A simple mathematical model of cell clustering by chemotaxis

• Published in: Mathematical biosciences Vol. 294; pp. 62 - 70
• Main Author: Harris, Paul J.
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.12.2017; Elsevier Science Ltd
• Subjects: Cell clustering; Cells; Chemotaxis; Clustering; Differential equations; Diffusion equation; Equations of motion; Mathematical model; Mathematical models; Organic chemistry; Runge-Kutta method; Signal processing; Cell clustering; Diffusion equation; Mathematical model; Equations of motion; Chemotaxis
• DOI: 10.1016/j.mbs.2017.10.008
• ISSN: 0025-5564; 1879-3134

•This paper presents a simple mathematical model of how cells (and small clusters of cells) can combine to form large clusters due to chemotaxis.•An exact expression is used to simulate how the chemical signals produced by the cells diffuses and spreads out.•The effect that changing some of the parameters in the model, such as the initial concentration strength and the diffusion constant, has on the final distribution of the cells is investigated and discussed. Chemotaxis is the process by which cells and clusters of cells follow chemical signals in order to combine and form larger clusters. The spreading of the chemical signal from any given cell can be modeled using the linear diffusion equation, and the standard equations of motion can be used to determine how a cell, or cluster of cells, moves in response to the chemical signal. The resulting differential equations for the cell locations are integrated through time using the fourth-order Runge–Kutta method. The effect which changing the initial concentration magnitude, diffusion constant and velocity damping parameter has on the shape of the final clusters of cells is investigated and discussed.