RNA topology remolds electrostatic stabilization of viruses

Modeling Viral Capsid Assembly: A Review of Computational Strategies and Applications

Viral capsid assembly is a complex and critical process, essential for understanding viral behavior, evolution, and the development of antiviral treatments, vaccines, and nanotechnology. Significant progress in studying viral capsid assembly has been achieved through various computational approaches, including molecular dynamics (MD) simulations, stochastic dynamics simulations, coarse-grained (CG) models, electrostatic analyses, lattice models, hybrid techniques, machine learning methods, and kinetic models. Each of these techniques offers unique advantages, and by integrating these diverse computational strategies, researchers can more accurately model the dynamic behaviors and structural features of viral capsids, deepening our understanding of the assembly process. This review provides a comprehensive overview of studies on viral capsid assembly, emphasizing their critical role in advancing our knowledge. It examines the contributions, strengths, and limitations of different computational methods, presents key computational works in the field, and analyzes milestone studies that have shaped current research.

Molecular Dynamics Characterization of the Free and Encapsidated RNA2 of CCMV with the oxRNA Model

The cowpea chlorotic mottle virus (CCMV) has emerged as a model system to assess the balance between electrostatic and topological features of single-stranded RNA viruses, specifically in the context of the viral self-assembly. Yet, despite its biophysical significance, little structural data on the RNA content of the CCMV virion is available. Here, the conformational dynamics of the RNA2 fragment of CCMV was assessed via coarse-grained molecular dynamics simulations, employing the oxRNA2 force field. The behavior of RNA2 was characterized both as a freely-folding molecule and within a mean-field depiction of the capsid. For the former, the role of the salt concentration, the temperature and of ad hoc constraints on the RNA termini was verified on the equilibrium properties of RNA2. For the latter, a multi-scale approach was employed to derive a potential profile of the viral cavity from atomistic structures of the CCMV capsid in solution. The conformational ensembles of the encapsidated RNA2 were significantly altered with respect to the freely-folding counterparts, as shown by the emergence of long-range motifs and pseudoknots. Finally, the role of the N-terminal tails of the CCMV subunits is highlighted as a critical feature in the construction of a proper electrostatic model of the CCMV capsid.

Effect of ionic strength on the assembly of simian vacuolating virus capsid protein around poly(styrene sulfonate)

Virus-like particles (VLPs) are noninfectious nanocapsules that can be used for drug delivery or vaccine applications. VLPs can be assembled from virus capsid proteins around a condensing agent, such as RNA, DNA, or a charged polymer. Electrostatic interactions play an important role in the assembly reaction. VLPs assemble from many copies of capsid protein, with a combinatorial number of intermediates. Hence, the mechanism of the reaction is poorly understood. In this paper, we combined solution small-angle X-ray scattering (SAXS), cryo-transmission electron microscopy (TEM), and computational modeling to determine the effect of ionic strength on the assembly of Simian Vacuolating Virus 40 (SV40)-like particles. We mixed poly(styrene sulfonate) with SV40 capsid protein pentamers at different ionic strengths. We then characterized the assembly product by SAXS and cryo-TEM. To analyze the data, we performed Langevin dynamics simulations using a coarse-grained model that revealed incomplete, asymmetric VLP structures consistent with the experimental data. We found that close to physiological ionic strength, [Formula: see text] VLPs coexisted with VP1 pentamers. At lower or higher ionic strengths, incomplete particles coexisted with pentamers and [Formula: see text] particles. Including the simulated structures was essential to explain the SAXS data in a manner that is consistent with the cryo-TEM images.

Spanning tree model and the assembly kinetics of RNA viruses

Single-stranded RNA (ssRNA) viruses self-assemble spontaneously in solutions that contain the viral RNA genome molecules and viral capsid proteins. The self-assembly of empty capsids can be understood on the basis of free energy minimization. However, during the self-assembly of complete viral particles in the cytoplasm of an infected cell, the viral genome molecules must be selected from a large pool of very similar host messenger RNA molecules and it is not known whether this also can be understood by free energy minimization. We address this question using a simple mathematical model, the spanning tree model, that was recently proposed for the assembly of small ssRNA viruses. We present a statistical physics analysis of the properties of this model. RNA selection takes place via a kinetic mechanism that operates during the formation of the nucleation complex and that is related to Hopfield kinetic proofreading.

Microcompartment assembly around multicomponent fluid cargoes

This article describes dynamical simulations of the assembly of an icosahedral protein shell around a bicomponent fluid cargo. Our simulations are motivated by bacterial microcompartments, which are protein shells found in bacteria that assemble around a complex of enzymes and other components involved in certain metabolic processes. The simulations demonstrate that the relative interaction strengths among the different cargo species play a key role in determining the amount of each species that is encapsulated, their spatial organization, and the nature of the shell assembly pathways. However, the shell protein–shell protein and shell protein–cargo component interactions that help drive assembly and encapsulation also influence cargo composition within certain parameter regimes. These behaviors are governed by a combination of thermodynamic and kinetic effects. In addition to elucidating how natural microcompartments encapsulate multiple components involved within reaction cascades, these results have implications for efforts in synthetic biology to colocalize alternative sets of molecules within microcompartments to accelerate specific reactions. More broadly, the results suggest that coupling between self-assembly and multicomponent liquid–liquid phase separation may play a role in the organization of the cellular cytoplasm.

