key: cord-0793472-553j3mir
authors: Sheik Amamuddy, Olivier; Afriyie Boateng, Rita; Barozi, Victor; Wavinya Nyamai, Dorothy; Tastan Bishop, Özlem
title: Novel dynamic residue network analysis approaches to study allosteric modulation: SARS-CoV-2 M(pro) and its evolutionary mutations as a case study
date: 2021-11-25
journal: Comput Struct Biotechnol J
DOI: 10.1016/j.csbj.2021.11.016
sha: ede32e20e049c3dc54efa38a259221027db77b57
doc_id: 793472
cord_uid: 553j3mir

The rational search for allosteric modulators and the allosteric mechanisms of these modulators in the presence of mutations is a relatively unexplored field. Here, we established novel in silico approaches and applied them to SARS-CoV-2 main protease (M(pro)) as a case study. First, we identified six potential allosteric modulators. Then, we focused on understanding the allosteric effects of these modulators on each of its protomers. We introduced a new combinatorial approach and dynamic residue network (DRN) analysis algorithms to examine patterns of change and conservation of critical nodes, according to five independent criteria of network centrality. We observed highly conserved network hubs for each averaged DRN metric on the basis of their existence in both protomers in the absence and presence of all ligands (persistent hubs). We also detected ligand specific signal changes. Using eigencentrality (EC) persistent hubs and ligand introduced hubs we identified a residue communication path connecting the allosteric binding site to the catalytic site. Finally, we examined the effects of the mutations on the behavior of the protein in the presence of selected potential allosteric modulators and investigated the ligand stability. One crucial outcome was to show that EC centrality hubs form an allosteric communication path between the allosteric ligand binding site to the active site going through the interface residues of domains I and II; and this path was either weakened or lost in the presence of some of the mutations. Overall, the results revealed crucial aspects that need to be considered in rational computational drug discovery.

With the advent of COVID-19, researchers, world-wide reacted quickly to design multiple potential inhibitors to abrogate viral protein activity using rational drug design approaches and wet lab experiments. This concept primarily involves targeting critical viral life-cycle proteins [1] [2] [3] [4] . The SARS-CoV-2 main protease (M pro ) protein plays a crucial role in the viral maturation cycle by lysing itself (autocatalysis) and other viral polyproteins 5 . This presents SARS-CoV-2 M pro as a key drug target for designing wide-spectrum 6, 7 anti-COVID-19 inhibitors or allosteric modulators that terminate the viral replication cycle 8 . Among the multitude of studied COVID-19 related proteins, the active site of SARS-CoV-2 M pro has been extensively targeted by virtual screening of both natural and non-natural compounds [9] [10] [11] . In contrast, the rational search for allosteric modulators of the protein is still relatively unexplored 12, 13 . Additionally, allosteric mechanisms in the presence of mutations are rarely considered in drug screening. In our previous study, a potential dual allosteric pocket of SARS-CoV-2 M pro was identified through multiple in silico tools in the presence of 50 early pandemic mutations 14 . These two pockets are mirrored across the dimer interface and are individually composed of residues from each protomer.

Continuing our previous SARS-CoV-2 M pro work 14 , we now set up alternative innovative therapeutic concepts to identify allosteric modulators in the presence of early evolutionary mutations of the virus. These concepts are explained under three subsequent sections:

PART I: Here, we identified potential allosteric modulators for the dimeric SARS-CoV-2 M pro protein, at a protonation state corresponding to pH 7.0, by screening it against 625 South African natural compounds 15, 16 . Parallel to this, we also docked the natural compounds against the M pro protein of one of the seven human coronaviruses, HCoV-OC43. Previously, HCoV-OC43 was suggested as a model to study SARS-HCoV without the need for Biosafety Level 3 facilities 17 .

This strain is, indeed, used as the laboratory strain. Both strains are under the genus Betacoronavirus, and HCoV-OC43 belongs to the subgenus Embecovirus, while SARS-CoV-2 is Sarbecovirus 18 . Thus, using in silico techniques we wanted to see if similar results would be obtained from the M pro protein in each strain. This analysis sheds light on potential considerations to factor in when transferring findings of whole virus particle experiments from HCoV-OC43 to SARS-CoV-2.

PART II: Next, our focus was to understand the allosteric effects of the selected hit compounds (PART I) on each protomer of the reference M pro protein (wild type, WT). In our previous study, we encountered the problem of protein symmetry, where we observed that protomer dynamics could be switched between identical copies of a protomer in a homodimer. Symmetry correction was performed by aligning single equilibrium conformations. In this study, we investigated the phenomenon in greater detail using a combinatorial approach to examine patterns of change and conservation of critical nodes, according to five independent criteria of network centrality (betweenness centrality (BC), closeness centrality (CC), degree centrality (DC), eigencentrality (EC) and katz centrality (KC)), used as averages. While doing so, we investigated the relationships and effectiveness of each metric in characterizing allosteric behavior. We hypothesized that allosteric change might be expressed through complex routes involving intraprotomeric and interprotomeric combinations of critical residues. By monitoring the centrality patterns of these residues across the homodimer under the influence of intrinsic (e.g. protein mutations and ligand binding) and extrinsic (simulation parameters) factors during molecular dynamics (MD) simulations, we aimed to extract further details from the homodimer state of the protease. To our knowledge this phenomenon is not commonly addressed in the case of homodimeric protein complexes, even though some other examples of asymmetric behavior of proteins have been reported, such as Hsp90 19 and KatG 20 . While the same phenomenon exists at the homomultimeric level 21 , a less complex case involving allosterically bound dimeric M pro is investigated herein, with a combinatorial approach as indicated in Table 1 which is only applicable to dimeric proteins.

