Q.58 The length of the minimum unique stretch of DNA sequence that can be found only once in a
3 billion base pairs long genome is
(A) 14 (B) 15 (C) 16 (D) 18
Minimum Unique DNA Stretch: 16th bp in 3 Billion Base Pairs Genome Explained
The minimum unique stretch of DNA sequence that appears only once in a 3 billion base pairs human genome is 16 base pairs. This calculation relies on the immense diversity of possible DNA sequences and the genome’s size.
Calculation Method
A unique sequence appears only once when possible combinations exceed genome positions. With 4 nucleotides (A, T, C, G), an n-base sequence yields 4n possibilities. For uniqueness in a 3 × 109 bp genome (one strand), require 4n > 3 × 109.
Solve log(4n) > log(3 × 109), so n log 4 > log(3 × 109). Here, log 4 ≈ 0.602, log(3 × 109) ≈ 9.477, thus n > 15.75. Smallest integer n is 16.
Options Analysis
| Option | Length | 4n Possibilities | Unique? | Explanation |
|---|---|---|---|---|
| (A) 14 | 14 bp | 268,435,456 | No | 414 = 2.68 × 108 < 3 × 109; many repeats expected. |
| (B) 15 | 15 bp | 1,073,741,824 | No | 415 = 1.07 × 109 < 3 × 109; still insufficient for uniqueness. |
| (C) 16 | 16 bp | 4,294,967,296 | Yes | 416 = 4.29 × 109 > 3 × 109; high probability of appearing once. |
| (D) 18 | 18 bp | 68,719,476,736 | Yes | 418 = 6.87 × 1010; exceeds needs, but not minimal. |
Genomics Applications
This 16 bp threshold guides unique probe design in microarrays, PCR primers, and NGS mapping. Shorter sequences risk non-specific binding; longer ones add unnecessary cost. In human genomics (≈3.2 Gb total, ≈3 Gb per haploid strand), 16-mers ensure specificity.
