Phenomenological modeling of durotaxis

Area of Science:

• Cell biology
• Biophysics
• Mechanobiology

Background:

• Cellular behavior varies significantly across substrates of differing rigidities.
• Cells display increased polarization on stiffer substrates, suggesting a link between mechanical properties and cell orientation.
• Focal adhesions, crucial for cell-substrate interaction, are influenced by substrate stiffness.

Purpose of the Study:

• To develop a computational model of a two-dimensional cell.
• To investigate how the distribution of focal adhesions, dependent on substrate rigidity, influences cell mechanics and motion.
• To explain the phenomenon of durotaxis, where cells preferentially migrate towards stiffer environments.

Main Methods:

• Constructed a two-dimensional cell model incorporating focal adhesion distribution.
• Modeled cell-exerted forces based on focal adhesion arrangement and substrate rigidity.
• Derived and validated a two-dimensional Fokker-Planck equation to describe cell dynamics.

Main Results:

• The model successfully reproduced experimental findings of increased persistence time on stiffer substrates.
• Demonstrated that stiffness-dependent focal adhesion distribution dictates cell motion.
• Validated the model by comparing its predictions to experimental durotaxis indices.

Conclusions:

• Focal adhesion arrangement plays a critical role in mediating stiffness-dependent cell behavior.
• The model provides a mechanistic explanation for durotaxis.
• This work offers insights into the interplay between cell mechanics, adhesion, and directed cell migration.