Building a viral capsid in the presence of genomic RNA

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.

Compositional complementarity between genomic RNA and coat proteins in positive-sense single-stranded RNA viruses

During packaging in positive-sense single-stranded RNA (+ssRNA) viruses, coat proteins (CPs) interact directly with multiple regions in genomic RNA (gRNA), but the underlying physicochemical principles remain unclear. Here we analyze the high-resolution cryo-EM structure of bacteriophage MS2 and show that the gRNA/CP binding sites, including the known packaging signal, overlap significantly with regions where gRNA nucleobase-density profiles match the corresponding CP nucleobase-affinity profiles. Moreover, we show that the MS2 packaging signal corresponds to the global minimum in gRNA/CP interaction energy in the unstructured state as derived using a linearly additive model and knowledge-based nucleobase/amino-acid affinities. Motivated by this, we predict gRNA/CP interaction sites for a comprehensive set of 1082 +ssRNA viruses. We validate our predictions by comparing them with site-resolved information on gRNA/CP interactions derived in SELEX and CLIP experiments for 10 different viruses. Finally, we show that in experimentally studied systems CPs frequently interact with autologous coding regions in gRNA, in agreement with both predicted interaction energies and a recent proposal that proteins in general tend to interact with own mRNAs, if unstructured. Our results define a self-consistent framework for understanding packaging in +ssRNA viruses and implicate interactions between unstructured gRNA and CPs in the process.

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.

The impact of local assembly rules on RNA packaging in a T = 1 satellite plant virus

The vast majority of viruses consist of a nucleic acid surrounded by a protective icosahedral protein shell called the capsid. During viral infection of a host cell, the timing and efficiency of the assembly process is important for ensuring the production of infectious new progeny virus particles. In the class of single-stranded RNA (ssRNA) viruses, the assembly of the capsid takes place in tandem with packaging of the ssRNA genome in a highly cooperative co-assembly process. In simple ssRNA viruses such as the bacteriophage MS2 and small RNA plant viruses such as STNV, this cooperative process results from multiple interactions between the protein shell and sites in the RNA genome which have been termed packaging signals. Using a stochastic assembly algorithm which includes cooperative interactions between the protein shell and packaging signals in the RNA genome, we demonstrate that highly efficient assembly of STNV capsids arises from a set of simple local rules. Altering the local assembly rules results in different nucleation scenarios with varying assembly efficiencies, which in some cases depend strongly on interactions with RNA packaging signals. Our results provide a potential simple explanation based on local assembly rules for the ability of some ssRNA viruses to spontaneously assemble around charged polymers and other non-viral RNAs in vitro.

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.

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.

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.

CAPLIB: A New Program Library for the Modeling and Analysis of Icosahedrally Symmetric Viral Capsids

A new program library named "CAPLIB" was developed for the modeling and analysis of icosahedrally symmetric virus capsids. CAPLIB is equipped with the mathematical data of 60 rotation matrices of icosahedral symmetry, 15 planes bisecting the entire capsid structure, and a table summarizing how the 60 asymmetric units (cells) are partitioned by the planes. CAPLIB contains the function to determine the cell numbers of atoms from the atomic positions and the function to determine the rotation axes and angles from the rotation matrices. Using CAPLIB, it is possible to generate the structure of any selected protein unit within the entire capsid by rotating a single protein unit structure. CAPLIB can classify Protein Data Bank files of capsids with the directions of rotation axes, rotate the protein structure onto the standard position, and perform various deformations of the entire capsid. The interface to the molecular graphics software, PyMOL, was also developed for efficient modeling of capsids.

