Mathematical Models of Cell Clustering Due to Chemotaxis

In biological experiments small clusters of cells have been observed to move together and combine to form larger clusters of cells. These cells move by a process called chemotaxis where the cells detect a chemical signal and its gradient, and move in the direction in which the signal is increasing. A number of mathematical models for simulating the motion of cells due to chemotaxis have been proposed, ranging from simple diffusion-reaction equations for finding the density of the cells to complete simulations of how the chemical receptors on the cell membrane react to the chemical signal and cause the cell membrane to move. This work presents a simple equations of motion model to describe how the cells move which is coupled to a diffusion equation solution of how the chemical signal spreads out from individual cells. The talk will be illustrated with some typical examples.