Hamiltonian path analysis of viral genomes

The pseudoknot region and poly-(C) tract comprise an essential RNA packaging signal for assembly of foot-and-mouth disease virus

Virus assembly is a crucial step for the completion of the viral replication cycle. In addition to ensuring efficient incorporation of viral genomes into nascent virions, high specificity is required to prevent incorporation of host nucleic acids. For picornaviruses, including FMDV, the mechanisms required to fulfil these requirements are not well understood. However, recent evidence has suggested that specific RNA sequences dispersed throughout picornavirus genomes are involved in packaging. Here, we have shown that such sequences are essential for FMDV RNA packaging and have demonstrated roles for both the pseudoknot (PK) region and the poly-(C) tract in this process, where the length of the poly-(C) tract was found to influence the efficiency of RNA encapsidation. Sub-genomic replicons containing longer poly-(C) tracts were packaged with greater efficiency in trans, and viruses recovered from transcripts containing short poly-(C) tracts were found to have greatly extended poly-(C) tracts after only a single passage in cells, suggesting that maintaining a long poly-(C) tract provides a selective advantage. We also demonstrated a critical role for a packaging signal (PS) located in the pseudoknot (PK) region, adjacent to the poly-(C) tract, as well as several other non-essential but beneficial PSs elsewhere in the genome. Collectively, these PSs greatly enhanced encapsidation efficiency, with the poly-(C) tract possibly facilitating nearby PSs to adopt the correct conformation. Using these data, we have proposed a model where interactions with capsid precursors control a transition between two RNA conformations, directing the fate of nascent genomes to either be packaged or alternatively to act as templates for replication and/or for protein translation.

Context-dependent structure formation of hairpin motifs in bacteriophage MS2 genomic RNA

Many functions of ribonucleic acid (RNA) rely on its ability to assume specific sequence-structure motifs. Packaging signals found in certain RNA viruses are one such prominent example of functional RNA motifs. These signals are short hairpin loops that interact with coat proteins and drive viral self-assembly. As they are found in different positions along the much longer genomic RNA, the formation of their correct structure occurs as a part of a larger context. Any changes to this context can consequently lead to changes in the structure of the motifs themselves. In fact, previous studies have shown that structure and function of RNA motifs can be highly context sensitive to the flanking sequence surrounding them. However, in what ways different flanking sequences influence the structure of an RNA motif they surround has yet to be studied in detail. We focus on a hairpin-rich region of the RNA genome of bacteriophage MS2-a well-studied RNA virus with a wide potential for use in biotechnology-and systematically examine context-dependent structural stability of 14 previously identified hairpin motifs, which include putative and confirmed packaging signals. Combining secondary and tertiary RNA structure prediction of the hairpin motifs placed in different contexts, ranging from the native genomic sequence to random RNA sequences and unstructured poly-U sequences, we determine different measures of motif structural stability. In this way, we show that while some motif structures can be stable in any context, others require specific context provided by the genome. Our results demonstrate the importance of context in RNA structure formation and how changes in the flanking sequence of an RNA motif sometimes lead to drastic changes in its structure. Structural stability of a motif in different contexts could provide additional insights into its functionality as well as assist in determining whether it remains functional when intentionally placed in other contexts.

Molecular frustration: a hypothesis for regulation of viral infections

The recent revolution in imaging techniques and results from RNA footprinting in situ reveal how the bacteriophage MS2 genome regulates both particle assembly and genome release. We have proposed a model in which multiple packaging signal (PS) RNA-coat protein (CP) contacts orchestrate different stages of a viral life cycle. Programmed formation and release of specific PS contacts with CP regulates viral particle assembly and genome uncoating during cell entry. We hypothesize that molecular frustration, a concept introduced to understand protein folding, can be used to better rationalize how PSs function in both particle assembly and genome release. More broadly this concept may explain the directionality of viral life cycles, for example, the roles of host cofactors in HIV infection. We propose that this is a universal principle in virology that explains mechanisms of host-virus interaction and suggests diverse therapeutic interventions.

