Studies on the assembly of a spherical plant virus. I. States of aggregation of the isolated protein

One-Step Purification Strategy for Cowpea Chlorotic Mottle Virus-Like Particles Produced by the IC-BEVS

Virus-like particles (VLP) of the cowpea chlorotic mottle virus (CCMV), a plant virus, have been shown to be safe and noncytotoxic vehicles for delivering various cargos, including nucleic acids and peptides, and as scaffolds for presenting epitopes. Thus, CCMV-VLP have acquired increasing attention to be used in fields such as gene therapy, drug delivery, and vaccine development. Regardless of their production method, most reports purify CCMV-VLP through a series of ultracentrifugation steps using sucrose density gradient ultracentrifugation, which is a complex and time-consuming process. Here, the use of anion exchange chromatography is described as a one-step protocol for purification of CCMV-VLP produced by the insect cell-baculovirus expression vector system (IC-BEVS).

DNA-origami-directed virus capsid polymorphism

Viral capsids can adopt various geometries, most iconically characterized by icosahedral or helical symmetries. Importantly, precise control over the size and shape of virus capsids would have advantages in the development of new vaccines and delivery systems. However, current tools to direct the assembly process in a programmable manner are exceedingly elusive. Here we introduce a modular approach by demonstrating DNA-origami-directed polymorphism of single-protein subunit capsids. We achieve control over the capsid shape, size and topology by employing user-defined DNA origami nanostructures as binding and assembly platforms, which are efficiently encapsulated within the capsid. Furthermore, the obtained viral capsid coatings can shield the encapsulated DNA origami from degradation. Our approach is, moreover, not limited to a single type of capsomers and can also be applied to RNA-DNA origami structures to pave way for next-generation cargo protection and targeting strategies.

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.

Electrostatic Screening, Acidic pH and Macromolecular Crowding Increase the Self-Assembly Efficiency of the Minute Virus of Mice Capsid In Vitro

The hollow protein capsids from a number of different viruses are being considered for multiple biomedical or nanotechnological applications. In order to improve the applied potential of a given viral capsid as a nanocarrier or nanocontainer, specific conditions must be found for achieving its faithful and efficient assembly in vitro. The small size, adequate physical properties and specialized biological functions of the capsids of parvoviruses such as the minute virus of mice (MVM) make them excellent choices as nanocarriers and nanocontainers. In this study we analyzed the effects of protein concentration, macromolecular crowding, temperature, pH, ionic strength, or a combination of some of those variables on the fidelity and efficiency of self-assembly of the MVM capsid in vitro. The results revealed that the in vitro reassembly of the MVM capsid is an efficient and faithful process. Under some conditions, up to ~40% of the starting virus capsids were reassembled in vitro as free, non aggregated, correctly assembled particles. These results open up the possibility of encapsidating different compounds in VP2-only capsids of MVM during its reassembly in vitro, and encourage the use of virus-like particles of MVM as nanocontainers.

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

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

The diversity of protein-protein interaction interfaces within T=3 icosahedral viral capsids

Some non-enveloped virus capsids assemble from multiple copies of a single type of coat-protein (CP). The comparative energetics of the diverse CP-CP interfaces present in such capsids likely govern virus assembly-disassembly mechanisms. The T = 3 icosahedral capsids comprise 180 CP copies arranged about two-, three-, five- and six-fold axes of (quasi-)rotation symmetry. Structurally diverse CPs can assemble into T = 3 capsids. Specifically, the Leviviridae CPs are structurally distinct from the Bromoviridae, Tombusviridae and Tymoviridae CPs which fold into the classic “jelly-roll” fold. However, capsids from across the four families are known to disassemble into dimers. To understand whether the overall symmetry of the capsid or the structural details of the CP determine virus assembly-disassembly mechanisms, we analyze the different CP-CP interfaces that occur in the four virus families. Previous work studied protein homodimer interfaces using interface size (relative to the monomer) and hydrophobicity. Here, we analyze all CP-CP interfaces using these two parameters and find that the dimerization interface (present between two CPs congruent through a two-fold axis of rotation) has a larger relative size in the Leviviridae than in the other viruses. The relative sizes of the other Leviviridae interfaces and all the jelly-roll interfaces are similar. However, the dimerization interfaces across families have slightly higher hydrophobicity, potentially making them stronger than other interfaces. Finally, although the CP-monomers of the jelly-roll viruses are structurally similar, differences in their dimerization interfaces leads to varied dimer flexibility. Overall, differences in CP-structures may induce different modes of swelling and assembly-disassembly in the T = 3 viruses.

