To explore the conformational space of TEM-1 and KPC-2 in the Apo_EQ (no ligand) and IB_EQ (inhibitor-bound) states, we started by running a set of equilibrium simulations (20 replicas of 250 ns each) that resulted in 5 µs of accumulated simulation time per system. Conformational changes during the simulations were assessed using their Cα root mean-square deviation (RMSD) profiles (Figure 2—figure supplement 2). The simulated systems were considered equilibrated beyond 50 ns as shown by RMSD convergence. In each case, the proteins remained close to their initial conformation during the course of 250 ns (Figure 2—figure supplement 2a). The average RMSD for Apo_EQ and IB_EQ states were between 0.10 and 0.12 nm for all systems (Figure 2—figure supplement 6). The low RMSD values are consistent with previously published results, which have also shown class A β-lactamase enzymes to be largely rigid and conformationally stable when studied on long timescales and rarely divergent from the initial structure (Gobeil et al., 2019; Galdadas et al., 2018). Conventional RMSD fitting procedure using all Cα atoms failed to separate regions of high versus low mobility. To resolve such regions, we used a fraction (%) of the Cα atoms for the alignment. Beyond this fraction, there is a sharp increase in the RMSD value for the remainder of the Cα atoms (Figure 2—figure supplement 2b). At 80%, the core of TEM-1 could be superimposed to less than 0.064 and 0.074 nm for Apo_EQ and IB_EQ states, respectively (Figure 2—figure supplement 2bi).

In the KPC-2 Apo_EQ state, the RMSD of 80% of the Cα atoms was below 0.060 nm, while the same subset of atoms had an RMSD below 0.066 nm in the IB_EQ state (Figure 2—figure supplement 2bii). This 80% fraction of Cα atoms constitutes the core of the enzyme and did not show any divergence from the initial reference structure (Figure 2—figure supplement 2c). RMSD values for the remaining 20% of Cα atoms varied between 0.16 and 0.23 nm. This apparent rigidity is consistent with the experimental finding, based upon, for example, thermal melting experiments Mehta et al., 2015, that KPC-2 is more stable than many other class A β-lactamases such as TEM-1. Some large conformational changes were observed in all replicates; these involved changes in conformations of the loops that connect secondary structural elements (Figure 2—figure supplement 3). To further validate the stability of the two systems, we analyzed structural properties including the radius of gyration (Rg; Figure S5), solvent accessible surface area (SASA; Figure 2—figure supplement 5), and the secondary structure of each enzyme over the simulated time (Figure 2—figure supplement 7). The values for these properties are listed in Figure 2—figure supplement 6.

A ligand that binds to an allosteric site can control protein function by affecting the active site (Laskowski et al., 2009). This generally occurs by altering the conformational ensemble that the protein adopts (Laskowski et al., 2009; Motlagh et al., 2014). To probe how ligand binding to an allosteric site affects the dynamics of β-lactamases, we calculated the Cα root-mean-square fluctuation (RMSF) for both Apo_EQ and IB_EQ states. Higher RMSF values correspond to greater flexibility during the simulation. Although the Cα RMSF profiles for Apo_EQ and IB_EQ states are similar, indicating similar dynamics, there are some discernible differences (Figure 2).

In equilibrium simulations of TEM-1 and KPC-2, the hydrophobic core of the enzyme is stable and shows limited fluctuations. Most of the RMSF variance is observed in loops that connect secondary structural elements (Figure 2). In TEM-1 IB_EQ, higher fluctuations are observed predominantly in three distinct regions when compared with the Apo_EQ enzyme; in the loops between helices α7 and α8 (residues 155–165), α9 and α10 (residues 196–200), and the hinge region including helix α11 (residues 213–224) (Figure 2A). The α11 and the α12 helices are part of a highly hydrophobic region that also constricts the allosteric pocket in all TEM-1 apo crystal structures. Binding of the ligand disrupts the hydrophobic interactions within this region, resulting in the opening of the allosteric pocket between helices α11 and α12 (Horn and Shoichet, 2004).

