Step 1: Understanding the Concept:
Vitamin $\text{B}_{12}$ (cobalamin) is a complex organometallic molecule containing a corrin ring coordinated to a cobalt ion.
It serves as an essential coenzyme for specific enzymatic reactions that involve either intramolecular carbon-carbon rearrangements or methyl group transfers.
Step 2: Detailed Explanation:
Let us examine each of the proposed enzymes to determine their dependence on cobalamin:
Methylmalonyl-CoA mutase (B): This mitochondrial enzyme catalyzes the conversion of L-methylmalonyl-CoA to succinyl-CoA, which is a critical step in the catabolism of odd-chain fatty acids and branched-chain amino acids. This enzyme requires adenosylcobalamin (coenzyme $\text{B}_{12}$) to generate a free radical intermediate that facilitates the carbon skeleton rearrangement.
Leucine aminomutase (C): This enzyme is found in certain microorganisms and catalyzes the migration of an amino group, converting L-$\alpha$-leucine to $\beta$-leucine. This isomerization reaction is dependent on coenzyme $\text{B}_{12}$.
Methionine synthase (D): This cytosolic enzyme transfers a methyl group from 5-methyltetrahydrofolate to homocysteine, producing tetrahydrofolate and methionine. It requires methylcobalamin as an essential intermediate methyl carrier.
Conversely, Dihydrofolate reductase (A) is an enzyme that reduces dihydrofolate to tetrahydrofolate using NADPH as an electron donor. It is entirely independent of cobalamin.
Step 3: Final Answer:
The three enzymes that require Vitamin $\text{B}_{12}$ are B, C, and D.