Structural puzzles in virology solved with an overarching icosahedral design principle

Exploring the Effects of Intersubunit Interface Mutations on Virus-Like Particle Structure and Stability

Virus-like particles (VLPs) from bacteriophage MS2 provide a platform to study protein self-assembly and create engineered systems for drug delivery. Here, we aim to understand the impact of intersubunit interface mutations on the local and global structure and function of MS2-based VLPs. In previous work, our lab identified locally supercharged double mutants [T71K/G73R] that concentrate positive charge at capsid pores, enhancing uptake into mammalian cells. To study the effects of particle size on cellular internalization, we combined these double mutants with a single point mutation [S37P] that was previously reported to switch particle geometry from T = 3 to T = 1 icosahedral symmetry. These new variants retained their enhanced cellular uptake activity and could deliver small-molecule drugs with efficacy levels similar to our first-generation capsids. Surprisingly, these engineered triple mutants exhibit increased thermostability and unexpected geometry, producing T = 3 particles instead of the anticipated T = 1 assemblies. Transmission electron microscopy revealed various capsid assembly states, including wild-type (T = 3), T = 1, and rod-like particles, that could be accessed using different combinations of these point mutations. Molecular dynamics experiments recapitulated the structural rationale in silico for the single point mutation [S37P] forming a T = 1 virus-like particle and showed that this assembly state was not favored when combined with mutations that favor rod-like architectures. Through this work, we investigated how interdimer interface dynamics influence VLP size and morphology and how these properties affect particle function in applications such as drug delivery.

Studying Biomolecular Protein Complexes via Origami and 3D-Printed Models

Living organisms are constructed from proteins that assemble into biomolecular complexes, each with a unique shape and function. Our knowledge about the structure-activity relationship of these complexes is still limited, mainly because of their small size, complex structure, fast processes, and changing environment. Furthermore, the constraints of current microscopic tools and the difficulty in applying molecular dynamic simulations to capture the dynamic response of biomolecular complexes and long-term phenomena call for new supplementary tools and approaches that can help bridge this gap. In this paper, we present an approach to comparing biomolecular and origami hierarchical structures and apply it to comparing bacterial microcompartments (BMCs) with spiral-based origami models. Our first analysis compares proteins that assemble the BMC with an origami model called "flasher", which is the unit cell of an assembled origami model. Then, the BMC structure is compared with the assembled origami model and based on the similarity, a physical scaled-up origami model, which is analogous to the BMC, is constructed. The origami model is translated into a computer-aided design model and manufactured via 3D-printing technology. Finite element analysis and physical experiments of the origami model and 3D-printed parts reveal trends in the mechanical response of the icosahedron, which is constructed from tiled-chiral elements. The chiral elements rotate as the icosahedron expands and we deduce that it allows the BMC to open gates for transmembrane passage of materials.

Point mutation in a virus-like capsid drives symmetry reduction to form tetrahedral cages

Protein capsids are a widespread form of compartmentalization in nature. Icosahedral symmetry is ubiquitous in capsids derived from spherical viruses, as this geometry maximizes the internal volume that can be enclosed within. Despite the strong preference for icosahedral symmetry, we show that simple point mutations in a virus-like capsid can drive the assembly of unique symmetry-reduced structures. Starting with the encapsulin from Myxococcus xanthus, a 180-mer bacterial capsid that adopts the well-studied viral HK97 fold, we use mass photometry and native charge detection mass spectrometry to identify a triple histidine point mutant that forms smaller dimorphic assemblies. Using cryoelectron microscopy, we determine the structures of a precedented 60-mer icosahedral assembly and an unexpected 36-mer tetrahedron that features significant geometric rearrangements around a new interaction surface between capsid protomers. We subsequently find that the tetrahedral assembly can be generated by triple-point mutation to various amino acids and that even a single histidine point mutation is sufficient to form tetrahedra. These findings represent a unique example of tetrahedral geometry when surveying all characterized encapsulins, HK97-like capsids, or indeed any virus-derived capsids reported in the Protein Data Bank, revealing the surprising plasticity of capsid self-assembly that can be accessed through minimal changes in the protein sequence.

Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra

We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.

Point mutation in a virus-like capsid drives symmetry reduction to form tetrahedral cages

Protein capsids are a widespread form of compartmentalisation in nature. Icosahedral symmetry is ubiquitous in capsids derived from spherical viruses, as this geometry maximises the internal volume that can be enclosed within. Despite the strong preference for icosahedral symmetry, we show that simple point mutations in a virus-like capsid can drive the assembly of novel symmetry-reduced structures. Starting with the encapsulin from Myxococcus xanthus, a 180-mer bacterial capsid that adopts the well-studied viral HK97 fold, we use mass photometry and native charge detection mass spectrometry to identify a triple histidine point mutant that forms smaller dimorphic assemblies. Using cryo-EM, we determine the structures of a precedented 60-mer icosahedral assembly and an unprecedented 36-mer tetrahedron that features significant geometric rearrangements around a novel interaction surface between capsid protomers. We subsequently find that the tetrahedral assembly can be generated by triple point mutation to various amino acids, and that even a single histidine point mutation is sufficient to form tetrahedra. These findings represent the first example of tetrahedral geometry across all characterised encapsulins, HK97-like capsids, or indeed any virus-derived capsids reported in the Protein Data Bank, revealing the surprising plasticity of capsid self-assembly that can be accessed through minimal changes in protein sequence.

