Effect of Delta and Omicron Mutations on the RBD-SD1 Domain of the Spike Protein in SARS-CoV-2 and the Omicron Mutations on RBD-ACE2 Interface Complex

The receptor-binding domain (RBD) is the essential part in the Spike-protein (S-protein) of SARS-CoV-2 virus that directly binds to the human ACE2 receptor, making it a key target for many vaccines and therapies. Therefore, any mutations at this domain could affect the efficacy of these treatments as well as the viral-cell entry mechanism. We introduce ab initio DFT-based computational study that mainly focuses on two parts: (1) Mutations effects of both Delta and Omicron variants in the RBD-SD1 domain. (2) Impact of Omicron RBD mutations on the structure and properties of the RBD-ACE2 interface system. The in-depth analysis is based on the novel concept of amino acid-amino acid bond pair units (AABPU) that reveal the differences between the Delta and/or Omicron mutations and its corresponding wild-type strain in terms of the role played by non-local amino acid interactions, their 3D shapes and sizes, as well as contribution to hydrogen bonding and partial charge distributions. Our results also show that the interaction of Omicron RBD with ACE2 significantly increased its bonding between amino acids at the interface providing information on the implications of penetration of S-protein into ACE2, and thus offering a possible explanation for its high infectivity. Our findings enable us to present, in more conspicuous atomic level detail, the effect of specific mutations that may help in predicting and/or mitigating the next variant of concern.


Introduction
Back in late 2019, a novel coronavirus, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), was first identified as the causative agent for the virus disease and named COVID-19 by the World Health Organization (WHO) [1]. SARS-CoV-2 is continuously evolving due to genetic mutations or viral recombination during genome replication, resulting in emerging many Variants of Concern (VOCs) [2]. These VOCs significantly alter virus properties such as infectivity, transmissibility, antigenicity, and pathogenicity [3]. Further, some VOCs have the ability to evade natural or vaccine-induced immunity, decrease susceptibility to therapeutic agents, cause more severe disease, and spread faster [4]. As a result of these consequences, the number of confirmed cases and deaths is approaching to reach 550 million confirmed cases and more than 6.34 million deaths by 5 July 2022 [1].
Besides that, this terrible pandemic has a devastating effect on social, emotional, and economic consequences with no end in sight [5]. In response, intensive efforts have resulted In this study, two well-known packages based on density functional theory (DFT) have been used: The Vienna ab initio Simulations package (VASP) [70] and the orthogonalized linear combination of atomic orbital OLCAO) technique [71]. These DFT calculations can provide a lot of key parameters that are useful in probing mutational impacts, as detailed in Supplementary Materials.
In Table 1, we list the result of AAPBU analysis for the 18 mutations sites from WT, among which 2 sites are for DV and 16 sites are for OV. WT T478 and OV K478 are listed twice, since they are in both DV and OV. For the details of the definitions of the AABP, nearest neighbor NN-AAPB, non-local neighbor NL-AAPB, contribution of hydrogen bonds to AABP (HB), number of non-local AAs, as well as partial charge (PC), consult the Supplementary Materials. Partial charge for the AABPU (PC*) will be presented in more detail in Section 2.1.4. Here, it should be mentioned that the values present in Table 1 are estimated for the entire AABPU, not for a single amino acid site (see Supplementary Materials).
From Table 1 and based on plots in Figures 1 and S1, we have extracted the following detailed description of the mutations which are as a rule missing in the characterization available in the literature. A succinct list of these observations is listed below. We focus on the relative quantitative differences as presented in Table 1, underlying the spectacular variety of mutation changes.
The largest contribution from hydrogen bonds (HB) to total AABP in WT is K417 (0.203 e − ) and in mutated one is OV R493 (0.200 e − ). This finding is similar to the one observed for the largest NL-AABP, indicating that HB plays a dominant role in NL-AABP. 8.
The smallest contribution from HB to total AABP in WT is T478 (0.022 e − ) and in mutated one is OV A484 (0.030 e − ). 9.
The overall comparison in number of HBs in the 18 mutation sites are further shown in Figure S2 for simplicity. OV R493 has the highest difference of HBs after mutation. The total difference in number of HB in 16 OV mutations sites (OV-WT) is 18 and in 2 DV mutations sites (DV-WT) is −1, inducting substantial change in the intramolecular HB distributions of OV RBD-SD1. 10. The largest number of NL AAs in WT is 10 at Q498 and N501 and for mutated one is 11 at R498 (OV). 11. The smallest number of NL AAs in WT is 1 at T478 and mutated one is 2 at S446 (OV) and N477 (OV e − ). 5. The largest NL-AABP in WT is K417 (0.203 e − ) and mutated one is OV R493 (0.194 e − ). 6. The smallest NL-AABP in WT is T478 (0.001 e − ) and mutated one is OV N477 (0.001 e − ). 7. The largest contribution from hydrogen bonds (HB) to total AABP in WT is K417 (0.203 e − ) and in mutated one is OV R493 (0.200 e − ). This finding is similar to the one observed for the largest NL-AABP, indicating that HB plays a dominant role in NL-AABP. 8. The smallest contribution from HB to total AABP in WT is T478 (0.022 e − ) and in mutated one is OV A484 (0.030 e − ). 9. The overall comparison in number of HBs in the 18 mutation sites are further shown in Figure S2 for simplicity. OV R493 has the highest difference of HBs after mutation. The total difference in number of HB in 16 OV mutations sites (OV-WT) is 18 and in 2 DV mutations sites (DV-WT) is −1, inducting substantial change in the intramolecular HB distributions of OV RBD-SD1. 10. The largest number of NL AAs in WT is 10 at Q498 and N501 and for mutated one is 11 at R498 (OV). 11. The smallest number of NL AAs in WT is 1 at T478 and mutated one is 2 at S446 (OV) and N477 (OV   In Figure 1, we compare the mutational changes in the shape of AABPU for the first 2 mutations in DV (WT L452, WT T478 to R452 and K478). They depend on the scale of the plot used. Fixed scale makes their boxes the same. Real scale reveals the change in the shape of AABPU. It can be seen that mutation L452R reduce its volume whereas mutation T478K increase its volume as listed in Table 1. Similar figures for 16 OV mutations are shown in Figure S1.
In Figure 2, we display each component of the AABPU data in Table 1 in bar graph form except the PC which will be discussed in Section 2.1.4. Figure 2a  AABP values for the 18 mutations and Figure 2b to f displays NN AABP, NL AABP, AABP from HB, Volume, and surface area of each AABP unit, respectively. It can be summarized briefly as follows: (1) Total AABP and NN AABP differs only slightly accentuating the importance of using sequence of AAs in proteins and their fundamental analysis.

