A theory for viral capsid assembly around electrostatic cores

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

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

Diffusion and molecular partitioning in hierarchically complex virus-like particles

Viruses are diverse infectious agents found in virtually every type of natural environment. Due to the range of conditions in which viruses have evolved, they exhibit a wide range of structure and function which has been exploited for biotechnology. The self-assembly process of virus-like particles (VLPs), derived from structural virus components, allows for the assembly of a hierarchy of materials. Because VLPs are robust in both their assembly and the final product, functionality can be incorporated through design of their building blocks or chemical modification after their synthesis and assembly. In particular, encapsulation of active enzymes inside VLP results in macromolecular concentration approximating that of cells, introducing excluded volume effects on encapsulated cargo which are not present in traditional experiments done on dilute proteins. This work reviews the hierarchical assembly of VLPs, experiments investigating diffusion in VLP systems, and methods for partitioning of chemical species in VLPs as functional biomaterials.

Spanning tree model and the assembly kinetics of RNA viruses

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

Single-particle studies of the effects of RNA-protein interactions on the self-assembly of RNA virus particles

Understanding the pathways by which simple RNA viruses self-assemble from their coat proteins and RNA is of practical and fundamental interest. Although RNA-protein interactions are thought to play a critical role in the assembly, our understanding of their effects is limited because the assembly process is difficult to observe directly. We address this problem by using interferometric scattering microscopy, a sensitive optical technique with high dynamic range, to follow the in vitro assembly kinetics of more than 500 individual particles of brome mosaic virus (BMV)-for which RNA-protein interactions can be controlled by varying the ionic strength of the buffer. We find that when RNA-protein interactions are weak, BMV assembles by a nucleation-and-growth pathway in which a small cluster of RNA-bound proteins must exceed a critical size before additional proteins can bind. As the strength of RNA-protein interactions increases, the nucleation time becomes shorter and more narrowly distributed, but the time to grow a capsid after nucleation is largely unaffected. These results suggest that the nucleation rate is controlled by RNA-protein interactions, while the growth process is driven less by RNA-protein interactions and more by protein-protein interactions and intraprotein forces. The nucleated pathway observed with the plant virus BMV is strikingly similar to that previously observed with bacteriophage MS2, a phylogenetically distinct virus with a different host kingdom. These results raise the possibility that nucleated assembly pathways might be common to other RNA viruses.

Microcompartment assembly around multicomponent fluid cargoes

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

Packaging contests between viral RNA molecules and kinetic selectivity

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

Polyelectrolyte Encapsulation and Confinement within Protein Cage-Inspired Nanocompartments

Protein cages are nanocompartments with a well-defined structure and monodisperse size. They are composed of several individual subunits and can be categorized as viral and non-viral protein cages. Native viral cages often exhibit a cationic interior, which binds the anionic nucleic acid genome through electrostatic interactions leading to efficient encapsulation. Non-viral cages can carry various cargo, ranging from small molecules to inorganic nanoparticles. Both cage types can be functionalized at targeted locations through genetic engineering or chemical modification to entrap materials through interactions that are inaccessible to wild-type cages. Moreover, the limited number of constitutional subunits ease the modification efforts, because a single modification on the subunit can lead to multiple functional sites on the cage surface. Increasing efforts have also been dedicated to the assembly of protein cage-mimicking structures or templated protein coatings. This review focuses on native and modified protein cages that have been used to encapsulate and package polyelectrolyte cargos and on the electrostatic interactions that are the driving force for the assembly of such structures. Selective encapsulation can protect the payload from the surroundings, shield the potential toxicity or even enhance the intended performance of the payload, which is appealing in drug or gene delivery and imaging.

