Final answer:
Clathrin is the protein essential for the process of the toxin affecting the patient's eyelid function entering cells via receptor-mediated endocytosis.
Step-by-step explanation:
The protein essential for the process of the toxin affecting the patient's eyelid function entering cells via receptor-mediated endocytosis is Clathrin. Clathrin is a protein that plays a crucial role in the formation of coated vesicles, which are responsible for transporting materials within cells. It is involved in receptor-mediated endocytosis, where specific receptors on the cell surface bind to their ligands, triggering the formation of clathrin-coated pits and subsequent vesicle formation.