Multiple scales and phases in discrete chains with application to folded proteins

Area of Science:

• Polymer Physics
• Structural Biology
• Biophysics

Background:

• Chiral heteropolymers, like proteins, exhibit complex behavior across multiple length scales.
• Understanding these scales is vital for protein conformational diversity, phase properties, and energy landscapes.
• Current methods lack systematic approaches to identify and distinguish these crucial length scales.

Purpose of the Study:

• To develop a methodology for systematically identifying different length scales in linear polymer chains.
• To introduce and analyze an order parameter capable of revealing multiple length scales and probing phase structure.
• To investigate the relationship between length scales, phase structure, and protein folding complexity.

Main Methods:

• Development of a novel order parameter based on a variant of Kadanoff's block-spin transformation.
• Application of coarse-graining techniques to piecewise linear polymer chains, including protein backbones.
• Analytical derivation and numerical verification of the order parameter's properties for chiral polymers.
• Validation using crystallographic protein structures from the Protein Data Bank.

Main Results:

• The proposed order parameter successfully identifies the presence of different length scales in chiral polymers.
• The order parameter reveals distinct phase traits within chiral heteropolymers depending on the scale of observation.
• Analysis of protein structures confirms the correlation between length scales, observed phases, and folding pathway complexity.

Conclusions:

• The developed methodology provides a systematic way to identify and distinguish multiple length scales in polymers.
• The order parameter serves as a valuable tool for probing the phase structure and conformational properties of proteins.
• Findings suggest a direct link between hierarchical length scales, protein phases, and the intricate nature of protein folding.