Erratum: Spontaneous Domain Formation in Spherically Confined Elastic Filaments [Phys. Rev. Lett. 123, 047801 (2019)].

This corrects the article DOI: 10.1103/PhysRevLett.123.047801.

Changes in total charge on spike protein of SARS-CoV-2 in emerging lineages.

Motivation: Charged amino acid residues on the spike protein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) have been shown to influence its binding to different cell surface receptors, its non-specific electrostatic interactions with the environment, and its structural stability and conformation. It is therefore important to obtain a good understanding of amino acid mutations that affect the total charge on the spike protein which have arisen across different SARS-CoV-2 lineages during the course of the virus' evolution. Results: We analyse the change in the number of ionizable amino acids and the corresponding total charge on the spike proteins of almost 2200 SARS-CoV-2 lineages that have emerged over the span of the pandemic. Our results show that the previously observed trend toward an increase in the positive charge on the spike protein of SARS-CoV-2 variants of concern has essentially stopped with the emergence of the early omicron variants. Furthermore, recently emerged lineages show a greater diversity in terms of their composition of ionizable amino acids. We also demonstrate that the patterns of change in the number of ionizable amino acids on the spike protein are characteristic of related lineages within the broader clade division of the SARS-CoV-2 phylogenetic tree. Due to the ubiquity of electrostatic interactions in the biological environment, our findings are relevant for a broad range of studies dealing with the structural stability of SARS-CoV-2 and its interactions with the environment. Availability and implementation: The data underlying the article are available in the Supplementary material.

On the nature of screening in charge-regulated macroion solutions.

We present a derivation of the screening length for a solution containing a charge-regulated macroion, e.g. protein, with its counterions. We show that it can be obtained directly from the second derivatives of the total free energy by taking recourse to the "uncertainty relation" of the Legendre transform, which connects the Hessians or the local curvatures of the free energy as a function of density and its Legendre transform, i.e., osmotic pressure, as a function of chemical potentials. Based on the Fowler-Guggenheim-Frumkin model of charge regulation, we then analyze the "screening resonance" and the "overscreening" of the screening properties of the charge-regulated macroion solution.

Close packings of identical proteins in small spherical capsids and similar proteinaceous shells.

Understanding the principles governing protein arrangement in viral capsids and structurally similar protein shells can enable the development of new antiviral strategies and the design of artificial protein cages for various applications. We study these principles within the context of the close packing problem, by analyzing dozens of small spherical shells assembled from a single type of protein. First, we use icosahedral spherical close packings containing 60T identical disks, where T ≤ 4, to rationalize the protein arrangement in twenty real icosahedral shells both satisfying and violating the paradigmatic Caspar-Klug model. We uncover a striking correspondence between the protein mass centers in the considered shells and the centers of disks in the close packings. To generalize the packing model, we consider proteins with a weak shape anisotropy and propose an interaction energy, minimization of which allows us to obtain spherical dense packings of slightly anisotropic structural units. In the case of strong anisotropy, we model the proteins as sequences of overlapping discs of different sizes, with minimum energy configuration not only resulting in packings, accurately reproducing locations and orientations of individual proteins, but also revealing that icosahedral packings that display the handedness of real capsids are energetically more favorable. Finally, by introducing effective disc charges, we rationalize the formation of inter-protein bonds in protein shells.

Electrostatic interactions between charge regulated spherical macroions.

We study the interaction between two charge regulating spherical macroions with dielectric interior and dissociable surface groups immersed in a monovalent electrolyte solution. The charge dissociation is modelled via the Frumkin-Fowler-Guggenheim isotherm, which allows for multiple adsorption equilibrium states. The interactions are derived from the solutions of the mean-field Poisson-Boltzmann type theory with charge regulation boundary conditions. For a range of conditions we find symmetry breaking transitions from symmetric to asymmetric charge distribution exhibiting annealed charge patchiness, which results in like-charge attraction even in a univalent electrolyte-thus fundamentally modifying the nature of electrostatic interactions in charge-stabilized colloidal suspensions.