RNA Virus Evolution via a Quasispecies-Based Model Reveals a Drug Target with a High Barrier to Resistance

The rapid occurrence of therapy-resistant mutant strains provides a challenge for anti-viral therapy. An ideal drug target would be a highly conserved molecular feature in the viral life cycle, such as the packaging signals in the genomes of RNA viruses that encode an instruction manual for their efficient assembly. The ubiquity of this assembly code in RNA viruses, including major human pathogens, suggests that it confers selective advantages. However, their impact on viral evolution cannot be assessed in current models of viral infection that lack molecular details of virus assembly. We introduce here a quasispecies-based model of a viral infection that incorporates structural and mechanistic knowledge of packaging signal function in assembly to construct a phenotype-fitness map, capturing the impact of this RNA code on assembly yield and efficiency. Details of viral replication and assembly inside an infected host cell are coupled with a population model of a viral infection, allowing the occurrence of therapy resistance to be assessed in response to drugs inhibiting packaging signal recognition. Stochastic simulations of viral quasispecies evolution in chronic HCV infection under drug action and/or immune clearance reveal that drugs targeting all RNA signals in the assembly code collectively have a high barrier to drug resistance, even though each packaging signal in isolation has a lower barrier than conventional drugs. This suggests that drugs targeting the RNA signals in the assembly code could be promising routes for exploitation in anti-viral drug design.

Kinetic constraints on self-assembly into closed supramolecular structures

Many biological and synthetic systems exploit self-assembly to generate highly intricate closed supramolecular architectures, ranging from self-assembling cages to viral capsids. The fundamental design principles that control the structural determinants of the resulting assemblies are increasingly well-understood, but much less is known about the kinetics of such assembly phenomena and it remains a key challenge to elucidate how these systems can be engineered to assemble in an efficient manner and avoid kinetic trapping. We show here that simple scaling laws emerge from a set of kinetic equations describing the self-assembly of identical building blocks into closed supramolecular structures and that this scaling behavior provides general rules that determine efficient assembly in these systems. Using this framework, we uncover the existence of a narrow range of parameter space that supports efficient self-assembly and reveal that nature capitalizes on this behavior to direct the reliable assembly of viral capsids on biologically relevant timescales.

A Model for Viral Assembly around an Explicit RNA Sequence Generates an Implicit Fitness Landscape

Previously, a stochastic model of single-stranded RNA virus assembly was created to model the cooperative effects between capsid proteins and genomic RNA that would occur in a packaging signal-mediated assembly process. In such an assembly scenario, multiple secondary structural elements from within the RNA, termed "packaging signals" (PS), contact coat proteins and facilitate efficient capsid assembly. In this work, the assembly model is extended to incorporate explicit nucleotide sequence information as well as simple aspects of RNA folding that would be occurring during the RNA/capsid coassembly process. Applying this paradigm to a dodecahedral viral capsid, a computer-derived nucleotide sequence is evolved de novo that is optimal for packaging the RNA into capsids, while also containing capacity for coding for a viral protein. Analysis of the effects of mutations on the ability of the RNA sequence to successfully package into a viral capsid reveals a complex fitness landscape where the majority of mutations are neutral with respect to packaging efficiency with a small number of mutations resulting in a near-complete loss of RNA packaging. Moreover, the model shows how attempts to ablate PSs in the viral RNA sequence may result in redundant PSs already present in the genome fulfilling their packaging role. This explains why recent experiments that attempt to ablate putative PSs may not see an effect on packaging. This modeling framework presents an example of how an implicit mapping can be made from genotype to a fitness parameter important for viral biology, i.e., viral capsid yield, with potential applications to theoretical models of viral evolution.

Impact of Hydrogen Bonding in the Binding Site between Capsid Protein and MS2 Bacteriophage ssRNA

MS2 presents a well-studied example of a single-stranded RNA virus for which the genomic RNA plays a pivotal role in the virus assembly process based on the packaging signal-mediated mechanism. Packaging signals (PSs) are multiple dispersed RNA sequence/structure motifs varying around a central recognition motif that interact in a specific way with the capsid protein in the assembly process. Although the discovery and identification of these PSs was based on bioinformatics and geometric approaches, in tandem with sophisticated experimental protocols, we approach this problem using large-scale ab initio computation centered on critical aspects of the consensus protein-RNA interactions recognition motif. DFT calculations are carried out on two nucleoprotein complexes: wild-type and mutated (PDB IDs: 1ZDH and 5MSF ). The calculated partial charge distribution of residues and the strength of hydrogen bonding (HB) between them enabled us to locate the exact binding sites with the strongest HBs, identified to be LYS43-A^-4, ARG49-C^-13, TYR85-C^-5, and LYS61-C^-5, due to the change in the sequence of the mutated RNA.

