The radial distribution function of worm-like chains.

Area of Science:

• Polymer Physics
• Statistical Mechanics
• Biophysics

Background:

• Semiflexible macromolecules are commonly modeled using the worm-like chain (WLC) model.
• The end-to-end distance distribution is a key parameter for the WLC model but lacks a closed-form solution.
• Existing approximations for the WLC model have limitations in accuracy and applicability.

Purpose of the Study:

• To address the challenge of selecting appropriate approximations for the worm-like chain model.
• To develop a unified, accurate expression for the end-to-end distance distribution of semiflexible chains.
• To investigate the influence of bridging molecules on the formation of short worm-like loops.

Main Methods:

• Comprehensive review of existing WLC approximations and exact limiting results.
• Development of a novel explicit expression interpolating between limiting cases.
• Validation against high-precision Monte Carlo simulation data.

Main Results:

• The proposed explicit expression accurately reproduces Monte Carlo data across a wide range of chain stiffness and configurations.
• The new formula provides a computationally inexpensive and accurate method for analyzing WLC conformations.
• Quantification of the enhancement effect of (protein) bridges on short worm-like loop formation.

Conclusions:

• The developed interpolation formula offers a significant advancement in modeling semiflexible macromolecules.
• This work provides a practical tool for researchers studying polymer physics and biophysics.
• The findings enhance our understanding of molecular conformations and interactions, particularly in loop formation.