Role of RNA Branchedness in the Competition for Viral Capsid Proteins

Evolution of Bipartite and Segmented Viruses from Monopartite Viruses

RNA viruses may be monopartite (all genes on one strand), multipartite (two or more strands packaged separately) or segmented (two or more strands packaged together). In this article, we consider competition between a complete monopartite virus, A, and two defective viruses, D and E, that have complementary genes. We use stochastic models that follow gene translation, RNA replication, virus assembly, and transmission between cells. D and E multiply faster than A when stored in the same host as A or when together in the same host, but they cannot multiply alone. D and E strands are packaged as separate particles unless a mechanism evolves that allows assembly of D + E segmented particles. We show that if defective viruses assemble rapidly into separate particles, the formation of segmented particles is selected against. In this case, D and E spread as parasites of A, and the bipartite D + E combination eliminates A if the transmissibility is high. Alternatively, if defective strands do not assemble rapidly into separate particles, then a mechanism for assembly of segmented particles is selected for. In this case, the segmented virus can eliminate A if transmissibility is high. Conditions of excess protein resources favor bipartite viruses, while conditions of excess RNA resources favor segmented viruses. We study the error threshold behavior that arises when deleterious mutations are introduced. Relative to bipartite and segmented viruses, deleterious mutations favor monopartite viruses. A monopartite virus can give rise to either a bipartite or a segmented virus, but it is unlikely that both will originate from the same virus.

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.

Relationships between RNA topology and nucleocapsid structure in a model icosahedral virus

The process of genome packaging in most of viruses is poorly understood, notably the role of the genome itself in the nucleocapsid structure. For simple icosahedral single-stranded RNA viruses, the branched topology due to the RNA secondary structure is thought to lower the free energy required to complete a virion. We investigate the structure of nucleocapsids packaging RNA segments with various degrees of compactness by small-angle x-ray scattering and cryotransmission electron microscopy. The structural differences are mild even though compact RNA segments lead on average to better-ordered and more uniform particles across the sample. Numerical calculations confirm that the free energy is lowered for the RNA segments displaying the larger number of branch points. The effect is, however, opposite with synthetic polyelectrolytes, in which a star topology gives rise to more disorder in the capsids than a linear topology. If RNA compactness and size account in part for the proper assembly of the nucleocapsid and the genome selectivity, other factors most likely related to the host cell environment during viral assembly must come into play as well.

How a Virus Circumvents Energy Barriers to Form Symmetric Shells

Previous self-assembly experiments on a model icosahedral plant virus have shown that, under physiological conditions, capsid proteins initially bind to the genome through an en masse mechanism and form nucleoprotein complexes in a disordered state, which raises the question as to how virions are assembled into a highly ordered structure in the host cell. Using small-angle X-ray scattering, we find out that a disorder-order transition occurs under physiological conditions upon an increase in capsid protein concentrations. Our cryo-transmission electron microscopy reveals closed spherical shells containing in vitro transcribed viral RNA even at pH 7.5, in marked contrast with the previous observations. We use Monte Carlo simulations to explain this disorder-order transition and find that, as the shell grows, the structures of disordered intermediates in which the distribution of pentamers does not belong to the icosahedral subgroups become energetically so unfavorable that the caps can easily dissociate and reassemble, overcoming the energy barriers for the formation of perfect icosahedral shells. In addition, we monitor the growth of capsids under the condition that the nucleation and growth is the dominant pathway and show that the key for the disorder-order transition in both en masse and nucleation and growth pathways lies in the strength of elastic energy compared to the other forces in the system including protein-protein interactions and the chemical potential of free subunits. Our findings explain, at least in part, why perfect virions with icosahedral order form under different conditions including physiological ones.