The Dynamics of Viruslike Capsid Assembly and Disassembly

Cowpea chlorotic mottle virus (CCMV) is a widely used model for virus replication studies. A major challenge lies in distinguishing between the roles of the interaction between coat proteins and that between the coat proteins and the viral RNA in assembly and disassembly processes. Here, we report on the spontaneous and reversible size conversion of the empty capsids of a CCMV capsid protein functionalized with a hydrophobic elastin-like polypeptide which occurs following a pH jump. We monitor the concentrations of T = 3 and T = 1 capsids as a function of time and show that the time evolution of the conversion from one T number to another is not symmetric: The conversion from T = 1 to T = 3 is a factor of 10 slower than that of T = 3 to T = 1. We explain our experimental findings using a simple model based on classical nucleation theory applied to virus capsids, in which we account for the change in the free protein concentration, as the different types of shells assemble and disassemble by shedding or absorbing single protein subunits. As far as we are aware, this is the first study confirming that both the assembly and disassembly of viruslike shells can be explained through classical nucleation theory, reproducing quantitatively results from time-resolved experiments

Computational Design of Single-Peptide Nanocages with Nanoparticle Templating

Protein complexes perform a diversity of functions in natural biological systems. While computational protein design has enabled the development of symmetric protein complexes with spherical shapes and hollow interiors, the individual subunits often comprise large proteins. Peptides have also been applied to self-assembly, and it is of interest to explore such short sequences as building blocks of large, designed complexes. Coiled-coil peptides are promising subunits as they have a symmetric structure that can undergo further assembly. Here, an α-helical 29-residue peptide that forms a tetrameric coiled coil was computationally designed to assemble into a spherical cage that is approximately 9 nm in diameter and presents an interior cavity. The assembly comprises 48 copies of the designed peptide sequence. The design strategy allowed breaking the side chain conformational symmetry within the peptide dimer that formed the building block (asymmetric unit) of the cage. Dynamic light scattering (DLS) and transmission electron microscopy (TEM) techniques showed that one of the seven designed peptide candidates assembled into individual nanocages of the size and shape. The stability of assembled nanocages was found to be sensitive to the assembly pathway and final solution conditions (pH and ionic strength). The nanocages templated the growth of size-specific Au nanoparticles. The computational design serves to illustrate the possibility of designing target assemblies with pre-determined specific dimensions using short, modular coiled-coil forming peptide sequences.

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.

The impact of size on particle drainage dynamics and antibody response

Vaccine-induced immune response can be greatly enhanced by mimicking pathogen properties. The size and the repetitive geometric shape of virus-like particles (VLPs) influence their immunogenicity by facilitating drainage to secondary lymphoid organs and enhancing interaction with and activation of B cells and innate humoral immune components. VLPs derived from the plant Bromovirus genus, specifically cowpea chlorotic mottle virus (CCMV), are T = 3 icosahedral particles. (T) is the triangulation number that refers to the number and arrangements of the subunits (pentamers and hexamers) of the VLPs. CCMV-VLPs can be easily expressed in an E. coli host system and package ssRNA during the expression process. Recently, we have engineered CCMV-VLPs by incorporating the universal tetanus toxin (TT) epitope at the N-terminus. The modified CCMV_TT-VLPs successfully form icosahedral particles T = 3, with a diameter of ~30 nm analogous to the parental VLPs. Interestingly, incorporating TT epitope at the C-terminus of CCMV_TT-VLPs results in the formation of Rod-shaped VLPs, ~1 μm in length and ~ 30 nm in width. In this study, we have investigated the draining kinetics and immunogenicity of both engineered forms (termed as Round-shaped CCMV_TT-VLPs and Rod-shaped CCMV_TT-VLPs) as potential B cell immunogens using different in vitro and in vivo assays. Our results reveal that Round-shaped CCMV_TT-VLPs are more efficient in draining to secondary lymphoid organs to charge professional antigen-presenting cells as well as B cells. Furthermore, compared to Rod-shaped CCMV_TT-VLPs, Round-shaped CCMV_TT-VLPs led to more than 100-fold increased systemic IgG and IgA responses accompanied by prominent formation of splenic germinal centers. Round-shaped CCMV_TT-VLPs could also polarize the induced T cell response toward Th1. To our knowledge, this is the first study investigating and comparing the draining kinetics and immunogenicity of one and the same VLP monomer forming nano-sized icosahedra or rods in the micrometer size.

Insight into N-terminal localization and dynamics of engineered virus-like particles

Virus-like particles composed of the cowpea chlorotic mottle virus (CCMV) capsid protein (CP) have been extensively studied as carrier systems in nanoscience. One well-established method to improve their stability under physiological conditions is to fuse a stimulus-responsive elastin-like polypeptide (ELP) to the N-terminus of the CPs. Even though the N-terminus should in principle be localized in the inner cavity of the protein cage, studies on the native CCMV revealed its accessibility on the particle surface. We verified that such phenomenon also applies to ELP-CCMVs, by exploiting the covalent functionalization of the CP N-terminal domain via a sortase A-mediated reaction. Western-blot analysis and Förster resonance energy transfer (FRET) experiments furthermore revealed this to be caused by both the external display of the N-termini and the interchange of CPs among preformed capsids. Our findings demonstrate the tunability of ELP-CCMV stability and dynamics and their potential effect on the exploitation of such protein cages as a drug delivery system.