Quantitative computational models of molecular self-assembly in systems biology

Molecular self-assembly is the dominant form of chemical reaction in living systems, yet efforts at systems biology modeling are only beginning to appreciate the need for and challenges to accurate quantitative modeling of self-assembly. Self-assembly reactions are essential to nearly every important process in cell and molecular biology and handling them is thus a necessary step in building comprehensive models of complex cellular systems. They present exceptional challenges, however, to standard methods for simulating complex systems. While the general systems biology world is just beginning to deal with these challenges, there is an extensive literature dealing with them for more specialized self-assembly modeling. This review will examine the challenges of self-assembly modeling, nascent efforts to deal with these challenges in the systems modeling community, and some of the solutions offered in prior work on self-assembly specifically. The review concludes with some consideration of the likely role of self-assembly in the future of complex biological system models more generally.

Genomic RNA folding mediates assembly of human parechovirus

Assembly of the major viral pathogens of the Picornaviridae family is poorly understood. Human parechovirus 1 is an example of such viruses that contains 60 short regions of ordered RNA density making identical contacts with the protein shell. We show here via a combination of RNA-based systematic evolution of ligands by exponential enrichment, bioinformatics analysis and reverse genetics that these RNA segments are bound to the coat proteins in a sequence-specific manner. Disruption of either the RNA coat protein recognition motif or its contact amino acid residues is deleterious for viral assembly. The data are consistent with RNA packaging signals playing essential roles in virion assembly. Their binding sites on the coat proteins are evolutionarily conserved across the Parechovirus genus, suggesting that they represent potential broad-spectrum anti-viral targets.The mechanism underlying packaging of genomic RNA into viral particles is not well understood for human parechoviruses. Here the authors identify short RNA motifs in the parechovirus genome that bind capsid proteins, providing approximately 60 specific interactions for virion assembly.

Preparation of MS2 Phage-Like Particles and Their Use As Potential Process Control Viruses for Detection and Quantification of Enteric RNA Viruses in Different Matrices

The detection and quantification of enteric RNA viruses is based on isolation of viral RNA from the sample followed by quantitative reverse transcription polymerase chain reaction (RT-qPCR). To control the whole process of analysis and in order to guarantee the validity and reliability of results, process control viruses (PCV) are used. The present article describes the process of preparation and use of such PCV– MS2 phage-like particles (MS2 PLP) – in RT-qPCR detection and quantification of enteric RNA viruses. The MS2 PLP were derived from bacteriophage MS2 carrying a unique and specific de novo-constructed RNA target sequence originating from the DNA of two extinct species. The amount of prepared MS2 particles was quantified using four independent methods – UV spectrophotometry, fluorimetry, transmission electron microscopy and a specifically developed duplex RT-qPCR. To evaluate the usefulness of MS2 PLP in routine diagnostics different matrices known to harbor enteric RNA viruses (swab samples, liver tissue, serum, feces, and vegetables) were artificially contaminated with specific amounts of MS2 PLP. The extraction efficiencies were calculated for each individual matrix. The prepared particles fulfill all requirements for PCV – they are very stable, non-infectious, and are genetically distinct from the target RNA viruses. Due to these properties they represent a good morphological and physiochemical model. The use of MS2 PLP as a PCV in detection and quantification of enteric RNA viruses was evaluated in different types of matrices.

Ins and Outs of Multipartite Positive-Strand RNA Plant Viruses: Packaging versus Systemic Spread

Viruses possessing a non-segmented genome require a specific recognition of their nucleic acid to ensure its protection in a capsid. A similar feature exists for viruses having a segmented genome, usually consisting of viral genomic segments joined together into one viral entity. While this appears as a rule for animal viruses, the majority of segmented plant viruses package their genomic segments individually. To ensure a productive infection, all viral particles and thereby all segments have to be present in the same cell. Progression of the virus within the plant requires as well a concerted genome preservation to avoid loss of function. In this review, we will discuss the "life aspects" of chosen phytoviruses and argue for the existence of RNA-RNA interactions that drive the preservation of viral genome integrity while the virus progresses in the plant.

