How do transmembrane protein alpha helixes bind to the membrane? 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.
Well, it binds via hydrophobic interacions - non-polar R groups are attracted to hydrophobic interior of the membrane via dispersion forces, and also don't disrupt the structure of water as if they would outside of membrane. It's the same thing which holds molecules of the membrane together.