key: cord-0998943-4mv6qwpc
authors: Corrêa Giron, Carolina; Laaksonen, Aatto; Barroso da Silva, Fernando L.
title: On the interactions of the receptor-binding domain of SARS-CoV-1 and SARS-CoV-2 spike proteins with monoclonal antibodies and the receptor ACE2
date: 2020-04-10
journal: bioRxiv
DOI: 10.1101/2020.04.05.026377
sha: a09d59d62a14b5bbf5de951cbd71687a5c042e27
doc_id: 998943
cord_uid: 4mv6qwpc

A new betacoronavirus named SARS-CoV-2 has emerged as a new threat to global health and economy. A promising target for both diagnosis and therapeutics treatments of the new disease named COVID-19 is the coronavirus (CoV) spike (S) glycoprotein. By constant-pH Monte Carlo simulations and the PROCEEDpKa method, we have mapped the electrostatic epitopes for four monoclonal antibodies and the angiotensin-converting enzyme 2 (ACE2) on both SARS-CoV-1 and the new SARS-CoV-2 S receptor binding domain (RBD) proteins. We also calculated free energy of interactions and shown that the S RBD proteins from both SARS viruses binds to ACE2 with similar affinities. However, the affinity between the S RBD protein from the new SARS-CoV-2 and ACE2 is higher than for any studied antibody previously found complexed with SARS-CoV-1. Based on physical chemical analysis and free energies estimates, we can shed some light on the involved molecular recognition processes, their clinical aspects, the implications for drug developments, and suggest structural modifications on the CR3022 antibody that would improve its binding affinities for SARS-CoV-2 and contribute to address the ongoing international health crisis.

The SARS-CoV-2, virus recently found in Wuhan, Hubei province, China and officially named by the World Health Organization (WHO), 1 has already spread through China from all continents (more than 168 countries), with 1,133,758 confirmed cases globally and 62,784 deaths (data as reported by Central European Time 5 April 2020). Due to the pandemic, the disease is not only affecting the health services, but also the economy in a global scale, interfering in the widespread displacement of people, tourism, local and even international markets. Once China's economy is a worldwide reference, its disruption leads to a global impact in the supply chains and the production itself. [1] [2] [3] The Coronaviridae family, to which SARS-CoV-2 belongs, includes a large variability of viruses and became recognized in the spring of 2003, when a human coronavirus caused severe acute respiratory syndrome (SARS). [4] [5] [6] [7] Based on phylogenetic analysis, the SARS-CoV-2 is classified as a lineage B betacoronavirus 8 and belongs to the same group as SARS-CoV-1 and HKU9-1, the bat coronavirus, demonstrating wide similarity with both genetically 9 (96,2% of sequence identity with HKU9-1). 10 The transmission was confirmed to be human-to-human once several medical care personnel and relatives got infected, 8, 9 but it is believed that it all started with an animal host, may it be a bat or another intermediate host. 7, 9, 11, 12 Even though the virus usually does not cause severe damage to the body, as will be explained below, the major concern is its high infectivity and pathogenicity. 8, 12, 13 The COVID-19 disease, caused by SARS-CoV-2 virus, 14 generally causes mild upper respiratory tract infections, resulting in fever and cough, yet it can also affect the lower respiratory tract. 12, 15, 16 SARS-CoV-2, on the other hand, usually remains asymptomatic in an early stage and then manifests itself with dyspnea, severe pneumonia and even death, 17 with fatality rates of about 10%. 18 Although many groups of researchers are combining their efforts to solve the mysteries of the new virus, some issues are still uncertain. Examples of these queries are the virus' incubation period, that may be longer than the 14 days scientists believed it to be previously, and the fatality rates for each age range. 19 Despite the fact that the virus' molecular mechanism is partially unknown, the SARS-CoV-2 has proteins, such as the Spike (S) glycoprotein, that densely decorates the viral external surface and can potentially be a key target for the development of vaccines and therapeutic antibodies (Abs). 8, [20] [21] [22] Due to the similarity of the receptor binding domain (RBD) in SARS-CoV-2 and SARS-CoV-1, the first strategy that has been used is to search for Abs that succeed interacting with both, once SARS-CoV-1 has been more widely studied. However, preliminary experimental studies have shown that many Abs that successfully interact with SARS-CoV-1 do not bind with SARS-CoV-2. 8 The spike protein, which is responsible for the "corona" (latin word for crown) appearance in all coronaviruses, is a type I glycoprotein that has an especial role in the interaction between the virus and the host cell. This protein attaches itself to specific cellular receptors and suffers a conformational change that enables the fusion of the virus and the cell. 4, 23, 24 Studies have shown that the SARS-CoV-2's S RBD protein interacts strongly with the Angiotensin-converting enzyme 2 (ACE2). 9, 24, 25 Therefore, aiming to develop better diagnosis tools, vaccines and therapeutic Abs, it was measured the competition of mAbs and the ACE2 for the binding to SARS-CoV-2 (named before 2019-nCoV 8, 26 ) RBD protein in order to enlighten the binding epitopes of these Abs. 8, 19 The focus of this article is to initially reproduce the observations of previous laboratory experiments by a theoretical approach. Secondly, we aim to contribute with the understanding of the molecular mechanisms involved in the SARS viral infection, and finally to show how to apply this knowledge to design new functional molecules. To achieve these goals, it was tested by constant-pH simulation methods the complexation between the S RBD proteins of SARS-CoV-1 and SARS-CoV-2 with the fragments of the monoclonal Abs (mAbs) 80R, CR3022, m396 and F26G29, measuring their binding affinities and quantifying the titratable amino acids that are involved in these interactions. Thus, using a theoretical method recently proposed to identify "electrostatic epitopes", 27 it is possible to identify the similarities and differences between these molecular complexes, and to map their origin and possible biological implications.

