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.

When pollen grains become exposed to the environment, they rapidly desiccate. To protect themselves until rehydration, the grains undergo characteristic infolding with the help of special structures in the grain wall-apertures-where the otherwise thick exine shell is absent or reduced in thickness. Recent theoretical studies have highlighted the importance of apertures for the elastic response and the folding of the grain. Experimental observations show that different pollen grains sharing the same number and type of apertures can nonetheless fold in quite diverse fashions. Using the thin-shell theory of elasticity, we show how both the absolute elastic properties of the pollen wall and the relative elastic differences between the exine wall and the apertures play an important role in determining pollen folding upon desiccation. Focusing primarily on colpate pollen, we delineate the regions of pollen elastic parameters where desiccation leads to a regular, complete closing of all apertures and thus to an infolding which protects the grain against water loss. Phase diagrams of pollen folding pathways indicate that an increase in the number of apertures leads to a reduction of the region of elastic parameters where the apertures close in a regular fashion. The infolding also depends on the details of the aperture shape and size, and our study explains how the features of the mechanical design of apertures influence the pollen folding patterns. Understanding the mechanical principles behind pollen folding pathways should also prove useful for the design of the elastic response of artificial inhomogeneous shells.

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.

We investigate a range of rule-based models of the in-plane structure of growing single-cell-thick epithelia represented by the distribution of frequencies of polygon classes. Within the Markovian framework introduced by Gibson et al. [Nature (London) 442, 1038 (2006)10.1038/nature05014], we discuss various topologically allowed cell division schemes assumed to control the structure of the tissue as well as a phenomenological Gaussian scheme, and we compute the stationary distributions for all of them. Some of the distributions reproduce those seen in tissues characterized by unbiased mitotic events but also in certain tissues with a preferred orientation of the mitotic plane or a cell-rearrangement process such as neighbor exchange. In addition, we propose the asynchronous-division variant of the model, which builds on the Lewis law and on the Aboav-Weaire law as well as on the fact that the dividing cells are larger than the resting cells. This generalization a posteriori validates the original model.

Abstract Some viruses package dsDNA together with large amounts of positively charged proteins, thought to help condense the genome inside the capsid with no evidence. Further, this role is not clear because these viruses have typically lower packing fractions than viruses encapsidating naked dsDNA. In addition, it has recently been shown that the major adenovirus condensing protein (polypeptide VII) is dispensable for genome encapsidation. Here, we study the morphology and mechanics of adenovirus particles with (Ad5-wt) and without (Ad5-VII-) protein VII. Ad5-VII- particles are stiffer than Ad5-wt, but DNA-counterions revert this difference, indicating that VII screens repulsive DNA-DNA interactions. Consequently, its absence results in increased internal pressure. The core is slightly more ordered in the absence of VII and diffuses faster out of Ad5-VII– than Ad5-wt fractured particles. In Ad5-wt unpacked cores, dsDNA associates in bundles interspersed with VII-DNA clusters. These results indicate that protein VII condenses the adenovirus genome by combining direct clustering and promotion of bridging by other core proteins. This condensation modulates the virion internal pressure and DNA release from disrupted particles, which could be crucial to keep the genome protected inside the semi-disrupted capsid while traveling to the nuclear pore.

We develop a clear theoretical description of radial swelling in virus-like particles that delineates the importance of electrostatic contributions to swelling in the absence of any conformational changes. The model couples the elastic parameters of the capsid-represented as a continuous elastic shell-to the electrostatic pressure acting on it. We show that different modifications of the electrostatic interactions brought about by, for instance, changes in pH or solution ionic strength are often sufficient to achieve the experimentally observed swelling (∼10% of the capsid radius). Additionally, we derive analytical expressions for the electrostatics-driven radial swelling of virus-like particles that enable one to quickly estimate the magnitudes of physical quantities involved.

Confined mixtures of a polymer and nonspecifically binding particles (condensers) are studied as models for viruses containing double-stranded DNA (polymer) and condensing proteins (particles). We explore a model in which all interactions between the packed content (polymer and particles) and its confinement are purely repulsive, with only a short-range attraction between the condensers and polymer to simulate binding. In the range of physical parameters applicable to viruses, the model predicts reduction of pressure in the system effected by the condensers, despite the reduction in free volume. Condensers are found to be interspersed throughout the spherical confinement and only partially wrapped in the polymer, which acts as an effective medium for the condenser interactions. Crowding of the viral interior influences the DNA and protein organization, producing a picture inconsistent with a chromatin-like, beads-on-a-string structure. The model predicts an organization of the confined interior compatible with experimental data on unperturbed adenoviruses and polyomaviruses, at the same time providing insight into the role of condensing proteins in the viral infectious cycles of related viral families.

