The variants of Concern (VOCs) Alpha (B.1.1.7), Beta (B.1.351), Delta (B.1.617), and Omicron 23A (XBB.1.5) were selected based on their global epidemiological impact and prevalence between January 2021 and January 2023 as identified by Nextstrain phylogenetic analysis (Figure 1) [13][14].

Consensus amino‑acid sequences of the Spike protein for each variant were retrieved from covSPECTRUM platform which aggregates genomic surveillance data from the GISAID database [15][16]. The selection of the sequences was based on “Consensus sequence” feature, which identifies the most frequent amino acid mutations at each position for a specific variant.

Each retrieved sequence was validated through a BLAST alignment against the reference sequence of SARS-CoV-2 Spike protein (NCBI ID: YP_009724390.1) to confirm the presence of lineage-defining mutations. Furthermore, sequences were cross-referenced with the GISAID (Figure 2) to ensure they accurately represented the international consensus for each Variant of Concern (VOC) at the time of the study.

Three‑dimensional structural models were generated using an experimentally determined Spike structure (PDB ID: 7JJI) as the primary template. This template was selected because it represents a full-length (FL) prefusion spike trimer including the transmembrane (TM) domain and cytoplasmic tail (CT), providing a more biologically relevant framework of the closed state (3-RBD-down) of Spike [17]. The experimentally based template was pre-processed by computationally removing all non-amino acid moieties to eliminate potential stereochemical interference. Missing residues—of wild type (WT) and VOCs structures—were reconstructed using homology modeling tools with the SWISS-MODEL pipeline.

In parallel, a fully computational model was developed to be used as a comparative template for assessing the impact of conformational changes of Spike protein. Unlike the experimental template, this in silico model has one RBD in the “up” (open) conformation, representing the state primed for interaction with the ACE2 receptor. For WT, both experimental‑based and computationally-model structures were generated in order to compare structural changes due to conformational rearrangement.

The comparative analysis between variants was conducted exclusively using the networks derived from the experimental-based template, due to its superior structural quality and stability.

The structural reliability of these models was further validated through complex network analysis, following the criteria of Pražnikar et al. (2019), which distinguishes correct structural models based on global topological signatures [18]. For this purpose, protein structure networks were constructed following the parameters described in the next section.

Protein structure networks were constructed for the spike trimer assemblies using alpha‑carbon (Cα) atoms as nodes. Edges between nodes were defined based on a distance threshold of 7 Å between Cα atoms. This distance threshold was applied indiscriminately to both intra-chain and inter-chain contacts, allowing for the capture of critical communication pathways across the protein.

The use of Cα nodes and a 7 Å cutoff is a well-established approach for identifying legitimate residue contacts while minimizing noise from side-chain fluctuations. A 7 Å threshold represents a “topological signature” of the first coordination shell in proteins. This ensures that the network captures all complete and non-occluded contacts, providing a reliable basis for interpreting centrality and information flow within the large-scale Spike trimer [19].

To ensure a statistically consistent comparison of network metrics between the “open” and “closed” states of WT Spike, the node sets were equalized across both structural scaffolds. The computational model was processed to match the sequence coverage of the experimental template for the final network construction.

Network analysis was performed using Python‑based computational tools implemented within the Anaconda data science environment, while visual representations were made with Cytoscape [20].

The following graph‑theoretical metrics were calculated: node degree, betweenness centrality, closeness centrality, clustering coefficient, eigenvector centrality, and eccentricity [21][22]. These measures allow the identification of residues involved in communication pathways and structural connectivity within the protein.

To establish a baseline for the protein’s mechanics, a comparative analysis was first performed between the “open” and “closed” states using the reference sequence (Wild-Type) structure for both the experimental-based template (3-RBD-down) and the computational-based template (1-RBD-up). This approach ensures that the fundamental topological shifts associated with the RBD transition are captured.

Subsequently, the analysis of SARS-CoV-2 of VOCs was conducted exclusively using networks derived from the experimentally based template. This strategy was chosen to maintain high structural fidelity across the comparative framework.

Statistical analyses were performed to evaluate topological differences across conformational states and viral variants. To determine the statistical significance of changes between the “open” (1-RBD-up) and “closed” (3-RBD-down) states, the non-parametric Mann-Whitney U test was employed, while for the comparative analysis among VOCs, a Welch’s ANOVA was conducted followed by post-hoc tests.

Analysis of genomic surveillance data revealed that the variants Alpha, Beta, Delta, and Omicron represented major waves of global SARS‑CoV‑2 transmission [23]. The temporal prevalence of these variants and their global distribution during the pandemic are illustrated in Figure 1.