Encapsidation of Different Plasmonic Gold Nanoparticles by the CCMV CP

Different types of gold nanoparticles have been synthesized that show great potential in medical applications such as medical imaging, bio-analytical sensing and photothermal cancer therapy. However, their stability, polydispersity and biocompatibility are major issues of concern. For example, the synthesis of gold nanorods, obtained through the elongated micelle process, produce them with a high positive surface charge that is cytotoxic, while gold nanoshells are unstable and break down in a few weeks due to the Ostwald ripening process. In this work, we report the self-assembly of the capsid protein (CP) of cowpea chlorotic mottle virus (CCMV) around spherical gold nanoparticles, gold nanorods and gold nanoshells to form virus-like particles (VLPs). All gold nanoparticles were synthesized or treated to give them a negative surface charge, so they can interact with the positive N-terminus of the CP leading to the formation of the VLPs. To induce the protein self-assembly around the negative gold nanoparticles, we use different pH and ionic strength conditions determined from a CP phase diagram. The encapsidation with the viral CP will provide the nanoparticles better biocompatibility, stability, monodispersity and a new biological substrate on which can be introduced ligands toward specific cells, broadening the possibilities for medical applications.

A minimal coarse-grained model for the low-frequency normal mode analysis of icosahedral viral capsids

The main goal of this work is the design of a coarse-grained theoretical model of minimal resolution for the study of the physical properties of icosahedral virus capsids within the linear-response regime. In this model the capsid is represented as an interacting many-body system whose composing elements are capsid subunits (capsomers), which are treated as three-dimensional rigid bodies. The total interaction potential energy is written as a sum of pairwise capsomer-capsomer interactions. Based on previous work [Gomez Llorente et al., Soft Matter, 2014, 10, 3560], a minimal and complete anisotropic binary interaction that includes a full Hessian matrix of independent force constants is proposed. In this interaction model, capsomers have rotational symmetry around an axis of order n > 2. The full coarse-grained model is applied to analyse the low-frequency normal-mode spectrum of icosahedral T = 1 capsids. The model performance is evaluated by fitting its predicted spectrum to the full-atom results for the Satellite Tobacco Necrosis Virus (STNV) capsid [Dykeman and Sankey, Phys. Rev. Lett., 2008, 100, 028101]. Two capsomer choices that are compatible with the capsid icosahedral symmetry are checked, namely pentamers (n = 5) and trimers (n = 3). Both subunit types provide fair fits, from which the magnitude of the coarse-grained force constants for a real virus is obtained. The model is able to uncover latent instabilities whose analysis is fully consistent with the current knowledge about the STNV capsid, which does not self-assemble in the absence of RNA and is thermally unstable. The straightforward generalisability of the model beyond the linear regime and its completeness make it a promising tool to theoretically interpret many experimental data such as those provided by the atomic force microscopy or even to better understand processes far from equilibrium such as the capsid self-assembly.

Kinetics of empty viral capsid assembly in a minimal model

The efficient construction of a protective protein shell or capsid is one of the most crucial steps in the replication cycle of a virus. The formation of the simplest capsid typically proceeds by the spontaneous assembly of identical building blocks. This process can also be achieved in vitro even in the absence of genetic material, thus opening the door to the production of artificial viral cages for a myriad of applications. In this work, we analyze the efficiency and the kinetic peculiarities of this self-assembly process using Brownian Dynamics simulations. We use a minimal model that considers identical assembly units and is able to reproduce successfully the correct final architecture of spherical capsids. The selection of a specific size and structure is achieved by changing a single parameter that imposes an angular anisotropy on the interaction. We analyze how the geometrical constraints of the interaction affect the efficiency of the assembly. We find that the optimal conditions for an efficient assembly from a kinetic point of view strongly depart from the lowest capsid energy corresponding to the minimum of the potential energy landscape. Our work illustrates the important differences between the equilibrium and dynamic characteristics of viral self-assembly, and provides important insights on how to design specific interactions for a successful assembly of artificial viral cages.

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.

Protocol for Efficient Cell-Free Synthesis of Cowpea Chlorotic Mottle Virus-Like Particles Containing Heterologous RNAs

We report a protocol for efficient cell-free synthesis of cowpea chlorotic mottle virus (CCMV)-like particles containing a broad range of lengths and sequences of RNA. Our protocol starts with a purified stock of wild-type CCMV (protocols for harvesting and purifying the virus are detailed elsewhere) and features three basic steps: disassembly of the CCMV and purification of the capsid protein (CP) from the viral RNA; coassembly of the purified CP and an RNA of choice; and characterization of the assembly products. We highlight several key factors that increase the yield of the assembly reaction: the CP should be uncleaved and sufficiently free of viral RNA; the length of the RNA should be between about 100 and 4000 nucleotides; and the stoichiometry of CP and RNA should be 6-1 by mass. Additionally, we point out that separating the assembly reaction into multiple steps-by successively lowering the ionic strength and then the pH of the assembly buffers-results in the highest yields of well-formed, nuclease-resistant, CCMV-like particles. Finally, we describe methods for characterizing the assembly products using native agarose gel electrophoresis and negative-stain transmission electron microscopy.

