Question

Why would two-nucleotide codons be insufficient to encode the number of amino acids in biological proteins?

Short answer

Two-nucleotide codons (\(4^2 = 16\) possible combinations) would be insufficient to encode the 20 common amino acids found in biological proteins; therefore, a minimum of three-nucleotide codons (\(4^3 = 64\) possible combinations) are used.

Step-by-step solution

Understanding the number of possible codons with two nucleotides

There are four types of nucleotides: adenine (A), cytosine (C), guanine (G), and thymine (T). If each codon has two nucleotides, the total number of possible codons would be \(4^2 = 16\) because each position in the codon can be one of four nucleotides.

Comparing the number of possible codons to the number of amino acids

There are 20 commonly occurring amino acids in biological proteins. However, as shown in the first step, there are only 16 possibilities for a two-nucleotide codon, which means not every amino acid can be uniquely encoded.

Concluding why two-nucleotide codons are insufficient

Since there are 20 amino acids but only 16 possible two-nucleotide codons, not every amino acid could be encoded by a two-nucleotide codon. Therefore, a minimum of three-nucleotide codons are used in biology, allowing for \(4^3 = 64\) possible combinations, more than enough to encode the 20 amino acids.