It should be noted that the starting Apo_EQ structure of TEM-1 was generated from the IB crystal structure, by the removal of the ligand from the allosteric binding site. During the Apo_EQ simulations, α12 helix behaves like a lid and closes over the empty, hydrophobic, allosteric binding site, and thus displays high RMSF at the C-terminal end of the enzyme. This conformational change recovers the structure of the apo crystal form, as observed, for example, in PDB id 1ZG4 (Stec et al., 2005), as reflected to the RMSD of ~0.07 nm after superposition of the structures. The rest of the loops displayed comparable fluctuations in both Apo_EQ and IB_EQ states.

The differences between the Apo_EQ and IB_EQ states were of similar magnitude in KPC-2. In KPC-2 IB_EQ, more extensive fluctuations than in Apo_EQ were also observed in the loops between α7 and α8 (residues 156–166), the hinge region, around α11 (residues 214–225), and in the loop between β7 and β8 (residues 238–243) (Figure 2b). Conversely, fluctuations are slightly higher in the Apo_EQ than IB_EQ state in the loop leading into the Ω-loop from α7 helix (residues 156–166). Overall, however, RMSFs are similar in analogous regions of the IB_EQ and Apo_EQ states in both TEM-1 and KPC-2, highlighting the conservation of structural dynamics in class A β-lactamases. However, there were some fluctuations that were unique and limited to each enzyme (Figure 2).

In both TEM-1 and KPC-2 IB_EQ states, interactions of the ligands in their respective allosteric binding sites contribute to enhanced fluctuations (i.e. larger than in the Apo forms) of the local structural elements (Figure 3—figure supplement 1). The sites in which the ligands bind are very different. In TEM-1, the binding site is deep and forms a hydrophobic cleft. The ligand penetrates to the core of the enzyme and is sandwiched between helices α11 and α12 (Horn and Shoichet, 2004). The FTA ligand remains tightly bound in the allosteric pocket throughout the simulations (Figure 3—figure supplement 2).

In KPC-2, the allosteric binding site is shallow and solvent-exposed even in the absence of the ligand. Although the distal end of the pocket is hydrophobic, there are some polar amino acids on the proximal surface (e.g. Arg83 and Gln86), which are exposed to the solvent. This shallow site forms a part of a larger pocket that is occluded by the side chain of Arg83 (α7 helix). In some of our IB_EQ simulations, the Arg83 side chain rotates, leading to the opening of a larger hidden pocket. This enlarged space is now accessible to the ligand for exploring various interactions. The tumbling of GTV increases the fluctuations in the complex (Figure 3—figure supplement 1c,d), however, the ligand does not leave the binding site (Figure 3—figure supplement 2).

To further highlight the structural changes occurring as a result of ligand binding, positional C deviations were calculated between IB_EQ and Apo_EQ systems for the equilibrated part of the simulations (Figure 3a,b). The Cα deviation values plotted are an average between simulation taken by combining all trajectories from Apo_EQ and IB_EQ simulations for that particular system. This is one of the simplest approaches, which can determine residues undergoing largest structural rearrangements. The averaged Cα positional deviations are mapped onto the averaged Apo_EQ structure to visualize the largest relative displacements in three dimensions (Figure 3c,d).

The hydrophobic cores of both TEM-1 and KPC-2 β-lactamase enzymes show little or no conformational change. The major differences between the Apo_EQ and IB_EQ states are in the loops connecting different secondary structure elements. In TEM-1, Cα deviations are observed in the loops between α4 and β5 (residues 112–116), α7 and α8 (residues 155–166), Ω-loop (residues 172–179), α9 and α10 (residues 196–200), hinge and α11 (residues 213–224), β7 and β8 (residues 238–243), and β9 and α12 (residues 267–272). There are some relatively minor deviations observed in loops β1-β2 (residues 51–55), β2-β3 (residues 61–65), α2-β4 (residues 86–93), α6-α7 (residues 143–144), β8-β9 (residues 252–258), and at the pivot of the α3 helix (residues 98–101). The hinge region and residues in helices α11 and α12 display the largest deviations. This is also in agreement with other experimental data that indicate the connection between the active site and the allosteric pocket studied in TEM-1 in the presence of BLIP inhibitor, seems to be mostly due to hinge region motions (Meneksedag et al., 2013).

