Micelle formation and crystallization as paradigms for virus assembly

Seeing Biomolecular Condensates Through the Lens of Viruses

Phase separation of viral biopolymers is a key factor in the formation of cytoplasmic viral inclusions, known as sites of virus replication and assembly. This review describes the mechanisms and factors that affect phase separation in viral replication and identifies potential areas for future research. Drawing inspiration from studies on cellular RNA-rich condensates, we compare the hierarchical coassembly of ribosomal RNAs and proteins in the nucleolus to the coordinated coassembly of viral RNAs and proteins taking place within viral factories in viruses containing segmented RNA genomes. We highlight the common characteristics of biomolecular condensates in viral replication and how this new understanding is reshaping our views of virus assembly mechanisms. Such studies have the potential to uncover unexplored antiviral strategies targeting these phase-separated states.

Relaxational dynamics of the T-number conversion of virus capsids

We extend a recently proposed kinetic theory of virus capsid assembly based on Model A kinetics and study the dynamics of the interconversion of virus capsids of different sizes triggered by a quench, that is, by sudden changes in the solution conditions. The work is inspired by in vitro experiments on functionalized coat proteins of the plant virus cowpea chlorotic mottle virus, which undergo a reversible transition between two different shell sizes (T = 1 and T = 3) upon changing the acidity and salinity of the solution. We find that the relaxation dynamics are governed by two time scales that, in almost all cases, can be identified as two distinct processes. Initially, the monomers and one of the two types of capsids respond to the quench. Subsequently, the monomer concentration remains essentially constant, and the conversion between the two capsid species completes. In the intermediate stages, a long-lived metastable steady state may present itself, where the thermodynamically less stable species predominate. We conclude that a Model A based relaxational model can reasonably describe the early and intermediate stages of the conversion experiments. However, it fails to provide a good representation of the time evolution of the state of assembly of the coat proteins in the very late stages of equilibration when one of the two species disappears from the solution. It appears that explicitly incorporating the nucleation barriers to assembly and disassembly is crucial for an accurate description of the experimental findings, at least under conditions where these barriers are sufficiently large.

Vital for Viruses: Intrinsically Disordered Proteins

Viruses infect all kingdoms of life; their genomes vary from DNA to RNA and in size from 2kB to 1 MB or more. Viruses frequently employ disordered proteins, that is, protein products of virus genes that do not themselves fold into independent three-dimensional structures, but rather, constitute a versatile molecular toolkit to accomplish a range of functions necessary for viral infection, assembly, and proliferation. Interestingly, disordered proteins have been discovered in almost all viruses so far studied, whether the viral genome consists of DNA or RNA, and whatever the configuration of the viral capsid or other outer covering. In this review, I present a wide-ranging set of stories illustrating the range of functions of IDPs in viruses. The field is rapidly expanding, and I have not tried to include everything. What is included is meant to be a survey of the variety of tasks that viruses accomplish using disordered proteins.

Electrostatic Theory of the Acidity of the Solution in the Lumina of Viruses and Virus-Like Particles

Recently, Maassen et al. measured an appreciable pH difference between the bulk solution and the solution in the lumen of virus-like particles, self-assembled in an aqueous buffer solution containing the coat proteins of a simple plant virus and polyanions (Maassen, S. J.; et al. Small 2018, 14, 1802081). They attribute this to the Donnan effect, caused by an imbalance between the number of negative charges on the encapsulated polyelectrolyte molecules and the number of positive charges on the RNA binding domains of the coat proteins that make up the virus shell or capsid. By applying Poisson-Boltzmann theory, we confirm this conclusion and show that simple Donnan theory is accurate even for the smallest of viruses and virus-like particles. This, in part, is due to the additional screening caused by the presence of a large number of immobile charges in the cavity of the shell. The presence of a net charge on the outer surface of the capsid we find in practice to not have a large effect on the pH shift. Hence, Donnan theory can indeed be applied to connect the local pH and the amount of encapsulated material. The large shifts up to a full pH unit that we predict must have consequences for applications of virus capsids as nanocontainers in bionanotechnology and artificial cell organelles.

Structures of additional crystal forms of Satellite tobacco mosaic virus grown from a variety of salts

The structures of new crystal forms of Satellite tobacco mosaic virus (STMV) are described. These belong to space groups I2, P21212 (a low-resolution form), R3 (H3) and P23. The R3 crystals are 50%/50% twinned, as are two instances of the P23 crystals. The I2 and P21212 crystals were grown from ammonium sulfate solutions, as was one crystal in space group P23, while the R3 and the other P23 crystals were grown from sodium chloride, sodium bromide and sodium nitrate. The monoclinic and orthorhombic crystals have half a virus particle as the asymmetric unit, while the rhombohedral and cubic crystals have one third of a virus particle. RNA segments organized about the icosahedral twofold axes were present in crystals grown from ammonium sulfate and sodium chloride, as in the canonical I222 crystals (PDB entry 4oq8), but were not observed in crystals grown from sodium bromide and sodium nitrate. Bromide and nitrate ions generally replaced the RNA phosphates present in the I222 crystals, including the phosphates seen on fivefold axes, and were also found at threefold vertices in both the rhombohedral and cubic forms. An additional anion was also found on the fivefold axis 5 Å from the first anion, and slightly outside the capsid in crystals grown from sodium chloride, sodium bromide and sodium nitrate, suggesting that the path along the symmetry axis might be an ion channel. The electron densities for RNA strands at individual icosahedral dyads, as well as at the amino-terminal peptides of protein subunits, exhibited a diversity of orientations, in particular the residues at the ends.