Nonequilibrium self-assembly dynamics of icosahedral viral capsids packaging genome or polyelectrolyte

The survival of viruses partly relies on their ability to self-assemble inside host cells. Although coarse-grained simulations have identified different pathways leading to assembled virions from their components, experimental evidence is severely lacking. Here, we use time-resolved small-angle X-ray scattering to uncover the nonequilibrium self-assembly dynamics of icosahedral viral capsids packaging their full RNA genome. We reveal the formation of amorphous complexes via an en masse pathway and their relaxation into virions via a synchronous pathway. The binding energy of capsid subunits on the genome is moderate (~7k_BT₀, with k_B the Boltzmann constant and T₀ = 298 K, the room temperature), while the energy barrier separating the complexes and the virions is high (~ 20k_BT₀). A synthetic polyelectrolyte can lower this barrier so that filled capsids are formed in conditions where virions cannot build up. We propose a representation of the dynamics on a free energy landscape.

The mechanism by which virus capsules assemble around RNA to package their genetic material is not clear. Here, the authors observed the assembly of the cowpea chlorotic mottle virus capsid around viral RNA or poly(styrene sulfonic acid) using time-resolved small-angle X-ray scattering measurements.

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.

Templated Formation of Luminescent Virus-like Particles by Tailor-Made Pt(II) Amphiphiles

Virus-like particles (VLPs) have been created from luminescent Pt(II) complex amphiphiles, able to form supramolecular structures in water solutions, that can be encapsulated or act as templates of cowpea chlorotic mottle virus capsid proteins. By virtue of a bottom-up molecular design, icosahedral and nonicosahedral (rod-like) VLPs have been constructed through diverse pathways, and a relationship between the molecular structure of the complexes and the shape and size of the VLPs has been observed. A deep insight into the mechanism for the templated formation of the differently shaped VLPs was achieved, by electron microscopy measurements (TEM and STEM) and bulk analysis (FPLC, DLS, photophysical investigations). Interestingly, the obtained VLPs can be visualized by their intense emission at room temperature, generated by the self-assembly of the Pt(II) complexes. The encapsulation of the luminescent species is further verified by their higher emission quantum yields inside the VLPs, which is due to the confinement effect of the protein cage. These hybrid materials demonstrate the potential of tailor-made supramolecular systems able to control the assembly of biological building blocks.

Protein Complexes and Virus-Like Particle Technology

Virus-like particle (VLP) technologies are based on virus-inspired artificial structures and the intrinsic ability of viral proteins to self-assemble at controlled conditions. Therefore, the basic knowledge about the mechanisms of viral particle formation is highly important for designing of industrial applications. As an alternative to genetic and chemical processes, different physical methods are frequently used for VLP construction, including well characterized protein complexes for introduction of foreign molecules in VLP structures.This chapter shortly discusses the mechanisms how the viruses form their perfectly ordered structures as well as the principles and most interesting application examples, how to exploit the structural and assembly/disassembly properties of viral structures for creation of new nanomaterials.

Investigating the thermal dissociation of viral capsid by lattice model

The dissociation of icosahedral viral capsids was investigated by a homogeneous and a heterogeneous lattice model. In thermal dissociation experiments with cowpea chlorotic mottle virus and probed by small-angle neutron scattering, we observed a slight shrinkage of viral capsids, which can be related to the strengthening of the hydrophobic interaction between subunits at increasing temperature. By considering the temperature dependence of hydrophobic interaction in the homogeneous lattice model, we were able to give a better estimate of the effective charge. In the heterogeneous lattice model, two sets of lattice sites represented different capsid subunits with asymmetric interaction strengths. In that case, the dissociation of capsids was found to shift from a sharp one-step transition to a gradual two-step transition by weakening the hydrophobic interaction between AB and CC subunits. We anticipate that such lattice models will shed further light on the statistical mechanics underlying virus assembly and disassembly.

Physical Ingredients Controlling Stability and Structural Selection of Empty Viral Capsids

One of the crucial steps in the viral replication cycle is the self-assembly of its protein shell. Typically, each native virus adopts a unique architecture, but the coat proteins of many viruses have the capability to self-assemble in vitro into different structures by changing the assembly conditions. However, the mechanisms determining which of the possible capsid shapes and structures is selected by a virus are still not well-known. We present a coarse-grained model to analyze and understand the physical mechanisms controlling the size and structure selection in the assembly of empty viral capsids. Using this model and Monte Carlo simulations, we have characterized the phase diagram and stability of T = 1,3,4,7 and snub cube shells. In addition, we have studied the tolerance of different shells to changes in physical parameters related to ambient conditions, identifying possible strategies to induce misassembly or failure. Finally, we discuss the factors that select the shape of a capsid as spherical, faceted, elongated, or decapsidated. Our model sheds important light on the ingredients that control the assembly and stability of viral shells. This knowledge is essential to get capsids with well-defined size and structure that could be used for promising applications in medicine or bionanotechnology.