Figure 1. Global prevalence of major SARS-CoV-2 variants during the COVID-19 pandemic.The figure illustrates the frequency of reported COVID-19 cases associated with the Alpha (B.1.1.7), Beta (B.1.351), Delta (B.1.617), and Omicron (XBB.1.5) variants over time. Data were obtained from global genomic surveillance platforms and represent the relative prevalence of each variant during different phases of the pandemic. Graph obtained from the Nextstrain [23].

Each variant contained characteristic mutations within the Spike protein sequence, particularly within the receptor‑binding domain and the N‑terminal domain. These mutations are known to influence receptor binding affinity, antibody recognition, and viral infectivity. The distribution and prevalence of mutations across the Spike protein sequence for each variant are shown in Figure 2.

Figure 2.Distribution and prevalence of mutations in the SARS-CoV-2 Spike protein across major variants. Heatmap representation of mutation frequencies within the Spike protein sequence for the Alpha, Beta, Delta, and Omicron variants. Darker colors indicate higher mutation prevalence at specific amino-acid positions. Data were compiled from the GISAID database [15].

Three‑dimensional structural models were successfully generated for the Spike protein trimer of WT and each variant. Structures derived from experimental templates included residues from positions 14 to 1146, whereas the original computational model incorporated the full sequence length (1 - 1273) and was subsequently processed to match the experimental template coverage. Representative structural models of the Spike protein for the Alpha, Beta, Delta, and Omicron variants, highlighting the mutations, are shown in Figure 3.

Models derived from the experimental template achieved an average QMEANDisCo score of 0.74 ± 0.05 and GMQE of 0.67, while these scores reflect some local uncertainty in highly flexible loops—inherent to the dynamic nature of the Spike protein and the limitations of experimental recovery in those regions—they indicate a high degree of structural reliability for the folded domains. In parallel, the fully computational model yielded a lower average QMEANDisCo score of 0.62 ± 0.05 and GMQE of 0.67. The slightly superior performance is likely attributed to the “closed” (3-RBD-down) conformation of the 7JJI template, since by maintaining all three RBDs in the down position, the structure achieves a more compact arrangement, which might reduce the conformational uncertainty of the protein’s flexible regions—particularly RBDs—by limiting their range of motion, compared to the open state. However, in terms of stability, recent studies demonstrate that SARS-CoV-2 variants have developed an “open spike” strategy, characterized by greater kinetic stability of the open conformation to facilitate interaction with the ACE2 receptor [25].

Figure 3.Three-dimensional structural models of SARS-CoV-2 Spike variants. Structural representations of the Spike protein trimers for the Alpha (A), Beta (B), Delta (C), and Omicron (D) variants. These models highlight the differences arising primarily from variant-specific mutations affecting the RBD and surrounding regions. Images obtained from ViralZone [24].

This divergence justifies our strategy of utilizing the experimentally based networks as the primary framework for variant comparison, as it provides a better topological scaffold for detecting mutation-induced changes without the added complexity of “up” state conformation.

Protein structure networks were generated for each conformational state to characterize the underlying residue interaction patterns. Visual representation of the trimer alignment (Figure 4(A)) and the resulting networks for the closed (Figure 4(B)) and open (Figure 4(C)) states reveals that while the global scaffold remains, the mechanical activation of the receptor-binding domain (RBD) induces a localized topological reconfiguration.

Networks generated for each variant displayed similar global connectivity patterns but showed local differences associated with mutation sites. The comparison of the protein structure network representation of the Spike protein VOCs is shown in Figure 5. The average node degree values fell within the expected range for correctly folded protein structures [18]. This indicates that the generated structural models maintain realistic residue interaction patterns.

Figure 4.Conformational and network representation of the SARS-CoV-2 Spike protein. (A) Structural alignment between the closed (all-RBD-down in green) and open (one-RBD-up in magenta) states. (B) Residue interaction network of the trimer in the closed state. (C) Residue interaction network in the open state. Nodes are colored by secondary structure, in red α-helices, in blue β-sheets and in grey loops.

Figure 5.Comparative protein structure networks across SARS-CoV-2 Variants of Concern (VOCs). Visual representation of the residue interaction networks in the closed state for (A) Alpha, (B) Beta, (C) Delta, and (D) Omicron variants. Nodes are colored by secondary structure: red (α-helices), blue (β-sheets), and grey (loops).

