Icosahedral capsid formation by capsomers and short polyions

Hierarchical assembly is more robust than egalitarian assembly in synthetic capsids

Self-assembly of complex and functional materials remains a grand challenge in soft material science. Efficient assembly depends on a delicate balance between thermodynamic and kinetic effects, requiring fine-tuning affinities and concentrations of subunits. By contrast, we introduce an assembly paradigm that allows large error-tolerance in the subunit affinity and helps avoid kinetic traps. Our combined experimental and computational approach uses a model system of triangular subunits programmed to assemble into T = 3 icosahedral capsids comprising 60 units. The experimental platform uses DNA origami to create monodisperse colloids whose three-dimensional geometry is controlled to nanometer precision, with two distinct bonds whose affinities are controlled to kBT precision, quantified in situ by static light scattering. The computational model uses a coarse-grained representation of subunits, short-ranged potentials, and Langevin dynamics. Experimental observations and modeling reveal that when the bond affinities are unequal, two distinct hierarchical assembly pathways occur, in which the subunits first form dimers in one case and pentamers in another. These hierarchical pathways produce complete capsids faster and are more robust against affinity variation than egalitarian pathways, in which all binding sites have equal strengths. This finding suggests that hierarchical assembly may be a general engineering principle for optimizing self-assembly of complex target structures.

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.

Molecular Dynamics Simulations of Deformable Viral Capsomers

Most coarse-grained models of individual capsomers associated with viruses employ rigid building blocks that do not exhibit shape adaptation during self-assembly. We develop a coarse-grained general model of viral capsomers that incorporates their stretching and bending energies while retaining many features of the rigid-body models, including an overall trapezoidal shape with attractive interaction sites embedded in the lateral walls to favor icosahedral capsid assembly. Molecular dynamics simulations of deformable capsomers reproduce the rich self-assembly behavior associated with a general T=1 icosahedral virus system in the absence of a genome. Transitions from non-assembled configurations to icosahedral capsids to kinetically-trapped malformed structures are observed as the steric attraction between capsomers is increased. An assembly diagram in the space of capsomer-capsomer steric attraction and capsomer deformability reveals that assembling capsomers of higher deformability into capsids requires increasingly large steric attraction between capsomers. Increasing capsomer deformability can reverse incorrect capsomer-capsomer binding, facilitating transitions from malformed structures to symmetric capsids; however, making capsomers too soft inhibits assembly and yields fluid-like structures.

Spanning tree model and the assembly kinetics of RNA viruses

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

Microcompartment assembly around multicomponent fluid cargoes

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

Packaging contests between viral RNA molecules and kinetic selectivity

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

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.

Viruses, Artificial Viruses and Virus-Based Structures for Biomedical Applications

Nanobiomaterials such as virus particles and artificial virus particles offer tremendous opportunities to develop new biomedical applications such as drug- or gene-delivery, imaging and sensing but also improve understanding of biological mechanisms. Recent advances within the field of virus-based systems give insights in how to mimic viral structures and virus assembly processes as well as understanding biodistribution, cell/tissue targeting, controlled and triggered disassembly or release and circulation times. All these factors are of high importance for virus-based functional systems. This review illustrates advances in mimicking and enhancing or controlling these aspects to a high degree toward delivery and imaging applications.

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

Topological effects on capsomer-polyion co-assembly

On the basis of a T = 1 icosahedral capsid model, the capsomer-polyion co-assembly process has been investigated by molecular dynamics simulations using capsomers with different net charge and charge distribution as well as linear, branched, and hyper-branched polyions. The assembly process was characterized in terms of the time-dependent cluster size probabilities, averaged cluster size, encapsulation efficiency, and polyion extension. The kinetics of the capsid formation displayed a two-step process. The first one comprised adsorption of capsomers on the polyion, driven by their electrostatic attraction, whereas the second one involved a relocation and/or reorientation of adsorbed capsomers, which rate is reduced upon increasing electrostatic interaction. We found that increased polyion branching facilitated a more rapid encapsulation process towards a higher yield. Moreover, the hyper-branched polyions were entirely encapsulated at all polyion-capsid charge ratios considered.

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.

Simulations show that virus assembly and budding are facilitated by membrane microdomains

For many viruses, assembly and budding occur simultaneously during virion formation. Understanding the mechanisms underlying this process could promote biomedical efforts to block viral propagation and enable use of capsids in nanomaterials applications. To this end, we have performed molecular dynamics simulations on a coarse-grained model that describes virus assembly on a fluctuating lipid membrane. Our simulations show that the membrane can promote association of adsorbed subunits through dimensional reduction, but it also introduces thermodynamic and kinetic effects that can inhibit complete assembly. We find several mechanisms by which membrane microdomains, such as lipid rafts, reduce these effects, and thus, enhance assembly. We show how these predicted mechanisms can be experimentally tested. Furthermore, the simulations demonstrate that assembly and budding depend crucially on the system dynamics via multiple timescales related to membrane deformation, protein diffusion, association, and adsorption onto the membrane.

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

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

IMPORTANCE

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

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

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