The alpha helix is a common structural motif in proteins, characterized by its unique geometric properties, specifically the pitch and rise. The pitch of the alpha helix refers to the distance along the helix axis for one complete turn, which measures 5.4 angstroms (Å). An angstrom is a unit of length equal to \(10^{-10}\) meters, making it a useful scale for atomic and molecular dimensions. In one complete turn of the alpha helix, there are 3.6 amino acid residues, indicating that the pitch represents the distance between two corresponding points after a full 360-degree rotation of the backbone.
In contrast, the rise is defined as the distance covered along the helix axis per amino acid residue. To calculate the rise, one can divide the pitch by the number of residues per turn. Thus, the rise can be calculated as follows:
\[ \text{Rise} = \frac{\text{Pitch}}{\text{Number of Residues}} = \frac{5.4 \, \text{Å}}{3.6} = 1.5 \, \text{Å} \]
This means that for each amino acid residue, the backbone rises 1.5 angstroms along the helix axis. Additionally, since there are 3.6 residues in one turn, the rotation of the backbone per residue can be calculated by dividing the total rotation (360 degrees) by the number of residues:
\[ \text{Rotation per Residue} = \frac{360 \, \text{degrees}}{3.6} = 100 \, \text{degrees} \]
Thus, the alpha helix backbone rotates 100 degrees for each amino acid residue, linking the concepts of rise and pitch to the helical structure's overall geometry. Understanding these parameters is crucial for calculating the length of an alpha helix, which will be explored further in subsequent discussions.