The structural changes Spike overcomes to shift from the closed (all-RBD-down) to the open (one-RBD-up) state induced a significant global rearrangement of the protein’s network topology. Statistical comparisons of centrality measures demonstrated that while the distributions of closeness centrality (p < 0.001), eigenvector centrality (p < 0.001), degree (p = 0.050), and eccentricity (p < 0.001) shifted significantly, the global communication of the backbone remained, as evidenced by the non-significant variations in betweenness centrality (p = 0.337) and the clustering coefficient (p = 0.070). Nevertheless, visual analysis of the centrality profiles reveals that despite the statistical stability of the overall betweenness distribution, there is a clear reorganization of communication pathways across the trimer; specifically, chain C exhibits a marked increase in betweenness peaks (Figure 6(A)) when its RBD is in the “up” position, suggesting a localized concentration of information flow. This is accompanied by a localized increase in eigenvector centrality (Figure 6(B)) and a marked change in eccentricity (Figure 6(C)), reflecting a redistribution of node influence and structural distance within the activated protomer which can also be observed in the distinct reduction in closeness centrality values within the Chain C RBD during activation, as the structural opening increases the shortest path distances between the protruding domain and the rest of the protein network (Figure 6(D)). The significant differences in degree distributions reflect a localized gain in connectivity for specific residues during the RBD extension (Figure 6(F)), whereas the stability of the clustering coefficient indicates that the local modularity and the density of neighboring interactions remain largely unaffected by the conformational change (Figure 6(E)). These hierarchical modifications indicate a transition toward a functionally primed state, consistent with the increased kinetic stability of open spike conformations observed by Yang and collaborators (2022).

Figure 6.Comparative analysis of network centrality metrics between the closed and open states of the SARS-CoV-2 Spike protein. The topological profiles for the Wild-Type reference sequence are shown for the “closed” (3-RBD-down, green line) and “open” (1-RBD-up, magenta line) conformations. The metrics include (A) Betweenness Centrality, (B) Eigenvector Centrality, (C) Eccentricity, (D) Closeness Centrality, (E) Clustering Coefficient, and (F) Degree.

The comparative analysis among VOCs within “closed” state, revealed that lineage-specific mutations induce a targeted reorganization of the protein’s hierarchical influence rather than a global structural breakdown. There were no significant differences in the distributions of betweenness centrality, closeness centrality, degree, and clustering coefficient across variants (p > 0.05), indicating a high degree of conservation in the trimer’s fundamental backbone (Figure 7). However, significant statistical divergence was identified in eigenvector centrality (EC) and eccentricity (p< 0.001), suggesting that mutations in Alpha, Beta, Delta, and Omicron variants strategically reconfigure node influence and structural distances. Post-hoc tests confirmed that Omicron was the most divergent lineage, showing significant differences in eigenvector centrality compared to all other variants (p < 0.001).

The nodes with the highest eigenvector centrality are those connected to other highly central nodes, making this metric a robust way of determining a node’s dominance and its role as a principal channel for information flow within the network [26][27]. Furthermore, changes in eccentricity between the VOCs (p = 0.011) shows a redistribution of the protein’s structural distances, since—an amino acid with high eccentricity in comparison to the network’s average—will be impacted more rapidly by other residues or, conversely, may easily affect numerous amino acids, suggesting that mutational shifts in both of this metrics optimize the speed and reach of allosteric signaling [26].

It is noticeable that while Alpha and Delta variants concentrate their primary values of EC in chain C and A, respectively, Omicron exhibits distributed EC values across the entire trimer. This transition from centralized to distributed dominance hubs may reflect an evolutionary trend towards a more resilient allosteric network. The topological characteristic of the Omicron variant identified in this study is strongly supported by recent Protein Contact Network (PCN) analyses, which similarly highlight Eigenvector Centrality as a distinctive topological feature of Omicron, contrasting with Alpha and Delta. Apparently, this shift is independent of the total number of mutations, representing instead a qualitative change in the role of mutated residues within the network [28].

Figure 7.Comparative network centrality profiles across SARS-CoV-2 Variants of Concern (VOCs). Topological distributions are shown for Alpha (dark blue), Beta (magenta), Delta (cyan), and Omicron (orange) variants in the closed state. The panels display (A) Betweenness Centrality, (B) Eigenvector Centrality, (C) Eccentricity, (D) Closeness Centrality, (E) Clustering Coefficient, and (F) Degree.

Centrality analysis also revealed that residues located within the receptor‑binding domain and the subunit interface exhibited high betweenness centrality values (Figure 7(A)). These residues likely act as communication hubs within the protein structure. Mutations present in certain variants were found near residues with high centrality values, suggesting that these mutations may alter structural communication pathways and influence long‑range interactions within the protein.

Comparative analysis between variants suggests that mutations associated with highly transmissible variants may affect network connectivity between structural domains of the Spike protein. In particular, changes near the receptor‑binding motif may influence communication between the S1 and S2 subunits, potentially altering conformational dynamics involved in viral entry [29]-[32].