Mathematically Modelling Cell Cluster Formation and Substrate Mobility

This paper will present a numerical method for modelling cell migration and aggregation due to chemotaxis where the cell is attracted towards the direction in which the concentration of a chemical signal is increasing. In the model presented here, each cell is represented by a system of springs connected together at node points on the cell’s membrane and on the boundary of the cell’s nucleus. The nodes located on a cell’s membrane are subject to a force which is proportional to the gradient of the concentration of the chemical signal which mimics the behaviour of the chemical receptors in the cell’s membrane. The model presented is a continuation of our previous work into, what happens when two (or more) cells collide and how their membranes connect to each other to form clusters of cells, and now expands upon this concept to explore what happens when cells decouple and migrate away from the cluster to potentially join/form new ones. Lastly, we will take a look at different cell migration substrates, and how numerically we can model how placing a cell in a different environment or on a different surface can change the way it migrates. The methods presented will be illustrated with a number of typical examples simulating cells moving in response to a chemical signal and how they combine to form clusters, decouple and how different helpful or hindering surfaces affect migration speed.