Packaging contests between viral RNA molecules and kinetic selectivity

The paper presents a statistical-mechanics model for the kinetic selection of viral RNA molecules by packaging signals during the nucleation stage of the assembly of small RNA viruses. The effects of the RNA secondary structure and folding geometry of the packaging signals on the assembly activation energy barrier are encoded by a pair of characteristics: the wrapping number and the maximum ladder distance. Kinetic selection is found to be optimal when assembly takes place under conditions of supersaturation and also when the concentration ratio of capsid protein and viral RNA concentrations equals the stoichiometric ratio of assembled viral particles. As a function of the height of the activation energy barrier, there is a form of order-disorder transition such that for sufficiently low activation energy barriers, kinetic selectivity is erased by entropic effects associated with the number of assembly pathways.

Relationships between RNA topology and nucleocapsid structure in a model icosahedral virus

The process of genome packaging in most of viruses is poorly understood, notably the role of the genome itself in the nucleocapsid structure. For simple icosahedral single-stranded RNA viruses, the branched topology due to the RNA secondary structure is thought to lower the free energy required to complete a virion. We investigate the structure of nucleocapsids packaging RNA segments with various degrees of compactness by small-angle x-ray scattering and cryotransmission electron microscopy. The structural differences are mild even though compact RNA segments lead on average to better-ordered and more uniform particles across the sample. Numerical calculations confirm that the free energy is lowered for the RNA segments displaying the larger number of branch points. The effect is, however, opposite with synthetic polyelectrolytes, in which a star topology gives rise to more disorder in the capsids than a linear topology. If RNA compactness and size account in part for the proper assembly of the nucleocapsid and the genome selectivity, other factors most likely related to the host cell environment during viral assembly must come into play as well.

Mechanisms of Scaffold-Mediated Microcompartment Assembly and Size Control

This article describes a theoretical and computational study of the dynamical assembly of a protein shell around a complex consisting of many cargo molecules and long, flexible scaffold molecules. Our study is motivated by bacterial microcompartments, which are proteinaceous organelles that assemble around a condensed droplet of enzymes and reactants. As in many examples of cytoplasmic liquid-liquid phase separation, condensation of the microcompartment interior cargo is driven by flexible scaffold proteins that have weak multivalent interactions with the cargo. Our results predict that the shell size, amount of encapsulated cargo, and assembly pathways depend sensitively on properties of the scaffold, including its length and valency of scaffold-cargo interactions. Moreover, the ability of self-assembling protein shells to change their size to accommodate scaffold molecules of different lengths depends crucially on whether the spontaneous curvature radius of the protein shell is smaller or larger than a characteristic elastic length scale of the shell. Beyond natural microcompartments, these results have important implications for synthetic biology efforts to target alternative molecules for encapsulation by microcompartments or viral shells. More broadly, the results elucidate how cells exploit coupling between self-assembly and liquid-liquid phase separation to organize their interiors.

Effect of the charge distribution of virus coat proteins on the length of packaged RNAs

Single-stranded RNA viruses efficiently encapsulate their genome into a protein shell called the capsid. Electrostatic interactions between the positive charges in the capsid protein's N-terminal tail and the negatively charged genome have been postulated as the main driving force for virus assembly. Recent experimental results indicate that the N-terminal tail with the same number of charges and same lengths packages different amounts of RNA, which reveals that electrostatics alone cannot explain all the observed outcomes of the RNA self-assembly experiments. Using a mean-field theory, we show that the combined effect of genome configurational entropy and electrostatics can explain to some extent the amount of packaged RNA with mutant proteins where the location and number of charges on the tails are altered. Understanding the factors contributing to the virus assembly could promote the attempt to block viral infections or to build capsids for gene therapy applications.

Genome Modularization Reveals Overlapped Gene Topology Is Necessary for Efficient Viral Reproduction

Sequence overlap between two genes is common across all genomes, with viruses having high proportions of these gene overlaps. Genome modularization and refactoring is the process of disrupting natural gene overlaps to separate coding sequences to enable their individual manipulation. The biological function and fitness effects of gene overlaps are not fully understood, and their effects on gene cluster and genome-level refactoring are unknown. The bacteriophage φX174 genome has ∼26% of nucleotides involved in encoding more than one gene. In this study we use an engineered φX174 phage containing a genome with all gene overlaps removed to show that gene overlap is critical to maintaining optimal viral fecundity. Through detailed phenotypic measurements we reveal that genome modularization in φX174 causes virion replication, stability, and attachment deficiencies. Quantitation of the complete phage proteome across an infection cycle reveals 30% of proteins display abnormal expression patterns. Taken together, we have for the first time comprehensively demonstrated that gene modularization severely perturbs the coordinated functioning of a bacteriophage replication cycle. This work highlights the biological importance of gene overlap in natural genomes and that reducing gene overlap disruption should be an integral part of future genome engineering projects.

