Optimal architectures of elongated viruses

Charge Detection Mass Spectrometry Reveals Favored Structures in the Assembly of Virus-Like Particles: Polymorphism in Norovirus GI.1

The main capsid protein (CP) of norovirus, the leading cause of gastroenteritis, is expected to self-assemble into virus-like particles with the same structure as the wild-type virus, a capsid with 180 CPs in a T = 3 icosahedron. Using charge detection mass spectrometry (CD-MS), we find that the norovirus GI.1 variant is structurally promiscuous, forming a wide variety of well-defined structures, some that are icosahedral capsids and others that are not. The structures that are present evolve with time and vary with solution conditions. The presence of icosahedral T = 3 and T = 4 capsids (240 CPs) under some conditions was confirmed by cryo-electron microscopy (cryo-EM). The cryo-EM studies also confirmed the presence of an unexpected prolate geometry based on an elongated T = 4 capsid with 300 CPs. In addition, CD-MS measurements indicate the presence of well-defined peaks with masses corresponding to 420, 480, 600, and 700 CPs. The peak corresponding to 420 CPs is probably due to an icosahedral T = 7 capsid, but this could not be confirmed by cryo-EM. It is possible that the T = 7 particles are too fragile to survive vitrification. There are no mass peaks associated with the T = 9 and T = 12 icosahedra with 540 and 720 CPs. The larger structures with 480, 600, and 700 CPs are not icosahedral; however, their measured charges suggest that they are hollow shells. The use of CD-MS to monitor virus-like particles assembly may have important applications in vaccine development and quality control.

Virtual indentation of the empty capsid of the minute virus of mice using a minimal coarse-grained model

A minimal coarse-grained model for T=1 viral capsids assembled from 20 protein rigid trimers has been designed by extending a previously proposed form of the interaction energy written as a sum of anisotropic pairwise interactions between the trimeric capsomers. The extension of the model has been performed to properly account for the coupling between two internal coordinates: the one that measures the intercapsomer distance and the other that gives the intercapsomer dihedral angle. The model has been able to fit with less than a 10% error the atomic force microscopy (AFM) indentation experimental data for the empty capsid of the minute virus of mice (MVM), providing in this way an admissible picture of the main mechanisms behind the capsid deformations. In this scenario, the bending of the intercapsomer dihedral angle is the angular internal coordinate that can support larger deformations away from its equilibrium values, determining important features of the AFM indentation experiments as the elastic constants along the three symmetry axes of the capsid and the critical indentations. From the value of one of the parameters of our model, we conclude that trimers in the MVM must be quite oblate tops, in excellent agreement with their known structure. The transition from the linear to the nonlinear regimes sampled in the indentation process appears to be an interesting topic for future research in physical virology.

Heterologous Assembly of Pleomorphic Bacterial Microcompartment Shell Architectures Spanning the Nano- to Microscale

Many bacteria use protein-based organelles known as bacterial microcompartments (BMCs) to organize and sequester sequential enzymatic reactions. Regardless of their specialized metabolic function, all BMCs are delimited by a shell made of multiple structurally redundant, yet functionally diverse, hexameric (BMC-H), pseudohexameric/trimeric (BMC-T), or pentameric (BMC-P) shell protein paralogs. When expressed without their native cargo, shell proteins have been shown to self-assemble into 2D sheets, open-ended nanotubes, and closed shells of ≈40 nm diameter that are being developed as scaffolds and nanocontainers for applications in biotechnology. Here, by leveraging a strategy for affinity-based purification, it is demonstrated that a wide range of empty synthetic shells, many differing in end-cap structures, can be derived from a glycyl radical enzyme-associated microcompartment. The range of pleomorphic shells observed, which span ≈2 orders of magnitude in size from ≈25 nm to ≈1.8 µm, reveal the remarkable plasticity of BMC-based biomaterials. In addition, new capped nanotube and nanocone morphologies are observed that are consistent with a multicomponent geometric model in which architectural principles are shared among asymmetric carbon, viral protein, and BMC-based structures.

