key: cord-0806162-w2gdbm42
authors: Ngo, Van A.; Jha, Ramesh K.
title: Identifying Key Determinants of SARS-CoV-2/ACE2 Tight Interaction
date: 2020-07-13
journal: bioRxiv
DOI: 10.1101/2020.07.13.199562
sha: 52b60c752f34232e51b18575942dddfaf5475e32
doc_id: 806162
cord_uid: w2gdbm42

SARS-CoV-2 virus, the causative agent of Covid-19, has fired up a global pandemic. The virus interacts with the human receptor angiotensin-converting enzyme 2 (ACE2) for invasion via receptor binding domain (RBD) on its spike protein. To provide a deeper understanding of this interaction, we performed microsecond simulations of the RBD-ACE2 complex for SARS- CoV-2 and compared it with the closely related SARS-CoV discovered in 2003. We show residues in the RBD of SARS-CoV-2 that were mutated from SARS-CoV, collectively help make RBD anchor much stronger to the N-terminal part of ACE2 than the corresponding residues on RBD of SARS-CoV. This would result in reduced dissociation rate of SARS-CoV-2 from human recep- tor protein compared to SARS-CoV. This phenomenon was consistently observed in simulations beyond 500 ns and was reproducible across different force fields. Altogether, our study shed light on the key residues and their dynamics at the virus spike and human receptor binding interface and advance our knowledge for the development of diagnostics and therapeutics to combat the pandemic efficiently.

It is vital to understand the mechanisms of SARS-CoV-2 in comparison to other coronavirus. [1] [2] [3] [4] [5] [6] [7] [8] One strategy is to zoom in to the molecular levels of how SARS-CoV-2 invades human cells. The first step of the invasion is to have its Spike proteins bind to human cells such as lung cells, whose surface expresses a lot of ACE2. The RBD of SARS-CoV-2 2 (dubbed RBD2 in this study) was identified to bind to ACE2 with an interface similar to the RBD of SARS-CoV (dubbed RBD1 hereafter) from 2003. 9 It was determined that RBD2 binds stronger to ACE2 than RBD1. 4, 10, 11 There are multiple mutations that are found in RBD2 that can explain why SARS-CoV-2 is more infectious than SARS-CoV. Specifically, residues G482/V483/E484/G485/F486/Q493/L455/N501 (based on RBD2 numbering) constituting a receptor binding motif (RBM) may cause a significant structural difference when comparing the crystal structures of RBD2 and RBD1. 2 Freeenergy calculations were also done for the mutations at these residues to compare how they contribute to overall binding affinities via a coarse grain model. 12 Using homology models for comparing the structures of Bat-CoV, SARS-CoV, and SARS-CoV-2, Ortega et. al. 5 proposed that the two loops of RBD2 might help enhancing its interactions with ACE2 with an improvement of 1.6 kcal/mol in the binding energy compared to RBD1. Amin et al. 13 showed this increase in the binding affinity may be attributed to the electrostatic interactions enhanced by the mutations appearing in RBD2. Most of these studies relied on short simulations, thus not revealing the dynamics of the interfaces. To aid the research community, the Shaw group 7 performed 10-75 µs molecular dynamics (MD) simulations of both RBD1 and RBD2 and how they bind to ACE2, and has granted a free access to many critical simulation data. However, how these residues change the conformations at the RBD2-ACE2 interface in comparison to the RBD1-ACE2 interface remains to be elucidated. Even though free-energy calculations 12 reveal relatively important levels of these residues at RBD2-ACE2 interface, how they dynamically co-operate to enhance the binding of RBD2 and how RBD2 may dynamically dissociate from ACE2 have not yet been explored.