Controlling the surface charge of simple viruses

The vast majority of plant viruses are unenveloped, i.e., they lack a lipid bilayer that is characteristic of most animal viruses. The interactions between plant viruses, and between viruses and surfaces, properties that are essential for understanding their infectivity and to their use as bionanomaterials, are largely controlled by their surface charge, which depends on pH and ionic strength. They may also depend on the charge of their contents, i.e., of their genes or-in the instance of virus-like particles-encapsidated cargo such as nucleic acid molecules, nanoparticles or drugs. In the case of enveloped viruses, the surface charge of the capsid is equally important for controlling its interaction with the lipid bilayer that it acquires and loses upon leaving and entering host cells. We have previously investigated the charge on the unenveloped plant virus Cowpea Chlorotic Mottle Virus (CCMV) by measurements of its electrophoretic mobility. Here we examine the electrophoretic properties of a structurally and genetically closely related bromovirus, Brome Mosaic Virus (BMV), of its capsid protein, and of its empty viral shells, as functions of pH and ionic strength, and compare them with those of CCMV. From measurements of both solution and gel electrophoretic mobilities (EMs) we find that the isoelectric point (pI) of BMV (5.2) is significantly higher than that of CCMV (3.7), that virion EMs are essentially the same as those of the corresponding empty capsids, and that the same is true for the pIs of the virions and of their cleaved protein subunits. We discuss these results in terms of current theories of charged colloidal particles and relate them to biological processes and the role of surface charge in the design of new classes of drug and gene delivery systems.

Avidity and surface mobility in multivalent ligand-receptor binding

Targeted drug delivery relies on two physical processes: the selective binding of a therapeutic particle to receptors on a specific cell membrane, followed by transport of the particle across the membrane. In this article, we address some of the challenges in controlling the thermodynamics and dynamics of these two processes by combining a simple experimental system with a statistical mechanical model. Specifically, we characterize and model multivalent ligand-receptor binding between colloidal particles and fluid lipid bilayers, as well as the surface mobility of membrane-bound particles. We show that the mobility of the receptors within the fluid membrane is key to both the thermodynamics and dynamics of binding. First, we find that the particle-membrane binding free energy-or avidity-is a strongly nonlinear function of the ligand-receptor affinity. We attribute the nonlinearity to a combination of multivalency and recruitment of fluid receptors to the binding site. Our results also suggest that partial wrapping of the bound particles by the membrane enhances avidity further. Second, we demonstrate that the lateral mobility of membrane-bound particles is also strongly influenced by the recruitment of receptors. Specifically, we find that the lateral diffusion coefficient of a membrane-bound particle is dominated by the hydrodynamic drag against the aggregate of receptors within the membrane. These results provide one of the first direct validations of the working theoretical framework for multivalent interactions. They also highlight that the fluidity and elasticity of the membrane are as important as the ligand-receptor affinity in determining the binding and transport of small particles attached to membranes.

Mechanisms of Scaffold-Mediated Microcompartment Assembly and Size Control

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

Molecular basis for protein-protein interactions

This minireview provides an overview on the current knowledge of protein-protein interactions, common characterisation methods to characterise them, and their role in protein complex formation with some examples. A deep understanding of protein-protein interactions and their molecular interactions is important for a number of applications, including drug design. Protein-protein interactions and their discovery are thus an interesting avenue for understanding how protein complexes, which make up the majority of proteins, work.

Osmotic stress and pore nucleation in charged biological nanoshells and capsids

A model system is proposed to investigate the chemical equilibrium and mechanical stability of biological spherical-like nanoshells in contact with an aqueous solution with added dissociated electrolyte of a given concentration. The ionic chemical equilibrium across the permeable shell is investigated in the framework of an accurate Density Functional Theory (DFT) that incorporates electrostatic and hardcore correlations beyond the traditional mean-field (e.g., Poisson-Boltzmann) limit. The accuracy of the theory is tested by a direct comparison with Monte Carlo (MC) simulations. A simple analytical expression is then deduced which clearly highlights the entropic, electrostatic, and self-energy contributions to the osmotic stress over the shell in terms of the calculated ionic profiles. By invoking a continuum mean-field elastic approach to account for the shell surface stress upon osmotic stretching, the mechanical equilibrium properties of the shell under a wide variety of ionic strengths and surface charges are investigated. The model is further coupled to a continuum mechanical approach similar in structure to a Classical Nucleation Theory (CNT) to address the question of mechanical stability of the shells against a pore nucleation. This allows us to construct a phase diagram which delimits the mechanical stability of capsids for different ionic strengths and shell surface charges.