Another aspect discussed in this research is the interaction between the S RBD protein from these viruses and the ACE2 in order to discover if the S RBD protein binds to either of them with higher affinity, because, if so, an antibody (Ab) might have smaller chances of binding. All this information together provided important insights to design more specific and effective neutralizing Abs which is relevant for the future prevention and treatment of this now widespread illness that should be immediately controlled. At the end, a new designed mAb candidate is proposed based on our present in silico findings.

Computational virology is an emergent research field that takes advantage of the progress from molecular and structural biology, immunology, bioinformatics and related areas to foster the understanding of virus, their evolutionary dynamics in nature, infectivity, pathogenesis, cell/hosttropism, viral assembly and their molecular interactions in general (including how to predict epitopes, how to design specific neutralizing antibodies and basically any drug design & discovery related to viral infections). [27] [28] [29] [30] [31] [32] [33] [34] In particular, structural and interactive aspects can benefit from the solid foundations that computational molecular simulation methods such as Molecular Dynamics (MD) 35, 36 and Monte Carlo (MC) 35, 37 have achieved to probe the thermodynamic, dynamics and interactive properties of biomolecules in material science, food and pharma (see refs. 38, 39 for reviews). Here, we applied a fast constant-pH MC scheme 40,41 for protein-protein studies 42, 43 to improve our understanding of the molecular interactions involving SARS-CoV-1 and 2 S RBD proteins and to identify key amino acids for the host-pathogen interactions.

Several molecular systems were investigated in the present study employing the two SARS-CoV-1 and 2 S RBD proteins (see Figure 1 ) with ACE2 and the fragments of the mAbs 80R, CR3022, m396, and F26G29. Typically, these fragments of mAbs are fusion proteins from variable regions of the heavy and light chains of immunoglobulins connected with a short linker peptide. Additional calculations were carried out for the SARS-CoV-2 S RBD with a new proposed mAb based on CR3022. For most of these macromolecules, three dimensional crystallographic structures are available at the RCSB Protein Data Bank (PDB): 44 a) the SARS-CoV-1 S RBD protein was extracted from the PDB id 2AJF (chain E, resolution 2.9Å, pH 7.5)

where it was found complexed with ACE2 (chain A) − see Figure 2 ; b) the fragment of the Ab 80R was taken out from the PDB id 2GHW (chain B, resolution 2.3Å, pH 4.6); c) the anti-SARS-CoV-1 m396 Ab was extracted from the PDB id 2G75 (chains A and B, resolution 2.28Å, pH 8.5) removing part of the chains to keep only the variable regions and the short linker peptide; d) F26G19 Fab was taken out from PDB id 3BGF (chains L and C, resolution 3.0Å, pH 5.5), following the same procedure used for m396. Missing regions in these proteins were built up using the "UCSF Chimera 1.11.2" interface 45 of the program "Modeller" with default parameters. 46 Figure 3 shows their final three-dimensional structures as used in this work. All PDB files were edited before the calculations. Water molecules and hetero atoms were completely removed from all used files. The "UCSF Chimera 1.11.2" package 45 was employed for all molecular visualizations and representations too.

