# Omicron BA.2.75 Subvariant of SARS-CoV-2 Is Expected to Have the Greatest Infectivity Compared with the Competing BA.2 and BA.5, Due to Most Negative Gibbs Energy of Binding

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Gibbs Energy of Binding and Dissociation Equilibrium Constant

_{B}is the rate of binding of SGP to hACE2, L

_{B}the binding phenomenological coefficient, T temperature and Δ

_{B}G the Gibbs energy of binding of SGP to hACE2 [4,52,53,54,55]. The binding phenomenological equation shows that the rate of binding is proportional to the negative value of the Gibbs energy of binding.

_{B}G⁰, is given by the equation

_{g}is the universal gas constant, T the temperature, and K

_{B}the binding equilibrium constant [52,59]. K

_{B}can be found as the reciprocal of the dissociation equilibrium constant, K

_{D}[59].

_{D}is defined through the free antigen concentration [A], free receptor concentration [R], and antigen–receptor complex concentration [AR] [52,59]

_{B}G⁰ is the thermodynamic driving force for the chemical reaction of antigen–receptor binding.

#### 2.2. The kinetic Method and Rate Constants

_{on}, is given by the law of mass action [60,61], depending on the concentration of the free antigen, [A], and the free receptor [R].

_{on}is the rate constant of the forward half-reaction, which is also known as the on-rate constant or association rate constant [54,59]. On the other hand, the backward half-reaction is AR → A + R, where the antigen receptor complex dissociates into free antigen and receptor. The rate of the backward half-reaction, r

_{off}, is

_{off}is the rate constant for the backward half-reaction, which is also known as the off-rate constant [54,59]. The rates of the forward and backward half-reactions are combined to find the overall binding rate, r

_{B}, through the equation [54]

#### 2.3. Binding Phenomenological Coefficient

_{B}. The binding phenomenological coefficient can be calculated using the equation [55]

_{D}for SARS-CoV-2 variants is very small, on the order of nM. Thus, the chemical equilibrium of antigen–receptor binding is shifted towards the antigen–receptor complex. This means that the majority of virus particles will be attached to host cells. This implies that the equilibrium concentration of the antigen receptor complex is approximately equal to the total concentration of virus particles in the organism: [AR]

^{eq}≈ [V]

_{tot}[54]. Therefore, the equation above is transformed into [54]

_{tot}is 1 × 10

^{7}RNA copies per gram of tissue. A SARS-CoV-2 virus particle contains a single copy of its RNA genome [64,65,66]. This means that the concentration of virus particles is 1 × 10

^{7}RNA copies per gram of tissue [54]. This is combined with the density of human tissues, which is 1050 g/dm

^{3}[67], resulting in a total concentration of virions of 1.74 × 10

^{−14}M [54]. This result is substituted into Equation (13) to find the value of L

_{B}.

#### 2.4. The Linear Method

_{B}, uses the binding phenomenological Equation (1), which belongs to linear nonequilibrium thermodynamics [55]. Equation (1) combines L

_{B}with the Gibbs energy of binding, Δ

_{B}G. The value of Δ

_{B}G is calculated from the standard Gibbs energy of binding, Δ

_{B}G⁰, using the equation

_{B}.

#### 2.5. Exponential Method

## 3. Results

^{−17}M/s, while for BA.5 it was 1.19 × 10

^{−17}M/s. Finally, for BA.2.75 it was 5.74 × 10

^{−18}M/s, while for BA.2.75 (N460K) it was 1.49 × 10

^{−15}M/s.

^{8}M/s, while for BA.5 it was 7.52 × 10

^{7}M/s. The binding equilibrium constant of the BA.2.75 variant was 4.55 × 10

^{8}M/s.

_{B}. The three methods were compared at various distances from equilibrium. The distance from equilibrium was quantified by the ratio of the reaction quotient, Q, and the binding equilibrium constant, K

_{B}. The equilibrium corresponds to the point where Q/K

_{B}= 1. To the left, the region where Q/K

_{B}< 1 corresponds to the reaction being incomplete. In that region, according to Equation (15), there are excess reactant molecules that have not yet formed the product. To the right, the region where Q/K

_{B}> 1 corresponds to the reaction exceeding equilibrium. In this region, according to Equation (15), the product concentration is greater than that predicted by the equilibrium constant. Thus, the reaction will tend to flow in reverse, with a negative reaction rate, until the excess product dissociates into reactants. The comparison was made with Q/K

_{B}spanning two orders of magnitude.

