Long range correlations and folding angle with applications to α-helical proteins

Area of Science:

• Polymer physics
• Biophysics
• Structural biology

Background:

• Chain-like macromolecules (e.g., proteins, polymers) exhibit greater conformational complexity than point particles.
• Characterizing the phase structure of long chains is challenging, often relying solely on the radius of gyration.
• Finite chain lengths introduce scaling corrections that complicate phase analysis.

Purpose of the Study:

• Introduce a novel metric, the folding angle, to characterize macromolecular chain phase structure.
• Complement the radius of gyration for a more comprehensive phase analysis.
• Investigate the relationship between the folding angle and scaling exponents.

Main Methods:

• Theoretical analysis establishing a mean-field relationship between folding angle and radius of gyration scaling exponent.
• Estimation of folding angle values for crystallographic alpha-helical protein structures.
• Computational methods using a semiclassical Born-Oppenheimer description for chiral chains.

Main Results:

• A theoretical link is proposed between the folding angle and the scaling exponent of the radius of gyration.
• Folding angle values were estimated for alpha-helical protein structures.
• A computational approach was demonstrated for determining the folding angle from experimental data.

Conclusions:

• The folding angle offers a valuable new tool for scrutinizing the phase structure of chain-like macromolecules.
• This metric provides complementary information to the radius of gyration, especially for finite chains.
• The study validates the folding angle's utility in analyzing protein structures and offers a computational pathway for its determination.