Models for cellular force generation and the cell-substrate interface

Cells are able to interact with their environments through a variety of chemical and physical signalling mechanisms, with it becoming increasingly clear that physical force plays a crucial role in determining cellular behaviour and coordination. It is clear that cells respond very differently depending on the mechanical properties of their environments; understanding these differences in their behaviour is crucial for tissue engineering applications and to understand how the mechanical microenvironment may affect, for example, cancer growth and invasion.

This project focuses on developing advanced mathematical models to describe the physical forces exerted by a single cell or cell layer when adhered to a gel layer and to elucidate the complex interplay between cellular dynamics and the mechanical microenvironment. The model context focuses on the most common biophysical experimental set-ups for investigating cellular forces. These experiments generally work from inferring cellular forces from measurements of the observed substrate deformation, using experimentally determined knowledge of the mechanical response of the designed substrates. The underlying substrates range from elastic gels (as for Traction Force Microscopy studies) to arrays of micropillars.

The modelling framework being developed is based in continuum elasticity theory additionally using active matter theory to describe cellular contractility, which is the primary mechanism of force generation. On the time scale of experimental observations the cell or cell layer is assumed to be in mechanical equilibrium. This project is developing detailed mathematical descriptions of the cell-gel interface and also of the mechanisms of force generation. A key objective is to explain the observed cellular adaptations to changes in the mechanical properties of the underlying gel. The models are being analysed and solved using both analytical approaches (exploiting approximations and symmetry arguments) and using Finite Element Methods.