The structural dynamics observed in KPC-2 were slightly different from TEM-1. In KPC-2, prominent Cα deviations were observed in the loops between β1 and β2 (residues 51–55), α2 and β4 (residues 88–93), α4 and β5 (residues 114–116), α7 and α8 (residues 156–166), Ω-loop (residues 172–179), β7 and β8 (residues 238–243), β8 and β9 (residues 252–258), in the loop between β4 and α3 leading up to the proximal end of α3 (residues 94–102) and in the hinge/α11 helix (residues 214–225). There are some minor deviations observed in α1-β1 (residues 39–42) and β9-α12 (residues 266–270). The most important ligand-induced Cα deviation is observed in the loop connecting the α4 helix to the β5 strand (residues 114–116). The deviation of the α4-β5 loop together with the deviation observed in the loop between β4 and α3 leading into α3 helix (residues 96–102) has the potential to deform the α3 helix-turn-α4 helix. The β4-α3 and α4-β5 loops form the basal pivot joint of the α3 and α4 helices and maintain the correct positioning of this helix-turn-helix at the periphery of the enzyme active site. The correct positioning of this loop is important as Trp105 lies on this loop. Mutagenesis studies have shown that a highly conserved aromatic amino acid at position 105 in class A β-lactamases (Tyr105 in TEM-1, Trp105 in KPC-2) is located at the perimeter of the active site and plays a crucial role in ligand recognition via favorable stacking interactions with the β-lactam ring (Papp-Wallace et al., 2010b; Doucet et al., 2004). The aromatic side chain at position 105 coordinates the binding of substrates not only via stacking and edge-to-face interactions but by also adopting ‘flipped-in’ or ‘flipped-out’ conformations (Galdadas et al., 2018; Papp-Wallace et al., 2010a; Papp-Wallace et al., 2010b). This has been proposed based on the conformations observed in the available crystal structures and confirmed by enhanced sampling MD simulations (Galdadas et al., 2018; Ke et al., 2012). Any perturbation that alters the conformation of α3-turn-α4 helix or deforms the α3-α4 pivot region would prevent α3 and α4 helices from correctly shaping the active site of the enzyme. This would result in the aromatic residue at 105 partially detaching from the edge of the active site and being unable to stabilize the incoming substrate as required for efficient catalysis. This explains the loss of β-lactam resistance in strains expressing KPC variants at position 102 or 108, as established in the MIC experiments reported previously (Galdadas et al., 2018).

To study signal propagation from the two allosteric sites, we ran 800 short nonequilibrium simulations, with a total sampling time of 4 µs for each system. The nonequilibrium simulations were initiated from regular intervals of the equilibrated part of the long IB_EQ simulation, starting at the 50 ns time point (Figure 2—figure supplement 1). In each simulation, the ligand was removed from its binding site and the resulting system was further simulated for 5 ns. The response of the system to the perturbation was determined using the Kubo-Onsager approach developed by Ciccotti and Ferrario, 2013; Ciccotti et al., 1979; Ciccotti and Ferrario, 2016. In this approach, the time evolution of the conformational changes induced by ligand removal can be determined by comparing the Apo_NE and IB_EQ simulations at equivalent points in time. The subtraction method, applied to multiple pairs of trajectories, effectively removes noise arising from fluctuations of the systems and allows residues that are involved in signal propagation to be identified. The disappearance of the ligand from its binding site generates a temporary localized vacuum, against which there is an immediate structural and solvent response. As the simulation progresses, the cascading conformational changes in response to the perturbation (removal of ligand) show the route by which structural response is transmitted through the protein.

Video supplements: Signal propagation in TEM-1 and KPC-2 as a result of the perturbation (ligand removal) in the allosteric binding site. The disappearance of the ligand from its binding site generates a localized vacuum, against which there is an immediate structural response by the enzyme. As the simulation progresses, the cascading conformational changes in response to the perturbation (ligand removal) show the route by which structural response is transmitted through the protein.

This approach has identified a general mechanism of signal propagation in nicotinic acetylcholine receptors, by analyzing their response to deletion of nicotine (Oliveira et al., 2019a). The difference in the position of Cα atoms is calculated between the short Apo_NE and IB_EQ simulations at specific time points. These differences are then averaged over all pairs of simulations to reveal the structural conformations associated with this response (Figure 4) and their statistical significance. The Cα coordinates of each residue in the Apo_NE were subtracted from the corresponding Cα atom coordinates of the IB_EQ simulation at specific points in time, namely 0.05, 0.5, 1, 3, and 5 ns. This resulted in a difference trajectory for each pair of simulations. The difference trajectories are averaged over the set of 800 simulations for each system. The low standard error (SE) calculated for the average between the Apo_NE and IB_EQ demonstrates the statistical significance of the results. Due to the short timescale (5 ns) of the nonequilibrium simulations, only small amplitude conformational changes will be observed.

