Step 1: Understanding the Concept:
Polynucleotide chains possess directionality and distinct chemical termini.
By convention, nucleotide sequences are written and read in the $5'$ to $3'$ direction.
Step 2: Detailed Explanation:
Let us analyze the chemical structure of the given tetranucleotide sequence $5'-\text{ATGC}-3'$:
- In any standard DNA strand, the $5'$ end of the first nucleotide has a free, unlinked $5'$ hydroxyl (or $5'$ phosphate) group.
- The $3'$ hydroxyl group of this first nucleotide is linked via a phosphodiester bond to the $5'$ phosphate of the next nucleotide, continuing down the chain.
- The last nucleotide at the $3'$ end of the sequence has a free, unlinked $3'$ hydroxyl group.
In the sequence ATGC:
- Deoxyadenylate (A) is the first nucleotide at the $5'$ terminus, meaning it possesses the free, unlinked $5'$ hydroxyl group.
- Deoxythymidylate (T) is the second nucleotide.
- Deoxycytidylate (C) is the third nucleotide.
- Deoxyguanylate (G) is the last nucleotide at the $3'$ terminus, possessing the free, unlinked $3'$ hydroxyl group.
Therefore, deoxyadenylate has the unlinked $5'$ hydroxyl group.
Step 3: Final Answer:
The nucleotide with the unlinked $5'$ hydroxyl group is deoxyadenylate.