Damped and persistent oscillations in a simple model of cell crawling

Area of Science:

• Biophysics
• Mathematical Biology
• Cell Biology

Background:

• Cell migration is a fundamental biological process crucial for development and disease.
• Understanding the mechanical and dynamic principles governing cell crawling is essential.
• Existing models may not fully capture the range of cell migration behaviors.

Purpose of the Study:

• To develop a simplified, one-dimensional, discrete, autonomous model of cell crawling.
• To analyze the general features of cell migration, including steady and oscillatory movement.
• To derive closed-form expressions for crawling speeds and internal forces.

Main Methods:

• Formulation of a model using three or four coupled first-order differential equations.
• Analysis of dimensionless parameters representing intracellular activity and cell mechanics.
• Development of two model versions: a basic elastic coupling model and a poroelastic model.

Main Results:

• The basic model demonstrates stable, steady forward crawling after transient oscillations.
• The poroelastic model exhibits steady-state oscillatory crawling.
• Closed-form expressions for speed and forces are derived in terms of model parameters.

Conclusions:

• A simple mathematical framework can effectively describe complex cell crawling dynamics.
• The model highlights the interplay between intracellular processes and passive mechanical properties in cell migration.
• The proposed models offer a basis for further investigation into cell motility.