Elucidating the Thermodynamic Driving Forces of Polyanion-Templated Virus-like Particle Assembly

A virus in its most simple form is comprised of a protein capsid that surrounds and protects the viral genome. The self-assembly of such structures, however, is a highly complex, multiprotein, multiinteraction process and has been a topic of study for a number of years. This self-assembly process is driven by the (mainly electrostatic) interaction between the capsid proteins (CPs) and the genome as well as by the protein-protein interactions, which primarily rely on hydrophobic interactions. Insight in the thermodynamics that is involved in virus and virus-like particle (VLP) formation is crucial in the detailed understanding of this complex assembly process. Therefore, we studied the assembly of CPs of the cowpea chlorotic mottle virus (CCMV) templated by polyanionic species (cargo), that is, single-stranded DNA (ssDNA), and polystyrene sulfonate (PSS) using isothermal titration calorimetry. By separating the electrostatic CP-cargo interaction from the full assembly interaction, we conclude that CP-CP interactions cause an enthalpy change of -3 to -4 kcal mol-1 CP. Furthermore, we quantify that upon reducing the CP-CP interaction, in the case of CCMV by increasing the pH to 7, the CP-cargo starts to dominate VLP formation. This is highlighted by the three times higher affinity between CP and PSS compared to CP and ssDNA, resulting in the disassembly of CCMV at neutral pH in the presence of PSS to yield PSS-filled VLPs.

Role of metallic core for the stability of virus-like particles in strongly coupled electrostatics

Electrostatic interactions play important roles in the formation and stability of viruses and virus-like particles (VLPs) through processes that often involve added, or naturally occurring, multivalent ions. Here, we investigate the electrostatic or osmotic pressure acting on the proteinaceous shell of a generic model of VLPs, comprising a charged outer shell and a metallic nanoparticle core, coated by a charged layer and bathed in an aqueous electrolyte solution. Motivated by the recent studies accentuating the role of multivalent ions for the stability of VLPs, we focus on the effects of multivalent cations and anions in an otherwise monovalent ionic solution. We perform extensive Monte-Carlo simulations based on appropriate Coulombic interactions that consistently take into account the effects of salt screening, the dielectric polarization of the metallic core, and the strong-coupling electrostatics due to multivalent ions. We specifically study the intricate roles these factors play in the electrostatic stability of the model VLPs. It is shown that while the insertion of a metallic nanoparticle by itself can produce negative, inward-directed, pressure on the outer shell, addition of only a small amount of multivalent counterions can robustly engender negative pressures, enhancing the VLP stability across a wide range of values for the system parameters.

Assembly and Characterization of HBc Derived Virus-like Particles with Magnetic Core

Core-virus like particles (VLPs) assembly is a kinetically complex cascade of interactions between viral proteins, nanoparticle's surface and an ionic environment. Despite many in silico simulations regarding this process, there is still a lack of experimental data. The main goal of this study was to investigate the capsid protein of hepatitis B virus (HBc) assembly into virus-like particles with superparamagnetic iron oxide nanoparticles (SPIONs) as a magnetic core in relation to their characteristics. The native form of HBc was obtained via agroinfection of Nicotiana benthamiana with pEAQ-HBc plasmid. SPIONs of diameter of 15 nm were synthesized and functionalized with two ligands, providing variety in ζ-potential and hydrodynamic diameter. The antigenic potential of the assembled core-VLPs was assessed with enzyme-linked immunosorbent assay (ELISA). Morphology of SPIONs and core-VLPs was evaluated via transmission electron microscopy (TEM). The most successful core-VLPs assembly was obtained for SPIONs functionalized with dihexadecyl phosphate (DHP) at SPIONs/HBc ratio of 0.2/0.05 mg/mL. ELISA results indicate significant decrease of antigenicity concomitant with core-VLPs assembly. In summary, this study provides an experimental assessment of the crucial parameters guiding SPION-HBc VLPs assembly and evaluates the antigenicity of the obtained structures.

