Quantifying the contribution of individual residues or residue groups to protein function is important to estimate the pathogenic effect of mutations (Stenson et al., 2017). Identifying the functional roles of individual residues has primarily been done through mutagenesis experiments (Matreyek et al., 2018). Bioinformatics methods have complemented these approaches through analysis of multiple sequence alignments (MSA) of homologous proteins and structural data (Poelwijk et al., 2016; Høie et al., 2022; Blaabjerg et al., 2023; Dunham and Beltrao, 2021; Hopf et al., 2017; Radivojac et al., 2013). Among these methods, computational techniques that can decode inter-residue evolutionary relationships from MSAs have paved the way for machine learning (ML)-based strategies that can predict protein structure (Jumper et al., 2021; Lin et al., 2023; Baek et al., 2021; Marks et al., 2012), stability (Broom et al., 2020), and function (Hopf et al., 2017) and extend the scope of computational protein design (Ding et al., 2024; Wu et al., 2019; Russ et al., 2020). A most recent approach has combined experimental data from three proteins, NUDT15, PTEN, and CYP2C9, on the stability and function with sequence and structural features to train an ML model to predict functional sites (Cagiada et al., 2023).

Functional sites are often regulated by both local and global interactions. Changes in these interactions are instrumental for functional events like substrate binding, catalysis, and conformational changes (Wodak et al., 2019). The development of physical models of protein dynamics and the increase in available computational power has stimulated the adoption of computational techniques (Campitelli et al., 2020; Rodrigues et al., 2021) to investigate the conformational dynamics of proteins, an essential component of the many biological functions (Henzler-Wildman and Kern, 2007; James and Tawfik, 2003). Different models have been proposed to describe the interactions between residues during simulations and network models have been particularly popular, including methods on single structures and molecular dynamics (MD) simulations data built by analysing the response to external forces on residue networks (Nevin Gerek et al., 2013), estimating the prevalence of non-covalent energy interaction networks in homologous proteins (Yehorova et al., 2024), or analysing linear or non-linear correlation in atomic fluctuations (Lange and Grubmüller, 2006; Osuna, 2021). These techniques have demonstrated their usefulness in extracting allosteric networks from structural data with applications in enzyme design (Osuna, 2021).

However, none of these techniques incorporate information on residue evolution into the computational approach, while it has been established that evolution through compensatory mutations in dynamic regions, like hinges and loops, can fine-tune protein structural dynamics and introduce promiscuity, thereby diversifying biological function. Assuming that protein functional dynamics is conserved during evolution, significant information on dynamic regions and substrate recognition sites should be recoverable using inter-residue coevolution scores extracted from MSAs (Granata et al., 2017; Liu and Bahar, 2012). Coevolution analysis and MD simulations have independently (Parente et al., 2015) and synergistically been combined in the past to identify important residues for function (Ponzoni et al., 2015; Sutto et al., 2015; Estabrook et al., 2005; Chen et al., 2011; Wang et al., 2013). Yet a method that combines hidden information on dynamics from evolution with direct information on local and global dynamics from conformational ensembles from MD is not yet available.

Here, we present DyNoPy, a computational method that can extract hidden information on functional sites from the combination of pairwise residue coevolution data and powerful descriptors of dynamics extracted from the analysis of MD ensembles. The method can detect coevolved dynamic couplings, that is, residue pairs with critical dynamical interactions that have been preserved during evolution. These pairs are extracted from a graph model of residue–residue interactions. Communities of important residue groups are detected, and critical sites are identified by their eigenvector centrality in the graph (Figure 1). We demonstrate the power of this approach on SHV-1 and PDC-3 β-lactamases of major clinical importance (Olehnovics et al., 2021; Chen et al., 2024). DyNoPy successfully detects residue couplings that align with previous studies, guide in the explanations of mutation sites with previously unexplained mechanisms, and provide predictions on plausible important sites for the emergence of clinically relevant variants.

Figure 1

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β-Lactamases are a group of enzymes capable of hydrolysing β-lactams, conferring resistance to β-lactam antibiotics (Poole, 2004). These enzymes are evolving rapidly as single amino acid substitutions are sufficient to drive their evolution and increase their catalytic spectrum and inhibitor resistance profile (Bush, 2018). The widespread dissemination of β-lactamases across different bacterial species and their extensive emergence highlight their global impact on antibiotic resistance (Bush, 2013). The rapid evolution of β-lactamases and their clinical significance (Bush, 2018) makes them an ideal target for evaluating the robustness of DyNoPy.

