Membranes must be able to separate or come together in order for the cells to absorb, transport, and release molecules. Receptor-mediated endocytosis is a common process in which cells take up molecules. In many cases, a large protein complex initially binds to a receptor located on the surface of the cell. Once the complex is bound to the receptor, specific proteins cause the membrane to invaginate. This ultimately causes the membrane to break off and fuse to form a vesicle.
This process is apparent when dealing with cholesterol in the blood (LDL). LDL binds to a specific integral membrane protein, LDL receptor. The LDL-LDL-receptor complex invaginates, therefore "breaking" the membrane. The LDL-LDL-receptor complex also separates such that LDL separates from the LDL recptor. The formed vesicle containing LDL fuses with a lysosome, which results in the degradation of LDL and the release of a cholesterol molecule.