Question

How many different amino acids could theoretically be encoded by nucleic acids containing four different nucleotides if (a) each nucleotide coded for one amino acid; (b) consecutive sequences of two nucleotides coded for one amino acid; (c) consecutive sequences of three nucleotides coded for one amino acid; (d) consecutive sequences of four nucleotides coded for one amino acid?

Short answer

(a) There would be $4$distinct amino acids that can be encoded by four different nucleotides in theory.

(b) There would be$16$distinct amino acids that can be encoded by four different nucleotides in theory.

(c) There would be $64$distinct amino acids that can be encoded by four different nucleotides in theory.

(d) There are $256$distinct amino acids that can be encoded by four different nucleotides in theory.

Step-by-step solution

Explanation for (a), If each nucleotide codes for one amino acid, the number of potential sequences of 4 nucleotides

The given is,

The number of nucleotides in the sequence$=1$

The possible number of sequence of 4 nucleotides$=4^{\mathrm{n}}$

Where,

$\mathrm{N}$is the number of nucleotides.

Thus,$4^{\mathrm{n}}=4^1=4$

Explanation for (b), If two nucleotide codes for one amino acid, the number of potential sequences of 4 nucleotides

The given is,

The number of nucleotides in the sequence $=2$

The possible number of sequence of 4 nucleotides$=4^{\mathrm{n}}$

Where,

$\mathrm{N}$is the number of nucleotides.

Thus,$4^{\mathrm{n}}=4^2=16$

Explanation for (c), If three nucleotide codes for one amino acid, the number of potential sequences of 4 nucleotides

The given is,

The number of nucleotides in the sequence$=3$

The possible number of sequence of 4 nucleotides$=4^{\mathrm{n}}$

Where,

$\mathrm{N}$is the number of nucleotides.

Thus,$4^{\mathrm{n}}=4^3=64$

Explanation for (d), If four nucleotide codes for one amino acid, the number of potential sequences of 4 nucleotides

The given is,

The number of nucleotides in the sequence$=4$

The possible number of sequence of 4 nucleotides$=4^{\mathrm{n}}$

Where,

$\mathrm{N}$is the number of nucleotides.

Thus,$4^{\mathrm{n}}=4^4=256$