Final answer:
Glycosylation and phosphorylation are the modifications responsible for targeting digestive enzymes to lysosomes, where they are active in the acidic environment needed for breaking down cellular waste.
Step-by-step explanation:
The modification responsible for targeting digestive enzymes to lysosomes is glycosylation and phosphorylation. In eukaryotes, lysosomes are vital for digestion and organelle recycling. The enzymes inside lysosomes are active in acidic conditions facilitated by a low pH, significantly different from the cytoplasmic environment.
After synthesis on the ribosome, proteins undergo a series of modifications. Initially, they are modified in the endoplasmic reticulum where they may receive glycosylation tags. After this initial modification, they move to the Golgi apparatus for further tagging which often includes phosphorylation. This tagging serves as a signal for directing these enzymes to their correct cellular location, which, in this case, is the lysosome.
Digestive enzymes are then packaged into vesicles and distributed via these vesicles. Proteins can be regulated and their activities controlled through post-translational modifications such as phosphorylation, which can indicate where a protein should be localized within the cell.