In this study, we demonstrated how the key residues F486/ N487/Y489/A475, some of which were previously identified as important, play a more critical and collective role at RBD2-ACE2 interface than other residues (for example, Q493/L455/N501) and the corresponding residues L486/N487/Y48/P475 at RBD1-ACE2 interface (Figure 1a) . We cross-examined these residues in two popular force fields (FFs), CHARMM36 14 and AMBER FF. 15 Understanding how these groups of residues dynamically and collectively respond to an applied "force" at RBD2-ACE2 interface may lead to an effective therapeutic design to specifically target these residues for battling the invasion of SARS-CoV-2 to the human host cells. To show such a collective response, we performed Umbrella Sampling (US) simulations of 4.8 µs in total per complex to compute the potential of mean forces (PMFs) for separating the RBDs from ACE2. Combining the results from long equilibration simulations and US simulations, we demonstrated that the dynamics of the residues at RBD1-ACE2 and RBD2-ACE2 interfaces are quantitatively different, that is, the loop, where F486/N487/Y489/A475 are located in RBD2, anchors strongly on ACE2, but the corresponding loop in RBD1 may lose its grip on ACE2.

For the MD simulations, we used the crystal structure (PDB:2AJF) 9 for RBD1-ACE2 complex, and the crystal structure (PDB:6M0J) 10 for RBD2-ACE2 complex (Figure 1b) . Note that the residue numbers in Figure 1a are consistent with the alignment in Ref. 2, 4, 6 . For simplicity and consistency, we refer to the same residue numbers for both complexes. The residue indices in the PDB:2AJF can be converted to the residue numbers shown in Figure 1a by adding 13 to indices less than 472 or by adding 14 to the indices otherwise since RBD2 showed an insertion of a residue at position 483. The missing loop (residues 375-381) in RBD1 was added by aligning RBD1 with RBD2; then the coordinates of the aligned loop (residues 389-394) was used to construct the coordinates for the missing loop in RBD1. We then used CHARMM 36 (C36) 14 force field (FF) to model the complexes. When building the models, we did not include glycans in either of the complexes. The asparagine (N90) linked glycan (on ACE2), close to the interface, showed better electron density in RBD1-ACE2 structure and showed an extended form consisting of three sugar units (PDB: 2AJF). The closest residue on RBD1, T402, showed a distance of > 4 Å from the glycan and would contribute weakly to the interaction. In RBD2-ACE2, N90 linked glycan lacked electron density and consisted of only one sugar unit. Another structure of RBD2-ACE2 (PDB:6M17) also showed only two sugar units linked to N90. In both RBD2 complexes, the nearest amino acid to the glycan sugar T415 was not expected to contribute to the binding interaction. Due to this discrepancy and a low binding energy contribution from glycan, the complexes were prepared in the absence of them. We included the Zn 2+ ion, which is coordinated by two histidine residues (H356 and H360) and a glutamate (E384) of ACE2. All histidine residues were modeled in the neutral and non-protonated state. We applied a patch of disulfide bond for all disulfide pairs as found in both RBDs and ACE2. 2, 9 The systems were then solvated with TIP3P water model. 16 0.15 M KCl was added to neutralize and mimic a physiological condition. The number of K + and Clwere kept at 102 and 78, respectively, for simulations of both RBD1-ACE2 and RBD2-ACE2 complexes. The total number of atoms in these two solvated systems were approximately 102,000 with a dimension of 75´83´162 Å 3 after minimization and 0.5 ns equilibration using NAMD 2.12. 17 The minimization step was done with conjugate gradient energy minimization method. 18 A cut-off distance of 12 Å and a switch distance of 10 Å was used to compute Lennard-Jones interactions. We enabled Particle Mesh Ewald summation method 19 to compute electrostatic interactions with a grid-size of 1.0 Å. We used Langevin dynamics together with Langevin Piston to keep temperature around 310 K and pressure at 1 atm. A timestep = 1 fs was used for the short equilibration simulations. To enable a larger integration timestep, we used PARMED 20 to re-partition hydrogen atoms bonded to protein heavy atoms (exclude water molecules), while keeping the total mass unchanged. 21 In this way, the dynamics of an entire protein may not noticeably change but the simulations can become more stable when using a timestep of 4 fs. We used AMBER version 16 22,23 in order to run efficiently on the GPU nodes using the same C36 FF and simulation parameters used in NAMD 2.12. Specifically, we can pack four replicas per GPUs-node without a cost of slowing down each of the four simulations per node via AMBER, while the same setup for the simulations using NAMD-GPU can experience a significant slowdown (data not shown). Since it has been shown that running multiple independent MD simulations in parallel can sample better than running a single long MD simulations, 24,25 we created 8 replicas of each complex, which were quickly equilibrated using NAMD 2.12. Each replica was further equilibrated using AMBER 16 for about 600 ns to collect data, which were saved every 1 ns for analysis. We collected data for a total of approximately 5 µs per complex. To compute a potential of mean force (PMF), which can be used to describe an effective interaction between the complexes as a function of the distance between the two centers of mass, we performed Umbrella Sampling (US) simulations ( Figure 1b) . [26] [27] [28] Typically, US simulations are prepared in a set of independent simulation windows, each of which has an applied or biased harmonic potential, e.g., UUS(Ri,R) = k(Ri -RRBD-ACE2) 2 /2, where k = 10 kcal/mol-Å 2 , RRBD-ACE2 is the biased distance between the centers of mass of an RBD and of ACE2 (for simplicity, we used only Ca atoms to compute the centers of mass); and Ri is a restraint position. We found the smallest value of Ri from the distribution of RRBD-ACE2 from the above 4.3 µs equilibration simulation. For instance, in the case of RBD1-ACE2 complex, the smallest value of Ri is 43 Å; in the case of RBD2-ACE2 complex, the smallest value of Ri is 46 Å. Then, we chose a last window with Ri ~ 70-75 Å to enable a complete separation between each RBD and ACE2. Since the harmonic potential induces a fluctuation of about 0.3-0.4 Å around each restraint position Ri, we used an increment of 0.5 Å between every adjacent window (Supplementary Figure S1 ) to ensure proper overlaps between the distributions of RRBD-ACE2 in any two adjacent windows. 29 Each window was run for 10-11 ns per replica, i.e., for 8 replicas, we collected approximately 80 ns per window. In total, we simulated for 60 windows with a total of 4.8 µs for each complex. We saved the values of RRBD-ACE2 every 1000 steps (=4 ps) and the biased configurations every 1 ns for each window. These values were then used to solve for a potential of mean force via Weighted Histogram Analysis Method. 27, 28 

