# Glassy adhesion dynamics govern transitions between sub-diffusive and super-diffusive cancer cell migration on viscoelastic substrates

## TL;DR

Cancer cells migrate differently on materials that change over time, with their movement patterns shifting based on the material's properties.

## Contribution

A new model called the glassy motor-clutch model explains how cancer cells transition between different migration modes on viscoelastic substrates.

## Key findings

- Slow-relaxing substrates cause sub-diffusive cancer cell migration due to prolonged adhesion trapping.
- Fast-relaxing substrates lead to super-diffusive migration by promoting larger cell steps.
- Actin polymerization and contractility influence adhesion dynamics and migration modes.

## Abstract

Cell migration is pivotal in cancer metastasis, where cells navigate the extracellular matrix (ECM) and invade distant tissues. While the ECM is viscoelastic, exhibiting time-dependent stress relaxation, its influence on cell migration remains poorly understood. Here, we employ an integrated experimental and modeling approach to investigate filopodial cancer cell migration on viscoelastic substrates and uncover a striking transition from sub-diffusive to super-diffusive behavior driven by the substrate’s viscous relaxation timescale. Conventional motor-clutch based migration models fail to capture these anomalous migration modes, as they overlook the complex adhesion dynamics shaped by broad distribution of adhesion lifetimes. To address this, we develop a glassy motor-clutch model that incorporates the rugged energy landscape of adhesion clusters, where multiple metastable states yield long-tailed adhesion timescales. Our model reveals that migration dynamics are governed by the interplay between cellular and substrate timescales: slow-relaxing substrates prolong trapping, leading to sub-diffusion, while fast-relaxing substrates promote larger steps limiting trapping, leading to super-diffusion. Additionally, we uncover the role of actin polymerization and contractility in modulating adhesion dynamics and driving anomalous migration. These findings establish a mechanistic framework linking substrate viscoelasticity to cell motility, with implications for metastasis and cancer progression.

This study introduces glassy adhesion dynamics within a motor–clutch framework, revealing the mechanism by which cellular and extracellular timescales interplay and govern anomalous cancer cell migration.