In this study, we applied DyNoPy to two model enzymes from different β-lactamase families: class A β-lactamase SHV-1 (a chromosomally encoded enzyme in Klebsiella pneumoniae) and class C β-lactamase PDC-3 (a chromosomally encoded enzyme in Pseudomonas aeruginosa) (Olehnovics et al., 2021; Chen et al., 2024; Figure 2). Both class A and class C β-lactamases comprise an α/β domain and an α helical domain, with the active site situated in between (Matagne et al., 1998; Philippon et al., 2022). Moreover, both enzymes target the carbonyl carbon of the β-lactams using a highly conserved serine residue (Palzkill, 2018; Jacoby, 2009). Despite these similarities, the structures of class A and class C β-lactamases are remarkably different (Figure 2—figure supplements 1 and 2). In class A β-lactamases, the active site is surrounded by three loops: the α3-α4 loop (residues 101–111), the Ω-loop (residues 164–179), and the hinge region (residues 213–218) (Galdadas et al., 2021). The Ω-loop is particularly critical as it positions N₁₇₀ to hydrogen bond with the E₁₆₆ via a conserved water molecule, which is essential for initiating the deacylation step (Kuzin et al., 1999). Compared to class A β-lactamases, the active site of class C β-lactamases is wider, conferring a broader substrate binding capability (Medeiros, 1997; Figure 2—figure supplement 3). The active site of class C β-lactamases can be divided into two parts: the R1 site and the R2 site (Jacoby, 2009). The R1 region is surrounded by the extended Ω-loop (residues 183–226), while the R2 site is enclosed by the R2-loop (residues 280–310) (Chen et al., 2024). The Ω-loop in class C β-lactamases is significantly longer than that in class A, enhancing the active site ability to accommodate diverse substrates and contributing to the extended spectrum profile of some class C enzymes (Chen et al., 2024).

Figure 2 with 3 supplements see all

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SHV-1 is a very well-characterized enzyme with a wealth of information on mutations and their corresponding effects on protein function. In contrast, the information available on PDC-3 remains limited. Essential catalytic residues in SHV-1 are S₇₀, K₇₃, S₁₃₀, E₁₆₆, N₁₇₀, K₂₃₄, G₂₃₆, and A₂₃₇ (Ambler et al., 1991), and conserved catalytic residues in PDC-3 include S₆₄, K₆₇, Y₁₅₀, N₁₅₂, K₃₁₅, T₃₁₆, and G₃₁₇. Highly conserved stretches of 3–9 hydrophobic residues, annotated as hydrophobic nodes, exist in class A β-lactamases and have been proven to be essential for protein stability (Galdadas et al., 2018). Residues defined as belonging to hydrophobic nodes within SHV-1 are listed in Supplementary file 1a.

In SHV-1, the predominant extended spectrum β-lactamase (ESBL) substitutions occur at L₃₅, G₂₃₈, and E₂₄₀, while R₄₃, E₆₄, D₁₀₄, A₁₄₆, G₁₅₆, D₁₇₉, R₂₀₂, and R₂₀₅ appear in ESBLs with lower frequency (Liakopoulos et al., 2016). Mutations at M₆₉, S₁₃₀, A₁₈₇, T₂₃₅, and R₂₄₄ are known to induce inhibitor resistance in the enzyme (Pagan-Rodriguez et al., 2004). In PDC-3, substitutions primarily occur on the Ω-loop, enhancing its flexibility to accommodate the bulky side chains of antibiotics, while deletions are more common in the R2-loop (Jacoby, 2009). The predominant Ω-loop mutations isolated from clinics are found at positions V₂₁₁, G₂₁₄, E₂₁₉, and Y₂₂₁ (Barnes et al., 2018).