Crystal structure of the potato leafroll virus coat protein and implications for viral assembly

Luteoviruses, poleroviruses, and enamoviruses are insect-transmitted, agricultural pathogens that infect a wide array of plants, including staple food crops. Previous cryo-electron microscopy studies of virus-like particles show that luteovirid viral capsids are built from a structural coat protein that organizes with T = 3 icosahedral symmetry. Here, we present the crystal structure of a truncated version of the coat protein monomer from potato leafroll virus at 1.80-Å resolution. In the crystal lattice, monomers pack into flat sheets that preserve the two-fold and three-fold axes of icosahedral symmetry and show minimal structural deviations when compared to the full-length subunits of the assembled virus-like particle. These observations have important implications in viral assembly and maturation and suggest that the CP N-terminus and its interactions with RNA play an important role in generating capsid curvature.

An Ultrastable Virus-Like Particle with a Carbon Dot Core and Expanded Sequence Plasticity

Ordered bio-inorganic hybridization has evolved for the generation of high-performance materials in living organisms and inspires novel strategies to design artificial hybrid materials. Virus-like particles (VLPs) are attracting extensive interest as self-assembling systems and platforms in the fields of biotechnology and nanotechnology. However, as soft nanomaterials, their structural stability remains a general and fundamental problem in various applications. Here, an ultrastable VLP assembled from the major capsid protein (VP1) of simian virus 40 is reported, which contains a carbon dot (C-dot) core. Co-assembly of VP1 with C-dots led to homogeneous T = 1 VLPs with a fourfold increase in VLP yields. The resultant hybrid VLPs showed markedly enhanced structural stability and sequence plasticity. C-dots and a polyhistidine tag fused to the inner-protruding N-terminus of VP1 contributed synergistically to these enhancements, where extensive and strong noncovalent interactions on the C-dot/VP1 interfaces are responsible according to cryo-EM 3D reconstruction, molecular simulation, and affinity measurements. C-dot-enhanced ultrastable VLPs can serve as a new platform, enabling the fabrication of new architectures for bioimaging, theranostics, nanovaccines, etc. The hybridization strategy is simple and can easily be extended to other VLPs and protein nanoparticle systems.

Physics of viral dynamics

Viral capsids are often regarded as inert structural units, but in actuality they display fascinating dynamics during different stages of their life cycle. With the advent of single-particle approaches and high-resolution techniques, it is now possible to scrutinize viral dynamics during and after their assembly and during the subsequent development pathway into infectious viruses. In this Review, the focus is on the dynamical properties of viruses, the different physical virology techniques that are being used to study them, and the physical concepts that have been developed to describe viral dynamics.

Geometric architecture of viruses

In the current SARS-CoV-2 disease (COVID-19) pandemic, the structural understanding of new emerging viruses in relation to developing effective treatment and interventions are very necessary. Viruses present remarkable differences in geometric shapes, sizes, molecular compositions and organizations. A detailed structural knowledge of a virion is essential for understanding the mechanisms of capsid assembly/disassembly, antigenicity, cell-receptor interaction, and designing therapeutic strategies. X-ray crystallography, cryo-electron microscopy and molecular simulations have elucidated atomic-level structure of several viruses. In view of this, a recently determined crystal structure of SARS-CoV-2 nucleocapsid has revealed its architecture and self-assembly very similar to that of the SARS-CoV-1 and the Middle-East respiratory syndrome virus (MERS-CoV). In structure determination, capsid symmetry is an important factor greatly contributing to its stability and balance between the packaged genome and envelope. Since the capsid protein subunits are asymmetrical, the maximum number of inter-subunit interactions can be established only when they are arranged symmetrically. Therefore, a stable capsid must be in a perfect symmetry and lowest possible free-energy. Isometric virions are spherical but geometrically icosahedrons as compared to complex virions that are both isometric and helical. Enveloped icosahedral or helical viruses are very common in animals but rare in plants and bacteria. Icosahedral capsids are defined by triangulation number (T = 1, 3, 4, 13, etc.), i.e., the identical equilateral-triangles formed of subunits. Biologically significant defective capsids with or without nucleic acids are common in enveloped alpha-, flavi- and hepadnaviruses. The self-assembling, stable and non-infectious virus-like particles have been widely exploited as vaccine candidates and therapeutic molecules delivery vehicles.

