Modelling the movement of interacting cell populations

Area of Science:

• Mathematical Biology
• Cellular Dynamics
• Computational Science

Background:

• Traditional mathematical modeling of cell movement primarily addresses single cell populations responding to environmental cues.
• Existing models often overlook the complexities arising from interactions between multiple distinct cell populations.

Purpose of the Study:

• To develop and present novel mathematical models for the movement and interaction of two or more cell populations.
• To extend existing single-population modeling frameworks to accommodate inter-population dynamics.
• To provide illustrative examples of these models in scenarios of cellular competition and aggregation.

Main Methods:

• Extension of single-population models to multi-population systems using intuitive conceptual frameworks.
• Formal model development employing transition probability methods.
• Derivation of model equations as a limiting form of a velocity-jump process.

Main Results:

• Development of a generic mathematical model for competing cell populations.
• Formulation of a model describing aggregation in cell populations influenced by chemical gradients.
• Demonstration of the applicability of transition probability and velocity-jump processes for multi-population modeling.

Conclusions:

• The proposed modeling approach effectively captures the dynamics of interacting cell populations.
• These models provide a framework for studying complex biological phenomena like competition and aggregation.
• The methods offer a versatile tool for advancing the mathematical understanding of cellular systems.