Packing and trimer-to-dimer protein reconstruction in icosahedral viral shells with a single type of symmetrical structural unit

Understanding the principles of protein packing and the mechanisms driving morphological transformations in virus shells (capsids) during their maturation can be pivotal for the development of new antiviral strategies. Here, we study how these principles and mechanisms manifest themselves in icosahedral viral capsids assembled from identical symmetric structural units (capsomeres). To rationalize such shells, we model capsomers as symmetrical groups of identical particles interacting with a short-range potential typical of the classic Tammes problem. The capsomere particles are assumed to retain their relative positions on the vertices of planar polygons placed on the spherical shell and to interact only with the particles from other capsomeres. Minimization of the interaction energy enforces equal distances between the nearest particles belonging to neighboring capsomeres and minimizes the number of different local environments. Thus, our model implements the Caspar and Klug quasi-equivalence principle and leads to packings strikingly similar to real capsids. We then study a reconstruction of protein trimers into dimers in a Flavivirus shell during its maturation, connecting the relevant structural changes with the modifications of the electrostatic charges of proteins, wrought by the oxidative switch in the bathing solution that is essential for the process. We highlight the key role of pr peptides in the shell reconstruction and show that the highly ordered arrangement of these subunits in the dimeric state is energetically favored at a low pH level. We also discuss the electrostatic mechanisms controlling the release of pr peptides in the last irreversible step of the maturation process.

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.

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.

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.

A minimal coarse-grained model for the low-frequency normal mode analysis of icosahedral viral capsids

The main goal of this work is the design of a coarse-grained theoretical model of minimal resolution for the study of the physical properties of icosahedral virus capsids within the linear-response regime. In this model the capsid is represented as an interacting many-body system whose composing elements are capsid subunits (capsomers), which are treated as three-dimensional rigid bodies. The total interaction potential energy is written as a sum of pairwise capsomer-capsomer interactions. Based on previous work [Gomez Llorente et al., Soft Matter, 2014, 10, 3560], a minimal and complete anisotropic binary interaction that includes a full Hessian matrix of independent force constants is proposed. In this interaction model, capsomers have rotational symmetry around an axis of order n > 2. The full coarse-grained model is applied to analyse the low-frequency normal-mode spectrum of icosahedral T = 1 capsids. The model performance is evaluated by fitting its predicted spectrum to the full-atom results for the Satellite Tobacco Necrosis Virus (STNV) capsid [Dykeman and Sankey, Phys. Rev. Lett., 2008, 100, 028101]. Two capsomer choices that are compatible with the capsid icosahedral symmetry are checked, namely pentamers (n = 5) and trimers (n = 3). Both subunit types provide fair fits, from which the magnitude of the coarse-grained force constants for a real virus is obtained. The model is able to uncover latent instabilities whose analysis is fully consistent with the current knowledge about the STNV capsid, which does not self-assemble in the absence of RNA and is thermally unstable. The straightforward generalisability of the model beyond the linear regime and its completeness make it a promising tool to theoretically interpret many experimental data such as those provided by the atomic force microscopy or even to better understand processes far from equilibrium such as the capsid self-assembly.

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.

Determination of Antibody Population Distributions for Virus-Antibody Conjugates by Charge Detection Mass Spectrometry

Virus-like particle (VLP) conjugates are being developed for biomedical applications; however, there is a lack of quantitative analytical methods to measure the extent of conjugation and modification of VLP based therapeutics. Charge detection mass spectrometry (CDMS) can measure mass distributions for large and heterogeneous complexes and is emerging as a valuable tool in the analysis of biologics. In this study, CDMS is used to characterize the stoichiometry and population distribution of antibodies covalently conjugated to the surface of a bacteriophage MS2 VLP. Initial CDMS analysis of the unconjugated MS2 particles suggested that they had packaged a broad distribution of exogenous genomic material. We developed procedures to remove the undesired genomic material from the VLP preparation and observed that, for the samples where the genomic fragments were removed, the antibody coupling reaction efficiency increased by almost a factor of 2. This meant there were (1) fewer VLPs with no antibodies bound, which is an important consideration for the efficacy of a targeted therapeutic and (2) fewer antibodies were wasted during the coupling reaction. CDMS could be employed in a similar manner as a tool to characterize coupling reaction product distributions and precursors and help inform the development of the next generation of conjugate-based therapies.

