Multiple travelling-wave solutions in a minimal model for cell motility

Area of Science:

• Biophysics
• Mathematical Biology
• Cellular Mechanics

Background:

• Two-phase flow models are established for simulating cell motility.
• Previous models often involve complex physical processes, hindering analysis.
• A simplified approach is needed to understand fundamental mechanisms of cell crawling.

Purpose of the Study:

• To formulate and analyze a minimal one-dimensional (1D), two-phase, poroviscous, reactive flow model for cell motility.
• To investigate the conditions necessary for cell polarization and movement.
• To explore the relationship between crawling speed and substrate adhesion strength.

Main Methods:

• Formulation of a simplified 1D, two-phase, poroviscous, reactive flow model.
• Stability analysis to determine conditions for movement initiation and cell polarization.
• Numerical simulations to identify and characterize travelling-wave solutions.

Main Results:

• The minimal model exhibits behaviors relevant to cell crawling, including polarization.
• Spatially asymmetric perturbations are necessary to induce movement in a uniform cytoplasm strip.
• Distinct families of travelling-wave solutions were identified, showing a bell-shaped dependence of crawling speed on adhesion strength.

Conclusions:

• A minimal two-phase flow model can capture essential aspects of cell motility and polarization.
• The model reproduces the experimentally observed phenomenon of optimal crawling speed at intermediate adhesion.
• This simplified model provides insights into the physical basis of cell crawling dynamics.