## 4. Discussion

_{on}, k

_{off}, and K

_{d}, reported by Cao et al. [51] for the currently dominant BA.2.75 Omicron variant. The Gibbs energy of binding of the BA.2.75 Omicron variant was calculated to be −49.41 kJ/mol (Table 1). BA.2.75 is increasing in frequency, and had been detected in at least 15 countries as of the end of July 2022. This means that BA.2.75 is suppressing the existing BA.4 and BA.5 variants. This leads to the conclusion that infectivity of BA.2.75 is greater than that of BA.4 and BA.5. In that case, BA.2.75 is characterized by a more negative Gibbs energy of binding than BA.4 and BA.5. Moreover, the rate of entry into host cells depends on three factors: the Gibbs energy of binding, the binding phenomenological coefficient, and temperature. The temperature at which the most biological processes occur is the physiological temperature of 37 °C. The calculated binding phenomenological coefficients are given in Table 1. The calculated rates of binding of the viral spike glycoprotein trimer (SGP) to the human angiotensin-converting enzyme 2 (ACE2) are given in Table 2. Relative to the BA.2 variant, BA.2.75 carries nine additional mutations in the spike glycoprotein [73,74]. Mutation causes change in elemental composition and empirical formulae, leading to changes in thermodynamic properties. The underlying mechanism of BA.2.75’s enhanced infectivity, especially compared with BA.5, remains unclear for now [51].

_{B}G⁰ values for several SARS-CoV-2 variants. The Δ

_{B}G⁰ values of BA.2 and BA.5 variants were −45.81 kJ/mol and −44.95 kJ/mol, respectively. Indeed, Δ

_{B}G⁰ of BA.2.75 is more negative than that of competing variants. This observation explains both the greater infectivity and suppression of previous variants by BA.2.75.

_{on}and k

_{off}rate constants [54,60,61]. The thermodynamic approach uses the binding phenomenological equation [54,55,75]. The exponential approach uses a more general exponential equation from nonequilibrium thermodynamics [54,55]. The results are shown in Table 2. The entry rates of BA.2 and BA.5 variants were found to be 6.58 × 10

^{−17}M/s and 1.19 × 10

^{−17}M/s, respectively. On the other hand, the entry rate of BA.2.75 was found to be 5.74 × 10

^{−18}M/s using the kinetic method. This can be explained by a difference in binding phenomenological coefficients, L

_{B}. However, the variant BA.2.75 (N460K) exhibited the greatest binding rate of 1.49 × 10

^{−15}M/s. Thus, the binding rate of BA.2.75 (N460K) is 23 times greater than that of BA.2 and 125 times greater than that of BA.5.

_{B}. The difference in the predicted r

_{B}values of the kinetic and exponential methods was below 1% for most of the analyzed Q/K

_{B}range. The only exception is the area close to equilibrium, with Q/K

_{B}values from 0.85 to 1.21, where the relative discrepancy was greater, due to small values of r

_{B}. The good agreement of the kinetic method and exponential method indicates that nonequilibrium thermodynamics can provide accurate predictions of rates of biological processes, based on thermodynamic properties. On the other hand, the linear method deviated more from the kinetic and exponential methods. The deviation was the smallest in the area close the equilibrium value of Q/K

_{B}= 1, being less than 10% for Q/K

_{B}values from 0.80 to 1.21. This can be explained by the assumption made in the linear method, i.e., that the driving force Δ

_{B}G is not high [55]. In the area close to equilibrium, the Δ

_{B}G was small (close to zero), making the linear method the most accurate. However, all three methods showed the same general trend throughout the analyzed range of Q/K

_{B}values. Thus, the simplicity of the linear method and its connection of thermodynamics and kinetics still make it a valuable tool in thermodynamic analysis of biological phenomena. This is in agreement with the results of refs. [4,55,76,77], who found that the linear method can accurately predict multiplication rates of microorganisms.

