Mathematical modelling in cell migration: tackling biochemistry in changing geometries

Area of Science:

• Cellular mechanochemistry
• Biophysics of cell migration
• Computational biology

Background:

• Directed cell migration involves sensing signals, cytoskeletal dynamics (actin polymerization, Myosin-II motors), and cell adhesion.
• Traditional reaction-diffusion models explain gradient sensing and polarization in simplified geometries.
• Recent research integrates biochemistry with cellular mechanics to model cell shape changes during migration.

Purpose of the Study:

• To review recent research coupling cell biochemistry with mechanics for migration modeling.
• To contrast interface tracking and interface capturing methods for modeling cell shape and movement.
• To highlight the importance of advanced modeling for understanding cell motion.

Main Methods:

• Review of recent literature on cell migration modeling.
• Comparison of interface tracking methods (explicit cell membrane representation).
• Comparison of interface capturing methods (implicit cell membrane modeling).

Main Results:

• Interface tracking explicitly models the cell membrane using moving points in 2D/3D.
• Interface capturing implicitly models the membrane via a level set approach, allowing topological changes.
• Both methods aim to link molecular-level processes to macroscopic cell behavior.

Conclusions:

• Coupling biochemical signaling with mechanical models is crucial for understanding directed cell migration.
• Interface capturing methods are becoming vital for data-driven, image-based modeling of complex cell shapes.
• Advanced computational approaches are essential for deciphering the mechanochemistry of cell motion.