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.

Allosteric Control of Icosahedral Capsid Assembly

During the life cycle of a virus, viral proteins and other components self-assemble to form an ordered protein shell called a capsid. This assembly process is subject to multiple competing constraints, including the need to form a thermostable shell while avoiding kinetic traps. It has been proposed that viral assembly satisfies these constraints through allosteric regulation, including the interconversion of capsid proteins among conformations with different propensities for assembly. In this article, we use computational and theoretical modeling to explore how such allostery affects the assembly of icosahedral shells. We simulate assembly under a wide range of protein concentrations, protein binding affinities, and two different mechanisms of allosteric control. We find that above a threshold strength of allosteric control, assembly becomes robust over a broad range of subunit binding affinities and concentrations, allowing the formation of highly thermostable capsids. Our results suggest that allostery can significantly shift the range of protein binding affinities that lead to successful assembly and thus should be taken into account in models that are used to estimate interaction parameters from experimental data.

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.

Identification of novel RNA secondary structures within the hepatitis C virus genome reveals a cooperative involvement in genome packaging

The specific packaging of the hepatitis C virus (HCV) genome is hypothesised to be driven by Core-RNA interactions. To identify the regions of the viral genome involved in this process, we used SELEX (systematic evolution of ligands by exponential enrichment) to identify RNA aptamers which bind specifically to Core in vitro. Comparison of these aptamers to multiple HCV genomes revealed the presence of a conserved terminal loop motif within short RNA stem-loop structures. We postulated that interactions of these motifs, as well as sub-motifs which were present in HCV genomes at statistically significant levels, with the Core protein may drive virion assembly. We mutated 8 of these predicted motifs within the HCV infectious molecular clone JFH-1, thereby producing a range of mutant viruses predicted to possess altered RNA secondary structures. RNA replication and viral titre were unaltered in viruses possessing only one mutated structure. However, infectivity titres were decreased in viruses possessing a higher number of mutated regions. This work thus identified multiple novel RNA motifs which appear to contribute to genome packaging. We suggest that these structures act as cooperative packaging signals to drive specific RNA encapsidation during HCV assembly.

Bacteriophage MS2 genomic RNA encodes an assembly instruction manual for its capsid

Using RNA-coat protein crosslinking we have shown that the principal RNA recognition surface on the interior of infectious MS2 virions overlaps with the known peptides that bind the high affinity translational operator, TR, within the phage genome. The data also reveal the sequences of genomic fragments in contact with the coat protein shell. These show remarkable overlap with previous predictions based on the hypothesis that virion assembly is mediated by multiple sequences-specific contacts at RNA sites termed Packaging Signals (PSs). These PSs are variations on the TR stem-loop sequence and secondary structure. They act co-operatively to regulate the dominant assembly pathway and ensure cognate RNA encapsidation. In MS2, they also trigger conformational change in the dimeric capsomere creating the A/B quasi-conformer, 60 of which are needed to complete the T=3 capsid. This is the most compelling demonstration to date that this ssRNA virus, and by implications potentially very many of them, assemble via a PS-mediated assembly mechanism.

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.

Interaction of Virus-Like Particles with Vesicles Containing Glycolipids: Kinetics of Detachment

Many viruses interact with their host cells via glycosphingolipids (GSLs) and/or glycoproteins present on the outer cell membrane. This highly specific interaction includes virion attachment and detachment. The residence time determined by the detachment is particularly interesting, since it is directly related to internalization and infection as well as to virion egress and spreading. In an attempt to deepen the understanding of virion detachment kinetics, we have used total internal reflection fluorescence (TIRF) microscopy to probe the interaction between individual fluorescently labeled GSL-containing lipid vesicles and surface-bound virus-like particles (VLPs) of a norovirus genotype II.4 strain. The distribution of the VLP-vesicle residence time was investigated for seven naturally occurring GSLs, all of which are candidates for the not yet identified receptor(s) mediating norovirus entry into host cells. As expected for interactions involving multiple GSL binding sites at a viral capsid, the detachment kinetics displayed features typical for a broad activation-energy distribution for all GSLs. Detailed inspection of these distributions revealed significant differences among the different GSLs. The results are discussed in terms of strength of the interaction, vesicle size, as well as spatial distribution and clustering of GSLs in the vesicle membrane.