Electronic Structure of Delta and Omicron RBD-SD1
In condensed matter physics, the electronic structure of a material, usually a crystalline material, is generally presented and interpreted in terms of the total density of states (TDOS)-a plot showing the distribution of the calculated energy eigenvalues as the number of states per energy level. The occupied portion or the valence band (VB) and unoccupied portion or the conduction band (CB) are separated by a band gap E g for insulators or a Fermi level (E F ) with no gaps for metals. In quantum chemistry, the top of VB and bottom of CB are respectively called HOMO (highest occupied molecular orbitals) or LUMO (lowest occupied molecular orbitals), separated by a HOMO-LUMO gap. In complex biomolecules similar, data can be presented since ab initio calculation using OLCAO method give all the energy eigenvalues. The TDOS can be resolved into partial DOS (PDOS) for each atom or a group of atoms in a specific structural unit, which are usually well-defined even for very complex crystals. In complex biomolecules such as in the present work, the decomposition of TDOS into PDOS is far more challenging but can still be done if the partial structural units are clearly specified. This provides insightful information for a deeper level of understanding in their electronic structure. Figure 3 shows the plot of TDOS for the RBD-SD1 unit for the three models WT, DV, and OV with slightly different total number of atoms of 4059, 4072, and 4123, respectively. They have only minor differences in TDOS since, for such large systems, the changes in atomic configurations are small. Their HOMO-LUMO gaps are about 1.68 eV. The TDOS is obtained from a huge number of energy eigenvalues for all atoms interacting in each model. The TDOS in Figure 3 can be resolved into 18 PDOS. They are discussed in Supplementary Materials in Section S2 (Partial density of states (PDOS) for WT, DV, and OV in RBD-SD1) and Figure S3.
VB and bottom of CB are respectively called HOMO (highest occupied molecular orbitals) or LUMO (lowest occupied molecular orbitals), separated by a HOMO-LUMO gap. In complex biomolecules similar, data can be presented since ab initio calculation using OLCAO method give all the energy eigenvalues. The TDOS can be resolved into partial DOS (PDOS) for each atom or a group of atoms in a specific structural unit, which are usually well-defined even for very complex crystals. In complex biomolecules such as in the present work, the decomposition of TDOS into PDOS is far more challenging but can still be done if the partial structural units are clearly specified. This provides insightful information for a deeper level of understanding in their electronic structure. Figure 3 shows the plot of TDOS for the RBD-SD1 unit for the three models WT, DV, and OV with slightly different total number of atoms of 4059, 4072, and 4123, respectively. They have only minor differences in TDOS since, for such large systems, the changes in atomic configurations are small. Their HOMO-LUMO gaps are about 1.68 eV. The TDOS is obtained from a huge number of energy eigenvalues for all atoms interacting in each model. The TDOS in Figure 3 can be resolved into 18 PDOS. They are discussed in SM in Section S2 (Partial density of states (PDOS) for WT, DV, and OV in RBD-SD1) and Figure S3.