An artificial protein cage made from a 12-membered ring

Artificial protein cages have great potential in diverse fields including as vaccines and drug delivery vehicles. TRAP-cage is an artificial protein cage notable for the way in which the interface between its ring-shaped building blocks can be modified such that the conditions under which cages disassemble can be controlled. To date, TRAP-cages have been constructed from homo-11mer rings, i.e., hendecamers. This is interesting as convex polyhedra with identical regular faces cannot be formed from hendecamers. TRAP-cage overcomes this limitation due to intrinsic flexibility, allowing slight deformation to absorb any error. The resulting TRAP-cage made from 24 TRAP 11mer rings is very close to regular with only very small errors necessary to allow the cage to form. The question arises as to the limits of the error that can be absorbed by a protein structure in this way before the formation of an apparently regular convex polyhedral becomes impossible. Here we use a naturally occurring TRAP variant consisting of twelve identical monomers (i.e., a dodecamer) to probe these limits. We show that it is able to form an apparently regular protein cage consisting of twelve TRAP rings. Comparison of the cryo-EM structure of the new cage with theoretical models and related cages gives insight into the rules of cage formation and allows us to predict other cages that may be formed given TRAP-rings consisting of different numbers of monomers.

pyCapsid: identifying dominant dynamics and quasi-rigid mechanical units in protein shells

SUMMARY

pyCapsid is a Python package developed to facilitate the characterization of the dynamics and quasi-rigid mechanical units of protein shells and other protein complexes. The package was developed in response to the rapid increase of high-resolution structures, particularly capsids of viruses, requiring multiscale biophysical analyses. Given a protein shell, pyCapsid generates the collective vibrations of its amino-acid residues, identifies quasi-rigid mechanical regions associated with the disassembly of the structure, and maps the results back to the input proteins for interpretation. pyCapsid summarizes the main results in a report that includes publication-quality figures.

AVAILABILITY AND IMPLEMENTATION

pyCapsid's source code is available under MIT License on GitHub. It is compatible with Python 3.8-3.10 and has been deployed in two leading Python package-management systems, PIP and Conda. Installation instructions and tutorials are available in the online documentation and in the pyCapsid's YouTube playlist. In addition, a cloud-based implementation of pyCapsid is available as a Google Colab notebook. pyCapsid Colab does not require installation and generates the same report and outputs as the installable version. Users can post issues regarding pyCapsid in the repository's issues section.

An interaction network approach predicts protein cage architectures in bionanotechnology

Protein nanoparticles play pivotal roles in many areas of bionanotechnology, including drug delivery, vaccination, and diagnostics. These technologies require control over the distinct particle morphologies that protein nanocontainers can adopt during self-assembly from their constituent protein components. The geometric construction principle of virus-derived protein cages is by now fairly well understood by analogy to viral protein shells in terms of Caspar and Klug's quasi-equivalence principle. However, many artificial, or genetically modified, protein containers exhibit varying degrees of quasi-equivalence in the interactions between identical protein subunits. They can also contain a subset of protein subunits that do not participate in interactions with other assembly units, called capsomers, leading to gaps in the particle surface. We introduce a method that exploits information on the local interactions between the capsomers to infer the geometric construction principle of these nanoparticle architectures. The predictive power of this approach is demonstrated here for a prominent system in nanotechnology, the AaLS pentamer. Our method not only rationalises hitherto discovered cage structures but also predicts geometrically viable options that have not yet been observed. The classification of nanoparticle architecture based on the geometric properties of the interaction network closes a gap in our current understanding of protein container structure and can be widely applied in protein nanotechnology, paving the way to programmable control over particle polymorphism.

Analyzing the Geometry and Dynamics of Viral Structures: A Review of Computational Approaches Based on Alpha Shape Theory, Normal Mode Analysis, and Poisson-Boltzmann Theories

The current SARS-CoV-2 pandemic highlights our fragility when we are exposed to emergent viruses either directly or through zoonotic diseases. Fortunately, our knowledge of the biology of those viruses is improving. In particular, we have more and more structural information on virions, i.e., the infective form of a virus that includes its genomic material and surrounding protective capsid, and on their gene products. It is important to have methods that enable the analyses of structural information on such large macromolecular systems. We review some of those methods in this paper. We focus on understanding the geometry of virions and viral structural proteins, their dynamics, and their energetics, with the ambition that this understanding can help design antiviral agents. We discuss those methods in light of the specificities of those structures, mainly that they are huge. We focus on three of our own methods based on the alpha shape theory for computing geometry, normal mode analyses to study dynamics, and modified Poisson-Boltzmann theories to study the organization of ions and co-solvent and solvent molecules around biomacromolecules. The corresponding software has computing times that are compatible with the use of regular desktop computers. We show examples of their applications on some outer shells and structural proteins of the West Nile Virus.

Understanding Virus Structure and Dynamics through Molecular Simulations

Viral outbreaks remain a serious threat to human and animal populations and motivate the continued development of antiviral drugs and vaccines, which in turn benefits from a detailed understanding of both viral structure and dynamics. While great strides have been made in characterizing these systems experimentally, molecular simulations have proven to be an essential, complementary approach. In this work, we review the contributions of molecular simulations to the understanding of viral structure, functional dynamics, and processes related to the viral life cycle. Approaches ranging from coarse-grained to all-atom representations are discussed, including current efforts at modeling complete viral systems. Overall, this review demonstrates that computational virology plays an essential role in understanding these systems.

Virus-like nanoparticles as a theranostic platform for cancer

Virus-like nanoparticles (VLPs) are natural polymer-based nanomaterials that mimic viral structures through the hierarchical assembly of viral coat proteins, while lacking viral genomes. VLPs have received enormous attention in a wide range of nanotechnology-based medical diagnostics and therapies, including cancer therapy, imaging, and theranostics. VLPs are biocompatible and biodegradable and have a uniform structure and controllable assembly. They can encapsulate a wide range of therapeutic and diagnostic agents, and can be genetically or chemically modified. These properties have led to sophisticated multifunctional theranostic platforms. This article reviews the current progress in developing and applying engineered VLPs for molecular imaging, drug delivery, and multifunctional theranostics in cancer research.

