I would post this in biology but as the question is biochemical in nature I decided this would be a more appropriate platform.

What I'm asking is how exactly does a transmembrane protein bind to the cell membrane? I realize that the transmembrane alpha helix is about 20 amino acids long with mostly hydrophobic amino acids as the inside of the membrane is hydrophobic.

What I don't realize is how exactly this alpha helix binds to the membrane and sticks to it? I've tried searching on the subject but I can't seem to find the answer. I found out that the alpha helix satisfies the hydrogen bonds internally leaving no polar R groups for the membrane as most groups are hydrophobic, but that only explains how it DOESN'T bind to the membrane.