Further, we, for the first time, introduced the concept of analyzing globally central nodes (i.e. the 5% most central nodes measured across all samples) for each of the five metrics of dynamic residue networks (DRNs). The metrics comprised averaged versions of BC, CC, DC, EC and KC.

Even though some of these metrics were, previously, used for protein structure analysis [22] [23] [24] to our knowledge, this is the second study that gathers five metrics information together in protein analysis and applies over molecular dynamics (MD) simulations 25 . Additionally, the hub data was itself reformulated as a set of network graphs, which were queried in order to decipher the complex patterns of hub conservation and transition (according to each DRN metric) from the apo state to one that is allosterically occupied.

PART III: Here, we examined the effects of mutations on allosteric behavior of the protein in the presence of selected potential allosteric modulators and investigated ligand stability.

Structure-based drug discovery approaches have been successfully used for the design of many orthosteric drugs 26 and to some extent allosteric modulators 27 for the treatment of communicable and non-communicable diseases. A good example is that of HIV protease inhibitors 28 . However, the impact of evolutionary mutations of pathogens, including those linked to drug resistance, is mostly undetermined in rational drug design. Depending on their position and physicochemical properties, mutations can modulate protein behavior by altering their stability and/or affinity to other interacting biological molecules [29] [30] [31] [32] . A more complex, yet subtle phenomenon may be observed at the level of entropic effects of mutations, whereby differences may be seen at the level of the rate of visiting certain states, and not by the mere presence or absence of a defined state (or set thereof) [33] [34] [35] . A classic case is the distance effect of pathogenic mutations that maintain protein function while gaining resistance 30, 36 ; hence our purpose is to understand the effect of evolutionary mutations in COVID-19 rational drug design.

We believe the information gleaned here may help to develop drugs that could potentially minimize the risks of having premature drug inactivation; and may reduce potential drug resistance effects to provide a longer-lasting treatment option.

For that purpose, mutant protein-allosteric modulator complexes were subjected to 20 ns allatom MD simulations at a fixed pH, and the results were, then, evaluated in the same manner as introduced in the second part of the article. The potential effectiveness of the allosteric modulators was identified in the presence of some of the early pandemic mutations of the protein. Even though no solid evidence of the effect of these mutations has been reported, involving them in drug development might help further our understanding of the enzyme's mechanics and pre-empt the most worrying feature of mutations: drug resistance.

Overall, the results of this study revealed crucial aspects that need to be considered in structure-based drug discovery such as the way in which the allosteric modulators should be identified; and how the stability of these modulators should be considered in the presence of mutations. We further argue that consideration of potential asymmetric behavior of homodimer proteins; of the novel DRN approaches and data analysis that are presented here would be applicable and useful in any computational drug discovery research.

The three-dimensional (3D) structure of the SARS-CoV-2 M pro was retrieved from Protein Data Bank (PDB) 37 (PDB ID: 5RFV 38 ) , and its dimeric unit assembled as described in our previous study 14 . In this study, we also utilized a set of 50 SARS-CoV-2 M pro mutant proteins that were prepared in our previous study 14 . The list of mutations that were acquired from the Global Initiative on Sharing All Influenza Data (GISAID) 39 as described in our previous work is presented in Table S1 53 .

5RFV was further used as a template to model the 3D structure of the human coronavirus strain (HCoV-OC43) M pro via MODELLER, using the automodel function parameterized with a slow refinement with loop deviation of 2.5 Å 40 . This protein is a homolog of the SARS-CoV-2 M pro , and the strain is generally used in inhibition assays in the laboratory. Prior to homology modelling, the HcoV-OC43 protein sequence was retrieved from the replicase polyprotein 1a record available from UniProt (Entry ID: P0C6U7; position 3247-3549), and was aligned against the sequence and structure of 5RFV using PROMALS3D 41 . The model with the lowest z-DOPE score was selected from a parallel run of 50 models. The PROPKA tool under the PDB2PQR algorithm 42 was, then, utilized to assign protonation states of all the proteins at a pH of 7. The calculations were done with the AMBER force field 43 .

Based on the assembled and protonated SARS-CoV-2 M pro dimeric structure, all 50 mutations were inserted using BIOVA Discovery Studio Visualizer 44 . This approach was utilized to minimize structural variations across the proteins. All mutated structures were subsequently protonated using the same procedure as for the reference structure.

A total of 623 compounds were first obtained from the South African natural compound database (SANCDB) 15, 16 . Partial charges were assigned to compounds and the protonated proteins using the Gasteiger-Hückel protocol in AutoDockTools (ADT) 45 . The AutoDock/Vina plugin from PyMOL was used to place the docking grid around the dimeric SARS-CoV-2 M pro reference protein. A docking box size of 65 x 71 x 80 Å with a grid spacing of 1 Å was centered at coordinates (0.00, 0.65 and 0.00). The exhaustiveness of 1000 was used, and the maximum number of docking poses was increased to 20. Blind docking (BD) simulations were performed in parallel, with 12 cores per job at the Center for High-Performance Computing (CHPC) using the QuickVina-W program 46 . After having docked the SANCDB compounds, the ligand PDBQT files were split into their separate poses before being converted to PDB format. Preliminary filtering was then applied using an in-house C++ script to every file to retain ligand poses that had a centroid distance of less than 10 Å to any of the allosteric pockets irrespective of binding energy. The pre-filtered poses were then manually curated in PyMOL (version 2.4) 47 to remove those that did not localize to the allosteric pocket. For each of the filtered ligands, the number of poses was tallied and ranked in ascending order of binding energy 48, 49 . The top six compounds from the SARS-CoV-2 M pro were then short-listed based on residue interactions for their respective lowest energy poses. HCoV-OC43 M pro underwent the same steps, to be used as a comparator.

