Allosteric communication between ACE2 active site and binding interface with SARS-CoV-2

Due to the unprecedented toll that COVID-19 has taken throughout the world, the extraordinary interest elicited by this pandemic from the scientific, medical, and pharmaceutical communities, as well as the general public, cannot be overstated. The causative agent of the COVID-19 disease is a novel coronavirus, SARS-CoV-2. The membrane of this virus is decorated with spike proteins, which are made of three identical copies of the S protein. The tip of each S protein fluctuates between “down” and “up” conformations.¹ In the “up” state, a receptor binding domain (RBD) is exposed to the solvent and is poised to attach to the host. Experiments^2,3 have established that viral invasion requires the presence of the angiotensin converting enzyme 2 (ACE2). ACE2 is a type-I transmembrane protein whose extracellular domain (recognized by the RBD) is a carboxypeptidase that cleaves substrates, such as angiotensin II (angII) and des-Arg9 bradykinin (DABK), which results in protection of lungs from injuries.^4,5 Structural studies revealed the conformation of the full spike,^1,6 the RBD-ACE2 complex,^7–9 and the receptor-bound spike,¹⁰ thereby setting the stage for getting near quantitative molecular insights using computational methods.^11–13 

Numerous investigations have focused on understanding which ACE2 and RBD loci contribute to viral recognition of the human receptor. Techniques, such as mutagenesis, structural analysis,¹⁴ and computer simulations,^15–18 have revealed the network of interactions (salt bridges, hydrogen bonds, and hydrophobic patches) that underly the stability of the complex. Deep Mutagenesis Scanning (DMS) allows us to evaluate how protein expression and binding are impacted by the replacement of selected ACE2¹⁹ and SARS-CoV-2 RBD²⁰ residues with any other amino acid. At the level of single-point-mutation, DMS provides an in-depth understanding of the ACE2-RBD interface. As the virus mutates, one can monitor the progress in terms of changes in affinity with respect to the human receptor. Occasionally, these substitutions have shown a competition between keeping a high affinity for ACE2 and hiding from the immune system.²¹ 

Here, we begin with the following consideration: on general grounds,²² the rigidity of the folded structure of proteins underlies their ability to sustain “action at a distance,” which implies that a local perturbation can have global consequences. Various aspects of the dynamics of the SARS-CoV-2 spike are aided by such long-range effects. For instance, the affinity of the spike for ACE2 increases if the population of the RBD-up conformation increases. Molecular Dynamics (MD) simulations enabled the identification of glycans that stabilize the up conformation of the RBD by occupying the volume freed after the upward movement of the RBD.¹¹ Mutations at hinge domains may stabilize/destabilize the RBD-up conformation and thus impact the affinity for ACE2, as revealed by other MD simulations²³ and experimental mutagenesis complemented with CryoEM.²⁴ Similarly, a combination of CryoEM studies²⁵ and MD simulations complemented with machine learning and network analysis²⁶ contributed to indicating the presence of long-range regulation of the up-down transition of the RBD operated by residue 614, which mutated early in the pandemic from D to G.²⁷ ACE2 binding to the spike protein resulted in the changes in the deuterium exchange profile far away from the receptor binding site, thus suggesting long-range allosteric regulation operated by ACE2,²⁸ which was also investigated using computational methods.²⁹ Coarse-grained (CG) models have identified a coupling between the RBD and the Fusion Peptide Proximal Region (FPPR) of the spike,³⁰ an idea initially put forth upon analyzing static structures.³¹ In addition, kinetic studies have shown that RBD binding to the receptor affects ACE2 catalytic activity for certain substrates, indicating a long-range connection between the ACE2-RBD binding interface and the ACE2 catalytic site.^32,33 Moreover, small molecule screening of ACE2-binding compounds revealed the existence of allosteric pathways that weaken the binding between the receptor and the RBD without affecting ACE2 catalytic activity.³⁴ 

