovirus particle is C₅₄₈₅₀₄H₈₁₇₅₇₁O₁₉₃₈₆₂N₁₅₇₂₈₂P₇₅₂₅S₃₀₆₀, with a molar mass of 13 MDa (Table 1). Its diameter is 27 nm [190]. Therefore, it can be seen that every virus has a characteristic molecular formula. This means that the molecular and empirical formulas can be used for rapid identification of viruses, especially for emerging viruses when little information is available about their properties. This is in agreement with the result that single-particle ICP-MS can be used for identification of viruses [191].

Based on the molecular formulas, empirical formulas of the norovirus particle, RNA and VP1 capsid protein were calculated for the first time in this research and are shown in Table 3. Empirical formulas are important since they can be used to analyze multiplication of viruses through biosynthesis reactions, as will be discussed below. The empirical formula of the Norovirus particle is CH_1.4905O_0.3534N_0.2867P_0.013719S_0.005579 (Table 3). The empirical formula of the constituents of the Norovirus particle are CH_1.2356O_0.7282N_0.4012P_0.104975 for the genomic RNA and CH_1.5289O_0.2971N_0.2695S_0.006418 for the VP1 capsid protein (Table 3). The empirical formula of the Norovirus particle resembles more closely that of the VP1 capsid protein in the content of H, O and S. The reason for this is that the protein is present in a greater amount in the virus particle than the RNA (Table 2). However, the virus particle also contains P, which is absent in proteins, but is present in the RNA.

Empirical formulas have been reported in the literature for other microorganisms. The empirical formula of the nucleocapsid of XBB.1.5 Kraken variant of SARS-CoV-2 is CH_1.573540O_0.342703N_0.312374P_0.00603S_0.00336 [153]. The empirical formula of the bacterium Escherichia coli is CH_1.918O_0.528N_0.257P_{1.76×10⁻²}S_{5.54×10⁻³}K_{5.87×10⁻³}Mg_{2.07×10⁻³}Ca_{8.36×10⁻⁴}Mn_{9.89×10⁻⁶}Fe_{7.82×10⁻⁵}Cu_{1.62×10⁻⁶}Zn_{2.41×10⁻⁵} [192]. The empirical formula of the yeast Saccharomyces cerevisiae is CH_1.613O_0.557N_0.158P_0.012S_0.003K_0.022Mg_0.003Ca_0.001 [134]. The empirical formula of the filamentous fungus Penicillium chrysogenum is CH_2.026O_0.511N_0.185P_{9.15×10⁻³}S_{4.17×10⁻³}K_{3.45×10⁻³}Mg_{1.47×10⁻³}Ca_{3.69×10⁻⁴}Mn_{1.08×10⁻⁵}Fe_{9.51×10⁻⁵}Cu_{1.24×10⁻⁶}Zn_{2.15×10⁻⁵} [192]. Therefore, every microorganism species has a characteristic empirical formula different from those of other microorganisms.

Based on the empirical formulas, thermodynamic properties of live matter were determined for the first time for Norovirus particles, genomic RNA and VP1 capsid protein, which are shown in Table 4. The Norovirus particle is characterized with a standard Gibbs energy of formation of −35.49 kJ/C-mol. Gibbs energies of the formation of Norovirus particle components are −121.32 kJ/C-mol for the genomic RNA and −22.58 kJ/C-mol for the VP1 capsid protein. Gibbs energy of formation of the VP1 capsid protein is greater (less negative) than that of the genomic RNA. This means that the VP1 capsid protein has a greater usable energy content than that of the genomic RNA.

Every virus species has a specific genetic and protein sequences. This us why it has an empirical formula different from other viruses. The different empirical formulas lead to different thermodynamic properties of live matter. Empirical formulas and thermodynamic properties of live matter are used to formulate biosynthesis reactions and calculate thermodynamic properties of biosynthesis, which show the energetic requirements and rates of virus multiplication. This means that biothermodynamic methodology has a potential to show how different genetic and protein sequences viruses can lead to different rates of multiplication and pathogenicity.

