How Cells Stay Together: A Mechanism for Maintenance of a Robust Cluster Explored by Local and Non-local Continuum...

Area of Science:

• Developmental biology
• Mathematical modeling
• Cellular dynamics

Background:

• Embryonic development involves precise cell migration for organ and tissue formation.
• Cells sometimes migrate collectively as cohesive clusters.
• Continuum models are essential for understanding large-scale cellular behaviors.

Purpose of the Study:

• To apply and extend a recent local approximation of non-local continuum models for cell migration.
• To investigate the formation, stability, and characteristics of cell clusters.
• To derive conditions for robust cluster formation in attractant-repellent chemotaxis scenarios.

Main Methods:

• Utilized a local approximation of non-local continuum models.
• Specified biologically-based cell-cell interactions to derive an effective Morse potential.
• Analyzed clustering instability, cluster existence, size, and stability.
• Derived an explicit condition for robust cluster existence under chemotaxis.

Main Results:

• Cell communication effectively generates an attraction-repulsion Morse potential.
• The study determines conditions for the existence and stability of cell clusters.
• An explicit condition guaranteeing robust clusters in attractant-repellent chemotaxis was derived.
• The accuracy of the local approximation was evaluated against the full non-local model.

Conclusions:

• The local approximation provides a valuable framework for studying cell clustering during development.
• Understanding cell-cell interactions is key to predicting robust cluster formation.
• This work offers insights into the mathematical underpinnings of collective cell migration.