Geometric Predictors of Knotted and Linked Arcs.

Area of Science:

• Polymer Physics
• Computational Biophysics
• Materials Science

Background:

• Proteins can sense topological features like knots and entanglements in DNA.
• Understanding polymer topology is crucial for predicting material properties.
• Existing methods for detecting polymer entanglements can be computationally intensive.

Purpose of the Study:

• To investigate if local geometric features can predict topological entanglements in generic polymers.
• To identify reliable geometric measures for detecting knots and links in polymer chains.
• To assess the robustness of these measures under varying conditions like confinement.

Main Methods:

• Conducted molecular simulations of knotted and linked semiflexible polymers.
• Analyzed four geometric measures: local curvature, local density, local 1D writhe, and nonlocal 3D writhe.
• Correlated geometric features with the location of topological entanglements.

Main Results:

• Local curvature was found to be an ineffective predictor of polymer entanglements.
• Maximum local density and local writhe segments strongly correlated (up to 90%) with knotted/linked polymer arcs.
• Nonlocal 3D writhe proved to be the most accurate geometric readout for pinpointing knot locations.
• High prediction accuracy was maintained across diverse knot types and under spherical confinement.

Conclusions:

• Local geometric features, specifically density and writhe, can serve as effective predictors of polymer topology.
• Nonlocal 3D writhe is a superior metric for identifying knot locations in polymers.
• These findings offer a computationally efficient approach for analyzing entanglements in polymer melts and gels.