Topological defects are distinctive signatures of liquid crystals. They profoundly affect the viscoelastic behaviour of the fluid by constraining the orientational structure in a way that inevitably requires global changes not achievable with any set of local deformations. In active nematic liquid crystals, topological defects not only dictate the global structure of the director, but also act as local sources of motion, behaving as self-propelled particles. In this article, we present a detailed analytical and numerical study of the mechanics of topological defects in active nematic liquid crystals.
We introduce an Active Vertex Model (AVM) for cell-resolution studies of the mechanics of confluent epithelial tissues consisting of tens of thousands of cells, with a level of detail inaccessible to similar methods. The AVM combines the Vertex Model for confluent epithelial tissues with active matter dynamics. This introduces a natural description of the cell motion and accounts for motion patterns observed on multiple scales. Furthermore, cell contacts are generated dynamically from positions of cell centres. This not only enables efficient numerical implementation, but provides a natural description of the T1 transition events responsible for local tissue rearrangements. The AVM also includes cell alignment, cell-specific mechanical properties, cell growth, division and apoptosis. In addition, the AVM introduces a flexible, dynamically changing boundary of the epithelial sheet allowing for studies of phenomena such as the fingering instability or wound healing. We illustrate these capabilities with a number of case studies.
Epithelial cell monolayers show remarkable long-range displacement and velocity correlations reminiscent of supercooled liquids and active nematics. Here we show that many of the observed features can be understood within the framework of active matter at high densities. In particular, we argue that uncoordinated but persistent cell motility coupled to the collective elastic modes of the cell sheet is sufficient to produce characteristic swirl-like correlations. This includes a divergent correlation length in the limit of infinite persistence time. We derive this result using both continuum active linear elasticity and a normal modes formalism, and validate analytical predictions with numerical simulations of two agent-based models of soft elastic particles and in-vitro experiments of confluent corneal epithelial cell sheets. Our analytical model is able to fit measured velocity correlation functions without any free parameters. SIGNIFICANCEUnderstanding how cells in confluent epithelial sheets coordinate to create coherent motion patterns is a central question in cell and developmental biology. We show that a simple active matter model that couples crawling of an individual cell to the elastic environment provided by the surrounding cells, faithfully captures large-scale coherent motion patterns observed in the epithelial cell monolayers. The linear elastic model can be analyzed analytically and is able to match numerical simulations of two complementary models without any fitting parameters. It is a good match for experiments on corneal epithelial cells.
We use molecular dynamics simulations to study the crystallization of spherical nucleic-acid (SNA) gold nanoparticle conjugates, guided by sequence-specific DNA hybridization events. Binary mixtures of SNA gold nanoparticle conjugates (inorganic core diameter in the 8−15 nm range) are shown to assemble into BCC, CsCl, AlB 2 , and Cr 3 Si crystalline structures, depending upon particle stoichiometry, number of immobilized strands of DNA per particle, DNA sequence length, and hydrodynamic size ratio of the conjugates involved in crystallization. These data have been used to construct phase diagrams that are in excellent agreement with experimental data from wet-laboratory studies.
Large crystalline molecular shells, such as some viruses and fullerenes, buckle spontaneously into icosahedra. Meanwhile multicomponent microscopic shells buckle into various polyhedra, as observed in many organelles. Although elastic theory explains one-component icosahedral faceting, the possibility of buckling into other polyhedra has not been explored. We show here that irregular and regular polyhedra, including some Archimedean and Platonic polyhedra, arise spontaneously in elastic shells formed by more than one component. By formulating a generalized elastic model for inhomogeneous shells, we demonstrate that coassembled shells with two elastic components buckle into polyhedra such as dodecahedra, octahedra, tetrahedra, and hosohedra shells via a mechanism that explains many observations, predicts a new family of polyhedral shells, and provides the principles for designing microcontainers with specific shapes and symmetries for numerous applications in materials and life sciences.crystalline shells | self-assembly U niform convex polyhedra, such as Platonic and Archimedean solids, have beguiled scientists, philosophers, and artists for millennia (1, 2). In our modern era, they are incorporated in the revolutionary Descartes's geometrization of nature and introduce aesthetic elements in the physical sciences (3). Although mathematicians have rigorously captured the "morphological essence" of such highly regular polytopes by classifying and formalizing their symmetries and isometries (4), the search for such structures in the realm of nature has been, for the most part, rather elusive.Notable attempts include Plato's description of the fundamental matter constituents (5) and Kepler's effort to fit the motion of planets by using those very same regular solids that Greeks identified centuries earlier (6). In recent times, polyhedral shapes have been identified at the microscopic level. Besides faceted small metal clusters (7) and hard-sphere clusters (8), there are many examples of polyhedral shells ranging from capsids of viruses (9), supramolecular organic and inorganic assemblies (10), "platonic" hydrocarbons and carbon molecules (11, 12), to protein-based bacterial organelles (13) including carboxysomes (14, 15) and multicomponent ligand assemblies (16), to name a few. The connection between the lowest-energy configuration of a complex system at the microscopic scale and geometric principles has fostered many scientific discoveries (17), and it is a guiding principle in advancing modern fundamental science (18). We explore this connection here to design a previously undescribed family of polyhedral shells.The most frequently observed polyhedral symmetry in selfassembled homogeneous elastic shells is the icosahedron, a polyhedron with the highest possible symmetry. A quantitative explanation of this account comes from the theory of elasticity (19,20), which describes how any spherical shell made of a homogenous, isotropic, elastic material can buckle into an icosahedron. The onset of such faceting is contro...
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