Related papers: Geometric frustration and solid-solid transitions …
How can dense biological tissue maintain sharp boundaries between coexisting cell populations? We explore this question within a simple vertex model for cells, focusing on the role of topology and tissue surface tension. We show that the…
Cross-sections of cell shapes in a tissue monolayer typically resemble a tiling of convex polygons. Yet, examples exist where the polygons are not convex with curved cell-cell interfaces, as seen in the adaxial epidermis. To date,…
The shapes of epithelial tissues result from a complex interplay of contractile forces in the cytoskeleta of the cells in the tissue, and adhesion forces between them. A host of discrete, cell-based models describe these forces by assigning…
We introduce two 2D mechanical models reproducing the evolution of two viscous tissues in contact. Their main property is to model the swirling cell motions while keeping the tissues segregated, as observed during vertebrate embryo…
Geometrically frustrated elastic ribbons exhibit, in many cases, significant changes in configuration depending on the relation between their width and thickness. We show that the existence of such a transition, and the scaling at which it…
The uniform director field obtained for the nematic ground state of the hard-rod model of liquid crystals in two dimensions reflects the high symmetry of the constituents of the liquid; It is a manifestation of the constituents' local…
Biological cells can actively tune their intracellular architecture according to their overall shape. Here we explore the rheological implication of such coupling in a minimal model of a dense cellular material where each cell exerts an…
Living cells respond to mechanical changes in the matrix surrounding them by applying contractile forces that are in turn transmitted to distant cells. We calculate the mechanical work that each cell performs in order to deform the matrix,…
Geometric frustration is recognized to generate complex morphologies in self-assembling particulate and molecular systems. In bulk states, frustrated drives structured arrays of topological defects. In the dilute limit, these systems have…
The capacity to precisely edit genomes has outpaced our ability to predict the consequences. A cell can be genetically perfect and therapeutically useless: edited exactly as intended, yet unstable, drifting toward unintended fates, or…
Geometric frustration emerges when local interaction energies in an ordered lattice structure cannot be simultaneously minimized, resulting in a large number of degenerate states. The numerous degenerate configurations may lead to practical…
The vertex model is widely used to describe the dynamics of epithelial tissues, because of its simplicity and versatility and the direct inclusion of biophysical parameters. Here, it is shown that quite generally, when cells modify their…
A continuum model of epithelial tissue mechanics was formulated using cellular-level mechanical ingredients and cell morphogenetic processes, including cellular shape changes and cellular rearrangements. This model can include finite…
Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer…
We present an adaptive geometry in which the yardstick co-deforms with space itself, formulated on cellular spaces where length is a count: distances are shortest cell-crossing counts. No cell shape, angles, or embedding are assumed; the…
Biological cells in soft materials can be modeled as anisotropic force contraction dipoles. The corresponding elastic interaction potentials are long-ranged ($\sim 1/r^3$ with distance $r$) and depend sensitively on elastic constants,…
Using a geometric formalism of elasticity theory we develop a systematic theoretical method for controlling and manipulating the mechanical response of slender solids to external loads. We formally express global mechanical properties…
Cell layers eliminate unwanted cells through the extrusion process, which underlines healthy versus flawed tissue behaviors. Although several biochemical pathways have been identified, the underlying mechanical basis including the forces…
Topological defects are ubiquitous on surfaces with orientational order fields. Here, we study equilibrium states generated by the feedback between geometry and nematic order on fluid membranes with an integer topological defect. When the…
Especially in one dimension, models with discrete and continuous symmetries display different physical properties, starting from the existence of long-range order. In this work, we that, by adding topological frustration, an…