An implementation of the Gillespie algorithm for RNA kinetics with logarithmic time update

In this paper I outline a fast method called KFOLD for implementing the Gillepie algorithm to stochastically sample the folding kinetics of an RNA molecule at single base-pair resolution. In the same fashion as the KINFOLD algorithm, which also uses the Gillespie algorithm to predict folding kinetics, KFOLD stochastically chooses a new RNA secondary structure state that is accessible from the current state by a single base-pair addition/deletion following the Gillespie procedure. However, unlike KINFOLD, the KFOLD algorithm utilizes the fact that many of the base-pair addition/deletion reactions and their corresponding rates do not change between each step in the algorithm. This allows KFOLD to achieve a substantial speed-up in the time required to compute a prediction of the folding pathway and, for a fixed number of base-pair moves, performs logarithmically with sequence size. This increase in speed opens up the possibility of studying the kinetics of much longer RNA sequences at single base-pair resolution while also allowing for the RNA folding statistics of smaller RNA sequences to be computed much more quickly.

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.

Asymmetric genome organization in an RNA virus revealed via graph-theoretical analysis of tomographic data

Cryo-electron microscopy permits 3-D structures of viral pathogens to be determined in remarkable detail. In particular, the protein containers encapsulating viral genomes have been determined to high resolution using symmetry averaging techniques that exploit the icosahedral architecture seen in many viruses. By contrast, structure determination of asymmetric components remains a challenge, and novel analysis methods are required to reveal such features and characterize their functional roles during infection. Motivated by the important, cooperative roles of viral genomes in the assembly of single-stranded RNA viruses, we have developed a new analysis method that reveals the asymmetric structural organization of viral genomes in proximity to the capsid in such viruses. The method uses geometric constraints on genome organization, formulated based on knowledge of icosahedrally-averaged reconstructions and the roles of the RNA-capsid protein contacts, to analyse cryo-electron tomographic data. We apply this method to the low-resolution tomographic data of a model virus and infer the unique asymmetric organization of its genome in contact with the protein shell of the capsid. This opens unprecedented opportunities to analyse viral genomes, revealing conserved structural features and mechanisms that can be targeted in antiviral drug design.

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.

Applying molecular crowding models to simulations of virus capsid assembly in vitro

Virus capsid assembly has been widely studied as a biophysical system, both for its biological and medical significance and as an important model for complex self-assembly processes. No current technology can monitor assembly in detail and what information we have on assembly kinetics comes exclusively from in vitro studies. There are many differences between the intracellular environment and that of an in vitro assembly assay, however, that might be expected to alter assembly pathways. Here, we explore one specific feature characteristic of the intracellular environment and known to have large effects on macromolecular assembly processes: molecular crowding. We combine prior particle simulation methods for estimating crowding effects with coarse-grained stochastic models of capsid assembly, using the crowding models to adjust kinetics of capsid simulations to examine possible effects of crowding on assembly pathways. Simulations suggest a striking difference depending on whether or not a system uses nucleation-limited assembly, with crowding tending to promote off-pathway growth in a nonnucleation-limited model but often enhancing assembly efficiency at high crowding levels even while impeding it at lower crowding levels in a nucleation-limited model. These models may help us understand how complicated assembly systems may have evolved to function with high efficiency and fidelity in the densely crowded environment of the cell.

