# Phenomenlogical Modeling of Durotaxis

## TL;DR

This paper presents a phenomenological model of cell durotaxis based on substrate stiffness-dependent focal adhesion distribution, reproducing experimental persistence and predicting directional movement towards stiffer substrates.

## Contribution

It introduces a novel 2D model linking focal adhesion distribution to cell motion and validates it with a Fokker-Planck equation, highlighting the role of adhesion in durotaxis.

## Key findings

- Model reproduces increased persistence on stiffer substrates
- Predicts cell movement towards stiffer regions (durotaxis)
- Derives a validated Fokker-Planck equation for the model

## Abstract

Cells exhibit qualitatively different behaviors on substrates with different rigidities. The fact that cells are more polarized on the stiffer substrate motivates us to construct a two-dimensional cell with the distribution of focal adhesions dependent on substrate rigidities. This distribution affects the forces exerted by the cell and thereby determines its motion. Our model reproduces the experimental observation that the persistence time is higher on the stiffer substrate. This stiffness dependent persistence will lead to durotaxis, the preference in moving towards stiffer substrates. This propensity is characterized by the durotaxis index first defined in experiments. We derive and validate a 2D corresponding Fokker-Planck equation associated with our model. Our approach highlights the possible role of the focal adhesion arrangement in durotaxis.