Genome packaging within icosahedral capsids and large-scale segmentation in viral genomic sequences

The assembly and maturation of viruses with icosahedral capsids must be coordinated with icosahedral symmetry. The icosahedral symmetry imposes also the restrictions on the cooperative specific interactions between genomic RNA/DNA and coat proteins that should be reflected in quasi-regular segmentation of viral genomic sequences. Combining discrete direct and double Fourier transforms, we studied the quasi-regular large-scale segmentation in genomic sequences of different ssRNA, ssDNA, and dsDNA viruses. The particular representatives included satellite tobacco mosaic virus (STMV) and the strains of satellite tobacco necrosis virus (STNV), STNV-C, STNV-1, STNV-2, Escherichia phages MS2, ϕX174, α3, and HK97, and Simian virus 40. In all their genomes, we found the significant quasi-regular segmentation of genomic sequences related to the virion assembly and the genome packaging within icosahedral capsid. We also found good correspondence between our results and available cryo-electron microscopy data on capsid structures and genome packaging in these viruses. Fourier analysis of genomic sequences provides the additional insight into mechanisms of hierarchical genome packaging and may be used for verification of the concepts of 3-fold or 5-fold intermediates in virion assembly. The results of sequence analysis should be taken into account at the choice of models and data interpretation. They also may be helpful for the development of antiviral drugs.

Self-assembly of convex particles on spherocylindrical surfaces

The precise control of assembly and packing of proteins and colloids on curved surfaces has fundamental implications in nanotechnology. In this paper, we describe dynamical simulations of the self-assembly of conical subunits around a spherocylindrical template, and a continuum theory for the bending energy of a triangular lattice with spontaneous curvature on a surface with arbitrary curvature. We find that assembly depends sensitively on mismatches between subunit spontaneous curvature and the mean curvature of the template, as well as anisotropic curvature of the template (mismatch between the two principal curvatures). Our simulations predict assembly morphologies that closely resemble those observed in experiments in which virus capsid proteins self-assemble around metal nanorods. Below a threshold curvature mismatch, our simulations identify a regime of optimal assembly leading to complete, symmetrical particles. Outside of this regime we observe defective particles, whose morphologies depend on the degree of curvature mismatch. To learn how assembly is affected by the nonuniform curvature of a spherocylinder, we also study the simpler cases of assembly around spherical and cylindrical cores. Our results show that both the intrinsic (Gaussian) and extrinsic (mean) curvatures of a template play significant roles in guiding the assembly of anisotropic subunits, providing a rich design space for the formation of nanoscale materials.

Defects and Chirality in the Nanoparticle-Directed Assembly of Spherocylindrical Shells of Virus Coat Proteins

Virus coat proteins of small isometric plant viruses readily assemble into symmetric, icosahedral cages encapsulating noncognate cargo, provided the cargo meets a minimal set of chemical and physical requirements. While this capability has been intensely explored for certain virus-enabled nanotechnologies, additional applications require lower symmetry than that of an icosahedron. Here, we show that the coat proteins of an icosahedral virus can efficiently assemble around metal nanorods into spherocylindrical closed shells with hexagonally close-packed bodies and icosahedral caps. Comparison of chiral angles and packing defects observed by in situ atomic force microscopy with those obtained from molecular dynamics models offers insight into the mechanism of growth, and the influence of stresses associated with intrinsic curvature and assembly pathways.

