Diffusion and Chemotaxis

Abstract

Diffusion is the movement of particles from high concentration to low concentration. It arises from the fact that all particles are constantly moving in random directions. Biological organisms, for instance, cells, move not only at random but also in response to the environment. This response often involves directed movement toward external stimulus or away from it. Such a movement is call “taxis.” Chemotaxis is a movement in response to chemical gradient, and haptotaxis is a response to adhesive gradient. Biological examples of chemotaxis and haptotaxis abound. In this chapter we give two examples of chemotaxis. The first example has to do with movement of amoebas during one phase of their lifecycle. The second example is concerned with the movement of endothelial cells in response to stimulus secreted by tumor cells. But first we need to develop general mathematical models of diffusion and chemotaxis.