Interatomic Bonding in Delta and Omicron RBD-SD1
The data for bond order (BO) vs. bond length (BL) distribution for all the atomic pairs in RBD-SD1 domain in WT, DV, and OV models are displayed in Figure 4. There are 20,299 data points for WT, 20,410 data points for DV, and 20,709 data points for OV for a total of 61,418 data points. The figure shows the atomic-scale interactions for all atoms in RBD-SD1 models within the BL range of up to 4.5 Å as well as the effect of mutations for each pair, demonstrating the detailed atomic-scale level that quantum chemical calculation can achieve. Of particular importance is the distribution of Hydrogen bonding (HB), which is ubiquitous. HB is probably the most important bonding in biomolecules but is seldom discussed in detail. The quantification of HB network has been pre-

Interatomic Bonding in Delta and Omicron RBD-SD1
The data for bond order (BO) vs. bond length (BL) distribution for all the atomic pairs in RBD-SD1 domain in WT, DV, and OV models are displayed in Figure 4. There are 20,299 data points for WT, 20,410 data points for DV, and 20,709 data points for OV for a total of 61,418 data points. The figure shows the atomic-scale interactions for all atoms in RBD-SD1 models within the BL range of up to 4.5 Å as well as the effect of mutations for each pair, demonstrating the detailed atomic-scale level that quantum chemical calculation can achieve. Of particular importance is the distribution of Hydrogen bonding (HB), which is ubiquitous. HB is probably the most important bonding in biomolecules but is seldom discussed in detail. The quantification of HB network has been previous described solely based on the HB in water, which forms a HB network [72]. It is usually assumed that HBs are weak, but they are of pivotal importance in any biological system, especially in proteins. Figure 4b shows that HB in RBD-SD1 can occur first at the BL close to 1.51 Å and with BO value close to 0.139 e − . They can be affected by mutations in both DV and OV but predominately in the OV. The change in number of HBs in 18 sites of WT in comparison to DV and OV are shown in Figure S2, as already listed in the HB contribution to the total AABP value in Section 2.1.1 and Table 1. The HB data in RBD-SD1 for WT, DV, and OV are briefly summarized in Table S1. There is a total of 12,142 HBs (4021 for WT, 4037 for DV, and 4084 for OV) out of 61,418 data points. From the HB data in Table S1, it can be said that the mutations in DV and OV increases the number of HBs in comparison to WT. Again, the strongest HB shown in Figure 4b first appears at BL of 1.51 Å with BO of 0.139 e − and then continues to other BL/BO combinations in Figure 4c,d with gradually decreased BO values. One can also discern on the unusual HBs of different types mostly with tetrahedrally bonded C [73], and we plan to make a separate and detailed analysis of these HBs in RBD-SD1 which will be presented in a separate publication [74]. number of HBs in comparison to WT. Again, the strongest HB shown in Figure 4b first appears at BL of 1.51 Å with BO of 0.139 e − and then continues to other BL/BO combinations in Figure 4c,d with gradually decreased BO values. One can also discern on the unusual HBs of different types mostly with tetrahedrally bonded C [73], and we plan to make a separate and detailed analysis of these HBs in RBD-SD1 which will be presented in a separate publication [74].  The above issues on specific types of interatomic bonding are seldom discussed in the literature, especially the very weak bonds. Only the full atomic scale ab initio calculation interpreted in the framework of the AABPs, as detailed in this work, gives access to these data.

Partial Charge Distribution of Delta and Omicron RBD-SD1
Partial charge (PC) is a key parameter in electrostatic potential of a biomolecule crucial for predicting the overall long-range intermolecular interactions. Our ab initio calculated PCs are potentially useful for computing this electrostatic interaction using Delphi software, for example [66,75]. It could also be used to improve the accuracy of the PCs used in the most of MD simulations. In this study, we have two types of PC. One is PC for each specific AAs (PC AA ), and another is PC for the entire AABPU unit (PC*). PC* is obtained adding up PC AA of all AAs involved in the AABPU. Figure 5a shows PC* distribution of the AABPU listed in Table 1  Additionally, the three mutations located outside of RBM (S371L, S373P, and S375F) together with Y505H exhibit no substantial change in their PC*. Finally, G446S, S477N, T478K, Q498R, N501Y, and T547K OV mutations cause a change in the charge distribution toward a more positively charged state, as with N440K and G496S mutations, but this time switching from negative to positive PC*. Similarly, E484A also alters the PC* toward positive state but remains in a negative state.
The partial charge is emerging as an important proxy for the quantification of mutational drift of the different VOC in particular, as it seems to increase in a steady progression towards the Omicron variant [68,76]. The appropriate quantification of the partial Additionally, the three mutations located outside of RBM (S371L, S373P, and S375F) together with Y505H exhibit no substantial change in their PC*. Finally, G446S, S477N, T478K, Q498R, N501Y, and T547K OV mutations cause a change in the charge distribution toward a more positively charged state, as with N440K and G496S mutations, but this time switching from negative to positive PC*. Similarly, E484A also alters the PC* toward positive state but remains in a negative state.
The partial charge is emerging as an important proxy for the quantification of mutational drift of the different VOC in particular, as it seems to increase in a steady progression towards the Omicron variant [68,76]. The appropriate quantification of the partial charge can only be obtained from ab initio DFT calculation and has profound implications since all major SARS-CoV-2 variants have been accumulating positive charges in solvent-exposed regions of the S-protein, especially its ACE2-binding sites or along the RBD epitopes that are targeted by many therapeutic antibodies. More specific, the accumulation of positive mutations in Omicron RBD results an increase in the total charge density of the S-protein, facilitating the recognition process with the negative charge of ACE2 (as will discuss later in Part 2) or participating in immune evasion [8,32,77].
In Figure 5b, we show the PC AA of the key AA at 18 mutation sites and compare with PC* for the whole unit of AABPU in Table 1. They basically mimic the results in Figure 5a, especially for the 2 DVs. The only exceptions are the two OV in G339D, K417N with negative PC*. Some of the differences between Figure 5a,b could be attributed to the fact that we performed our simulation at neutral pH, while the pH impact could play an important role in the partial charge distribution and regulation. A more detailed investigation in this respect is clearly beyond the scope of the current investigation.

