Electrostatics-Driven Inflation of Elastic Icosahedral Shells as a Model for Swelling of Viruses

Mechanics of inactive swelling and bursting of porate pollen grains

The structure of pollen grains, which is typically characterized by soft apertures in an otherwise stiff exine shell, guides their response to changes in the humidity of the environment. These changes can lead to desiccation of the grain and its infolding but also to excessive swelling of the grain and even its bursting. Here we use an elastic model to explore the mechanics of pollen grain swelling and the role of soft, circular apertures (pores) in this process. Small, circular apertures typically occur in airborne and allergenic pollen grains so that the bursting of such grains is important in the context of human health. We identify and quantify a mechanical weakness of the pores, which are prone to rapid inflation when the grain swells to a critical extent. The inflation occurs as a sudden transition and may induce bursting of the grain and release of its content. This process crucially depends on the size of the pores and their softness. Our results provide insight into the inactive part of the mechanical response of pollen grains to hydration when they land on a stigma as well as bursting of airborne pollen grains during changes in air humidity.

Relative humidity in droplet and airborne transmission of disease

A large number of infectious diseases are transmitted by respiratory droplets. How long these droplets persist in the air, how far they can travel, and how long the pathogens they might carry survive are all decisive factors for the spread of droplet-borne diseases. The subject is extremely multifaceted and its aspects range across different disciplines, yet most of them have only seldom been considered in the physics community. In this review, we discuss the physical principles that govern the fate of respiratory droplets and any viruses trapped inside them, with a focus on the role of relative humidity. Importantly, low relative humidity-as encountered, for instance, indoors during winter and inside aircraft-facilitates evaporation and keeps even initially large droplets suspended in air as aerosol for extended periods of time. What is more, relative humidity affects the stability of viruses in aerosol through several physical mechanisms such as efflorescence and inactivation at the air-water interface, whose role in virus inactivation nonetheless remains poorly understood. Elucidating the role of relative humidity in the droplet spread of disease would permit us to design preventive measures that could aid in reducing the chance of transmission, particularly in indoor environment.

Buckling transitions and soft-phase invasion of two-component icosahedral shells

What is the optimal distribution of two types of crystalline phases on the surface of icosahedral shells, such as of many viral capsids? We here investigate the distribution of a thin layer of soft material on a crystalline convex icosahedral shell. We demonstrate how the shapes of spherical viruses can be understood from the perspective of elasticity theory of thin two-component shells. We develop a theory of shape transformations of an icosahedral shell upon addition of a softer, but still crystalline, material onto its surface. We show how the soft component "invades" the regions with the highest elastic energy and stress imposed by the 12 topological defects on the surface. We explore the phase diagram as a function of the surface fraction of the soft material, the shell size, and the incommensurability of the elastic moduli of the rigid and soft phases. We find that, as expected, progressive filling of the rigid shell by the soft phase starts from the most deformed regions of the icosahedron. With a progressively increasing soft-phase coverage, the spherical segments of domes are filled first (12 vertices of the shell), then the cylindrical segments connecting the domes (30 edges) are invaded, and, ultimately, the 20 flat faces of the icosahedral shell tend to be occupied by the soft material. We present a detailed theoretical investigation of the first two stages of this invasion process and develop a model of morphological changes of the cone structure that permits noncircular cross sections. In conclusion, we discuss the biological relevance of some structures predicted from our calculations, in particular for the shape of viral capsids.

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.

pH stability and disassembly mechanism of wild-type simian virus 40

Viruses are remarkable self-assembled nanobiomaterial-based machines, exposed to a wide range of pH values. Extreme pH values can induce dramatic structural changes, critical for the function of the virus nanoparticles, including assembly and genome uncoating. Tuning cargo-capsid interactions is essential for designing virus-based delivery systems. Here we show how pH controls the structure and activity of wild-type simian virus 40 (wtSV40) and the interplay between its cargo and capsid. Using cryo-TEM and solution X-ray scattering, we found that wtSV40 was stable between pH 5.5 and 9, and only slightly swelled with increasing pH. At pH 3, the particles aggregated, while capsid protein pentamers continued to coat the virus cargo but lost their positional correlations. Infectivity was only partly lost after the particles were returned to pH 7. At pH 10 or higher, the particles were unstable, lost their infectivity, and disassembled. Using time-resolved experiments we discovered that disassembly began by swelling of the particles, poking a hole in the capsid through which the genetic cargo escaped, followed by a slight shrinking of the capsids and complete disassembly. These findings provide insight into the fundamental intermolecular forces, essential for SV40 function, and for designing virus-based nanobiomaterials, including delivery systems and antiviral drugs.