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?

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.

Tuning the pH-triggered self-assembly of dendritic peptide amphiphiles using fluorinated side chains

We report the synthesis of a series of anionic dendritic peptide amphiphiles of increasing hydrophobic character and describe their self-assembly into supramolecular nanorods using pH and ionic strength dependent state diagrams.

Characterization of Viral Capsid Protein Self-Assembly around Short Single-Stranded RNA

For many viruses, the packaging of a single-stranded RNA (ss-RNA) genome is spontaneous, driven by capsid protein-capsid protein (CP) and CP-RNA interactions. Furthermore, for some multipartite ss-RNA viruses, copackaging of two or more RNA molecules is a common strategy. Here we focus on RNA copackaging in vitro by using cowpea chlorotic mottle virus (CCMV) CP and an RNA molecule that is short (500 nucleotides (nts)) compared to the lengths (≈3000 nts) packaged in wild-type virions. We show that the degree of cooperativity of virus assembly depends not only on the relative strength of the CP-CP and CP-RNA interactions but also on the RNA being short: a 500-nt RNA molecule cannot form a capsid by itself, so its packaging requires the aggregation of multiple CP-RNA complexes. By using fluorescence correlation spectroscopy (FCS), we show that at neutral pH and sufficiently low concentrations RNA and CP form complexes that are smaller than the wild-type capsid and that four 500-nt RNAs are packaged into virus-like particles (VLPs) only upon lowering the pH. Further, a variety of bulk-solution techniques confirm that fully ordered VLPs are formed only upon acidification. On the basis of these results, we argue that the observed high degree of cooperativity involves equilibrium between multiple CP/RNA complexes.

Production and applications of engineered viral capsids

As biological agents, viruses come in an astounding range of sizes, with varied shapes and surface morphologies. The structures of viral capsids are generally assemblies of hundreds of copies of one or a few proteins which can be harnessed for use in a wide variety of applications in biotechnology, nanotechnology, and medicine. Despite their complexity, many capsid types form as homogenous populations of precise geometrical assemblies. This is important in both medicine, where well-defined therapeutics are critical for drug performance and federal approval, and nanotechnology, where precise placement affects the properties of the desired material. Here we review the production of viruses and virus-like particles with methods for selecting and manipulating the size, surface chemistry, assembly state, and interior cargo of capsid. We then discuss many of the applications used in research today and the potential commercial and therapeutic products from engineered viral capsids.

Electrophoretic mobilities of a viral capsid, its capsid protein, and their relation to viral assembly

The self-assembly of many viral capsids is dominated by protein-protein electrostatic interactions. To have a better understanding of this process, it is important to know how the protein and the capsid surface charges vary as a function of the pH and ionic strength. In this work, using phase analysis light scattering, we measured the electrophoretic mobility (EM) of the cowpea chlorotic mottle virus (CCMV), its capsid protein (CP), and a cleaved CP that lacks its basic terminus, as a function of pH and ionic strength. The EM measurements of the CP are difficult to carry out due to its tendency to self-assemble into capsids; we show how to circumvent this problem by appropriately changing the CP concentration. We found that the isoelectric points (pIs) of the virion and of the CP are insensitive to ionic strength. The onset of multishell structures in the phase diagram of the CCMV CP as a function of ionic strength and pH (and its absence in the brome mosaic virus (BMV) CP phase diagram) can be related to the pI of the capsid. We propose that the transition from multiwall shells to nanotube structures is due to a change in the spontaneous curvature of the CP at its pI. A nonzero limit of the EM at high ionic strength is characteristic of a soft colloid, but a near identity of the EMs of empty capsids and those containing RNA indicates that the EM reflects only the charge distribution in the CP. The Henry equation has been used to provide approximate values of the capsid surface charge as a function of pH and I.

A two-stage mechanism of viral RNA compaction revealed by single molecule fluorescence

Long RNAs often exist as multiple conformers in equilibrium. For the genomes of single-stranded RNA viruses, one of these conformers must include a compacted state allowing the RNA to be confined within the virion. We have used single molecule fluorescence correlation spectroscopy to monitor the conformations of viral genomes and sub-fragments in the absence and presence of coat proteins. Cognate RNA-coat protein interactions in two model viruses cause a rapid collapse in the hydrodynamic radii of their respective RNAs. This is caused by protein binding at multiple sites on the RNA that facilitate additional protein-protein contacts. The collapsed species recruit further coat proteins to complete capsid assembly with great efficiency and fidelity. The specificity in RNA-coat protein interactions seen at single-molecule concentrations reflects the packaging selectivity seen for such viruses in vivo. This contrasts with many in vitro reassembly measurements performed at much higher concentrations. RNA compaction by coat protein or polycation binding are distinct processes, implying that defined RNA-coat protein contacts are required for assembly.

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.