Unusual Mathematical Approaches Untangle Nervous Dynamics

The massive amount of available neurodata suggests the existence of a mathematical backbone underlying neuronal oscillatory activities. For example, geometric constraints are powerful enough to define cellular distribution and drive the embryonal development of the central nervous system. We aim to elucidate whether underrated notions from geometry, topology, group theory and category theory can assess neuronal issues and provide experimentally testable hypotheses. The Monge’s theorem might contribute to our visual ability of depth perception and the brain connectome can be tackled in terms of tunnelling nanotubes. The multisynaptic ascending fibers connecting the peripheral receptors to the neocortical areas can be assessed in terms of knot theory/braid groups. Presheaves from category theory permit the tackling of nervous phase spaces in terms of the theory of infinity categories, highlighting an approach based on equivalence rather than equality. Further, the physical concepts of soft-matter polymers and nematic colloids might shed new light on neurulation in mammalian embryos. Hidden, unexpected multidisciplinary relationships can be found when mathematics copes with neural phenomena, leading to novel answers for everlasting neuroscientific questions. For instance, our framework leads to the conjecture that the development of the nervous system might be correlated with the occurrence of local thermal changes in embryo–fetal tissues.

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.

Biophysical Modeling of SARS-CoV-2 Assembly: Genome Condensation and Budding

The COVID-19 pandemic caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) has spurred unprecedented and concerted worldwide research to curtail and eradicate this pathogen. SARS-CoV-2 has four structural proteins: Envelope (E), Membrane (M), Nucleocapsid (N), and Spike (S), which self-assemble along with its RNA into the infectious virus by budding from intracellular lipid membranes. In this paper, we develop a model to explore the mechanisms of RNA condensation by structural proteins, protein oligomerization and cellular membrane-protein interactions that control the budding process and the ultimate virus structure. Using molecular dynamics simulations, we have deciphered how the positively charged N proteins interact and condense the very long genomic RNA resulting in its packaging by a lipid envelope decorated with structural proteins inside a host cell. Furthermore, considering the length of RNA and the size of the virus, we find that the intrinsic curvature of M proteins is essential for virus budding. While most current research has focused on the S protein, which is responsible for viral entry, and it has been motivated by the need to develop efficacious vaccines, the development of resistance through mutations in this crucial protein makes it essential to elucidate the details of the viral life cycle to identify other drug targets for future therapy. Our simulations will provide insight into the viral life cycle through the assembly of viral particles de novo and potentially identify therapeutic targets for future drug development.

Circumventing the packaging limit of AAV-mediated gene replacement therapy for neurological disorders

INTRODUCTION

Gene therapy provides the exciting opportunity of a curative single treatment for devastating diseases, eradicating the need for chronic medication. Adeno-associated viruses (AAVs) are among the most attractive vector carriers for gene replacement in vivo. Yet, despite the success of recent AAV-based clinical trials, the clinical use of these vectors has been limited. For instance, the AAV packaging capacity is restricted to ~4.7 kb, making it a substantial challenge to deliver large gene products.

AREAS COVERED

In this review, we explore established and emerging strategies that circumvent the packaging limit of AAVs to make them effective vehicles for gene replacement therapy of monogenic disorders, with a particular focus on diseases affecting the nervous system. We report historical references, design remarks, as well as strengths and weaknesses of these approaches. We additionally discuss examples of neurological disorders for which such strategies have been attempted.

EXPERT OPINION

The field of AAV-gene therapy has experienced enormous advancements in the last decade. However, there is still ample space for improvement aimed at overcoming existing challenges that are slowing down the progressive trajectory of this field.

Exact Solution for Elastic Networks on Curved Surfaces

The problem of characterizing the structure of an elastic network constrained to lie on a frozen curved surface appears in many areas of science and has been addressed by many different approaches, most notably, extending linear elasticity or through effective defect interaction models. In this Letter, we show that the problem can be solved by considering nonlinear elasticity in an exact form without resorting to any approximation in terms of geometric quantities. In this way, we are able to consider different effects that have been unwieldy or not viable to include in the past, such as a finite line tension, explicit dependence on the Poisson ratio, or the determination of the particle positions for the entire lattice. Several geometries with rotational symmetry are solved explicitly. Comparison with linear elasticity reveals an agreement that extends beyond its strict range of applicability. Implications for the problem of the characterization of virus assembly are also discussed.

Virus-like Particles: Fundamentals and Biomedical Applications

Nanotechnology is a fast-evolving field focused on fabricating nanoscale objects for industrial, cosmetic, and therapeutic applications. Virus-like particles (VLPs) are self-assembled nanoparticles whose intrinsic properties, such as heterogeneity, and highly ordered structural organization are exploited to prepare vaccines; imaging agents; construct nanobioreactors; cancer treatment approaches; or deliver drugs, genes, and enzymes. However, depending upon the intrinsic features of the native virus from which they are produced, the therapeutic performance of VLPs can vary. This review compiles the recent scientific literature about the fundamentals of VLPs with biomedical applications. We consulted different databases to present a general scenario about viruses and how VLPs are produced in eukaryotic and prokaryotic cell lines to entrap therapeutic cargo. Moreover, the structural classification, morphology, and methods to functionalize the surface of VLPs are discussed. Finally, different characterization techniques required to examine the size, charge, aggregation, and composition of VLPs are described.