Systematic analysis of biological roles of charged amino acid residues located throughout the structured inner wall of a virus capsid

Structure-based mutational analysis of viruses is providing many insights into the relationship between structure and biological function of macromolecular complexes. We have systematically investigated the individual biological roles of charged residues located throughout the structured capsid inner wall (outside disordered peptide segments) of a model spherical virus, the minute virus of mice (MVM). The functional effects of point mutations that altered the electrical charge at 16 different positions at the capsid inner wall were analyzed. The results revealed that MVM capsid self-assembly is rather tolerant to point mutations that alter the number and distribution of charged residues at the capsid inner wall. However, mutations that either increased or decreased the number of positive charges around capsid-bound DNA segments reduced the thermal resistance of the virion. Moreover, mutations that either removed or changed the positions of negatively charged carboxylates in rings of acidic residues around capsid pores were deleterious by precluding a capsid conformational transition associated to through-pore translocation events. The results suggest that number, distribution and specific position of electrically charged residues across the inner wall of a spherical virus may have been selected through evolution as a compromise between several different biological requirements.

Biophysical analysis of BMV virions purified using a novel method

Brome mosaic virus (BMV) has been successfully loaded with different types of nanoparticles. However, studies concerning its application as a nanoparticle carrier demand high-purity virions in large amounts. Existing BMV purification protocols rely on multiple differential ultracentrifugation runs of the initially purified viral preparation. Herein, we describe an alternative method for BMV purification based on ion-exchange chromatography and size-exclusion chromatography (SEC) yielding 0.2mg of virus from 1g of plant tissue. Our method is of similar efficiency to previously described protocols and can easily be scaled up. The method results in high-quality BMV preparations as confirmed by biophysical analyses, including cryogenic transmission electron microscopy (cryo-TEM), dynamic light scattering (DLS), static light scattering (SLS), and circular dichroism (CD) measurements and attenuated total reflection Fourier transform infrared spectroscopy (ATR-FTIR) spectroscopy. Our results revealed that purified BMV capsids are stable and monodisperse and can be used for further downstream applications. In this work, we also characterize secondary structure and size fluctuations of the BMV virion at different pH values.

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

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

Many-molecule encapsulation by an icosahedral shell

We computationally study how an icosahedral shell assembles around hundreds of molecules. Such a process occurs during the formation of the carboxysome, a bacterial microcompartment that assembles around many copies of the enzymes ribulose 1,5-bisphosphate carboxylase/ oxygenase and carbonic anhydrase to facilitate carbon fixation in cyanobacteria. Our simulations identify two classes of assembly pathways leading to encapsulation of many-molecule cargoes. In one, shell assembly proceeds concomitantly with cargo condensation. In the other, the cargo first forms a dense globule; then, shell proteins assemble around and bud from the condensed cargo complex. Although the model is simplified, the simulations predict intermediates and closure mechanisms not accessible in experiments, and show how assembly can be tuned between these two pathways by modulating protein interactions. In addition to elucidating assembly pathways and critical control parameters for microcompartment assembly, our results may guide the reengineering of viruses as nanoreactors that self-assemble around their reactants.

DOI:http://dx.doi.org/10.7554/eLife.14078.001

Bacterial microcompartments are protein shells that are found inside bacteria and enclose enzymes and other chemicals required for certain biological reactions. For example, the carboxysome is a type of microcompartment that enables the bacteria to convert the products of photosynthesis into sugars. During the formation of a microcompartment, the outer protein shell assembles around hundreds of enzymes and chemicals. This formation process is tightly controlled and involves multiple interactions between the shell proteins and the cargo – the enzymes and other reaction ingredients – they will enclose. Understanding how to control which enzymes are encapsulated within microcompartments could help researchers to re-engineer the microcompartments so that they contain drugs or other useful products.