To probe the implications of this “action at a distance” in the context of the RBD-ACE2 complex, we construct Elastic Network Models (ENMs)^35,36 of the metallopeptidase domain of the human receptor ACE2 in isolation³⁷ and in complex with the SARS-CoV-2 RBD^7,8,38 [Fig. 1(a)]. ENMs are coarse-grained representations in which all of the components interact via harmonic potentials. The advantage of this simplified energy function is that it underlies a model that can be solved exactly using numerical methods. In addition, under the premise that long-range movement of the system is well described by a subset of ENM soft modes, we can identify the conformational transition of the whole complex stimulated by the detachment of the RBD. We complement the ENM analysis by using the Structural Perturbation Method (SPM).^39–41 This technique enables the prediction of the Allostery Wiring Diagram (AWD), which represents a network of residues that drives large-scale mechanical movement. Combining these two techniques, we observe the emergence of a dynamical connection between the RBD-binding interface of ACE2 and its catalytic cleft, indicating that RBD might function as a regulator of ACE2 enzymatic activity. This observation provides a molecular rationale for recent kinetic studies that showed how the RBD, S-protein, and spike alter the catalytic activity of ACE2.^32,33 Furthermore, we predict that the area around G502 plays a critical role in complex dissociation.

The ENM is a coarse-grained (CG) representation of a protein based on an energy function in which all interactions are harmonic. In our model, each amino acid is represented using two-beads: one for the backbone, and the other for the side-chain. Glycine is an exception, requiring only a single backbone bead. The strength of the interaction parameters was obtained from a second-order expansion of the Self-Organized Polymer (SOP) model energy function,⁴² which uses the Betancourt–Thirumalai statistical potential⁴³ to confer sequence specificity (details are in the supplementary material). All pairwise interactions were treated in the same way, including those at the interface between RBD and ACE2.

In order to solve the ENM, we computed the modes and frequencies of the bound complexes [Fig. 1(a)] by obtaining, respectively, the 3N-dimensional (N is the number of beads) eigenvectors (v_n) and the 3N eigenvalues (h_n) of the Hessian matrix, $Ĥ$ (see supplementary material). We neglect the first six eigenvectors and eigenvalues because they are associated with the rigid body movement of the complex. For this calculation, we considered only the protein components—RBD [333-527 for SARS-CoV-2 (PDBID: 6LZG), 33-526 for an alternative SARS-CoV-2 complex (PDBID:6M0J), and 323-502 for SARS-CoV (PDBID: 2AJF)] and ACE2 [19-614 for the complex with SARS-CoV-2 (PDBID: 6LZG), 19-615 for the complex with SARS-CoV (PDBID: 2AJF), in isolation (PDBID: 1R42 and PDBID: 1R4L), or for an alternative SARS-CoV-2 complex (PDBID: 6M0J)], ignoring residues that were not resolved (376-381 in the RBD of PDBID: 2AJF), ions (zinc and chloride, which is not consistently solved; for instance, it is found in structure PDBID: 2AJF but not in PDBID: 6LZG), water, and sugars. If multiple conformations of the side-chains were available, the one listed as “A” was selected. It is worth remarking that although MD simulations have highlighted the importance of N-linked glycosylation of the receptor in the interaction with the RBD,^13,44–51 experiments showed that ablating the ACE2 glycans has a minimal impact on the dissociation constant.^50–56 In addition, N-linked glycosylation is not required for ACE2 activity either.⁵⁵ Thus, given the dynamical nature of the polysaccharides, as vividly illustrated by Casalino et al.,¹¹ at least to a first approximation, it is consistent with the ENM, which accounts for small fluctuations around the experimental structure, to ignore the glycans. However, we cannot exclude that glycans could affect some of the modes obtained via ENM analysis. In principle, one could perform an ENM analysis using various glycans conformations sampled via MD and probe such effect. Although interesting, we did not perform this test. In order to test the impact in ENM and SPM of the lack of residues 376-381 in the ACE2-RBD complex for SARS-CoV, we removed the corresponding residues (389-394) from the SARS-CoV-2 RBD, re-run the calculations, and found, in Fig. S5, that the results were nearly identical to those obtained using the wild type (WT) RBD. In addition, in the present study, we consider only the peptidase domain of human ACE2. In the original structure of ACE2, the collectrin homology domain (CHD) displayed weak electron density map (PDBID: 1R4L, and 1R42).³⁷ X-ray structures of human ACE2 in complex with SARS-CoV (PDBID: 2AJF) and SARS-CoV-2 (PDBID: 6LZG and PDBID: 6M0J) RBD do not include the CHD. Thus, we focused our attention to the metallopeptidase domain. It should be noted that Cryo-EM images have revealed the structure of the CHD in a human ACE2 dimer complexed with two amino acid transporters.⁷ However, the CHD is involved in dimerization of ACE2, and thus, it is not clear to which extent its structure is affected by the presence of the dimer and by the interaction with the membrane.