In TEM-1, the allosteric site is sandwiched between the α11 and α12 helices. Adjacent to this binding site is the hinge region (residues 213–218), whose dynamics have previously been examined by NMR and shown to have low order parameters indicating high mobility (Gobeil et al., 2019; Savard and Gagné, 2006). This is also the site of perturbation in the nonequilibrium simulations and so the point of origin of the allosteric signal. Located on the loop between the distal end of the α11 helix and β7 is a highly conserved Trp229 residue. The indole ring of Trp229 is sandwiched between two other highly conserved residues, Pro226 and Pro251, present in loops α11-β7 and β8-β9, respectively. The π/aliphatic stacked arrangement of tryptophan-proline is a very tight interaction and is similar in geometry to that observed in complexes of proline-rich motif binding families, including the EVH1 and GYF binding domains, with their peptide ligands (Ball et al., 2005; Freund et al., 1999; Reinhard et al., 1996; Zondlo, 2013). The perturbation destabilizes this stacked arrangement resulting in an extension of an inherently highly mobile region. After 50 ps of simulation, the Cα deviations have propagated and can be observed in the loop between β1 and β2. Interestingly, the loops at the basal pivot of 3 and 4 also responded rapidly to ligand removal. These loops are ~33 Å away from the allosteric binding site and can affect the spatial position of the turn between helix α3 and α4. The α3-turn-α4 helix forms the boundary of the active site, and it is on this turn where the Tyr105 residue, important for substrate recognition, is positioned. These results clearly demonstrate the coupling between the distal allosteric site and catalytically relevant regions of the enzyme. As the signal propagates within the protein, there is a gradual and cumulative increase in the Cα deviations in the aforementioned loops. In particular, the loop between the α9 and α10 helices, which is positioned just below the β1-β2 loop, displays high deviations and forms a focal point for the signal to bifurcate in two directions. First, major deviations are observed laterally toward loop α7-α8 and onward into the Ω-loop (Figure 4a,b). Second, more minor deviations move into the loop between α2 and β4 and onward into the basal pivot of α3-turn-α4 helix. There is another shorter route at the top of the enzyme that the signal can take to go from the allosteric binding site to the Ω-loop, via the proximal end of α12 helix and across the loop between β9 and α12 helix (Figure 4a,b).

In KPC-2, the allosteric pocket is shallower and lies between helices α2 and α7. Residues from three loops (α6-α7, α7-α8, and α2-β4) are in close proximity to this binding site. An additional loop, α9-α10, is linked to this binding site via the distal end of the α2 helix. The perturbation in this binding site results in enhanced mobility of the α2-β4 loop, which leads directly into β4 and onward to the basal pivot of the α3 helix. The proximal end of the α3 helix and the distal end of the α4 helix, which forms the pivot point of the α3-turn-α4 structure, display high deviations (Figure 4c). The highly conserved aromatic amino acid, Trp105, is located on this turn. The distance between the allosteric binding site and the α3 helix is ~27 Å. Other major deviations are also observed in the Ω-loop as the simulation progresses (Figure 4c). The Ω-loop is directly linked to the allosteric binding site via loop α7-α8. Some minor deviations are also observed in the loop connecting β9 and the α12 helix.

In both TEM-1 and KPC-2, the removal of the ligand at the beginning of the nonequilibrium simulations does not result in large conformational changes. The subsequent Cα deviations trace the route of the propagating signals (Figure 3—figure supplement 212). In TEM-1, α11 and the hinge region, loops β1-β2 and β8-β9, respond rapidly to the perturbation and display comparable RMSD values to the equilibrated simulations. Similarly, in KPC-2, only loops α2-β4 and α7-α8 respond rapidly to the perturbation. The other structural elements take longer to respond, and their conformational rearrangements are not fully sampled in the Apo_NE simulations. It is worth emphasizing that while the short nonequilibrium simulation can be an excellent tool to study an immediate structural response toward a perturbation, the timescale of nonequilibrium MD does not represent a real timescale and thus should not be compared directly with equilibrium simulations. Nevertheless, nonequilibrium MD can identify the sequence of events and pathways involved.