Recent studies have used microscopy to visualize how microcompartments are assembled. However, most of the intermediate structures that form during assembly are too small and short-lived to be seen. It has therefore not been possible to explore in detail how shell proteins collect the necessary cargo and then assemble into an ordered shell with the cargo on the inside. Experiments alone are probably not enough to understand the process, especially since microcompartment assembly can currently only be studied within live cells or cellular extract. Within these complex environments it is difficult to determine the effect of any individual factor on the overall assembly process.

Perlmutter, Mohajerani and Hagan have now taken a different approach by developing computational and theoretical models to explore how microcompartments assemble. Computer simulations showed that microcompartments could assemble by two pathways. In one pathway, the protein shell and cargo coalesce at the same time. In the other pathway, the cargo molecules first assemble into a large disordered complex, with the shell proteins attached on the outside. The shell proteins then assemble, carving out a piece of the cargo complex. The simulations showed that many factors affect how the shell assembles, such as the strengths of the interactions between the shell proteins and the cargo. They also identified a factor that controls how much cargo ends up inside the assembled shell.

Perlmutter, Mohajerani and Hagan found that, in addition to revealing how microcompartments may assemble within their natural setting, the simulations provided guidance on how to re-engineer microcompartments to assemble around other components. This would enable researchers to create customizable compartments that self-assemble within bacteria or other host organisms, for example to carry out carbon fixation or make biofuels.

A future challenge will be to investigate other aspects of microcompartment assembly, such as the factors that control the size of these compartments.

DOI:http://dx.doi.org/10.7554/eLife.14078.002

Allosteric Control of Icosahedral Capsid Assembly

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

Core protein: A pleiotropic keystone in the HBV lifecycle

Hepatitis B Virus (HBV) is a small virus whose genome has only four open reading frames. We argue that the simplicity of the virion correlates with a complexity of functions for viral proteins. We focus on the HBV core protein (Cp), a small (183 residue) protein that self-assembles to form the viral capsid. However, its functions are a little more complicated than that. In an infected cell Cp modulates almost every step of the viral lifecycle. Cp is bound to nuclear viral DNA and affects its epigenetics. Cp correlates with RNA specificity. Cp assembles specifically on a reverse transcriptase-viral RNA complex or, apparently, nothing at all. Indeed Cp has been one of the model systems for investigation of virus self-assembly. Cp participates in regulation of reverse transcription. Cp signals completion of reverse transcription to support virus secretion. Cp carries both nuclear localization signals and HBV surface antigen (HBsAg) binding sites; both of these functions appear to be regulated by contents of the capsid. Cp can be targeted by antivirals - while self-assembly is the most accessible of Cp activities, we argue that it makes sense to engage the broader spectrum of Cp function. This article forms part of a symposium in Antiviral Research on "From the discovery of the Australia antigen to the development of new curative therapies for hepatitis B: an unfinished story."

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.

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

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

Using Markov state models to study self-assembly

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

Recent Developments in Molecular Simulation Approaches to Study Spherical Virus Capsids

Viruses are a particularly challenging systems to study via molecular simulation methods. Virus capsids typically consist of over 100 subunit proteins and reach dimensions of over 100 nm; solvated viruses capsid systems can be over 1 million atoms in size. In this review, I will present recent developments which have attempted to overcome the significant computational expense to perform simulations which can inform experimental studies, make useful predictions about biological phenomena and calculate material properties relevant to nanotechnology design efforts.