4.2. Virus–Host Interactions of the Norovirus with Enterocytes

Based on the determined empirical formulas and thermodynamic properties of the Norovirus, a biothermodynamic model of the interactions of Norovirus with its host cells will be developed. This will be carried out with biosynthesis equations, thermodynamic properties of biosynthesis and phenomenological equations.

Biosynthesis reactions are macrochemical reactions that show how nutrients are transformed into new live matter by organisms [150,193]. The biosynthesis reaction of the Norovirus particles is

1.2760 CH_1.798O_0.4831N_0.2247S_0.022472 + 0.3628 O₂ + 0.0137 HPO₄²⁻ + 0.0188 HCO₃⁻ → CH_1.4905O_0.3534N_0.2867P_0.013719S_0.005579 + 0.0231 SO₂²⁻ + 0.1232 H₂O + 0.2948 H₂CO₃

(15)

where CH_1.798O_0.4831N_0.2247S_0.022472 represents amino acids and CH_1.4905O_0.3534N_0.2867P_0.013719S_0.005579 is the empirical formula of newly synthetized Norovirus particles (Table 5).

Biosynthesis reactions were also found for the constituents of the Norovirus particles: RNA and VP1 capsid proteins. The biosynthesis reaction of the genomic RNA of the Norovirus is

1.7855 CH_1.798O_0.4831N_0.2247S_0.022472 + 1.1408 O₂ + 0.1050 HPO₄²⁻ → CH_1.2356O_0.7282N_0.4012P_0.104975 + 0.0401 SO₂²⁻ + 0.3190 H₂O + 0.1297 HCO₃⁻ + 0.6558 H₂CO₃

(16)

where CH_1.2356O_0.7282N_0.4012P_0.104975 is the empirical formula of Norovirus genomic RNA (Table 5). The biosynthesis reaction of the Norovirus VP1 capsid protein is

1.1994 CH_1.798O_0.4831N_0.2247S_0.022472 + 0.2459 O₂ + 0.0411 HCO₃⁻ → CH_1.5289O_0.2971N_0.2695S_0.006418 + 0.0205 SO₂²⁻ + 0.0937 H₂O + 0.2405 H₂CO₃

(17)

where CH_1.5289O_0.2971N_0.2695S_0.006418 is the empirical formula of the Norovirus VP1 capsid protein (Table 5). The biosynthesis reaction of the Norovirus particle is more similar to that of the VP1 capsid protein than that of the genomic RNA, in the stoichiometric coefficients for amino acids, O₂ and SO₂²⁻. The reason for this is that the VP1 capsid proteins comprise a larger portion of the Norovirus particle. This means that biosynthesis of the VP1 protein takes a major part of the nutrients required to produce the Norovirus particle. However, the biosynthesis reaction of the Norovirus particle also contains HPO₄²⁻, which is not present in the biosynthesis reaction of the VP1 capsid protein, but is needed to produce the genomic RNA.

Biosynthesis reactions lead to change in Gibbs energy, which is called Gibbs energy of biosynthesis [53,150]. Gibbs energy of biosynthesis of the Norovirus is −162.85 kJ/C-mol (Table 6). Norovirus replicates in the intestinal tissue [194]. The biosynthesis reaction of the small intestine tissue is

0.7961 CH_1.798O_0.4831N_0.2247S_0.022472 + 0.3211 CH₂O + 0.0028 HPO₄²⁻ + 0.0252 HCO₃⁻ + 0.0038 Na⁺ + 0.0044 K⁺ + 0.0024 Cl⁻ → CH_1.6480O_0.2310N_0.1789P_0.0028S_0.0054Na_0.0038K_0.0044Cl_0.0024 + 0.0125 SO₂²⁻ + 0.0843 H₂O + 0.1423 H₂CO₃

(18)

where CH₂O is the empirical formula of carbohydrates and CH_1.6480O_0.2310N_0.1789P_0.0028S_0.0054Na_0.0038K_0.0044Cl_0.0024 is the empirical formula of live matter of the small intestine tissue [43]. Gibbs energy of biosynthesis of the small intestine tissue is −16.85 kJ/C-mol [43]. Thus, the Gibbs energy of the biosynthesis of the Norovirus is much more negative than that of its host tissue.