To rank the relative importance of each residue at the interfaces of RBD1 and RBD2 with ACE2, we computed the "bound" probability of each pair at the interfaces during the 5-µs equilibrium simulations. Figure 2a-b shows a relative ranking of pairs of residues at the interface: high probabilities indicate highly interactive pairs, while low probabilities indicate weakly interacting pairs. To the best of our knowledge, such a complete ranking has not been reported in previous studies, even though calculations of relative changes of interaction energies or free-energies were done for some of the pairs and mutations. 12,13 Figure 2a -b shows that both interfaces have almost the same number of interacting pairs. However, if counting stable pairs that have probability larger than 60% (i.e., in close contact 60% of the total simulation time), there are only 22 ± 2 pairs in RBD1-ACE2 interface, while RBD2-ACE2 showed substantially higher, 35 ± 1 stable pairs at the interface. Among these stable pairs, the mutations from RBD1 to RBD2, namely, Y455L, L456F, Y498Q, T501N and L486F appear to noticeably enhance the probabilities of interaction with the residues of ACE2 with multiple pairs having probabilities close to 100%. The green brackets in Figure 2b indicate two groups of neighboring residue clusters that have a substantial increase in interactions in RBD2-ACE2 interface compared to the similar clusters in RBD1-ACE2 interface. This suggests that they are key residues that differentiate RBD2-ACE2 binding interface from RBD1-ACE2 binding interface.

(a-b) Probability of pairs of residues found within 3.5 Å at the interfaces between RBD1 or RBD2 with ACE2 during simulations of 5 µs per system using C36 FF. A stable pair is defined to have a probability larger than 60% during the simulation times, i.e, forming a pair within 3.5 Å for more than 60% of a simulation trajectory. Green brackets indicate clusters of residues that are on average more stable in RBD2-ACE2 interface than the corresponding clusters in RBD1-ACE2 interface.

