Rotational Angle Of Alpha Helix Calculator

Rotation Angle per Residue Formula:

\[ \Omega = \cos^{-1}\left(\frac{1 - 4\cos^2\left(\frac{\phi + \psi}{2}\right)}{3}\right) \]

Rotation Angle per Residue (Ω):

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1. What is the Rotational Angle of Alpha Helix?

The rotational angle per residue (Ω) of an alpha helix describes the angular rotation between consecutive amino acid residues along the helical axis. This parameter is crucial for understanding the structural properties and stability of alpha-helical proteins.

2. How Does the Calculator Work?

The calculator uses the rotation angle formula:

\[ \Omega = \cos^{-1}\left(\frac{1 - 4\cos^2\left(\frac{\phi + \psi}{2}\right)}{3}\right) \]

Where:

\( \Omega \) — Rotation angle per residue (radians)
\( \phi \) — Dihedral angle around negative 65° (radians)
\( \psi \) — Dihedral angle around negative 45° (radians)

Explanation: The formula calculates the angular rotation between consecutive residues based on their backbone dihedral angles φ and ψ, which typically adopt values around -65° and -45° respectively in alpha-helices.

3. Importance of Rotation Angle Calculation

Details: The rotation angle per residue is fundamental for understanding helical pitch, structural stability, and the overall geometry of alpha-helical proteins. It helps in predicting protein folding patterns and designing synthetic peptides.

4. Using the Calculator

Tips: Enter dihedral angles φ and ψ in radians. Typical values for alpha-helices are around -1.1345 radians (-65°) for φ and -0.7854 radians (-45°) for ψ. Both values must be valid non-zero numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical rotation angle per residue in alpha-helices?
A: In ideal alpha-helices, the rotation angle per residue is approximately 100° or 1.745 radians, corresponding to 3.6 residues per turn.

Q2: Why are specific dihedral angles used for alpha-helices?
A: The dihedral angles around -65° (φ) and -45° (ψ) allow optimal hydrogen bonding and steric constraints that stabilize the alpha-helical structure.

Q3: Can this calculator be used for other helical structures?
A: This specific formula is designed for alpha-helices. Other helical structures like 3₁₀-helices or pi-helices have different characteristic dihedral angles and rotation parameters.

Q4: How does the rotation angle affect helical properties?
A: The rotation angle determines the helical pitch, number of residues per turn, and overall compactness of the helical structure.

Q5: What units should be used for input angles?
A: The calculator requires angles in radians. To convert from degrees to radians, multiply by π/180 (approximately 0.0174533).