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 1.**A comparison of the kinetic, linear, and exponential methods for calculating the overall binding rate, r

_{B}. The comparison was made for various distances from equilibrium, quantified by Q/K

_{B}. The equilibrium corresponds to Q/K

_{B}= 1. The region where Q/K

_{B}< 1 corresponds to the reaction being incomplete, with unreacted reactants that will form the product once the equilibrium is achieved. The region where Q/K

_{B}> 1 corresponds to the reaction “overshooting” the equilibrium, with excess product formed that will decompose into the reactants when the equilibrium is reached. (

**a**) A comparison over a wide span of Q/K

_{B}, from 0.1 to 10. (

**b**) Comparison close to equilibrium, with Q/K

_{B}between 0.5 and 1.5. The full blue line (

**―**) represents the kinetic method, the orange dot-and-dash line (

**- ∙ -**) represents the linear method, while the dashed gray line (

**- - -**) represents the exponential method. The calculated overall binding rates have been multiplied by 10

^{15}for clearer presentation.

**Table 1.**Standard thermodynamic properties of the binding of SARS-CoV-2 variants. The table shows the association rate constant, k

_{on}, dissociation rate constant, k

_{off}, dissociation equilibrium constant, K

_{d}, binding phenomenological coefficient, L

_{B}, binding equilibrium constant, K

_{B}, and standard Gibbs energy of binding, Δ

_{B}G⁰; data taken at 25 °C. The k

_{on}, k

_{off}, and K

_{d}data were taken from ref. [51].

Name | k_{on} (M^{−1}s^{−1}) | k_{off} (s^{−1}) | K_{d} (M) | L_{B} (mol^{2} K/J s dm^{3}) | K_{B} (M^{−1}) | Δ_{B}G⁰ (kJ/mol) |
---|---|---|---|---|---|---|

BA.2 | 4.06 × 10^{6} | 3.82 × 10^{−2} | 9.40 × 10^{−9} | 8.01 × 10^{−17} | 1.06 × 10^{8} | −45.81 |

BA.4/5 | 5.30 × 10^{5} | 7.07 × 10^{−3} | 1.33 × 10^{−8} | 1.48 × 10^{−17} | 7.52 × 10^{7} | −44.95 |

BA.2.75 | 1.88 × 10^{6} | 4.22 × 10^{−3} | 2.20 × 10^{−9} | 8.68 × 10^{−18} | 4.55 × 10^{8} | −49.41 |

BA.2.75 (Q493R) | 8.85 × 10^{5} | 5.64 × 10^{−3} | 6.40 × 10^{−9} | 1.19 × 10^{−17} | 1.56 × 10^{8} | −46.77 |

BA.2.75 (S446G) | 3.36 × 10^{6} | 1.18 × 10^{−2} | 3.50 × 10^{−9} | 2.47 × 10^{−17} | 2.86 × 10^{8} | −48.26 |

BA.2.75 (N460K) | 3.87 × 10^{7} | 5.02 × 10^{−1} | 1.38 × 10^{−8} | 1.12 × 10^{−15} | 7.25 × 10^{7} | −44.86 |

B.1.1.7 (Alpha) | 7.38 × 10^{5} | 3.55 × 10^{−3} | 4.80 × 10^{−9} | 7.43 × 10^{−18} | 2.08 × 10^{8} | −47.48 |

B.1.351 (Beta) | 5.42 × 10^{5} | 7.31 × 10^{−3} | 1.35 × 10^{−8} | 1.54 × 10^{−17} | 7.41 × 10^{7} | −44.92 |

P.1 (Gamma) | 3.77 × 10^{5} | 6.29 × 10^{−3} | 1.67 × 10^{−8} | 1.32 × 10^{−17} | 5.99 × 10^{7} | −44.39 |

B.1.617.2 (Delta) | 7.21 × 10^{5} | 7.84 × 10^{−3} | 1.09 × 10^{−8} | 1.65 × 10^{−17} | 9.17 × 10^{7} | −45.45 |