Emergence of highly conserved dynamic couplings

DyNoPy builds a pairwise model of conserved dynamic couplings detected by combining coevolution scores and information on functional motions into a score J_ij (see ‘Methods’ and Figure 1). To this end, a dynamic descriptor should be selected. When the descriptor is associated with functional conformational changes, it is expected that functionally relevant couplings will report higher scores. Dynamic descriptors can be selected from commonly used geometrical collective variables (CVs) for the analysis of MD trajectories (see ‘Methods’). As expected, the average J matrix score varies across the different CVs, with some of them showing no signal of dynamic coupling (Figure 3A).

Figure 3 with 1 supplement see all

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SHV-1 and PDC-3 exhibit distinct dynamics, requiring a different choice of the CV that best captures the functional dynamics. For SHV-1, the global first principal component (PC1) proved to be the most effective feature, identifying 571 residue pairs with a J_ij value greater than 0. Conversely, PDC-3 requires selection of more localized features that can extract the Ω-loop dynamics from the overall protein motion. Among the dynamic descriptors, the partial first time-lagged component (TC1_partial) performed best for PDC-3, detecting 216 residue pairs with a J_ij value greater than 0. Consequently, PC1 and TC1_partial were selected to build the J matrix for SHV-1 and PDC-3, respectively. The performance of all 12 CVs for each protein was assessed and listed in Supplementary file 1b.

The importance of dynamical information is evident when coevolution couplings (${\gamma }_{ij}$) and conserved dynamic couplings (J_ij) are compared: the number of non-zero couplings decreases from 40% to <2% of total residue pairs in the protein (Figure 3B) when information from the dynamics descriptor is added. Thus, the inclusion of protein dynamics in coevolution studies acts as an effective filter that rules out residue pairs that do not have significant correlations with functional motions. Moreover, when relying only on ${\gamma }_{ij}$, all the residues in SHV-1 and PDC-3 are included within four identified communities (Supplementary file 1c), suggesting that coevolution scores (${\gamma }_{ij}$) alone do not effectively discriminate residues relevant for protein functions. Furthermore, it would be hard to distinguish critical core residues for each community using only ${\gamma }_{ij}$ as the eigenvector centrality (EVC) values for the residues do not show remarkable differences (Figure 3—figure supplement 1A and B). This means that detailed dynamic investigation of the top residues is needed to determine which pairs should be picked up and further analysed. On the other hand, it is much easier to identify essential residues based on J scores calculated as clear outliers with significantly higher EVC values could be seen for almost all communities (Figure 3—figure supplement 1C and D; Parente et al., 2015; Negre et al., 2018). In conclusion, the lack of specificity in the statistically based coevolution analysis supports the choice of incorporating a score for the correlation between residue interactions and dynamic behaviours that enables deconvolution of community information.

DyNoPy reveals critical residues and predicts evolutionary pathways in SHV-1

DyNoPy identified eight meaningful communities, each consisting of at least three strongly coupled residues within SHV-1 (Figure 3C). All crucial catalytic residues and critical substitution sites previously mentioned participating in one of these communities with the exceptions of R₄₃, R₂₀₂, and S₁₃₀. Residues previously known to have critical role in function or conferring ESBLs/IRBLs phenotype are either directly coupled to protein dynamics or act as a central hub. The hubs interact with residues with either a role in catalysis or structural stability through their membership of hydrophobic nodes (Olehnovics et al., 2021). Furthermore, DyNoPy identified key positions (L₁₆₂ and N₁₃₆) within some communities that are known to undergo substitutions, conferring an ESBL phenotype in other class A β-lactamases. These substitutions have not yet emerged in the SHV family, providing insightful predictions about the potential future evolution of the enzyme. Detailed discussions of communities with secondary importance for protein function (communities 3, 8, and 9) is provided in the Appendix (Appendix 2—figure 1).

DyNoPy predicts mutation hotspots in SHV-1

DyNoPy detects critical mutation sites (L₁₆₂ and N₁₃₆) that are known to extend the range of substrates in other class A β-lactamases but have not yet emerged as variants in the SHV family. These sites have not been modified in the SHV family because of their plausible central role within the communities as they are mediating couplings with key functional residues essential for catalytic activity and structural stability, indicating their critical role in protein function and the potential lower mutation rate. These findings provide insightful predictions about the potential future evolution of the enzyme, as well as plausible explanations for why these mutations have not yet appeared.

