Step 1: Understanding the Concept:
An adapter is a short, chemically synthesized, double-stranded DNA molecule that has one blunt end and one sticky end. It is used to convert blunt-ended DNA fragments (which are hard to ligate) into fragments with sticky ends (which are easy to ligate).
Step 2: Detailed Explanation:
The logical sequence of this cloning strategy is as follows:
1. A: Artificial synthesis of an adapter: The specific oligonucleotide sequence must be synthesized first.
2. C: Blunt end ligation: The blunt end of the adapter is ligated to the blunt-ended DNA molecule of interest. At this stage, the adapter is typically synthesized without a \(5^{\prime}\)-phosphate to prevent it from ligating to itself (forming dimers).
3. B: Treating with polynucleotide kinase: After the adapter is attached to the target DNA, Polynucleotide Kinase (PNK) is used to add phosphate groups to the \(5^{\prime}\) ends of the sticky portion of the adapter. This makes the molecule ready for the next ligation step.
4. D: Joining two DNA molecules with sticky ends: Now that the target DNA has "phosphorylated sticky ends," it can be easily ligated into a vector that has complementary sticky ends.
Thus, the correct order is A \(\rightarrow\) C \(\rightarrow\) B \(\rightarrow\) D.
Step 3: Final Answer:
The methodological sequence is Synthesis \(\rightarrow\) Blunt Ligation \(\rightarrow\) Phosphorylation \(\rightarrow\) Sticky Ligation. Option 2 is correct.