To probe whether the use of a different force field may change the outcomes of the key residues in the interfaces, we compared the probabilities with those obtained from the simulations using modified AMBER ff88SB FF 15 performed by the Shaw group. 7 In this AMBER-FF model, RBD1-ACE2 interface shows 29 ± 2 stable pairs, which are again substantially lesser than 39 ± 1 stable pairs in RBD2-ACE2 having bound probabilities larger than 60% (Supplementary Figure S2) . As a result, the AMBER FF quantitatively yields more stable pairs that the C36 FF. Particularly, the AMBER FF predicts two salt-bridges (R403-E37 and K417-D30) in the RBD2-ACE2 complex, compared to only one salt-bridge when modeled by the C36 FF (K417-D30). However, the Y455L, L456F, Y498Q, T501N and L486F mutations (Supplementary Figure S2) are also found to enhance the same clusters of interactions in RBD2-ACE2 interface (Figure 2b) . Hence, regardless of the FFs, the RBD2-ACE2 interface shows stronger inter-molecular interactions than the RBD1-ACE1 interface involving the same group of residue positions (Figure 2b) . The clusters of the important residues are consistent with the finding 2 that residues L455 and F486 and N501 of SARS-CoV-2 are perhaps the most critical residues that increase the interactions between RBD2 and ACE2 in comparison with the interactions between RBD1 and ACE2 with Y455, L486 and T501 residues on RBD1. Note that L486F, Y498Q and D501 (instead of T501) to N mutations were found when the sequences of bat coronavirus RaTG13 and SARS-CoV-2 were compared. 2 Other key residues of RBD2 identified previously, 2 are Q493 and S494 of which Q493 is also seen to have stable interactions with ACE2 (Figure 2b and Supplementary Figure S2) , while S494 was not detectable in both RBD1-ACE2 and RBD2-ACE2 interactions, suggesting that S494 may not play any critical role at the interface as proposed in the previous study. New residues such as K417, Y473 and A475, which were not reported earlier 2 but proposed to be important in others work 5, 8, 13 , emerged to be important for RBD2-ACE2 interface and enhanced the interaction compared to RBD1-ACE2 with V417 and P475 residues. Particularly, the V417K mutation created a salt-bridge with D30 (on ACE2), thus contributing to an increase in the electrostatic interactions 8 and compensating for coulomb energy due to mutation R439N and loss of distal R439-E329 electrostatic interaction (seen in RBD1-ACE2 interface). 13 Overall, regardless of the FFs there are the same key clusters of residues in RBD2-ACE2 complex responsible for enhancing the interactions at the interface of RBD2-ACE2 complex; however, the AMBER-FF model yielded a measurable stronger interface with higher number of stable pairs than the C36-FF model.

