Final answer:
Prokaryotic Topoisomerase I and Gyrase (Topoisomerase II) both act on double-stranded DNA. Gyrase introduces negative supercoils and requires ATP, while Topoisomerase I removes positive supercoils without needing ATP.
Step-by-step explanation:
Both Topoisomerase I and Gyrase act on double-stranded DNA, not single-stranded. Gyrase introduces negative supercoils into DNA to help in the compaction and organization of the chromosome, while Topoisomerase I primarily removes positive supercoils, thereby relaxing the DNA.
Gyrase requires the energy from ATP hydrolysis to perform its function, whereas Topoisomerase I does not require ATP to relax the positively supercoiled DNA. These enzymes are essential for managing DNA topology during processes such as replication and transcription, allowing prokaryotic cells to efficiently pack their DNA within the limited cell volume and to relieve the torsional stress that arises from unwinding the DNA double helix.