Final answer:
A protein with both a mitochondrial presequence and an ER signal peptide might first target the ER but could be rerouted to the mitochondria post-translationally. Peripheral membrane proteins synthesized in the ER lumen are generally transported to the outside of the plasma membrane.
Step-by-step explanation:
When a protein carries both a mitochondrial presequence and an ER signal peptide, it may be targeted to the endoplasmic reticulum (ER) first as protein synthesis initiates. However, because mitochondrial protein transfer is post-translational, the presence of a mitochondrial targeting sequence suggests that even if the protein initially enters the ER pathway, it may subsequently be redirected to the mitochondria after synthesis. The definitive destination could depend on the context within the cell and the affinities of the transport machineries for the respective signal sequences.
Peripheral membrane proteins synthesized inside the ER lumen typically end up on the outside of the plasma membrane, as proteins in the ER lumen are secreted or become part of the plasma membrane during the vesicle-mediated trafficking and fusion processes.