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.

Kinetics of empty viral capsid assembly in a minimal model

The efficient construction of a protective protein shell or capsid is one of the most crucial steps in the replication cycle of a virus. The formation of the simplest capsid typically proceeds by the spontaneous assembly of identical building blocks. This process can also be achieved in vitro even in the absence of genetic material, thus opening the door to the production of artificial viral cages for a myriad of applications. In this work, we analyze the efficiency and the kinetic peculiarities of this self-assembly process using Brownian Dynamics simulations. We use a minimal model that considers identical assembly units and is able to reproduce successfully the correct final architecture of spherical capsids. The selection of a specific size and structure is achieved by changing a single parameter that imposes an angular anisotropy on the interaction. We analyze how the geometrical constraints of the interaction affect the efficiency of the assembly. We find that the optimal conditions for an efficient assembly from a kinetic point of view strongly depart from the lowest capsid energy corresponding to the minimum of the potential energy landscape. Our work illustrates the important differences between the equilibrium and dynamic characteristics of viral self-assembly, and provides important insights on how to design specific interactions for a successful assembly of artificial viral cages.

Self-assembly of convex particles on spherocylindrical surfaces

The precise control of assembly and packing of proteins and colloids on curved surfaces has fundamental implications in nanotechnology. In this paper, we describe dynamical simulations of the self-assembly of conical subunits around a spherocylindrical template, and a continuum theory for the bending energy of a triangular lattice with spontaneous curvature on a surface with arbitrary curvature. We find that assembly depends sensitively on mismatches between subunit spontaneous curvature and the mean curvature of the template, as well as anisotropic curvature of the template (mismatch between the two principal curvatures). Our simulations predict assembly morphologies that closely resemble those observed in experiments in which virus capsid proteins self-assemble around metal nanorods. Below a threshold curvature mismatch, our simulations identify a regime of optimal assembly leading to complete, symmetrical particles. Outside of this regime we observe defective particles, whose morphologies depend on the degree of curvature mismatch. To learn how assembly is affected by the nonuniform curvature of a spherocylinder, we also study the simpler cases of assembly around spherical and cylindrical cores. Our results show that both the intrinsic (Gaussian) and extrinsic (mean) curvatures of a template play significant roles in guiding the assembly of anisotropic subunits, providing a rich design space for the formation of nanoscale materials.

Defects and Chirality in the Nanoparticle-Directed Assembly of Spherocylindrical Shells of Virus Coat Proteins

Virus coat proteins of small isometric plant viruses readily assemble into symmetric, icosahedral cages encapsulating noncognate cargo, provided the cargo meets a minimal set of chemical and physical requirements. While this capability has been intensely explored for certain virus-enabled nanotechnologies, additional applications require lower symmetry than that of an icosahedron. Here, we show that the coat proteins of an icosahedral virus can efficiently assemble around metal nanorods into spherocylindrical closed shells with hexagonally close-packed bodies and icosahedral caps. Comparison of chiral angles and packing defects observed by in situ atomic force microscopy with those obtained from molecular dynamics models offers insight into the mechanism of growth, and the influence of stresses associated with intrinsic curvature and assembly pathways.

Characterization of AAV vector particle stability at the single-capsid level

Virus families have evolved different strategies for genome uncoating, which are also followed by recombinant vectors. Vectors derived from adeno-associated viruses (AAV) are considered as leading delivery tools for in vivo gene transfer, and in particular gene therapy. Using a combination of atomic force microscopy (AFM), biochemical experiments, and physical modeling, we investigated here the physical properties and stability of AAV vector particles. We first compared the morphological properties of AAV vectors derived from two different serotypes (AAV8 and AAV9). Furthermore, we triggered ssDNA uncoating by incubating vector particles to increasing controlled temperatures. Our analyses, performed at the single-particle level, indicate that genome release can occur in vitro via two alternative pathways: either the capsid remains intact and ejects linearly the ssDNA molecule, or the capsid is ruptured, leaving ssDNA in a compact entangled conformation. The analysis of the length distributions of ejected genomes further revealed a two-step ejection behavior. We propose a kinetic model aimed at quantitatively describing the evolution of capsids and genomes along the different pathways, as a function of time and temperature. This model allows quantifying the relative stability of AAV8 and AAV9 particles.