Energies and pressures in viruses: contribution of nonspecific electrostatic interactions

We summarize some aspects of electrostatic interactions in the context of viruses. A simplified but, within well defined limitations, reliable approach is used to derive expressions for electrostatic energies and the corresponding osmotic pressures in single-stranded RNA viruses and double-stranded DNA bacteriophages. The two types of viruses differ crucially in the spatial distribution of their genome charge which leads to essential differences in their free energies, depending on the capsid size and total charge in a quite different fashion. Differences in the free energies are trailed by the corresponding characteristics and variations in the osmotic pressure between the inside of the virus and the external bathing solution.

Electrostatic self-energy of a partially formed spherical shell in salt solution: application to stability of tethered and fluid shells as models for viruses and vesicles

We investigate the electrostatics of a partially formed, charged spherical shell in a salt solution. We solve the problem numerically at the Poisson-Boltzmann level and analytically in the Debye-Hückel regime. From the results on energetics of partially formed shells we examine the stability of tethered (crystalline) and fluid shells toward rupture. We delineate different regimes of stability, where, for fluid shells, we also include the effects of bending elasticity of the shells. Our analysis shows how charging of the shell induces its instability toward rupture but also provides insight regarding growth of charged shells.

Monitoring structural transitions in icosahedral virus protein cages by site-directed spin labeling

This work describes an approach for calculating and measuring dipolar interactions in multispin systems to monitor conformational changes in icosahedral protein cages using site-directed spin labeling. Cowpea chlorotic mottle virus (CCMV) is used as a template that undergoes a pH-dependent reversible capsid expansion wherein the protein cage swells by 10%. The sequence-position-dependent geometric presentation of attached spin-label groups provides a strategy for targeting amino acid residues most probative of structural change. The labeled protein cage residues and structural transition were found to affect the local mobility and dipolar interactions of the spin label, respectively. Line-shape changes provided a spectral signature that could be used to follow the conformational change in CCMV coat dynamics. The results provide evidence for a concerted swelling process in which the cages exist in only two structural forms, with essentially no intermediates. This methodology can be generalized for all symmetry types of icosahedral protein architectures to monitor protein cage dynamics.

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.

Multishell structures of virus coat proteins

Under conditions of low ionic strength and a pH ranging between about 3.7 and 5.0, solutions of purified coat proteins of cowpea chlorotic mottle virus (CCMV) form spherical multishell structures in the absence of viral RNA. The outer surfaces of the shells in these structures are negatively charged, whereas the inner surfaces are positively charged due to a disordered cationic N-terminal domain of the capsid protein, the arginine-rich RNA-binding motif that protrudes into the interior. We show that the main forces stabilizing these multishells are counterion release combined with a lower charge density in the RNA-binding motif region of the outer shells due to their larger radii of curvature, arguing that these compensate for the outer shells not being able to adopt the smaller, optimal, radius of curvature of the inner shell. This explains why the structures are only stable at low ionic strengths at pHs for which the outer surface is negatively charged and why the larger outer shells are not observed separately in solution. We show how to calculate the free energy of shells of nonoptimal radius of curvature from the elastic properties of the native shell. The spacing between shells is determined mainly by the entropic elasticity of the RNA-binding motifs. Although we focus on CCMV multishells, we also predict the solution conditions under which multishells formed by CCMV coat protein mutants with a lower RNA-binding motif charge are stable, and we examine other viruses as well. We conclude that at a given surface charge density, the boundaries separating regions of stable multishells with different numbers of shells shift to lower ionic strengths upon either increasing the length of the RNA-binding motif, increasing the stiffness of the shells, or decreasing the charge per RNA-binding motif.

Proton-driven assembly of the Rous Sarcoma virus capsid protein results in the formation of icosahedral particles

In a mature and infectious retroviral particle, the capsid protein (CA) forms a shell surrounding the genomic RNA and the replicative machinery of the virus. The irregular nature of this capsid shell precludes direct atomic resolution structural analysis. CA hexamers and pentamers are the fundamental building blocks of the capsid, however the pentameric state, in particular, remains poorly characterized. We have developed an efficient in vitro protocol for studying the assembly of Rous sarcoma virus (RSV) CA that involves mild acidification and produces structures modeling the authentic viral capsid. These structures include regular spherical particles with T = 1 icosahedral symmetry, built from CA pentamers alone. These particles were subject to cryoelectron microscopy (cryo-EM) and image processing, and a pseudo-atomic model of the icosahedron was created by docking atomic structures of the constituent CA domains into the cryo-EM-derived three-dimensional density map. The N-terminal domain (NTD) of CA forms pentameric turrets, which decorate the surface of the icosahedron, while the C-terminal domain (CTD) of CA is positioned underneath, linking the pentamers. Biophysical analysis of the icosahedral particle preparation reveals that CA monomers and icosahedra are the only detectable species and that these exist in reversible equilibrium at pH 5. These same acidic conditions are known to promote formation of a RSV CA CTD dimer, present within the icosahedral particle, which facilitates capsid assembly. The results are consistent with a model in which RSV CA assembly is a nucleation-limited process driven by very weak protein-protein interactions.