When this study started, no experimental structure was available for the RBD of SARS-CoV-2 S protein. A model was built up at the SWISS-MODEL workspace (YP_009724390.1) based on the NCBI reference sequence NC_045512. 47 The root-mean-square deviation (RMSD) of atomic positions between this modeled structure for the RBD of SARS-CoV-2 S protein and the available one for SARS-CoV-1 (PDB id 2AJF) is 0.638Å. The structural comparison between the RBD proteins of both SARS viruses can be seen in Figure 1 . Recently, new experimental structures were solved. For example, a cryo-EM structure is now available for the prefusion S glycoprotein with a single incomplete RBD (PDB id 6VSB, resolution 3.46Å). The RMSD between our model and the S RBD (chain A) from this structure is 0.790Å. This number is closer to the RMSD differences between two chains of the same experimental (PDB id 6VSB) trimer structure (e.g. 0.668Å for chain A x chain B, and 0.732Å for chain A x chain C). Such diversity of possible conformations might motivate further studies exploring their effects on the theoretical predictions. These RMSD values also indicate that the modeled structure for the SARS-CoV-2 virus as used here is reasonable and within the expected conformational fluctuations from any other structure that could have been chosen for this work. Moreover, an intrinsic assumption here is that an experimental structure obtained at a given and specific physical chemical condition (ionic strength, pH, PEG6000 concentration, etc.) is valid in another condition. 27 Only standard amino acids of chain A (ACE2) and E (SARS-CoV-1 S RBD) are shown in a molecular representation using spheres for its atoms. Atoms are colored accordingly to their amino acids physical chemical properties: red for acid amino acids, blue for base amino acids and gray for non-titrating amino acids. For a better visualization of the interface, the ACE2 structure was translated ~12 Å.

CR3022 is a particularly successful SARS-CoV-1 neutralizing human mAb first isolated from a convalescent patient by ter Meulen and co-authors. 48 For the present study, its three dimensional structure (see Figure 3 ) was built up at the SWISS-MODEL workspace 47 The fragments of the mAbs 80R (PDB id 2GHW), CR3022 (modeledsee the text for details), F26G19 (PDB id 3BGF) and m396 (PDB id 2G75) are shown in a ribbon representation.

A large diversity of models is available for MD and MC molecular simulations. 38, [49] [50] [51] [52] The need to repeat the calculations on several different physical chemical conditions and to obtain free energy of interactions at them drives the options to the so-called cost-effective coarse-grained (CG) models. These CG models offer the possibility to explore the main physical features of a system with a reduced number of parameters and lower computational costs. 27, 42, 43 During the last years, a fast constant-pH (CpH) CG model has been devised to successfully study proteinprotein interactions of several biological systems (including host-pathogens interactions). 27, 42, 43, 53, 54 The possibility to fully consider the pH effects makes this modeling approach more appealing and appropriated to address this problem. 27,55 A sketch of the simulations model is given in Figure 4 . The S RBD proteins and the fragments of the mAbs were modeled as rigid bodies (i.e. bond lengths, angles, and dihedral angles are kept fixed) formed by a set of amino acids placed at positions given by their three-dimensional structures as described above. This additional approximation is justified by the prohibitive computational costs of constant-pH methods with pH-dependent conformational changes. 52, 56, 57 Moreover, it is known that SARS-CoV-1 S protein does not exhibit large conformational changes upon the binding to ACE2 at least. 58 Each group of atoms that define an amino acid is converted in a single charged Lennard-Jones (LJ) sphere of radius (Ri) and valence zi. This CG process turns a protein atomistic structure as a collection of charged LJ particles representing their amino acids. The centers-of-masses of the beads (mimicking amino acids) are used to place them accordingly to the coordinates given by the three-dimensional structures. The values of Ri for each type of amino acids were taken from ref. 53 . The valences of all ionizable residues are a function of the solution pH. The fast proton titration scheme (FPTS) 40, 41, 52 was employed both to initially assign these valences zi´s for the amino acids and to let them vary during the simulation sampling at a given pH. This method has proved to predict pKa´s with a very good accuracy at low computational costs. 41 The fundamental physical chemical basis of this titration scheme, its numerical implementation, benchmarks, discussions related to its approximations, pros and cons can be found in previous publications. 40, 41, 52, 59 As illustrated in Figure 4 , two proteins are placed in an electroneutral open cylindrical simulation box, and free to translate back and forward along the axis in which their centers are laying, rotate in any direction and titrate. In this example, these two proteins are the modeled three dimensional structure of the SARS-CoV-2 S RBD and the crystallographic structure of the fragment of the mAb 80R. Unless otherwise specified, simulation runs were carried out with a cell of radius (rcyl) and height (lcyl) equals to 150 and 200Å, respectively. The static dielectric constant was set to 78.7 (assuming a temperature of 298K). Counter-ions and added salt particles were represented implicitly using a screening term, i.e., for two ionizable amino acids i and j, the screening is given by [exp(-κrij)] where κ is the modified inverse Debye length, and rij is the interparticle separation distance. 27, 42, 43, 60 Additionally, a simplified simulation box with only one protein present was used to characterize the titration properties of a single macromolecule.