How a Virus Circumvents Energy Barriers to Form Symmetric Shells

Previous self-assembly experiments on a model icosahedral plant virus have shown that, under physiological conditions, capsid proteins initially bind to the genome through an en masse mechanism and form nucleoprotein complexes in a disordered state, which raises the question as to how virions are assembled into a highly ordered structure in the host cell. Using small-angle X-ray scattering, we find out that a disorder-order transition occurs under physiological conditions upon an increase in capsid protein concentrations. Our cryo-transmission electron microscopy reveals closed spherical shells containing in vitro transcribed viral RNA even at pH 7.5, in marked contrast with the previous observations. We use Monte Carlo simulations to explain this disorder-order transition and find that, as the shell grows, the structures of disordered intermediates in which the distribution of pentamers does not belong to the icosahedral subgroups become energetically so unfavorable that the caps can easily dissociate and reassemble, overcoming the energy barriers for the formation of perfect icosahedral shells. In addition, we monitor the growth of capsids under the condition that the nucleation and growth is the dominant pathway and show that the key for the disorder-order transition in both en masse and nucleation and growth pathways lies in the strength of elastic energy compared to the other forces in the system including protein-protein interactions and the chemical potential of free subunits. Our findings explain, at least in part, why perfect virions with icosahedral order form under different conditions including physiological ones.

Physical virology: From virus self-assembly to particle mechanics

Viruses are highly ordered supramolecular complexes that have evolved to propagate by hijacking the host cell's machinery. Although viruses are very diverse, spreading through cells of all kingdoms of life, they share common functions and properties. Next to the general interest in virology, fundamental viral mechanisms are of growing importance in other disciplines such as biomedicine and (bio)nanotechnology. However, in order to optimally make use of viruses and virus-like particles, for instance as vehicle for targeted drug delivery or as building blocks in electronics, it is essential to understand their basic chemical and physical properties and characteristics. In this context, the number of studies addressing the mechanisms governing viral properties and processes has recently grown drastically. This review summarizes a specific part of these scientific achievements, particularly addressing physical virology approaches aimed to understand the self-assembly of viruses and the mechanical properties of viral particles. Using a physicochemical perspective, we have focused on fundamental studies providing an overview of the molecular basis governing these key aspects of viral systems. This article is categorized under: Biology-Inspired Nanomaterials > Protein and Virus-Based Structures Nanotechnology Approaches to Biology > Nanoscale Systems in Biology.

RNA-Mediated Virus Assembly: Mechanisms and Consequences for Viral Evolution and Therapy

Viruses, entities composed of nucleic acids, proteins, and in some cases lipids lack the ability to replicate outside their target cells. Their components self-assemble at the nanoscale with exquisite precision-a key to their biological success in infection. Recent advances in structure determination and the development of biophysical tools such as single-molecule spectroscopy and noncovalent mass spectrometry allow unprecedented access to the detailed assembly mechanisms of simple virions. Coupling these techniques with mathematical modeling and bioinformatics has uncovered a previously unsuspected role for genomic RNA in regulating formation of viral capsids, revealing multiple, dispersed RNA sequence/structure motifs [packaging signals (PSs)] that bind cognate coat proteins cooperatively. The PS ensemble controls assembly efficiency and accounts for the packaging specificity seen in vivo. The precise modes of action of the PSs vary between viral families, but this common principle applies across many viral families, including major human pathogens. These insights open up the opportunity to block or repurpose PS function in assembly for both novel antiviral therapy and gene/drug/vaccine applications.

Packaging of Genomic RNA in Positive-Sense Single-Stranded RNA Viruses: A Complex Story

The packaging of genomic RNA in positive-sense single-stranded RNA viruses is a key part of the viral infectious cycle, yet this step is not fully understood. Unlike double-stranded DNA and RNA viruses, this process is coupled with nucleocapsid assembly. The specificity of RNA packaging depends on multiple factors: (i) one or more packaging signals, (ii) RNA replication, (iii) translation, (iv) viral factories, and (v) the physical properties of the RNA. The relative contribution of each of these factors to packaging specificity is different for every virus. In vitro and in vivo data show that there are different packaging mechanisms that control selective packaging of the genomic RNA during nucleocapsid assembly. The goals of this article are to explain some of the key experiments that support the contribution of these factors to packaging selectivity and to draw a general scenario that could help us move towards a better understanding of this step of the viral infectious cycle.

Electrostatics-Driven Inflation of Elastic Icosahedral Shells as a Model for Swelling of Viruses

We develop a clear theoretical description of radial swelling in virus-like particles that delineates the importance of electrostatic contributions to swelling in the absence of any conformational changes. The model couples the elastic parameters of the capsid-represented as a continuous elastic shell-to the electrostatic pressure acting on it. We show that different modifications of the electrostatic interactions brought about by, for instance, changes in pH or solution ionic strength are often sufficient to achieve the experimentally observed swelling (∼10% of the capsid radius). Additionally, we derive analytical expressions for the electrostatics-driven radial swelling of virus-like particles that enable one to quickly estimate the magnitudes of physical quantities involved.

A modelling paradigm for RNA virus assembly

Virus assembly, a key stage in any viral life cycle, had long been considered to be primarily driven by protein-protein interactions and nonspecific interactions between genomic RNA and capsid protein. We review here a modelling paradigm for RNA virus assembly that illustrates the crucial roles of multiple dispersed, specific interactions between viral genomes and coat proteins in capsid assembly. The model reveals how multiple sequence-structure motifs in the genomic RNA, termed packaging signals, with a shared coat protein recognition motif enable viruses to overcome a viral assembly-equivalent of Levinthal's Paradox in protein folding. The fitness advantages conferred by this mechanism suggest that it should be widespread in viruses, opening up new perspectives on viral evolution and anti-viral therapy.