Protein cage assembly across multiple length scales

Within the materials science community, proteins with cage-like architectures are being developed as versatile nanoscale platforms for use in protein nanotechnology. Much effort has been focused on the functionalization of protein cages with biological and non-biological moieties to bring about new properties of not only individual protein cages, but collective bulk-scale assemblies of protein cages. In this review, we report on the current understanding of protein cage assembly, both of the cages themselves from individual subunits, and the assembly of the individual protein cages into higher order structures. We start by discussing the key properties of natural protein cages (for example: size, shape and structure) followed by a review of some of the mechanisms of protein cage assembly and the factors that influence it. We then explore the current approaches for functionalizing protein cages, on the interior or exterior surfaces of the capsids. Lastly, we explore the emerging area of higher order assemblies created from individual protein cages and their potential for new and exciting collective properties.

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.

Hybrid Assembly toward Enhanced Thermal Stability of Virus-like Particles and Antibacterial Activity of Polyoxometalates

In an effort to improve both the stability of virus-like particles (VLPs) and the medical activity of polyoxometalates (POMs), a new hybrid assembly system between human papillomavirus (HPV) capsid protein L1 and a europium-containing POM (EuW₁₀) has been constructed, for the first time, via the electrostatic interactions between them. The co-assembly of EuW₁₀ and HPV 16 L1-pentamer (L1-p) in buffer solution resulted in the encapsulation of POMs in the cavity of VLPs, which was further confirmed by cesium chloride (CsCl) gradient ultracentrifugation, SDS-PAGE, dynamic light scattering, and transmission electron microscopy, whereas the post-assembly of EuW₁₀ with the as-prepared VLPs leads to the adsorption of POMs only on the external surface of particles, and both cases improved the thermal and storage stabilities of VLPs obviously. Particularly, the encapsulation of POMs in VLPs largely improved the antibacterial activity of EuW₁₀, and thereby, the present study will be significant for both the stability improvement of protein vaccines and the development of POM medicine.

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.

Computational virology: From the inside out

Viruses typically pack their genetic material within a protein capsid. Enveloped viruses also have an outer membrane made up of a lipid bilayer and membrane-spanning glycoproteins. X-ray diffraction and cryoelectron microscopy provide high resolution static views of viral structure. Molecular dynamics (MD) simulations may be used to provide dynamic insights into the structures of viruses and their components. There have been a number of simulations of viral capsids and (in some cases) of the inner core of RNA or DNA packaged within them. These simulations have generally focussed on the structural integrity and stability of the capsid and/or on the influence of the nucleic acid core on capsid stability. More recently there have been a number of simulation studies of enveloped viruses, including HIV-1, influenza A, and dengue virus. These have addressed the dynamic behaviour of the capsid, the matrix, and/or of the outer envelope. Analysis of the dynamics of the lipid bilayer components of the envelopes of influenza A and of dengue virus reveals a degree of biophysical robustness, which may contribute to the stability of virus particles in different environments. Significant computational challenges need to be addressed to aid simulation of complex viruses and their membranes, including the need to integrate structural data from a range of sources to enable us to move towards simulations of intact virions. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Equilibrium self-assembly of small RNA viruses

We propose a description for the quasiequilibrium self-assembly of small, single-stranded (ss) RNA viruses whose capsid proteins (CPs) have flexible, positively charged, disordered tails that associate with the negatively charged RNA genome molecules. We describe the assembly of such viruses as the interplay between two coupled phase-transition-like events: the formation of the protein shell (the capsid) by CPs and the condensation of a large ss viral RNA molecule. Electrostatic repulsion between the CPs competes with attractive hydrophobic interactions and attractive interaction between neutralized RNA segments mediated by the tail groups. An assembly diagram is derived in terms of the strength of attractive interactions between CPs and between CPs and the RNA molecules. It is compared with the results of recent studies of viral assembly. We demonstrate that the conventional theory of self-assembly, which does describe the assembly of empty capsids, is in general not applicable to the self-assembly of RNA-encapsidating virions.

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?

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.

Modeling Viral Capsid Assembly

I present a review of the theoretical and computational methodologies that have been used to model the assembly of viral capsids. I discuss the capabilities and limitations of approaches ranging from equilibrium continuum theories to molecular dynamics simulations, and I give an overview of some of the important conclusions about virus assembly that have resulted from these modeling efforts. Topics include the assembly of empty viral shells, assembly around single-stranded nucleic acids to form viral particles, and assembly around synthetic polymers or charged nanoparticles for nanotechnology or biomedical applications. I present some examples in which modeling efforts have promoted experimental breakthroughs, as well as directions in which the connection between modeling and experiment can be strengthened.

Role of charge regulation and size polydispersity in nanoparticle encapsulation by viral coat proteins

Nanoparticles can be encapsulated by virus coat proteins if their surfaces are functionalized to acquire a sufficiently large negative charge. A minimal surface charge is required to overcome (i) repulsive interactions between the positively charged RNA-binding domains on the proteins and (ii) the loss of mixing and translational entropy of RNA and capsid coat proteins. Here, we present a model describing the encapsulation of spherical particles bearing weakly acidic surface groups and investigate how charge regulation and size polydispersity impact upon the encapsulation efficiency of gold nanoparticles by model coat proteins. We show that the surface charge density of these particles cannot be assumed fixed, but that it adjusts itself to minimize electrostatic repulsion between the charges on them and maximize the attractive interaction with the RNA binding domains on the proteins. Charge regulation in combination with the natural variation of particle radii has a large effect on the encapsulation efficiency: it makes it much more gradual despite its inherently cooperative nature. Our calculations rationalize recent experimental observations on the coassembly of gold nanoparticles by brome mosaic virus coat proteins.