100 ns all-atom molecular dynamics (MD) simulations were conducted using GROMACS (version 2019) 50 for SARS-CoV-2 M pro reference protein and the HCoV-OC43 strain homolog protein both in the absence and presence of six hit compounds bound at the previously identified allosteric site. In order to investigate the effect of mutations, 50 ligand-bound SARS-CoV-2 M pro mutants were similarly taken into 20 ns MD for each of the six compounds. GROMACScompatible structure and ligand topology input files were derived using the AMBER03 force field 43 and the ACPYPE tool 51 respectively. A total of 314 systems [(reference protein x 6) + (homolog protein x 6) + Apo-reference protein + Apo-homolog protein + (50 mutant x 6 compounds)] were solvated using the TIP3P water model 52 in a cubic box, with a minimum distance of 1 nm between the box edge and the protein. All systems were subsequently neutralized with 0.15 M NaCl. Solvated systems were first minimized for 5000 steps using the steepest descent algorithm until the relaxed systems converged to a maximum force of 1000 kJ/mol/nm. Following minimization, systems were equilibrated at constant number, volume and temperature (NVT) at 300 K temperature and constant volume using the modified Berendsen thermostat algorithm 53 followed by NPT (constant number of particles, pressure and temperature) at 1 bar pressure and constant volume and temperature ensemble using the Parrinello-Rahman barostat algorithm 54 In all ensembles, systems coupling groups and time constraints were set at 0.1 ps. All bonds were constrained under the LINCS holonomic constraints algorithm 55 whereas the Particle-mesh Ewald (PME) algorithm 56 was set to include the contribution of long-range electrostatic interactions. The overall MD protocol was carried out on the Center for High-Performance Computing (CHPC), Cape Town, South Africa using 384 cores with total of ~2,921,472 CPU hours. Structure coordinates were written after every 10 ps and periodic boundary conditions (PBC) were removed.

To study the effect of ligand binding on the active site, as well as on inter-and intra-domain residue dynamics over the course of MD simulations, dynamic residue network analysis (DRN) was done using MDM-TASK-web scripts 57 . DRN 58 was applied on the last 10 ns trajectories of the apo and ligand-bound M pro systems, after post-processing the MD trajectories to remove previously introduced water molecules, sodium and chloride ions. Residue network analysis uses graph theory concepts and characterizes residues in a protein structure in which each amino acid is represented as a node and inter-connected residues (C β -C β and in Gly C α -C α atoms) are depicted as edges based on a specified cut-off distance (6.7 Å) 58 . DRNs were analysed based on five metrics; averaged betweenness centrality (BC), averaged closeness centrality (CC), averaged degree centrality (DC), averaged eigencentrality (EC) and averaged katz centrality (KC) via the cal_network.py script incorporated in the web server, MDM-TASK-web 57 . Each of the metrics is a time-averaged summary of the network metrics obtained during MD simulations.

The averaged BC metric is defined as how often a residue is traversed along the shortest paths connecting every other residue pairs 59 . This metric was calculated based on the equation:

where δ(s,t|v) symbolises the number of shortest paths bridged between a residue n and other nodes s and t. δ(s,t) denotes the averaged shortest paths existing between residues s and t where s and t are part of the set V, which comprises the set of all nodes, while m indicates the overall number of frames.

Averaged closeness centrality (CC) of a residue is calculated as the reciprocal of the average number of the shortest paths linking a residue n and all other residues in the network.

(2)

where d (v, u) is the total distance between residue v and all other residues u.

Additionally, metric degree centrality (DC) defines the number of neighboring nodes (the local connectivity) around a given node. It is normalized by both the number of nodes in the network and the number of MD frames. The equation for computing the averaged DC is as follows:

where n indicates the number of residues, m denotes the number of frames; A ijk indicates adjacency in time frame i, being 1 if residues with indices j and k are adjacent and 0 otherwise. Eigencentrality (EC) measures the high centrality given to high degree residue, or to a residue that is connected to other high degree residues. The procedure for calculating EC is summarized here, and further details are in the literature 60 . The formula for the computation of EC for a single residue i for the k th frame is as follows:

The weighted multiplication operation between the adjacency matrix A is repeated against the vector EC until convergence. A ij is an adjacency, k is a frame, EC ik is the j th component of the EC vector for the k th frame, and n is the number of nodes. The averaged EC for the i th node is then computed from the matrix of EC likewise using MDM-TASK-web as follows:

Lastly, the Katz centrality (KC) measures the relative degree of influence of a residue i within connected residues in a network. The procedure for calculating KC is summarized here, and further details are in the literature 60 . The KC of node i is

where A represents the adjacency matrix and KC is the eigenvector computed by NetworkX in MDM-TASK-web. α and β denoted the attenuation factor and weight assigned to the immediate neighbors of node i. The same metric is computed for each frame before averaging the value across frames for each residue. This approach was performed separately for each of the 5 metrics.

For each DRN metric, a global network was built using as nodes the detected globally central hubs for all of the reference protein states (ApoA/B, SANC00302A/B, SANC00303A/B, SANC00467A/B, SANC00468A/B, SANC00469A/B), which have as labels components of the protein state and protomer to which each hub residue belongs. These labels were inserted as nodes, and undirected edges were created from them by linking their respective hub nodes to them. As this global network was too dense to analyze, a sub-network was extracted for each individual complex and was merged to the apo protomers. In this way, one could identify whether a hub was shared, gained or lost from the apo state upon ligand binding. This representation was applied and analyzed in a systematic manner (according to Table 1 ) to investigate whether ligand binding had any effect, as we posited that the effects of a ligand's presence in the allosteric site may manifest itself not only in the bound protomer, but also in the unbound one. In this way it was possible to track patterns of hub conservation and divergence. 