We validated the model by comparing the scaled and normalized B-factors with experiments (see the supplementary material and Fig. S8). The location and height of many peaks were reproduced correctly without adjusting any model parameters.

We constructed an ensemble of dissociated structures [Fig. 1(b), see details in the supplementary material and Figs. S9(a)–S9(f)] to correct our lack of knowledge of the mechanism of complex disruption. We considered 27 dissociation pathways [see Fig. 1(b) for a pictorial representation, and for additional details, see the supplementary material and Fig. S9] in which the ACE2 is intact, and the RBD is rigidly displaced away from the ACE2.

Next, we identified the mode (v_n) that provides the most accurate description of the rigid-body displacement of the RBD [one with the largest “overlap” defined in the supplementary material, Eqs. (S18) and (S19)] and analyzed the mode-induced conformational changes in the ACE2 and RBD (Fig. 2). We neglected rigid body movements [colored blue, with negative indices in Fig. 2(a)], which are not associated with the disruption of interactions at the interface. We ensured that the mode with the largest overlap is dominant (at the top, or within the top three) for most of the displacement vectors considered. As a final test of the robustness of the results, we also performed calculations using a different procedure in which both ACE2 and RBD are aligned after the RBD is displaced [Fig. S9(g), in this case, both ACE2 and RBD move]. We verified that aligning both ACE2 and RBD did not change the eigenvector associated with the largest overlap [Fig. S9(h)].

The calculation of the AWD is based on the premise that the key residues associated with the conformational transitions between distinct allosteric states have the largest effect on the few low-frequency, soft modes that describe the large-scale movement. This can be probed by perturbing the interactions of each residue and monitoring the response along a mode. The SPM signal [ω_i(v_n), defined in Eq. (S20)] is a result of the response to a perturbation of the interactions of one group with the rest of the protein along a selected mode. The network of residues with the largest responses to a local perturbation [that is, $ωi(vn)>2ω̄i(vn)$⁠, where $ω̄i(vn)$ is the average SPM signal along mode n, see Eq. (S25) and Zheng et al.³⁹] constitutes the AWD. Additional details of the ENM and SPM are in the supplementary material.

Following Vu et al.,⁵⁷ we define the local stiffness κ_i of bead i as the elastic energy stored in that bead divided by the local mobility. The average energy stored is the average of the SPM signal for bead i along an eigenvector divided by the eigenvalue and summed over all the modes and is given by $⟨ΔEi⟩=∑n=73Nωi(vn)/(βhn)$⁠, where i is a bead, n refers to one of the eigenvalues not associated with rigid body motion, β = 1/(k_BT), and h_n is the nth eigenvalue of the Hessian matrix. Note that ω_i(v_n) and h_n have the units of stiffness in this manuscript so ΔE_i is energy. The mobility of bead i is obtained from the B-factor, B_i, obtained from simulations [Eqs. (S15) and (S16)], that is $⟨u⃗i2⟩=3/(8π2)Bi$⁠, with $u⃗i$ being the displacement from the equilibrium position of bead i. The local stiffness is $κi=⟨ΔEi⟩/⟨u⃗i2⟩$⁠.