Pathways for virus assembly around nucleic acids

Understanding the pathways by which viral capsid proteins assemble around their genomes could identify key intermediates as potential drug targets. In this work, we use computer simulations to characterize assembly over a wide range of capsid protein-protein interaction strengths and solution ionic strengths. We find that assembly pathways can be categorized into two classes, in which intermediates are either predominantly ordered or disordered. Our results suggest that estimating the protein-protein and the protein-genome binding affinities may be sufficient to predict which pathway occurs. Furthermore, the calculated phase diagrams suggest that knowledge of the dominant assembly pathway and its relationship to control parameters could identify optimal strategies to thwart or redirect assembly to block infection. Finally, analysis of simulation trajectories suggests that the two classes of assembly pathways can be distinguished in single-molecule fluorescence correlation spectroscopy or bulk time-resolved small-angle X-ray scattering experiments.

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).

RNA topology remolds electrostatic stabilization of viruses

Simple RNA viruses efficiently encapsulate their genome into a nano-sized protein shell: the capsid. Spontaneous coassembly of the genome and the capsid proteins is driven predominantly by electrostatic interactions between the negatively charged RNA and the positively charged inner capsid wall. Using field theoretic formulation we show that the inherently branched RNA secondary structure allows viruses to maximize the amount of encapsulated genome and make assembly more efficient, allowing viral RNAs to out-compete cellular RNAs during replication in infected host cells.

The assembly pathway of an icosahedral single-stranded RNA virus depends on the strength of inter-subunit attractions

The strength of attraction between capsid proteins (CPs) of cowpea chlorotic mottle virus (CCMV) is controlled by the solution pH. Additionally, the strength of attraction between CP and the single-stranded RNA viral genome is controlled by ionic strength. By exploiting these properties, we are able to control and monitor the in vitro co-assembly of CCMV CP and single-stranded RNA as a function of the strength of CP-CP and CP-RNA attractions. Using the techniques of velocity sedimentation and electron microscopy, we find that the successful assembly of nuclease-resistant virus-like particles (VLPs) depends delicately on the strength of CP-CP attraction relative to CP-RNA attraction. If the attractions are too weak, the capsid cannot form; if they are too strong, the assembly suffers from kinetic traps. Separating the process into two steps-by first turning on CP-RNA attraction and then turning on CP-CP attraction-allows for the assembly of well-formed VLPs under a wide range of attraction strengths. These observations establish a protocol for the efficient in vitro assembly of CCMV VLPs and suggest potential strategies that the virus may employ in vivo.

To build a virus on a nucleic acid substrate

Many viruses package their genomes concomitant with assembly. Here, we show that this reaction can be described by three coefficients: association of capsid protein (CP) to nucleic acid (NA), KNA; CP-CP interaction, ω; and α, proportional to the work required to package NA. The value of α can vary as NA is packaged. A phase diagram of average lnα versus lnω identifies conditions where assembly is likely to fail or succeed. NA morphology can favor (lnα > 0) or impede (lnα < 0) assembly. As lnω becomes larger, capsids become more stable and assembly becomes more cooperative. Where (lnα + lnω) < 0, the CP is unable to contain the NA, so that assembly results in aberrant particles. This phase diagram is consistent with quantitative studies of cowpea chlorotic mottle virus, hepatitis B virus, and simian virus 40 assembling on ssRNA and dsDNA substrates. Thus, the formalism we develop is suitable for describing and predicting behavior of experimental studies of CP assembly on NA.

Budding pathway in the templated assembly of viruslike particles

A new pathway for the assembly of viral capsid protein around inorganic nanoparticle cores was observed by time-course light scattering and cryo-electron tomography. Gold nanoparticles with an average diameter of 11.3 nm have been used as a template for the assembly of Brome mosaic virus (BMV) capsid protein at different concentrations. At least at low protein concentrations the kinetic features of the scattering and extinction measurements are consistent with the initial rapid formation of large nanoparticle-protein clusters, which subsequently separate into individual viruslike particles (VLPs). The occurrence of multiparticle clusters at short times after mixing nanoparticles and proteins was confirmed by cryo-EM. Cryo-electron tomography of the multiparticle clusters yielded an average surface-to-surface interparticle distance of ∼7.5 nm, equivalent to ∼1.5 times the thickness of a protein shell. We propose a scenario in which VLP generation may take place through monomer exchange between aggregated particles with defect-ridden or incomplete shells, leading to the formation of stable icosahedral shells, which eventually bud off the aggregate. Together with results from previous works, the findings highlight the astonishing versatility of plant virus capsid protein assembly. This previously unknown mechanism for VLP formation has features that may have relevance for the crowded environment characterizing virus factories in the cell.

