A mathematical model of cell movement and clustering due to chemotaxis

• Published in: Journal of theoretical biology Vol. 575; p. 111646
• Main Authors: Farmer, Adam, Harris, Paul J.
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 07.11.2023
• Subjects: Cell clustering; Cell migration; Cell Movement - physiology; Chemotaxis; Chemotaxis - physiology; Cluster Analysis; Mathematical modelling; Models, Biological; Models, Theoretical; Cell clustering; Mathematical modelling; Chemotaxis; Cell migration
• ISSN: 0022-5193; 1095-8541; 1095-8541
• DOI: 10.1016/j.jtbi.2023.111646

This paper presents 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. In particular, the model developed here will consider what happens when two (or more) cells collide and how their membranes connect to each other to form clusters of cells. The methods described in this paper 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. •Motion of cells in response to a diffusing chemical signal.•Cells emitting the chemical signal rather that it being in the environment.•Formation of clusters after the cells have collided.•Numerical examples which simulate the behaviour of real cells.