Modeling adhesion in stochastic and mean-field models of cell migration

Area of Science:

• Computational Biology
• Mathematical Biology
• Biophysics

Background:

• Cell adhesion is crucial for tissue development, homeostasis, wound healing, and cancer metastasis.
• Existing models like cellular Potts and partial differential equations (PDEs) have limitations in computational cost or capturing discrete cell dynamics.
• Cellular automaton models offer a promising approach to address these limitations.

Purpose of the Study:

• To develop and analyze an on-lattice agent-based model (ABM) for cell migration and adhesion in a two-cell-type population.
• To compare the ABM with traditional partial differential equation (PDE) models.
• To propose improved discrete mean equations that better represent the ABM's behavior.

Main Methods:

• Development of an on-lattice agent-based model (ABM) simulating cell migration and adhesion.
• Derivation and comparison of corresponding partial differential equations (PDEs) to the ABM.
• Formulation of discrete mean equations based on ABM observations.

Main Results:

• Partial differential equation (PDE) models were found to be incapable of simulating cell aggregation and sorting.
• The agent-based model (ABM) successfully demonstrated cell aggregation and sorting phenomena.
• A set of discrete mean equations was proposed, offering a better representation of the ABM's dynamics in 1D and 2D.

Conclusions:

• Agent-based models provide a more suitable framework than traditional PDEs for studying discrete cell behaviors like aggregation and sorting.
• The developed discrete mean equations offer improved accuracy in capturing the emergent dynamics observed in the agent-based model.
• This work highlights the utility of cellular automata for modeling complex cell-cell interactions in biological systems.