Analysing mechanical stress and strain in individual cells within epithelial tissue

Abstract

Cells in living organisms are constantly subjected to mechanical perturbations. It is vital that cells are able to adapt and respond to mechanical stimuli in order to maintain tissue homeostasis, and to facilitate developmental processes such as gastrulation. Cells may experience tensile (stretching), compressive (squashing) and shearing forces (a combination of tensile and compressive forces). It is known that stretch- ing single cells or epithelial tissue explants via applying an external force changes cell division. The mitotic spindle, which controls the direction of cell division, aligns with the direction of applied mechanical force in stretched epithelial tissues and the proliferation rate of cells increases. Much of the knowledge about changes in cell division is obtained from stretch experiments where force is applied instantly, in a manner that is biologically analogous to wounding experiments. However, little is known about how the rate of stretch affects the regulation of cell division. In particular, it is interesting to know how cell division behaviour may change in an environment where a tensile force is experienced over a long period of time, such as has been observed during early development. Mathematical models are able to provide insights into the mechanical description of tissues, in particular the possible mechanical stress (force per unit area) and the mechanical strain (deformation) the cells are experiencing. The vertex model is a popular model used for modelling epithelial tissue. In this work the vertex model is presented in a novel incidence matrix formulation that explicitly states mathematically the topology of the cells, something which is normally lacking in the classical implementation of the vertex model. This model shows how applied mechanical force at the periphery of an epithelial monolayer diffuses inwards in a manner that can be described with the use of a ‘Cell Laplacian’, a discrete operator which is analogous to the classic Laplacian. Using experimental datasets of living tissue explants, the vertex model is used here to provide a description of the mechanical environment within a living tissue layer. The mechanical stresses of individual cells can be estimated from cell geometries obtained from confocal images. A description of the shear strain and shear stress of a cell, a feature that has not been presented for the vertex model previously, is presented here to complement descriptions of the isotropic stress. Xenopus laevis tissue explants from embryos are stretched to the same degree at different rates; a fast-instant stretch and a slow-incremental stretch. Notably, the slow-stretch experiment does not result in an increase in proliferation, however the divisions that occur still align with the direction of stretch. Measured descriptions of cell geometric properties show that the cells in fast-stretched tissue experience a greater increase in apical area which is resolved over time, whereas the apical area of cells in slow-stretched tissue is more consistent. Despite this, the changes in cell strain appear to be similar between the two stretch protocols. Estimates of mechanical stress provided by the vertex model suggest how stretching the tissue changes the mechanical environment. There is an induction of a distinctive structure of isotropic stress arising from the application of force that persists over time. There is also an increase in the level of shear stress within the tissue, which reduces after the stretch, in the apical cells of both slow- and fast-stretched tissue. Complementary mathematical simulations of monolayers under the influence of the different stretch protocols suggest that the total monolayer mechanical energy and the shear stress within the fast-stretched tissue increase to a greater degree than that of the slow-stretched tissue. The work presented in this project highlights the benefits of interdisciplinary research and forms the foundations of possible fu

Date of Award	1 Aug 2022
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Oliver Jensen (Supervisor) & Sarah Woolner (Supervisor)