Dynamics and Similarity Laws for Adhering Vesicles in Haptotaxis

We study vesicle dynamics induced by an adhesion gradient. This kind of migration is named haptotaxis in biology. The problem is fully solved as a free boundary one, including hydrodynamics flows. First, we analyze adhesion at equilibrium. We then determine the propulsion velocity as a function of various parameters. We find a persistent mixture of rolling and sliding. Similarity laws are extracted analytically both for the adhesion area and propulsion velocity by means of dimensional and scaling arguments. Our results markedly differ from classical results of nondeformable migrating entities.