The biosyntheses of new virus particles and host cell building blocks are chemical reactions that are out of equilibrium [17,53,54]. These reactions (Equations (15) and (18)) share the same reactants, like amino acids. This means that new virus particles and host cell building blocks are produced from the same precursors [43,195,196]. A precursor molecule can either be incorporated into a new virus particle or a host cell structure. Since the amount of precursors is limited, the virus and its host cell must compete [8,197,198]. Therefore, the biosynthesis of new virus particles and host cell building blocks are competitive chemical reactions.

Since virus multiplication and biosynthesis of host cell building blocks are nonequilibrium processes, they can be analyzed with the methodology of nonequilibrium thermodynamics [54,70,199]. Phenomenological equations belong to nonequilibrium thermodynamics and show how rates of processes depend on their driving forces [54,177]. Gibbs energy of biosynthesis represents the driving force of the biosynthesis process [54,155,200]. The biosynthesis phenomenological equation shows how biosynthesis rate, r_bs, depends on Gibbs energy of biosynthesis, Δ_bsG:

$$r_{bs}=-{\displaystyle \frac{L_{bs}}{T}}{∆}_{bs}G$$

(19)

where L_bs is the biosynthesis phenomenological coefficient [154,179,201]. Due to the minus sign, a more negative Gibbs energy of biosynthesis implies a greater biosynthesis rate.

Gibbs energy of biosynthesis of the Norovirus is −162.85 kJ/C-mol (Table 6), while that of the small intestine tissue is −16.85 kJ/C-mol [43]. Thus, the Norovirus has a much more negative Gibbs energy of biosynthesis than its host tissue. This means that, according to the biosynthesis phenomenological equation, it can achieve a much greater biosynthesis rate. Due to the greater rate of the Norovirus biosynthesis reaction, more precursors will be consumed by the biosynthesis of new virus particles. Additionally, the host cell metabolic machinery will produce more virus particles than host cell building blocks. In that way, the virus will hijack the host cell metabolic machinery for its multiplication.

Due to the more negative Gibbs energy of biosynthesis, the virus will have a higher biosynthesis rate. Due to the higher biosynthesis rate, more resources will be consumed by the production of new virus particles and the host cell metabolic machinery will produce more new virus particles than host cell building blocks. Since the host cell metabolic machinery produces mostly new virus particles, it is hijacked by the virus.

Except for biosynthesis precursors, viruses also compete with their host cells for metabolic energy, which comes in the form of ATP [202,203]. Viral multiplication and host cell metabolic processes use the common stock of cellular ATP. Therefore, the virus has to compete with its host cell for ATP. Fast replicating viruses may even hijack and compartmentalize the energy-producing enzymes to provide a readily available source of ATP for viral replication [202]. Moreover, some viruses hijack cellular metabolic enzymes to reprogram cell metabolism and stimulate ATP production in processes like glycolysis [203]. However, ATP itself is not the ultimate source of energy in a cell. Energy comes from degradation of nutrients in catabolic processes [53,134,150]. ATP just transfers energy from catabolic to anabolic processes [53,150,204]. The generation of more ATP causes the upregulation of catabolism. Faster catabolism is needed to generate more ATP, which is needed for virus replication. However, the virus and its host cell share the cellular metabolic machinery. This means that increase in catabolism rate generates more ATP, which can be used not only by the virus, but also by the host cell. A higher catabolism rate and more ATP provide a greater potential for biosynthesis processes. However, this potential still has to be exploited by the virus. If a virus has a Gibbs energy of biosynthesis equal to that of the host cell, then the excess ATP can be used equally to drive the biosynthesis of new viruses and host cell building blocks. In order to exploit the excess ATP, the virus must have a greater biosynthesis rate. A greater biosynthesis rate implies that the biosynthesis of new virus particles will proceed at a greater rate than that of host cell building blocks. Due to the greater reaction rate, the rate of consumption of ATP by the virus will be greater than that of its host cell. In this way, the virus will be able to exploit the increase in ATP production by catabolism.