Impact of the topology of viral RNAs on their encapsulation by virus coat proteins

Single-stranded RNAs of simple viruses seem to be topologically more compact than other types of single-stranded RNA. It has been suggested that this has an evolutionary purpose: more compact structures are more easily encapsulated in the limited space that the cavity of the virus capsid offers. We employ a simple Flory theory to calculate the optimal amount of polymers confined in a viral shell. We find that the free energy gain or more specifically the efficiency of RNA encapsidation increases substantially with topological compactness. We also find that the optimal length of RNA encapsidated in a capsid increases with the degree of branching of the genome even though this effect is very weak. Further, we show that if the structure of the branching of the polymer is allowed to anneal, the optimal loading increases substantially.

The crystallographic structure of Panicum Mosaic Virus (PMV)

The structure of Panicum Mosaic Virus (PMV) was determined by X-ray diffraction analysis to 2.9Å resolution. The crystals were of pseudo symmetry F23; the true crystallographic unit cell was of space group P2(1) with a=411.7Å, b=403.9Å and c=412.5Å, with β=89.7°. The asymmetric unit was two entire T=3 virus particles, or 360 protein subunits. The structure was solved by conventional molecular replacement from two distant homologues, Cocksfoot Mottle Virus (CfMV) and Tobacco Necrosis Virus (TNV), of ∼20% sequence identity followed by phase extension. The model was initially refined with exact icosahedral constraints and then with icosahedral restraints. The virus has Ca(++) ions octahedrally coordinated by six aspartic acid residues on quasi threefold axes, which is completely different than for either CfMV or TNV. Amino terminal residues 1-53, 1-49 and 1-21 of the A, B and C subunits, respectively, and the four C-terminal residues (239-242) are not visible in electron density maps. The additional ordered residues of the C chain form a prominent "arm" that intertwines with symmetry equivalent "arms" at icosahedral threefold axes, as was seen in both CfMV and TNV. A 17 nucleotide hairpin segment of genomic RNA is icosahedrally ordered and bound at 60 equivalent sites at quasi twofold A-B subunit interfaces at the interior surface of the capsid. This segment of RNA may serve as a conformational switch for coat protein subunits, as has been proposed for similar RNA segments in other viruses.

Theory of supramolecular co-polymerization in a two-component system

As a first step to understand the role of molecular or chemical polydispersity in self-assembly, we put forward a coarse-grained model that describes the spontaneous formation of quasi-linear polymers in solutions containing two self-assembling species. Our theoretical framework is based on a two-component self-assembled Ising model in which the chemical bidispersity, i.e., the presence of two distinct chemical entities, is parameterized in terms of the strengths of the binding free energies that depend on the monomer species involved in the pairing interaction. Depending upon the relative values of the binding free energies involved, different morphologies of assemblies that include both components are formed, exhibiting random, blocky or alternating ordering of the two components in the assemblies. Analyzing the model for the case of blocky ordering, which is of most practical interest, we find that the transition from conditions of minimal assembly to those characterized by strong polymerization can be described by a critical concentration that depends on the concentration ratio of the two species. Interestingly, the distribution of monomers in the assemblies is different from that in the original distribution, i.e., the ratio of the concentrations of the two components put into the system. The monomers with a smaller binding free energy are more abundant in short assemblies and monomers with a larger binding affinity are more abundant in longer assemblies. Under certain conditions the two components congregate into separate supramolecular polymeric species and in that sense phase separate. We find strong deviations from the expected growth law for supramolecular polymers even for modest amounts of a second component, provided it is chemically sufficiently distinct from the main one.

Langevin dynamics simulation of polymer-assisted virus-like assembly

Starting from a coarse grained representation of the building units of the minute virus of mice and a flexible polyelectrolyte molecule, we have explored the mechanism of assembly into icosahedral structures with the help of Langevin dynamics simulations and the parallel tempering technique. Regular icosahedra with appropriate symmetry form only in a narrow range of temperature and polymer length. Within this region of parameters where successful assembly would proceed, we have systematically investigated the growth kinetics. The assembly of icosahedra is found to follow the classical nucleation and growth mechanism in the absence of the polymer, with the three regimes of nucleation, linear growth, and slowing down in the later stage. The calculated average nucleation time obeys the laws expected from the classical nucleation theory. The linear growth rate is found to obey the laws of secondary nucleation as in the case of lamellar growth in polymer crystallization. The same mechanism is seen in the simulations of the assembly of icosahedra in the presence of the polymer as well. The polymer reduces the nucleation barrier significantly by enhancing the local concentration of subunits via adsorbing them on their backbone. The details of growth in the presence of the polymer are also found to be consistent with the classical nucleation theory, despite the smallness of the assembled structures.

