Chapter 23, Problem 47A

Interpretation Introduction

Interpretation:

The number of different ways to arrange three different amino acids, four different amino acids and, five different amino acids in a peptide should be determined.

Concept introduction:

Proteins are polymeric biomolecules which are formed by the polymerisation of amino acids. Amino acids are the organic molecules with $–{\text{NH}}_{\text{2}}$ and −COOH functional groups bonded on same carbon atom of the molecule.

They polymerise by peptide linkage to form dipeptide, oligopeptide and polypeptide molecules. Each peptide bond formation is a condensation reaction that occurs with the elimination of water molecule.

The mathematical expression for calculating number of different ways for arranging amino acids:

Number of different ways to arrange amino acids = ${20}^n$

Where, n = number of amino acids

Answer to Problem 47A

Number of different ways to arrange three amino acids = 8000

Number of different ways to arrange four amino acids = 160000

Number of different ways to arrange five amino acids = 3200000

Explanation of Solution

Number of different ways to arrange amino acids = ${20}^n$

Three different amino acids:

Value of n = 3

Thus,

Number of different ways to arrange three amino acids = ${20}^3$

= $8000$

Four different amino acids:

Value of n = 4

Thus,

Number of different ways to arrange four amino acids = ${20}^4$

= $160000$

Five different amino acids:

Value of n = 5

Thus,

Number of different ways to arrange five amino acids = ${20}^5$

= $3200000$