The perturbations of the two enzymes here are different but show some striking common features. In both TEM-1 and KPC-2 systems, even though the point of origin of perturbation (i.e. allosteric site) is different, the signal leads to common endpoints at the pivot of α3-turn-α4 helix and in the Ω-loop. Thus, simulations of two different class A β-lactamases, starting from two distinct allosteric sites, identify a common mechanism by which catalytic activity may be disrupted by conformational changes close to the active site. The results from the nonequilibrium simulations also correlate well with experimental data, which suggest that the Ω-loop plays a critical role in ligand binding by altering the conformation of Glu166 and Asn170 which are involved in both acylation and deacylation reactions (Chudyk et al., 2014; Pan et al., 2017; Brown et al., 2009; Fritz et al., 2018; Banerjee et al., 1998).

Dynamical cross-correlation analysis provides information about the pathways of signal propagation and also some insights into the timescales of allosteric communication in TEM-1 and KPC-2 β-lactamases. Dynamic cross-correlation maps (DCCMs) have been previously used to identify networks of coupled residues in several enzymes (Agarwal et al., 2004; Hester et al., 2019; Agarwal et al., 2012).

Using a similar approach, DCCMs were calculated for the Apo_EQ and IB_EQ simulations and also for the Apo_NE nonequilibrium simulations (Figure 5). In these figures, the green regions represent no to slightly positive correlations, while yellow regions represent moderate negative correlations. Negative correlations imply residues moving toward or away from each other in correlated fashion (such as shown by fluctuating hydrogen bonds); for large regions this represents global conformational fluctuations (also referred to as breathing motions) (Agarwal et al., 2004). The results depicted in Figure 5a indicate that in the case of TEM-1 Apo_EQ (Figure 5a, left), β11 helix shows high negative correlation with β12 terminal helix. This represents the lid motion of β12 helix, which moves to shut the empty, hydrophobic, allosteric binding site in the TEM-1 Apo_EQ structure (see above). This motion is, however, not observed in the ligand bound TEM-1 IB_EQ simulations. The TEM-1 IB_EQ system shows a substantial increase in correlations, representing changes in the dynamical communications due to the presence of the allosteric ligand (Figure 5a, middle). The binding of the ligand changes the overall global conformational fluctuations of TEM-1, as represented by the increase in yellow regions in the DCCMs. Furthermore, a number of negative correlations (encircled red regions in DCCMs) also increase in other regions of the protein on ligand binding. The DCCM collectively computed from all nonequilibrium trajectories for TEM-1 (Figure 5a, right, Figure 5—figure supplement 1) also shows a further increase in the areas of negative correlations (encircled). Interestingly, DCCM also identifies the pathway of allosteric communication (Figure 5—figure supplement 1), with notable correlations between the regions β1-β2:α2-β4, α3-α4:α2-β4, β4-α3:α7-α8, β3-α2:Ω, α9-α10:β1-β2, β3-α2:β8-β9, α5-α6:α12, hinge-α11:α1-β1, β8-β9:α4-β5, β7:α12, and α11:α12. These results indicate that the presence of ligand in TEM-1 increases the dynamic communication between regions that are independent in the Apo_EQ simulations. This is particularly evident in the nonequilibrium trajectories that show the largest changes from the case of Apo_EQ TEM-1, identifying changes in correlation as the system adjusts to the absence of the ligand.