Local rules for the self-assembly of a non-quasi-equivalent viral capsid

The structures of many large bacteriophages, such as the P23-77 capsids, do not adhere strictly to the quasi-equivalence principle of viral architecture. Although the general architecture of the P23-77 capsids is classed as T=28d, it self-assembles from multiple copies of two types of coat protein subunits, and the resulting hexameric capsomers do not conform to the Caspar-Klug paradigm. There are two types of hexamers with distinct internal organization, that are located at specific positions in the capsid. It is an open problem which assembly mechanism can lead to such a complex capsid organization. Here we propose a simple set of local rules that can explain how such non-quasi-equivalent capsid structures can arise as a result of self-assembly.

The International Virus Bioinformatics Meeting 2022

The International Virus Bioinformatics Meeting 2022 took place online, on 23-25 March 2022, and has attracted about 380 participants from all over the world. The goal of the meeting was to provide a meaningful and interactive scientific environment to promote discussion and collaboration and to inspire and suggest new research directions and questions. The participants created a highly interactive scientific environment even without physical face-to-face interactions. This meeting is a focal point to gain an insight into the state-of-the-art of the virus bioinformatics research landscape and to interact with researchers in the forefront as well as aspiring young scientists. The meeting featured eight invited and 18 contributed talks in eight sessions on three days, as well as 52 posters, which were presented during three virtual poster sessions. The main topics were: SARS-CoV-2, viral emergence and surveillance, virus-host interactions, viral sequence analysis, virus identification and annotation, phages, and viral diversity. This report summarizes the main research findings and highlights presented at the meeting.

Topological and Multivalent Effects in Glycofullerene Oligomers as EBOLA Virus Inhibitors

The synthesis of new biocompatible antiviral materials to fight against the development of multidrug resistance is being widely explored. Due to their unique globular structure and excellent properties, [60]fullerene-based antivirals are very promising bioconjugates. In this work, fullerene derivatives with different topologies and number of glycofullerene units were synthesized by using a SPAAC copper free strategy. This procedure allowed the synthesis of compounds 1–3, containing from 20 to 40 mannose units, in a very efficient manner and in short reaction times under MW irradiation. The glycoderivatives were studied in an infection assay by a pseudotyped viral particle with Ebola virus GP1. The results obtained show that these glycofullerene oligomers are efficient inhibitors of EBOV infection with IC₅₀s in the nanomolar range. In particular, compound 3, with four glycofullerene moieties, presents an outstanding relative inhibitory potency (RIP). We propose that this high RIP value stems from the appropriate topological features that efficiently interact with DC-SIGN.

Protein Cages: From Fundamentals to Advanced Applications

Proteins that self-assemble into polyhedral shell-like structures are useful molecular containers both in nature and in the laboratory. Here we review efforts to repurpose diverse protein cages, including viral capsids, ferritins, bacterial microcompartments, and designed capsules, as vaccines, drug delivery vehicles, targeted imaging agents, nanoreactors, templates for controlled materials synthesis, building blocks for higher-order architectures, and more. A deep understanding of the principles underlying the construction, function, and evolution of natural systems has been key to tailoring selective cargo encapsulation and interactions with both biological systems and synthetic materials through protein engineering and directed evolution. The ability to adapt and design increasingly sophisticated capsid structures and functions stands to benefit the fields of catalysis, materials science, and medicine.

Assembly mechanism of the pleomorphic immature poxvirus scaffold

In Vaccinia virus (VACV), the prototype poxvirus, scaffold protein D13 forms a honeycomb-like lattice on the viral membrane that results in formation of the pleomorphic immature virion (IV). The structure of D13 is similar to those of major capsid proteins that readily form icosahedral capsids in nucleocytoplasmic large DNA viruses (NCLDVs). However, the detailed assembly mechanism of the nonicosahedral poxvirus scaffold has never been understood. Here we show the cryo-EM structures of the D13 trimer and scaffold intermediates produced in vitro. The structures reveal that the displacement of the short N-terminal α-helix is critical for initiation of D13 self-assembly. The continuous curvature of the IV is mediated by electrostatic interactions that induce torsion between trimers. The assembly mechanism explains the semiordered capsid-like arrangement of D13 that is distinct from icosahedral NCLDVs. Our structures explain how a single protein can self-assemble into different capsid morphologies and represent a local exception to the universal Caspar-Klug theory of quasi-equivalence.

Immature poxviruses are characterized by nonicosahedral semiordered protein scaffolds critical for morphogenesis. Here, the authors use cryo-EM structures of Vaccinia virus D13 scaffold intermediates to explain their assembly mechanism.

Recruitment of Mobile Genetic Elements for Diverse Cellular Functions in Prokaryotes

Prokaryotic genomes are replete with mobile genetic elements (MGE) that span a continuum of replication autonomy. On numerous occasions during microbial evolution, diverse MGE lose their autonomy altogether but, rather than being quickly purged from the host genome, assume a new function that benefits the host, rendering the immobilized MGE subject to purifying selection, and resulting in its vertical inheritance. This mini-review highlights the diversity of the repurposed (exapted) MGE as well as the plethora of cellular functions that they perform. The principal contribution of the exaptation of MGE and their components is to the prokaryotic functional systems involved in biological conflicts, and in particular, defense against viruses and other MGE. This evolutionary entanglement between MGE and defense systems appears to stem both from mechanistic similarities and from similar evolutionary predicaments whereby both MGEs and defense systems tend to incur fitness costs to the hosts and thereby evolve mechanisms for survival including horizontal mobility, causing host addiction, and exaptation for functions beneficial to the host. The examples discussed demonstrate that the identity of an MGE, overall mobility and relationship with the host cell (mutualistic, symbiotic, commensal, or parasitic) are all factors that affect exaptation.