Physical virology: From virus self-assembly to particle mechanics

Viruses are highly ordered supramolecular complexes that have evolved to propagate by hijacking the host cell's machinery. Although viruses are very diverse, spreading through cells of all kingdoms of life, they share common functions and properties. Next to the general interest in virology, fundamental viral mechanisms are of growing importance in other disciplines such as biomedicine and (bio)nanotechnology. However, in order to optimally make use of viruses and virus-like particles, for instance as vehicle for targeted drug delivery or as building blocks in electronics, it is essential to understand their basic chemical and physical properties and characteristics. In this context, the number of studies addressing the mechanisms governing viral properties and processes has recently grown drastically. This review summarizes a specific part of these scientific achievements, particularly addressing physical virology approaches aimed to understand the self-assembly of viruses and the mechanical properties of viral particles. Using a physicochemical perspective, we have focused on fundamental studies providing an overview of the molecular basis governing these key aspects of viral systems. This article is categorized under: Biology-Inspired Nanomaterials > Protein and Virus-Based Structures Nanotechnology Approaches to Biology > Nanoscale Systems in Biology.

RNA Homopolymers Form Higher-Curvature Virus-like Particles Than Do Normal-Composition RNAs

Unlike double-stranded DNA, single-stranded RNA can be spontaneously packaged into spherical capsids by viral capsid protein (CP) because it is a more compact and flexible polymer. Many systematic investigations of this self-assembly process have been carried out using CP from cowpea chlorotic mottle virus, with a wide range of sequences and lengths of single-stranded RNA. Among these studies are measurements of the relative packaging efficiencies of these RNAs into spherical capsids. In this work, we address a fundamental issue that has received very little attention, namely the question of the preferred curvature of the capsid formed around different RNA molecules. We show in particular that homopolymers of RNA-polyribouridylic acid and polyriboadenylic acid-form exclusively T = 2-sized (∼22-nm diameter) virus-like particles (VLPs) when mixed with cowpea chlorotic mottle virus CP, independent of their length, ranging from 500 to more than 4000 nucleotides. This is in contrast to "normal-composition" RNAs (i.e., molecules with comparable numbers of each of the four nucleotides and hence capable of developing a large amount of secondary structure because of intramolecular complementarity/basepairing); a curvature corresponding to T = 3-size (∼28 nm in diameter) is preferred for the VLPs formed with such RNAs. Our work is consistent with the preferred curvature of VLPs being a consequence of interaction of CP with RNA-in particular, the presence or absence of short RNA duplexes-and suggests that the equilibrium size of the capsid results from a trade-off between this optimum size and the cost of confinement.

Virus-Inspired Function in Engineered Protein Cages

The structural and functional diversity of proteins combined with their genetic programmability has made them indispensable modern materials. Well-defined, hollow protein capsules have proven to be particularly useful due to their ability to compartmentalize macromolecules and chemical processes. To this end, viral capsids are common scaffolds and have been successfully repurposed to produce a suite of practical protein-based nanotechnologies. Recently, the recapitulation of viromimetic function in protein cages of nonviral origin has emerged as a strategy to both complement physical studies of natural viruses and produce useful scaffolds for diverse applications. In this perspective, we review recent progress toward generation of virus-like behavior in nonviral protein cages through rational engineering and directed evolution. These artificial systems can aid our understanding of the emergence of viruses from existing cellular components, as well as provide alternative approaches to tackle current problems, and open up new opportunities, in medicine and biotechnology.

Experimental and Theoretical Determination of the pH inside the Confinement of a Virus-Like Particle

In biology, a variety of highly ordered nanometer-size protein cages is found. Such structures find increasing application in, for example, vaccination, drug delivery, and catalysis. Understanding the physiochemical properties, particularly inside the confinement of a protein cage, helps to predict the behavior and properties of new materials based on such particles. Here, the relation between the bulk solution pH and the local pH inside a model protein cage, based on virus-like particles (VLPs) built from the coat proteins of the cowpea chlorotic mottle virus, is investigated. The pH is a crucial parameter in a variety of processes and is potentially significantly influenced by the high concentration of charges residing on the interior of the VLPs. The data show a systematic more acidic pH of 0.5 unit inside the VLP compared to that of the bulk solution for pH values above pH 6, which is explained using a theoretical model based on a Donnan equilibrium. The model agrees with the experimental data over almost two orders of magnitude, while below pH 6 the experimental data point to a buffering capacity of the VLP. These results are a first step in a better understanding of the physiochemical conditions inside a protein cage.