L_162, positioned at the start of the Ω-loop and adjacent to the crucial catalytic residue E_166, is assigned as the core residue for community 1 (Figure 4A). While it remains conserved in the SHV family, variants of L₁₆₂ have been isolated in other class A β-lactamase and are known to expand the enzyme catalytic spectrum. Single amino acid substitution at L₁₆₂ can intensify antibiotic resistance in BEL-1 (Pozzi et al., 2016), a class A ESBL clinical variant, exhibiting robust resistance to ticarcillin and ceftazidime (Bogaerts et al., 2007). BEL-2 diverges from BEL-1 by single amino acid substitution (L₁₆₂F), which alters the kinetic properties of the enzyme significantly and increases its affinity towards expanded-spectrum cephalosporins (Poirel et al., 2010). The relationship between L₁₆₂ and protein catalytic functions can be explained using DyNoPy model as there are couplings with catalytic important residues M₆₉, K₇₃, E₁₆₆, and K₂₃₄. Moreover, the BEL case has confirmed that L₁₆₂F mutation significantly destabilizes the overall protein structure, highlighting the crucial role of L₁₆₂ in maintaining protein stability (Pozzi et al., 2016). DyNoPy accurately identifies the centrality of L₁₆₂ by reporting its connections with 28 backbone residues, including 9 hydrophobic node residues critical for protein stability. Among these, five hydrophobic residues are part of the α2 node: V₇₅, L₇₆, G₇₈, V₈₀, and L₈₁, highlighting the contribution of L₁₆₂ to the stability of the α2 helix (Olehnovics et al., 2021).

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Just like L₁₆₂, N₁₃₆ undergoes advantageous mutations in other class A β-lactamases while remains highly conserved within the SHV family. It is the core residue for community 7 (Figure 5B). This residue forms a hydrogen bond with E₁₆₆, stabilizing the Ω-loop (Bös and Pleiss, 2008). Although DyNoPy did not detect this direct interaction between N₁₃₆ and E₁₆₆, the established relationship between N₁₃₆ and N₁₇₀ highlights the role of N₁₃₆ in influencing E₁₆₆. N₁₇₀, an essential catalytic residue located on the Ω-loop, contributes to priming the water molecule for the deacylation step with E₁₆₆ (Agarwal et al., 2023), and is directly coupled with N₁₃₆. Due to the essential contribution of N₁₃₆ in facilitating E₁₆₆ to maintain its proper orientation, it was previously thought to be intolerant to mutations as substitution of asparagine to alanine at this position would make the enzyme lose its function completely (Cao et al., 2020). However, N₁₃₆D substitution has emerged as a new clinical variant very recently in PenL, a class A β-lactamase, by increasing its ability in hydrolysing ceftazidime (Cao et al., 2020), suggesting that this site has potential to mutate. This gain of function is mainly triggered by the increased flexibility of the Ω-loop (Cao et al., 2020). DyNoPy correctly detects a dynamical relationship between N₁₃₆ and the Ω-loop (residues 164–179). Six residues present in the Ω-loop participate within this community, including R₁₆₄ and D₁₇₉. These two residues are critical as they are forming the ‘bottleneck’ of the Ω-loop which is essential for the correct position of E₁₆₆ (Parwana et al., 2024). D₁₇₉ is also a critical mutation site for SHV-1. Single amino acid substitutions like D₁₇₉A, D₁₇₉N, and D₁₇₉G are enough for the extended spectrum phenotype (Liakopoulos et al., 2016).

Figure 5

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DyNoPy detects residue couplings essential for protein stability

DyNoPy identifies residue couplings critical for protein functional motions, particularly associated with protein stability. These residue pairs exhibit strong relationships as they are not only directly coupled with each other but also forms various indirect couplings via other residues. As a result, both residues are considered as core residues inside these communities. It is expected that disruption of these couplings through mutation could compromise collective motions essential for enzyme activity.

As the secondary core residues in community 1 (Figure 4A), F₇₂ is showing a strong coupling with the primary core residue L₁₆₂ and also forms nine indirect couplings with L₁₆₂, including via the catalytic K₂₃₄. This network of direct and indirect relationships reveals the importance of F₇₂ and L₁₆₂ coupling in maintaining protein functional motions. Interestingly, previous studies identified a small hydrophobic cavity formed by L₁₆₂ and F₇₂, together with L₁₃₉, and L₁₄₈, which is essential for the stability of the active site (Pozzi et al., 2016). Notably, DyNoPy successfully recovers the key residues of this local hydrophobic cavity (L₁₆₂, F₇₂, and L₁₄₈).