In vitro quantification of the relative packaging efficiencies of single-stranded RNA molecules by viral capsid protein

While most T=3 single-stranded RNA (ssRNA) viruses package in vivo about 3,000 nucleotides (nt), in vitro experiments have demonstrated that a broad range of RNA lengths can be packaged. Under the right solution conditions, for example, cowpea chlorotic mottle virus (CCMV) capsid protein (CP) has been shown to package RNA molecules whose lengths range from 100 to 10,000 nt. Furthermore, in each case it can package the RNA completely, as long as the mass ratio of CP to nucleic acid in the assembly mixture is 6:1 or higher. Yet the packaging efficiencies of the RNAs can differ widely, as we demonstrate by measurements in which two RNAs compete head-to-head for a limited amount of CP. We show that the relative efficiency depends nonmonotonically on the RNA length, with 3,200 nt being optimum for packaging by the T=3 capsids preferred by CCMV CP. When two RNAs of the same length-and hence the same charge-compete for CP, differences in packaging efficiency are necessarily due to differences in their secondary structures and/or three-dimensional (3D) sizes. For example, the heterologous RNA1 of brome mosaic virus (BMV) is packaged three times more efficiently by CCMV CP than is RNA1 of CCMV, even though the two RNAs have virtually identical lengths. Finally, we show that in an assembly mixture at neutral pH, CP binds reversibly to the RNA and there is a reversible equilibrium between all the various RNA/CP complexes. At acidic pH, excess protein unbinds from RNA/CP complexes and nucleocapsids form irreversibly.

RNA encapsidation by SV40-derived nanoparticles follows a rapid two-state mechanism

Remarkably, uniform virus-like particles self-assemble in a process that appears to follow a rapid kinetic mechanism. The mechanisms by which spherical viruses assemble from hundreds of capsid proteins around nucleic acid, however, are yet unresolved. Using time-resolved small-angle X-ray scattering (TR-SAXS), we have been able to directly visualize SV40 VP1 pentamers encapsidating short RNA molecules (500mers). This assembly process yields T = 1 icosahedral particles comprised of 12 pentamers and one RNA molecule. The reaction is nearly one-third complete within 35 ms, following a two-state kinetic process with no detectable intermediates. Theoretical analysis of kinetics, using a master equation, shows that the assembly process nucleates at the RNA and continues by a cascade of elongation reactions in which one VP1 pentamer is added at a time, with a rate of approximately 10(9) M(-1) s(-1). The reaction is highly robust and faster than the predicted diffusion limit. The emerging molecular mechanism, which appears to be general to viruses that assemble around nucleic acids, implicates long-ranged electrostatic interactions. The model proposes that the growing nucleo-protein complex acts as an electrostatic antenna that attracts other capsid subunits for the encapsidation process.

Simulating microbial systems: addressing model uncertainty/incompleteness via multiscale and entropy methods

Most systems of interest in the natural and engineering sciences are multiscale in character. Typically available models are incomplete or uncertain. Thus, a probabilistic approach is required. We present a deductive multiscale approach to address such problems, focusing on virus and cell systems to demonstrate the ideas. There is usually an underlying physical model, all factors in which (e.g., particle masses, charges, and force constants) are known. For example, the underlying model can be cast in terms of a collection of N-atoms evolving via Newton's equations. When the number of atoms is 10(6) or more, these physical models cannot be simulated directly. However, one may only be interested in a coarse-grained description, e.g., in terms of molecular populations or overall system size, shape, position, and orientation. The premise of this chapter is that the coarse-grained equations should be derived from the underlying model so that a deductive calibration-free methodology is achieved. We consider a reduction in resolution from a description for the state of N-atoms to one in terms of coarse-grained variables. This implies a degree of uncertainty in the underlying microstates. We present a methodology for modeling microbial systems that integrates equations for coarse-grained variables with a probabilistic description of the underlying fine-scale ones. The implementation of our strategy as a general computational platform (SimEntropics™) for microbial modeling and prospects for developments and applications are discussed.

Atomic force microscopy investigation of viruses

Atomic force microscopy (AFM) has proven to be a valuable approach to delineate the architectures and detailed structural features of a wide variety of viruses. These have ranged from small plant satellite viruses of only 17 nm to the giant mimivirus of 750 nm diameter, and they have included diverse morphologies such as those represented by HIV, icosahedral particles, vaccinia, and bacteriophages. Because it is a surface technique, it provides images and information that are distinct from those obtained by electron microscopy, and in some cases, at even higher resolution. By enzymatic and chemical dissection of virions, internal structures can be revealed, as well as DNA and RNA. The method is relatively rapid and can be carried out on both fixed and unfixed samples in either air or fluids, including culture media. It is nondestructive and even non-perturbing. It can be applied to individual isolated virus, as well as to infected cells. AFM is still in its early development and holds great promise for further investigation of biological systems at the nanometer scale.

Atomic force microscopy in imaging of viruses and virus-infected cells

Atomic force microscopy (AFM) can visualize almost everything pertinent to structural virology and at resolutions that approach those for electron microscopy (EM). Membranes have been identified, RNA and DNA have been visualized, and large protein assemblies have been resolved into component substructures. Capsids of icosahedral viruses and the icosahedral capsids of enveloped viruses have been seen at high resolution, in some cases sufficiently high to deduce the arrangement of proteins in the capsomeres as well as the triangulation number (T). Viruses have been recorded budding from infected cells and suffering the consequences of a variety of stresses. Mutant viruses have been examined and phenotypes described. Unusual structural features have appeared, and the unexpectedly great amount of structural nonconformity within populations of particles has been documented. Samples may be imaged in air or in fluids (including culture medium or buffer), in situ on cell surfaces, or after histological procedures. AFM is nonintrusive and nondestructive, and it can be applied to soft biological samples, particularly when the tapping mode is employed. In principle, only a single cell or virion need be imaged to learn of its structure, though normally images of as many as is practical are collected. While lateral resolution, limited by the width of the cantilever tip, is a few nanometers, height resolution is exceptional, at approximately 0.5 nm. AFM produces three-dimensional, topological images that accurately depict the surface features of the virus or cell under study. The images resemble common light photographic images and require little interpretation. The structures of viruses observed by AFM are consistent with models derived by X-ray crystallography and cryo-EM.