Impact of BA.1, BA.2, and BA.4/BA.5 Omicron mutations on therapeutic monoclonal antibodies.

The emergence of Omicron SARS-CoV-2 subvariants (BA.1, BA.2, BA.4, and BA.5), with an unprecedented number of mutations in their receptor-binding domain (RBD) of the spike-protein, has fueled a resurgence of COVID-19 infections, posing a major challenge to the efficacy of existing vaccines and monoclonal antibody (mAb) therapeutics. We conducted a systematic molecular dynamics (MD) simulation to investigate how the RBD mutations of these subvariants affect the interactions with broad mAbs including AstraZeneca (COV2-2196 and COV2-2130), Brii Biosciences (BRII-196), Celltrion (CT-P59), Eli Lilly (LY-CoV555 and LY-CoV016), Regeneron (REGN10933 and REGN10987), Vir Biotechnology (S309), and S2X259. Our results show a complete loss of binding for COV2-2196, BRII-196, CT-P59, and LY-CoV555 with all Omicron RBDs. Additionally, REGN10987 totally loses its binding with BA.1, but retains a partial binding with BA.2 and BA.4/5. The binding reduction is significant for LY-CoV016 and REGN10933 but moderate for COV2-2130. S309 and S2X259 retain their binding with BA.1 but exhibit decreased binding with other subvariants. We introduce a mutational escape map for each mAb to identify the key RBD sites and the corresponding critical mutations. Overall, our findings suggest that the majority of therapeutic mAbs have diminished or missing activity against Omicron subvariants, indicating the urgent need for a new therapeutic mAb with a better design.

Curvature effects in interfacial acidity of amphiphilic vesicles.

We analyze the changes in the vicinal acidity (pH) at a spherical amphiphilic membrane. The membrane is assumed to contain solvent accessible, embedded, dissociable, charge-regulated moieties. Basing our approach on the linear Debye-Hückel approximation, as well as on the nonlinear Poisson-Boltzmann theory, together with the general Frumkin-Fowler-Guggenheim adsorption isotherm model of the charge-regulation process, we analyze and review the dependence of the local pH on the position, as well as bulk electrolyte concentration, bulk pH, and curvature of the amphiphilic single membrane vesicle. With appropriately chosen adsorption parameters of the charge-regulation model, we find a good agreement with the available experimental data.

Evolutionary changes in the number of dissociable amino acids on spike proteins and nucleoproteins of SARS-CoV-2 variants.

The spike protein of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is responsible for target recognition, cellular entry, and endosomal escape of the virus. At the same time, it is the part of the virus that exhibits the greatest sequence variation across the many variants which have emerged during its evolution. Recent studies have indicated that with progressive lineage emergence, the positive charge on the spike protein has been increasing, with certain positively charged amino acids (AAs) improving the binding of the spike protein to cell receptors. We have performed a detailed analysis of dissociable AAs of more than 1400 different SARS-CoV-2 lineages, which confirms these observations while suggesting that this progression has reached a plateau with Omicron and its subvariants and that the positive charge is not increasing further. Analysis of the nucleocapsid protein shows no similar increase in positive charge with novel variants, which further indicates that positive charge of the spike protein is being evolutionarily selected for. Furthermore, comparison with the spike proteins of known coronaviruses shows that already the wild-type SARS-CoV-2 spike protein carries an unusually large amount of positively charged AAs when compared to most other betacoronaviruses. Our study sheds light on the evolutionary changes in the number of dissociable AAs on the spike protein of SARS-CoV-2, complementing existing studies and providing a stepping stone towards a better understanding of the relationship between the spike protein charge and viral infectivity and transmissibility.

Integration of Cypoviruses into polyhedrin matrix.