The strong interplay between V₁₀₃ and S₁₀₆, which are both residues on the α3-α4 loop, is seen in community 5 (Figure 4C). These residues not only interact with each other directly but are also indirectly coupled via 22 other residues. This community emphasizes the significance of hydrophobic nodes in SHV stability and dynamics. Within the analysed 48 residues, 27 are hydrophobic, out of which 15 residues act as nodes critical for enzyme stabilization. Hydrophobic nodes stabilize their own secondary structures and interconnect to stabilize the overall protein (Galdadas et al., 2021). V₁₀₃ and S₁₀₆ themselves are hydrophobic nodes, stabilizing α3 helix and α4 helix, respectively, and are strongly coupled with each other. In CTX-M, another class A enzyme, N₁₀₆S is a common substitution that results in improved thermodynamic stability and compensate for the loss in stability of the variants (Lu et al., 2022). Interestingly, this residue is already a serine in SHV but still implies its pivotal role in protein stability.

DyNoPy provides valid explanations for mutation sites

During the evolution of β-lactamases, single mutations on specific sites that are distant from the functional sites have been observed to significantly alter protein catalytic functions. Additionally, single mutations on some surface exposed residues can dramatically increase protein stability. Understanding how these distant mutations impact function and stability becomes a major challenge in understanding protein evolutionary pathways. Communities extracted by DyNoPy show these residues linked with functional important residues, providing a rational for these mutation sites with unknown functions.

Mutations of G₁₅₆ are limited but they lead to ESBL phenotype in the SHV family (Liakopoulos et al., 2016). G₁₅₆ is the central residue for community 4 (Figure 4B), but it is distant from the active site, over 20 Å away from the catalytic serine S₇₀. Clinical variant SHV-27 has extended resistance ability towards cefotaxime, ceftazidime, and aztreonam (Corkill et al., 2001). It differs from SHV-1 by single amino acid substitution G₁₅₆D, suggesting that it has directly evolved from SHV-1 (Corkill et al., 2001). Limited research has been done on position G₁₅₆, and the understanding of how it affects the enzyme catalytic properties given that it is far away from the active site is still unclear. Based on our results, we suggest that this residue is essential for the overall protein function because of its 11 coevolved dynamic couplings with protein dynamics, including A₁₄₆, another ESBL substitution site.

SHV-38, another ESBL that is capable of hydrolysing carbapenems, harbours a single A₁₄₆V substitution compared to SHV-1 (Poirel et al., 2003). Like G₁₅₆, A₁₄₆ is 16.8 Å away from S₇₀ but shows an ability in altering protein catalytic function. The A₁₄₆-G₁₅₆ residue pair shows a strong coevolutionary signal and strong correlation with protein overall dynamics, implying that there may compensatory mutations at these sites with potential to emerge in the SHV family in the future. These two residues are not connected to any catalytic residues but their coupling to functional dynamics can offer plausible explanation to ESBL activity of these two mutations.

Unlike other substitution sites that are adjacent to the active site, R₂₀₅ is situated more than 20 Å away from catalytic serine S₇₀. Its side chain points outwards from the protein, exposing to the solvent. The R₂₀₅L substitution often co-occurs with other ESBL mutations and is thought to indirectly contribute to the ESBL phenotype by compensating for stability loss induced by other mutations (Ben Achour et al., 2009). SHV-3 is an ESBL that exhibits significant resistance to cefotaxime and ceftriaxone (Nicolas et al., 1989). Two substitutions in this enzyme, R₂₀₅L and G₂₃₈S, extend its resistance profile (Nicolas et al., 1989). Thus, it is promising to see that DyNoPy detected these two mutation sites together within community 6 (Figure 5A).