Virus Assembly Pathways Inside a Host Cell

Simple RNA viruses self-assemble spontaneously and encapsulate their genome into a shell called the capsid. This process is mainly driven by the attractive electrostatics interaction between the positive charges on capsid proteins and the negative charges on the genome. Despite its importance and many decades of intense research, how the virus selects and packages its native RNA inside the crowded environment of a host cell cytoplasm in the presence of an abundance of nonviral RNA and other anionic polymers has remained a mystery. In this paper, we perform a series of simulations to monitor the growth of viral shells and find the mechanism by which cargo-coat protein interactions can impact the structure and stability of the viral shells. We show that coat protein subunits can assemble around a globular nucleic acid core by forming nonicosahedral cages, which have been recently observed in assembly experiments involving small pieces of RNA. We find that the resulting cages are strained and can easily be split into fragments along stress lines. This suggests that such metastable nonicosahedral intermediates could be easily reassembled into the stable native icosahedral shells if the larger wild-type genome becomes available, despite the presence of a myriad of nonviral RNAs.

Predicting the capsid architecture of phages from metagenomic data

Tailed phages are viruses that infect bacteria and are the most abundant biological entities on Earth. Their ecological, evolutionary, and biogeochemical roles in the planet stem from their genomic diversity. Known tailed phage genomes range from 10 to 735 kilobase pairs thanks to the size variability of the protective protein capsids that store them. However, the role of tailed phage capsids’ diversity in ecosystems is unclear. A fundamental gap is the difficulty of associating genomic information with viral capsids in the environment. To address this problem, here, we introduce a computational approach to predict the capsid architecture (T-number) of tailed phages using the sequence of a single gene—the major capsid protein. This approach relies on an allometric model that relates the genome length and capsid architecture of tailed phages. This allometric model was applied to isolated phage genomes to generate a library that associated major capsid proteins and putative capsid architectures. This library was used to train machine learning methods, and the most computationally scalable model investigated (random forest) was applied to human gut metagenomes. Compared to isolated phages, the analysis of gut data reveals a large abundance of mid-sized (T = 7) capsids, as expected, followed by a relatively large frequency of jumbo-like tailed phage capsids (T ≥ 25) and small capsids (T = 4) that have been under-sampled. We discussed how to increase the method’s accuracy and how to extend the approach to other viruses. The computational pipeline introduced here opens the doors to monitor the ongoing evolution and selection of viral capsids across ecosystems.

Visualising Viruses

Viruses pose a challenge to our imaginations. They exert a highly visible influence on the world in which we live, but operate at scales we cannot directly perceive and without a clear separation between their own biology and that of their hosts. Communication about viruses is therefore typically grounded in mental images of virus particles. Virus particles, as the infectious stage of the viral replication cycle, can be used to explain many directly observable properties of transmission, infection and immunity. In addition, their often striking beauty can stimulate further interest in virology. The structures of some virus particles have been determined experimentally in great detail, but for many important viruses a detailed description of the virus particle is lacking. This can be because they are challenging to describe with a single experimental method, or simply because of a lack of data. In these cases, methods from medical illustration can be applied to produce detailed visualisations of virus particles which integrate information from multiple sources. Here, we demonstrate how this approach was used to visualise the highly variable virus particles of influenza A viruses and, in the early months of the COVID-19 pandemic, the virus particles of the then newly characterised and poorly described SARS-CoV-2. We show how constructing integrative illustrations of virus particles can challenge our thinking about the biology of viruses, as well as providing tools for science communication, and we provide a set of science communication resources to help visualise two viruses whose effects are extremely apparent to all of us.

The Protein Folding Problem: The Role of Theory

The protein folding problem was first articulated as question of how order arose from disorder in proteins: How did the various native structures of proteins arise from interatomic driving forces encoded within their amino acid sequences, and how did they fold so fast? These matters have now been largely resolved by theory and statistical mechanics combined with experiments. There are general principles. Chain randomness is overcome by solvation-based codes. And in the needle-in-a-haystack metaphor, native states are found efficiently because protein haystacks (conformational ensembles) are funnel-shaped. Order-disorder theory has now grown to encompass a large swath of protein physical science across biology.

Minimal Design Principles for Icosahedral Virus Capsids

The geometrical structures of single- and multiple-shell icosahedral virus capsids are reproduced as the targets that minimize the cost corresponding to relatively simple design functions. Capsid subunits are first identified as building blocks at a given coarse-grained scale and then represented in these functions as point particles located on an appropriate number of concentric spherical surfaces. Minimal design cost is assigned to optimal spherical packings of the particles. The cost functions are inspired by the packings favored for the Thomson problem, which minimize the electrostatic potential energy between identical charged particles. In some cases, icosahedral symmetry constraints are incorporated as external fields acting on the particles. The simplest cost functions can be obtained by separating particles in disjoint nonequivalent sets with distinct interactions, or by introducing interacting holes (the absence of particles). These functions can be adapted to reproduce any capsid structure found in real viruses. Structures absent in Nature require significantly more complex designs. Measures of information content and complexity are assigned to both the cost functions and the capsid geometries. In terms of these measures, icosahedral structures and the corresponding cost functions are the simplest solutions.

Programmable icosahedral shell system for virus trapping

Broad-spectrum antiviral platforms that can decrease or inhibit viral infection would alleviate many threats to global public health. Nonetheless, effective technologies of this kind are still not available. Here, we describe a programmable icosahedral canvas for the self-assembly of icosahedral shells that have viral trapping and antiviral properties. Programmable triangular building blocks constructed from DNA assemble with high yield into various shell objects with user-defined geometries and apertures. We have created shells with molecular masses ranging from 43 to 925 MDa (8 to 180 subunits) and with internal cavity diameters of up to 280 nm. The shell interior can be functionalized with virus-specific moieties in a modular fashion. We demonstrate this virus-trapping concept by engulfing hepatitis B virus core particles and adeno-associated viruses. We demonstrate the inhibition of hepatitis B virus core interactions with surfaces in vitro and the neutralization of infectious adeno-associated viruses exposed to human cells.

