Step 1: Concept
Nucleases are specialized enzymes that cleave the phosphodiester bonds holding nucleic acid backbones together. They vary in their preference for single-stranded or double-stranded substrates and can act either internally or from the ends of strands.
Step 2: Meaning
A "single-stranded nick" is a clean break in the phosphodiester backbone of just one strand within a double-stranded DNA molecule, leaving the opposing template strand completely intact.
Step 3: Analysis
* S1 nuclease (A): Specifically targets and degrades single-stranded DNA or RNA molecules, meaning it does not create clean individual nicks in double-stranded helices.
* Exonuclease III (B): Chews along DNA sequentially from the ends of strands (5' to 3' or 3' to 5'), meaning it cannot cut internally to make a nick.
* DNase I (C): An endonuclease that cleaves internally. In the presence of magnesium ions ($\text{Mg}^{2+}$), it cuts each strand independently, making random single-stranded nicks along double-stranded DNA.
* Terminal transferase (D): An enzyme that adds nucleotides to the ends of strands without using a template; it does not cut DNA backbones.
Step 4: Conclusion
Therefore, DNase I is the enzyme used to introduce random single-stranded nicks into double-stranded DNA templates. This corresponds to option C.
Final Answer: (C)