Question

How many different tripeptides can be made that contain the amino acids alanine, serine, and glycine?

Short answer

There are 27 different tripeptides that can be made with the amino acids alanine, serine, and glycine.

Step-by-step solution

List the given amino acids

We are given the following amino acids: - Alanine (A) - Serine (S) - Glycine (G)

Determine the number of choices for each position

A tripeptide contains three positions in its chain. Since we have three amino acids (A, S, G) to choose from, we have three choices for each position.

Calculate the total number of different tripeptides

To find the total number of different tripeptides, we can use the counting principle, which states that if there are n ways to perform the first action, m ways to perform the second action, and so on, then there are n * m * ... ways to perform all actions in sequence. In this case, there are three actions (choosing an amino acid for each position), and there are three ways to perform each action (three amino acids to choose from). Therefore, we have: Total number of different tripeptides = 3 * 3 * 3

Calculate the result

Using the calculation from Step 3, we find the total number of different tripeptides: Total number of different tripeptides = 3 * 3 * 3 = \(3^3\) = 27 There are 27 different tripeptides that can be made with the amino acids alanine, serine, and glycine.

Key concepts

Amino Acids

Amino acids are the building blocks of proteins. They play a vital role in biochemistry and are crucial for various biological functions. Every amino acid has a carboxyl group (-COOH) and an amino group (-NH2), which are attached to the same carbon atom, called the alpha carbon.

Amino acids vary based on the side chain or R group attached to the alpha carbon, which gives them different properties and roles in proteins. The exercise provides three amino acids: alanine, serine, and glycine.

• **Alanine (A):** A non-polar and hydrophobic amino acid. It is often found in proteins where minimal polar interactions are desired.
• **Serine (S):** A polar amino acid that can participate in hydrogen bonding due to its hydroxyl (-OH) group in its side chain, making it more reactive and involved in enzymatic processes.
• **Glycine (G):** The simplest amino acid with a single hydrogen as its side chain. It's very flexible and often found in tight turns within proteins because it minimizes steric hindrance.

These amino acids can be linked together to form peptides, the building blocks of proteins.

Counting Principle

The counting principle is a fundamental concept in combinatorics used to determine the number of ways different events can occur. It states that if one event can occur in 'n' ways, and a second event can occur independently in 'm' ways, the total number of ways both events can occur is the product of their individual ways, 'n' times 'm'.
So, if you have several events that follow this pattern, you simply multiply the number of choices for each event.

In our exercise example:

• There are three positions to be filled with amino acids.
• For each position, there are 3 possible amino acids to choose from: Ala, Ser, Gly.
• Thus, the total number of combinations of the three positions is calculated by multiplying: 3 (choices for the first position) * 3 (choices for the second position) * 3 (choices for the third position).

This gives us a total combination count of 27 tripeptides, using the three amino acids.

Permutation

Permutation refers to arranging all members of a set into some sequence or order. In the context of forming tripeptides, each different sequence of amino acids forms a unique tripeptide. This takes into account every possible sequence, meaning that the order in which the amino acids are arranged is important.

Considering the exercise, the permutation of three distinct items (alanine, serine, glycine) for three positions implies calculating different arrangements of these items. Using permutation, the formula for arranging n distinct items into n slots is given by:\[ n! \]However, since each of the three positions can be filled by any of the three amino acids, each position permutation is calculated independently and multiplied, yielding:\[ 3 \times 3 \times 3 = 3^3 = 27 \]This demonstrates how permutation is applied in biochemistry to understand possible arrangements of components.

Biochemistry

Biochemistry is the branch of science that explores the chemical processes within and related to living organisms. It is an interdisciplinary field, combining biology and chemistry, to explore the mechanisms of life.

One of the key interests in biochemistry is understanding how proteins function, since proteins are made of chains of amino acids. Peptides like tripeptides are excellent models for studying proteins' structure and function.

• **Tripeptides:** These consist of three amino acids linked by peptide bonds. They serve as short protein fragments that can reveal insights into protein folding and function.
• **Link to biochemistry:** Understanding how small peptides form and behave can illuminate larger biological systems. The study of peptide chains helps unravel complex biochemical pathways and protein interactions.

Biochemistry delves into these processes, helping us understand how subtle changes in amino acid sequence affect the larger protein and its function in living systems.