Confining annealed branched polymers inside spherical capsids

The Lifshitz equation for the confinement of a linear polymer in a spherical cavity of radius R has the form of the Schrödinger equation for a quantum particle trapped in a potential well with flat bottom and infinite walls at radius R. We show that the Lifshitz equation of a confined annealed branched polymer has the form of the Schrödinger equation for a quantum harmonic oscillator. The resulting confinement energy has a 1/R4 dependence on the confinement radius R, in contrast to the case of confined linear polymers, which have a 1/R2 dependence. We discuss the application of this result to the problem of the confinement of single-stranded RNA molecules inside spherical capsids.

The different faces of mass action in virus assembly

The spontaneous encapsulation of genomic and non-genomic polyanions by coat proteins of simple icosahedral viruses is driven, in the first instance, by electrostatic interactions with polycationic RNA binding domains on these proteins. The efficiency with which the polyanions can be encapsulated in vitro, and presumably also in vivo, must in addition be governed by the loss of translational and mixing entropy associated with co-assembly, at least if this co-assembly constitutes a reversible process. These forms of entropy counteract the impact of attractive interactions between the constituents and hence they counteract complexation. By invoking mass action-type arguments and a simple model describing electrostatic interactions, we show how these forms of entropy might settle the competition between negatively charged polymers of different molecular weights for co-assembly with the coat proteins. In direct competition, mass action turns out to strongly work against the encapsulation of RNAs that are significantly shorter, which is typically the case for non-viral (host) RNAs. We also find that coat proteins favor forming virus particles over nonspecific binding to other proteins in the cytosol even if these are present in vast excess. Our results rationalize a number of recent in vitro co-assembly experiments showing that short polyanions are less effective at attracting virus coat proteins to form virus-like particles than long ones do, even if both are present at equal weight concentrations in the assembly mixture.

The effect of RNA stiffness on the self-assembly of virus particles

Under many in vitro conditions, some small viruses spontaneously encapsidate a single stranded (ss) RNA into a protein shell called the capsid. While viral RNAs are found to be compact and highly branched because of long distance base-pairing between nucleotides, recent experiments reveal that in a head-to-head competition between an ssRNA with no secondary or higher order structure and a viral RNA, the capsid proteins preferentially encapsulate the linear polymer! In this paper, we study the impact of genome stiffness on the encapsidation free energy of the complex of RNA and capsid proteins. We show that an increase in effective chain stiffness because of base-pairing could be the reason why under certain conditions linear chains have an advantage over branched chains when it comes to encapsidation efficiency. While branching makes the genome more compact, RNA base-pairing increases the effective Kuhn length of the RNA molecule, which could result in an increase of the free energy of RNA confinement, that is, the work required to encapsidate RNA, and thus less efficient packaging.

RNA Base Pairing Determines the Conformations of RNA Inside Spherical Viruses

Many simple RNA viruses enclose their genetic material by a protein shell called the capsid. While the capsid structures are well characterized for most viruses, the structure of RNA inside the shells and the factors contributing to it remain poorly understood. We study the impact of base pairing on the conformations of RNA and find that it undergoes a swollen coil to globule continuous transition as a function of the strength of the pairing interaction. We also observe a first order transition and kink profile as a function of RNA length. All these transitions could explain the different RNA profiles observed inside viral shells.