Confining annealed branched polymers inside spherical capsids

The Lifshitz equation for the confinement of a linear polymer in a spherical cavity of radius R has the form of the Schrödinger equation for a quantum particle trapped in a potential well with flat bottom and infinite walls at radius R. We show that the Lifshitz equation of a confined annealed branched polymer has the form of the Schrödinger equation for a quantum harmonic oscillator. The resulting confinement energy has a 1/R4 dependence on the confinement radius R, in contrast to the case of confined linear polymers, which have a 1/R2 dependence. We discuss the application of this result to the problem of the confinement of single-stranded RNA molecules inside spherical capsids.

Oligonucleotide Length-Dependent Formation of Virus-Like Particles

Understanding the assembly pathway of viruses can contribute to creating monodisperse virus-based materials. In this study, the cowpea chlorotic mottle virus (CCMV) is used to determine the interactions between the capsid proteins of viruses and their cargo. The assembly of the capsid proteins in the presence of different lengths of short, single-stranded (ss) DNA is studied at neutral pH, at which the protein-protein interactions are weak. Chromatography, electrophoresis, microscopy, and light scattering data show that the assembly efficiency and speed of the particles increase with increasing length of oligonucleotides. The minimal length required for assembly under the conditions used herein is 14 nucleotides. Assembly of particles containing such short strands of ssDNA can take almost a month. This slow assembly process enabled the study of intermediate states, which confirmed a low cooperative assembly for CCMV and allowed for further expansion of current assembly theories.

The different faces of mass action in virus assembly

The spontaneous encapsulation of genomic and non-genomic polyanions by coat proteins of simple icosahedral viruses is driven, in the first instance, by electrostatic interactions with polycationic RNA binding domains on these proteins. The efficiency with which the polyanions can be encapsulated in vitro, and presumably also in vivo, must in addition be governed by the loss of translational and mixing entropy associated with co-assembly, at least if this co-assembly constitutes a reversible process. These forms of entropy counteract the impact of attractive interactions between the constituents and hence they counteract complexation. By invoking mass action-type arguments and a simple model describing electrostatic interactions, we show how these forms of entropy might settle the competition between negatively charged polymers of different molecular weights for co-assembly with the coat proteins. In direct competition, mass action turns out to strongly work against the encapsulation of RNAs that are significantly shorter, which is typically the case for non-viral (host) RNAs. We also find that coat proteins favor forming virus particles over nonspecific binding to other proteins in the cytosol even if these are present in vast excess. Our results rationalize a number of recent in vitro co-assembly experiments showing that short polyanions are less effective at attracting virus coat proteins to form virus-like particles than long ones do, even if both are present at equal weight concentrations in the assembly mixture.

Compactness of viral genomes: effect of disperse and localized random mutations

Genomes of single-stranded RNA viruses have evolved to optimize several concurrent properties. One of them is the architecture of their genomic folds, which must not only feature precise structural elements at specific positions, but also allow for overall spatial compactness. The latter was shown to be disrupted by random synonymous mutations, a disruption which can consequently negatively affect genome encapsidation. In this study, we use three mutation schemes with different degrees of locality to mutate the genomes of phage MS2 and Brome Mosaic virus in order to understand the observed sensitivity of the global compactness of their folds. We find that mutating local stretches of their genomes' sequence or structure is less disruptive to their compactness compared to inducing randomly-distributed mutations. Our findings are indicative of a mechanism for the conservation of compactness acting on a global scale of the genomes, and have several implications for understanding the interplay between local and global architecture of viral RNA genomes.

The effect of RNA stiffness on the self-assembly of virus particles

Under many in vitro conditions, some small viruses spontaneously encapsidate a single stranded (ss) RNA into a protein shell called the capsid. While viral RNAs are found to be compact and highly branched because of long distance base-pairing between nucleotides, recent experiments reveal that in a head-to-head competition between an ssRNA with no secondary or higher order structure and a viral RNA, the capsid proteins preferentially encapsulate the linear polymer! In this paper, we study the impact of genome stiffness on the encapsidation free energy of the complex of RNA and capsid proteins. We show that an increase in effective chain stiffness because of base-pairing could be the reason why under certain conditions linear chains have an advantage over branched chains when it comes to encapsidation efficiency. While branching makes the genome more compact, RNA base-pairing increases the effective Kuhn length of the RNA molecule, which could result in an increase of the free energy of RNA confinement, that is, the work required to encapsidate RNA, and thus less efficient packaging.

Varieties of charge distributions in coat proteins of ssRNA+ viruses

A major part of the interactions involved in the assembly and stability of icosahedral, positive-sense single-stranded RNA (ssRNA+) viruses is electrostatic in nature, as can be inferred from the strong pH- and salt-dependence of their assembly phase diagrams. Electrostatic interactions do not act only between the capsid coat proteins (CPs), but just as often provide a significant contribution to the interactions of the CPs with the genomic RNA, mediated to a large extent by positively charged, flexible N-terminal tails of the CPs. In this work, we provide two clear and complementary definitions of an N-terminal tail of a protein, and use them to extract the tail sequences of a large number of CPs of ssRNA+  viruses. We examine the pH-dependent interplay of charge on both tails and CPs alike, and show that-in contrast to the charge on the CPs-the net positive charge on the N-tails persists even to very basic pH values. In addition, we note a limit to the length of the wild-type genomes of those viruses which utilize positively charged tails, when compared to viruses without charged tails and similar capsid size. At the same time, we observe no clear connection between the charge on the N-tails and the genome lengths of the viruses included in our study.