Thermodynamics of nanospheres encapsulated in virus capsids

We investigate the thermodynamics of complexation of functionalized charged nanospheres with viral proteins. The physics of this problem is governed not only by electrostatic interaction between the proteins and the nanosphere cores (screened by salt ions), but also by configurational degrees of freedom of the charged protein N tails. We approach the problem by constructing an appropriate complexation free-energy functional. On the basis of both numerical and analytical studies of this functional we construct the phase diagram for the assembly which contains the information on the assembled structures that appear in the thermodynamical equilibrium, depending on the size and surface charge density of the nanosphere cores. We show that both the nanosphere core charge and its radius determine the size of the capsid that forms around the core.

Invariant polymorphism in virus capsid assembly

Directed self-assembly of designed viral capsids holds significant potential for applications in materials science and medicine. However, the complexity of preparing these systems for assembly and the difficulty of quantitative experimental measurements on the assembly process have limited access to critical mechanistic questions that dictate the final product yields and isomorphic forms. Molecular simulations provide a means of elucidating self-assembly of viral proteins into icosahedral capsids and are the focus of the present study. Using geometrically realistic coarse-grained models with specialized molecular dynamics methods, we delineate conditions of temperature and coat protein concentration that lead to the spontaneous self-assembly of T = 1 and T = 3 icosahedral capsids. In addition to the primary product of icosahedral capsids, we observe a ubiquitous presence of nonicosahedral yet highly symmetric and enclosed aberrant capsules in both T = 1 and T = 3 systems. This polymorphism in assembly products recapitulates the scope and morphology of particle types that have been observed in mis-assembly experiments of virus capsids. Moreover, we find that this structural polymorphism in the end point structures is an inherent property of the coat proteins and arises from condition-dependent kinetic mechanisms that are independent of the elemental mechanisms of capsid growth (as long as the building blocks of the coat proteins are all monomeric, dimeric, or trimeric) and the capsid T number. The kinetic mechanisms responsible for self-assembly of icosahedral capsids and aberrant capsules are deciphered; the self-assembly of icosahedral capsids requires a high level of assembly fidelity, whereas self-assembly of nonicosahedral capsules is a consequence of an off-pathway mechanism that is prevalent under nonoptimal conditions of temperature or protein concentration during assembly. The latter case involves kinetically trapped dislocations of pentamer-templated proteins with hexameric organization. These findings provide insights into the complex processes that govern viral capsid assembly and suggest some features of the assembly process that can be exploited to control the assembly of icosahedral capsids and nonicosahedral capsules.

Generalized structural polymorphism in self-assembled viral particles

The protein shells, called capsids, of nearly all spherical viruses adopt icosahedral symmetry; however, self-assembly of such empty structures often occurs with multiple misassembly steps resulting in the formation of aberrant structures. Using simple models that represent the coat proteins preassembled in the two different predetermined species that are common motifs of viral capsids (i.e., pentameric and hexameric capsomers), we perform molecular dynamics simulations of the spontaneous self-assembly of viral capsids of different sizes containing T = 1,3,4,7,9,12,13,16, and 19 proteins in their icosahedral repeating unit. We observe, in addition to icosahedral capsids, a variety of nonicosahedral yet highly ordered and enclosed capsules. Such structural polymorphism is demonstrated to be an inherent property of the coat proteins, independent of the capsid complexity and the elementary kinetic mechanisms. Moreover, there exist two distinctive classes of polymorphic structures: aberrant capsules that are larger than their respective icosahedral capsids, in T = 1-7 systems; and capsules that are smaller than their respective icosahedral capsids when T = 7-19. Different kinetic mechanisms responsible for self-assembly of those classes of aberrant structures are deciphered, providing insights into the control of the self-assembly of icosahedral capsids.

Mechanisms of size control and polymorphism in viral capsid assembly

We simulate the assembly dynamics of icosahedral capsids from subunits that interconvert between different conformations (or quasi-equivalent states). The simulations identify mechanisms by which subunits form empty capsids with only one morphology but adaptively assemble into different icosahedral morphologies around nanoparticle cargoes with varying sizes, as seen in recent experiments with brome mosaic virus (BMV) capsid proteins. Adaptive cargo encapsidation requires moderate cargo-subunit interaction strengths; stronger interactions frustrate assembly by stabilizing intermediates with incommensurate curvature. We compare simulation results to experiments with cowpea chlorotic mottle virus empty capsids and BMV capsids assembled on functionalized nanoparticles and suggest new cargo encapsidation experiments. Finally, we find that both empty and templated capsids maintain the precise spatial ordering of subunit conformations seen in the crystal structure even if interactions that preserve this arrangement are favored by as little as the thermal energy, consistent with experimental observations that different subunit conformations are highly similar.

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.