Controlling forces and pathways in self-assembly using viruses and DNA

The ability of both viruses and DNA to self-assemble in solution has continues to enable numerous applications at the nanoscale. Here we review the relevant interactions dictating the assembly of these structures, as well as discussing how they can be exploited experimentally. Because self-assembly is a process, we discuss various strategies for achieving spatial and temporal control. Finally, we highlight a few examples of recent advances that exploit the features of these nanostructures.

Bacterial microcompartments insights into the structure, mechanism, and engineering applications

Bacterial microcompartments are large supramolecular assemblies, resembling viruses in size and shape, found inside many bacterial cells. A protein-based shell encapsulates a series of sequentially acting enzymes in order to sequester certain sensitive metabolic processes within the cell. Crystal structures of the individual shell proteins have revealed details about how they self-assemble and how pores through their centers facilitate molecular transport into and out of the microcompartments. Biochemical and genetic studies have shown that enzymes are directed to the interior in some cases by special targeting sequences in their termini. Together, these findings open up prospects for engineering bacterial microcompartments with novel functionalities for applications ranging from metabolic engineering to targeted drug delivery.

Encapsulation of a polymer by an icosahedral virus

The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication and enable use of capsids in nanomaterials applications. To this end, we perform Brownian dynamics on a coarse-grained model that describes the dynamics of icosahedral capsid assembly around a flexible polymer. We identify several mechanisms by which the polymer plays an active role in its encapsulation, including cooperative polymer-protein motions. These mechanisms are related to experimentally controllable parameters such as polymer length, protein concentration and solution conditions. Furthermore, the simulations demonstrate that assembly mechanisms are correlated with encapsulation efficiency, and we present a phase diagram that predicts assembly outcomes as a function of experimental parameters. We anticipate that our simulation results will provide a framework for designing in vitro assembly experiments on single-stranded RNA virus capsids.

Mechanisms of capsid assembly around a polymer

Capsids of many viruses assemble around nucleic acids or other polymers. Understanding how the properties of the packaged polymer affect the assembly process could promote biomedical efforts to prevent viral assembly or nanomaterials applications that exploit assembly. To this end, we simulate on a lattice the dynamical assembly of closed, hollow shells composed of several hundred to 1000 subunits, around a flexible polymer. We find that assembly is most efficient at an optimum polymer length that scales with the surface area of the capsid; polymers that are significantly longer than optimal often lead to partial-capsids with unpackaged polymer "tails" or a competition between multiple partial-capsids attached to a single polymer. These predictions can be tested with bulk experiments in which capsid proteins assemble around homopolymeric RNA or synthetic polyelectrolytes. We also find that the polymer can increase the net rate of subunit accretion to a growing capsid both by stabilizing the addition of new subunits and by enhancing the incoming flux of subunits; the effects of these processes may be distinguishable with experiments that monitor the assembly of individual capsids.

Biophysical and atomic force microscopy characterization of the RNA from satellite tobacco mosaic virus

Agarose gel electrophoresis, circular dichroism and differential scanning calorimetry showed that single-stranded RNA from satellite tobacco mosaic virus transforms from a conformationally ‘closed state’ at 4°C to a more conformationally ‘open state’ at 65°C. The transition is reversible and shows no hysteresis. Atomic force microscopy (AFM) allowed visualization of the two states and indicated that the conformationally ‘closed state’ probably corresponds to the native encapsidated conformation, and that the ‘open state’ represents a conformation, characterized as short, thick chains of domains, as a consequence of the loss of tertiary interactions. Heating from 75°C to 85°C in the presence of EDTA was necessary to further unravel the ‘open’ conformation RNA into extended chains of lengths >280 nm. Virus exposed to low concentrations of phenol at 65°C, extruded RNA as distinctive ‘pigtails’ in a synchronous fashion, and these ‘pigtails’ then elongated, as the RNA was further discharged by the particles. Moderate concentrations of phenol at 65°C produced complete disruption of virions and only remains of decomposed particles and disordered RNA were evident. AFM images of RNA emerging from disrupted virions appear most consistent with linear arrangements of structural domains.