To energetically differentiate the interfaces, we computed the probability r(RRBD-ACE2) for a distance RRBD-ACE2 between the center of mass of an RBD and ACE2; and a free energy was computed as -kBTlog(r(RRBD-ACE2)), where kB is the Boltzmann constant and T = 310 K is the simulated temperature. Figure 3 shows the free-energy profiles computed for the RBD1-ACE2 and RBD2-ACE2 complexes using the two FFs. When modeled with the C36 FF, the global free-energy profile of RBD1-ACE2 complex with a global minimum (at RRBD-ACE2 = 47-48.5Å) was broader than RBD2-ACE2 complex that showed a global minimum (at RRBD-ACE2 » 50 Å) (Figure 3) . This suggests that the RBD1-ACE2 interface is less tight than the RBD2-ACE2 interface. When modeled by the AMBER FF, the global energy minima of the two complexes are also located at different positions (RRBD-ACE2 = 44 Å vs. RRBD-ACE2 = 47 Å); and the shape of the free-energy profile of RBD1-ACE2 complex for RRBD-ACE2 > 44 Å is approximately linear with R, in contrast to the parabolic shape of RBD2-ACE2 complex. In consistency with the C36-FF model, this suggests that, the RBD2-ACE2 interface has stronger interactions than the RBD1-ACE2 interface. By comparing the free-energy profiles of each complex modeled by the two FFs, we observed that the complex modeled by the AMBER FF has stronger interactions than the complex modeled by the C36 FF. For instance, RBD2-ACE2 complex, if moved apart from the global minimum by 2 Å, shows a free energy increase of 4 kBT in the AMBER-FF model, but only about 2 kBT in the C36-FF model (Figure 3a) . This is consistent with the above observation based on the pairs of residues at the interfaces (Figure 2b and Supplementary Figure S2) . To this end, even though we observed distinguishable features of the interactions modeled by the two FFs, one similarity stands out clear: the RBD2-ACE2 interface has stronger interaction energies than the RBD1-ACE2 interface as concluded in previous studies, [2] [3] [4] [5] 8, [10] [11] [12] [13] 30 which results in more stable pairs of interacting residues in the RBD2-ACE2 interface than the RBD1-ACE2 interface as observed in Figure 2 . Particularly for RBD1-ACE2 complex, both FFs apparently yield a meta-stable state, which is not evident in the RBD2-ACE2 complex. To the best of our knowledge, this observation has not been reported in any previous studies. To partially explain such meta-stable state observed in the C36-FF, Figure  3b shows a snapshot compared to a dynamical structure of RBD1 and its X-ray structure: initially, the loop having L486 and N487 is in close contact to the residues (L79, M82, Y83) of ACE2; at 0.5 µs, it loses its grip on ACE2 and moves up to 23 Å away from ACE2 residues. This is not observed in case of RBD2-ACE2 complex, which remains similar to the crystal structure as shown in Figure 1b . To further quantify the behavior of this loop, we measured the distance d between the Ca atoms of L486 in RBD1 (or F486 in RBD2) and L79 of ACE2 during the course of simulations. Figure 3c shows that in case of RBD1-ACE2 complex, while there is the highest peak in the distribution obtained from the AMBER-FF at d = 11 Å, the broader distribution obtained from the C36-FF has two peaks at d = 8 Å and d = 15 Å, and non-zero values at d ~25 Å. This is also consistent with the above observations that the C36-FF models weaker interactions, particularly between the RBD1 and ACE2 at d ~25 Å than the AMBER-FF. In RBD2-ACE2 complex, the distance is very stable at 7-7.5 Å as indicated by the very sharp peak in simulations using both FFs (Figure 3c) . However, in RBD1-ACE2 complex, the distributions shift to larger distances in case of both FFs. This suggests that the localized F486 at RBD2-ACE2 interface may have a significantly stronger grip on ACE2 than the corresponding non-polar residue L486 in RBD1. To this end, these results imply that the mutation L486F in RBD2 of SARS-CoV-2 might be the most consequential as F486 on SARS-CoV-2 has a more stable interaction with the ACE2 helices than L486 on SARS-CoV (Figure 3b) ; the L486 in RBD1 can move away from ACE2, resulting into less effective binding.