The SARS-CoV-2 M pro protein comprises 306 residues 2 and is active in its dimeric state at a pH of 7.0 6,61 . The dimeric functional state regulates catalytic turnover using the subunit flip-flop mechanism where the two monomers are used alternately for acylation and deacylation steps 62, 63 . Each monomer (designated protomer A and B) harbors three distinct domains (I-III) 2,10 and contains a His-Cys catalytic dyad signature (HIS41 and CYS145) located within a well-defined hydrophobic substrate-binding site between domain I and II (Figure 1) . The catalytic dyad residues are key for hydrolysis in which His41 functions as a general base 6, 64 . SARS-CoV-2 M pro domains I (residue 10-99) and II (100-183) consist of antiparallel β-barrel structure 2 that form the catalytic domains of the protein as the active site is located between domain I and II.

Domain III (198-303) is predominantly antiparallel α-helices 61,65 and connected to the catalytic domains by a long loop region (184) (185) (186) (187) (188) (189) (190) (191) (192) (193) (194) (195) (196) (197) . This domain is involved in the regulation of enzymatic activity of the virus 66 . The interaction interface, which is crucial for dimerization and enzymatic activity, is formed between domain II of protomer A and N-finger region (1-9) of protomer B and vice versa 64, 67 . These two N-finger signatures interact with Glu166 to maintain the correct orientation of the substrate-binding site subsite S1. The N-finger feature is similar to that of previously reported M pro from other coronaviruses 8, 61, 68, 69 . Each protomer has subsites (S1 -S5) located in the active site cavity and the active site cavity comprises the following residues: In our previous study, we identified dual allosteric pockets located at the interface of protomer A and B (Figure 1 ), that concur with key residues for functional dimerization and enzymatic activities 53 . The residues of this allosteric pocket of SARS-CoV -2 M pro are ALA116, TYR118,   SER123, GLY124, SER139, and LEU141 on protomer A and residues LYS5, MET6, ALA7,   PHE8, THR111, GLN127, PHE291, ASP295, ARG298, Interestingly, from the literature, El-Baba TJ et al., 12 also identified a compound (x1187), via mass spectroscopy based assay, binding to this region, slowing the rate of substrate processing of the enzyme. This compound has very low MSC Tanimoto similarity scores to our SANCDB compounds; ranging from 0.12 to 0.25 78 .

Ligand RMSD graphs of the last 10 ns of the 100 ns MD simulations ( Figure 2B ) showed that these six compounds behaved slightly differently in the M pro protein of SARS-CoV-2 compared to that of HCoV-OC43.Overall, the RMSD distributions spanned a range of under 1 Å, with the exception of SANC00408 in HCoV-OC43, which produced a significantly wider range. Ligand RMSDs of the 100 ns simulations are presented in Figure S1 . The different behavior of the compounds can be attributed to the compound-protein residue interaction differences obtained from the docking stage ( Figure 2C , Table S2 ), as well as the residue differences between the two homologous proteins at the allosteric sites ( Figure 2D ). Residues ALA7, PHE8, GLN127, PHE291 and ARG298 of SARS-CoV-2 M pro are respectively replaced by VAL7, ASN8, HIS127, LEU291 and GLN298 in the M pro in the HCoV-OC43 lab strain ( Figure 2D ). In SARS-CoV-2, residues ALA7 and PHE8 form part of the N-finger -a region crucial for dimer stabilization 79 . GLN127, PHE291 and ARG298 have also been reported to play important roles in the dimerization and the enzymatic activity of SARS-CoV M pro 80 . In SARS-CoV-2 M pro , several ligand interactions (such as hydrogen bond, hydrophobic and pi interactions) with allosteric site residues were observed (Table S2) in HCoV-OC43 may be responsible for the altered pocket topology and charges that together result in different ligand-binding patterns.

Our results indicate that the use of this strain for experimentation on allosteric modulation in SARS-CoV-2 M pro may have some limitations.

PART II:

Depending on the level of resolution desired for the analysis of homodimers, comparing MDsimulated pairs of a homodimeric protein can introduce conceptual challenges. For instance, one cannot easily know with certainty whether protomer A (or sections thereof) in one dimer behaves the same as its homologous position in protomer A in the second dimer. While a simpler protomer assignment approach based on permuted structural alignments was used in our earlier work 14 for single conformations, our attempt here investigates this issue in more depth, firstly by isolating potential hubs, and secondly by producing a representation of all the possible hub node combinations (Table 1 ) in order to obtain a scheme by which hub node importance can be assessed. While a hub is generally accepted as a high connectivity (degree) node, it has also been used to mean high BC 81 , but can also be understood as any node that may cause non-negligible topological alterations to a network when removed 82 . In this analysis the term is used in its more general sense to mean any node that forms part of the set of highest centrality nodes, here arbitrarily specified as the top 5% centrality nodes measured across all related samples, for any

given averaged centrality metric. This procedure differs from the identification of 1 to 2 standard deviation from the mean or top 5% residues in individual samples that we generally used in our previous studies [83] [84] [85] , in that it considers the strongest actors across samples and shows how other non-hub residues behave at the homologous position. We assume that investigating hub transitions in this manner is more likely to detect the most significant shifts in residue importance when exposed to a particular environment. We also used this approach to be able to handle the large amount of centrality data present in the current analysis. Preliminary examination of Figure 3 showed that there are some residues that preserve their hub statuses. We, here, introduce the following terms: (1) Constitutive hub: If a hub is present in both protomers of the reference protein and remains as a hub irrespective of the apo or a ligandbound state, it will be called a constitutive hub (see Table 1 ; score 4); (2) Persistent hub: If a hub remains across all systems compared, then the hub will be called persistent; in Part II, across all systems would be apo protomers and all ligand-bound dimers of reference protein, and in Part III it would be both protomers of the reference and mutant proteins with a specific ligand. (3) Superpersistent hub: In Part III, we will use the concept of a "Super-persistent hub", meaning that the hub is persistent across all the ligands considered in both reference and mutant proteins. Most of the constitutive and persistent hubs are metric-specific giving a different perspective to the network. As the five averaged centrality metrics refer to different measures of importance within a network, these terms will be used with respect to a given centrality metric and will not be shared between them. centrality values are colored white, through yellow, orange and red to black. Measurements for the ligand-bound protomer (chain A) have been systematically presented on the left side, while those of the unbound protomer are on the right -this does not apply to the apo state.

