Question
A hypothetical prokaryote-like organism on Mars uses DNA to RNA to protein, but its DNA contains only A and T and its proteins use 17 amino acids. What is the minimum number of bases required in each fixed-length codon?
Answer: the minimum codon length is 5 bases.
If a codon has positions and each position can contain either A or T, the number of distinct codons is
The code needs at least 17 distinct codons to assign one to each amino acid.
- Four-base codons provide combinations, which is one too few.
- Five-base codons provide combinations, which is enough.
Therefore, the shortest possible fixed-length codon contains 5 bases. The 15 combinations left after assigning one codon to each of the 17 amino acids could be unused, redundant, or reserved for signals; their exact roles are not needed to determine the minimum length.
Why the exponent matters
Each added codon position doubles the number of possible sequences because it adds another independent A-or-T choice. That is why the capacity grows as 2, 4, 8, 16, 32 rather than increasing by two each time.
Evidence boundary
This answer solves the publicly indexed prompt as a fixed-length coding-capacity problem with two DNA bases and 17 amino acids. It does not claim that such Martian organisms exist, and it does not assign a required function to the unused codons.
Sources
These references support the concepts and methods used in the explanation above.