Adhesion of a vesicle on an elastic substrate: 2D analysis.

Cell or vesicle adhesion plays an essential role in a plethora of physiological activities. In this study, we established a theoretical model to explore the adhesion behavior of a vesicle adhering on an elastic substrate. Based upon the free energy functional of the system, the governing equation set and the transversality boundary conditions were derived. The morphology of the vesicle-substrate system and the phase diagram were presented, and it was found that there exist different wrapping states depending on the work of adhesion and bending stiffness. Finally, the adhesion behavior of a vesicle to a rigid substrate was investigated. These analyses are beneficial to understanding the mechanism of cell motility, and cast a new light on the droplet wrapped by a membrane when input the voltage.