According to Figure 3 , MET17, THR111, PHE112 and CYS128 hub residues were found to be unaltered from the reference protein apo state, or upon any selected ligand binding irrespective of protomer for the averaged BC. At individual ligand level, each of these hubs is constitutive and indicates that there is no ligand effect due to preserved symmetry (Table 1 , score 4).

For the entire system (apo + 6 ligand systems), these hubs are persistent hubs indicating that the allosteric modulators did not change the information path for these key residues; and any loss to these hubs may disrupt the communication.

Residues MET17 and CYS128 had been previously picked up from multiple simulations, but

were not examined in depth in our previous work involving several M pro mutants in the apo state 14 . The current analysis of the networks derived from the MD simulations further showed that all conserved averaged BC hubs occurred as intrachain or interchain hinges within the dimer 

CC is calculated as the inverse of the average of the shortest path length from the node to every other node; hence identifies the central nodes which are closer to most of the nodes. Previously we showed that residues with low average shortest path are correlated with the low mobility (increased rigidity) of the protein 59 . Thus, high CC values are most likely to occur within the protein core. Previously, CC metric calculations over single static structures were used to identify active site residues with the support of other approaches, e.g. conservation, solvent accessibility 86, 87 to distinguish them from residues located in the core. Here, our persistent 

EC measures both the number of connections of a given node and its relevance in terms of information flow. It is based on a recursive allocation of centrality on the basis of nodes that draw importance from that of their successive connections, given that initial centrality is based on DC. Based on this calculation, one would expect high EC values to also have high DC values, or be in spatial proximity to high connectivity residues. However, we found that many of the high DC residues did not show up among the EC hubs, suggesting that EC is mostly gained via proximities to high DC residues, and do not necessarily have high connectivities themselves.

Persistent hubs of averaged EC for the M pro reference protein comprised residues ALA7, LEU115 and VAL125 (Figure 3) . LEU115 is the only residue that maintained its importance according to averaged DC and EC measurements. Weighted residue contact analysis of this residue showed that LEU115 maintained high contact frequencies (>0.60) with residues CYS117, PRO122, VAL125 and SER147, irrespective of ligand binding. SER10 and VAL13 also showed high frequencies, except in the presence of SANC00302 where notable contact asymmetry was experienced; a similar pattern was observed for residues VAL148 and GLY149

in the presence of SANC00467. 3D visualization of the EC residues shows that it is concentrated around the interface of protomers A and B ( Figure 4D ). The main message here is that high DC residues are sharing centrality to their immediate neighbors, and that the vicinity of the dimer interface seems to be the most residue-crowded area within the dimer. One should also bear in mind that centrality may also be coming from further degrees of separation. Other residues picked up as hubs in DC may be surrounded by fewer residues of high centrality, thus giving them less importance.

KC measures the relative degree of influence of a residue i within connected residues in a network. Irrespective of chain and ligand binding, nodes VAL36, VAL125 and GLY146 remained as hub nodes according to the averaged KC metric (Figure 3) .

Visualization of the averaged KC metric ( Figure 4E ) showed that this metric is an intermediate between averaged EC and averaged DC, with the former being more conservative than the latter when assigning relative node importance. Persistent averaged KC hub 125 was also central according to averaged EC; and VAL36, GLY146 were also persistent hubs The reasons for the high centrality values for residues SER10, LEU115 and VAL125 are as explained in averaged EC, with the main difference being that the effect of distal nodes was reduced due to the dampening coefficient. In this manner, averaged KC appears to improve the resolving power of averaged EC.

Overall, the heat map representation of the identified hubs according to the global top 5%

foreach of the five DRN metrics (Figure 3 ) allowed us to identify persistent hubs according to each of the centrality measurements, suggesting that they are exposing different key aspects of mechanical signal transduction within the protease regardless of apo and allosteric ligand bound forms of both monomers (Figure 4A-E) . Collectively, these persistent hubs are spreading out from the allosteric site along the protein interface as well as to the antiparallel beta strands ( Figure 5 ). Even though previously it is not reported, we believe that the antiparallel beta strands, and especially the first two nearest to the dimer interface, are functionally highly important.

We also identified a number of changes to hub existence in the presence of potential allosteric modulators and these changes were investigated as explained in the next section. 

We also observed another layer of information within the homodimer, which exists due to the symmetry of the protomers, despite the adjustment made to present the ligand-bound protomer as the one left-hand side (protomer A) in Figure 3 . We hypothesize that it is possible for a homodimer to switch states, because of their sequence identity. This is likely true for the apo state, but may also apply to the asymmetrically occupied allosteric sites, depending on how effective the allosteric pocket occupation is. This approach may also reveal if allosteric activity is manifested as a change of hub symmetry in the protein dynamics -for instance one or more hubs consistently appearing in one or even both of the protomers, when the allosteric site is occupied by a ligand. For this reason, the same data set (Figure 3 ) is further analyzed using another concept that we demonstrate in this section.