The electrostatic interactions[ ( )] between any two ionizable amino acids of valences and are given by: Protein-protein interactions are also controlled by other physical contributions (van der Waals interactions, hydrophobic effect, and excluded volume repulsion). 27, 42, 43 A simple and effective way to include their effects is by means of a LJ term [uvdw(rij)] between the beads (amino acids). 27 Mathematically, for any two beads (charged or neutral ones) i and j, uvdw(rij) is given by 6 ], [2] where σij (= Ri + Rj) is the separation distance of two amino acids i and j at contact. For instance, σij for the pair VAL-GLU is 7.2Å (= RVAL + RGLU, where RVAL = 3.4Å and RGLU = 3.8Åsee ref. 53 ). The possibility to use different sizes for these beads allows the incorporation of non-specific contributions from the hydrophobic effect in the model. 43 This should preserve the macromolecular hydrophobic moments 61 and contributes to guide a correct docking orientation at short separation distances. 27 The term εLJ regulates the strength of the attractive forces in the system. 27, 42, 43 Typically, εLJ is assumed to be universal for any biomolecular system and equals to 0.124 kJ/mol. 42, 43, 53, 62 This should correspond to a Hamaker constant of ca. 9kBT (kB = 1.380×10 -23 m 2 kgs -2 K -1 is the Boltzmann constant, and T is the temperature in Kelvin) for amino acid pairs. 43, 53, 63 However, this value might result in both an over or an underestimation of the attraction depending on the biomolecular system. 42, 43, 62 For instance, εLJ equals to 1.7kBT (a value 34 times greater than 0.124 kJ/mol) was necessary to reproduce experimental data for the histatin-5 adsorption to a hydrophilic silica surface. 62 Conversely, the -lactoglobulin-lactoferrin complexation seems to be overestimated by the usual value of εLJ. 43 Consequently, our research strategy has been to adopt the consensus value of 0.05kBT (= 0.124 kJ/mol) for εLJ. This also implies that the outcomes should be interpreted with relative caution bearing in mind all the intrinsic approaches assumed in the modeling. The direct impact is seen in the free energy derivatives as discussed later at the results section.

Combining Eqs. (1) and (2), the total system's interaction energy for a given configuration

can be written as:

, [3] where { } are amino acid positions and is their total number. This includes both charged and neutral beads. This model was solved by Metropolis MC simulations that were performed at physiological ionic strength (150mM) and different pH conditions. The choice to simulate at pH 4.6 and 7.0 was motivated by the needs to understand the low and neutral pH conditions (e.g. low pH of endosomes). Furthermore, it seems controversial in the experimental works if the acidification is essential or not for uptake of cell-free SARS virus. 22, 23, 25 The exact value of the acid pH condition is unknown. We made a choice to use the pH value of the crystallographic environment more acid among the studied structures (pH 4.6 for PDB id 2GHW). This also made possible to easily investigate the behavior of the systems at intermediate conditions by interpolation from the present outcomes.

After the proper equilibration of the simulated molecular systems, long production runs were carried out. Simulations whose focus was on titration properties [Z(pH) and pKas] required 

Antibody-antigen recognition is a challenger and intensive research field. 27, [64] [65] [66] It is a molecular process that involves different physical intermolecular interactions. Electrostatic interactions deserve a special attention in this process for several reasons [e.g. is long range nature, the fact that the interface antibody-antigen has a peculiar electrostatic pattern (richer in titratable groups) that is different than other general protein-protein interfaces, 65 etc.]. 27, 55 Such facts contribute to shift the canonical view of the "lock and key" (with a clear focus on the protein surface) to a broader definition that led to the "electrostatic epitopes" (EE) concept. 27 This means that inner titratable groups (not only the ones at the epitope-paratope interface) can also participate in the interplay of interactions with Abs.

The EEs are the core idea of the PROCEEDpKa method 27 where pKa shifts are used to identify the key amino acids responsible for a host-pathogen association. It applies the fact that the location of these shifts is a practical mean to probe molecular interactions as before demonstrated. 67 Moreover, this can be easily measured during computer simulations of a proteinprotein complexation. The predictive properties of this powerful tool have been previously i) statistically analyzed for flaviviruses, ii) compared to other bioinformatic tools (that often ignore that pH and ionic strength can drastically affect the complexation process) and iii) discussed in details in a preceding work. 27 The capacity of this method to test EE for specific mAbs makes it even more appealing for the present study where four known mAbs should be investigated. For the sake of convenience, predicted EE for the studied systems were graphically compared at the sequence level. The pairwise sequence alignments were generated by the server EMBOSS Needle 68 with default settings.