A multidisciplinary approach to the identification of the protein-RNA connectome in double-stranded RNA virus capsids

How multi-segmented double-stranded RNA (dsRNA) viruses correctly incorporate their genomes into their capsids remains unclear for many viruses, including Bluetongue virus (BTV), a Reoviridae member, with a genome of 10 segments. To address this, we used an RNA-cross-linking and peptide-fingerprinting assay (RCAP) to identify RNA binding sites of the inner capsid protein VP3, the viral polymerase VP1 and the capping enzyme VP4. Using a combination of mutagenesis, reverse genetics, recombinant proteins and in vitro assembly, we validated the importance of these regions in virus infectivity. Further, to identify which RNA segments and sequences interact with these proteins, we used viral photo-activatable ribonucleoside crosslinking (vPAR-CL) which revealed that the larger RNA segments (S1-S4) and the smallest segment (S10) have more interactions with viral proteins than the other smaller segments. Additionally, using a sequence enrichment analysis we identified an RNA motif of nine bases that is shared by the larger segments. The importance of this motif for virus replication was confirmed by mutagenesis followed by virus recovery. We further demonstrated that these approaches could be applied to a related Reoviridae member, rotavirus (RV), which has human epidemic impact, offering the possibility of novel intervention strategies for a human pathogen.

Genome-regulated Assembly of a ssRNA Virus May Also Prepare It for Infection

Many single-stranded, positive-sense RNA viruses regulate assembly of their infectious virions by forming multiple, cognate coat protein (CP)-genome contacts at sites termed Packaging Signals (PSs). We have determined the secondary structures of the bacteriophage MS2 ssRNA genome (gRNA) frozen in defined states using constraints from X-ray synchrotron footprinting (XRF). Comparison of the footprints from phage and transcript confirms the presence of multiple PSs in contact with CP dimers in the former. This is also true for a virus-like particle (VLP) assembled around the gRNA in vitro in the absence of the single-copy Maturation Protein (MP) found in phage. Since PS folds are present at many sites across gRNA transcripts, it appears that this genome has evolved to facilitate this mechanism of assembly regulation. There are striking differences between the gRNA-CP contacts seen in phage and the VLP, suggesting that the latter are inappropriate surrogates for aspects of phage structure/function. Roughly 50% of potential PS sites in the gRNA are not in contact with the protein shell of phage. However, many of these sit adjacent to, albeit not in contact with, PS-binding sites on CP dimers. We hypothesize that these act as PSs transiently during assembly but subsequently dissociate. Combining the XRF data with PS locations from an asymmetric cryo-EM reconstruction suggests that the genome positions of such dissociations are non-random and may facilitate infection. The loss of many PS-CP interactions towards the 3' end of the gRNA would allow this part of the genome to transit more easily through the narrow basal body of the pilus extruding machinery. This is the known first step in phage infection. In addition, each PS-CP dissociation event leaves the protein partner trapped in a non-lowest free-energy conformation. This destabilizes the protein shell which must disassemble during infection, further facilitating this stage of the life-cycle.

Compositional complementarity between genomic RNA and coat proteins in positive-sense single-stranded RNA viruses

During packaging in positive-sense single-stranded RNA (+ssRNA) viruses, coat proteins (CPs) interact directly with multiple regions in genomic RNA (gRNA), but the underlying physicochemical principles remain unclear. Here we analyze the high-resolution cryo-EM structure of bacteriophage MS2 and show that the gRNA/CP binding sites, including the known packaging signal, overlap significantly with regions where gRNA nucleobase-density profiles match the corresponding CP nucleobase-affinity profiles. Moreover, we show that the MS2 packaging signal corresponds to the global minimum in gRNA/CP interaction energy in the unstructured state as derived using a linearly additive model and knowledge-based nucleobase/amino-acid affinities. Motivated by this, we predict gRNA/CP interaction sites for a comprehensive set of 1082 +ssRNA viruses. We validate our predictions by comparing them with site-resolved information on gRNA/CP interactions derived in SELEX and CLIP experiments for 10 different viruses. Finally, we show that in experimentally studied systems CPs frequently interact with autologous coding regions in gRNA, in agreement with both predicted interaction energies and a recent proposal that proteins in general tend to interact with own mRNAs, if unstructured. Our results define a self-consistent framework for understanding packaging in +ssRNA viruses and implicate interactions between unstructured gRNA and CPs in the process.

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.