Self consistent field theory of virus assembly

The ground state dominance approximation (GSDA) has been extensively used to study the assembly of viral shells. In this work we employ the self-consistent field theory (SCFT) to investigate the adsorption of RNA onto positively charged spherical viral shells and examine the conditions when GSDA does not apply and SCFT has to be used to obtain a reliable solution. We find that there are two regimes in which GSDA does work. First, when the genomic RNA length is long enough compared to the capsid radius, and second, when the interaction between the genome and capsid is so strong that the genome is basically localized next to the wall. We find that for the case in which RNA is more or less distributed uniformly in the shell, regardless of the length of RNA, GSDA is not a good approximation. We observe that as the polymer-shell interaction becomes stronger, the energy gap between the ground state and first excited state increases and thus GSDA becomes a better approximation. We also present our results corresponding to the genome persistence length obtained through the tangent-tangent correlation length and show that it is zero in case of GSDA but is equal to the inverse of the energy gap when using SCFT.

The different faces of mass action in virus assembly

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

Plant virus nanoparticles: Novel and robust nanocarriers for drug delivery and imaging

Nanoparticles have been gained much attention for biomedical applications. A promising type of nanocarriers is viral nanoparticles (VNPs) which are natural bio-nanomaterials derived from different type of viruses. Amongst VNPs, plant VNPs present several pros over general nanoparticles such as liposomes, dendrimers or quantum dots. Some of these advantages include: degradability, safety for human, known structures to atomic level, possibility of attaching ligand with vigorous control on structure, availability for genetic and chemical manipulations and very flexible methods to prepare them. Variety of plant viruses have been modified by chemical and genetic modification of their inner cavities and their outer-surfaces. These modifications provide suitable sites for attachment of markers and drug molecules for vascular imaging and tumor targeting. In this review a brief description of plant virus nanoparticles and their biomedical applications especially in drug delivery is provided. The methods of loading cargos in these VNPs and their final biofate are also reviewed.

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

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

Hidden symmetry of small spherical viruses and organization principles in "anomalous" and double-shelled capsid nanoassemblies

We propose the principles of structural organization in spherical nanoassemblies with icosahedral symmetry constituted by asymmetric protein molecules. The approach modifies the paradigmatic geometrical Caspar and Klug (CK) model of icosahedral viral capsids and demonstrates the common origin of both the "anomalous" and conventional capsid structures. In contrast to all previous models of "anomalous" viral capsids the proposed modified model conserves the basic structural principles of the CK approach and reveals the common hidden symmetry underlying all small viral shells. We demonstrate the common genesis of the "anomalous" and conventional capsids and explain their structures in the same frame. The organization principles are derived from the group theory analysis of the positional order on the spherical surface. The relationship between the modified CK geometrical model and the theory of two-dimensional spherical crystallization is discussed. We also apply the proposed approach to complex double-shelled capsids and capsids with protruding knob-like proteins. The introduced notion of commensurability for the concentric nanoshells explains the peculiarities of their organization and helps to predict analogous, but yet undiscovered, double-shelled viral capsid nanostructures.

Physical Ingredients Controlling Stability and Structural Selection of Empty Viral Capsids

One of the crucial steps in the viral replication cycle is the self-assembly of its protein shell. Typically, each native virus adopts a unique architecture, but the coat proteins of many viruses have the capability to self-assemble in vitro into different structures by changing the assembly conditions. However, the mechanisms determining which of the possible capsid shapes and structures is selected by a virus are still not well-known. We present a coarse-grained model to analyze and understand the physical mechanisms controlling the size and structure selection in the assembly of empty viral capsids. Using this model and Monte Carlo simulations, we have characterized the phase diagram and stability of T = 1,3,4,7 and snub cube shells. In addition, we have studied the tolerance of different shells to changes in physical parameters related to ambient conditions, identifying possible strategies to induce misassembly or failure. Finally, we discuss the factors that select the shape of a capsid as spherical, faceted, elongated, or decapsidated. Our model sheds important light on the ingredients that control the assembly and stability of viral shells. This knowledge is essential to get capsids with well-defined size and structure that could be used for promising applications in medicine or bionanotechnology.

