Random Walker Models for Durotaxis

TL;DR

This paper uses simplified random walk models to investigate durotaxis, demonstrating that cells need to sense stiffness gradients rather than just substrate stiffness to effectively move towards stiffer tissue regions.

Contribution

It introduces a minimal one-dimensional model showing the importance of gradient sensing for effective durotaxis, challenging previous claims that persistence alone suffices.

Findings

Gradient sensing is essential for efficient durotaxis.

Persistence without gradient sensing leads to poor transport.

One-dimensional models reveal key behaviors of cell movement.

Abstract

Motile biological cells in tissue often display the phenomenon of durotaxis, i.e. they tend to move towards stiffer parts of substrate tissue. The mechanism for this behavior is not completely understood. We consider simplified models for durotaxis based on the classic persistent random walker scheme. We show that even a one-dimensional model of this type sheds interesting light on the classes of behavior cells might exhibit. Our results strongly indicate that cells must be able to sense the gradient of stiffness in order to show the effects observed in experiment. This is in contrast to the claims in recent publications that it is sufficient for cells to be more persistent in their motion on stiff substrates to show durotaxis: i.e., if would be enough to sense the value of the stiffness. We show that these cases give rise to extremely inefficient transport towards stiff regions. Gradient sensing is almost certainly the selected behavior.