Scaffold properties are a key determinant of the size and shape of self-assembled virus-derived particles

Controlling the geometry of self-assembly will enable a greater diversity of nanoparticles than now available. Viral capsid proteins, one starting point for investigating self-assembly, have evolved to form regular particles. The polyomavirus SV40 assembles from pentameric subunits and can encapsidate anionic cargos. On short ssRNA (≤814 nt), SV40 pentamers form 22 nm diameter capsids. On RNA too long to fit a T = 1 particle, pentamers forms strings of 22 nm particles and heterogeneous particles of 29-40 nm diameter. However, on dsDNA SV40 forms 50 nm particles composed of 72 pentamers. A 7.2-Å resolution cryo-EM image reconstruction of 22 nm particles shows that they are built of 12 pentamers arranged with T = 1 icosahedral symmetry. At 3-fold vertices, pentamers each contribute to a three-helix triangle. This geometry of interaction is not seen in crystal structures of T = 7 viruses and provides a structural basis for the smaller capsids. We propose that the heterogeneous particles are actually mosaics formed by combining different geometries of interaction from T = 1 capsids and virions. Assembly can be trapped in novel conformations because SV40 interpentamer contacts are relatively strong. The implication is that by virtue of their large catalog of interactions, SV40 pentamers have the ability to self-assemble on and conform to a broad range of shapes.

Hepatitis virus capsid polymorph stability depends on encapsulated cargo size

Protein cages providing a controlled environment to encapsulated cargo are a ubiquitous presence in any biological system. Well-known examples are capsids, the regular protein shells of viruses, which protect and deliver the viral genome. Since some virus capsids can be loaded with nongenomic cargoes, they are interesting for a variety of applications ranging from biomedical delivery to energy harvesting. A question of vital importance for such applications is how does capsid stability depend on the size of the cargo? A nanoparticle-templated assembly approach was employed here to determine how different polymorphs of the Hepatitis B virus icosahedral capsid respond to a gradual change in the encapsulated cargo size. It was found that assembly into complete virus-like particles occurs cooperatively around a variety of core diameters, albeit the degree of cooperativity varies. Among these virus-like particles, it was found that those of an outer diameter corresponding to an icosahedral array of 240 proteins (T = 4) are able to accommodate the widest range of cargo sizes.

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.

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

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

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

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

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.

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.

Impact of charge variation on the encapsulation of nanoparticles by virus coat proteins

Electrostatic interaction is the driving force for the encapsulation by virus coat proteins of nanoparticles such as quantum dots, gold particles and magnetic beads for, e.g., imaging and therapeutic purposes. In recent experimental work, Daniel et al (2010 ACS Nano 4 3853-60) found the encapsulation efficiency to sensitively depend on the interplay between the surface charge density of negatively charged gold nanoparticles and the number of positive charges on the RNA binding domains of the proteins. Surprisingly, these experiments reveal that despite the highly cooperative nature of the co-assembly at low pH, the efficiency of encapsulation is a gradual function of their surface charge density. We present a simple all-or-nothing mass action law combined with an electrostatic interaction model to explain the experiments. We find quantitative agreement with experimental observations, supporting the existence of a natural statistical charge distribution between nanoparticles.

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.

An examination of the electrostatic interactions between the N-terminal tail of the Brome Mosaic Virus coat protein and encapsidated RNAs

The coat protein of positive-stranded RNA viruses often contains a positively charged tail that extends toward the center of the capsid and interacts with the viral genome. Electrostatic interaction between the tail and the RNA has been postulated as a major force in virus assembly and stabilization. The goal of this work is to examine the correlation between electrostatic interaction and amount of RNA packaged in the tripartite Brome Mosaic Virus (BMV). Nanoindentation experiment using atomic force microscopy showed that the stiffness of BMV virions with different RNAs varied by a range that is 10-fold higher than that would be predicted by electrostatics. BMV mutants with decreased positive charges encapsidated lower amounts of RNA while mutants with increased positive charges packaged additional RNAs up to ∼900 nt. However, the extra RNAs included truncated BMV RNAs, an additional copy of RNA4, potential cellular RNAs, or a combination of the three, indicating that change in the charge of the capsid could result in several different outcomes in RNA encapsidation. In addition, mutant with specific arginines changed to lysines in the capsid also exhibited defects in the specific encapsidation of BMV RNA4. The experimental results indicate that electrostatics is a major component in RNA encapsidation but was unable to account for all of the observed effects on RNA encapsidation. Thermodynamic modeling incorporating the electrostatics was able to predict the approximate length of the RNA to be encapsidated for the majority of mutant virions, but not for a mutant with extreme clustered positive charges. Cryo-electron microscopy of virions that encapsidated an additional copy of RNA4 revealed that, despite the increase in RNA encapsidated, the capsid structure was minimally changed. These results experimentally demonstrated the impact of electrostatics and additional restraints in the encapsidation of BMV RNAs, which could be applicable to other viruses.