Part 2 2.2.1. Differences and Similarities between Unbound Omicron RBD and Bound RBD with ACE2
The RBD-ACE2 interface model, is discussed below in Section 3.2, contains 311 AAs (194 in RBD and 117 in ACE2), with the Omicron RBD having 15 mutations, one less compared to the unbound RBD-SD1 model in Part 1, since the subdomain SD1 is not included.
Data from Table 2 together with Figures 6 and S4 show considerable changes when compared with Table 1 (Figures 2 and S2) in Part 1. Most of these changes are due to the mutations in AABPU that result in stronger interactions between RBD with ACE2. Here are some observations comparing the RBD-ACE2 and RBD-SD1 models: (a) There are different AABP values (in Tables 1 and 2) because of the differences in number of NL interacting AAs. However, 10 out of 15 AAs exhibit similar trend of total AABP, i.e., either total AABP of WT is higher, or total AABP of OV is higher in both tables. This difference in the remaining 5 AAs could be traced to the fact that there is an extra SD1 in Part 1 and RBD's interaction with ACE2 in Part 2. (b) K417 (WT) has the highest NL AABP in both RBD-ACE2 and RBD-SD1 models. Similarly, Q493, E484, and Y505 from WT and R493, and R498 from OV, have higher NL AABP in both cases. (c) R493 from OV has significant contributions in both the models. (d) The difference (OV-WT) in total number of HBs for 15 mutations sites is 17 for RBD-SD1, whereas it is 8 for RBD-ACE2 due to the dissimilarity in the number of NL AAs. (e) There are differences in volume and surface values for AABPU, since the number of NL AAs are quite different. (f) Most of the volume and surface area of AABPU increase after mutation in both models. However, there is decrease in volume in four cases (K417N, G446S, E484A, and Y505H) of RBD-ACE2 and three cases (S371L, K417N, and E484A) of RBD-SD1 model. The change in the surface area follows the change in volume closely but not exactly, since the shape of each AABPU alters due to difference in NN and NL AAs. Figure 6 shows the complexity of the changes in the AABPU of the RBD at the interface with ACE2. Similar figures such as Figure S1 in Part 1 can be plotted but are not included here. Additional figures involving the ACE2 part of the interface will be presented later in Sections 2.2.2 and 2.2.3.

