Final answer:
DNA replication is the process that requires DNA ligase, an enzyme that joins Okazaki fragments on the lagging strand. In prokaryotic transcription, the sigma subunit is involved in initiation. Digestion of sucrose, unlike DNA replication or translation, represents a catabolic process.
Step-by-step explanation:
The process in question that requires the activity of DNA ligase is DNA replication. During DNA replication, DNA ligase has an essential role in joining the Okazaki fragments on the lagging strand by forming covalent bonds between the sugar-phosphate backbones of adjacent DNA segments. In eukaryotic cells, DNA replication occurs in the nucleus and involves multiple enzymes beside DNA ligase, such as DNA polymerases and helicases. Whereas in prokaryotic cells, the process is similar but takes place in the cytoplasm and may involve slightly different enzymes and regulatory sequences.
During transcription, specifically in prokaryotes, the σ (sigma) subunit of the RNA polymerase is involved in the initiation stage, helping the core RNA polymerase recognize and bind to the promoter sequence. This stage is critical for the correct commencement of transcription, where RNA polymerase synthesizes messenger RNA (mRNA) based on the DNA template. Elongation carries on with the addition of ribonucleotides; during termination, a specific sequence causes the completed mRNA molecule to be released.
Regarding catabolic processes, the digestion of sucrose is considered catabolic because it breaks down larger molecules into simpler ones, releasing energy in the process. This contrasts with anabolic processes such as DNA replication or RNA translation, which involve building complex molecules from simpler ones and require the input of energy.