On a poroviscoelastic model for cell crawling

Area of Science:

• Biophysics
• Mathematical Biology
• Rheology

Background:

• Cell motility is crucial for biological processes.
• Existing two-phase models for cell motility employ various constitutive assumptions.
• Understanding the fundamental mechanics of cell crawling is an ongoing challenge.

Purpose of the Study:

• To present a minimal, one-dimensional, two-phase, viscoelastic, reactive flow model for cell crawling.
• To demonstrate that simple viscoelastic models can capture essential features of cell motility.
• To investigate the role of parameter selection in model stability and behavior.

Main Methods:

• Development of a minimal, one-dimensional, two-phase, viscoelastic, reactive flow model.
• Utilizing an upper-convected Maxwell model for constitutive assumptions.
• Performing stability analysis to determine conditions for initiating cell crawling.
• Numerical simulations to find travelling-wave solutions and analyze crawling velocity.

Main Results:

• The minimal viscoelastic model exhibits key features relevant to cell motility.
• Demonstrated that improper parameter choices can render the model ill-posed.
• Stability analysis showed that symmetry-breaking perturbations initiate crawling in a stationary cytoplasm strip.
• Numerical results revealed a steady travelling-wave solution with crawling velocity dependent on adhesion strength.

Conclusions:

• Even simplified two-phase viscoelastic models can effectively represent cell motility phenomena.
• Careful parameter selection is critical for the well-posedness and predictive power of such models.
• The model provides a theoretical basis for understanding how perturbations drive cell crawling and how adhesion influences velocity.