Icosahedral packing of RNA viral genomes

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.

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.

In vitro functional analysis of gRNA sites regulating assembly of hepatitis B virus

The roles of RNA sequence/structure motifs, Packaging Signals (PSs), for regulating assembly of an HBV genome transcript have been investigated in an efficient in vitro assay containing only core protein (Cp) and RNA. Variants of three conserved PSs, within the genome of a strain not used previously, preventing correct presentation of a Cp-recognition loop motif are differentially deleterious for assembly of nucleocapsid-like particles (NCPs). Cryo-electron microscopy reconstruction of the T = 4 NCPs formed with the wild-type gRNA transcript, reveal that the interior of the Cp shell is in contact with lower resolution density, potentially encompassing the arginine-rich protein domains and gRNA. Symmetry relaxation followed by asymmetric reconstruction reveal that such contacts are made at every symmetry axis. We infer from their regulation of assembly that some of these contacts would involve gRNA PSs, and confirmed this by X-ray RNA footprinting. Mutation of the ε stem-loop in the gRNA, where polymerase binds in vivo, produces a poor RNA assembly substrate with Cp alone, largely due to alterations in its conformation. The results show that RNA PSs regulate assembly of HBV genomic transcripts in vitro, and therefore may play similar roles in vivo, in concert with other molecular factors.

Core Protein-Directed Antivirals and Importin β Can Synergistically Disrupt HBV Capsids

Viral structural proteins can have multiple activities. Antivirals that target structural proteins have potential to exhibit multiple antiviral mechanisms. Hepatitis B Virus (HBV) core protein (Cp) is involved in most stages of the viral lifecycle: it assembles into capsids, packages viral RNA, is a metabolic compartment for reverse transcription, interacts with nuclear trafficking machinery, and disassembles to release the viral genome into the nucleus. During nuclear localization, HBV capsids bind to host importins (e.g. Impβ) via Cp's C-terminal domain (CTD); the CTD is localized to the interior of the capsid and is transiently exposed on the exterior. We used HAP12 as a representative Cp Allosteric Modulators (CpAMs), a class of antivirals that inappropriately stimulates and misdirects HBV assembly and deforms capsids. CpAM impact on other aspects of the HBV lifecycle is poorly understood. We investigated how HAP12 influenced the interactions between empty or RNA-filled capsids with Impβ and trypsin in vitro. We showed that HAP12 can modulate CTD accessibility and capsid stability, depending on the saturation of HAP12-binding sites. We demonstrated that Impβ synergistically contributes to capsid disruption at high levels of HAP12 saturation, using electron microscopy to visualize disruption and rearrangement of Cp dimers into aberrant complexes. However, RNA-filled capsids resisted the destabilizing effects of HAP12 and Impβ. In summary, we show host protein-induced catalysis of capsid disruption, an unexpected additional mechanism of action for CpAMs. Potentially, untimely capsid disassembly can hamper the HBV lifecycle and also cause the virus to become vulnerable to host innate immune responses. IMPORTANCE The HBV core, an icosahedral complex of 120 copies of the homodimeric core (capsid) protein with or without packaged nucleic acid, is transported to the host nucleus by its interaction with host importin proteins. Importin-core interaction requires the core protein C-terminal domain, which is inside the capsid, to "flip" to the capsid exterior. Core-protein directed drugs that affect capsid assembly and stability have been developed recently. We show that these molecules can, synergistically with importins, disrupt capsids. This mechanism of action, synergism with host protein, has potential to disrupt the virus lifecycle and activate the innate immune system.

RNA nanotechnology to build a dodecahedral genome of single-stranded RNA virus

The quest for artificial RNA viral complexes with authentic structure while being non-replicative is on its way for the development of viral vaccines. RNA viruses contain capsid proteins that interact with the genome during morphogenesis. The sequence and properties of the protein and genome determine the structure of the virus. For example, the Pariacoto virus ssRNA genome assembles into a dodecahedron. Virus-inspired nanotechnology has progressed remarkably due to the unique structural and functional properties of viruses, which can inspire the design of novel nanomaterials. RNA is a programmable biopolymer able to self-assemble sophisticated 3D structures with rich functionalities. RNA dodecahedrons mimicking the Pariacoto virus quasi-icosahedral genome structures were constructed from both native and 2'-F modified RNA oligos. The RNA dodecahedron easily self-assembled using the stable pRNA three-way junction of bacteriophage phi29 as building blocks. The RNA dodecahedron cage was further characterized by cryo-electron microscopy and atomic force microscopy, confirming the spontaneous and homogenous formation of the RNA cage. The reported RNA dodecahedron cage will likely provide further studies on the mechanisms of interaction of the capsid protein with the viral genome while providing a template for further construction of the viral RNA scaffold to add capsid proteins for the assembly of the viral nucleocapsid as a model. Understanding the self-assembly and RNA folding of this RNA cage may offer new insights into the 3D organization of viral RNA genomes. The reported RNA cage also has the potential to be explored as a novel virus-inspired nanocarrier.

