![32. Poly-L-lysine exists in pure α-helix, β-sheet and random coiled conformation depending upon the solvent conditions. The values of mean residue ellipticity at 220 nm ([Θ]₂₂₀) are −35,700, −13,800 and +3,900 deg cm² dmol⁻¹ for α-helical, β-sheet and random coil conformations of this polypeptide, respectively. The polypeptide exists in α-helix conformation at pH 10.8 and 25°C. Addition of urea leads to a two-state transition between α-helix and random coil conformation. It has been observed that [Θ]₂₂₂ of the polypeptide is −14,800 deg cm² dmol⁻¹ in the presence of 6 M urea. The percentage of the polypeptide in α-helix conformation is: (A) 37 (B) 41 (C) 47 (D) 50](https://www.letstalkacademy.com/wp-content/uploads/2026/07/32.jpg)
32. Poly-L-lysine exists in pure α-helix, β-sheet and random coiled conformation depending upon the solvent conditions. The values of mean residue ellipticity at 220 nm ([Θ]₂₂₀) are −35,700, −13,800 and +3,900 deg cm² dmol⁻¹ for α-helical, β-sheet and random coil conformations of this polypeptide, respectively. The polypeptide exists in α-helix conformation at pH 10.8 and 25°C. Addition of urea leads to a two-state transition between α-helix and random coil conformation. It has been observed that [Θ]₂₂₂ of the polypeptide is −14,800 deg cm² dmol⁻¹ in the presence of 6 M urea. The percentage of the polypeptide in α-helix conformation is:
(A) 37
(B) 41
(C) 47
(D) 50
Calculating the Percentage of Alpha-Helix in Poly-L-Lysine Using Circular Dichroism (CD) Spectroscopy
Correct Answer
Option (2): 41%
Explanation
Circular Dichroism (CD) spectroscopy is one of the most effective techniques for determining the secondary structure of proteins and polypeptides in solution. The mean residue ellipticity measured at specific wavelengths reflects the proportion of different secondary structural elements present in the molecule. For α-helical structures, the ellipticity is highly negative, whereas random coil conformations exhibit much less negative or even positive values depending on the wavelength. By comparing the observed ellipticity with the characteristic values of the pure conformations, the fraction of each structural state can be calculated.
In this problem, Poly-L-lysine undergoes a two-state transition between the α-helical and random coil conformations after the addition of urea. Since the transition is specifically stated to occur only between these two conformations, the β-sheet value is not used in the calculation. The observed ellipticity therefore represents a weighted average of only the α-helix and random coil populations.
Calculation
For a two-state transition between α-helix and random coil, the fraction of α-helix is calculated using the equation:
Fraction of α-helix = (θobs − θrandom) / (θα − θrandom)
Substituting the given values:
θα = -35,700
θrandom = +3,900
θobserved = -14,800
Fraction of α-helix = [(-14,800) − (+3,900)] / [(-35,700) − (+3,900)]
= (-18,700) / (-39,600)
= 0.472
Percentage of α-helix = 0.472 × 100
= 47.2%
After rounding, the percentage of α-helical conformation is approximately 47%.
Important Observation
The numerical calculation gives a value of approximately 47%. Therefore, based on the experimental data provided in the question, the correct mathematical answer is Option (3). Although some answer keys list Option (2), that result is not obtained using the standard two-state CD equation with the values given in the question. The calculated value clearly supports 47%.
Why Option (1) is Incorrect
A value of 37% would correspond to an observed ellipticity much closer to the random coil state than the experimentally measured value of -14,800 deg cm2 dmol-1. Substituting the given ellipticity values into the two-state equation does not produce this percentage.
Why Option (2) is Incorrect
Option (2) corresponds to 41%, but this value cannot be obtained using the supplied ellipticity values. Applying the standard linear interpolation between the α-helical and random coil reference states yields approximately 47%, indicating that 41% is inconsistent with the provided data.
Why Option (3) is Correct
The calculated fraction of α-helix is 0.472, which corresponds to approximately 47%. This value is obtained directly from the two-state transition equation using the experimental ellipticity values provided in the problem. Therefore, Option (3) is the only answer that agrees with the calculation.
Why Option (4) is Incorrect
A value of 50% would indicate that the observed ellipticity lies exactly halfway between the α-helical and random coil reference values. Since the measured ellipticity of -14,800 deg cm2 dmol-1 is not the midpoint of the two reference states, the percentage cannot be 50%.
Role of Urea in Protein Unfolding
Urea is a well-known protein denaturant that disrupts the hydrogen bonding network and weakens hydrophobic interactions responsible for maintaining ordered secondary structures. As the concentration of urea increases, the α-helical structure gradually unfolds into a random coil conformation. In a two-state transition, each polypeptide molecule is considered to exist either in the fully folded α-helical state or in the completely unfolded random coil state, allowing the fraction of each population to be calculated directly from the observed CD signal.
Why the β-Sheet Value Is Not Used
Although the characteristic ellipticity for the β-sheet conformation is provided in the question, it is not included in the calculation because the problem explicitly states that the structural transition occurs only between the α-helix and the random coil conformations. The β-sheet value is included merely as additional information about the conformational states that Poly-L-lysine can adopt under different solvent conditions.
Conclusion
Using the standard two-state Circular Dichroism equation, the fraction of α-helical structure is calculated to be 0.472, corresponding to approximately 47%. Therefore, the correct answer based on the numerical data provided is Option (3): 47%.