The Effect of RNA Secondary Structure on the Self-Assembly of Viral Capsids

Previous work has shown that purified capsid protein (CP) of cowpea chlorotic mottle virus (CCMV) is capable of packaging both purified single-stranded RNA molecules of normal composition (comparable numbers of A, U, G, and C nucleobases) and of varying length and sequence, and anionic synthetic polymers such as polystyrene sulfonate. We find that CCMV CP is also capable of packaging polyU RNAs, which-unlike normal-composition RNAs-do not form secondary structures and which act as essentially structureless linear polymers. Following our canonical two-step assembly protocol, polyU RNAs ranging in length from 1000 to 9000 nucleotides (nt) are completely packaged. Surprisingly, negative-stain electron microscopy shows that all lengths of polyU are packaged into 22-nm-diameter particles despite the fact that CCMV CP prefers to form 28-nm-diameter (T = 3) particles when packaging normal-composition RNAs. PolyU RNAs >5000 nt in length are packaged into multiplet capsids, in which a single RNA molecule is shared between two or more 22-nm-diameter capsids, in analogy with the multiplets of 28-nm-diameter particles formed with normal-composition RNAs >5000 nt long. Experiments in which viral RNA competes for viral CP with polyUs of equal length show that polyU, despite its lack of secondary structure, is packaged more efficiently than viral RNA. These findings illustrate that the secondary structure of the RNA molecule-and its absence-plays an essential role in determining capsid structure during the self-assembly of CCMV-like particles.

Sizes of Long RNA Molecules Are Determined by the Branching Patterns of Their Secondary Structures

Long RNA molecules are at the core of gene regulation across all kingdoms of life, while also serving as genomes in RNA viruses. Few studies have addressed the basic physical properties of long single-stranded RNAs. Long RNAs with nonrepeating sequences usually adopt highly ramified secondary structures and are better described as branched polymers. To test whether a branched polymer model can estimate the overall sizes of large RNAs, we employed fluorescence correlation spectroscopy to examine the hydrodynamic radii of a broad spectrum of biologically important RNAs, ranging from viral genomes to long noncoding regulatory RNAs. The relative sizes of long RNAs measured at low ionic strength correspond well to those predicted by two theoretical approaches that treat the effective branching associated with secondary structure formation-one employing the Kramers theorem for calculating radii of gyration, and the other featuring the metric of maximum ladder distance. Upon addition of multivalent cations, most RNAs are found to be compacted as compared with their original, low ionic-strength sizes. These results suggest that sizes of long RNA molecules are determined by the branching pattern of their secondary structures. We also experimentally validate the proposed computational approaches for estimating hydrodynamic radii of single-stranded RNAs, which use generic RNA structure prediction tools and thus can be universally applied to a wide range of long RNAs.

Effects of RNA branching on the electrostatic stabilization of viruses

Many single-stranded (ss) ribonucleic acid (RNA) viruses self-assemble from capsid protein subunits and the nucleic acid to form an infectious virion. It is believed that the electrostatic interactions between the negatively charged RNA and the positively charged viral capsid proteins drive the encapsidation, although there is growing evidence that the sequence of the viral RNA also plays a role in packaging. In particular, the sequence will determine the possible secondary structures that the ssRNA will take in solution. In this work, we use a mean-field theory to investigate how the secondary structure of the RNA combined with electrostatic interactions affects the efficiency of assembly and stability of the assembled virions. We show that the secondary structure of RNA may result in negative osmotic pressures while a linear polymer causes positive osmotic pressures for the same conditions. This may suggest that the branched structure makes the RNA more effectively packaged and the virion more stable.

A Prüfer-Sequence Based Algorithm for Calculating the Size of Ideal Randomly Branched Polymers

Branched polymers can be represented as tree graphs. A one-to-one correspondence exists between a tree graph comprised of N labeled vertices and a sequence of N - 2 integers, known as the Prüfer sequence. Permutations of this sequence yield sequences corresponding to tree graphs with the same vertex-degree distribution but (generally) different branching patterns. Repeatedly shuffling the Prüfer sequence we have generated large ensembles of random tree graphs, all with the same degree distributions. We also present and apply an efficient algorithm to determine graph distances directly from their Prüfer sequences. From the (Prüfer sequence derived) graph distances, 3D size metrics, e.g., the polymer's radius of gyration, Rg, and average end-to-end distance, were then calculated using several different theoretical approaches. Applying our method to ideal randomly branched polymers of different vertex-degree distributions, all their 3D size measures are found to obey the usual N(1/4) scaling law. Among the branched polymers analyzed are RNA molecules comprised of equal proportions of the four-randomly distributed-nucleotides. Prior to Prüfer shuffling, the vertices of their representative tree graphs, these "random-sequence" RNAs exhibit an Rg ∼ N(1/3) scaling.

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?