Building polyhedra by self-assembly: theory and experiment

We investigate the utility of a mathematical framework based on discrete geometry to model biological and synthetic self-assembly. Our primary biological example is the self-assembly of icosahedral viruses; our synthetic example is surface-tension-driven self-folding polyhedra. In both instances, the process of self-assembly is modeled by decomposing the polyhedron into a set of partially formed intermediate states. The set of all intermediates is called the configuration space, pathways of assembly are modeled as paths in the configuration space, and the kinetics and yield of assembly are modeled by rate equations, Markov chains, or cost functions on the configuration space. We review an interesting interplay between biological function and mathematical structure in viruses in light of this framework. We discuss in particular: (i) tiling theory as a coarse-grained description of all-atom models; (ii) the building game-a growth model for the formation of polyhedra; and (iii) the application of these models to the self-assembly of the bacteriophage MS2. We then use a similar framework to model self-folding polyhedra. We use a discrete folding algorithm to compute a configuration space that idealizes surface-tension-driven self-folding and analyze pathways of assembly and dominant intermediates. These computations are then compared with experimental observations of a self-folding dodecahedron with side 300 μm. In both models, despite a combinatorial explosion in the size of the configuration space, a few pathways and intermediates dominate self-assembly. For self-folding polyhedra, the dominant intermediates have fewer degrees of freedom than comparable intermediates, and are thus more rigid. The concentration of assembly pathways on a few intermediates with distinguished geometric properties is biologically and physically important, and suggests deeper mathematical structure.

Using Markov state models to study self-assembly

Markov state models (MSMs) have been demonstrated to be a powerful method for computationally studying intramolecular processes such as protein folding and macromolecular conformational changes. In this article, we present a new approach to construct MSMs that is applicable to modeling a broad class of multi-molecular assembly reactions. Distinct structures formed during assembly are distinguished by their undirected graphs, which are defined by strong subunit interactions. Spatial inhomogeneities of free subunits are accounted for using a recently developed Gaussian-based signature. Simplifications to this state identification are also investigated. The feasibility of this approach is demonstrated on two different coarse-grained models for virus self-assembly. We find good agreement between the dynamics predicted by the MSMs and long, unbiased simulations, and that the MSMs can reduce overall simulation time by orders of magnitude.

Solving a Levinthal's paradox for virus assembly identifies a unique antiviral strategy

One of the important puzzles in virology is how viruses assemble the protein containers that package their genomes rapidly and efficiently in vivo while avoiding triggering their hosts' antiviral defenses. Viral assembly appears directed toward a relatively small subset of the vast number of all possible assembly intermediates and pathways, akin to Levinthal's paradox for the folding of polypeptide chains. Using an in silico assembly model, we demonstrate that this reduction in complexity can be understood if aspects of in vivo assembly, which have mostly been neglected in in vitro experimental and theoretical modeling assembly studies, are included in the analysis. In particular, we show that the increasing viral coat protein concentration that occurs in infected cells plays unexpected and vital roles in avoiding potential kinetic assembly traps, significantly reducing the number of assembly pathways and assembly initiation sites, and resulting in enhanced assembly efficiency and genome packaging specificity. Because capsid assembly is a vital determinant of the overall fitness of a virus in the infection process, these insights have important consequences for our understanding of how selection impacts on the evolution of viral quasispecies. These results moreover suggest strategies for optimizing the production of protein nanocontainers for drug delivery and of virus-like particles for vaccination. We demonstrate here in silico that drugs targeting the specific RNA-capsid protein contacts can delay assembly, reduce viral load, and lead to an increase of misencapsidation of cellular RNAs, hence opening up unique avenues for antiviral therapy.

The asymmetric structure of an icosahedral virus bound to its receptor suggests a mechanism for genome release

Simple, spherical RNA viruses have well-understood, symmetric protein capsids, but little structural information is available for their asymmetric components, such as minor proteins and their genomes, which are vital for infection. Here, we report an asymmetric structure of bacteriophage MS2, attached to its receptor, the F-pilus. Cryo-electron tomography and subtomographic averaging of such complexes result in a structure containing clear density for the packaged genome, implying that the conformation of the genome is the same in each virus particle. The data also suggest that the single-copy viral maturation protein breaks the symmetry of the capsid, occupying a position that would be filled by a coat protein dimer in an icosahedral shell. This capsomere can thus fulfill its known biological roles in receptor and genome binding and suggests an exit route for the genome during infection.

