Dynamics and similarity laws for adhering vesicles in haptotaxis

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