Percolation Theory Reveals Biophysical Properties of Virus-like Particles

The viral protein containers that encapsulate a virus' genetic material are repurposed as virus-like particles in a host of nanotechnology applications, including cargo delivery, storage, catalysis, and vaccination. These viral architectures have evolved to sit on the knife's edge between stability, to provide adequate protection for their genetic cargoes, and instability, to enable their efficient and timely release in the host cell environment upon environmental cues. By introducing a percolation theory for viral capsids, we demonstrate that the geometric characteristics of a viral capsid in terms of its subunit layout and intersubunit interaction network are key for its disassembly behavior. A comparative analysis of all alternative homogeneously tiled capsid structures of the same stoichiometry identifies evolutionary drivers favoring specific viral geometries in nature and offers a guide for virus-like particle design in nanotechnology.

Evolution of a virus-like architecture and packaging mechanism in a repurposed bacterial protein

Viruses are ubiquitous pathogens of global impact. Prompted by the hypothesis that their earliest progenitors recruited host proteins for virion formation, we have used stringent laboratory evolution to convert a bacterial enzyme that lacks affinity for nucleic acids into an artificial nucleocapsid that efficiently packages and protects multiple copies of its own encoding messenger RNA. Revealing remarkable convergence on the molecular hallmarks of natural viruses, the accompanying changes reorganized the protein building blocks into an interlaced 240-subunit icosahedral capsid that is impermeable to nucleases, and emergence of a robust RNA stem-loop packaging cassette ensured high encapsidation yields and specificity. In addition to evincing a plausible evolutionary pathway for primordial viruses, these findings highlight practical strategies for developing nonviral carriers for diverse vaccine and delivery applications.

On symmetry breaking of dual polyhedra of non-crystallographic group H3

The study of the polyhedra described in this paper is relevant to the icosahedral symmetry in the assembly of various spherical molecules, biomolecules and viruses. A symmetry-breaking mechanism is applied to the family of polytopes {\cal V}_{H_{3}}(\lambda) constructed for each type of dominant point λ. Here a polytope {\cal V}_{H_{3}}(\lambda) is considered as a dual of a {\cal D}_{H_{3}}(\lambda) polytope obtained from the action of the Coxeter group H₃ on a single point \lambda\in{\bb R}^{3}. The H₃ symmetry is reduced to the symmetry of its two-dimensional subgroups H₂, A₁ × A₁ and A₂ that are used to examine the geometric structure of {\cal V}_{H_{3}}(\lambda) polytopes. The latter is presented as a stack of parallel circular/polygonal orbits known as the `pancake' structure of a polytope. Inserting more orbits into an orbit decomposition results in the extension of the {\cal V}_{H_{3}}(\lambda) structure into various nanotubes. Moreover, since a {\cal V}_{H_{3}}(\lambda) polytope may contain the orbits obtained by the action of H₃ on the seed points (a, 0, 0), (0, b, 0) and (0, 0, c) within its structure, the stellations of flat-faced {\cal V}_{H_{3}}(\lambda) polytopes are constructed whenever the radii of such orbits are appropriately scaled. Finally, since the fullerene C₂₀ has the dodecahedral structure of {\cal V}_{H_{3}}(a,0,0), the construction of the smallest fullerenes C₂₄, C₂₆, C₂₈, C₃₀ together with the nanotubes C_20+6N, C_20+10N is presented.

Fishing for phages in metagenomes: what do we catch, what do we miss?

Metagenomics and metatranscriptomics have become the principal approaches for discovery of novel bacteriophages and preliminary characterization of their ecology and biology. Metagenomic sequencing dramatically expanded the known diversity of tailed and non-tailed phages with double-stranded DNA genomes and those with single-stranded DNA genomes, whereas metatranscriptomics led to the discovery of thousands of new single-stranded RNA phages. Apart from expanding phage diversity, metagenomics studies discover major novel groups of phages with unique features of genome organization, expression strategy and virus-host interaction, such as the putative order 'crAssvirales', which includes the most abundant human-associated viruses. The continued success of metagenomics hinges on the combination of the most powerful computational methods for phage genome assembly and analysis including harnessing CRISPR spacers for the discovery of novel phages and host assignment. Together, these approaches could make a comprehensive characterization of the earth phageome a realistic goal.

Effect of receptors on the resonant and transient harmonic vibrations of Coronavirus

The paper is concerned with the vibration characteristics of the Coronavirus family. There are some 25-100 receptors, commonly called spikes protruding from the envelope shell of the virus. Spikes, resembling the shape of a hot air balloon, may have a total mass similar to the mass of the lipid bi-layer shell. The lipid proteins of the virus are treated as homogeneous elastic material and the problem is formulated as the interaction of thin elastic shell with discrete masses, modeled as short conical cross-sectional beams. The system is subjected to ultrasonic excitation. Using the methods of structural acoustics, it is shown that the scattered pressure is very small and the pressure on the viral shell is simply the incident pressure. The modal analysis is performed for a bare shell, a single spike, and the spike-decorated shell. The predicted vibration frequencies and modes are shown to compare well with the newly derived closed-form solutions for a single spike and existing analytical solutions for thin shells. The fully nonlinear dynamic simulation of the transient response revealed the true character of the complex interaction between local vibration of spikes and global vibration of the multi-degree-of-freedom system. It was shown that harmonic vibration at or below the lowest resonant modes can excite large amplitude vibration of spikes. The associated maximum principal strain in a spike can reach large values in a fraction of a millisecond. Implications for possible tearing off spikes from the shell are discussed. Another important result is that after a finite number of cycles, the shell buckles and collapses, developing internal contacts and folds with large curvatures and strains exceeding 10%. For the geometry and elastic properties of the SARS-CoV-2 virus, these effects are present in the range of frequencies close to the ones used for medical ultrasound diagnostics.