One of the central questions in the understanding of the COVID-19, its pathology including the high transmissibility, and the possible therapeutic interventions to control the epidemics spreading is to decipher and prevent the molecular interactions between the S protein and ACE2. 25 tendency to bind to the ACE2 at both pH regimes. This agrees quite well with the experimental results measured by the biolayer interferometry binding (BLI) assay as reported by Walls and coauthors using the functional subunit of the S protein responsible for binding to the host cell receptor. 24 The measured binding affinity (KD) was 5.0±0.1nM for the system SARS-CoV-1 S RDB(also referred to as the domain B 58 )-ACE2 and 1.2±0.1nM for the SARS-CoV-2 S RBD-ACE2. Yet, other experimental measurements using the S1 domain (this is the subunit that contains both the RBD and the N-terminal domain 58 ) might suggest an inverted behavior where SARS-CoV-2 S1 domain would have a tendency for a stronger bind to ACE2 (KD=15.0±0.1nM) 75 in comparison to SARS-CoV-1 S (KD=15.2nM) 8 . This small experimental difference of 0.2nM could be due to several reasons including the experimental uncertainties that were not reported in Tian's work. 8 In contrast to these results, another recent study 20 advocated that SARS-CoV-2 has greater binding affinity for ACE2 than SARS-CoV-1. Even so, both the present theoretical and previously reported experimental data do agree that SARS-CoV-1 S RBD and SARS-CoV-2 S RBD have similar attraction to the ACE2. This high binding affinity implies that all human organs rich on ACE2 (oral and nasal mucosa, lung, stomach, small intestine, colon, skin, lymph nodes, thymus, bone marrow, spleen, liver, kidney, and brain) 76,77 can be easily infected. A clear opportunity for the virus is the lung alveolar epithelial cells and enterocytes of the small intestine, where ACE2 is abundant. 76 Note that the simulations were performed with a single RBD protein in the absence of the full structure of the S protein and the others two chains of the homotrimeric S glycoprotein. This brings with it the evidence that the other structural parts of the S1 subunit, the S2 subunit and the two other chains are not essential for the individual pair of RBD-ACE2 complexation. Also, this observation supports the argument that the dissociation of the S1 subunit complexed with ACE2 can happen without the interruption of the infection. This also allows the S2 subunit to transit from a metastable prefusion to its post-fusion state as a second step in the viral infection. 58, 78 At pH 4.6 which is closer to the low pH that occur outside the cell, 23, 79 the association between the SARS-CoV-1 S RBD protein and ACE2 showed a free energy depth [βwmin] of −1.02 at the separation distance of 50.0Å (see Figure 1a) . Conversely, for SARS-CoV-2 S RBD, βwmin is −0.95 at the separation distance of 49.5Å. The estimated standard deviations are 0.01kBT for all studied cases. Such computed measurements of βw(r) obtained by CG models that smooth the free-energy landscape must be interpreted with care as we already have pointed out above. By one side, it can be used a simple thermodynamic criterion that a negative free energy value (βwmin<0) would result in a molecular complex. Conversely, any free energy value smaller than the thermal energy (1 kBT) would indicate an unstable association. The observed difference ( βwmin) of 0.07 between the two RDB proteins is greater than the estimated statistical errors.

However, we prefer to interpret such small differences as tendencies of the system. Based on previous studies 27, 42, 43, 54, 60 where we have observed either that the computed complexation was weaker than the experimental measurements or too much stronger, we feel safer to use this data (and the others discussed below) in relative terms (i.e. comparing different situations). This allows us to successfully predict experimental observations respecting the limits of such CG models. 27, 42, 43, 54 The similarities between their free energy minima are relatively amplified at pH 4.6 ( βwmin=0.07 as seen above) in comparison with pH 7.0 where βwmin is −1.11 and −1.06 ( βwmin=0.05). Both viral S RBD proteins have their affinities to ACE2 slightly raised when pH is increased from the acid to the neutral regime. This somewhat higher binding affinity at neutral pH suggests that the role of pH for RBD proteins constantly under debate at the literature 22, 25, 73, 80 might not be so critical for the infection. It also reinforces the possibility that the viral cell invasion is not a pH-dependent process. Indeed, it seems that pH is more relevant for the next steps to continue the viral infection and not at the first entry level. This possible non pH-depend process might increase the opportunities for the SARS viruses to easily infect cells and therefore to contribute to its high infectivity. This might limit the use of chloroquine as an efficient drug against COVID-19 since its first action is to increase the cell pH. At least a neutral pH solution will not prevent the binding of the RBD to ACE2. On the opposite as it can favor this affinity. Another important aspect is the evaluation of putative mAbs that could bind to the RBD of the new SARS-CoV-2. Following the work of Tian and collaborators, 8 we investigated the interactions between the two SARS S RBD proteins with some of the most potent SARS-CoV-1 S RBD specific neutralizing antibodies (80R, F26G19, m396, CR3022). Figure 6 shows the free energy profiles at the acid regime and physiological salt conditions. For all studied fragments of Abs, a relatively stronger attraction is always observed for the S RBD protein from the SARS-CoV-1 interacting with any of these mAbs. This can be better seen in Figure 6b Moreover, the work of Tian and co-authors suggested that only for CR3022 it was experimentally measured a reasonable binding. 8 The combination of these information could indicate that a threshold of −0.67KBT for βwmin can be used to better refine the theoretical binding predictions of these macromolecular complexations (i.e. all viral protein-protein systems with a value of βwmin smaller than −0.67KBT are expected to experience binding in vivo at least). Table   S1 summarizes the values of βwmin given between parenthesis. It should be noted that the attraction between the S RBD proteins and ACE2 (βwmin equals to −1.02 and −0.95 for SARS-CoV-1 and SARS-CoV-2, respectively) is always stronger than what was calculated to any studied mAb including to the CR3022 (βwmin equals to −0.85 and −0.79 for SARS-CoV-1 and SARS-CoV-2, respectively) for both SARS viruses (see table S1). The same tendency was experimentally verified. 8 It was measured by BLI assay a KD of 6.3 nM for the binding of CR3022 to SARS-CoV-2 S RBD which corresponds to a fraction of 0.41 of the KD measured for the binding of ACE2 to the same RBD (KD equals to 15.2nM). 8

