  Chemotaxis and haptotaxis have been a main theme in the macroscopic study of
bacterial and cellular motility. In this work we investigate the influence
these processes have on the shape and motility of fast migrating cells. We note
that despite their biological and modelling differences, the cells exhibit many
similarities in their migration. We moreover see, that after an initial
adjustment phase, the cells obtain a stable shape and their motion is similar
to advection.
