According to the fluid mosaic model, proteins are integrated to the membrane via van der Waals forces. But aside from membrane interaction, these proteins also interact with the intracelluar and extracellular matrix, especially for transmembrae proteins. These interactions include, but are not limited to, hydrophobic, hydrophilic and ionic interactions.
Membrane proteins move laterally in a phospholipid bilayer but generally not up and down. Why would this be so?