In order to shed more insight into the dissociation events of the RBDs from ACE2, we computed the PMFs of the two complexes via umbrella sampling (US) simulations using the C36 FF (see Methods). Note that the free-energy profiles shown in Figure 3a can be poorly sampled at distances away from the global minima, while the US sampling helps to improve rare statistics at those distances. [26] [27] [28] 31, 32 Figure 4a shows that the PMFs for completely dissociating the RBDs from ACE2 around RRBD-ACE2 = 70 Å are markedly different (the finite size effects 33 were not excluded from the profiles; so, there is a slight increase at the end of the curves due to the periodic images). We also observed that the meta-stable states in the RBD1-ACE2 complex (Figure 3a) become much shallower at R = 52 Å (Figure 4a) . The dissociation free energy, DG can be measured as the free-energy difference between R = 70 Å and R ~ 50 Å, which is the global free-energy minimum. Our calculation of DG shows that it costs DG1 = 4.3 ± 0.8 and DG2 = 15.0 ± 0.8 kcal/mol for RBD1 and RBD2 respectively to completely dissociate from ACE2. In other words, the binding of RBD2 to ACE2 yields about 11 kcal/mol more energy than the binding of RBD1. This DDGMD (= DG2 -DG1) is almost three times the value estimated by a coarse-grain model (4.3 kcal/mol) in a recently published work. 12 This discrepancy may largely come from the simulated parameters (or FFs). It should be noted that DDGMD was computed without a thorough sampling of relative rotational and conformational dynamics of the RBDs and ACE2. The calculations also assumed that the entire conformations of both RBDs and ACE2 are unchanged before the binding. These dynamics if accounted may change the absolute value of DDGMD, but likely DDGMD remains positive, indicating that RBD2-ACE2 complex is tighter than RBD1-ACE2 complex. In order to determine which residues of RBD2 are critical and behave collectively during the dissociation of the complex, we computed the probabilities of the stable residue pairs (Figure  2) at the interface as a function of the biasing distance between the two centers of mass of RBD2 and ACE2 (Figure 4b) . Figure 4b shows that while the two clusters of residues (L455/F456/Y473 and Q493/T500/N501/G502/Y505) of RBD2 dissociate from ACE2 at R = 55 Å (5 Å away from the global minimum), the cluster of residues F486/N487/Y489/A475 (Figure 4c ) remains in contact with ACE2 with a probability of 60% at R = 70 Å. Note that the similar pattern of the changes in the probabilities of these residues indicate that, this cluster of residues behaves as a "sticky" anchor of the Spike protein of SARS-CoV-2 that holds on the binding region of ACE2. In contrast, as observed in Figure 3b -c, the similar cluster of L486/N487/Y489/P475 in RBD1 does not have a strong grip on ACE2. These clearly distinguishable outcomes suggest that the mutations L486F and P475A play a critical role that makes RBD2 noticeably stickier to ACE2 than RBD1. In other words, the dynamics of these key residues add a new mechanistic picture of why SARS-CoV-2 is more infectious than SARS-CoV.

In this study, we present a simulation data of approximately 20 µs in total (2´5 µs equilibration and 2´4.8 µs US simulations), which show key stable pairs between the SARS-CoV or SARS-CoV-2 RBDs (Figure 2 ) and the human receptor ACE2. We showed three clusters of residues that have enhanced interactions in RBD2 and ACE2. Particularly, one cluster of residues, including F486/N487/Y489/A475, is perhaps the most critical cluster of amino acids that appear to collectively induce strong interactions between RBD2 and ACE2 (Figure 3c and Figure 4 ). This cluster of residues could act as an anchor that strongly holds on the N-terminal part of ACE2. In contrast, the corresponding set of residues L486/N487/Y489/P475 of RBD1 can loosen its grip from ACE2 (Figure 3b-c) . The observations were consistent across different forcefields. The dramatic difference in the dynamics of these residue clusters is only observed in MD simulations of beyond 500 ns, which most previous studies 2-5,8,10-13,30 did not achieve. The results build our understanding of key determinants of molecular recognition of SARS-CoV-2 and human receptor protein and brings opportunities to target the residue clusters for specific and sensitive binders for therapeutics and diagnostics alike. Figure S1 : Distributions of RRBD-ACE2 from the US sampling simulations. Figure S2 . Pairs of residues at the RBD1-ACE2 and RBD2-ACE2 interfaces modeled by the AMBER ff88SB FF AUTHOR INFORMATION Corresponding Author *rjha@lanl.gov *ngov@lanl.gov ORCID Van A. Ngo: 0000-0001-8350-1203 Ramesh K. Jha: 0000-0001-5904-3441

Funding was provided by the United States Department of Energy through the CARES (Coronavirus Aid, Relief, and Economic Security) Act (#KP160101).