For each allosterically bound ligand, a network was built using the detected centrality hubs as nodes, and the chains to which they belong. A subnetwork was then prepared by combining the edges from the apo protomers A and B, and those from the ligand-exposed dimer, while also tracking the protomer labels, given the ligands had settled at one chain of the blindly docked dimer (Figures 6 -10) . As indicated before the ligand was assigned to protomer A. In the case of SANC00467 where the compound bound to chain B, the chain label was swapped. The systematic hub representation was done to further investigate whether ligand binding had an effect, keeping a record of the chain labels, as we hypothesized that a ligand's presence in the allosteric site may manifest its effects not only in the bound protomer, but also in the unbound protomer, within the same dimer.

The hub data set was analyzed based on the logic described in Table 1 . To simplify the terminology used to describe the presence of hubs within any combination of protomers, the term "score" is used to specify the number of protomers where the hub is present. In other words, if a hub is present in both protomers of the apo protein, the hub (irrespective of the DRN metric) will have a score of 2. Similarly, if a hub is present in each protomer of the apo dimer, and in each protomer of the ligand-bound dimer, this hub will have a score of 4 (constitutive hub). Further, higher confidence was assumed on the basis of complete loss or complete gain of any hub in each constitutive protomer from either the apo protein or the ligand-exposed enzyme. Lower confidence was assumed when a single hub was gained (i.e. score 0 to 1, or 1 to 2) or lost (i.e. score 1 to 0, or 2 to 1) within a single protomer, out of all four protomers (i.e. the set of protomers: apo chains A/B and complex chains A/B), to account for the part stochasticity of MD simulations. Higher confidence was given to these weaker signals when they were conserved across several ligand-bound states. Cases where asymmetric hub distributions occurred (i.e. a hub was found in only one protomer from each of the apo and the ligand-bound dimers) were ambiguous, given the fact that the apo dimer already expressed both hub states.

Here we will mainly focus on cases where we observed score of 2 and score of 1 gains or losses from each ligand-bound dimer with respect to the apo protein, in order to extract high likelihood ligand-induced changes.

While PHE140 was a constitutive hub in the presence of SANC00630, SANC00468 completely lost node 140 upon ligand binding (score of 2 loss). SANC00630 gained hub 13 (score of 2 gain) with respect to apo structure (Figure 6 ). The loss of BC from this "chameleon" switch residue (PHE140) suggests contact loss in its vicinity. VAL13, on the other hand, is found close to the N-finger -in a region where we previously reported lengthening and shortening of the alpha helix and suggested its possible involvement in dimer stability 14 .

While there are many score 1 hub gains and losses with each ligand-bound dimer (with respect to the dimeric apo protein), we report the ones which have the highest conservation among all these lower confidence cases, independent of the bound ligand. Hub residue GLY11 systematically changed from a score of 0 in the apo dimer to a score of 1 in the dimeric complexes, suggesting an increased use or stabilization around this residue upon ligand binding.

Coincidentally, hub residue SER10 systematically transited from a score of 1 in the apo state to a score of 0 upon ligand binding. The fact that these two residues are next to each other, and in fact interact with their interprotomeric counterpart suggests a possible rerouting of information flow in their vicinity upon introduction of a ligand. Score 2 to 1 (i.e. from the apo to the ligand-bound dimer) changes appeared not as consistent, but showed some agreement on hub nodes being lost from one of the "chameleon switches" in subsite S1, similar to what was seen more strongly in the presence of SANC00468, where both nodes were lost. This was observed for residues SER139 and/or PHE140 when exposed to SANC00302, SANC00303, SANC00467 and SANC00469. Score 1 to 0 changes were not observed when shifting the reference protein from an apo to a ligand-bound state, for any of the centrality metrics. Red, orange, blue and green nodes (and edges) depict the protomers (apo chains A and B, and complex chains A and B, respectively) to which a hub belongs. Each node is also scaled by its score -i.e. the number of edges it holds. Hubs that are present in all 4 protomers are in purple. Score 2 loss and gains from the reference are colored yellow and cyan, respectively. Score 1 losses and gains are colored brown. Inconclusive hubs are in grey.

SER10 was a constitutive hub to five ligand-bound states, except SANC00302. Score 2 gains of high CC hubs were observed for residue 4 and 5 in the presence of SANC00302, SANC00303

and SANC00468 -residue 4 also experienced a score 1 gain in the presence of SANC00630, while residue 5 experienced a similar gain in the presence of SANC00469 (Figure 7) . THR111

was also gained as a score of 2 hub, only in the presence of SANC00468. GLY138, which is part of the S1 subsite, manifested itself as a hub in only one monomer of the apo protein, transitioning to a score of 0 upon ligand binding in five out of the six bound states. Upon visual inspection, we find that this residue is next to residue ARG4 on the alternate protomer, even though they do not appear to interact via non-bonded interactions. By measuring the change in , when merged with the apo protein, in each case. Red, orange, blue and green nodes (and edges) depict the protomers (apo chains A and B, and complex chains A and B, respectively) to which a hub belongs. Each node is also sized by its score -i.e. the number of edges it holds. Hubs that are present in all 4 protomers are in purple. Score 2 loss and gains from the reference are colored yellow and cyan, respectively. Score 1 losses and gains are colored brown. Inconclusive hubs are in grey.

LEU115 was a constitutive hub to five ligand-bound states, except SANC00302 (Figure 8) .

Scaffold-related conservation patterns were not apparent using this metric, however some differences did occur. Residue LEU115, which occurs in proximity to the persistent hub, PHE150, was highly crowded and formed several durable contacts with its neighbors, namely VAL114, ALA116, CYS117, PRO122 and VAL125. LEU115 had a high frequency contact with PRO9 in only one chain in the presence of SANC00469 and a low frequency contact with VAL13 in only in one chain in the presence of SANC00302.