Physics of viral dynamics

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

Rewriting nature's assembly manual for a ssRNA virus

Satellite tobacco necrosis virus (STNV) is one of the smallest viruses known. Its genome encodes only its coat protein (CP) subunit, relying on the polymerase of its helper virus TNV for replication. The genome has been shown to contain a cryptic set of dispersed assembly signals in the form of stem-loops that each present a minimal CP-binding motif AXXA in the loops. The genomic fragment encompassing nucleotides 1-127 is predicted to contain five such packaging signals (PSs). We have used mutagenesis to determine the critical assembly features in this region. These include the CP-binding motif, the relative placement of PS stem-loops, their number, and their folding propensity. CP binding has an electrostatic contribution, but assembly nucleation is dominated by the recognition of the folded PSs in the RNA fragment. Mutation to remove all AXXA motifs in PSs throughout the genome yields an RNA that is unable to assemble efficiently. In contrast, when a synthetic 127-nt fragment encompassing improved PSs is swapped onto the RNA otherwise lacking CP recognition motifs, assembly is partially restored, although the virus-like particles created are incomplete, implying that PSs outside this region are required for correct assembly. Swapping this improved region into the wild-type STNV1 sequence results in a better assembly substrate than the viral RNA, producing complete capsids and outcompeting the wild-type genome in head-to-head competition. These data confirm details of the PS-mediated assembly mechanism for STNV and identify an efficient approach for production of stable virus-like particles encapsidating nonnative RNAs or other cargoes.

Protein Assembly: Versatile Approaches to Construct Highly Ordered Nanostructures

Nature endows life with a wide variety of sophisticated, synergistic, and highly functional protein assemblies. Following Nature's inspiration to assemble protein building blocks into exquisite nanostructures is emerging as a fascinating research field. Dictating protein assembly to obtain highly ordered nanostructures and sophisticated functions not only provides a powerful tool to understand the natural protein assembly process but also offers access to advanced biomaterials. Over the past couple of decades, the field of protein assembly has undergone unexpected and rapid developments, and various innovative strategies have been proposed. This Review outlines recent advances in the field of protein assembly and summarizes several strategies, including biotechnological strategies, chemical strategies, and combinations of these approaches, for manipulating proteins to self-assemble into desired nanostructures. The emergent applications of protein assemblies as versatile platforms to design a wide variety of attractive functional materials with improved performances have also been discussed. The goal of this Review is to highlight the importance of this highly interdisciplinary field and to promote its growth in a diverse variety of research fields ranging from nanoscience and material science to synthetic biology.

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.

Revealing the density of encoded functions in a viral RNA

We present direct experimental evidence that assembly of a single-stranded RNA virus occurs via a packaging signal-mediated mechanism. We show that the sequences of coat protein recognition motifs within multiple, dispersed, putative RNA packaging signals, as well as their relative spacing within a genomic fragment, act collectively to influence the fidelity and yield of capsid self-assembly in vitro. These experiments confirm that the selective advantages for viral yield and encapsidation specificity, predicted from previous modeling of packaging signal-mediated assembly, are found in Nature. Regions of the genome that act as packaging signals also function in translational and transcriptional enhancement, as well as directly coding for the coat protein, highlighting the density of encoded functions within the viral RNA. Assembly and gene expression are therefore direct molecular competitors for different functional folds of the same RNA sequence. The strongest packaging signal in the test fragment, encodes a region of the coat protein that undergoes a conformational change upon contact with packaging signals. A similar phenomenon occurs in other RNA viruses for which packaging signals are known. These contacts hint at an even deeper density of encoded functions in viral RNA, which if confirmed, would have profound consequences for the evolution of this class of pathogens.