Y₁₀₅ and R₂₆₆ are the core residues for community 6 (Figure 5A). Y₁₀₅ is situated on the α3-α4 loop positioned at the left side of the binding pocket. It is an important catalytic residue that recognizes and binds to the thiazolidine ring of penicillins or β-lactamase inhibitors (Bethel et al., 2006). There is very limited information on the role of R₂₆₆, except that it may stabilize the Ω-loop in the SHV family similar to the analogous T₂₆₆ in TEM (Kuzin et al., 1999). G₂₃₈ is coupled with an essential catalytic residue Y₁₀₅, which further links with other catalytic functional residues: S₇₀ and A₂₃₇, and R₂₆₆, a residue that is known to stabilize the Ω-loop. This indicates that mutations on G₂₃₈ would result in an alteration on protein catalytic function, as well as an increased flexibility of the protein, which strongly aligns with previous finding (Nicolas et al., 1989). Its linked mutation site R₂₀₅ does not show direct coupling with any catalytic residues. Instead, it is directly coupled with R_266, which we mentioned as an Ω-loop stabilizer. Thus, it is not surprising that R₂₀₅ substitution alone is never observed in nature (Neubauer et al., 2020) as it would not give significant evolutionary advantage to the protein.

Insights into the unexplained functional sites of PDC-3

Unlike the extensively studied SHV-1, the functional roles of individual amino acids in PDC-3 remain largely unexplored. This gap in understanding serves as welcome challenge for interpreting the effects of mutations and the dynamic behaviour of PDC-3 from our results. Although several mutation hotspots, such as those on the Ω-loop (Barnes et al., 2018), have been identified, very little is known about the specific contributions of individual amino acids on the functionality of PDC-3.

In PDC-3, mutations have primarily been reported in the Ω-loop. They enhance its flexibility to accommodate the bulky side chains of antibiotics, while deletions are more common in the R2-loop (Jacoby, 2009). DyNoPy detected five communities in total (Figure 3D), with all the four predominant Ω-loop mutations appearing in these communities. Communities 3, 4 and 5 are discussed in the Appendix (Appendix 2—figure 2). Furthermore, DyNoPy also detected several previously unexplored Ω-loop residues.

G₂₁₄, a known mutation site in PDC-3, is the core residue in community 1. Another two essential mutation sites, E₂₁₉ and Y₂₂₁, also participate in this community, directly coupled with G₂₁₄ (Figure 6A). G₂₁₄ also has direct couplings with four other Ω-loop residues: A₁₉₅, A₁₉₇, G₂₁₂, and L₂₁₆. Previous results have demonstrated that substitutions of glycine to alanine or arginine at 214 significantly destabilize the Ω-loop (Chen et al., 2024). The strong correlation between G₂₁₄ and these Ω-loop residues emphasizes the significant contribution of G₂₁₄ towards the stability of the Ω-loop, which corroborates with previous results (Chen et al., 2024). Moreover, substitutions such as G₂₁₄A and G₂₁₄R and mutations on E₂₁₉ and Y₂₂₁ do not affect R2 loop flexibility, resulting in the smaller active site volume among variants (Chen et al., 2024) because none of the residues from the R2 loop are detected in this community, offering plausible explanation to the previously unexplained phenomenon.

Figure 6

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G₂₀₄ is the core residue of community 2, coupled with 73 other residues, most of which are distant from the catalytic site, suggesting plausible crucial role in the overall protein stability like L₁₆₂ in SHV-1 (Figure 6B). G₂₀₄, a newly emerged mutation site in the PDC family (67), is located on the short β-sheet β5a within the Ω-loop, near the hinge region between β8 and β9 just above the active site. The only known variant of G₂₀₄ is PDC-466, which was derived from PDC-462 (A₈₉V, Q₁₂₀K, V₂₁₁A, N₃₂₀S), with an addition of G₂₀₄D (Colque et al., 2021). Coupling of G₂₀₄ to several catalytically important residues, including K₆₇, K₃₁₅, and T₃₁₆ can suggest that mutations at this site can negatively impact catalytic power. This offers a plausible explanation of seeing fewer variants at this site, and mutations at this site could have an impact on the hydrolysing capabilities of PDC variants. This should be confirmed by further experimental studies of variants of G₂₀₄. Unlike G₂₁₄, E₂₁₉, and Y₂₂₁ mutations which do not influence the dynamics of the R2 loop, substitutions on V₂₁₁, a member of Ω-loop, have an impact on the dynamics of the R2 loop because of its indirect couplings, through G₂₀₄ to R2-loop residues (Chen et al., 2024). Two less critical substitution sites, H₁₈₈ and V₃₂₉, were also observed in community 2.

