If a cell were to use only 10 of the 20 possible amino acids, how much effect would you expect this to have on protein diversity? Calculate and compare the number of different sequences that can be generated by randomly assembling either 10 or 20 amino acids into peptides that are five residues long.

Verified step by step guidance

1. Identify the number of possible sequences for each scenario: To calculate the number of different sequences that can be generated, use the formula n^k, where n is the number of amino acids available and k is the length of the peptide. In this case, k = 5.
2. Calculate the number of sequences using 10 amino acids: Substitute n = 10 into the formula, so the calculation becomes 10^5.
3. Calculate the number of sequences using 20 amino acids: Substitute n = 20 into the formula, so the calculation becomes 20^5.
4. Compare the results: Calculate the ratio of the number of sequences possible with 20 amino acids to those possible with 10 amino acids to understand the impact on protein diversity.
5. Interpret the findings: A higher number of available amino acids significantly increases the diversity of possible peptide sequences, which can affect the structure and function of proteins in an organism.

Key Concepts

Amino Acids and Proteins

Amino acids are the building blocks of proteins, with 20 standard types that combine in various sequences to form polypeptides. The sequence and composition of amino acids determine a protein's structure and function, making the choice of amino acids critical for protein diversity.

Combinatorial Mathematics

Combinatorial mathematics involves calculating the number of ways to arrange or combine items. In this context, it helps determine the number of unique peptide sequences that can be formed from a set number of amino acids, which is essential for understanding the impact of using fewer amino acids on protein diversity.

Peptide Length and Sequence Variability

The length of a peptide, in this case, five residues, significantly influences the number of possible sequences. Each position in the peptide can be occupied by any of the available amino acids, leading to exponential growth in sequence variability as the number of amino acids increases, thereby affecting overall protein diversity.