Properties and Interactions at RBD-ACE2 Interface
The total density of states (TDOS) for the interface model RBD-ACE2 has been calculated in the usual manner, as in part 1. The TDOS is resolved into PDOS for RBD and ACE2 in Figure 7, with each panel containing the WT and OV parts. As expected, these PDOS plots are very close to each other, with only minor differences in peak structures in all biomolecules. The HOMO-LUMO gaps for RBD and ACE2 are 1.83 eV and 1.47 eV in RBD and ACE2, respectively. Based on the HOMO-LUMO gap, the Fermi level can be analyzed and modified to prepare materials such as sensors [78].
Interaction between RBD and ACE2 is illustrated in Figure 8 with the AABP values. Figure 8a,b focus on the bonding between mutated and unmutated AAs of RBD and ACE2, comparing their AABP values, respectively. Adding the AABP values gives us the total AABP of 1.33 e − and 1.46 e − for WT and OV, respectively. Hence, the OV has stronger binding with ACE2 than WT. The present interface calculation is superior to our past calculation on RBM-ACE2 [68], since the current calculation includes the entire RBD. Unlike the first part of the present work, our RBD-ACE2 analysis is limited to a comparison of the Omicron with WT and does not include the Delta variant. The binding strength of Delta RBD with ACE2 versus Omicron is still debated. Previous studies have shown that the DV RBD-ACE2 binding is tighter than the Omicron binding [79][80][81], while others have observed the opposite or similar in both [82][83][84][85].  Figure 6 shows the complexity of the changes in the AABPU of the RBD at the face with ACE2. Similar figures such as Figure S1 in Part 1 can be plotted but are n cluded here. Additional figures involving the ACE2 part of the interface will be pr ed later in Sections 2.2.2 and 2.2.3. The total density of states (TDOS) for the interface model RBD-ACE2 has been calculated in the usual manner, as in part 1. The TDOS is resolved into PDOS for RBD and ACE2 in Figure 7, with each panel containing the WT and OV parts. As expected, these PDOS plots are very close to each other, with only minor differences in peak structures in all biomolecules. The HOMO-LUMO gaps for RBD and ACE2 are 1.83 eV and 1.47 eV in RBD and ACE2, respectively. Based on the HOMO-LUMO gap, the Fermi level can be analyzed and modified to prepare materials such as sensors [78]. Interaction between RBD and ACE2 is illustrated in Figure 8 with the AABP values. Figure 8a,b focus on the bonding between mutated and unmutated AAs of RBD and ACE2, comparing their AABP values, respectively. Adding the AABP values gives us the total AABP of 1.33 e − and 1.46 e − for WT and OV, respectively. Hence, the OV has stronger binding with ACE2 than WT. The present interface calculation is superior to our past calculation on RBM-ACE2 [68], since the current calculation includes the entire RBD. Unlike the first part of the present work, our RBD-ACE2 analysis is limited to a comparison of the Omicron with WT and does not include the Delta variant. The binding strength of Delta RBD with ACE2 versus Omicron is still debated. Previous studies have shown that the DV RBD-ACE2 binding is tighter than the Omicron binding [79][80][81], while others have observed the opposite or similar in both [82][83][84][85]. We now analyze the interactions with specific mutations sites. In the case of OV, 7 (K440, N477, R493, S496, R498, Y501, and H505) out of 15 mutated AA interact with ACE2, whereas in the case of WT, 8 (K417, G446, E484, Q493, G496, Q498, N501, and Y505) out of 15 AAs interact with ACE2. Thus, OV interface loses interaction with ACE2 with N417, S446, A484 AAs and gains interaction with K440 and N477. In particular, mutated AAs K440, N477, R493, and S496 show an increase in interaction with ACE2. In our past calculation of interface, RBM-ACE2 mutated Y501 showed higher AABP with ACE2 [68], which is consistent with previous findings that describe the increase in binding affinity [77,86,87]. Nevertheless, we noted a slight decrease in AABP with ACE2 of Y501 in comparison to N501. In addition, the Y501 interaction with Y41 and D355 has decreased a little in comparison to RBM-ACE2 model [68]. The 7 mutated AAs of RBD interacts with 13 AAs (S19, T20, Q24, K31, H34, E35, E37, D38, Y41, Q42, E329, K353, and D355) of ACE2. Among them, E329 and S19 have strongest bonding with RBD. These 13 AAs are marked in Figure 8c, clearly showing their proximity to the interface. These AAs can be considered as potential targets, since the structure of ACE2 and its interaction with RBD is critical for antibody and drug design [88,89].
Mutated AAs are definitely the main reason for enhanced interaction between RBD and ACE2. These mutated AAs have an effect not only on the strength of binding with ACE2, but also on the intramolecular interactions of unmutated AAs in the RBD, changing their NN and NL bonding (see Table 2). These NN and NL AAs can be both mutated and unmutated ones. Hence, indirectly unmutated AAs also play an important role in changing the overall bonding at the interface. In the RBD, there are 17 unmutated AAs in case of OV and 16 AAs in case of WT that interact with ACE2. The change in interaction of these AAs between WT and OV is also an important point to be considered. OV RBD gains interaction with R403, V445, S494, and loses interaction with F490 and F497. We now analyze the interactions with specific mutations sites. In the case of OV, 7 (K440, N477, R493, S496, R498, Y501, and H505) out of 15 mutated AA interact with ACE2, whereas in the case of WT, 8 (K417, G446, E484, Q493, G496, Q498, N501, and Y505) out of 15 AAs interact with ACE2. Thus, OV interface loses interaction with ACE2 with N417, S446, A484 AAs and gains interaction with K440 and N477. In particular, mutated AAs K440, N477, R493, and S496 show an increase in interaction with ACE2. In our past calculation of interface, RBM-ACE2 mutated Y501 showed higher AABP with ACE2 [68], which is consistent with previous findings that describe the increase in binding affinity [77,86,87]. Nevertheless, we noted a slight decrease in AABP with ACE2 of Y501 in comparison to N501. In addition, the Y501 interaction with Y41 and D355 has The AAs in ACE2 interacting with unmutated AAs of RBD are listed in x-axis of Figure 8b. Among them, E23, T27, F28, D30, L45, L79, M82, Y83, Q325, N330, G354, and R357 only interact with unmutated AAs of RBD. Adding up all these interactions gives the total interface AABP values and shows stronger interaction in OV compared to WT. Hence, these AAs can also be considered as a potential target for disruption.

