Question

REFLECT AND APPLY 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

The number of different molecules is \ \[ 20^{100} \]

Step-by-step solution

Understand the Problem

Determine how many possible protein molecules can be synthesized with 100 amino acid residues, where each position in the chain can be occupied by any of the 20 available amino acids.

Determine the Number of Choices for Each Position

Realize that each of the 100 positions in the protein chain can be filled by one of 20 amino acids. This implies that the number of choices for each position is 20.

Calculate the Total Number of Possible Molecules

Since each of the 100 positions has 20 possible choices, the total number of different molecules is given by the formula: \ \[ 20^{100} \] \ This represents 20 choices for the first position, 20 for the second, and so on up to the 100th position.

Express the Result

The number of different 100-mer molecules that can be synthesized is \ \[ 20^{100} \]

Key concepts

amino acids

Amino acids are the building blocks of proteins. Each amino acid consists of a central carbon atom bonded to four different groups: an amino group (NH2), a carboxyl group (COOH), a hydrogen atom, and a distinctive side chain or R group. The R group varies among different amino acids and determines their unique properties.
Amino acids link together through peptide bonds to form proteins. The sequence of amino acids in a protein determines its structure and function.
Protein synthesis is a process where these amino acids are arranged in a specified sequence to create a functional protein.
Understanding amino acids is crucial because:

• There are 20 different standard amino acids.
• Each has distinct properties affecting the protein's structure.
• The sequence and combination of amino acids \(\rightarrow\) diversity in protein functionality.

polypeptide chain

A polypeptide chain is a single, linear chain of many amino acids bonded together by peptide bonds. During protein synthesis, this chain folds into a specific three-dimensional structure to form a functional protein.
Here are the key aspects of polypeptide chains to remember:

• Starts with a special amino acid called Methionine (AUG).
• Each sequence of three amino acids (codon) corresponds to a particular amino acid.
• The primary sequence dictates how the polypeptide will fold.

Protein structure levels include:

• Primary: Linear sequence of amino acids.
• Secondary: Formation of alpha-helices and beta-sheets.
• Tertiary: The three-dimensional shape created by the folds.
• Quaternary: Multiple polypeptide chains coming together.

This hierarchical structure is vital for understanding how proteins function and how mutations in amino acids can affect the protein’s function.

combinatorial possibilities

Combinatorial possibilities in protein synthesis refer to the vast number of ways amino acids can be arranged in a protein. If you have 20 different amino acids and want to form a 100-residue polypeptide, each position in the chain can be occupied by any of the 20 amino acids.
For a 100-residue polypeptide, the number of different possible sequences can be calculated using the formula \[ 20^{100} \]. This represents every position in the 100-mer being an independent choice of one out of 20 amino acids.
Breaking it down:

• The first position has 20 possible choices.
• The second position also has 20 choices.
• This continues up to the 100th position.

So, the total number of different sequences is an astronomical number, \[ 20^{100} \], showcasing the immense diversity of proteins that can be synthesized from just 20 amino acids.
This high number of possible combinations allows a vast variety of proteins with unique structures and functions, underlying the complexity and versatility of biological systems.