We show that substrates with nonzero Gaussian curvature influence the organization of stress fibers and direct the migration of cells. To study the role of Gaussian curvature, we developed a ...sphere-with-skirt surface in which a positive Gaussian curvature spherical cap is seamlessly surrounded by a negative Gaussian curvature draping skirt, both with principal radii similar to cell-length scales. We find significant reconfiguration of two subpopulations of stress fibers when fibroblasts are exposed to these curvatures. Apical stress fibers in cells on skirts align in the radial direction and avoid bending by forming chords across the concave gap, whereas basal stress fibers bend along the convex direction. Cell migration is also strongly influenced by the Gaussian curvature. Real-time imaging shows that cells migrating on skirts repolarize to establish a leading edge in the azimuthal direction. Thereafter, they migrate in that direction. This behavior is notably different from migration on planar surfaces, in which cells typically migrate in the same direction as the apical stress fiber orientation. Thus, this platform reveals that nonzero Gaussian curvature not only affects the positioning of cells and alignment of stress fiber subpopulations but also directs migration in a manner fundamentally distinct from that of migration on planar surfaces.
We use a regular arrangement of kirigami elements to demonstrate an inverse design paradigm for folding a flat surface into complex target configurations. We first present a scheme using arrays of ...disclination defect pairs on the dual to the honeycomb lattice; by arranging these defect pairs properly with respect to each other and choosing an appropriate fold pattern a target stepped surface can be designed. We then present a more general method that specifies a fixed lattice of kirigami cuts to be performed on a flat sheet. This single pluripotent lattice of cuts permits a wide variety of target surfaces to be programmed into the sheet by varying the folding directions.
Significance How can flat surfaces be transformed into useful three-dimensional structures? Recent research on origami techniques has led to algorithmic solutions to the inverse design problem of prescribing a set of folds to form a desired target surface. The fold patterns generated are often very complex and so require a convoluted series of deformations from the flat to the folded state, making it difficult to implement these designs in self-assembling systems. We propose a design paradigm that employs lattice-based kirigami elements, combining the folding of origami with cutting and regluing techniques. We demonstrate that this leads to a pluripotent design in which a single kirigami pattern can be robustly manipulated into a variety of three-dimensional shapes.
Entropically Driven Helix Formation Snir, Yehuda; Kamien, Randall D
Science (American Association for the Advancement of Science),
02/2005, Letnik:
307, Številka:
5712
Journal Article
Recenzirano
The helix is a ubiquitous motif for biopolymers. We propose a heuristic, entropically based model that predicts helix formation in a system of hard spheres and semiflexible tubes. We find that the ...entropy of the spheres is maximized when short stretches of the tube form a helix with a geometry close to that found in natural helices. Our model could be directly tested with wormlike micelles as the tubes, and the effect could be used to self-assemble supramolecular helices.
Programmable shape-shifting materials can take different physical forms to achieve multifunctionality in a dynamic and controllable manner. Although morphing a shape from 2D to 3D via programmed ...inhomogeneous local deformations has been demonstrated in various ways, the inverse problem—finding how to program a sheet in order for it to take an arbitrary desired 3D shape—is much harder yet critical to realize specific functions. Here, we address this inverse problem in thin liquid crystal elastomer (LCE) sheets, where the shape is preprogrammed by precise and local control of the molecular orientation of the liquid crystal monomers. We show how blueprints for arbitrary surface geometries can be generated using approximate numerical methods and how local extrinsic curvatures can be generated to assist in properly converting these geometries into shapes. Backed by faithfully alignable and rapidly lockable LCE chemistry, we precisely embed our designs in LCE sheets using advanced top-down microfabrication techniques. We thus successfully produce flat sheets that, upon thermal activation, take an arbitrary desired shape, such as a face. The general design principles presented here for creating an arbitrary 3D shape will allow for exploration of unmet needs in flexible electronics, metamaterials, aerospace and medical devices, and more.
Drop drying and deposition phenomena reveal a rich interplay of fundamental science and engineering, give rise to fascinating everyday effects (coffee rings), and influence technologies ranging from ...printing to genotyping. Here we investigate evaporation dynamics, morphology, and deposition patterns of drying lyotropic chromonic liquid crystal droplets. These drops differ from typical evaporating colloidal drops primarily due to their concentration-dependent isotropic, nematic, and columnar phases. Phase separation occurs during evaporation, and in the process creates surface tension gradients and significant density and viscosity variation within the droplet. As a result, the drying multiphase drops exhibit different convective currents, drop morphologies, and deposition patterns (coffee-rings).
The order parameter of the smectic liquid crystal phase is the same as that of a superfluid or superconductor, namely a complex scalar field. We show that the essential difference in boundary ...conditions between these systems leads to a markedly different topological structure of the defects. Screw and edge defects can be distinguished topologically. This implies an invariant on an edge dislocation loop so that smectic defects can be topologically linked not unlike defects in ordered systems with non-Abelian fundamental groups.
The smectic order of wrinkles Aharoni, Hillel; Todorova, Desislava V; Albarrán, Octavio ...
Nature communications,
07/2017, Letnik:
8, Številka:
1
Journal Article
Recenzirano
Odprti dostop
A thin elastic sheet lying on a soft substrate develops wrinkled patterns when subject to an external forcing or as a result of geometric incompatibility. Thin sheet elasticity and substrate response ...equip such wrinkles with a global preferred wrinkle spacing length and with resistance to wrinkle curvature. These features are responsible for the liquid crystalline smectic-like behaviour of such systems at intermediate length scales. This insight allows better understanding of the wrinkling patterns seen in such systems, with which we explain pattern breaking into domains, the properties of domain walls and wrinkle undulation. We compare our predictions with numerical simulations and with experimental observations.
Chirality, ubiquitous in complex biological systems, can be controlled and quantified in synthetic materials such as cholesteric liquid crystal (CLC) systems. In this work, we study spherical shells ...of CLC under weak anchoring conditions. We induce anchoring transitions at the inner and outer boundaries using two independent methods: by changing the surfactant concentration or by raising the temperature close to the clearing point. The shell confinement leads to new states and associated surface structures: a state where large stripes on the shell can be filled with smaller, perpendicular substripes, and a focal conic domain (FCD) state, where thin stripes wrap into at least two, topologically required, double spirals. Focusing on the latter state, we use a Landau–de Gennes model of the CLC to simulate its detailed configurations as a function of anchoring strength. By abruptly changing the topological constraints on the shell, we are able to study the interconversion between director defects and pitch defects, a phenomenon usually restricted by the complexity of the cholesteric phase. This work extends the knowledge of cholesteric patterns, structures that not only have potential for use as intricate, self-assembly blueprints but are also pervasive in biological systems.
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