Proteins are naturally occurring polymers formed by condensation reactions of amino acids, which have the general structure In this structure, \(-\mathrm{R}\) represents \(-\mathrm{H},-\mathrm{CH}_{3},\) or another group of atoms; there are 20 different natural amino acids, and each has one of 20 different R groups. (a) Draw the general structure of a protein formed by condensation polymerization of the generic amino acid shown here. (b) When only a few amino acids react to make a chain, the product is called a "peptide" rather than a protein; only when there are 50 amino acids or more in the chain would the molecule be called a protein. For three amino acids (distinguished by having three different R groups, R1, R2, and R3), draw the peptide that results from their condensation reactions. (c) The order in which the R groups exist in a peptide or protein has a huge influence on its biological activity. To distinguish different peptides and proteins, chemists call the first amino acid the one at the \({ }^{\prime \prime} \mathrm{N}\) terminus" and the last one the one at the "C terminus." From your drawing in part (b) you should be able to figure out what "N terminus" and "C terminus" mean. How many different peptides can be made from your three different amino acids?

Step by step solution

01

Draw the general structure of a protein

Proteins result from a condensation polymerization process between amino acids, which have a general structure in the form of an amino group (NH2), a carboxyl group (COOH) and an R group. In a condensation reaction, a water molecule is formed by removing one hydrogen atom from the amino group of one amino acid and a hydroxyl group from the carboxyl group of the other amino acid: Amino Acid 1: -NH2 – COOH Amino Acid 2: -NH2 – COOH Upon reaction, the following peptide bond is formed: (-NH2 – CO – NH – COOH) The general structure of a protein formed consists of multiple such peptide chains bonded together.

02

Draw the structure of a peptide formed from three different amino acids

First, let's define three different amino acids distinguished by different R groups R1, R2, and R3: Amino Acid 1: -NH2 – COOH (R1) Amino Acid 2: -NH2 – COOH (R2) Amino Acid 3: -NH2 – COOH (R3) Now, let's make a peptide from these three amino acids by going through the following condensation reactions: Amino Acid 1 + Amino Acid 2: -NH2 – CO – NH – COOH (R1 – R2) Amino Acids 1 & 2 + Amino Acid 3: -NH2 – CO – NH – CO – NH – COOH (R1 – R2 – R3) The resulting peptide can be represented as: R1 – R2 – R3

03

Understand N-terminus and C-terminus

N-terminus is the end of the peptide with a free amino group (-NH2), while the C-terminus is the end with a free carboxyl group (-COOH). In our R1 – R2 – R3 peptide, R1 would be the N-terminus, and R3 would be the C-terminus.

04

Calculate the number of different peptides

To find out the number of distinct peptides that can be formed from three different amino acids, we can use the permutation concept from combinatorics. The number of permutations for a set of three unique amino acids is 3! (factorial), which can be calculated as: 3! = 3 × 2 × 1 = 6 Thus, there are six distinct peptides that can be formed from the three unique amino acids.

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