Question

You know that there are twenty different types of naturally occurring amino acids and four different types of bases in the DNA. A combination of 3 such bases codes for a specific amino acid. If instead there are 96 different amino acids and 12 different bases in the DNA, then the minimum number of combination of bases required to form a codon is:

• A. 6
• B. 3
• C. 2
• D. 4

Hint:

To determine the minimum number of bases per codon needed to encode a given number of amino acids, use the formula \( \text{Number of combinations} = (\text{Number of bases})^{\text{Number of bases per codon}} \), and solve for \( n \).

Answer 1

The Correct Option is C

To find the minimum number of base combinations needed to code for 96 distinct amino acids, we can apply the formula for the number of possible combinations: \[ \text{Number of combinations} = (\text{Number of bases})^{\text{Number of bases per codon}} \] In this case: - There are 12 different base types in DNA. - We need to determine how many bases per codon are necessary to produce at least 96 different amino acids. Let \( n \) represent the number of bases required per codon. The total number of possible codons will be \( 12^n \), and we want this value to be at least 96. \[ 12^n \geq 96 \] Now, calculating the powers of 12: - \( 12^1 = 12 \) - \( 12^2 = 144 \) Since \( 12^2 = 144 \) exceeds 96, the minimum number of bases per codon required is 2. Thus, the correct answer is \( \boxed{2} \). Option (A): Incorrect. \( 12^6 \) would result in a much higher number than necessary.
Option (B): Incorrect. \( 12^3 \) provides more than 96 codons, and 3 bases per codon is unnecessary.
Option (C): Correct. The minimum number of bases per codon is 2, as \( 12^2 = 144 \) exceeds 96.
Option (D): Incorrect. Using 4 bases per codon would create far more combinations than needed, but 2 bases is the minimum required.