Next, we explored basic physical chemical aspects that could offer a simple and quick reasoning to understand the above free energy results and eventually be used as descriptors to scan databases of mAbs to filter promising ideal candidates. Although different driven forces can result in protein-protein complexation, 42, 43 pH and charge-charge interactions seems especially important for viral proteins. 27, 55, [81] [82] [83] [84] [85] Indeed, the protein net charges numbers (Z) obtained as function of the solution pH show that the SARS-CoV-2 S RDB protein is always slightly more positively charged than SARS-CoV-1 S RDB protein at the same physical chemical environment (Z equals to 5.2 and 5.5, respectively, for them at pH 4.6) − see table 1. Since all studied fragments of Abs are also positively charged at pH 4.6 (Z equals to 9.1, 4.2, 2.7, 5.8 for 80R, CR3022, m396 and F26G19, respectively), it can be easily seen that the order observed for the binding affinities above in the free energy analyses do follow a simple charge-charge rule for the mAbs with similar surface area (A~10,000 Å 2 ). For the SARS-CoV-1 S RDB protein, from the weaker to the stronger repulsive cases in terms of the Coulomb contributions (Zi*Zj assuming the same Bjerrum length, salt screening and separation distances 42, 43, 86 ) , the predicted order for the binding affinity is 80R (5.2*9.1=47.3) < F26G19 (5.2*5.8=30.2) < CR3022 (5.2*4.2=21.8). This agrees with the previous free energy analyses (see above). As large is A, larger is the attractive van der Waals interactions that can overcome the charge-charge repulsion. This can also explain why m396 (that is smaller and has roughly half of A) is less attracted to the RBD proteins even being slightly less positively charged (Z equals to 2.7 at pH 4.6) than the others (Z~5-6).

Similarly, this is the physical reason to understand the stronger binding affinity that ACE2 (A=25,290Å 2 ) has to the S RBD proteins. Although ACE2 (Z=5.4) and F26G19 (Z=5.8) have similar Zs, the molecular surface of ACE2 is ca. 2.5 times larger than F26G29 (A=10,120Å 2 ).

We tested the van der Waals (vdw) contribution comparing w(r) for CR3022 and m396 in a model where all electrostatic interactions where completely switched off and only vdw interactions are considered. This test-case system is shown in Figure S1 . It can be seen that m396 in this hypothetical test does have a weaker binding affinity to SARS-CoV-2 S RBD protein in comparison to CR3022 confirming the arguments above presented. and R194) can be seen in Figure 7 at the wild type structure of CR3022. The main physical chemical reasoning to design this new functional molecule was to reduce the net charge of CR3022 in general together with a decrease of the repulsion for groups that are closely located at the host-pathogen interface. Two amino acids substitutions (K170A and R194A) are suggested at this biological interface while the other one (K12E) is more peripheral (see Figure 7 ). Doing such mutations, the Z of the new molecule (labeled CR3022') drops down from +4.2 to +1.2 at pH 4.6 and from +1.0 to −3.0 at pH 7.0.

The binding affinity of this computer-designed molecule was tested. The calculated w(r) for this new fragment of mAb is given in Figure 8 . As it can be seen, CR3022' is now able to bind with an equivalent binding affinity to what was observed for the SARS-CoV-1S RBD-CR3022

system. βwmin decreased from −0.79 to −0.85 recovering the value found for the SARS-CoV-1 S RBD-CR3022 case − see Figure 6 and Table S1 . Therefore, this is a promising designed mAb candidate to be carefully and systematically examined in further experimental assays. 