Supporting Information for "Identifying Key Determinants of SARS-CoV-2/ACE2 Tight Interac-

Van A. Ngo, 1 * and Ramesh K. Jha 2 * Figure S1 . Distribution of RRBD-ACE2 computed from the US sampling. Figure S2 . (a-b) Probability of pairs of residues found within 3.5 Å at the interfaces between RBD1-2 with ACE2 during simulations of 10 µs per system using AMBER ff88SB FF 15 performed by the Shaw group. 7 A stable pair is defined to have a probability larger than 60% during the simulation times, i.e, forming a pair within 3.5 Å for more than 60% of a simulation trajectory. Green brackets indicate clusters of residues that are on average more stable in RBD2-ACE2 interface than the corresponding clusters in RBD1-ACE2 interface.

Cell Entry Mechanisms of SARS-CoV-2

Structural Basis of Receptor Recognition by SARS-CoV-2

Exploring the Binding Mechanism and Accessible Angle of SARS-CoV-2 Spike and ACE2 by Molecular Dynamics Simulation and Free Energy Calculation

Structure, Function, and Antigenicity of the SARS-CoV-2 Spike Glycoprotein

Role of Changes in SARS-CoV-2 Spike Protein in the Interaction with the Human ACE2 Receptor: An in Silico Analysis. EXCLI J. 19Doc410 ISSN

The Proximal Origin of SARS-CoV-2

Molecular Dynamics Simulations Related to SARS-CoV-2. D. E. Shaw Research Technical Data

Structural Basis for the Recognition of SARS-CoV-2 by Full-Length Human ACE2

Structure of SARS Coronavirus Spike Receptor-Binding Domain Complexed with Receptor

Structure of the SARS-CoV-2 Spike Receptor-Binding Domain Bound to the ACE2 Receptor

Structure of the 2019-NCoV Spike in the Prefusion Conformation

Critical Differences Between the Binding Features of the Spike Proteins of SARS-CoV-2 and SARS-CoV

Comparing the Binding Interactions in the Receptor Binding Domains of SARS-CoV-2 and SARS-CoV

Optimization of the Additive CHARMM All-Atom Protein Force Field Targeting Improved Sampling of the Backbone ϕ, ψ and Side-Chain χ 1 and χ 2 Dihedral Angles

Improved Side-Chain Torsion Potentials for the Amber Ff99SB Protein Force Field

Comparison of Simple Potential Functions for Simulating Liquid Water

Scalable Molecular Dynamics with NAMD

Methods of Conjugate Gradients for Solving Linear Systems

A Smooth Particle Mesh Ewald Method

Long-Time-Step Molecular Dynamics through Hydrogen Mass Repartitioning

The Amber Biomolecular Simulation Programs

Accurate Estimation of Protein Folding and Unfolding Times: Beyond Markov State Models

Markov State Models from Short Non-Equilibrium Simulations-Analysis and Correction of Estimation Bias

Nonphysical Sampling Distributions in Monte Carlo Free-Energy Estimation: Umbrella Sampling

THE Weighted Histogram Analysis Method for Free-Energy Calculations on Biomolecules. I. The Method

The Calculation of the Potential of Mean Force Using Computer Simulations

Analysis of the Statistical Error in Umbrella Sampling Simulations by Umbrella Integration

Systematic Comparison of Two Animalto-Human Transmitted Human Coronaviruses: SARS-CoV-2 and SARS-CoV

Parallel-Pulling Protocol for Free-Energy Evaluation

Estimation of Potentials of Mean Force from Nonequilibrium Pulling Simulations Using Both Minh-Adib Estimator and Weighted Histogram Analysis Method

Ion Permeation through a Narrow Channel: Using Gramicidin to Ascertain All-Atom Molecular Dynamics Potential of Mean Force Methodology and Biomolecular Force Fields

For Table of Contents Use Only Identifying Key Determinants of SARS-CoV-2/ACE2 Tight Interactions Van A. Ngo, 1 * and Ramesh K

The authors declare no competing financial interest.