In order to perform its lifecycle inside a host cell, a virus must enter the host cell [161]. The virus achieves this through the process of antigen-receptor binding [18,19]. Antigen-receptor binding represents a chemical process [10,15,22]. The driving force of antigen-receptor binding is Gibbs energy of binding [21]. The rate of antigen-receptor binding, r_B, depends on Gibbs energy of binding, Δ_BG, according to the binding phenomenological equation

$$r_B=-{\displaystyle \frac{L_B}{T}}{∆}_{B}G$$

(20)

where L_B is the binding phenomenological coefficient [21]. A virus with a more negative Gibbs energy of binding will achieve a greater binding rate [21,153,173]. This will allow it to enter its host cells more efficiently [21,153,173]. Gibbs energy of binding of the Norovirus is between −20.89 and −28.08 kJ/mol (Table 7). The negative Gibbs energy of binding means that the antigen-receptor binding is a spontaneous process, and the virus will be able to infect a host cell that possesses the appropriate receptor.

Susceptibility and permissiveness are important properties of interactions between viruses and their host cells. Susceptibility shows the ability of a virus to enter into its host cell [205,206,207]. Permissiveness represents the potential of a virus to multiply inside the host cell [205,206]. To achieve a successful infection, a virus must enter a cell that is susceptible and permissive [205,206]. Susceptibility and permissiveness can be analyzed with the methodology of biothermodynamics. Gibbs energy of binding shows the ability of viruses to enter into host cells. A virus must have a negative Gibbs energy of binding to enter into a host cell. A more negative Gibbs energy of binding implies a greater rate of binding and entry into host cells, according to the binding phenomenological equation. This means that Gibbs energy of binding indicates susceptibility. Additionally, Gibbs energy of biosynthesis shows the ability of a virus to multiply inside a host cell. A virus must have a more negative Gibbs energy of binding than its host cell to multiply, according to the biosynthesis phenomenological equation. This means that Gibbs energy of biosynthesis indicates permissiveness. Therefore, biothermodynamics can be used to determine susceptibility and permissiveness of viruses, based on their genetic sequences, protein sequences and morphologies. This means that biothermodynamics can show susceptibility and permissiveness of cells to viruses when little information about them is available. This means that biothermodynamics methodology can be a useful tool for analysis of emerging viruses.

4.3. Virus–Virus Interaction of Norovirus with Rotavirus

Noroviruses and Rotaviruses are among leading causes of acute gastroenteritis worldwide [208,209,210]. The host cells of the Norovirus and Rotavirus are enterocytes [194,211]. Therefore, it is interesting to analyze what happens when the Norovirus and Rotavirus circulate in a population, at the same time. Gibbs energy of binding of the Rotavirus is between −24.69 and −22.20 kJ/mol [14]. The biosynthesis reaction of the Rotavirus is

1.2117 CH_1.798O_0.4831N_0.2247S_0.022472 + 0.2659 O₂ + 0.0081 HPO₄²⁻ + 0.0232 HCO₃₋ → CH_1.5354O_0.3334N_0.2723P_0.008089S_0.007530 + 0.0197 SO₂²⁻ + 0.1022 H₂O + 0.2350 H₂CO₃

(21)

where CH_1.5354O_0.3334N_0.2723P_0.008089S_0.007530 is the empirical formula of newly formed virus particles [14]. Gibbs energy of biosynthesis of the Rotavirus is −120.95 kJ/C-mol [14]. On the other hand, Norovirus is characterized by a Gibbs energy of binding between −20.89 and −28.08 kJ/mol (Table 7) and Gibbs energy of biosynthesis of −162.85 kJ/C-mol (Table 6). Therefore, Norovirus and Rotavirus have similar Gibbs energies of binding (Figure 1). This means that Norovirus and Rotavirus will enter into host cells at similar rates. However, Gibbs energy of biosynthesis of Norovirus is more negative than that of Rotavirus (Figure 2). This means that Norovirus will multiply faster in host cells. This means that if Norovirus and Rotavirus circulate in the population at the same time, Norovirus will have an advantage over Rotavirus in multiplication inside host cells, while both viruses will enter into host cells at the same rate. This means that the Norovirus should have a slight advantage over Rotavirus. However, this is not enough for Norovirus to suppress Rotavirus, and both viruses will be present in the population. Thus, Norovirus and Rotavirus should be able to perform coinfection. Indeed, Norovirus and Rotavirus have been reported in the literature to perform coinfection [212,213,214,215,216,217,218,219].

