![30. At 25°C values of [Θ]₂₂₂, the mean residue ellipticity at 222 nm, are −33,000 and −3,000 deg cm² dmol⁻¹ for a polypeptide existing in α-helical (α) and β-structure (β), respectively. If this polypeptide undergoes a two-state heat-induced α → β transition, and a value of [Θ]₂₂₂ = −18,000 deg cm² dmol⁻¹ is observed at 60°C, then this observation leads to the conclusion that the α helix conversion to β-structure: (A) 40% (B) 50% (C) 55% (D) 60%](https://www.letstalkacademy.com/wp-content/uploads/2026/07/30.jpg)
30. At 25°C values of [Θ]₂₂₂, the mean residue ellipticity at 222 nm, are −33,000 and −3,000 deg cm² dmol⁻¹ for a polypeptide existing in α-helical (α) and β-structure (β), respectively. If this polypeptide undergoes a two-state heat-induced α → β transition, and a value of [Θ]₂₂₂ = −18,000 deg cm² dmol⁻¹ is observed at 60°C, then this observation leads to the conclusion that the α helix conversion to β-structure:
(A) 40%
(B) 50%
(C) 55%
(D) 60%
Alpha-Helix to Beta-Sheet Conversion Using Circular Dichroism (CD) Spectroscopy
Correct Answer
Option (2): 50%
Explanation
Circular Dichroism (CD) spectroscopy is one of the most reliable techniques for monitoring changes in protein secondary structure. The signal recorded at 222 nm is particularly sensitive to the presence of α-helices because peptide bonds arranged in a helical conformation produce a strong negative ellipticity at this wavelength. In contrast, β-sheet structures exhibit a much weaker negative ellipticity. Therefore, any transition from an α-helix to a β-sheet can be quantitatively monitored by measuring the change in mean residue ellipticity at 222 nm.
In this problem, the completely α-helical polypeptide has a mean residue ellipticity of -33,000 deg cm2 dmol-1, whereas the completely β-structured polypeptide has an ellipticity of -3,000 deg cm2 dmol-1. The observed ellipticity at 60°C is -18,000 deg cm2 dmol-1. Since the transition is described as a two-state process, the observed CD signal represents a linear combination of only two structural populations: α-helix and β-sheet. No intermediate conformations are assumed to contribute significantly to the measured ellipticity.
Calculation
For a two-state transition, the fraction of α-helix remaining is calculated using the relationship:
Fraction of α-helix = (θobs − θβ) / (θα − θβ)
Substituting the given values:
θα = -33,000
θβ = -3,000
θobs = -18,000
Fraction of α-helix = [(-18,000) − (-3,000)] / [(-33,000) − (-3,000)]
= (-15,000) / (-30,000)
= 0.50
This result indicates that 50% of the original α-helical structure remains at 60°C.
Since the question asks for the percentage of α-helix converted into β-structure, the conversion is calculated as:
Conversion = (1 − Fraction of α-helix) × 100
= (1 − 0.50) × 100
= 50%
Why Option (1) is Incorrect
Option (1) suggests that only 40% of the α-helical structure has converted into β-sheet. If this were true, the remaining α-helical content would be 60%, corresponding to a mean residue ellipticity more negative than the observed value of -18,000 deg cm2 dmol-1. Therefore, this option is inconsistent with the experimental data.
Why Option (2) is Correct
Option (2) correctly represents the result obtained from the two-state transition model. The observed ellipticity lies exactly halfway between the values for the fully α-helical and fully β-sheet conformations. This indicates that half of the molecules retain the α-helical structure while the other half have converted into β-sheet, giving a conversion of 50%.
Why Option (3) is Incorrect
Option (3) assumes that more than half of the α-helical structure has been converted into β-sheet. Such a conversion would produce an observed ellipticity closer to the β-sheet value of -3,000 deg cm2 dmol-1. Since the experimental value is exactly midway between the two reference states, this option cannot be correct.
Why Option (4) is Incorrect
Option (4) indicates a 60% conversion to β-sheet, implying that only 40% of the α-helical structure remains. This would correspond to an ellipticity significantly less negative than -18,000 deg cm2 dmol-1. Therefore, this option does not agree with the observed CD measurement.
Understanding Two-State Structural Transitions
A two-state transition assumes that the polypeptide exists only in two conformational states throughout the structural change. During the α-helix to β-sheet transition, each molecule is considered to be either completely α-helical or completely β-structured, without stable intermediate conformations. As a result, the observed ellipticity is directly proportional to the relative populations of the two structural states, allowing the fraction of each conformation to be calculated using a simple linear equation.
Role of Mean Residue Ellipticity at 222 nm
The mean residue ellipticity at 222 nm is widely used as a quantitative indicator of α-helical content because the peptide backbone in an α-helix generates a characteristic strong negative CD signal at this wavelength. As α-helices are converted into β-sheet structures, the magnitude of the negative ellipticity decreases. Monitoring these changes provides a straightforward method for following heat-induced conformational transitions and estimating the proportion of each secondary structural element present in solution.
Conclusion
The observed ellipticity at 60°C is exactly halfway between the characteristic values of the completely α-helical and completely β-sheet conformations. According to the two-state transition model, this indicates that 50% of the original α-helical structure has been converted into β-sheet. Therefore, the correct answer is Option (2): 50%.