Shapes of a single, long DNA molecule condensed in a confinement of a virus capsid are described as conformations optimizing a model free energy functional accounting for the interplay between the bending energy of the DNA and the surface energy of the DNA bundled in a “rope”. The rope is formed by bundled DNA brought together by (self-)attractive interactions. The conformations predicted by the model depend on the shape of the confinement, the total amount of the packed DNA but also on the relative contributions of the bending and surface energies. Some of the conformations found were not predicted previously, but many previously proposed DNA conformations, some of which are seemingly contradictory, were found as the solutions of the model. The results show that there are many possible packing conformations of the DNA and that the one which realizes in a particular virus depends on the capsid geometry and the nature of condensing agents.

Genome packing in adenovirus has long evaded precise description, since the viral dsDNA molecule condensed by proteins (core) lacks icosahedral order characteristic of the virus protein coating (capsid). We show that useful insights regarding the organization of the core can be inferred from the analysis of spatial distributions of the DNA and condensing protein units (adenosomes). These were obtained from the inspection of cryo-electron tomography reconstructions of individual human adenovirus particles. Our analysis shows that the core lacks symmetry and strict order, yet the adenosome distribution is not entirely random. The features of the distribution can be explained by modeling the condensing proteins and the part of the genome in each adenosome as very soft spheres, interacting repulsively with each other and with the capsid, producing a minimum outward pressure of ∼0.06 atm. Although the condensing proteins are connected by DNA in disrupted virion cores, in our models a backbone of DNA linking the adenosomes is not required to explain the experimental results in the confined state. In conclusion, the interior of an adenovirus infectious particle is a strongly confined and dense phase of soft particles (adenosomes) without a strictly defined DNA backbone.

The large-scale production of graphene monolayer greatly relies on epitaxial samples which often display stress-relaxation features in the form of wrinkles. Wrinkles of graphene on Ir(111) are found to exhibit a fairly well ordered interconnecting network which is characterized by low-energy electron microscopy (LEEM). The high degree of quasi-hexagonal network arrangement for the graphene aligned to the underlying substrate can be well described as a (non-Poissonian) Voronoi partition of a plane. The results obtained strongly suggest that the wrinkle network is frustrated at low temperatures, retaining the order inherited from elevated temperatures when the wrinkles interconnect in junctions which most often join three wrinkles. Such frustration favors the formation of multi-lobed wrinkles which are found in scanning tunneling microscopy (STM) measurements. The existence of multiple lobes is explained within a model accounting for the interplay of the van der Waals attraction between graphene and iridium and bending energy of the wrinkle. The presented study provides new insights into wrinkling of epitaxial graphene and can be exploited to further expedite its application.

We examine in vivo ejection of noncondensed DNA from tailed bacteriophages into bacteria. The ejection is dominantly governed by the physical conditions in the bacteria. The confinement of the DNA in the virus capsid only slightly helps the ejection, becoming completely irrelevant during its last stages. A simple calculation based on the premise of condensed DNA in the cell enables us to estimate the maximal bacterial turgor pressure against which the ejection can still be fully realized. The calculated pressure (similar to 5 atm) shows that the ejection of DNA into Gram-negative bacteria could proceed spontaneously, i.e., without the need to invoke active mechanisms.

From the analysis of sizes of approximately 130 small icosahedral viruses we find that there is a typical structural capsid protein, having a mean diameter of 5 nm and a mean thickness of 3 nm, with more than two thirds of the analyzed capsid proteins having thicknesses between 2 nm and 4 nm. To investigate whether, in addition to the fairly conserved geometry, capsid proteins show similarities in the way they interact with one another, we examined the shapes of the capsids in detail. We classified them numerically according to their similarity to sphere and icosahedron and an interpolating set of shapes in between, all of them obtained from the theory of elasticity of shells. In order to make a unique and straightforward connection between an idealized, numerically calculated shape of an elastic shell and a capsid, we devised a special shape fitting procedure, the outcome of which is the idealized elastic shape fitting the capsid best. Using such a procedure we performed statistical analysis of a series of virus shapes and we found similarities between the capsid elastic properties of even very different viruses. As we explain in the paper, there are both structural and functional reasons for the convergence of protein sizes and capsid elastic properties. Our work presents a specific quantitative scheme to estimate relatedness between different proteins based on the details of the (quaternary) shape they form (capsid). As such, it may provide an information complementary to the one obtained from the studies of other types of protein similarity, such as the overall composition of structural elements, topology of the folded protein backbone, and sequence similarity.

We use a spring-and-plaquette network model to analyze the repulsion between elastic disks in contact. By studying various 2D geometries, we find that as disks approach the incompressibility limit the many-body effects become dominant and the disk-disk interaction is not pairwise additive. Upon compression, the disks undergo a transition from the localized to the distributed deformation regime accompanied by a steep increase of energy consistent with the onset of a hard core. These results shed new light on the structures formed by deformable objects such as soft nanocolloids.