Partial Charge and Mechanism of Penetration
As mentioned in Section 2.1.4, we have calculated two types of partial charge (PC)one is for each AAs (PC AA ), and another is for the entire AABPU unit (PC*). PC* is obtained adding up PC AA of all AAs involved in the AABPU. PC* of AABPU are listed in Table 2 for 15 sites in RBD for both WT and OV of the interface model. They are also plotted in Figure 9a. Ten out of fifteen Omicron mutations have changed PC* toward positive values, indicating a significant change in its surface charge distribution that affects either ACE2 binding or antibody binding or both [8,90]. the total interface AABP values and shows stronger interaction in OV compared to WT. Hence, these AAs can also be considered as a potential target for disruption.

Partial Charge and Mechanism of Penetration
As mentioned in Section 2.1.4, we have calculated two types of partial charge (PC)-one is for each AAs (PC AA ), and another is for the entire AABPU unit (PC*). PC* is obtained adding up PC AA of all AAs involved in the AABPU. PC* of AABPU are listed in Table 2 for 15 sites in RBD for both WT and OV of the interface model. They are also plotted in Figure 9a. Ten out of fifteen Omicron mutations have changed PC* toward positive values, indicating a significant change in its surface charge distribution that affects either ACE2 binding or antibody binding or both [8,90].  Table 3 shows PC AA for 15 AAs in both WT and OV interface model. They are plotted in Figure 9b for easy visualization. Here, the shift toward positive PC is in 11 out of 15 AAs. One of the studies had cited N440K, T478K, Q493R, Q498R, and Y505H to have positive charge [76,91]. All these AAs falls under the 11 AAs shown in Figure 9b. Both PC AA and PC* show an increase in PC in most cases of OV, which is consistent with other studies [92][93][94]. The sum of PC AA for 15 AAs in WT and OV shown in Table 3 is −0.727  Table 3 shows PC AA for 15 AAs in both WT and OV interface model. They are plotted in Figure 9b for easy visualization. Here, the shift toward positive PC is in 11 out of 15 AAs. One of the studies had cited N440K, T478K, Q493R, Q498R, and Y505H to have positive charge [76,91]. All these AAs falls under the 11 AAs shown in Figure 9b. Both PC AA and PC* show an increase in PC in most cases of OV, which is consistent with other studies [92][93][94]. The sum of PC AA for 15 AAs in WT and OV shown in Table 3 is −0.727 e − and 2.185 e − , respectively. Similarly, the sum of PC* for 15 AABPU shown in Table 2 is 0.122 e − and 4.910 e − , respectively. This is a noticeable increase in PC after mutation, which will further increase the electrostatic interaction between RBD and ACE2 or/and RBD and antibodies. This could be one of the major reasons for the rapid infectivity of OV and evade the immunity response from vaccine or other antibody therapeutics.
The interacting AAs at the RBD-ACE2 interface can be both mutated and unmutated. We further analyze PC AA values for the AAs having interaction at the interface between RBD (Figure 10a) and ACE2 (Figure 10b) in WT and OV models. The vertical green lines show common interface interacting AAs in both WT and OV, whereas the vertical red lines show the mutated AAs in RBD. There are 5 vertical red lines in Figure 10a representing 5 mutated AAs (Q493R, G496S, Q498R, N501Y, and Y505H), which interact with ACE2. Among these 5 mutated AAs 4 have changed PC AA to positive direction, which is consistent with other studies [92][93][94]. Other unmutated interacting AAs in RBD at the interface have changed PC AA in both positive and negative direction. AAs marked by vertical black lines are interacting in either WT or OV interface. There are 12 such AAs in RBD and 6 of them, R403, K440, V445, N477, S494, and Y495, are only interface interacting in OV, and the remaining 6 AAs K417, G446, G447, E484, F490, and F497 are only interface interacting in WT. In the case of ACE2, there are just 5 AAs marked by black vertical lines. T20, L45, and E329 are the only interface interacting in OV and E23 and H34 are the only interface interacting WT. T20, L45, and E329 in OV can be considered as important AAs of ACE2 since they also interact with mutated AAs of RBD. For interacting AAs in ACE2, only F28 and G354 yield a changed PC AA from positive to negative. All remaining AAs have changes in the same direction, i.e., either to positive or to negative PC AA . This indicates that most of the changes at the interface are due to mutated AAs in RBD.  In Figure 11, we display the PC AA for the RBD-ACE2 interface model in the form of standard solvent excluded layer for both WT ((a), (b), (c), (d)) and OV ((e), (f), (g), (h)). Figure 11c,g shows separated RBD and ACE2, which are further rotated in Figure 11d,h with highly positively and negatively charged AA marked. Comparison of PC AA of RBD shows the increase in positive charge in R493, K478, R457, and R498 marked in Figure  11h. Similarly, the PC AA of ACE2 shows the increase in negative charge in E23 and D30, and positive charge in L353 marked in Figure 11h. PC AA of all AAs in ACE2 for both WT and OV are listed in Table S2 and Table S3, respectively. Similarly, PC AA of all AAs in RBD for both WT and OV are listed in Table S4 and Table S5, respectively.

