Final answer:
As proteins are translated into the ER lumen, they undergo structural modifications. Peripheral membrane proteins would be transported via vesicles to the Golgi apparatus and then to the plasma membrane, ultimately residing on the outside of the plasma membrane.
Step-by-step explanation:
Protein Destination After Synthesis in the ER Lumen
When a protein is synthesized in the ribosomes and enters the ER lumen, it undergoes various structural modifications, including folding and acquiring side chains. These proteins are destined for various locations within the cell. If a peripheral membrane protein is synthesized within the ER lumen, its ultimate location would be determined by whether it is associated with the ER membrane itself or targeted for another destination. These proteins typically do not end up in the cytosol; instead, they are directed to the plasma membrane outside the cell or to an internal organelle membrane. The proteins are transported by vesicles to the Golgi apparatus for further modification and then are sorted for inclusion in the plasma membrane or secretion from the cell.
Peripheral membrane proteins, after being modified within the Golgi apparatus, are incorporated on the plasma membrane's external side once vesicles containing these proteins fuse with the plasma membrane. Hence, a peripheral membrane protein synthesized inside the ER lumen would end up on the outside of the plasma membrane.