Osmotic stress and pore nucleation in charged biological nanoshells and capsids

A model system is proposed to investigate the chemical equilibrium and mechanical stability of biological spherical-like nanoshells in contact with an aqueous solution with added dissociated electrolyte of a given concentration. The ionic chemical equilibrium across the permeable shell is investigated in the framework of an accurate Density Functional Theory (DFT) that incorporates electrostatic and hardcore correlations beyond the traditional mean-field (e.g., Poisson-Boltzmann) limit. The accuracy of the theory is tested by a direct comparison with Monte Carlo (MC) simulations. A simple analytical expression is then deduced which clearly highlights the entropic, electrostatic, and self-energy contributions to the osmotic stress over the shell in terms of the calculated ionic profiles. By invoking a continuum mean-field elastic approach to account for the shell surface stress upon osmotic stretching, the mechanical equilibrium properties of the shell under a wide variety of ionic strengths and surface charges are investigated. The model is further coupled to a continuum mechanical approach similar in structure to a Classical Nucleation Theory (CNT) to address the question of mechanical stability of the shells against a pore nucleation. This allows us to construct a phase diagram which delimits the mechanical stability of capsids for different ionic strengths and shell surface charges.

Hidden symmetry of the anomalous bluetongue virus capsid and its role in the infection process

Clear understanding of the principles that control the arrangement of proteins and their self-assembly into viral shells is very important for the development of antiviral strategies. Here we consider the structural peculiarities and hidden symmetry of the anomalous bluetongue virus (BTV) capsid. Each of its three concentric shells violates the paradigmatic geometrical model of Caspar and Klug, which is otherwise well suited to describe most of the known icosahedral viral shells. As we show, three icosahedral spherical lattices, which are commensurate with each other and possess locally hexagonal (primitive or honeycomb) order, underlie the proteinaceous shells of the BTV capsid. This interpretation of the multishelled envelope allows us to discuss the so-called "symmetry mismatch" between its layers. We also analyze the structural stability of the considered spherical lattices on the basis of the classical theory of spherical packing and relate the proximity of the outer spherical lattice to destabilization with the fact that during infection of the cell VP2 trimers are detached from the surface of the BTV capsid. An electrostatic mechanism that can assist in this detachment is discussed in detail.

Effect of aqueous medium on low-frequency dynamics, chemical activity and physical properties of a spherical virus

In this work, we have studied the effect of size and aqueous medium on the low-frequency dynamics, physical properties like melting temperature and glass transition temperature and chemical properties like catalytic activation energy of spherical virus using Lindemann's criteria and Arrhenius relation under their dynamic limit. The melting temperature and catalytic activation energy decrease with decreasing size of spherical virus. The glass transition temperature which increases with decreasing size of the virus is analyzed through the size dependent melting temperature. The melting temperature and catalytic activation energy of spherical virus of particular size increases when it is embedded in glycerol or water due to mismatch of the physical properties at the interface of virus and surrounding medium. In addition, the glass transition temperature of free and glycerol/water embedded virus using low-frequency vibrational modes has been calculated under the framework of elastic continuum approximation model. The glass transition temperature of spherical virus decreases with size when embedded in glycerol or water. A correlation between [Formula: see text] and [Formula: see text] is also drawn for spherical viruses. The study can be useful for spherical virus borne therapy i.e. in detecting and killing of the spherical viruses using a principle based on acoustic phonons (sound waves) resonance.Communicated by Ramaswamy H. Sarma.

pH-induced morphological changes of proteinaceous viral shells

Changes in environmental pH can induce morphological changes in empty proteinaceous shells of bacteriophages in vitro that are very similar to changes occurring in viral capsids in vivo after encapsidation of DNA. These changes in capsid shape and size cannot be explained with a simple elastic model alone. We propose a new theoretical framework that combines the elasticity of thin icosahedral shells with the pH dependence of capsid charge distribution. Minimization of the sum of elastic and electrostatic free energies leads to equilibrium shapes of viral shells that depend on a single elastic parameter and the detailed configuration of the imbedded protein charges. Based on the in vitro shell reconstructions of bacteriophage HK97 we elucidate the details of how the reversible transition between Prohead II and Expansion Intermediate II states of the HK97 procapsid is induced by pH changes, as well as some other features of the bacteriophage maturation.