Unlike in other viruses, in Cypoviruses the genome is doubly protected since their icosahedral capsids are embedded into a perfect polyhedrin crystal. Current experimental methods cannot resolve the resulting interface structure and we propose a symmetry-based approach to predict it. We reveal a remarkable match between the surfaces of Cypovirus and the outer polyhedrin matrix. The match arises due to the preservation of the common tetragonal symmetry, allowing perfect contacts of polyhedrin trimers with VP1 and VP5 capsid proteins. We highlight a crucial role of the VP5 proteins in embedding the Cypovirus into the polyhedrin matrix and discuss the relationship between the nucleoside triphosphatase activity of the proteins and their role in the superstructure formation. Additionally, we propose an electrostatic mechanism that drives the viral superstructure disassembly occurring in the alkaline environment of the insect intestines. Our study may underpin novel strategies for engineering proteinaceous nanocontainers in diverse biotechnological and chemical applications.

A Note on Vestigial Osmotic Pressure.

Recent experiments have indicated that at least a part of the osmotic pressure across the giant unilamellar vesicle (GUV) membrane was balanced by the rapid formation of the monodisperse daughter vesicles inside the GUVs through an endocytosis-like process. Therefore, we investigated a possible osmotic role played by these daughter vesicles for the maintenance of osmotic regulation in the GUVs and, by extension, in living cells. We highlighted a mechanism whereby the daughter vesicles acted as osmotically active solutes (osmoticants), contributing an extra vestigial osmotic pressure component across the membrane of the parent vesicle, and we showed that the consequences were consistent with experimental observations. Our results highlight the significance of osmotic regulation in cellular processes, such as fission/fusion, endocytosis, and exocytosis.

Towards Quantum-Chemical Level Calculations of SARS-CoV-2 Spike Protein Variants of Concern by First Principles Density Functional Theory.

The spike protein (S-protein) is a crucial part of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), with its many domains responsible for binding, fusion, and host cell entry. In this review we use the density functional theory (DFT) calculations to analyze the atomic-scale interactions and investigate the consequences of mutations in S-protein domains. We specifically describe the key amino acids and functions of each domain, which are essential for structural stability as well as recognition and fusion processes with the host cell; in addition, we speculate on how mutations affect these properties. Such unprecedented large-scale ab initio calculations, with up to 5000 atoms in the system, are based on the novel concept of amino acid-amino acid-bond pair unit (AABPU) that allows for an alternative description of proteins, providing valuable information on partial charge, interatomic bonding and hydrogen bond (HB) formation. In general, our results show that the S-protein mutations for different variants foster an increased positive partial charge, alter the interatomic interactions, and disrupt the HB networks. We conclude by outlining a roadmap for future computational research of biomolecular virus-related systems.

Packing and trimer-to-dimer protein reconstruction in icosahedral viral shells with a single type of symmetrical structural unit.

Understanding the principles of protein packing and the mechanisms driving morphological transformations in virus shells (capsids) during their maturation can be pivotal for the development of new antiviral strategies. Here, we study how these principles and mechanisms manifest themselves in icosahedral viral capsids assembled from identical symmetric structural units (capsomeres). To rationalize such shells, we model capsomers as symmetrical groups of identical particles interacting with a short-range potential typical of the classic Tammes problem. The capsomere particles are assumed to retain their relative positions on the vertices of planar polygons placed on the spherical shell and to interact only with the particles from other capsomeres. Minimization of the interaction energy enforces equal distances between the nearest particles belonging to neighboring capsomeres and minimizes the number of different local environments. Thus, our model implements the Caspar and Klug quasi-equivalence principle and leads to packings strikingly similar to real capsids. We then study a reconstruction of protein trimers into dimers in a Flavivirus shell during its maturation, connecting the relevant structural changes with the modifications of the electrostatic charges of proteins, wrought by the oxidative switch in the bathing solution that is essential for the process. We highlight the key role of pr peptides in the shell reconstruction and show that the highly ordered arrangement of these subunits in the dimeric state is energetically favored at a low pH level. We also discuss the electrostatic mechanisms controlling the release of pr peptides in the last irreversible step of the maturation process.

Hidden symmetry of the flavivirus protein shell and pH-controlled reconstruction of the viral surface.

