Rotational Angle of Alpha Helix Calculator

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✖Dihedral angles around negative 65° is residues in α-helices typically adopt backbone dihedral angles around (-65)°.ⓘ Dihedral angles around negative 65° [φ]			+10% -10%
✖Dihedral Angles around negative 45° is residues in α-helices typically adopt backbone dihedral angles around -45°.ⓘ Dihedral Angles around negative 45° [ψ]			+10% -10%

✖Rotation angle per residue is rotation angle Ω per residue of any polypeptide helix with trans isomers.ⓘ Rotational Angle of Alpha Helix [Ω]

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Formula

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Rotational Angle of Alpha Helix

Formula

`"Ω" = acos((1-(4*cos((("φ"+"ψ")/2)^2)))/3)`

Example

`"147.6447°"=acos((1-(4*cos((("45°"+"35°")/2)^2)))/3)`

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Rotational Angle of Alpha Helix Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rotation Angle per Residue = acos((1-(4*cos(((Dihedral angles around negative 65°+Dihedral Angles around negative 45°)/2)^2)))/3)
Ω = acos((1-(4*cos(((φ+ψ)/2)^2)))/3)
This formula uses 2 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

Rotation Angle per Residue - (Measured in Radian) - Rotation angle per residue is rotation angle Ω per residue of any polypeptide helix with trans isomers.
Dihedral angles around negative 65° - (Measured in Radian) - Dihedral angles around negative 65° is residues in α-helices typically adopt backbone dihedral angles around (-65)°.
Dihedral Angles around negative 45° - (Measured in Radian) - Dihedral Angles around negative 45° is residues in α-helices typically adopt backbone dihedral angles around -45°.

STEP 1: Convert Input(s) to Base Unit

Dihedral angles around negative 65°: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
Dihedral Angles around negative 45°: 35 Degree --> 0.610865238197901 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Ω = acos((1-(4*cos(((φ+ψ)/2)^2)))/3) --> acos((1-(4*cos(((0.785398163397301+0.610865238197901)/2)^2)))/3)

Evaluating ... ...

Ω = 2.57688590649503

STEP 3: Convert Result to Output's Unit

2.57688590649503 Radian -->147.644686728936 Degree (Check conversion here)

FINAL ANSWER

147.644686728936 ≈ 147.6447 Degree <-- Rotation Angle per Residue

(Calculation completed in 00.004 seconds)

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Created by Soupayan banerjee

National University of Judicial Science (NUJS), Kolkata

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Rotational Angle of Alpha Helix Formula

Rotation Angle per Residue = acos((1-(4*cos(((Dihedral angles around negative 65°+Dihedral Angles around negative 45°)/2)^2)))/3)
Ω = acos((1-(4*cos(((φ+ψ)/2)^2)))/3)

What is alpha helix?

The alpha helix (α-helix) is a common motif in the secondary structure of proteins and is a right hand-helix conformation in which every backbone N−H group hydrogen bonds to the backbone C=O group of the amino acid located four residues earlier along the protein sequence.

How to Calculate Rotational Angle of Alpha Helix?

Rotational Angle of Alpha Helix calculator uses Rotation Angle per Residue = acos((1-(4*cos(((Dihedral angles around negative 65°+Dihedral Angles around negative 45°)/2)^2)))/3) to calculate the Rotation Angle per Residue, The Rotational Angle of Alpha Helix formula is defined as the general formula for the rotation angle Ω per residue of any polypeptide helix with trans isomers is given by the equation. Rotation Angle per Residue is denoted by Ω symbol.

How to calculate Rotational Angle of Alpha Helix using this online calculator? To use this online calculator for Rotational Angle of Alpha Helix, enter Dihedral angles around negative 65° (φ) & Dihedral Angles around negative 45° (ψ) and hit the calculate button. Here is how the Rotational Angle of Alpha Helix calculation can be explained with given input values -> 8459.417 = acos((1-(4*cos(((0.785398163397301+0.610865238197901)/2)^2)))/3).

FAQ

What is Rotational Angle of Alpha Helix?

The Rotational Angle of Alpha Helix formula is defined as the general formula for the rotation angle Ω per residue of any polypeptide helix with trans isomers is given by the equation and is represented as Ω = acos((1-(4*cos(((φ+ψ)/2)^2)))/3) or Rotation Angle per Residue = acos((1-(4*cos(((Dihedral angles around negative 65°+Dihedral Angles around negative 45°)/2)^2)))/3). Dihedral angles around negative 65° is residues in α-helices typically adopt backbone dihedral angles around (-65)° & Dihedral Angles around negative 45° is residues in α-helices typically adopt backbone dihedral angles around -45°.

How to calculate Rotational Angle of Alpha Helix?

The Rotational Angle of Alpha Helix formula is defined as the general formula for the rotation angle Ω per residue of any polypeptide helix with trans isomers is given by the equation is calculated using Rotation Angle per Residue = acos((1-(4*cos(((Dihedral angles around negative 65°+Dihedral Angles around negative 45°)/2)^2)))/3). To calculate Rotational Angle of Alpha Helix, you need Dihedral angles around negative 65° (φ) & Dihedral Angles around negative 45° (ψ). With our tool, you need to enter the respective value for Dihedral angles around negative 65° & Dihedral Angles around negative 45° and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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