Role of surface charge density in nanoparticle-templated assembly of bromovirus protein cages

Self-assembling icosahedral protein cages have potentially useful physical and chemical characteristics for a variety of nanotechnology applications, ranging from therapeutic or diagnostic vectors to building blocks for hierarchical materials. For application-specific functional control of protein cage assemblies, a deeper understanding of the interaction between the protein cage and its payload is necessary. Protein-cage encapsulated nanoparticles, with their well-defined surface chemistry, allow for systematic control over key parameters of encapsulation such as the surface charge, hydrophobicity, and size. Independent control over these variables allows experimental testing of different assembly mechanism models. Previous studies done with Brome mosaic virus capsids and negatively charged gold nanoparticles indicated that the result of the self-assembly process depends on the diameter of the particle. However, in these experiments, the surface-ligand density was maintained at saturation levels, while the total charge and the radius of curvature remained coupled variables, making the interpretation of the observed dependence on the core size difficult. The current work furnishes evidence of a critical surface charge density for assembly through an analysis aimed at decoupling the surface charge and the core size.

Understanding the concentration dependence of viral capsid assembly kinetics--the origin of the lag time and identifying the critical nucleus size

The kinetics for the assembly of viral proteins into a population of capsids can be measured in vitro with size exclusion chromatography or dynamic light scattering, but extracting mechanistic information from these studies is challenging. For example, it is not straightforward to determine the critical nucleus size or the elongation time (the time required for a nucleus to grow to completion). In this work, we study theoretical and computational models for capsid assembly to show that the critical nucleus size can be determined from the concentration dependence of the assembly half-life and that the elongation time is revealed by the length of the lag phase. Furthermore, we find that the system becomes kinetically trapped when nucleation becomes fast compared to elongation. Implications of this constraint for determining elongation mechanisms from experimental assembly data are discussed.

Energy landscapes for shells assembled from pentagonal and hexagonal pyramids

We present new rigid body potentials that should favour efficient self-assembly of pentagonal and hexagonal pyramids into icosahedral shells over a wide range of temperature. By adding an extra repulsive site opposite the existing apex sites of the pyramids considered in a previously published model, frustrated energy landscapes are transformed into systems identified with self-assembling properties. The extra interaction may be considered analogous to a hydrophobic-hydrophilic repulsion, as in micelle formation.

Molecular recognition of poly(A) by small ligands: an alternative method of analysis reveals nanomolar, cooperative and shape-selective binding

A few drug-like molecules have recently been found to bind poly(A) and induce a stable secondary structure (T(m) approximately 60 degrees C), even though this RNA homopolymer is single-stranded in the absence of a ligand. Here, we report results from experiments specifically designed to explore the association of small molecules with poly(A). We demonstrate that coralyne, the first small molecule discovered to bind poly(dA), binds with unexpectedly high affinity (K(a) >10(7) M(-1)), and that the crescent shape of coralyne appears necessary for poly(A) binding. We also show that the binding of similar ligands to poly(A) can be highly cooperative. For one particular ligand, at least six ligand molecules are required to stabilize the poly(A) self-structure at room temperature. This highly cooperative binding produces very sharp transitions between unstructured and structured poly(A) as a function of ligand concentration. Given the fact that junctions between Watson-Crick and A.A duplexes are tolerated, we propose that poly(A) sequence elements and appropriate ligands could be used to reversibly drive transitions in DNA and RNA-based molecular structures by simply diluting/concentrating a sample about the poly(A)-ligand 'critical concentration'. The ligands described here may also find biological or medicinal applications, owing to the 3'-polyadenylation of mRNA in living cells.

Controlling viral capsid assembly with templating

We develop coarse-grained models that describe the dynamic encapsidation of functionalized nanoparticles by viral capsid proteins. We find that some forms of cooperative interactions between protein subunits and nanoparticles can dramatically enhance rates and robustness of assembly, as compared to the spontaneous assembly of subunits into empty capsids. For large core-subunit interactions, subunits adsorb onto core surfaces en masse in a disordered manner, and then undergo a cooperative rearrangement into an ordered capsid structure. These assembly pathways are unlike any identified for empty capsid formation. Our models can be directly applied to recent experiments in which viral capsid proteins assemble around functionalized inorganic nanoparticles [Sun, Proc. Natl. Acad. Sci. U.S.A. 104, 1354 (2007)]. In addition, we discuss broader implications for understanding the dynamic encapsidation of single-stranded genomic molecules during viral replication and for developing multicomponent nanostructured materials.

Curvature dependence of viral protein structures on encapsidated nanoemulsion droplets

Virus-like particles are biomimetic delivery vehicles that cloak nanoscale cores inside coatings of viral capsid proteins, offering the potential for protecting their contents and targeting them to particular tissues and cells. To date, encapsidation has been demonstrated only for a relatively limited variety of core materials, such as compressible polymers and facetted nanocrystals, over a narrow range of cores sizes and of pH and ionic strength. Here, we encapsidate spherical nanodroplets of incompressible oil stabilized by adsorbed anionic surfactant using cationic capsid protein purified from cowpea chlorotic mottle virus. By imaging with transmission electron microscopy we show that, as the droplets become larger than the wild-type RNA core, the protein is forced to self-assemble into spherical shells that are not perfect icosahedra having special triangulation numbers characteristic of the Caspar-Klug hierarchy. Consequently, the distribution of protein conformations on larger droplets is significantly different than in the wild-type shell.