We defined a 3N-vector C given by the difference in the location of the beads for a model of ACE2 in the apo, open-binding-cleft state [PDBID: 1R42, Fig. S11(a)] and in the inhibitor-bound conformation, in which the clam-shaped enzyme is closed [PDBID: 1R4L, Fig. S11(a)]. In addition, we defined a similar reaction-coordinate for the complex between SARS-CoV-2 and ACE2 [see Fig. S11(b)]. In this case, a structure of closed ACE2 in the RBD-bound state was not available. We constructed it by combining ACE2 from PDBID:1R4L to the RBD from PDBID:6LZG after residues 18-85 of ACE2 of the two structures were aligned using PyMol,⁵⁸ resulting in a rms of 1.48 Å over 549 atoms [see Fig. S11(b)]. After aligning the ACE2 in the open and closed conformations, we used these structures to create a new vector C for the RBD and ACE2 complex either by aligning only ACE2 or both ACE2 and the RBD.

Molecular structures were rendered with PyMol.⁵⁸ Pictorial representations and assembly of the figures were made using Inkscape (https://inkscape.org). Matplotlib⁵⁹ and Jupyter notebooks⁶⁰ were also used to plot and analyze the data.

We start by addressing the following question: What are the local and long-range responses that are elicited by the dissolution of the RBD-ACE2 complex?

The dynamics of the ACE2-RBD complex is described by performing a normal mode analysis of the ENM for the complex. Often, long-range, collective movements are encoded within a small set of low-eigenvalue modes. Therefore, we sought the modes that provide the best description [largest overlap, see Eqs. (S18) and (S19)] of the dissociation of the viral RBD and the receptor. As shown in Fig. 2(a), mode 2 (with the second smallest, non-zero eigenvalue) has the largest overlap with most of the dissociation pathways considered (as explained in Sec. II, the six lowest eigenvectors are ignored because they describe rigid body motions). Although other modes could be relevant, we focused only on the dominant one.

Along mode 2, the RBD rotates away from the ACE2 in a counter-clockwise manner. Figure 2(c) shows that the interacting pairs at the interface in the “front” of the complex get closer, whereas there is a domain visible from the “back” of the ensemble that separates along the dominant mode. Previous MD simulations of the complex showed that the two ends of the interface break native contacts more frequently than the central section,¹³ in qualitative agreement with oscillation along mode 2. The principal component obtained from the analysis of MD simulations of the RBD-ACE2 ensemble shows a rotary movement (Fig. S5A in Ghorbani et al.¹⁷) which, upon visual inspection, resembles the displacement of RBD in mode 2. Finally, on the basis of MD simulations,⁶¹ it was proposed that the last section of the complex to dissociate corresponds to residues 470–490. This is in qualitative agreement with our results, which show that this region moves closer to the receptor during the rotary movement in Fig. 2(c).

Coupled with the dissociation of the RBD is the opening of the binding cleft of ACE2, in agreement with adaptive biasing force simulations.⁶¹ We illustrate this in Multimedia Movie 1, which shows the movement of all the beads of the system along mode 2. We discuss the implications of this concerted movement in Sec. III D.