Building polyhedra by self-assembly: theory and experiment

We investigate the utility of a mathematical framework based on discrete geometry to model biological and synthetic self-assembly. Our primary biological example is the self-assembly of icosahedral viruses; our synthetic example is surface-tension-driven self-folding polyhedra. In both instances, the process of self-assembly is modeled by decomposing the polyhedron into a set of partially formed intermediate states. The set of all intermediates is called the configuration space, pathways of assembly are modeled as paths in the configuration space, and the kinetics and yield of assembly are modeled by rate equations, Markov chains, or cost functions on the configuration space. We review an interesting interplay between biological function and mathematical structure in viruses in light of this framework. We discuss in particular: (i) tiling theory as a coarse-grained description of all-atom models; (ii) the building game-a growth model for the formation of polyhedra; and (iii) the application of these models to the self-assembly of the bacteriophage MS2. We then use a similar framework to model self-folding polyhedra. We use a discrete folding algorithm to compute a configuration space that idealizes surface-tension-driven self-folding and analyze pathways of assembly and dominant intermediates. These computations are then compared with experimental observations of a self-folding dodecahedron with side 300 μm. In both models, despite a combinatorial explosion in the size of the configuration space, a few pathways and intermediates dominate self-assembly. For self-folding polyhedra, the dominant intermediates have fewer degrees of freedom than comparable intermediates, and are thus more rigid. The concentration of assembly pathways on a few intermediates with distinguished geometric properties is biologically and physically important, and suggests deeper mathematical structure.

Encapsidated hepatitis B virus reverse transcriptase is poised on an ordered RNA lattice

Assembly of a hepatitis B virus (HBV) virion begins with the formation of an RNA-filled core composed of a symmetrical capsid (built of core protein), viral pregenomic RNA, and viral reverse transcriptase. To generate the circular dsDNA genome of HBV, reverse transcription requires multiple template switches within the confines of the capsid. To date, most anti-HBV therapeutics target this reverse transcription process. The detailed molecular mechanisms of this crucial process are poorly understood because of the lack of structural information. We hypothesized that capsid, RNA, and viral reverse transcriptase would need a precise geometric organization to accomplish reverse transcription. Here we present the asymmetric structure of authentic RNA-filled cores, determined to 14.5-Å resolution from cryo-EM data. Capsid and RNA are concentric. On the interior of the RNA, we see a distinct donut-like density, assigned to viral reverse transcriptase, which pins the viral pregenomic RNA to the capsid inner surface. The observation of a unique ordered structure inside the core suggests that assembly and the first steps of reverse transcription follow a single, determinate pathway and strongly suggests that all subsequent steps in DNA synthesis do as well.

Packaging signals in two single-stranded RNA viruses imply a conserved assembly mechanism and geometry of the packaged genome

The current paradigm for assembly of single-stranded RNA viruses is based on a mechanism involving non-sequence-specific packaging of genomic RNA driven by electrostatic interactions. Recent experiments, however, provide compelling evidence for sequence specificity in this process both in vitro and in vivo. The existence of multiple RNA packaging signals (PSs) within viral genomes has been proposed, which facilitates assembly by binding coat proteins in such a way that they promote the protein-protein contacts needed to build the capsid. The binding energy from these interactions enables the confinement or compaction of the genomic RNAs. Identifying the nature of such PSs is crucial for a full understanding of assembly, which is an as yet untapped potential drug target for this important class of pathogens. Here, for two related bacterial viruses, we determine the sequences and locations of their PSs using Hamiltonian paths, a concept from graph theory, in combination with bioinformatics and structural studies. Their PSs have a common secondary structure motif but distinct consensus sequences and positions within the respective genomes. Despite these differences, the distributions of PSs in both viruses imply defined conformations for the packaged RNA genomes in contact with the protein shell in the capsid, consistent with a recent asymmetric structure determination of the MS2 virion. The PS distributions identified moreover imply a preferred, evolutionarily conserved assembly pathway with respect to the RNA sequence with potentially profound implications for other single-stranded RNA viruses known to have RNA PSs, including many animal and human pathogens.

Evidence that viral RNAs have evolved for efficient, two-stage packaging

Genome packaging is an essential step in virus replication and a potential drug target. Single-stranded RNA viruses have been thought to encapsidate their genomes by gradual co-assembly with capsid subunits. In contrast, using a single molecule fluorescence assay to monitor RNA conformation and virus assembly in real time, with two viruses from differing structural families, we have discovered that packaging is a two-stage process. Initially, the genomic RNAs undergo rapid and dramatic (approximately 20-30%) collapse of their solution conformations upon addition of cognate coat proteins. The collapse occurs with a substoichiometric ratio of coat protein subunits and is followed by a gradual increase in particle size, consistent with the recruitment of additional subunits to complete a growing capsid. Equivalently sized nonviral RNAs, including high copy potential in vivo competitor mRNAs, do not collapse. They do support particle assembly, however, but yield many aberrant structures in contrast to viral RNAs that make only capsids of the correct size. The collapse is specific to viral RNA fragments, implying that it depends on a series of specific RNA-protein interactions. For bacteriophage MS2, we have shown that collapse is driven by subsequent protein-protein interactions, consistent with the RNA-protein contacts occurring in defined spatial locations. Conformational collapse appears to be a distinct feature of viral RNA that has evolved to facilitate assembly. Aspects of this process mimic those seen in ribosome assembly.