To refine this analysis at the sequence level, the PROCEEDpKa method 27 Similarities with a high score are marked with ";" and c) the ones with low positive score are indicated by ".". Gaps are represented by "-". Numbers are used to guide the identification of the amino acids sequence numbers. CR3022' by the electrostatic method. Data for CR3022 is the same shown in Figure 9 . All other details are also as in Figure 9 .

Free energies of interactions were calculated for several molecular complexes involving the RBD of SARS-CoV-1 and 2 spike proteins. The present theoretical results confirmed that both RBD proteins have similar binding affinity to the ACE2 as previously reported in experimental studies. This is observed at both acid and neutral pH regimes which probably indicates that the medium pH it is not so relevant for the beginning of the viral cell invasion. pH seems to be more important for the next steps of the viral infection and not at the first entry level. This has a direct implication for the drug development since the proposal of some like chloroquine is to raise cell pH.

Analyzing the interactions between these RBD proteins and the SARS-CoV-1 S RBD specific neutralizing mAbs (80R, F26G19, m396, CR3022) allowed us to reproduce the experimental results. The only mAb with measured affinities for the SARS-CoV-2 S RBD protein by BLI assay was CR3020 8 which was also the one with higher affinity quantified in the present theoretical study. Moreover, we could map their electrostatic epitopes and identify that all mAbs tend to share the same titratable residues, and they are like the residues involved in the interaction with ACE2. However, the RBD protein responsible for COVID-19 clearly has more titratable residues interacting with ACE2 than its precursor suggesting that its binding to ACE2 might be less specific. This can explain the general difficulty that mAbs can experience to completely block the SARS-CoV-2 S RBD-ACE2 interaction.

Charge-charge interactions were found to be a good simple descriptor for a fast screening to the designing of improved mAb for diagnostics, therapeutics and vaccines. Our theoretical approach, while still being further developed, has identified three amino acids substitution that can increase the binding affinity of CR3022 to the RBD protein responsible for the present pandemic. These results can contribute to guide the design of new functional and high specific mAbs providing a cost-and-time-effective computational framework towards the development of better diagnostic strategies and an effective treatment and/or vaccine for COVID-19.

This work has been supported in part by the "Fundação de Amparo à Pesquisa do Estado de São b) Van der Waals contributions to the free energy profiles for the interaction of RBD proteins with two monoclonal antibodies (CR3022 and m396). Table S1 . Values of the simulated free energy depth of the interactions for the association between the RBD proteins from both SARS-CoV-1 and SARS-CoV-2 and the monoclonal antibodies and ACE2 at physiological salt concentration (150mM). Data extracted from Figure 2 .

All values of βwmin are given in kBT units. between the centers of mass of SARS-CoV-2 S RBD proteins and two monoclonal antibodies (CR30220 and m396) without the electrostatic contributions. All other details as in Figure 6a .

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Genomic Variance of the 2019-nCoV Coronavirus

The Proximal Origin of SARS-CoV-2

COVID-19 Infection: Origin, Transmission, and Characteristics of Human Coronaviruses

Molecular Immune Pathogenesis and Diagnosis of COVID-19

The Species Severe Acute Respiratory Syndrome-Related Coronavirus: Classifying 2019-NCoV and Naming It SARS-CoV-2

Clinical Features of Patients Infected with 2019 Novel Coronavirus in Wuhan

Novel Coronavirus (2019-NCoV) Outbreak: A New Challenge

Coronavirus Infections and Immune Responses

Molecular Diagnosis of a Novel Coronavirus (2019-NCoV) Causing an Outbreak of Pneumonia

Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) and Coronavirus Disease-2019 (COVID-19): The Epidemic and the Challenges

Cryo-EM Structure of the 2019-NCoV Spike in the Prefusion Conformation

A Conformation-Dependent Neutralizing Monoclonal Antibody Specifically Targeting Receptor-Binding Domain in Middle East Respiratory Syndrome Coronavirus Spike Protein

Characterization of Severe Acute Respiratory Syndrome-Associated Coronavirus (SARS-CoV) Spike Glycoprotein-Mediated Viral Entry

Structure, Function, and Evolution of Coronavirus Spike Proteins

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

The Secret Life of ACE2 as a Receptor for the SARS Virus

A Distinct Name Is Needed for the New Coronavirus

Identification of Electrostatic Epitopes in Flavivirus by Computer Simulations: The PROCEEDpKa Method

A New Era of Virus Bioinformatics

Advances in Experimental Medicine and Biology

Unraveling the Web of Viroinformatics: Computational Tools and Databases in Virus Research

Immunoinformatics and Epitope Prediction in the Age of Genomic Medicine

The Unequivocal Preponderance of Biocomputation in Clinical Virology

Multiscale Modelization in a Small Virus: Mechanism of Proton Channeling and Its Role in Triggering Capsid Disassembly