A score 2 hub gain was experienced by VAL18 when exposed to SANC00303, SANC00467, SANC00468, SANC00469 and SANC00630. The same residue incurred a score 1 gain in the presence of SANC00302. Upon contact visualization, we found the systematic significant increase in contact frequency between VAL18 and GLN69 in each protomer upon ligand binding. While their C-alpha distances were relatively similar throughout the apo and ligandbound M pro (averaging 0.59 nm), the C-beta distances were significantly larger in the apo (average of 0.69 and 0.70 nm in the apo protomers) compared to those of the ligand-bound states (averages ranging from 0.63 to 0.65 nm), which suggests a rotational decrease of the C-beta distance upon ligand binding. A score 2 gain was also experienced by residue GLY29 when exposed to SANC00468 and SANC00630. 3D visualization shows that GLY29 is H-bonded to VAL18, and together with GLN69 they form a geodesic path travelling directly across antiparallel beta strands. The proximity and arrangement of these three residues may suggest they may act in a concerted manner.

Score 2 losses were observed for VAL86 when exposed to SANC00467 and SANC00468; and

for residues LEU253 and VAL296 in the presence of SANC00302, indicating that the connectivity around these areas was reduced. Conserved score 1 to 0 changes were observed for residue TYR126 in the presence of ligand binding, suggesting a possible increase in local compaction in that area in the presence of any of the ligands. 

PRO9 and SER10 were constitutive hubs to five ligand-bound states, except SANC00302 ( Figure 9 ). GLY146 experienced a score 2 gain in the presence of SANC00302 and SANC00630. The same was observed for CYS38 in the presence of SANC00302. While score 1 gains from 1 to 2 were not completely conserved, hub score changes from 0 to 1 were conserved, comprising residues MET17, ASN28 and GLY29 in the presence of ligand binding, suggesting an increase in centrality in the vicinity of these residues. Visual inspection shows that MET17 is proximal to ASN28, which is next to GLY29 on a beta strand. The high averaged EC for MET17

is likely due to its high degree centrality combined to that of VAL18. It is possible that ligand binding further stabilizes its residue neighborhood, compared to the absence of occupation of the allosteric pocket. Hub residues ASN28 and GLY29 appear to draw centrality from the higher degree centrality residues VAL36 and VAL18. Together these domains I residues line the Red, orange, blue and green nodes (and edges) depict the protomers (apo chains A and B, and complex chains A and B, respectively) to which a hub belongs. Each node is also sized by its score -i.e. the number of edges it holds. Hubs that are present in all 4 protomers are in purple. Score 2 loss and gains from the reference are colored yellow and cyan, respectively. Score 1 losses and gains are colored brown. Inconclusive hubs are in grey. Figure 10 . The path traced by averaged EC hubs, starting from the allosteric ligand towards the catalytic residue. The protease is depicted by a cartoon representation onto which the averaged EC hub residues are overlaid as sphere representations, together with the non-hub catalytic residues HIS41 and CYS145 (circled in orange). EC persistent hub residues are circled in black; the alternate path is circled in blue; and the one triggered by the binding of all ligands is circled in green. One of the compounds is also shown in stick figure representation, as an example.

SER10 and LEU115 were constitutive hubs to five ligand-bound states, except SANC00302

( Figure 11) . SER10 was also a constitutive hub and LEU115 was a persistent hub in EC. KC hubs residues VAL36, GLY146, LEU115 were also central according to averaged DC. Regarding the variations in ligand motion, a more stable conformation (unimodal distribution) was observed across SANC00468, SANC00467 and SANC00469 bound to mutant proteins, followed by SANC00630 as compared to the conformational stability of SANC00302 and SANC00303 (Figure 12 ). This observation was in agreement with docking results where the first four compounds exhibited high stability through various hydrogen bond interactions with key allosteric site residues ( Figure 2C , Table S2 ). A closer view of each ligand revealed the subtle movement of the bromide SANC00302 and SANC00303 and the hydroxyl groups of SANC00630 in some mutant proteins as seen from the bimodal distributions (Figure 12 ). Figure 12 was further evaluated to calculate a consensus score across six ligands within each mutant system. For that, a table (Table S3 ) was prepared in which the y-axis contained individual mutant proteins and x-axis was for six ligands. For each ligand, kernel plots were checked and the ligands with a unimodal distribution in each mutant protein system received a tick (✓) in the table; the selected ones are also indicated in Figure 12 with black oval shape in the x-axis. Surprisingly, out of 50 mutant proteins, only three of them (A173V, N274D and R279C) received a consensus score of six (Table S3) , meaning all ligands in these mutant proteins stayed stable over the MD simulation. Over all the systems, the best performing ligands were SANC00468 and SANC00469, which gave highly stable motions for 43 and 41 mutant samples, respectively ( Table S3) . ( Figure S2-S6) ; and extracted the persistent hubs on the basis of their conservation in both reference protein and mutants bound to a specific ligand ( Table 2) . If a persistent hub is retained across all the ligand systems (in both protomers), then we called it a super-persistent hub.

In the case of averaged BC ( Table 2 LEU115 was also the key persistent hub according to KC metric, and it was only lost in the presence of SANC00302 due to absence of the hub node in protomer B of reference protein (Table 2, Figure S6 ). Two new persistent hubs (residues 10 and 150) were introduced in the presence of SANC00469. Interestingly, the persistent hub, VAL36 was lost across all allosteric modulators according to averaged KC metric. 70 . Here we propose to use DRN metric analysis and define the cold spots as the regions that are the least affected or not affected at all, by mutations. In the previous sections, we introduced persistent hubs and super-persistent hubs, and we will consider the cold spots as being those hubs that are super-persistent, or almost so. The super-persistent hubs of CC metric are all located mainly in the interface of the dimer as well as in the first two antiparallel beta strands. We believe, these regions should be strongly considered in structure based drug discovery.

