M5 mesoscopic and macroscopic models for mesenchymal motion.

Area of Science:

• Computational Biology
• Biophysics
• Mathematical Biology

Background:

• Mesenchymal motion is critical for biological processes like tumor metastasis.
• Cellular movement through 3D fiber networks is influenced by network directionality and degradation.
• Existing models may not fully capture the dynamic interplay between cell motion and evolving tissue structure.

Purpose of the Study:

• To develop novel mesoscopic (individual-based) and macroscopic (population-based) models for mesenchymal motion in dynamic fiber networks.
• To investigate how cell movement is guided by network orientation and affected by protease-mediated degradation.
• To analyze the temporal dynamics of cell migration within changing tissue environments.

Main Methods:

• Derivation of a mesoscopic model using a transport equation for correlated random walks.
• Development of a macroscopic drift-diffusion equation derived from the mesoscopic model.
• Coupling of the mesoscopic and macroscopic models with differential equations describing network degradation (directed and undirected cases).

Main Results:

• The mesoscopic model captures correlated random walks of cells.
• The macroscopic model describes cell motion as a drift-diffusion process with time-varying drift velocity and diffusion tensor.
• The derived models explicitly account for the time-varying nature of the fiber network due to degradation.

Conclusions:

• The developed models provide a framework for understanding mesenchymal cell migration in dynamic tissues.
• The models highlight the importance of network directionality and degradation in influencing cell movement patterns.
• These models have potential applications in studying tumor invasion and tissue engineering.