Simple rules for efficient assembly predict the layout of a packaged viral RNA

Single-stranded RNA (ssRNA) viruses, which include major human pathogens, package their genomes as they assemble their capsids. We show here that the organization of the viral genomes within the capsids provides intriguing insights into the highly cooperative nature of the assembly process. A recent cryo-electron microscopy structure of bacteriophage MS2, determined with only 5-fold symmetry averaging, has revealed the asymmetric distribution of its encapsidated genome. Here we show that this RNA distribution is consistent with an assembly mechanism that follows two simple rules derived from experiment: (1) the binding of the MS2 maturation protein to the RNA constrains its conformation into a loop, and (2) the capsid must be built in an energetically favorable way. These results provide a new level of insight into the factors that drive efficient assembly of ssRNA viruses in vivo.

Nematic ordering of polymers in confined geometry applied to DNA packaging in viral capsids

A density functional theory of the spatial distribution and biaxial nematic order of polymers of arbitrary length and rigidity inside a spherical cavity is proposed. The local order of different chain segments is considered as an alignment to a spatially varying director field of cylindrical symmetry. The steric interactions are taken into account in the second virial approximation. Polymer density and orientational order distributions inside the spherically cavity are the principal results. It was found that short and flexible polymers were located at the center of the sphere and were orientationaly disordered. Upon increasing polymer length and/or polymer rigidity, the location of the polymer was continuously shifted toward the surface of the spherical cavity and the polymer segments became gradually more aligned. Parameters have been selected to model the behavior of genomes in spherical viral capsids.

Encapsulation of a polymer by an icosahedral virus

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

Direct observation of multiple pathways of single-stranded DNA stretching

We observed multiple pathways of stretching single-stranded polydeoxynucleotides, poly(dA). Poly(dA) has been shown to undergo unique transitions under mechanical force, and such transitions were attributed to the stacking characteristics of poly(dA). Using single-molecule manipulation studies, we found that poly(dA) has two stretching pathways at high forces. The previously observed pathway has a free energy that is less than what is expected of single-stranded DNA with a random sequence, indicating the existence of a novel conformation of poly(dA) at large extensions. We also observed stepwise transitions between the two pathways by pulling the molecule with constant force, and found that the transitions are cooperative. These results suggest that the unique mechanical property of poly(dA) may play an important role in biological processes such as gene expression.

Mechanisms of capsid assembly around a polymer

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

A theory for viral capsid assembly around electrostatic cores

We develop equilibrium and kinetic theories that describe the assembly of viral capsid proteins on a charged central core, as seen in recent experiments in which brome mosaic virus capsids assemble around nanoparticles functionalized with polyelectrolyte. We model interactions between capsid proteins and nanoparticle surfaces as the interaction of polyelectrolyte brushes with opposite charge using the nonlinear Poisson Boltzmann equation. The models predict that there is a threshold density of functionalized charge, above which capsids efficiently assemble around nanoparticles, and that light scatter intensity increases rapidly at early times without the lag phase characteristic of empty capsid assembly. These predictions are consistent with and enable interpretation of preliminary experimental data. However, the models predict a stronger dependence of nanoparticle incorporation efficiency on functionalized charge density than measured in experiments and do not completely capture a logarithmic growth phase seen in experimental light scatter. These discrepancies may suggest the presence of metastable disordered states in the experimental system. In addition to discussing future experiments for nanoparticle-capsid systems, we discuss broader implications for understanding assembly around charged cores such as nucleic acids.

Heparin binding induces conformational changes in Adeno-associated virus serotype 2

Adeno-associated virus serotype 2 (AAV2) uses heparan sulfate proteoglycan as a cell surface-attachment receptor. In this study the structures of AAV2 alone and complexed with heparin were determined to approximately 18A resolution using cryo-electron microscopy and three-dimensional image reconstruction. A difference map showed positive density, modeled as heparin, close to the icosahedral twofold axes and between the protrusions that surround the threefold axes of the capsid. Regions of the model near the threefold place the receptor in close proximity to basic residues previously identified as part of the heparin binding site. The region of the model near the twofold axes identifies a second contact site, not previously characterized but which is also possibly configured by heparin binding. The difference map also revealed two significant conformational changes: (I) at the tops of the threefold protrusions, which have become flattened in the complex, and (II) at the fivefold axes where the top of the channel is widened possibly in response to movement of the HI loops in the capsid proteins. Ordered density in the interior of the capsid in the AAV2-heparin complex was interpreted as nucleic acid, consistent with the presence of non-viral DNA in the expressed capsids.