Finding Hamiltonian and Longest (s,t)-Paths of C-Shaped Supergrid Graphs in Linear Time

A graph is called Hamiltonian connected if it contains a Hamiltonian path between any two distinct vertices. In the past, we proved the Hamiltonian path and cycle problems for general supergrid graphs to be NP-complete. However, they are still open for solid supergrid graphs. In this paper, first we will verify the Hamiltonian cycle property of C-shaped supergrid graphs, which are a special case of solid supergrid graphs. Next, we show that C-shaped supergrid graphs are Hamiltonian connected except in a few conditions. For these excluding conditions of Hamiltonian connectivity, we compute their longest paths. Then, we design a linear-time algorithm to solve the longest path problem in these graphs. The Hamiltonian connectivity of C-shaped supergrid graphs can be applied to compute the optimal stitching trace of computer embroidery machines, and construct the minimum printing trace of 3D printers with a C-like component being printed.

Programmable polymorphism of a virus-like particle

Virus-like particles (VLPs) have significant potential as artificial vaccines and drug delivery systems. The ability to control their size has wide ranging utility but achieving such controlled polymorphism using a single protein subunit is challenging as it requires altering VLP geometry. Here we achieve size control of MS2 bacteriophage VLPs via insertion of amino acid sequences in an external loop to shift morphology to significantly larger forms. The resulting VLP size and geometry is controlled by altering the length and type of the insert. Cryo electron microscopy structures of the new VLPs, in combination with a kinetic model of their assembly, show that the abundance of wild type (T = 3), T = 4, D3 and D5 symmetrical VLPs can be biased in this way. We propose a mechanism whereby the insert leads to a change in the dynamic behavior of the capsid protein dimer, affecting the interconversion between the symmetric and asymmetric conformers and thus determining VLP size and morphology.

Machine-learning a virus assembly fitness landscape

Realistic evolutionary fitness landscapes are notoriously difficult to construct. A recent cutting-edge model of virus assembly consists of a dodecahedral capsid with 12 corresponding packaging signals in three affinity bands. This whole genome/phenotype space consisting of 312 genomes has been explored via computationally expensive stochastic assembly models, giving a fitness landscape in terms of the assembly efficiency. Using latest machine-learning techniques by establishing a neural network, we show that the intensive computation can be short-circuited in a matter of minutes to astounding accuracy.

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.

Individual subunits of a rhinovirus causing common cold exhibit largely different protein-RNA contact site conformations

Rhinoviruses cause the common cold. They are icosahedral, built from sixty copies each of the capsid proteins VP1 through VP4 arranged in a pseudo T = 3 lattice. This shell encases a ss(+) RNA genome. Three-D classification of single and oligomeric asymmetric units computationally excised from a 2.9 Å cryo-EM density map of rhinovirus A89, showed that VP4 and the N-terminal extension of VP1 adopt different conformations within the otherwise identical 3D-structures. Analysis of up to sixty classes of single subunits and of six classes of subunit dimers, trimers, and pentamers revealed different orientations of the amino acid residues at the interface with the RNA suggesting that local asymmetry is dictated by disparities of the interacting nucleotide sequences. The different conformations escape detection by 3-D structure determination of entire virions with the conformational heterogeneity being only indicated by low density. My results do not exclude that the RNA follows a conserved assembly mechanism, contacting most or all asymmetric units in a specific way. However, as suggested by the gradual loss of asymmetry with increasing oligomerization and the 3D-structure of entire virions reconstructed by using Euler angles selected in the classification of single subunits, RNA path and/or folding likely differ from virion to virion.

From analysis of up to sixty classes of single subunits and of six classes of subunit dimers, trimers, and pentamers, Dieter Blaas demonstrates different orientations of the amino acid residues at the interface with the RNA. This study suggests that RNA path and/or folding is likely to differ from virion to virion.

A multiscale model of virus pandemic: Heterogeneous interactive entities in a globally connected world

This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called SARS-CoV-2 Severe Acute Respiratory Syndrome, corona virus n.2. The study is developed within a multiscale framework accounting for the interaction of different spatial scales, from the small scale of the virus itself and cells, to the large scale of individuals and further up to the collective behaviour of populations. An interdisciplinary vision is developed thanks to the contributions of epidemiologists, immunologists and economists as well as those of mathematical modellers. The first part of the contents is devoted to understanding the complex features of the system and to the design of a modelling rationale. The modelling approach is treated in the second part of the paper by showing both how the virus propagates into infected individuals, successfully and not successfully recovered, and also the spatial patterns, which are subsequently studied by kinetic and lattice models. The third part reports the contribution of research in the fields of virology, epidemiology, immune competition, and economy focussed also on social behaviours. Finally, a critical analysis is proposed looking ahead to research perspectives.

