Chapter 15.5, Problem 19WE

To determine

To calculate: The number of different sequences of amino acid in a 6-residue long fragment of protein molecule.

Answer to Problem 19WE

The number of different sequences of amino acid in a 6-residue long fragment of protein moleculeare $64,000,000$ .

Explanation of Solution

Given information:

The number of naturally occurring amino acids are 20 and 6-residue long fragment of protein molecule is to be formed.

Formula used:

Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Calculation:

Consider the provided information that number of naturally occurring amino acids are 20 and 6-residue long fragment of protein molecule is to be formed.

Let 6-residue long fragment of protein moleculebe $\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}\boxed{}$ .

For each residue 20 choices are there as number of naturally occurring amino acids are 20.

So each residue of 6-residue long fragment of protein molecule is filled with any 1 of 20 amino acid.

  $\boxed{20}\boxed{20}\boxed{20}\boxed{20}\boxed{20}\boxed{20}$

Recall that Fundamental counting principle states that if there are m ways to make a selection and n ways to make a second selection then there are $m\times n$ number of ways in which two selection can be made.

Therefore, the number of ways to select are,

  $\begin{array}{c}20\times 20\times 20\times 20\times 20\times 20={20}^6\\ =64,000,000\end{array}$

Thus, the number of different sequences of amino acid in a 6-residue long fragment of protein molecule are $64,000,000$ .