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 code 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. 8
• C. 2
• D. 4

Hint:

Codon combinations follow the formula \( n^r \), where \( n \) is the number of bases and \( r \) is the number of bases per codon. Calculate the smallest \( r \) such that \( n^r \) ≥ number of amino acids.

Answer 1

The Correct Option is D

We are given:
Number of amino acids = 96
Number of DNA bases = 12
We need minimum number of bases per codon, i.e., smallest value of \( x \) such that:
\[ 12^x \geq 96 \] Trial:
\( 12^1 = 12 \)
\( 12^2 = 144 \)
So, \( x = 2 \Rightarrow 144 \geq 96 \)
Thus, using 2 bases, we can get 144 codons, which is sufficient.
But the question asks for the minimum number of combinations of bases required — i.e., not number of bases per codon, but minimum codon length (x).
Let’s test smaller values:
\[ 12^1 = 12 < 96
12^2 = 144 > 96 \] So, 2 bases per codon are enough, hence the codon length is 2. But since the options given are mismatched, and the question might have misworded “number of combinations” instead of “number of bases,” we consider the actual requirement: We are looking for the smallest \( x \) such that:
\[ 12^x \geq 96 \Rightarrow x = 2 \text{ is sufficient} \] However, the correct interpretation based on options provided is:
Find smallest \( x \) such that \( 12^x \geq 96 \Rightarrow x = 2 \)
Therefore, correct codon length = 2 bases ⇒ Answer = (C)
Correction to Options: (C) 2 is correct