BA.1 | 1.04 × 10^{6} | 1.07 × 10^{−2} | 1.03 × 10^{−8} | 2.25 × 10^{−17} | 9.71 × 10^{7} | −45.59 |

BA.2.12.1 | 9.08 × 10^{5} | 9.41 × 10^{−3} | 1.04 × 10^{−8} | 1.98 × 10^{−17} | 9.62 × 10^{7} | −45.56 |

BA.3 | 1.54 × 10^{6} | 3.16 × 10^{−2} | 2.04 × 10^{−8} | 6.59 × 10^{−17} | 4.90 × 10^{7} | −43.89 |

BA.2.75 (H339) | 2.81 × 10^{6} | 6.72 × 10^{−3} | 2.40 × 10^{−9} | 1.41 × 10^{−17} | 4.17 × 10^{8} | −49.20 |

**Table 2.**The binding rates of SARS-CoV-2 variants. The table shows r

_{kin}, r

_{TD}, and r

_{exp}: binding rates calculated using the kinetic, thermodynamic, and exponential methods, respectively. The values were calculated at Q = 0.91 K

_{B}.

Name | r_{kin} (M/s) | r_{TD} (M/s) | r_{exp} (M/s) |
---|---|---|---|

BA.2 | 6.58 × 10^{−17} | 6.34 × 10^{−17} | 6.64 × 10^{−17} |

BA.4/5 | 1.19 × 10^{−17} | 1.17 × 10^{−17} | 1.23 × 10^{−17} |

BA.2.75 | 5.74 × 10^{−18} | 6.88 × 10^{−18} | 7.20 × 10^{−18} |

BA.2.75 (Q493R) | 1.03 × 10^{−17} | 9.42 × 10^{−18} | 9.86 × 10^{−18} |

BA.2.75 (S446G) | 1.98 × 10^{−17} | 1.95 × 10^{−17} | 2.05 × 10^{−17} |

BA.2.75 (N460K) | 1.49 × 10^{−15} | 8.88 × 10^{−16} | 9.29 × 10^{−16} |

B.1.1.7 (Alpha) | 6.03 × 10^{−18} | 5.89 × 10^{−18} | 6.16 × 10^{−18} |

B.1.351 (Beta) | 1.29 × 10^{−17} | 1.22 × 10^{−17} | 1.27 × 10^{−17} |

P.1 (Gamma) | 1.11 × 10^{−17} | 1.05 × 10^{−17} | 1.10 × 10^{−17} |

B.1.617.2 (Delta) | 1.40 × 10^{−17} | 1.31 × 10^{−17} | 1.37 × 10^{−17} |

BA.1 | 1.88 × 10^{−17} | 1.78 × 10^{−17} | 1.86 × 10^{−17} |

BA.2.12.1 | 1.70 × 10^{−17} | 1.57 × 10^{−17} | 1.64 × 10^{−17} |

BA.3 | 5.15 × 10^{−17} | 5.22 × 10^{−17} | 5.47 × 10^{−17} |

BA.2.75 (H339) | 1.22 × 10^{−17} | 1.12 × 10^{−17} | 1.17 × 10^{−17} |

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**MDPI and ACS Style**

Popovic, M.
Omicron BA.2.75 Subvariant of SARS-CoV-2 Is Expected to Have the Greatest Infectivity Compared with the Competing BA.2 and BA.5, Due to Most Negative Gibbs Energy of Binding. *BioTech* **2022**, *11*, 45.
https://doi.org/10.3390/biotech11040045

**AMA Style**

Popovic M.
Omicron BA.2.75 Subvariant of SARS-CoV-2 Is Expected to Have the Greatest Infectivity Compared with the Competing BA.2 and BA.5, Due to Most Negative Gibbs Energy of Binding. *BioTech*. 2022; 11(4):45.
https://doi.org/10.3390/biotech11040045

**Chicago/Turabian Style**

Popovic, Marko.
2022. "Omicron BA.2.75 Subvariant of SARS-CoV-2 Is Expected to Have the Greatest Infectivity Compared with the Competing BA.2 and BA.5, Due to Most Negative Gibbs Energy of Binding" *BioTech* 11, no. 4: 45.
https://doi.org/10.3390/biotech11040045