Moments and distribution functions for polypeptide chains. Poly-L-alanine.

Area of Science:

• Polymer Physics
• Statistical Mechanics
• Computational Chemistry

Background:

• Understanding polypeptide chain configurations is crucial for predicting their physical and chemical properties.
• Statistical mechanical averages provide insights into the average behavior of polymer chains.
• Poly-L-alanines (PLA) serve as a model system for studying polypeptide behavior.

Purpose of the Study:

• To calculate statistical mechanical averages of vectors and tensors for PLA configurations.
• To analyze how these averages change with increasing peptide unit numbers (xu).
• To determine the chain length at which simplified polymer models become applicable.

Main Methods:

• Calculation of statistical mechanical averages for vectors and tensors characterizing PLA configurations (xu = 2-400).
• Expression of quantities in a reference frame fixed to the first peptide unit.
• Computation of configurational averages of Cartesian tensors up to the sixth rank from the displacement vector.

Main Results:

• The persistence vector (a) rapidly converges to a limit (a infinity) for increasing chain length.
• For chains with xu > 50, even moments of fourth and sixth rank of the reduced vector (p) are accurately represented by a freely jointed chain model.
• Asymmetry in the moments of p is observed for xu < 50, with approximate spherical symmetry emerging only for xu >= 100.

Conclusions:

• The study quantifies the convergence of PLA configuration averages and identifies key chain lengths for model simplification.
• For longer poly-L-alanines (xu >= 100), the distribution of displacement vectors around the persistence vector approaches spherical symmetry.
• These findings aid in the development and validation of computational models for polypeptide behavior.