Implication of RBD-ACE2 Interface on Omicron Variants of SARS-CoV-2
It is well known that the Omicron variant causes higher infectivity [95]. Based on large-scale ab initio calculations, we provided some fundamental analysis for 15 mutations in OV and its interaction with ACE2. This includes AABP values indicating the strength of bonding. From AABP, we have analyzed all possible interactions between RBD and ACE2 and have identified all prominent AAs in both RBD and ACE2 that participating in the interaction. Here, AABP value predicts the strengthening of bonding between RBD and ACE2. Adding up all AABP values for interacting AAs between RBD-ACE2, we obtained a higher value for OV (1.46 e − ) in comparison to WT (1.33 e − ). Among the mutated AAs, K440, N477, R493, and S496 show an increase in binding with ACE2. AAs from ACE2 that interact with mutated and unmutated AAs of RBD have been identified to be S19 and E329, having the strongest bonding with OV RBD.
From the PC calculations, the increase in positive charge in both PC* and PC AA in OV is observed. This dominance in positive charge as a result of mutation is consistent with studies, which suggests development of negatively charged antibodies for better binding [92,94]. Based on PC of interacting AAs, it can be claimed that 80% of the interacting mutated AAs at the interface have changed the partial charge in positive direction. T20, L45, and E329 of ACE2 are the prominent AAs since they interact with RBD in OV, whereas this interaction is absent in WT. Prominent changes of PC in the surface of both RBD and ACE2 are identified to be R493, K478, R457, and R498 in RBD and E23 and D30 in ACE2. One of the interesting observations is R493 and R498 with noticeable change of PC in the surface have higher AABP values among 15 mutated AAs. This shows the connection between AABP and PC. The overall increase in volume, increase in sum of AABP between the RBD and ACE2 in OV, and change of PC of most of mutated AAs toward positive charges are important observations which can make OV more lethal and dangerous. The change in PC after mutation has functional implications, as

Implication of RBD-ACE2 Interface on Omicron Variants of SARS-CoV-2
It is well known that the Omicron variant causes higher infectivity [95]. Based on large-scale ab initio calculations, we provided some fundamental analysis for 15 mutations in OV and its interaction with ACE2. This includes AABP values indicating the strength of bonding. From AABP, we have analyzed all possible interactions between RBD and ACE2 and have identified all prominent AAs in both RBD and ACE2 that participating in the interaction. Here, AABP value predicts the strengthening of bonding between RBD and ACE2. Adding up all AABP values for interacting AAs between RBD-ACE2, we obtained a higher value for OV (1.46 e − ) in comparison to WT (1.33 e − ). Among the mutated AAs, K440, N477, R493, and S496 show an increase in binding with ACE2. AAs from ACE2 that interact with mutated and unmutated AAs of RBD have been identified to be S19 and E329, having the strongest bonding with OV RBD.
From the PC calculations, the increase in positive charge in both PC* and PC AA in OV is observed. This dominance in positive charge as a result of mutation is consistent with studies, which suggests development of negatively charged antibodies for better binding [92,94]. Based on PC of interacting AAs, it can be claimed that 80% of the interacting mutated AAs at the interface have changed the partial charge in positive direction. T20, L45, and E329 of ACE2 are the prominent AAs since they interact with RBD in OV, whereas this interaction is absent in WT. Prominent changes of PC in the surface of both RBD and ACE2 are identified to be R493, K478, R457, and R498 in RBD and E23 and D30 in ACE2. One of the interesting observations is R493 and R498 with noticeable change of PC in the surface have higher AABP values among 15 mutated AAs. This shows the connection between AABP and PC. The overall increase in volume, increase in sum of AABP between the RBD and ACE2 in OV, and change of PC of most of mutated AAs toward positive charges are important observations which can make OV more lethal and dangerous. The change in PC after mutation has functional implications, as the electrostatic charge modifies its ability to bind strongly with ACE2 or escape for antibody.

RBD-SD1 in S-Protein
The present work consists of two parts. The first part is described here, and it focuses on the receptor-binding domain (RBD) with subdomain 1 (SD1) of the SARS-CoV-2 Sprotein, which is referred to as the RBD-SD1 model and shown in Figure 12. The initial structure for the region of RBD-SD1 was obtained from Woo et al. (PDB ID: 6VSB) [96], which originated from Wrapp et al. [41].