Using recent Zika virus structural data we reveal a hidden symmetry of protein order in immature and mature flavivirus shells, violating the Caspar-Klug paradigmatic model of capsid structures. We show that proteins of the outer immature shell layer exhibit trihexagonal tiling, while proteins from inner and outer layers conjointly form a double-shelled close-packed structure, based on a common triangular spherical lattice. Within the proposed structural model, we furthermore rationalize the structural organization of misassembled non-infectious subviral particles that have no inner capsid. We consider a pH-controlled structural reconstruction of the outer shell from the trimeric to the dimeric state, and demonstrate that this transition, occurring during the virus maturation, can be induced by changes in protein charges at lower pH, leading to a decrease in the electrostatic interaction free energy. This transition could also be assisted by electrostatic attraction of shell proteins to the interposed lipid membrane substrate separating the shells.

Odd viscosity-induced Hall-like transport of an active chiral fluid.

Broken time-reversal and parity symmetries in active spinner fluids imply a nondissipative "odd viscosity," engendering phenomena unattainable in traditional passive or active fluids. Here we show that the odd viscosity itself can lead to a Hall-like transport when the active chiral fluid flows through a quenched matrix of obstacles, reminiscent of the anomalous Hall effect. The Hall-like velocity depends significantly on the spinner activity and longitudinal flow due to the interplay between odd viscosity and spinner-obstacle collisions. Our findings underscore the importance of odd viscosity in active chiral matter and elucidate its essential role in the anomalous Hall-like effect.

Quantum Chemical Computation of Omicron Mutations Near Cleavage Sites of the Spike Protein.

The attachment of the spike protein in SARS-CoV-2 to host cells and the initiation of viral invasion are two critical processes in the viral infection and transmission in which the presence of unique furin (S1/S2) and TMPRSS2 (S2') cleavage sites play a pivotal role. We provide a detailed analysis of the impact of the BA.1 Omicron mutations vicinal to these cleavage sites using a novel computational method based on the amino acid-amino acid bond pair unit (AABPU), a specific protein structural unit as a proxy for quantifying the atomic interaction. Our study is focused mainly on the spike region between subdomain 2 (SD2) and the central helix (CH), which contains both S1/S2 and S2' cleavage sites. Based on ab initio quantum calculations, we have identified several key features related to the electronic structure and bonding of the Omicron mutations that significantly increase the size of the relevant AABPUs and the positive charge. These findings enable us to conjecture on the biological role of Omicron mutations and their specific effects on cleavage sites and identify the principles that can be of some value in analyzing new variants.

Effect of Delta and Omicron Mutations on the RBD-SD1 Domain of the Spike Protein in SARS-CoV-2 and the Omicron Mutations on RBD-ACE2 Interface Complex.

The receptor-binding domain (RBD) is the essential part in the Spike-protein (S-protein) of SARS-CoV-2 virus that directly binds to the human ACE2 receptor, making it a key target for many vaccines and therapies. Therefore, any mutations at this domain could affect the efficacy of these treatments as well as the viral-cell entry mechanism. We introduce ab initio DFT-based computational study that mainly focuses on two parts: (1) Mutations effects of both Delta and Omicron variants in the RBD-SD1 domain. (2) Impact of Omicron RBD mutations on the structure and properties of the RBD-ACE2 interface system. The in-depth analysis is based on the novel concept of amino acid-amino acid bond pair units (AABPU) that reveal the differences between the Delta and/or Omicron mutations and its corresponding wild-type strain in terms of the role played by non-local amino acid interactions, their 3D shapes and sizes, as well as contribution to hydrogen bonding and partial charge distributions. Our results also show that the interaction of Omicron RBD with ACE2 significantly increased its bonding between amino acids at the interface providing information on the implications of penetration of S-protein into ACE2, and thus offering a possible explanation for its high infectivity. Our findings enable us to present, in more conspicuous atomic level detail, the effect of specific mutations that may help in predicting and/or mitigating the next variant of concern.

On the nature of screening in Voorn-Overbeek type theories.

