Final answer:
The GTP-binding protein responsible for initiating vesicle formation and regulating the COPII coat assembly in the endomembrane system is Sar1.
Step-by-step explanation:
The GTP-binding protein that plays a regulatory role by initiating vesicle formation and by regulating the assembly of the vesicle's COPII coat is Sar1. During the process of protein trafficking in the endomembrane system, Sar1 is involved in the budding of vesicles from the rough endoplasmic reticulum (RER).
These vesicles then move towards the Golgi apparatus, carrying packaged proteins that will be further processed. It's also worth noting that other molecular players, such as dynamin and clathrin, are involved in this complex process of vesicle formation and protein sorting within the cell.