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The asymmetric structure of a virus receptor complex is described

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The density for ordered genomic RNA was observed in the structure

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Viral maturation protein was visualized

Nonicosahedral pathways for capsid expansion

For a significant number of viruses a structural transition of the protein container that encapsulates the viral genome forms an important part of the life cycle and is a prerequisite for the particle becoming infectious. Despite many recent efforts the mechanism of this process is still not fully understood, and a complete characterization of the expansion pathways is still lacking. We present here a coarse-grained model that captures the essential features of the expansion process and allows us to investigate the conditions under which a viral capsid becomes unstable. Based on this model we demonstrate that the structural transitions in icosahedral viral capsids are likely to occur through a low-symmetry cascade of local expansion events spreading in a wavelike manner over the capsid surface.

Packaging signals in two single-stranded RNA viruses imply a conserved assembly mechanism and geometry of the packaged genome

The current paradigm for assembly of single-stranded RNA viruses is based on a mechanism involving non-sequence-specific packaging of genomic RNA driven by electrostatic interactions. Recent experiments, however, provide compelling evidence for sequence specificity in this process both in vitro and in vivo. The existence of multiple RNA packaging signals (PSs) within viral genomes has been proposed, which facilitates assembly by binding coat proteins in such a way that they promote the protein-protein contacts needed to build the capsid. The binding energy from these interactions enables the confinement or compaction of the genomic RNAs. Identifying the nature of such PSs is crucial for a full understanding of assembly, which is an as yet untapped potential drug target for this important class of pathogens. Here, for two related bacterial viruses, we determine the sequences and locations of their PSs using Hamiltonian paths, a concept from graph theory, in combination with bioinformatics and structural studies. Their PSs have a common secondary structure motif but distinct consensus sequences and positions within the respective genomes. Despite these differences, the distributions of PSs in both viruses imply defined conformations for the packaged RNA genomes in contact with the protein shell in the capsid, consistent with a recent asymmetric structure determination of the MS2 virion. The PS distributions identified moreover imply a preferred, evolutionarily conserved assembly pathway with respect to the RNA sequence with potentially profound implications for other single-stranded RNA viruses known to have RNA PSs, including many animal and human pathogens.

A new paradigm for the roles of the genome in ssRNA viruses

Recent work with RNA phages and an ssRNA plant satellite virus challenges the widely held view that the sequences and structures of genomic RNAs are unimportant for virion assembly. In the T=3 phages, RNA–coat protein interactions occur throughout the genome, defining the quasiconformers of their protein shells. In the plant virus, there are multiple packaging signals dispersed throughout the genome that overcome electrostatic barriers to protein self-assembly. Both viral coat proteins cause the solution structures of their cognate genomes to collapse into a form that is readily encapsidated in a two-stage assembly process. Such similar behavior in two structurally unrelated viral protein folds implies that this might be a conserved feature of many viral assembly reactions. These results suggest a highly defined structure for the RNA in the virions, consistent with recent structural studies. They also have implications both for subsequent genome release during infection and for the evolution of viral sequences.

Packaging signals in single-stranded RNA viruses: nature's alternative to a purely electrostatic assembly mechanism

The formation of a protective protein container is an essential step in the life-cycle of most viruses. In the case of single-stranded (ss)RNA viruses, this step occurs in parallel with genome packaging in a co-assembly process. Previously, it had been thought that this process can be explained entirely by electrostatics. Inspired by recent single-molecule fluorescence experiments that recapitulate the RNA packaging specificity seen in vivo for two model viruses, we present an alternative theory, which recognizes the important cooperative roles played by RNA–coat protein interactions, at sites we have termed packaging signals. The hypothesis is that multiple copies of packaging signals, repeated according to capsid symmetry, aid formation of the required capsid protein conformers at defined positions, resulting in significantly enhanced assembly efficiency. The precise mechanistic roles of packaging signal interactions may vary between viruses, as we have demonstrated for MS2 and STNV. We quantify the impact of packaging signals on capsid assembly efficiency using a dodecahedral model system, showing that heterogeneous affinity distributions of packaging signals for capsid protein out-compete those of homogeneous affinities. These insights pave the way to a new anti-viral therapy, reducing capsid assembly efficiency by targeting of the vital roles of the packaging signals, and opens up new avenues for the efficient construction of protein nanocontainers in bionanotechnology.