Question

Most proteins contain more than 100 amino acid residues. If you decided to synthesize a " 100 -mer," with 20 different amino acids available for each position, how many different molecules could you make?

Short answer

\[20^{100}\]

Step-by-step solution

- Understanding the Problem

Determine how many possible amino acids can occupy each position in a 100-mer protein. There are 20 different amino acids available for each position.

- Using the Multiplication Principle

Understand that each amino acid position in the sequence can be occupied by any of the 20 amino acids, and there are 100 positions overall in the 100-mer.

- Calculating the Total Number of Combinations

Apply the multiplication principle: the total number of different molecules is obtained by raising the number of choices (20) to the power of the number of positions (100). Thus, the total number of different molecules is given by \[ 20^{100} \].

Key concepts

Amino Acid Sequences

Proteins are made up of long chains of amino acids. Each unique sequence of amino acids forms a different protein. Think of it like letters in a sentence; changing the order changes the meaning.
The order in which the amino acids are arranged determines the protein's structure and function. Amino acids are the building blocks of proteins, and there are 20 different types of amino acids used by the body.
To synthesize a protein, these amino acids are linked together in a specific sequence. In this example, we are looking at a protein that has 100 positions, meaning it is made up of 100 amino acids linked together.
It is important to understand that each position in this sequence can be occupied by any of the 20 available amino acids, making the potential variations immense.

Multiplication Principle

The multiplication principle is a fundamental concept in combinatorics. It helps us determine the total number of possible outcomes when dealing with multiple choices.
For each amino acid position in a protein sequence, we have 20 different amino acids to choose from. The multiplication principle tells us that to find the total number of possible protein sequences, we need to multiply the number of choices available for each position.
In mathematical terms, for a protein with 100 positions (a 100-mer), where each position can be one of 20 different amino acids, the total number of combinations is calculated as: \[20^{100}\].
This large number illustrates the immense diversity of protein structures that can be formed with even just a chain of 100 amino acids.

Protein Diversity

The vast number of potential amino acid sequences translates into a tremendous diversity of proteins. Different sequences result in proteins with different shapes and functions.
Protein diversity is crucial for the body's functionality. Proteins play a wide range of roles, such as enzymes, hormones, and antibodies. The body's ability to produce a large variety of proteins is essential for adapting to different needs and functions.
In this example, calculating \[20^{100}\] gives us an idea of the sheer number of different proteins that could theoretically be created, each with unique properties. This underlines the importance of every aspect of protein synthesis, from the sequence of amino acids to the final folded structure of the protein.