# Cell Shape and Durotaxis Explained from Cell-Extracellular Matrix Forces and Focal Adhesion Dynamics

## TL;DR

This paper explains how cell shape and movement on different stiffness surfaces arise from focal adhesion dynamics and cell-ECM forces using a computational model.

## Contribution

A hybrid model combining cellular Potts and finite-element methods with focal adhesion dynamics explains cell shape and durotaxis in a unified framework.

## Key findings

- Cell shape changes on varying ECM stiffness are explained by focal adhesion stabilization and traction forces.
- Durotaxis emerges naturally from the same model assumptions about focal adhesion dynamics.
- Durotaxis speed increases with steeper stiffness gradients but reaches a saturation point.

## Abstract

Many cells are small and rounded on soft extracellular matrices (ECM), elongated on stiffer ECMs, and flattened on hard ECMs. Cells also migrate up stiffness gradients (durotaxis). Using a hybrid cellular Potts and finite-element model extended with ODE-based models of focal adhesion (FA) turnover, we show that the full range of cell shape and durotaxis can be explained in unison from dynamics of FAs, in contrast to previous mathematical models. In our 2D cell-shape model, FAs grow due to cell traction forces. Forces develop faster on stiff ECMs, causing FAs to stabilize and, consequently, cells to spread on stiff ECMs. If ECM stress further stabilizes FAs, cells elongate on substrates of intermediate stiffness. We show that durotaxis follows from the same set of assumptions. Our model contributes to the understanding of the basic responses of cells to ECM stiffness, paving the way for future modeling of more complex cell-ECM interactions.

•A cellular Potts model is extended with the mechanical response of focal adhesions•Mechanical cell-ECM reciprocity leads to cell spreading, elongation, and durotaxis•Cell-generated planar stresses may cooperatively strengthen focal adhesion patches•Predicted durotaxis speed increases with gradient steepness until saturation point

A cellular Potts model is extended with the mechanical response of focal adhesions

Mechanical cell-ECM reciprocity leads to cell spreading, elongation, and durotaxis

Cell-generated planar stresses may cooperatively strengthen focal adhesion patches

Predicted durotaxis speed increases with gradient steepness until saturation point

Biological Sciences; Cell Biology; Biophysics; In Silico Biology; Biomaterials; Structural Biology; Biochemistry; Biocomputational Method