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The actin cortex is a thin layer of actin, myosin, and actin binding proteins that underlies the membrane of most animal cells. It is highly dynamic and can undergo remodelling on time-scales of tens of seconds thanks to protein turnover and myosin-mediated contractions. The cortex enables cells to resist external mechanical stresses, controls cell shape, and allows cells to exert forces on their neighbours. Thus, its mechanical properties are key to its physiological function. Here, we give an overview of how cortex composition, structure, and dynamics control cortex mechanics and cell shape. We use mitosis as an example to illustrate how global and local regulation of cortex mechanics give rise to a complex series of cell shape changes., Comment: Review

Soft materials often exhibit a distinctive power-law viscoelastic response arising from broad distribution of time-scales present in their complex internal structure. A promising tool to accurately describe the rheological behaviour of soft materials is fractional calculus. However, its use in the scientific community remains limited due to the unusual notation and non-trivial properties of fractional operators. This review aims to provide a clear and accessible description of fractional viscoelastic models for a broad audience, and to demonstrate the ability of these models to deliver a unified approach for the characterisation of power-law materials. The use of a consistent framework for the analysis of rheological data would help classify the empirical behaviours of soft and biological materials, and better understand their response., Comment: 28 pages, 12 figures. Soft Matter (2020)

The balance between stretching and bending deformations characterizes shape transitions of thin elastic sheets. While stretching dominates the mechanical response in tension, bending dominates in compression after an abrupt buckling transition. Recently, experimental results in suspended living epithelial monolayers have shown that, due to the asymmetry in surface stresses generated by molecular motors across the thickness $e$ of the epithelium, the free edges of such tissues spontaneously curl out-of-plane, stretching the sheet in-plane as a result. This suggests that a competition between bending and stretching sets the morphology of the tissue margin. In this study, we use the framework of non-euclidean plates to incorporate active pre-strain and spontaneous curvature to the theory of thin elastic shells. We show that, when the spontaneous curvature of the sheet scales like $1/e$, stretching and bending energies have the same scaling in the limit of a vanishingly small thickness and therefore both compete, in a way that is continuously altered by an external tension, to define the three-dimensional shape of the tissue.

Cell competition is a quality control mechanism in tissues that results in the elimination of less fit cells. Over the past decade, the phenomenon of cell competition has been identified in many physiological and pathological contexts, driven either by biochemical signaling or by mechanical forces within the tissue. In both cases, competition has generally been characterized based on the elimination of loser cells at the population level, but significantly less attention has been focused on determining how single-cell dynamics and interactions regulate population-wide changes. In this review, we describe quantitative strategies and outline the outstanding challenges in understanding the single cell rules governing tissue-scale competition dynamics. We propose quantitative metrics to characterize single cell behaviors in competition and use them to distinguish the types and outcomes of competition. We describe how such metrics can be measured experimentally using a novel combination of high-throughput imaging and machine learning algorithms. We outline the experimental challenges to quantify cell fate dynamics with high-statistical precision, and describe the utility of computational modeling in testing hypotheses not easily accessible in experiments. In particular, cell-based modeling approaches that combine mechanical interaction of cells with decision-making rules for cell fate choices provide a powerful framework to understand and reverse-engineer the diverse rules of cell competition., Comment: Review article