Models for the mechanics of epithelial cell sheets

Abstract
(no more than 4,000 characters
including spaces, clearly explain which EPSRC research area the project relates to - for more info see overleaf) Epithelial cell sheets are a central feature of embryonic development in animals. In adults, they form the surface of many organs, such as eyes, skin and intestines. They actively shape the organism through internally generated active stresses, and are able to grow, renew themselves and repair wounds. The main driver of these active stresses is the cytoskeleton, composed of actin, myosin and microtubules, which both provides a scaffold for the cell and generates forces.
Understanding how epithelial cell sheets work mechanically will allow us to better understand their biological function and also to better engineer tissues, ultimately with clinical applications. Moreover, insights achieved here can be applied to a broader range biological tissues.

Recent experimental results on Drosophila and chick embryos have shown that forces are primarily due to the actomyosin cytoskeletal cortex and that they take the form of correlated contractions along cell-cell junctions and of the apical cell surface.
In this project, we will focus on vertex models of epithelial cell sheets. In such models, the sheet is represented by a polygonal tiling, providing a map from a complex biological situation to a graph problem, where cell surfaces correspond to faces and cell-cell junctions to edges. This microscopic approach, in contrast to a continuum approach, allows us to include details of cell shape and active force generation.
Informed by experiment, we will combine a passive energy functional for cell shapes with active mechanics consisting of contractions. Our model will include feedback and viscoelasticity. We will then systematically explore the resulting emergent sheet behaviour, including polarisation of the tissue, spontaneous flow, contraction and the emergence of instabilities -- all of which are biologically significant. This will be carried out through a combination of direct numerical simulations using our own simulation code, and analytical work. The latter will include homogenisation theory as well as normal modes as direct methods to coarse-grain a regular tissue, potentially paired with continuum PDE approaches such as active gel theory and active nematics.

Our research is timely: the existence of active contractile forces in cell sheets has long been known, but they are only beginning to be systematically studied in realistic microscopic models of cell sheets such as vertex models. Moreover, our methods encompass computational, theoretical and hybrid quasi-continuum approaches to address epithelial sheets at both cellular and tissue scales.

This research falls into several sub-categories of the EPSRC portfolio: 'Biophysics and Soft Matter Physics' in the Physical Sciences category, 'Mathematical Biology' and 'Continuum mechanics' in the Mathematical Sciences category, and finally 'Biomaterials and Tissues' in the Healthcare Technologies category.

While we have no formal collaborators in this project, we expect to produce direct predictions for in-vitro epithelial cell sheets which can be compared to experimental data from existing collaborators of the supervisors.