We use SPM to extract the AWD associated with mode 2. The AWD in Figs. 3(a) and 3(b) shows how the response to detachment involves more than merely the residues at the ACE2 interface. Two pathways connect the interior of ACE2 with the interface [Fig. 3(a)]: one dominated by polar residues, including Q81 (pink circle in Fig. 3(a), which has among the strongest SPM signals [Fig. 3(c)]. The other branch [Fig. 3(b)] reaches the active site of the ACE2 peptidase domain, establishing a connection between the binding interface and the catalytic domain that will be discussed in detail in Sec. III D. The dominant contribution along this branch is provided by G502 on the RBD and G354 of ACE2 [Fig. 3(b)]. G502 is in the middle of a thick section of the AWD network dominated by backbone beads and hydrophobic side-chains, and its SPM signal is the strongest [Fig. 3(c)]. We remark that another computational investigation of allosteric pathways in ACE2 identified a connection between the binding interface with the RBD and the catalytic core of ACE2.²⁹ Next, we focus our attention on G502.

From Fig. 3(b), it is clear that the region associated with the initiation of the detachment [cyan in Fig. 2(c)] surrounds the RBD residue G502. The strong SPM signal of G502 [Fig. 3(c)] prompts further investigation of the local interactions associated with the AWD and the initiation of dissolution of the complex. First of all, G502 fits tightly in a small recess on the surface of ACE2,²⁰ in agreement with the thick network of interactions surrounding G502 highlighted here and in another computational study, in which it was pointed out that among various interfacial residues mutated to alanine, the one most detrimental for the binding affinity is G502A.¹⁷ In addition, G502 forms a hydrogen bond with the backbone of K353, which is the residue at the center of the so-called “hot spot 353”^14,62 and is believed to stabilize the complex.^18,63 ACE2 residue K353 forms an intra-receptor salt-bridge with D38, which could contribute to the stability of the complex because binding ACE2 to the RBD de-solvates it, making the surrounding environment more hydrophobic.⁶² Indeed, structures of ACE2 without RBD show that the salt bridge could be either intact (PDBID: 6M18⁷) or broken (PDBID: 1R42³⁷). Mutation of K353 to Ala⁶² or His⁶⁴ reduces significantly the binding affinity of ACE2 for SARS-CoV RBD. In agreement with these observations, our local stiffness analysis shows that K353 is the residue that most rigidifies when binding RBD (Fig. 4). This appears significant, in particular, because most of the receptor softens upon RBD binding.

The hydrogen bond between G502 and K353 backbones might facilitate the formation of this salt bridge. Accordingly, a computational study suggested that residue G502 is replaced by proline in a number of coronaviruses, which are predicted to interact poorly with the human ACE2 receptor.⁶⁵ Notably, G502P would not form the hydrogen bond with K353.

Our ENM and SPM analyses provide three different indications that the binding of RBD may impact ACE2 catalytic activity. First, as introduced in Sec. III A, Fig. 2(b) shows the opening of the binding cleft enclosing the ACE2 active site [where the zinc ion is located,³⁷ see the orange sphere in Fig. 2(b)]. The opening of ACE2 is opposite to the movement observed in the presence of an inhibitor of the catalytic function bound to the active site of the enzyme,³⁷ which, instead, triggers the closing of the binding cleft. The connection between the dissociation of RBD and the opening of the ACE2 binding cleft is further reinforced by the observation that both of these movements are best described by mode 2 [see Fig. 2(a), Multimedia Movie 1, and Fig. S11(c)].

Second, as we anticipated before, the AWD associated with mode 2 reaches the active site of the ACE2 peptidase domain, with the zinc-binding consensus sequence (³⁷⁴HExxH³⁷⁸ + E⁴⁰², see Towler et al.³⁷) involved in the network [zinc is shown in orange in Fig. 3(a)].

Third, we computed the stiffness along a reaction coordinate connecting the open-cleft to closed-cleft states (see Sec. II and Fig. S11). The stiffness is given by the eigenvalues associated with the modes that best describe the open-to-close transition. For both the isolated ACE2 and ACE2 with RBD, mode 1 and mode 2 have the largest overlap with the open-to-close reaction coordinate [see Fig. S11(c)]. The corresponding eigenvalues are $≈3.32$ pN/nm (with largest overlap) and 5.82 pN/nm for ACE2 and $≈1.07$ pN/nm and $≈2.09$ pN/nm (with largest overlap) for the complex. The smaller values obtained when the RBD is bound to ACE2 are indicative of the fact that RBD might facilitate fluctuations of the open-to-close transition, thus affecting the catalytic activity of ACE2.