Length of encapsidated cargo impacts stability and structure of in vitro assembled alphavirus core-like particles

In vitro assembly of alphavirus nucleocapsid cores, called core-like particles (CLPs), requires a polyanionic cargo. There are no sequence or structure requirements to encapsidate single-stranded nucleic acid cargo. In this work, we wanted to determine how the length of the cargo impacts the stability and structure of the assembled CLPs. We hypothesized that cargo neutralizes the basic region of the alphavirus capsid protein and if the cargo is long enough, it will also act to scaffold the CP monomers together. Experimentally we found that CLPs encapsidating short 27mer oligonucleotides were less stable than CLPs encapsidating 48mer or 90mer oligonucleotides under different chemical and thermal conditions. Furthermore, cryo-EM studies showed there were structural differences between CLPs assembled with 27mer and 48mer cargo. To mimic the role of the cargo in CLP assembly we made a mutant (4D) where we substituted a cluster of four Lys residues in the CP with four Asp residues. We found that these few amino acid substitutions were enough to initiate CLP assembly in the absence of cargo. The cargo-free 4D CLPs show higher resistance to ionic strength and increased temperature compared to wild-type cargo containing CLPs suggesting their CLP assembly mechanism might also be different.

RNA Base Pairing Determines the Conformations of RNA Inside Spherical Viruses

Many simple RNA viruses enclose their genetic material by a protein shell called the capsid. While the capsid structures are well characterized for most viruses, the structure of RNA inside the shells and the factors contributing to it remain poorly understood. We study the impact of base pairing on the conformations of RNA and find that it undergoes a swollen coil to globule continuous transition as a function of the strength of the pairing interaction. We also observe a first order transition and kink profile as a function of RNA length. All these transitions could explain the different RNA profiles observed inside viral shells.

Impact of a nonuniform charge distribution on virus assembly

Many spherical viruses encapsulate their genomes in protein shells with icosahedral symmetry. This process is spontaneous and driven by electrostatic interactions between positive domains on the virus coat proteins and the negative genomes. We model the effect of the nonuniform icosahedral charge distribution from the protein shell instead using a mean-field theory. We find that this nonuniform charge distribution strongly affects the optimal genome length and that it can explain the experimentally observed phenomenon of overcharging of virus and viruslike particles.

Nanocaged platforms: modification, drug delivery and nanotoxicity. Opening synthetic cages to release the tiger

Nanocages (NCs) have emerged as a new class of drug-carriers, with a wide range of possibilities in multi-modality medical treatments and theranostics. Nanocages can overcome such limitations as high toxicity caused by anti-cancer chemotherapy or by the nanocarrier itself, due to their unique characteristics. These properties consist of: (1) a high loading-capacity (spacious interior); (2) a porous structure (analogous to openings between the bars of the cage); (3) enabling smart release (a key to unlock the cage); and (4) a low likelihood of unfavorable immune responses (the outside of the cage is safe). In this review, we cover different classes of NC structures such as virus-like particles (VLPs), protein NCs, DNA NCs, supramolecular nanosystems, hybrid metal-organic NCs, gold NCs, carbon-based NCs and silica NCs. Moreover, NC-assisted drug delivery including modification methods, drug immobilization, active targeting, and stimulus-responsive release mechanisms are discussed, highlighting the advantages, disadvantages and challenges. Finally, translation of NCs into clinical applications, and an up-to-date assessment of the nanotoxicology considerations of NCs are presented.

Combining Protein Cages and Polymers: from Understanding Self-Assembly to Functional Materials

Protein cages, such as viruses, are well-defined biological nanostructures which are highly symmetrical and monodisperse. They are found in various shapes and sizes and can encapsulate or template non-native materials. Furthermore, the proteins can be chemically or genetically modified giving them new properties. For these reasons, these protein structures have received increasing attention in the field of polymer-protein hybrid materials over the past years, however, advances are still to be made. This Viewpoint highlights the different ways polymers and protein cages or their subunits have been combined to understand self-assembly and create functional materials.

Effects of RNA branching on the electrostatic stabilization of viruses

Many single-stranded (ss) ribonucleic acid (RNA) viruses self-assemble from capsid protein subunits and the nucleic acid to form an infectious virion. It is believed that the electrostatic interactions between the negatively charged RNA and the positively charged viral capsid proteins drive the encapsidation, although there is growing evidence that the sequence of the viral RNA also plays a role in packaging. In particular, the sequence will determine the possible secondary structures that the ssRNA will take in solution. In this work, we use a mean-field theory to investigate how the secondary structure of the RNA combined with electrostatic interactions affects the efficiency of assembly and stability of the assembled virions. We show that the secondary structure of RNA may result in negative osmotic pressures while a linear polymer causes positive osmotic pressures for the same conditions. This may suggest that the branched structure makes the RNA more effectively packaged and the virion more stable.