KPC-2 shows even more interesting behavior (Figure 5b). Simulations of Apo_EQ KPC-2 show overall more correlated regions than TEM-1 Apo_EQ system (as indicated by the more extensive yellow regions in the DCCM), with further increases in the presence of the inhibitor (indicated by a number of orange regions). However, the DCCM collectively computed from all nonequilibrium trajectories for KPC-2 shows a reduction in regions of cross-correlations, a contrast from the case of TEM-1. To obtain a better understanding, the DCCMs from individual 5 ns nonequilibrium trajectories were also computed and analyzed. These reveal interesting trends as depicted in Figure 5—figure supplement 2. For most nonequilibrium trajectories, the maps are similar with a decrease in dynamic correlations; however, for several trajectories (shown in Figure 5—figure supplement 2), the maps indicate a significant increase in the correlations. The DCCMs computed from individual trajectories show behavior similar to averaged nonequilibrium trajectories in TEM-1 with a number of regions showing high negative correlations (as highlighted by widespread presence of small red regions in the DCCMs). Overall, these results indicate that the perturbation in KPC-2 generates a dynamical response that is much faster than that observed in TEM-1. A plausible explanation for the faster response in KPC-2 is that the more solvent-exposed ligand binding site is surrounded by dynamic surface loops that respond to the perturbation more quickly than the allosteric binding site in TEM-1, which is buried in the hydrophobic core of the protein. This is consistent with the experimental observations that motions can occur on different timescales and can vary greatly between different β-lactamases (Gobeil et al., 2019).

A number of clinical variants that extend hydrolytic activity to encompass additional β-lactams such as oxyiminocephalosporins, and/or enhance enzyme stability, have been identified for both the TEM-1 and KPC-2 β-lactamase enzymes (Palzkill, 2018; Clark et al., 2016; Naas et al., 2017). Some of these have been crystallized and their protein structure deposited in the PDB. While many of these amino acid substitutions (e.g. TEM-1 mutations at residues Glu104 in the α3-turn-α4, Arg164 on the Ω-loop, and Ala237, Gly238, and Glu240 on the β7 strand) directly affect important structural features such as the active site or the Ω-loop, some are of uncertain structural significance. Even when enzyme structures are known, the connections between the positions of clinical variants, protein structure, and their functional implications are often not clear. There is particular uncertainty and interest in the effects of mutations more distant from the active site.

To assess how many of these clinically relevant substitutions lie on the allosteric communication pathway, their spatial positions were identified and mapped onto the 3D structures of TEM-1 and KPC-2. The site of the mutation was plotted as a sphere on its unique Cα position on the structure (Figure 6), which was rendered to represent the allosteric communication pathways shown in Figure 4.

For TEM-1, 45 of the 90, and for KPC-2 15 out of the 25, amino acid positions known to vary in clinical isolates could be mapped onto the allosteric communication pathway. Notably, in TEM-1, residues such as Gly92 preceding α4, His153 at the end of α7, and Ala224 preceding α11 have all been associated with ESBL and/or inhibitor-resistant phenotypes identified in the clinic (Palzkill, 2018). Residues such as M182 and A184, which precede α9 and are not on the communication pathway per se, are however surrounded on all sides by loops that are involved in the communication network (Figure 6—figure supplement 1). For KPC enzymes, for which less information is available, characterized variants that have emerged in the clinic differ mostly in activity toward ceftazidime 58 and feature substitutions at positions (104, 240, 274) closer to the active site. As more sequences emerge and their phenotypic consequences are described (Tooke et al., 2021), however, it will then be of interest to establish the properties of KPC variants featuring substitutions at positions (e.g. 92, 93), which lie along the communication pathways described here. We propose that some of these variants differ in allosteric properties, and further, that these differences relate to variances in their clinically relevant spectrum of activity. If our hypothesis is correct, 50% or more of known clinically important variants in these two enzymes may differ in their allosteric behavior, indicating that this is a fundamentally important property in determining their spectrum of catalytic activity. The relationship between sequence (especially substitutions remote from the active site), protein dynamics, spectrum of activity, catalytic turnover, and allosteric behavior will be an important future direction in understanding AMR due to β-lactamase enzymes (Tooke et al., 2021).