Experimental studies have shown that catalytic activity is not necessary for SARS-CoV or SARS-CoV-2 RBD binding to ACE2. In particular, mutations of the zinc-binding sequence preventing catalysis do not suppress SARS-CoV⁶⁶ or SARS-CoV-2¹⁹ binding to ACE2. In addition, an inhibitor of ACE2 did not impact SARS-CoV binding or infection, and ACE2 binding to a fusion protein including a segment of the SARS-CoV spike did not affect the receptor catalytic activity.⁶⁴ On the other hand, a different inhibitor of ACE2 reduces cell fusion mediated by SARS-CoV.⁶⁷ A computational study suggested that the closed ACE2 could have a higher affinity for SARS-CoV-2 RBD;⁶¹ however, another MD study reported a weakening of the SARS-CoV-2-RBD binding enthalpy for the inhibitor-bound receptor.⁶⁸ More recently, a different set of MD simulations suggested that while ACE2 binding to the SARS-CoV RBD tends to close the receptor catalytic site, the SARS-CoV-2 RBD has a weaker effect on the receptor conformation.²⁹ A more direct test of RBD impact on ACE2 catalysis emerged from the experiments by Lu and Sun,³² and Kiseleva et al.,³³ who reported that the presence of SARS-CoV-2 RBD (and to a lesser extent SARS-CoV) increased the peptidase activity of ACE2 in a concentration- and substrate-dependent manner. The studies differ in their kinetic analysis: both report an increase of k_cat due to RBD but only Lu and Sun observe changes in K_m. Our simulations suggest that the clam shell-like open-to-close transition of ACE2 is facilitated by RBD binding, and we suggest that this provides a structural paradigm for the increase in k_cat. The observation that RBD binding could facilitate the closing of ACE2 was already made by Lu and Sun on the basis of the examination of static structures.³² Our study reinforces this observation by providing a dynamic picture connecting RBD binding with ACE2 activity. However, at present, our analysis cannot explain why the increased peptidase activity is substrate-dependent; structural information and possibly higher resolution methods might be necessary in order to understand this observation. In addition, we note that an experimental study shows the reduction of deuterium exchange in ACE2 bound to RBD or the spike protein as compared to free ACE2, which is indicative of enhanced ACE2 stability upon RBD binding.²⁸  Prima facie, this seems to be in contrast with the reduction in ACE2 stiffness occurring upon RBD binding and possibly even with the enhancement of ACE2 closing proclivity stimulated by RBD binding. Experiments measuring deuterium exchange for the closed ACE2 receptor would help clarify the relationship between ACE2 catalytic activity and deuterium exchange.

In the following, we address a different question: Can we establish differences and similarities between SARS-CoV and SARS-CoV-2 on the basis of the analysis of both local and long-range interactions?

Mode 2 provides the best description (highest overlap) of the dissociation of the ACE2-RBD complex for both SARS-CoV-2 [Fig. 2(a)] and SARS-CoV [Fig. S1(a)]. Comparison between Figs. 2(b) and 2(c) and Figs. S1(b) and S1(c) show that mode 2 is similar for the ACE2 complex with SARS-CoV-2 and SARS-CoV: in both cases, the binding cleft opens as the RBD rotates away from ACE2. In both viruses, the domain that initiates detachment involves the segment of the RBD surrounding the conserved G502 in SARS-CoV-2 and G488 in SARS-CoV.