The three-dimensional structure of ryegrass mottle virus at 2.9 A resolution

The crystal structure of the sobemovirus Ryegrass mottle virus (RGMoV) has been determined at 2.9 A resolution. The coat protein has a canonical jellyroll beta-sandwich fold. In comparison to other sobemoviruses the RGMoV coat protein is missing several residues in two of the loop regions. The first loop contributes to contacts between subunits around the quasi-threefold symmetry axis. The altered contact interface results in tilting of the subunits towards the quasi-threefold axis. The assembly of the T=3 capsid of sobemoviruses is controlled by the N-termini of C subunits forming a so-called beta-annulus. The other loop that is smaller in the RGMoV structure contains a helix that participates in stabilization of the beta-annulus in other sobemoviruses. The loss of interaction between the RGMoV loop and the beta-annulus has been compensated for by additional interactions between the N-terminal arms. As a consequence of these differences, the diameter of the RGMoV particle is 8 A smaller than that of the other sobemoviruses. The interactions of coat proteins in sobemovirus capsids involve calcium ions. Depletion of calcium ions results in particle swelling, which is considered a first step in disassembly. We could not identify any density for metal ions in the proximity of the conserved residues normally involved in calcium binding, but the RGMoV structure does not show any signs of swelling. A likely reason is the low pH (3.0) of the crystallization buffer in which the groups interacting with the calcium ions are not charged.

Symmetry, equivalence, and molecular self-assembly

Molecular self-assembly at equilibrium is fundamental to the fields of biological self-organization, the development of novel environmentally responsive polymeric materials, and nanofabrication. Our approach to understanding the principles governing this process is inspired by existing models and measurements for the self-assembly of actin, tubulin, and the ubiquitous icosahedral shell structures of viral capsids. We introduce a family of simple potentials that give rise to the self-assembly of linear polymeric, random surface ("membrane"), tubular ("nanotube"), and hollow icosahedral structures that are similar in many respects to their biological counterparts. The potentials involve equivalent particles and an interplay between directional (dipolar, multipolar) and short-range (van der Waals) interactions. Specifically, we find that the dipolar potential, having a continuous rotational symmetry about the dipolar axis, gives rise to chain formation, while particles with multipolar potentials, having discrete rotational symmetries (square quadrupole or triangular ring of dipoles or "hexapole"), lead to the self-assembly of open sheet, nanotube, and hollow icosahedral geometries. These changes in the geometry of self-assembly are accompanied by significant changes in the kinetics of the organization.

The role of subunit hinges and molecular "switches" in the control of viral capsid polymorphism

The coat protein (CP) of cowpea chlorotic mottle virus assembles exclusively into a T=3 capsid in vivo and, under proper conditions, in vitro. The N-terminal domain of CP has been implicated in proper assembly and was viewed as a required switch for mediating hexamer and pentamer formation in T=3 assembly. We observed that a mutant CP lacking most of the N-terminal domain, NDelta34, assembles, in vitro, into statistically predictable numbers of: native-like T=3 capsids of 90 dimers; "T=2" capsids of 60 dimers; T=1 capsids of 30 dimers. We generated cryo-EM image reconstructions of each form and built pseudo-atomic models based on the subunits from the crystal structure of plant-derived T=3 virus allowing a detailed comparison of stabilizing interactions in the three assemblies. The statistical nature of the distribution of assembly products and the observed structures indicates that the N-terminus of CP is not a switch that is required to form the proper ratio of hexamers and pentamers for T=3 assembly; rather, it biases the direction of assembly to T=3 particles from the possibilities available to NDelta34 through flexible dimer hinges and variations in subunit contacts. Our results are consistent with a pentamer of dimers (PODs) nucleating assembly in all cases but subunit dimers can be added with different trajectories that favor specific T=3 or T=1 global particle geometries. Formation of the "T=2" particles appears to be fundamentally different in that they not only nucleate with PODs, but assembly propagates by the addition of mostly, if not exclusively PODs generating an entirely new subunit interface in the process. These results show that capsid geometry is flexible and may readily adapt to new requirements as the virus evolves.

Elasticity theory and shape transitions of viral shells

Recently, continuum elasticity theory has been applied to explain the shape transition of icosahedral viral capsids--single-protein-thick crystalline shells--from spherical to "buckled" or faceted as their radius increases through a critical value determined by the competition between stretching and bending energies of a closed two-dimensional (2D) elastic network. In the present work we generalize this approach to capsids with nonicosahedral symmetries, e.g., spherocylindrical and conical shells. One key additional physical ingredient is the role played by nonzero spontaneous curvature. Another is associated with the special way in which the energy of the 12 topologically required fivefold sites depends on the "background" local curvature of the shell in which they are embedded. Systematic evaluation of these contributions leads to a shape "phase" diagram in which transitions are observed from icosahedral to spherocylindrical capsids as a function of the ratio of stretching to bending energies and of the spontaneous curvature of the 2D protein network. We find that the transition from icosahedral to spherocylindrical symmetry is continuous or weakly first order near the onset of buckling, leading to extensive shape degeneracy. These results are discussed in the context of experimentally observed variations in the shapes of a variety of viral capsids.