RBD-SD1 in S-Protein
The present work consists of two parts. The first part is described here, and it focuses on the receptor-binding domain (RBD) with subdomain 1 (SD1) of the SARS-CoV-2 S-protein, which is referred to as the RBD-SD1 model and shown in Figure 12. The initial structure for the region of RBD-SD1 was obtained from Woo et al. (PDB ID: 6VSB) [96], which originated from Wrapp et al. [41]. In this part we compared Delta variant (DV) and Omicron variant (OV) with the Wild type (WT). There are total of 4059, 4072, and 4123 atoms in WT, DV, and OV model, respectively. From Woo et al.'s structure, we chose chain A of S-protein in its up confirmation. Sequence 330-591 was selected from the S-protein for RBD-SD1 (6VSB_1_2_1) model [96]. The glycans associated with the PDB are removed. Furthermore, hydrogen atoms were added using the Leap module with ff14SB force field in the AMBER package [97]. Sequence 330-591 was selected from the S-protein for RBD-SD1 (6VSB_1_2_1) model [96]. The glycans associated with the PDB are removed. Furthermore, hydrogen atoms were added using the Leap module with ff14SB force field in the AMBER package [97]. For RBD-SD1 DV, the two L452R and T478K mutations, shown in Figure 12a,b were generated using Dunbrack backbone-dependent rotamer library, as implemented in the UCSF Chimera package [98].

RBD-ACE2 Interface Complex
The second part of the present work focuses on the interactions at the interface between RBD and a portion of ACE2 for WT and OV. The structures of the interfaces were obtained from the PDB ID 6M0J [102] for the WT and from PDB ID 7WBP [103] for the OV. The model constructed for the calculation of RBD-ACE2 is displayed in Figure 13. Amino acids were included from the sequence S19-I88 and G319-T365 in the ACE2 region [66,68] and from sequence T333-G526 in RBD. The entire model has 311 amino acids (194 in RBD and 117 in ACE2). There are 4817 and 4873 atoms in the WT and OV interface models, respectively. In this OV RBD-ACE2 model there are only fifteen mutations since SD1 is not included. All the fifteen OV mutations are marked with red color in Figure 13. Hydrogen atoms were added using the Leap module with ff14SB force field in the AMBER package [97]. and T547K, as shown in Figure 12a,c. The conformations of K417N and N501Y were modeled using PDB ID 7V80 [99], while T478K used 7ORA [100]. The remaining thirteen OV mutations were modeled using the conformations with the highest probabilities from the Dunbrack backbone-dependent rotamer library [101].

RBD-ACE2 Interface Complex
The second part of the present work focuses on the interactions at the interface between RBD and a portion of ACE2 for WT and OV. The structures of the interfaces were obtained from the PDB ID 6M0J [102] for the WT and from PDB ID 7WBP [103] for the OV. The model constructed for the calculation of RBD-ACE2 is displayed in Figure 13. Amino acids were included from the sequence S19-I88 and G319-T365 in the ACE2 region [66,68] and from sequence T333-G526 in RBD. The entire model has 311 amino acids (194 in RBD and 117 in ACE2). There are 4817 and 4873 atoms in the WT and OV interface models, respectively. In this OV RBD-ACE2 model there are only fifteen mutations since SD1 is not included. All the fifteen OV mutations are marked with red color in Figure 13. Hydrogen atoms were added using the Leap module with ff14SB force field in the AMBER package [97].

Conclusions
In summary, we have provided a detailed account of the mutational effect of Delta and Omicron variants in the SARS-CoV-2 virus, based on large-scale ab initio quantum calculations, invoking the novel concept of AABPU as a special biomolecular unit. Part 1 is focused on the RBD-SD1 domain, showing that the Omicron mutations are much more significant than Delta mutations. We presented the change in the structure of residues involved in mutation, including the changes in pertinent hydrogen bonding. Part 2 presents the calculation of the Wild type and Omicron RBD-ACE2 interface complex, showing the much more enhanced binding between RBD and ACE2, providing additional evidence for the increased infectivity of Omicron variants. Specific mutations and their locations at the interface in both RBD and ACE2 are pointed out. We also obtained a detailed partial charge distribution on all the involved AABPUs and their respective central amino acid. These are very valuable data for experimental and clinical scientists.

Conclusions
In summary, we have provided a detailed account of the mutational effect of Delta and Omicron variants in the SARS-CoV-2 virus, based on large-scale ab initio quantum calculations, invoking the novel concept of AABPU as a special biomolecular unit. Part 1 is focused on the RBD-SD1 domain, showing that the Omicron mutations are much more significant than Delta mutations. We presented the change in the structure of residues involved in mutation, including the changes in pertinent hydrogen bonding. Part 2 presents the calculation of the Wild type and Omicron RBD-ACE2 interface complex, showing the much more enhanced binding between RBD and ACE2, providing additional evidence for the increased infectivity of Omicron variants. Specific mutations and their locations at the interface in both RBD and ACE2 are pointed out. We also obtained a detailed partial charge distribution on all the involved AABPUs and their respective central amino acid. These are very valuable data for experimental and clinical scientists. The results of our computations shed additional light on the properties of the emerging VOCs all the way down to the atomic scale.