The shape of the overall AWD is similar for SARS-CoV-2 and SARS-CoV [see Figs. 3(a) and 3(b) with Figs. S2(a) and S2(b)]. A quantitative comparison between the two AWDs shows a robust correlation (Pearson coefficient $≥0.8$⁠, see Fig. S3). However, there are a number of outliers reflecting the reorganization of the network due to mutations and subtle structural changes. Many of these outliers occur around the area at the “back” of the complex, which initiates detachment (see Fig. S3). Here, both G502 and V503 in SARS-CoV-2 and the corresponding SARS-CoV residues (G488 and I489) have among the strongest SPM signals. However, the contribution of the glycine is larger in SARS-CoV-2 than in SARS-CoV, whereas SARS-CoV I489 has a much stronger signal than the corresponding SARS-CoV-2 valine.

The changes in ACE2 local stiffness due to RBD binding have a similar profile in SARS-CoV-2 (Fig. 4) and SARS-CoV (Fig. S4). In both cases, binding the viral protein stiffens the residues at the interface, whereas the rest of the receptor appears to soften. A quantitative comparison show that the stiffness profiles in the presence of SARS-CoV and SARS-CoV-2 nearly overlap (Figs. S6 and S7). As a control, we compute the change in stiffness obtained for two structures of the SARS-CoV-2 RBD-ACE2 complex (PDBID: 6LZG, and PDBID: 6M0J, see Figs. S6 and S7). The histograms in Figs. S6(e)–S7(e) reveal that the distribution of the discrepancy between the two viruses is slightly broader than the control, although the mean is nearly the same.

Overall, these global assessments of the SARS-CoV-2 and SARS-CoV RBDs in complex with ACE2 show strong similarities. We surmise that these global measurements are more sensitive to the overall morphology of the constructs than to changes in sequence or localized structural reorganization. We note here that a recent computational study showed differences in ACE2 tendency to open/close the active site in the presence of SARS-CoV and SARS-CoV-2 RBDs, with SARS-CoV favoring the closed state.

We conclude by reiterating our major findings. (1) Local and long-range responses are triggered upon dissolution or formation of the ACE2-RBD complex. Our study proposes a mechanism of complex disruption that begins with the movement of a region surrounding G502, a conserved glycine that tightly fits into a small ACE2 recess. Dissociation of RBD is coupled with the opening of the ACE2 binding cleft, and fluctuations of the binding cleft are larger when the ACE2 is in complex with RBD. These observations underlie a connection between RBD binding and ACE2 activity, which has been recently illustrated via experiments.^32,33 (2) The overall properties of SARS-CoV and SARS-CoV-2 RBD’s interaction with ACE2 are similar, reflecting the closely related morphologies of these two complexes. However, sequence and structural differences result in localized differences between the allosteric signals elicited by virus dissociation from ACE2.

Supplementary material includes mathematical and numerical details on our implementation of ENM and SPM (see Secs. I–III of the text and Figs. S9 and S10). In addition, Sec. IV and Figs. S1, S2, and S4 report on our analysis done for SARS-CoV. Figure. S3 shows a comparison between SARS-CoV and SARS-CoV-2, while Fig. S5 is a control for this comparison (see Sec. II in the main text). Figures S7 and S8 compare the rigidity among different complexes, and Fig. S9 displays the rescaled B-factors for both experiments and simulations for different structures. Finally, Fig. S11 refers to the structural changes associated with the closing of the ACE2 binding cleft.

We thank Clark Templeton and Ron Elber for contributing to an earlier version of this manuscript. We also thank Jason McLellan for his interest, and Carlos Simmerling for his useful comments. M.L.M. thanks to Atreya Dey for pointing out a typo in the supplementary material. This work was supported by the National Science Foundation (Grant No. CHE 19-00093) and the Welch Foundation (Grant No. F-0019) administered through the Collie-Welch chair.

The authors have no conflicts to disclose.

Mauro L. Mugnai: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – original draft (equal). D. Thirumalai: Conceptualization (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Writing – original draft (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.