Mechanisms of kinetic trapping in self-assembly and phase transformation

In self-assembly processes, kinetic trapping effects often hinder the formation of thermodynamically stable ordered states. In a model of viral capsid assembly and in the phase transformation of a lattice gas, we show how simulations in a self-assembling steady state can be used to identify two distinct mechanisms of kinetic trapping. We argue that one of these mechanisms can be adequately captured by kinetic rate equations, while the other involves a breakdown of theories that rely on cluster size as a reaction coordinate. We discuss how these observations might be useful in designing and optimising self-assembly reactions.

Simulated self-assembly of the HIV-1 capsid: protein shape and native contacts are sufficient for two-dimensional lattice formation

We report Monte Carlo simulations of the initial stages of self-assembly of the HIV-1 capsid protein (CA), using a coarse-grained representation that mimics the CA backbone structure and intermolecular contacts observed experimentally. A simple representation of N-terminal domain/N-terminal domain and N-terminal domain/C-terminal domain interactions, coupled with the correct protein shape, is sufficient to drive formation of an ordered lattice with the correct hexagonal symmetry in two dimensions. We derive an approximate concentration/temperature phase diagram for lattice formation, and we investigate the pathway by which the lattice develops from initially separated CA dimers. Within this model, lattice formation occurs in two stages: 1), condensation of CA dimers into disordered clusters; and 2), nucleation of the lattice by the appearance of one hexamer unit within a cluster. Trimers of CA dimers are important early intermediates, and pentamers are metastable within clusters. Introduction of a preformed hexamer at the beginning of a Monte Carlo run does not directly seed lattice formation, but does facilitate the formation of large clusters. We discuss possible connections between these simulations and experimental observations concerning CA assembly within HIV-1 and in vitro.

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.

Modern biomolecular mass spectrometry and its role in studying virus structure, dynamics, and assembly

Over a century since its development, the analytical technique of mass spectrometry is blooming more than ever, and applied in nearly all aspects of the natural and life sciences. In the last two decades mass spectrometry has also become amenable to the analysis of proteins and even intact protein complexes, and thus begun to make a significant impact in the field of structural biology. In this Review, we describe the emerging role of mass spectrometry, with its different technical facets, in structural biology, focusing especially on structural virology. We describe how mass spectrometry has evolved into a tool that can provide unique structural and functional information about viral-protein and protein-complex structure, conformation, assembly, and topology, extending to the direct analysis of intact virus capsids of several million Dalton in mass. Mass spectrometry is now used to address important questions in virology ranging from how viruses assemble to how they interact with their host.

Virus assembly, allostery and antivirals

Assembly of virus capsids and surface proteins must be regulated to ensure that the resulting complex is an infectious virion. In this review, we examine assembly of virus capsids, focusing on hepatitis B virus and bacteriophage MS2, and formation of glycoproteins in the alphaviruses. These systems are structurally and biochemically well-characterized and are simplest-case paradigms of self-assembly. Published data suggest that capsid and glycoprotein assembly is subject to allosteric regulation, that is regulation at the level of conformational change. The hypothesis that allostery is a common theme in viruses suggests that deregulation of capsid and glycoprotein assembly by small molecule effectors will be an attractive antiviral strategy, as has been demonstrated with hepatitis B virus.