Step 1: Understanding the Concept:
Topoisomerases are enzymes that regulate DNA supercoiling by transiently cutting the DNA backbone, allowing the strands to untangle or relax before resealing the cuts.
Step 2: Detailed Explanation:
- Statement A is correct: Type I topoisomerases catalyze the relaxation of supercoiled DNA by introducing a transient single-strand break in the phosphodiester backbone. Type II enzymes break both strands (making Statement B incorrect).
- Statement C is correct: By cutting one strand, passing the unbroken strand through the gap, and resealing the cut, Topoisomerase-I changes the topological linking number (\(Lk\)) of DNA in steps of 1 (i.e., \(\Delta Lk = \pm 1\)). Type II enzymes change the linking number in steps of 2 (making Statement D incorrect).
- Thus, statements (A) and (C) are correct.
Step 3: Final Answer:
The correct statements for Topoisomerase-I are (A) and (C) only.