Sequence Dependence of Viral RNA Encapsidation

We develop a Flory mean-field theory for viral RNA (vRNA) molecules that extends the current RNA folding algorithms to include interactions between different sections of the secondary structure. The theory is applied to sequence-selective vRNA encapsidation. The dependence on sequence enters through a single parameter: the largest eigenvalue of the Kramers matrix of the branched polymer obtained by coarse graining the secondary structure. Differences between the work of encapsidation of vRNA molecules and of randomized isomers are found to be in the range of 20 kBT, more than sufficient to provide a strong bias in favor of vRNA encapsidation. The method is applied to a packaging competition experiment where large vRNA molecules compete for encapsidation with two smaller RNA species that together have the same nucleotide sequence as the large molecule. We encounter a substantial, generic free energy bias, that also is of the order of 20 kBT, in favor of encapsidating the single large RNA molecule. The bias is mainly the consequence of the fact that dividing up a large vRNA molecule involves the release of stored elastic energy. This provides an important, nonspecific mechanism for preferential encapsidation of single larger vRNA molecules over multiple smaller mRNA molecules with the same total number of nucleotides. The result is also consistent with recent RNA packaging competition experiments by Comas-Garcia et al.1 Finally, the Flory method leads to the result that when two RNA molecules are copackaged, they are expected to remain segregated inside the capsid.

Modeling Effects of RNA on Capsid Assembly Pathways via Coarse-Grained Stochastic Simulation

The environment of a living cell is vastly different from that of an in vitro reaction system, an issue that presents great challenges to the use of in vitro models, or computer simulations based on them, for understanding biochemistry in vivo. Virus capsids make an excellent model system for such questions because they typically have few distinct components, making them amenable to in vitro and modeling studies, yet their assembly can involve complex networks of possible reactions that cannot be resolved in detail by any current experimental technology. We previously fit kinetic simulation parameters to bulk in vitro assembly data to yield a close match between simulated and real data, and then used the simulations to study features of assembly that cannot be monitored experimentally. The present work seeks to project how assembly in these simulations fit to in vitro data would be altered by computationally adding features of the cellular environment to the system, specifically the presence of nucleic acid about which many capsids assemble. The major challenge of such work is computational: simulating fine-scale assembly pathways on the scale and in the parameter domains of real viruses is far too computationally costly to allow for explicit models of nucleic acid interaction. We bypass that limitation by applying analytical models of nucleic acid effects to adjust kinetic rate parameters learned from in vitro data to see how these adjustments, singly or in combination, might affect fine-scale assembly progress. The resulting simulations exhibit surprising behavioral complexity, with distinct effects often acting synergistically to drive efficient assembly and alter pathways relative to the in vitro model. The work demonstrates how computer simulations can help us understand how assembly might differ between the in vitro and in vivo environments and what features of the cellular environment account for these differences.

Functional analysis of the N-terminal basic motif of a eukaryotic satellite RNA virus capsid protein in replication and packaging

Efficient replication and assembly of virus particles are integral to the establishment of infection. In addition to the primary role of the capsid protein (CP) in encapsidating the RNA progeny, experimental evidence on positive sense single-stranded RNA viruses suggests that the CP also regulates RNA synthesis. Here, we demonstrate that replication of Satellite tobacco mosaic virus (STMV) is controlled by the cooperative interaction between STMV CP and the helper virus (HV) Tobacco mosaic virus (TMV) replicase. We identified that the STMV CP-HV replicase interaction requires a positively charged residue at the third position (3R) in the N-terminal 13 amino acid (aa) motif. Far-Northwestern blotting showed that STMV CP promotes binding between HV-replicase and STMV RNA. An STMV CP variant having an arginine to alanine substitution at position 3 in the N-terminal 13aa motif abolished replicase-CP binding. The N-terminal 13aa motif of the CP bearing alanine substitutions for positively charged residues located at positions 5, 7, 10 and 11 are defective in packaging full-length STMV, but can package a truncated STMV RNA lacking the 3' terminal 150 nt region. These findings provide insights into the mechanism underlying the regulation of STMV replication and packaging.

Role of Genome in the Formation of Conical Retroviral Shells

Human immunodeficiency virus (HIV) capsid proteins spontaneously assemble around the genome into a protective protein shell called the capsid, which can take on a variety of shapes broadly classified as conical, cylindrical, and irregular. The majority of capsids seen in in vivo studies are conical in shape, while in vitro experiments have shown a preference for cylindrical capsids. The factors involved in the selection of the unique shape of HIV capsids are not well understood, and in particular the impact of RNA on the formation of the capsid is not known. In this work, we study the role of the genome and its interaction with the capsid protein by modeling the genomic RNA through a mean-field theory. Our results show that the confinement free energy for a homopolymeric model genome confined in a conical capsid is lower than that in a cylindrical capsid, at least when the genome does not interact with the capsid, which seems to be the case in in vivo experiments. Conversely, the confinement free energy for the cylinder is lower than that for a conical capsid if the genome is attracted to the capsid proteins as the in vitro experiments. Understanding the factors that contribute to the formation of conical capsids may shed light on the infectivity of HIV particles.