Peptides as models for the structure and function of viral capsid proteins: Insights on dengue virus capsid

The structural organization of viral particles is among the most astonishing examples of molecular self-assembly in nature, involving proteins, nucleic acids, and, sometimes, lipids. Proper assembly is essential to produce well structured infectious virions. A great variety of structural arrangements can be found in viral particles. Nucleocapsids, for instance, may display highly ordered geometric shapes or consist in macroscopically amorphous packs of the viral genome. Alphavirus and flavivirus are viral genera that exemplify these extreme cases, the former comprising viral particles structured with a T = 4 icosahedral symmetry, whereas flavivirus capsids have no regular geometry. Dengue virus is a member of flavivirus genus and is used in this article to illustrate how viral protein-derived peptides can be used advantageously over full-length proteins to unravel the foundations of viral supramolecular assemblies. Membrane- and viral RNA-binding data of capsid protein-derived dengue virus peptides are used to explain the amorphous organization of the viral capsid. Our results combine bioinformatic and spectroscopic approaches using two- or three-component peptide and/or nucleic acid and/or lipid systems.

Charge Detection Mass Spectrometry Identifies Preferred Non-Icosahedral Polymorphs in the Self-Assembly of Woodchuck Hepatitis Virus Capsids

Woodchuck hepatitis virus (WHV) is prone to aberrant assembly in vitro and can form a broad distribution of oversized particles. Characterizing aberrant assembly products is challenging because they are both large and heterogeneous. In this work, charge detection mass spectrometry (CDMS) is used to measure the distribution of WHV assembly products. CDMS is a single-particle technique where the masses of individual ions are determined from simultaneous measurement of each ion's charge and m/z (mass-to-charge) ratio. Under relatively aggressive, assembly promoting conditions, roughly half of the WHV assembly products are T=4 capsids composed of exactly 120 dimers while the other half are a broad distribution of larger species that extends to beyond 210 dimers. There are prominent peaks at around 132 dimers and at 150 dimers. In part, the 150 dimer complex can be attributed to elongating a T=4 capsid along its 5-fold axis by adding a ring of hexamers. However, most of the other features cannot be explained by existing models for hexameric defects. Cryo-electron microscopy provides evidence of elongated capsids. However, image analysis reveals that many of them are not closed but have "spiral-like" morphologies. The CDMS data indicate that oversized capsids have a preference for growth by addition of 3 or 4 dimers, probably by completion of hexameric vertices.

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.

Biomolecular engineering of virus-like particles aided by computational chemistry methods

Multi-scale investigation of VLP self-assembly aided by computational methods is facilitating the design, redesign, and modification of functionalized VLPs.

Directing peptide crystallization through curvature control of nanotubes

In the absence of efficient crystallization methods, the molecular structures of fibrous assemblies have so far remained rather elusive. In this paper, we present a rational method to crystallize the lanreotide octapeptide by modification of a residue involved in a close contact. Indeed, we show that it is possible to modify the curvature of the lanreotide nanotubes and hence their diameter. This fine tuning leads to crystallization because the radius of curvature of the initially bidimensional peptide wall can be increased up to a point where the wall is essentially flat and a crystal is allowed to grow along a third dimension. By comparing X-ray diffraction data and Fourier transform Raman spectra, we show that the nanotubes and the crystals share similar cell parameters and molecular conformations, proving that there is indeed a structural continuum between these two morphologies. These results illustrate a novel approach to crystallization and represent the first step towards the acquisition of an Å-resolution structure of the lanreotide nanotubes β-sheet assembly.

A minimal representation of the self-assembly of virus capsids

Viruses are biological nanosystems with a capsid of protein-made capsomer units that encloses and protects the genetic material responsible for their replication. Here we show how the geometrical constraints of the capsomer-capsomer interaction in icosahedral capsids and the requirement of low frustration fix the form of the shortest and universal truncated multipolar expansion of the two-body interaction between capsomers. The structures of many of the icosahedral and related virus capsids are located as single lowest energy states of a potential energy surface built from this interaction. Our minimalist representation is consistent with other models known to produce a controllable and efficient self-assembly, and unveils relevant features of the natural design of the capsids. It promises to be very useful in physical virology and may also be of interest in fields of nanoscience and nanotechnology where similar hollow convex structures are relevant.

