Condensed Matter Theory

Abstract:

Many integrable statistical mechanical models possess a fractional-spin conserved current. Such currents have been constructed by utilising quantum-group algebras and ideas from “discrete holomorphicity”. I find them naturally and much more generally using a braided tensor category, a topological structure arising in knot invariants, anyons and conformal field theory. I derive a simple constraint on the Boltzmann weights admitting a conserved current, generalising one found using quantum-group algebras. The resulting trigonometric weights are typically those of a critical integrable lattice model, so the method here gives a linear way of “Baxterising”, i.e. building a solution of the Yang-Baxter equation out of topological data. It also illuminates why many models do not admit a solution. I discuss many examples in geometric and local models, including (perhaps) a new solution.

Abstract:

Actomyosin machinery endows cells with contractility at a single-cell level. However, within a monolayer, cells can be contractile or extensile based on the direction of pushing or pulling forces exerted by their neighbours or on the substrate. It has been shown that a monolayer of fibroblasts behaves as a contractile system while epithelial or neural progentior monolayers behave as an extensile system. Through a combination of cell culture experiments and in silico modelling, we reveal the mechanism behind this switch in extensile to contractile as the weakening of intercellular contacts. This switch promotes the build-up of tension at the cell–substrate interface through an increase in actin stress fibres and traction forces. This is accompanied by mechanotransductive changes in vinculin and YAP activation. We further show that contractile and extensile differences in cell activity sort cells in mixtures, uncovering a generic mechanism for pattern formation during cell competition, and morphogenesis.