# Cells ‘walk’ to firm ground

A new mathematical model may explain how body cells get their shapes and what makes them move within a tissue. The model provides fundamental knowledge for applications in tissue engineering, amongst other things. Publication in open-access journal iScience.

Body cells can take on different shapes and move within a tissue. Previous mathematical models have proposed explanations for a particular shape or movement of a cell, but did not explain these phenomena in unison. Roeland Merks, professor of Mathematical biology at the Institute of Biology Leiden (IBL) and the Mathematical Institute (MI) and his former PhD candidate Lisanne Rens of the Centrum Wiskunde & Informatica (CWI) developed a mathematical model that can explain various phenomena of the mechanical interaction between cells and their environment. How cells behave in a tissue is important in, for example, tissue engineering. The mechanical interaction between cells and their environment also appears to play a role in diseases such as cancer and liver cirrhosis.

## Flat like a pancake

Body tissues are made up of cells that live within a structure called the extracellular matrix (ECM). The ECM gives shape and firmness to tissues and the cells that lie in them. Mechanical forces between the ECM and cells give cells a certain shape: on a soft surface, cells are often round and small, on a firm surface the cells spread out like pancakes, and on a surface of intermediate stiffness cells become elongated. Merks explains: 'Our model shows that the effect of substrate stiffness on cell shape can be explained by the interaction between the forces that cells exert on their environment, how easily the environment yields to those forces, and the response of the focal adhesions, which are the ‘feet’ of cells. They become stronger as they experience more forces.’

## Grip on the surface

So it seems that the ‘feet’ of cells have more grip on a stiff surface. This degree of grip also appears to play a role in the movement of cells. Merks: ‘The feet adhere slightly more strongly to the stiffer side of the matrix than to the softer side. If the cells constantly pull themselves off of the substrate and make new connections to the substrate, the stronger connections on the stiffer side persist for longer. In this way, the cell gradually moves in the stiffer direction.’ According to Merks, the model provides insights that contribute to fundamental knowledge about how cells behave in tissues: ‘The insights are important for tissue engineering, and also for a better understanding of blood vessel growth and the spread of tumour cells. We have added another piece of fundamental knowledge.’

Publication: Rens, E.G., Merks, R.M.H., Cell Shape and Durotaxis Explained from Cell-Extracellular Matrix Forces and Focal Adhesion Dynamics, iScience 23, 101488  (2020), doi: https://doi.org/10.1016/j.isci.2020.101488