Equilibrium mechanisms of self-limiting assembly

Self-assembly is a ubiquitous process in synthetic and biological systems, broadly defined as the spontaneous organization of multiple subunits (e.g. macromolecules, particles) into ordered multi-unit structures. The vast majority of equilibrium assembly processes give rise to two states: one consisting of dispersed disassociated subunits, and the other, a bulk-condensed state of unlimited size. This review focuses on the more specialized class of self-limiting assembly, which describes equilibrium assembly processes resulting in finite-size structures. These systems pose a generic and basic question, how do thermodynamic processes involving non-covalent interactions between identical subunits "measure" and select the size of assembled structures? In this review, we begin with an introduction to the basic statistical mechanical framework for assembly thermodynamics, and use this to highlight the key physical ingredients that ensure equilibrium assembly will terminate at finite dimensions. Then, we introduce examples of self-limiting assembly systems, and classify them within this framework based on two broad categories: self-closing assemblies and open-boundary assemblies. These include well-known cases in biology and synthetic soft matter - micellization of amphiphiles and shell/tubule formation of tapered subunits - as well as less widely known classes of assemblies, such as short-range attractive/long-range repulsive systems and geometrically-frustrated assemblies. For each of these self-limiting mechanisms, we describe the physical mechanisms that select equilibrium assembly size, as well as potential limitations of finite-size selection. Finally, we discuss alternative mechanisms for finite-size assemblies, and draw contrasts with the size-control that these can achieve relative to self-limitation in equilibrium, single-species assemblies.

Geometrical manipulation of complex supramolecular tessellations by hierarchical assembly of amphiphilic platinum(II) complexes

Here we report complex supramolecular tessellations achieved by the directed self-assembly of amphiphilic platinum(II) complexes. Despite the twofold symmetry, these geometrically simple molecules exhibit complicated structural hierarchy in a columnar manner. A possible key to such an order increase is the topological transition into circular trimers, which are noncovalently interlocked by metal···metal and π-π interactions, thereby allowing for cofacial stacking in a prismatic assembly. Another key to success is to use the immiscibility of the tailored hydrophobic and hydrophilic sidechains. Their phase separation leads to the formation of columnar crystalline nanostructures homogeneously oriented on the substrate, featuring an unusual geometry analogous to a rhombitrihexagonal Archimedean tiling. Furthermore, symmetry lowering of regular motifs by design results in an orthorhombic lattice obtained by the coassembly of two different platinum(II) amphiphiles. These findings illustrate the potentials of supramolecular engineering in creating complex self-assembled architectures of soft materials.

Design and Applications of Water-Soluble Coordination Cages

Compartmentalization of the aqueous space within a cell is necessary for life. In similar fashion to the nanometer-scale compartments in living systems, synthetic water-soluble coordination cages (WSCCs) can isolate guest molecules and host chemical transformations. Such cages thus show promise in biological, medical, environmental, and industrial domains. This review highlights examples of three-dimensional synthetic WSCCs, offering perspectives so as to enhance their design and applications. Strategies are presented that address key challenges for the preparation of coordination cages that are soluble and stable in water. The peculiarities of guest binding in aqueous media are examined, highlighting amplified binding in water, changing guest properties, and the recognition of specific molecular targets. The properties of WSCC hosts associated with biomedical applications, and their use as vessels to carry out chemical reactions in water, are also presented. These examples sketch a blueprint for the preparation of new metal-organic containers for use in aqueous solution, as well as guidelines for the engineering of new applications in water.

Scaling Theory of a Polymer Ejecting from a Cavity into a Semi-Space

A two-stage model is developed in order to understand the scaling behaviors of single polymers ejecting from a spherical cavity through a nanopore. The dynamics of ejection is derived by balancing the free energy change with the energy dissipation during a process. The ejection velocity is found to vary with the number of monomers in the cavity, m, as mz1/(Nx1D3z1) at the confined stage, and it turns to be m−z2 at the non-confined stage, where N is the chain length and D the cavity diameter. The exponents are shown to be z1=(3ν−1)−1, z2=2ν and x1=1/3, with ν being the Flory exponent. The profile of the velocity is carefully verified by performing Langevin dynamics simulations. The simulations further reveal that, at the starting point, the decreasing of m can be stalled for a good moment. It suggests the existence of a pre-stage that can be explained by using the concept of a classical nucleation theory. By trimming the pre-stage, the ejection time are properly studied by varying N, D, and ϕ0 (the initial volume fraction). The scaling properties of the nucleation time are also analyzed. The results fully support the predictions of the theory. The physical pictures are given for various ejection conditions that cover the entire parameter space.

The Missing Tailed Phages: Prediction of Small Capsid Candidates

Tailed phages are the most abundant and diverse group of viruses on the planet. Yet, the smallest tailed phages display relatively complex capsids and large genomes compared to other viruses. The lack of tailed phages forming the common icosahedral capsid architectures T = 1 and T = 3 is puzzling. Here, we extracted geometrical features from high-resolution tailed phage capsid reconstructions and built a statistical model based on physical principles to predict the capsid diameter and genome length of the missing small-tailed phage capsids. We applied the model to 3348 isolated tailed phage genomes and 1496 gut metagenome-assembled tailed phage genomes. Four isolated tailed phages were predicted to form T = 3 icosahedral capsids, and twenty-one metagenome-assembled tailed phages were predicted to form T < 3 capsids. The smallest capsid predicted was a T = 4/3 ≈ 1.33 architecture. No tailed phages were predicted to form the smallest icosahedral architecture, T = 1. We discuss the feasibility of the missing T = 1 tailed phage capsids and the implications of isolating and characterizing small-tailed phages for viral evolution and phage therapy.