To study allosteric modulation of class A β-lactamases, we started by identifying crystal structures of TEM-1 and KPC-2 β-lactamases with allosteric ligands bound. From the ~80 structures present in the PDB, there are only two crystal structures of class A β-lactamases that have a ligand bound in an allosteric pocket. For TEM-1, the 1.45 Å crystal structure in complex with FTA [3-(4-phenylamino-phenylamino)−2-(1h-tetrazol5-yl)-acrylonitrile] was chosen as the starting structure (PDB id: 1PZP) for this work Horn and Shoichet, 2004. In this structure, the inhibitor binds between helices α11 and α12 (Figure 1a), in a site ~16 Å away from the active site Ser70. Two unstructured residues from the C-terminal end (His289, Trp290) were removed from the crystal structure. For KPC-2, the 1.35 Å crystal structure in complex with a coumarin phosphonate analogue, GTV [(5,7-dimethyl-2-oxo-2h-1-benzopyran-4-yl)methylphosphonic acid], was chosen as the starting structure (PDB id: 6D18) (Pemberton et al., 2019). GTV binds in three sites on KPC-2 (Figure 1b): the first is in the active site (orthosteric ligand); the second site is adjacent to helix α6 (allosteric ligand 1); and the third (allosteric ligand 2) is on the distal end of the enzyme, ~16 Å from the active site Ser70 in between helices α2 and α7. The orthosteric and allosteric ligand 1 (Figure 1b) were discarded because of their direct proximity to the active site and replaced by water. Three unstructured residues from the N-terminal end (His23, Met24, Leu25) and seven from the C-terminal end (Leu288-Gly294) were removed from the starting structure to avoid any simulation artifacts arising as a result of terminal fraying during simulations.

The protonation states of the amino acid side chains were determined at pH 7.0, using the ProteinPrepare functionality as implemented in the high-throughput molecular dynamics (HTMD) framework (Martínez, 2015; Doerr et al., 2016). Charges were assigned on the basis of their local environment, via optimization of the hydrogen-bonding network of the protonated structure (Martínez, 2015).

Parameters for the ligands were generated using the Antechamber tool (Case et al., 2005). The geometry was optimized at the B3LYP/6-31G(d) level and RESP charges were fitted using electrostatic potential obtained at the HF/6-31G(d) level. The necessary nonbonded parameters for the dynamics of the ligands were adopted from GAFF2 (Wang et al., 2004).

All complexes were set up using tleap, as implemented in the Amber MD package. The Amber ff14SB forcefield (Maier et al., 2015) was used for the protein. In total, four complexes were set up, including an allosteric IB (inhibitor-bound) and an Apo (no ligand) system for both TEM-1 and KPC-2 β-lactamases. The Apo system was generated by removing the inhibitor from the allosteric binding site. In all simulated complexes, there is no ligand bound to the orthosteric site. Each complex was solvated using TIP3P water in a cubic box, whose edge was set to at least 10 Å from the closest solute atom (Mark and Nilsson, 2001). The systems were neutralized using K⁺ and Cl^- counter ions. The simulation protocol was identical for each system. The systems were minimized and relaxed under NPT conditions for 5 ns at 1 atm. The temperature was increased to 300 K using a time step of 4 fs, rigid bonds and a cutoff of 9 Å, and particle mesh Ewald summations switched on for long-range electrostatics (Essmann et al., 1995). During the equilibration step, the protein’s backbone and the ligand atoms were restrained by a spring constant set at 1 kcal mol⁻¹ Å⁻², while the ions and solvent were free to move. The production simulations were run in the NVT ensemble using a Langevin thermostat with a damping constant of 0.1 ps and hydrogen mass repartitioning scheme to achieve a time step of 4 fs (Feenstra et al., 1999). The final production step was run without any restraints. All simulations were run using the ACEMD MD engine as implemented in the HTMD framework (Doerr et al., 2016). Visualization of the simulations was done using the VMD package (Humphrey et al., 1996).

The analysis was carried out using GROMACS tools (Abraham et al., 2015), MDLovofit (Martínez, 2015), and in-house scripts (Oliveira et al., 2019a). All systems were considered equilibrated after 50 ns. The dynamic cross-correlations for Cα-Cα were calculated using cpptraj analysis program (Roe and Cheatham, 2013). The results were plotted using in-house scripts and visualized using MATLAB (http://www.mathworks.com).

An independent-samples Student’s t-test was used to compare the Apo_EQ and IB_EQ RMSFs and to assess the significance of the differences observed (Oliveira et al., 2019a; Roy and Laughton, 2010). The sample size used for the t-test was the 20 RMSF profiles of the Apo_EQ and IB_EQ independent simulations. The assumption used for the t-test was that the samples from the two states were independent, the dependent variable was normally distributed, and the variances of the dependent variable were equal.

The figures were made using PyMol (http://www.schrodinger.com), VMD (Humphrey et al., 1996), ChimeraX (Goddard et al., 2018), Protein Imager (3dproteinimaging.com) (Tomasello et al., 2020), and Molsoft ICM-Pro package (http://www.molsoft.com).