Understanding Molecular Simulation: From Algorithms to Applications

The Art of Molecular Dynamics Simulation

Understanding and Controlling Food Protein Structure and Function in Foods: Perspectives from Experiments and Computer Simulations

Thirty-Five Years of Biomolecular Simulation: Development of Methodology, Force Fields and Software

Fast Proton Titration Scheme for Multiscale Modeling of Protein Solutions

Benchmarking a Fast Proton Titration Scheme in Implicit Solvent for Biomolecular Simulations

Electrostatics Analysis of the Mutational and PH Effects of the N-Terminal Domain Self-Association of the Major Ampullate Spidroin

On the Complexation of Whey Proteins. Food Hydrocoll

The Protein Data Bank

A Visualization System for Exploratory Research and Analysis

Comparative Protein Structure Modeling Using Modeller

A Web-Based Environment for Protein Structure Homology Modelling

Human Monoclonal Antibody Combination against SARS Coronavirus: Synergy and Coverage of Escape Mutants

Coarse-Grained Protein Models and Their Applications

Molecular Modelling -Principles and Applications

Development of Constant-PH Simulation Methods in Implicit Solvent and Applications in Biomolecular Systems

Torbjörn \AAkesson. Molecular Evidence of Stereo-Specific Lactoferrin Dimers in Solution

A Revised Order of Subunits in Mammalian Septin Complexes

Insights into the ZIKV NS1 Virology from Different Strains through a Fine Analysis of Physicochemical Properties

OPEP6: A New Constant-PH Molecular Dynamics Simulation Scheme with OPEP Coarse-Grained Force Field

Constant-PH Hybrid Nonequilibrium Molecular Dynamics−Monte Carlo Simulation Method

Stabilized Coronavirus Spikes Are Resistant to Conformational Changes Induced by Receptor Recognition or

Fast Coarse-Grained Model for RNA Titration

Protein-RNA Complexation Driven by the Charge Regulation Mechanism

Hydrophobic Moments and Protein Structure

Integrating All-Atom and Coarse-Grained Simulations-Toward Understanding of IDPs at Surfaces

Anisotropic Interactions in Protein Mixtures: Self Assembly and Phase Behavior in Aqueous Solution

Polyspecificity, and Heterospecificity of Antibody-Antigen Recognition

Antigen-Antibody Interface Properties: Composition, Residue Interactions, and Features of 53 Non-Redundant Structures

Don't Blame It All on Antibodies -The Need for Exhaustive Characterisation, Appropriate Handling, and Addressing the Issues That Affect Specificity

Computationally Mapping PKa Shifts Due to the Presence of a Polyelectrolyte Chain around Whey Proteins

A General Method Applicable to the Search for Similarities in the Amino Acid Sequence of Two Proteins

Receptor-Binding Domain as a Target for Developing SARS Vaccines

Renin-Angiotensin System in Human Coronavirus Pathogenesis

Activation of Viruses by Host Proteases

Set, Fuse! The Coronavirus Spike Protein and Acquisition of Fusion Competence

Receptor and Viral Determinants of SARS-Coronavirus Adaptation to Human ACE2

SARS-CoV-2 Cell Entry Depends on ACE2 and TMPRSS2 and Is Blocked by a Clinically Proven Protease Inhibitor

Unexpected Receptor Functional Mimicry Elucidates Activation of Coronavirus Fusion

Tissue Distribution of ACE2 Protein, the Functional Receptor for SARS Coronavirus. A First Step in Understanding SARS Pathogenesis

High Expression of ACE2 Receptor of 2019-NCoV on the Epithelial Cells of Oral Mucosa

Cryo-EM Structure of the SARS Coronavirus Spike Glycoprotein in Complex with Its Host Cell Receptor ACE2

Host Cell Proteases: Critical Determinants of Coronavirus Tropism and Pathogenesis

PH-Induced Alterations in the Fusogenic Spike Protein of Semliki Forest Virus

Exploring Designability of Electrostatic Complementarity at an Antigen-Antibody Interface Directed by Mutagenesis

PH-Dependent Entry of Severe Acute Respiratory Syndrome Coronavirus Is Mediated by the Spike Glycoprotein and Enhanced by Dendritic Cell Transfer through DC-SIGN

PH-Dependent Conformational Flexibility of the SARS-CoV Main Proteinase (Mpro) Dimer: Molecular Dynamics Simulations and Multiple X-Ray Structure Analyses

Effect of PH and Temperature on the Infectivity of Human Coronavirus 229E

Anti-Severe Acute Respiratory Syndrome Coronavirus Spike Antibodies Trigger Infection of Human Immune Cells via a PH-and Cysteine Protease-Independent Fc R Pathway

Electrostatics in Macromolecular Solutions. In Food Colloids