Problem 84 - Chemistry Principles and Practice

Question

How many different tripeptides can be formed that contain one glycine, one valine, and one alanine?

Step-by-Step Solution

Answer

6 different tripeptides can be formed.

Step 1: Understanding Tripeptides

A tripeptide is a chain of three amino acids linked together by peptide bonds. Here, we have three specific amino acids: glycine (G), valine (V), and alanine (A).

Step 2: Permutations of Amino Acids

To form different tripeptides, we consider the permutations of the three amino acids. The number of permutations of three distinct items is calculated using the factorial function: \[3! = 3 \times 2 \times 1 = 6\]

Step 3: Listing All Permutations

Let's list all possible permutations of the three amino acids G, V, and A: 1. GVA 2. GAV 3. VAG 4. VGA 5. AGV 6. AVG

Step 4: Conclusion

Since each permutation represents a different tripeptide, the number of different tripeptides that can be formed is 6. This is because each order of the amino acids constitutes a unique sequence.

Key Concepts

Amino Acids

Amino acids are the building blocks of proteins, crucial for various biological processes in living organisms. Each amino acid has a central carbon atom, known as the alpha carbon, bonded to four groups: an amino group (\(-NH_2\)), a carboxyl group (\(-COOH\)), a hydrogen atom, and a side chain (R group) that determines the characteristics of each amino acid.
Glycine, valine, and alanine are three examples of the twenty standard amino acids.

• **Glycine** is the simplest amino acid with hydrogen as its R group.
• **Valine** has a more complex branched side chain, contributing to its hydrophobic nature.
• **Alanine** has a methyl group as its side chain, making it nonpolar, yet smaller than valine.

The sequence in which amino acids are arranged governs the function of the polypeptides and proteins they form. This is why understanding tripeptides and their combinations are essential for comprehending larger polypeptides.

Permutations

Permutations are a fundamental concept in combinatorics, which deal with the arrangement of a set of items. In the context of amino acids, permutations refer to the different ways we can order these building blocks to form different peptide sequences.
For tripeptides composed of three amino acids like glycine, valine, and alanine, we calculate the possible sequences using the concept of factorial, denoted as \(!\). The factorial of a number \(n\), written as \(n!\), is the product of all positive integers up to \(n\).
In the exercise, the formula \(3! = 3 \times 2 \times 1 = 6\) is used to determine that there are six distinct ways to arrange three amino acids:

• GVA
• GAV
• VAG
• VGA
• AGV
• AVG

Each unique arrangement results in a different tripeptide, highlighting how permutations impact the diversity of peptide sequences.

Peptide Bonds

Peptide bonds are crucial chemical bonds formed between amino acids that create peptide chains. These bonds are formed through a condensation reaction between the carboxyl group of one amino acid and the amino group of another, releasing a molecule of water in the process.
This bond formation leads to the creation of dipeptides, tripeptides, and various larger polypeptides based on the number and sequence of linked amino acids.

• In a tripeptide, two peptide bonds connect three amino acids in a specific sequence, determining its structure and potential function.
• Peptide bonds are strong and covalent, offering stability to the polypeptide chain.
• The sequence and chemical properties of the constituent amino acids influence the overall functionality of the peptide.

Understanding peptide bonds is essential to grasp how complex proteins are structured and function in biological organisms, as these bonds underpin the formation of all protein structures.