Physical Principles in the Self-Assembly of a Simple Spherical Virus

Viruses are unique among living organisms insofar as they can be reconstituted "from scratch", that is, synthesized from purified components. In the simplest cases, their "parts list" numbers only two: a single molecule of nucleic acid and many (but a very special number, i.e., multiples of 60) copies of a single protein. Indeed, the smallest viral genomes include essentially only two genes, on the order of a thousand times fewer than the next-simplest organisms like bacteria and yeast. For these reasons, it is possible and even fruitful to take a reductionist approach to viruses and to understand how they work in terms of fundamental physical principles. In this Account, we discuss our recent physical chemistry approach to studying the self-assembly of a particular spherical virus (cowpea chlorotic mottle virus) whose reconstitution from RNA and capsid protein has long served as a model for virus assembly. While previous studies have clarified the roles of certain physical (electrostatic, hydrophobic, steric) interactions in the stability and structure of the final virus, it has been difficult to probe these interactions during assembly because of the inherently short lifetimes of the intermediate states. We feature the role of pH in tuning the magnitude of the interactions among capsid proteins during assembly: in particular, by making the interactions between proteins sufficiently weak, we are able to stall the assembly process and interrogate the structure and composition of particular on-pathway intermediates. Further, we find that the strength of the lateral attractions between RNA-bound proteins plays a key role in addressing several outstanding questions about assembly: What determines the pathway or pathways of assembly? What is the importance of kinetic traps and hysteresis? How do viruses copackage multiple short (compared with wild-type) RNAs or single long RNAs? What determines the relative packaging efficiencies of different RNAs when they are forced to compete for an insufficient supply of protein? And what is the limit on the length of RNA that can be packaged by CCMV capsid protein?

Adsorption of annealed branched polymers on curved surfaces

The behavior of annealed branched polymers near adsorbing surfaces plays a fundamental role in many biological and industrial processes. Most importantly single stranded RNA in solution tends to fold up and self-bind to form a highly branched structure. Using a mean field theory, we both perturbatively and numerically examine the adsorption of branched polymers on surfaces of several different geometries in a good solvent. Independent of the geometry of the wall, we observe that as branching density increases, surface tension decreases. However, we find a coupling between the branching density and curvature in that a further lowering of surface tension occurs when the wall curves towards the polymer, but the amount of lowering of surface tension decreases when the wall curves away from the polymer. We find that for branched polymers confined into spherical cavities, most of branch-points are located in the vicinity of the interior wall and the surface tension is minimized for a critical cavity radius. For branch polymers next to sinusoidal surfaces, we find that branch-points accumulate at the valleys while end-points on the peaks.

Role of RNA Branchedness in the Competition for Viral Capsid Proteins

To optimize binding-and packaging-by their capsid proteins (CP), single-stranded (ss) RNA viral genomes often have local secondary/tertiary structures with high CP affinity, with these "packaging signals" serving as heterogeneous nucleation sites for the formation of capsids. Under typical in vitro self-assembly conditions, however, and in particular for the case of many ssRNA viruses whose CP have cationic N-termini, the adsorption of CP by RNA is nonspecific because the CP concentration exceeds the largest dissociation constant for CP-RNA binding. Consequently, the RNA is saturated by bound protein before lateral interactions between CP drive the homogeneous nucleation of capsids. But, before capsids are formed, the binding of protein remains reversible and introduction of another RNA species-with a different length and/or sequence-is found experimentally to result in significant redistribution of protein. Here we argue that, for a given RNA mass, the sequence with the highest affinity for protein is the one with the most compact secondary structure arising from self-complementarity; similarly, a long RNA steals protein from an equal mass of shorter ones. In both cases, it is the lateral attractions between bound proteins that determines the relative CP affinities of the RNA templates, even though the individual binding sites are identical. We demonstrate this with Monte Carlo simulations, generalizing the Rosenbluth method for excluded-volume polymers to include branching of the polymers and their reversible binding by protein.

Synonymous mutations reduce genome compactness in icosahedral ssRNA viruses

Recent studies have shown that single-stranded (ss) viral RNAs fold into more compact structures than random RNA sequences with similar chemical composition and identical length. Based on this comparison, it has been suggested that wild-type viral RNA may have evolved to be atypically compact so as to aid its encapsidation and assist the viral assembly process. To further explore the compactness selection hypothesis, we systematically compare the predicted sizes of >100 wild-type viral sequences with those of their mutants, which are evolved in silico and subject to a number of known evolutionary constraints. In particular, we enforce mutation synonynimity, preserve the codon-bias, and leave untranslated regions intact. It is found that progressive accumulation of these restricted mutations still suffices to completely erase the characteristic compactness imprint of the viral RNA genomes, making them in this respect physically indistinguishable from randomly shuffled RNAs. This shows that maintaining the physical compactness of the genome is indeed a primary factor among ssRNA viruses' evolutionary constraints, contributing also to the evidence that synonymous mutations in viral ssRNA genomes are not strictly neutral.

Inverted critical adsorption of polyelectrolytes in confinement

What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density σc-defining the adsorption-desorption transition-are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of σc for the concave interfaces versus the Debye screening length 1/κ and the extent of confinement a for these three interfaces for small κa values. For large κa the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/κ. We also rationalize how σc(κ) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption-the effect often hard to tackle theoretically-putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids.

