Step 1: Understanding the Concept:
Exonucleases are enzymes that catalyze the hydrolytic removal of nucleotides from the terminal ends of nucleic acid molecules.
Different exonucleases target specific substrates (DNA or RNA, single-stranded or double-stranded) and show distinct directional preferences (5'$\rightarrow$3' or 3'$\rightarrow$5').
Step 2: Detailed Explanation:
Let us evaluate both statements:
1. Statement I: Bal31 is an exonuclease isolated from the marine bacterium Alteromonas espejiana.
It functions as a double-stranded exonuclease that simultaneously removes nucleotides from both the 5' and 3' termini of double-stranded DNA.
This activity progressively shortens both strands of linearized DNA from both ends. Thus, Statement I is correct.
2. Statement II: E. coli Exonuclease III is a template-dependent, 3'$\rightarrow$5' exonuclease.
It catalyzes the step-wise removal of mononucleotides starting from the 3'-hydroxyl terminus of double-stranded DNA.
Crucially, it only degrades one strand of the double helix at a time, leaving the complementary strand intact as a single-stranded 5' overhang.
It cannot degrade both strands simultaneously. Thus, Statement II is incorrect.
Therefore, only Statement I is correct.
Step 3: Final Answer:
Only Statement I is correct, and Statement II is incorrect, which corresponds to Option (A).