Enzymes that can breakdown the phosphodiester bonds of genetic material are present in the following cell organelle.
Nucleases are the enzymes that can breakdown the phosphodiester bonds of nucleic acids such as DNA are present in Lysosomes. Nucleases are a type of hydrolases. Nucleolus is having the enzymes needed for rRNA formation (RNA polymerase I). Mitochondria have respiratory enzymes; Chloroplasts have enzymes of photosynthesis and protein synthesis.