Problem 25 - Chemistry: Principles and Reactions

Question

(a) How many tripeptides can be made from glycine, alanine, and leucine, using each amino acid only once per tripeptide? (b) Write the structural formulas of these tripeptides and name them in the shorthand abbreviation used for showing amino acid sequences.

Step-by-Step Solution

Answer

Provide the shorthand abbreviations and structural formulas of these tripeptides. Answer: There are 6 possible tripeptides that can be formed using glycine, alanine, and leucine. The shorthand abbreviations are: 1. Glycine-Alanine-Leucine (GAL) 2. Glycine-Leucine-Alanine (GLA) 3. Alanine-Glycine-Leucine (AGL) 4. Alanine-Leucine-Glycine (ALG) 5. Leucine-Glycine-Alanine (LGA) 6. Leucine-Alanine-Glycine (LAG) You may draw the structural formulas yourself by connecting the amino acids in the specified order.

Step 1: Determine the number of possible tripeptides

To determine the number of possible tripeptides, we will use the permutation formula, which is defined as n!/(n-r)!, where n is the number of items to choose from (in this case, the number of amino acids), and r is the number of items being chosen (in this case, 3 since we are finding tripeptides). In our problem, n = 3 and r = 3, so the formula becomes: P(3,3) = 3!/(3-3)! P(3,3) = 3!/0! Since 0! is equal to 1, this simplifies to: P(3,3) = 3! Calculating 3! (3 factorial) means multiplying 3 by every positive integer below it: P(3,3) = 3 * 2 * 1 = 6 There are 6 possible tripeptides that can be formed using glycine, alanine, and leucine.

Step 2: List the possible tripeptides

To list the possible tripeptides, we will combine the three amino acid components in every possible distinct order: 1. Glycine-Alanine-Leucine 2. Glycine-Leucine-Alanine 3. Alanine-Glycine-Leucine 4. Alanine-Leucine-Glycine 5. Leucine-Glycine-Alanine 6. Leucine-Alanine-Glycine These are the 6 possible tripeptides that can be formed from glycine, alanine, and leucine.

Step 3: Write the shorthand abbreviations

Now, we'll write the shorthand abbreviations for each tripeptide using the standard single-letter abbreviations for each amino acid: 1. Glycine-Alanine-Leucine: GAL 2. Glycine-Leucine-Alanine: GLA 3. Alanine-Glycine-Leucine: AGL 4. Alanine-Leucine-Glycine: ALG 5. Leucine-Glycine-Alanine: LGA 6. Leucine-Alanine-Glycine: LAG

Step 4: Conclusion

In conclusion, there are 6 possible tripeptides that can be formed using glycine, alanine, and leucine, each used only once per tripeptide. These tripeptides are: 1. Glycine-Alanine-Leucine (GAL) 2. Glycine-Leucine-Alanine (GLA) 3. Alanine-Glycine-Leucine (AGL) 4. Alanine-Leucine-Glycine (ALG) 5. Leucine-Glycine-Alanine (LGA) 6. Leucine-Alanine-Glycine (LAG) Structural formulas for these tripeptides can be drawn by connecting the amino acids in the specified order.

Key Concepts

Amino Acids

Amino acids are the fundamental building blocks of proteins and peptides. Each amino acid consists of a central carbon atom (called the alpha carbon), to which four different groups are attached: an amino group (-NH₂), a carboxyl group (-COOH), a hydrogen atom, and a unique side chain that determines the characteristics and properties of the amino acid. There are 20 standard amino acids that are commonly found in proteins, each with distinct biochemical roles.

In this exercise, we are focusing on three specific amino acids: glycine, alanine, and leucine. Glycine is the simplest amino acid with a hydrogen atom as its side chain, which makes it achiral. Alanine has a methyl group (-CH₃) as its side chain, making it slightly more complex. Leucine has a more extended hydrocarbon side chain, making it non-polar and hydrophobic. Understanding these basic properties helps in predicting the behavior of peptides and proteins they form.

Permutation Formula

When constructing tripeptides, it's essential to determine the number of possible sequences that can be created using a given set of amino acids. This is where the permutation formula becomes useful. The permutation formula is used to calculate the number of ways to arrange a subset of items from a larger set, without repetition. The formula is given by \( n!/(n-r)! \), where \( n \) is the total number of items to choose from, and \( r \) is the number of items to arrange.

In our problem involving glycine, alanine, and leucine, we have a total of 3 amino acids, and we are creating sequences made of these 3 amino acids, which means both \( n \) and \( r \) are 3. Therefore, we plug these values into the formula to get:

• \( P(3,3) = 3!/(3-3)! \)
• Since \( 0! \) is equal to 1, this simplifies to \( P(3,3) = 3! \)
• Calculating \( 3! \) involves multiplying 3 by 2 and then by 1, giving us a total of 6 possible permutations.

This calculation demonstrates that there are 6 distinct ways to arrange our 3 amino acids into tripeptides, each utilizing all three amino acids once.

Protein Sequences

Protein sequences refer to the specific order of amino acids in a peptide or protein. Each sequence determines the structure and function of the resulting protein. In this exercise, the sequences are tripeptides, which are short chains consisting of three amino acids.

Here, we use the three amino acids—glycine, alanine, and leucine—to form different peptide sequences. By permuting these three, we end up with these six sequences:

• Glycine-Alanine-Leucine (GAL)
• Glycine-Leucine-Alanine (GLA)
• Alanine-Glycine-Leucine (AGL)
• Alanine-Leucine-Glycine (ALG)
• Leucine-Glycine-Alanine (LGA)
• Leucine-Alanine-Glycine (LAG)

These simple 3-letter codes are a shorthand for identifying peptide sequences, making it easier to communicate and understand protein structure and function. Knowing the sequence is crucial since even slight changes in the order can significantly affect the protein's properties and efficacy.