A simple mathematical model of cell clustering by chemotaxis

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 modelled 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.