5. Conclusions

The empirical formula and thermodynamic properties of Norovirus were determined for the first time. The empirical formula of the Norovirus particle is CH_1.4905O_0.3534N_0.2867P_0.013719S_0.005579. The empirical formula of the Norovirus genomic RNA is CH_1.2356O_0.7282N_0.4012P_0.104975, while that of the VP1 capsid protein is CH_1.5289O_0.2971N_0.2695S_0.006418. Gibbs energy of formation of the Norovirus particle is −35.49 kJ/C-mol. The empirical formula and Gibbs energy of formation of Norovirus are different from those of other microorganisms. Norovirus has a Gibbs energy of binding between −20.89 and −28.08 kJ/mol.

A biothermodynamic analysis of the interactions of Norovirus with its host cells was conducted. Gibbs energy of biosynthesis of the Norovirus is −162.85 kJ/C-mol. On the other hand, Gibbs energy of biosynthesis of enterocytes is −16.85 kJ/C-mol. Therefore, the virus has a much more negative Gibbs energy of biosynthesis than its host cell. New virus particles and host cell building blocks are produced from the same precursors, like amino acids. A precursor molecule can either be incorporated into a new virus particle or a structure of the host cell. This is why the virus and host cell compete for precursors. Virus multiplication and biosynthesis of host cell building blocks are processes out of equilibrium. This means that they are governed by phenomenological equations of nonequilibrium thermodynamics. According to phenomenological equations, the rate of biosynthesis will be higher for a process with more negative Gibbs energy. Therefore, since the virus has a more negative Gibbs energy, biosynthesis of new virus particles will be faster than biosynthesis of the host cell building blocks. Due to the greater biosynthesis rate, more precursors will be consumed by the biosynthesis of new virus particles. Additionally, the host cell metabolic machinery will produce much more virus particles than host cell building blocks. In that way, the virus will hijack the host cell metabolic machinery for its multiplication. Therefore, due to the more negative Gibbs energy of biosynthesis, the virus will have a higher biosynthesis rate. Due to the higher biosynthesis rate, resources will be diverted into production of new virus particles and the host cell metabolic machinery will produce new virus particles more than host cell building blocks. Since the host cell metabolic machinery produces mostly new virus particles, it is hijacked by the virus.

Except for biosynthesis precursors, the virus and its host cell compete for metabolic energy, which comes in the form of a shared cellular stock of ATP. ATP transfers energy from catabolism where it is generated to biosynthesis processes. Some viruses upregulate catabolism to produce more ATP, which can be used for the production of new virus particles. However, the increased production of ATP provides a higher potential for biosynthesis not only for the virus, but also for its host cell. In order to exploit the increased ATP production, the virus must have a higher biosynthesis rate than its host cell. Due to the higher biosynthesis rate, production of new viruses will consume more ATP than production of host cell building blocks. To achieve a higher biosynthesis rate, the virus must have a more negative Gibbs energy of biosynthesis than its host cell. Therefore, the more negative Gibbs energy allows the virus to exploit the increased potential for biosynthesis provided by upregulated catabolism and increased ATP production.

An analysis was made of the virus–virus interactions between Norovirus and Rotavirus. Norovirus and Rotavirus have similar Gibbs energies of binding. This means that both viruses will be able to enter into host cells at similar rates. Norovirus has a more negative Gibbs energy of biosynthesis than Rotavirus, which means that it should multiply faster in host cells. This gives Norovirus an advantage, but is not enough to allow it to suppress Rotavirus. Therefore, Norovirus and Rotavirus should be able to perform coinfection.