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.

Structural puzzles in virology solved with an overarching icosahedral design principle

Viruses have evolved protein containers with a wide spectrum of icosahedral architectures to protect their genetic material. The geometric constraints defining these container designs, and their implications for viral evolution, are open problems in virology. The principle of quasi-equivalence is currently used to predict virus architecture, but improved imaging techniques have revealed increasing numbers of viral outliers. We show that this theory is a special case of an overarching design principle for icosahedral, as well as octahedral, architectures that can be formulated in terms of the Archimedean lattices and their duals. These surface structures encompass different blueprints for capsids with the same number of structural proteins, as well as for capsid architectures formed from a combination of minor and major capsid proteins, and are recurrent within viral lineages. They also apply to other icosahedral structures in nature, and offer alternative designs for man-made materials and nanocontainers in bionanotechnology.

A coarse-grained model of the expansion of the human rhinovirus 2 capsid reveals insights in genome release

Human rhinoviruses are causative agents of the common cold. In order to release their RNA genome into the host during a viral infection, these small viruses must undergo conformational changes in their capsids, whose detailed mechanism is strictly related to the process of RNA extrusion, which has been only partially elucidated. We study here a mathematical model for the structural transition between the native particle of human rhinovirus type 2 and its expanded form, viewing the process as an energy cascade, i.e. a sequence of metastable states with decreasing energy connected by minimum energy paths. We explore several transition pathways and discuss their implications for the RNA exit process.

Spontaneous Domain Formation in Spherically Confined Elastic Filaments

Although the free energy of a genome packing into a virus is dominated by DNA-DNA interactions, ordering of the DNA inside the capsid is elasticity driven, suggesting general solutions with DNA organized into spool-like domains. Using analytical calculations and computer simulations of a long elastic filament confined to a spherical container, we show that the ground state is not a single spool as assumed hitherto, but an ordering mosaic of multiple homogeneously ordered domains. At low densities, we observe concentric spools, while at higher densities, other morphologies emerge, which resemble topological links. We discuss our results in the context of metallic wires, viral DNA, and flexible polymers.

RNA-Mediated Virus Assembly: Mechanisms and Consequences for Viral Evolution and Therapy

Viruses, entities composed of nucleic acids, proteins, and in some cases lipids lack the ability to replicate outside their target cells. Their components self-assemble at the nanoscale with exquisite precision-a key to their biological success in infection. Recent advances in structure determination and the development of biophysical tools such as single-molecule spectroscopy and noncovalent mass spectrometry allow unprecedented access to the detailed assembly mechanisms of simple virions. Coupling these techniques with mathematical modeling and bioinformatics has uncovered a previously unsuspected role for genomic RNA in regulating formation of viral capsids, revealing multiple, dispersed RNA sequence/structure motifs [packaging signals (PSs)] that bind cognate coat proteins cooperatively. The PS ensemble controls assembly efficiency and accounts for the packaging specificity seen in vivo. The precise modes of action of the PSs vary between viral families, but this common principle applies across many viral families, including major human pathogens. These insights open up the opportunity to block or repurpose PS function in assembly for both novel antiviral therapy and gene/drug/vaccine applications.

A modelling paradigm for RNA virus assembly

Virus assembly, a key stage in any viral life cycle, had long been considered to be primarily driven by protein-protein interactions and nonspecific interactions between genomic RNA and capsid protein. We review here a modelling paradigm for RNA virus assembly that illustrates the crucial roles of multiple dispersed, specific interactions between viral genomes and coat proteins in capsid assembly. The model reveals how multiple sequence-structure motifs in the genomic RNA, termed packaging signals, with a shared coat protein recognition motif enable viruses to overcome a viral assembly-equivalent of Levinthal's Paradox in protein folding. The fitness advantages conferred by this mechanism suggest that it should be widespread in viruses, opening up new perspectives on viral evolution and anti-viral therapy.