DyNoPy generates a graph representation of the protein structure that captures the couplings between amino acid residues contributing to the functional dynamics of the protein. Residues are represented as graph nodes, and conserved dynamic couplings are recorded as edges. Edge weights quantify the strength of these couplings. The model is built on two assumptions: residue pairs should have (a) coevolved and their (b) time-dependent interactions correlate with a functional conformational change.

Therefore, edge weights ($J_{ij}$) for residue $i$ and $j$ are calculated as

where ${\gamma }_{ij}$ is the scaled coevolution score and ${\rho }_{ij}$ is the degree of correlation with the selected functional conformational change. α and β are weights assigned to ${\gamma }_{ij}$ and ${\rho }_{ij}$ that have a sum of 1. The relative weight of the scaled coevolution score (α) is set to 0.5 in this study. When either of the assumptions listed above is not met, $J_{\mathit{i}\mathit{j}}$ is set to zero.

All files required to run the simulations (topology, coordinates, input), processed trajectories (xtc), corresponding coordinates (pdb), can be downloaded from https://doi.org/10.57760/sciencedb.15876 (PDC-3) and https://doi.org/10.5281/zenodo.13693144 (SHV-1). DyNoPy is available at https://github.com/alepandini/DyNoPy, (copy archived at Pandini, 2024).

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Author details

1. Manming Xu

   UCL School of Pharmacy, London, United Kingdom

   Contribution

   Formal analysis, Validation, Investigation, Visualization, Writing - original draft

   Contributed equally with

   Sarath Chandra Dantu and Shozeb Haider

   Competing interests

   No competing interests declared

2. Sarath Chandra Dantu

   Department of Computer Science, Brunel University London, Uxbridge, United Kingdom

   Contribution

   Conceptualization, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing – review and editing

   Contributed equally with

   Manming Xu and Shozeb Haider

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-2019-5311

3. James A Garnett

   Centre for Host-Microbiome Interactions, Faculty of Dentistry, Oral & Craniofacial Sciences, King’s College London, London, United Kingdom

   Contribution

   Conceptualization, Investigation, Writing – review and editing

   Competing interests

   No competing interests declared

4. Robert A Bonomo

   1. Research Service, Louis Stokes Cleveland Department of Veterans Affairs Medical Center, Cleveland, United States
   2. Department of Molecular Biology and Microbiology, Case Western Reserve University School of Medicine, Cleveland, United States
   3. Department of Medicine, Case Western Reserve University School of Medicine, Cleveland, United States
   4. Departments of Pharmacology, Biochemistry, and Proteomics and Bioinformatics Case Western Reserve University School of Medicine, Cleveland, United States
   5. CWRU-Cleveland VAMC Center for Antimicrobial Resistance and Epidemiology (Case VA CARES), Cleveland, United States

   Contribution

   Validation, Project administration, Writing – review and editing

   Competing interests

   No competing interests declared

5. Alessandro Pandini

   Department of Computer Science, Brunel University London, Uxbridge, United Kingdom

   Contribution

   Conceptualization, Software, Formal analysis, Supervision, Validation, Investigation, Visualization, Methodology, Project administration, Writing – review and editing

   For correspondence

   alessandro.pandini@brunel.ac.uk

   Competing interests

   No competing interests declared

6. Shozeb Haider

   1. UCL School of Pharmacy, London, United Kingdom
   2. University of Tabuk (PFSCBR), Tabuk, Saudi Arabia
   3. UCL Center for Advanced Research Computing, University College London, London, United Kingdom

   Contribution

   Conceptualization, Resources, Formal analysis, Supervision, Validation, Investigation, Visualization, Methodology, Project administration, Writing – review and editing

   Contributed equally with

   Manming Xu and Sarath Chandra Dantu

   For correspondence

   shozeb.haider@ucl.ac.uk

   Competing interests

   Reviewing editor, eLife

   "This ORCID iD identifies the author of this article:" 0000-0003-2650-2925

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