A non local model for cell migration in response to mechanical stimuli

Area of Science:

• Cell biology
• Biophysics
• Mathematical modeling

Background:

• Cell migration is crucial for physiological and pathological processes.
• Cell migration can be influenced by mechanical stimuli from the substrate, including stiffness (durotaxis) and stress/strain (tensotaxis).
• These mechanical migration processes are less understood than chemical-based chemotaxis.

Purpose of the Study:

• To develop a mathematical model simulating single-cell migration in response to mechanical stimuli.
• To model both durotaxis and tensotaxis using a unified mathematical framework.
• To provide a computational tool for understanding cell-substrate mechanical interactions.

Main Methods:

• Formulated non-local integro-differential equations of motion for single cells.
• Incorporated a stochastic term to model random Brownian motion.
• Defined mechanical stimuli based on literature data for durotaxis and hyperelastic solid mechanics for tensotaxis.

Main Results:

• The model simulates cell polarization and motility changes based on substrate properties.
• Numerical simulations qualitatively reproduce experimental scenarios for durotaxis and tensotaxis.
• The model integrates cell behavior with substrate mechanical properties.

Conclusions:

• The proposed mathematical model offers a framework for studying cell migration driven by mechanical cues.
• The model can simulate durotaxis and tensotaxis, contributing to a better understanding of cell-mechanics interactions.
• This approach aids in exploring cellular responses to complex mechanical environments.