In this section we zoomed into the global top 5% averaged metric calculations for reference and 50 mutant protein systems in the presence of allosteric modulators (Figure S2-S6 Protomer A of M pro -SANC00302 reference protein -ligand complex has 18 centrality hubs for EC (residues 7, 10, 17, 28, 29, 38, 113, 115, 116, 117, 122, 124, 125, 146, 147, 148, 149, 150) , including the path residues identified in Section 3.5.4 (Figure 13 ). When we collectively mapped these centrality hubs to the protein-ligand system, we had another very interesting observation:

These centrality hubs form a communication path between the allosteric ligand binding site to the active site going through the interface residues of Domain I and II (Figure 14A ). In the case of Protomer A of M pro -SANC00468 reference protein -ligand complex, some new centrality hubs are gained (9, 11, 13, 14) , and some lost (38, 149) compared to that of M pro -SANC00302

system; totaling to 20 EC hub residues (7, 9, 10, 11, 13, 14, 17, 28, 29, 113, 115, 116, 117, 122, 124, 125, 146, 147, 148, 150) (Figure 13 ). Figure 14B) . Extreme examples to the loss of the communication path in the presence of SANC00468 include G15S, G71S and A173V mutants. A173V-SANC00468 complex with 8 EC hubs (7, 9, 10, 11, 113, 115, 124 , 125) is presented in Figure 14D .

In this study we have provided important new insights towards computational drug discovery, and applied them to SARS-CoV-2 M pro protein.

Here, we will list the novel aspects and link to our findings for M pro protein.

We previously proposed a post-hoc analysis approach of MD simulations using DRN analysis to consider the dynamic nature of functional proteins and protein-drug complexes and to probe the impact of mutations and their allosteric effects. We also established a tool for DRN 57 and developed an algorithm to pinpoint key hub residues, meaning any node that forms part of the set of highest centrality nodes for any given averaged centrality metric.

We investigated the hub transition when exposed to a particular environment (i.e. ligand binding) by considering these strongest actors (hubs) across samples and showed how other non-hub residues behave at the homologous position. The key reason for using DRN analysis in M pro protein was to tackle the problem of protein symmetry that we identified in our previous study 14 , where we observed that protomer dynamics could be switched between identical copies of a protomer in a homodimer. In this study, we investigated the phenomenon in greater detail using a combinatorial approach to examine patterns of change and conservation of critical nodes, according to five independent criteria of network centrality. Asymmetric behavior of multimeric proteins, in general, is not considered in computational analysis. To our knowledge, this is the first study of this problem using five DRN metrics, and emphasizing the importance of this aspect while analyzing a protein's allosteric behavior in the presence of ligands and mutations.

Applications of our approaches pinpointed a number of important aspects in SARS-CoV-2 M pro protein: (1) we identified hubs that stayed the same in apo and upon a ligand binding (constitutive hubs) indicating that there is no ligand effect from symmetry; (2) we captured different persistent hubs from each metric, and collectively they gave us highly crucial functional residues which were spreading out from the allosteric site to the interface and antiparallel beta strands. We believe that the antiparallel beta strands, especially the first two near to the dimer interface, are crucial in the mechanical signal transduction; (3) we also looked at the symmetry problem and analyzed hub losses and gains in the presence of allosteric modulators. The identified residues informed us about communication changes due to the presence of ligand and allosteric communication residues. A few examples of hub gains and losses that we observed in functional residues are VAL13 (next to the N-finger), GLY 138 (part of S1 subsite) and PHE140

(chameleon switch). We also observed a number of hub transitions in antiparallel beta strands;

(4) very interestingly, we showed that EC centrality hubs form ligand specific communication paths between the allosteric ligand binding site to the active site going through the interface residues of domains I and II.

In general, structure based drug discovery approaches have been used successfully for the design of many orthosteric drugs and to some extent of allosteric modulators. However, the impact of evolutionary mutations of pathogens is mostly undetermined in rational drug design;

even though the information obtained may help to develop drugs that could circumvent or reduce potential drug resistance issues. Here, we applied this concept to identify potential allosteric Collectively, our approaches offer routes for novel rational drug discovery methods and provide computationally feasible platforms (1) to determine globally central nodes that form part of the set of highest centrality nodes (hubs) for any given averaged centrality metric; (2) to identify key functional residues implicated in allosteric signaling in the presence of allosteric modulators; (3) to understand the potential asymmetric behavior of dimeric proteins under internal and external forces and to distinguish those introduced by ligand binding or by evolutionary mutations; (4) to utilize five DRN metrics to pinpoint cold spot residues that can potentially be chosen for structure guided drug discovery.

Finally, experimental verification of the predicted M pro inhibitors, and thus of the algorithms presented here, is highly desirable; and we hope that this study will inspire wet-lab investigation.

The Supporting Information is available free of charge at Table S1 : List of mutations and sample IDs extracted from GISAID database. Table S2 : Molecular interactions established between hits and their respective allosteric site residues in SARS-CoV-2 M pro . In black and red labels are residues from protomer A and B respectively. indicates highly stable motion. The consensus score across each mutant system is the number of '✓' entries in that row. 

The authors declare no competing financial interest.

All data reported in this article are presented in the article and the Supporting Information section. Dynamic residue network analysis metric scripts are implemented in the MDM-TASK-web platform (https://mdmtaskweb.rubi.ru.ac.za/) and are available at https://github.com/RUBi-ZA/MD-TASK/tree/mdm-task-web. MD simulations will be made available upon request.

Authors acknowledge the use of the Centre for High Performance Computing (CHPC), Cape

Town, South Africa for the simulations. Authors thank Dr Thommas M. Musyoka for the Tanimoto coefficient score calculations.

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