Final answer:
Proteins arrive in the membrane of lipid droplets through a process called protein insertion. These proteins are synthesized in the endoplasmic reticulum and targeted to the droplet membrane through specific signals or interactions with other proteins.
Step-by-step explanation:
Lipid droplets have proteins embedded in their membrane through a process called protein insertion. These proteins are synthesized in the endoplasmic reticulum (ER) and transported to the lipid droplet membrane. The ER synthesizes the proteins as integral membrane proteins, which means they have hydrophobic regions that can interact with the hydrophobic lipid bilayer of the droplet membrane. The proteins are then targeted to the droplet membrane by specific targeting signals or interacting with other proteins.