Chapter 6, Problem 1P

Answers to all problems are at the end of this book. Detailed solutions are available in the Student Solutions Manual, Study Guide, and Problems Book.

Determining the Length of a Keratin Molecule The central rod domain of a keratin protein is approximately 312 residues in length. What is the length (in A) of the keratin rod domain? If this same peptide segment were a true $\alpha$-helix how long would it be? If the same segment were a β-sheet, what would its length be?

Interpretation Introduction

To Determine: The length of the keratin rod domain should be determined along with the length of the peptide segment when the same peptide segment were a true a helix. Length of the segment should be determined when the same segment were a ß sheet.

Introduction: One turn of a helix represents $3.6$ amino acid residues. For true a helix, each amino acid residue extends $\text{1}\text{.5 }\stackrel{\text{o}}{\text{A}}$ along the axis of the helix. So, the length of one turn is $3.6\times 1.5\stackrel{\text{o}}{\text{A}}\text{= 5}\text{.4 }\stackrel{\text{o}}{\text{A}}$ . This is referred to as the pitch of the helix. But keratin protein has a distorted alpha-helix with a pitch length of $\text{5}\text{.1 }\stackrel{\text{o}}{\text{A}}$

Beta sheet structure can be pictured as a twofold helix with two residues per turn. The distance between residues in the anti-parallel pleated sheet is $\text{3}\text{.47 }\stackrel{\text{o}}{\text{A}}$ and $\text{3}\text{.25 }\stackrel{\text{o}}{\text{A}}$ in the parallel pleated sheet.

Explanation of Solution

The length of the keratin rod domain = $\frac{5.1\stackrel{\text{o}}{\text{A}}}{1\text{ turn}}\times \frac{1\text{ turn}}{3.6\text{ residues}}\times 312\text{ residues = 442 }\stackrel{\text{o}}{\text{A}}$

If the segment were a true helix = $\frac{5.4\stackrel{\text{o}}{\text{A}}}{1\text{ turn}}\times \frac{1\text{ turn}}{3.6\text{ residues}}\times 312\text{ residues = 468 }\stackrel{\text{o}}{\text{A}}$

If the segment were an antiparallel beta-sheet = $3.47\stackrel{\text{o}}{\text{A}}\times \text{ 312 residues = 1083 }\stackrel{\text{o}}{\text{A}}$

If the segment were a parallel beta-sheet = $3.25\stackrel{\text{o}}{\text{A}}\times \text{ 312 residues = 1014 }\stackrel{\text{o}}{\text{A}}$