The Role of Packaging Sites in Efficient and Specific Virus Assembly

During the life cycle of many single-stranded RNA viruses, including many human pathogens, a protein shell called the capsid spontaneously assembles around the viral genome. Understanding the mechanisms by which capsid proteins selectively assemble around the viral RNA amidst diverse host RNAs is a key question in virology. In one proposed mechanism, short sequences (packaging sites) within the genomic RNA promote rapid and efficient assembly through specific interactions with the capsid proteins. In this work, we develop a coarse-grained particle-based computational model for capsid proteins and RNA that represents protein-RNA interactions arising both from nonspecific electrostatics and from specific packaging site interactions. Using Brownian dynamics simulations, we explore how the efficiency and specificity of assembly depend on solution conditions (which control protein-protein and nonspecific protein-RNA interactions) and the strength and number of packaging sites. We identify distinct regions in parameter space in which packaging sites lead to highly specific assembly via different mechanisms and others in which packaging sites lead to kinetic traps. We relate these computational predictions to in vitro assays for specificity in which cognate viral RNAs compete against non-cognate RNAs for assembly by capsid proteins.

Mechanisms of virus assembly

Viruses are nanoscale entities containing a nucleic acid genome encased in a protein shell called a capsid and in some cases are surrounded by a lipid bilayer membrane. This review summarizes the physics that govern the processes by which capsids assemble within their host cells and in vitro. We describe the thermodynamics and kinetics for the assembly of protein subunits into icosahedral capsid shells and how these are modified in cases in which the capsid assembles around a nucleic acid or on a lipid bilayer. We present experimental and theoretical techniques used to characterize capsid assembly, and we highlight aspects of virus assembly that are likely to receive significant attention in the near future.

Biomolecular engineering of virus-like particles aided by computational chemistry methods

Multi-scale investigation of VLP self-assembly aided by computational methods is facilitating the design, redesign, and modification of functionalized VLPs.

Viral capsids: kinetics of assembly under transient conditions and kinetics of disassembly

The available kinetic models of assembly of viral protein capsids are focused primarily on the situations in vitro where the amount of protein is fixed. In vivo, however, the viral protein synthesis and capsid assembly occur under transient conditions in parallel with viral genome replication. Herein, a kinetic model describing the latter case of capsid assembly is proposed with emphasis on the period corresponding to the initial stage of viral genome replication. The analysis is aimed at small icosahedral capsids. With biologically reasonable values of model parameters, the model predicts rapid exponential growth of the populations of monomers and fully assembled capsids during the transient period of genome replication. Under the subsequent steady-state conditions with respect to replication, the monomer population is predicted to be nearly constant while the number of fully assembled capsids increases linearly. The kinetics of capsid disassembly, described briefly as well under conditions of negligible monomer concentration, exhibit a short induction period when the number of proteins in a capsid is only slightly smaller than in the beginning, followed by more rapid protein detachment. According to calculations, the latter kinetics may strongly depend on protein degradation.

Weighing polyelectrolytes packaged in viruslike particles

This Letter reports on the remarkable selectivity of capsid proteins for packaging synthetic polyelectrolytes in viruslike particles. By applying the contrast variation method in small-angle neutron scattering, we accurately estimated the mean mass of packaged polyelectrolytes ⟨Mp⟩ and that of the surrounding capsid ⟨Mcap⟩. Remarkably, the mass ratio ⟨Mp⟩/⟨Mcap⟩ was invariant for polyelectrolyte molecular weights spanning more than 2 orders of magnitude. To do so, capsids either packaged several chains simultaneously or selectively retained the shortest chains that could fit the capsid interior. Our data are in qualitative agreement with theoretical predictions based on free energy minimization and emphasize the importance of protein self-energy. These findings may give new insights into the nonspecific origin of genome selectivity for a number of viral systems.

Role of electrostatics in the assembly pathway of a single-stranded RNA virus

We have recently discovered (R. D. Cadena-Nava et al., J. Virol. 86:3318-3326, 2012, doi:10.1128/JVI.06566-11) that the in vitro packaging of RNA by the capsid protein (CP) of cowpea chlorotic mottle virus is optimal when there is a significant excess of CP, specifically that complete packaging of all of the RNA in solution requires sufficient CP to provide charge matching of the N-terminal positively charged arginine-rich motifs (ARMS) of the CPs with the negatively charged phosphate backbone of the RNA. We show here that packaging results from the initial formation of a charge-matched protocapsid consisting of RNA decorated by a disordered arrangement of CPs. This protocapsid reorganizes into the final, icosahedrally symmetric nucleocapsid by displacing the excess CPs from the RNA to the exterior surface of the emerging capsid through electrostatic attraction between the ARMs of the excess CP and the negative charge density of the capsid exterior. As a test of this scenario, we prepare CP mutants with extra and missing (relative to the wild type) cationic residues and show that a correspondingly smaller and larger excess, respectively, of CP is needed for complete packaging of RNA.

IMPORTANCE

Cowpea chlorotic mottle virus (CCMV) has long been studied as a model system for the assembly of single-stranded RNA viruses. While much is known about the electrostatic interactions within the CCMV virion, relatively little is known about these interactions during assembly, i.e., within intermediate states preceding the final nucleocapsid structure. Theoretical models and coarse-grained molecular dynamics simulations suggest that viruses like CCMV assemble by the bulk adsorption of CPs onto the RNA driven by electrostatic attraction, followed by structural reorganization into the final capsid. Such a mechanism facilitates assembly by condensing the RNA for packaging while simultaneously concentrating the local density of CP for capsid nucleation. We provide experimental evidence of such a mechanism by demonstrating that efficient assembly is initiated by the formation of a disordered protocapsid complex whose stoichiometry is governed by electrostatics (charge matching of the anionic RNA and the cationic N termini of the CP).