Radial distribution of RNA genomes packaged inside spherical viruses

The problem of RNA genomes packaged inside spherical viruses is studied. The RNA-capsid attraction is assumed to be nonspecific and occurs at the inner capsid surface only. For weak attraction, RNA concentration is maximum at the center of the capsid to maximize their configurational entropy. For stronger attraction, RNA concentration peaks near the capsid surface. In the latter case, the competition between the branching of RNA secondary structure and its adsorption to the inner capsid results in the formation of a dense layer of RNA near capsid surface. The layer thickness is a slowly varying (logarithmic) function of the capsid inner radius. Consequently, the amount of RNA packaged is proportional to the capsid area (or the number of proteins) instead of its volume. The numerical profiles describe reasonably well the observed RNA concentration profiles of various viruses.

Controlling viral capsid assembly with templating

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

Structural transitions of encapsidated polyelectrolytes

Conformations and structural transitions of polyelectrolytes strictly confined onto a spherical 2D surface have been investigated by scaling descriptions based on physical arguments concerning polyelectrolyte adsorption onto planar surface and liquid crystals as well as by Monte Carlo simulations using a bead-spring model with short-range and electrostatic repulsions. In case of the electrostatic screened regime, a disordered-ordered (spiral) transition at increasing persistence length of the chain was found. It was predicted that the transition occurred when the persistence length is comparable with the mean spacing between adjacent strands of the ordered chain. The presence of a non-screened electrostatic repulsion led to a more complex behavior with i) a re-entrant order-disorder transition and ii) a tennis ball texture as an additional smectic/nematic structure. The various competing structures given by the theory were recovered by the Monte Carlo simulations, which also indicated that the tennis ball texture was favored over the spiral structure by the long-range interactions for semi-flexible chains.

Monte Carlo simulations of flexible polyelectrolytes inside viral capsids with dodecahedral charge distribution

Structural properties of encapsidated flexible polyelectrolytes in viral capsids with dodecahedral charge distribution have been investigated by Monte Carlo simulations using a coarse-grained model. Several capsid charge distributions ranging from a homogeneous surface charge distribution (lambda=0) to a complete dodecahedral distribution (lambda=1) at constant total capsid charge and fixed radial location of the capsid charges have been considered. The radial and lateral organizations of the polyelectrolyte have been examined as a function of the polyelectrolyte length and capsid charge distribution. With short polyelectrolytes a single polyelectrolyte layer was formed at the inner capsid surface, whereas at increasing polyelectrolyte length also a uniform polyelectrolyte density inside the surface layer was established. At low lambda , the polyelectrolyte layer was laterally isotropic, but at lambda> or =0.05 a dodecahedral structure started to appear. At lambda=1 , the polyelectrolyte followed essentially a path along the edges of a dodecahedron. With sufficiently long chains, all edges were decorated with polyelectrolyte, facilitated by loop formation. For an undercharged capsid, the capsid counterions inside the capsid also adopted a dodecahedral distribution.

Mathematical virology: a novel approach to the structure and assembly of viruses

Understanding the structure and life cycle of viruses is a fascinating challenge with a crucial impact on the public health sector. In the early 1960s, Caspar & Klug (Caspar & Klug 1962 Cold Spring Harbor Symp. Quant. Biol. 27, 1-24) established a theory for the prediction of the surface structures of the protein shells, called viral capsids, which encapsulate and hence provide protection for the viral genome. It is of fundamental importance in virology, with a broad spectrum of applications ranging from the image analysis and classification of experimental data to the construction of assembly models. However, experimental results have provided evidence for the fact that it is incomplete and, in particular, cannot account for the structures of Papovaviridae, which are of particular interest because they contain cancer-causing viruses. This gap has recently been closed by the viral tiling theory, which describes the locations of the protein subunits and inter-subunit bonds in viral capsids based on mathematical tools from the area of quasicrystals. The predictions and various recent applications of the new theory are presented, and it is discussed how further research along these lines may lead to new insights in virology and the design of anti-viral therapeutics.

Physics of RNA and viral assembly

The overview discusses the application of physical arguments to structure and function of single-stranded viral RNA genomes.