Q.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

The key idea here is to understand how the number of possible unique codons relates to the number of base types and the length of the codon.

The number of unique codons that can be formed from n different types of bases, where each codon consists of k bases, is given by n^k. This is because for each of the k positions in the codon, there are n independent choices for the base.

1. In the original scenario, there are 4 types of bases and 3 bases per codon. This allows for 4³ = 64 unique codons, which is sufficient to code for 20 different amino acids. …

Concept and Intuition

In genetics, a "codon" is a sequence of bases (nucleotides) in DNA or RNA that codes for a specific amino acid. The fundamental idea is that each unique amino acid must have at least one unique codon assigned to it. This means the total number of possible unique codons must be greater than or equal to the total number of different amino acids that need to be coded for.

Imagine you have B different types of bases. If a codon is formed by a sequence of n bases, then for each position in the codon, you have B choices.

For example, if a codon has 1 base (n=1), you can form B¹ = B unique codons.

If a codon has 2 bases (n=2), you have B choices for the first position and B choices for the second position, leading to B times B = B² unique codons.

In general, for a codon of n bases, there are B^n possible unique combinations.

We need to find the smallest integer n such that B^n is sufficient to code for all given amino acids. This translates to the inequality:

B^n ge Number of Amino Acids

Step-by-step Solution

1. Understand the current biological context (given information):

   The problem first provides context from naturally occurring DNA:

   • Number of different types of amino acids = 20
   • Number of different types of bases in DNA = 4 (A, T, C, G)
   • Number of bases in a codon = 3

   Let's verify this with our concept. If there are 4 bases and 3 bases per codon, the total number of unique codons possible is 4³ = 4 times 4 times 4 = 64. Since 64 ge 20, this number of codons is indeed sufficient to code for all 20 naturally occurring amino acids. This confirms our understanding of the relationship between bases, codon length, and amino acids.

2. Identify the parameters for the new scenario:

   The problem then asks us to consider a hypothetical situation:

   • New number of different types of amino acids = 96
   • New number of different types of bases in DNA = 12 …