Recent Developments in Molecular Simulation Approaches to Study Spherical Virus Capsids

Viruses are a particularly challenging systems to study via molecular simulation methods. Virus capsids typically consist of over 100 subunit proteins and reach dimensions of over 100 nm; solvated viruses capsid systems can be over 1 million atoms in size. In this review, I will present recent developments which have attempted to overcome the significant computational expense to perform simulations which can inform experimental studies, make useful predictions about biological phenomena and calculate material properties relevant to nanotechnology design efforts.

Theoretical studies on assembly, physical stability and dynamics of viruses

All matter has to obey the general laws of physics and living matter is not an exception. Viruses have not only learnt how to cope with them, but have managed to use them for their own survival. In this chapter we will review some of the exciting physics behind viruses and discuss simple physical models that can shed some light on different aspects of the viral life cycle and viral properties. In particular, we will focus on how the structure and shape of the capsid, its assembly and stability, and the entry and exit of viral particles and their genomes can be understood using fundamental physics theories.

Physics of shell assembly: line tension, hole implosion, and closure catastrophe

The self-assembly of perfectly ordered closed shells is a challenging process involved in many biological and nanoscale systems. However, most of the aspects that determine their formation are still unknown. Here we investigate the growth of shells by simulating the assembly of spherical structures made of N identical subunits. Remarkably, we show that the formation and energetics of partially assembled shells are dominated by an effective line-tension that can be described in simple thermodynamic terms. In addition, we unveil two mechanisms that can prevent the correct formation of defect-free structures: "hole implosion," which leads to a premature closure of the shell; and "closure catastrophe," which causes a dramatic production of structural disorder during the later stages of the growth of big shells.

Energies and pressures in viruses: contribution of nonspecific electrostatic interactions

We summarize some aspects of electrostatic interactions in the context of viruses. A simplified but, within well defined limitations, reliable approach is used to derive expressions for electrostatic energies and the corresponding osmotic pressures in single-stranded RNA viruses and double-stranded DNA bacteriophages. The two types of viruses differ crucially in the spatial distribution of their genome charge which leads to essential differences in their free energies, depending on the capsid size and total charge in a quite different fashion. Differences in the free energies are trailed by the corresponding characteristics and variations in the osmotic pressure between the inside of the virus and the external bathing solution.

Built-in mechanical stress in viral shells

Mechanical properties of biological molecular aggregates are essential to their function. A remarkable example are double-stranded DNA viruses such as the φ29 bacteriophage, that not only has to withstand pressures of tens of atmospheres exerted by the confined DNA, but also uses this stored elastic energy during DNA translocation into the host. Here we show that empty prolated φ29 bacteriophage proheads exhibit an intriguing anisotropic stiffness which behaves counterintuitively different from standard continuum elasticity predictions. By using atomic force microscopy, we find that the φ29 shells are approximately two-times stiffer along the short than along the long axis. This result can be attributed to the existence of a residual stress, a hypothesis that we confirm by coarse-grained simulations. This built-in stress of the virus prohead could be a strategy to provide extra mechanical strength to withstand the DNA compaction during and after packing and a variety of extracellular conditions, such as osmotic shocks or dehydration.

The structure of elongated viral capsids

There are many viruses whose genetic material is protected by a closed elongated protein shell. Unlike spherical viruses, the structure and construction principles of these elongated capsids are not fully known. In this article, we have developed a general geometrical model to describe the structure of prolate or bacilliform capsids. We show that only a limited set of tubular architectures can be built closed by hemispherical icosahedral caps. In particular, the length and number of proteins adopt a very special set of discrete values dictated by the axial symmetry (fivefold, threefold, or twofold) and the triangulation number of the caps. The results are supported by experimental observations and simulations of simplified physical models. This work brings about a general classification of elongated viruses that will help to predict their structure, and to design viral cages with tailored geometrical properties for biomedical and nanotechnological applications.