By using a recently formulated Legendre transform approach to the thermodynamics of charged systems, we explore the general form of the screening length in the Voorn-Overbeek-type theories, which remains valid also in the cases where the entropy of the charged component(s) is not given by the ideal gas form as in the Debye-Hückel theory. The screening length consistent with the non-electrostatic terms in the free energy ansatz for the Flory-Huggins and Voorn-Overbeek type theories, derived from the local curvature properties of the Legendre transform, has distinctly different behavior than the often invoked standard Debye screening length, though it reduces to it in some special cases.

Binding Interactions between Receptor-Binding Domain of Spike Protein and Human Angiotensin Converting Enzyme-2 in Omicron Variant.

The emergence of new SARS-CoV-2 Omicron variant of concern (OV) has exacerbated the COVID-19 pandemic because of a large number of mutations in the spike protein, particularly in the receptor-binding domain (RBD), resulting in highly contagious and/or vaccine-resistant strains. Herein, we present a systematic analysis based on detailed molecular dynamics (MD) simulations in order to understand how the OV RBD mutations affect the ACE2 binding. We show that the OV RBD binds to ACE2 more efficiently and tightly predominantly because of strong electrostatic interactions, thereby promoting increased infectivity and transmissibility compared to other strains. Some of the OV RBD mutations are predicted to affect the antibody neutralization either through their role in the S-protein conformational changes, such as S371L, S373P, and S375F, or through changing its surface charge distribution, such as G339D, N440K, T478K, and E484A. Other mutations, such as K417N, G446S, and Y505H, decrease the ACE2 binding, whereas S447N, Q493R, G496S, Q498R, and N501Y tend to increase it.

Mutations of Omicron Variant at the Interface of the Receptor Domain Motif and Human Angiotensin-Converting Enzyme-2.

The most recent Omicron variant of SARS-CoV-2 has caused global concern and anxiety. The only thing certain about this strain, with a large number of mutations in the spike protein, is that it spreads quickly, seems to evade immune defense, and mitigates the benefits of existing vaccines. Based on the ultra-large-scale ab initio computational modeling of the receptor binding motif (RBM) and the human angiotensin-converting enzyme-2 (ACE2) interface, we provide the details of the effect of Omicron mutations at the fundamental atomic scale level. In-depth analysis anchored in the novel concept of amino acid-amino acid bond pair units (AABPU) indicates that mutations in the Omicron variant are connected with (i) significant changes in the shape and structure of AABPU components, together with (ii) significant increase in the positive partial charge, which facilitates the interaction with ACE2. We have identified changes in bonding due to mutations in the RBM. The calculated bond order, based on AABPU, reveals that the Omicron mutations increase the binding strength of RBM to ACE2. Our findings correlate with and are instrumental to explain the current observations and can contribute to the prediction of next potential new variant of concern.

Delta Variant with P681R Critical Mutation Revealed by Ultra-Large Atomic-Scale Ab Initio Simulation: Implications for the Fundamentals of Biomolecular Interactions.

The SARS-CoV-2 Delta variant is emerging as a globally dominant strain. Its rapid spread and high infection rate are attributed to a mutation in the spike protein of SARS-CoV-2 allowing for the virus to invade human cells much faster and with an increased efficiency. In particular, an especially dangerous mutation P681R close to the furin cleavage site has been identified as responsible for increasing the infection rate. Together with the earlier reported mutation D614G in the same domain, it offers an excellent instance to investigate the nature of mutations and how they affect the interatomic interactions in the spike protein. Here, using ultra large-scale ab initio computational modeling, we study the P681R and D614G mutations in the SD2-FP domain, including the effect of double mutation, and compare the results with the wild type. We have recently developed a method of calculating the amino-acid-amino-acid bond pairs (AABP) to quantitatively characterize the details of the interatomic interactions, enabling us to explain the nature of mutation at the atomic resolution. Our most significant finding is that the mutations reduce the AABP value, implying a reduced bonding cohesion between interacting residues and increasing the flexibility of these amino acids to cause the damage. The possibility of using this unique mutation quantifiers in a machine learning protocol could lead to the prediction of emerging mutations.