Simulations of Phage T7 Capsid Expansion Reveal the Role of Molecular Sterics on Dynamics

Molecular dynamics techniques provide numerous strategies for investigating biomolecular energetics, though quantitative analysis is often only accessible for relatively small (frequently monomeric) systems. To address this limit, we use simulations in combination with a simplified energetic model to study complex rearrangements in a large assembly. We use cryo-EM reconstructions to simulate the DNA packaging-associated 3 nm expansion of the protein shell of an initially assembled phage T7 capsid (called procapsid or capsid I). This is accompanied by a disorder-order transition and expansion-associated externalization displacement of the 420 N-terminal tails of the shell proteins. For the simulations, we use an all-atom structure-based model (1.07 million atoms), which is specifically designed to probe the influence of molecular sterics on dynamics. We find that the rate at which the N-terminal tails undergo translocation depends heavily on their position within hexons and pentons. Specifically, trans-shell displacements of the hexon E subunits are the most frequent and hexon A subunits are the least frequent. The simulations also implicate numerous tail translocation intermediates during tail translocation that involve topological traps, as well as sterically induced barriers. The presented study establishes a foundation for understanding the precise relationship between molecular structure and phage maturation.

Surface stresses in complex viral capsids and non-quasi-equivalent viral architectures

Many larger and more complex viruses deviate from the capsid layouts predicted in the seminal Caspar-Klug theory of icosahedral viruses. Instead of being built from one type of capsid protein (CP), they code for multiple distinct structural proteins that either break the local symmetry of the CP building blocks (capsomers) in specific positions or exhibit auxiliary proteins that stabilize the capsid shell. We investigate here the hypothesis that this occurs as a response to mechanical stress. For this, we construct a coarse-grained model of a viral capsid, derived from the experimentally determined atomistic positions of the CPs, that represents the basic features of protein organization in the viral capsid as described in Caspar-Klug theory. We focus here on viruses in the PRD1-adenovirus lineage. For T = 28 viruses in this lineage, which have capsids formed from two distinct structural proteins, we show that the tangential shear stress in the viral capsid concentrates at the sites of local symmetry breaking. In the T = 21, 25 and 27 capsids, we show that stabilizing proteins decrease the tangential stress. These results suggest that mechanical properties can act as selective pressures on the evolution of capsid components, offsetting the coding cost imposed by the need for such additional protein components.

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.

Unveiling the Hidden Rules of Spherical Viruses Using Point Arrays

Since its introduction, the Triangulation number has been the most successful and ubiquitous scheme for classifying spherical viruses. However, despite its many successes, it fails to describe the relative angular orientations of proteins, as well as their radial mass distribution within the capsid. It also fails to provide any critical insight into sites of stability, modifications or possible mutations. We show how classifying spherical viruses using icosahedral point arrays, introduced by Keef and Twarock, unveils new geometric rules and constraints for understanding virus stability and key locations for exterior and interior modifications. We present a modified fitness measure which classifies viruses in an unambiguous and rigorous manner, irrespective of local surface chemistry, steric hinderance, solvent accessibility or Triangulation number. We then use these point arrays to explain the immutable surface loops of bacteriophage MS2, the relative reactivity of surface lysine residues in CPMV and the non-quasi-equivalent flexibility of the HBV dimers. We then explain how point arrays can be used as a predictive tool for site-directed modifications of capsids. This success builds on our previous work showing that viruses place their protruding features along the great circles of the asymmetric unit, demonstrating that viruses indeed adhere to these geometric constraints.

Icosadeltahedral Geometry of Geodesic Domes, Fullerenes and Viruses: A Tutorial on the T-Number

The Caspar–Klug (CK) classification of viruses is discussed by parallel examination of geometry of icosahedral geodesic domes, fullerenes, and viruses. The underlying symmetry of all structures is explained and thoroughly visually represented. Euler’s theorem on polyhedra is used to calculate the number of vertices, edges, and faces in domes, number of atoms, bonds, and pentagonal and hexagonal rings in fullerenes, and number of proteins and protein–protein contacts in viruses. The T-number, the characteristic for the CK classification, is defined and discussed. The superposition of fullerene and dome designs is used to obtain a representation of a CK virus with all the proteins indicated. Some modifications of the CK classifications are sketched, including elongation of the CK blueprint, fusion of two CK blueprints, dodecahedral view of the CK shapes, and generalized CK designs without a clearly visible geometry of the icosahedron. These are compared to cases of existing viruses.

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.

Structures of Three Actinobacteriophage Capsids: Roles of Symmetry and Accessory Proteins

Here, we describe the structure of three actinobacteriophage capsids that infect Mycobacterium smegmatis. The capsid structures were resolved to approximately six angstroms, which allowed confirmation that each bacteriophage uses the HK97-fold to form their capsid. One bacteriophage, Rosebush, may have a novel variation of the HK97-fold. Four novel accessory proteins that form the capsid head along with the major capsid protein were identified. Two of the accessory proteins were minor capsid proteins and showed some homology, based on bioinformatic analysis, to the TW1 bacteriophage. The remaining two accessory proteins are decoration proteins that are located on the outside of the capsid and do not resemble any previously described bacteriophage decoration protein. SDS-PAGE and mass spectrometry was used to identify the accessory proteins and bioinformatic analysis of the accessory proteins suggest they are used in many actinobacteriophage capsids.