Contact matrix method to capture the features of knot conformations
Neda Abbasi Taklimi1, Franco Ferrari1, Marcin Radosław Piątek1
1University of Szczecin, CASA* and Institute of Physics, Szczecin, Poland.
Physical Review. E
|November 18, 2025
Summary
A new method uses contact matrices and color maps to analyze the structure of topologically constrained polymer rings. This approach, coupled with the Wang-Landau algorithm, reveals phase transitions and structural rearrangements in complex polymer systems.
Area of Science:
- Polymer physics
- Computational chemistry
- Statistical mechanics
Background:
- Recent advances in chromosome capture techniques inspire new methods for studying polymer ring organization.
- Topological constraints significantly influence the structural properties of polymer systems.
- Understanding polymer ring structure is crucial for various fields, including materials science and molecular biology.
Purpose of the Study:
- To develop and apply a novel computational method for analyzing the structural organization of topologically constrained polymer rings.
- To investigate the structural rearrangements and phase transitions in knotted polymer rings and polycatenanes.
- To provide a visualization tool for understanding complex polymer structures at different temperatures.
Main Methods:
- A compartment-based approach to define contacts between different parts of polymer rings.
- Development of contact matrices (M[over ¯]_{ab}) to quantify inter-compartment contacts during simulations.
- Integration with the Wang-Landau algorithm to compute the density of states and generate contact matrices at any temperature.
- Visualization of contact matrices using color maps to identify structural properties and phase transitions.
Main Results:
- The method successfully visualizes structural properties of polymer rings averaged over extensive simulations (>10^11 conformations).
- Distinct color map patterns were identified and associated with different phases of knotted polymer rings and polycatenanes.
- Phase transitions were detected through specific heat capacity plots, correlating with observed color map changes.
- The results align with traditional observables and direct simulation snapshot analysis.
Conclusions:
- The proposed method provides an effective way to study the structural organization and phase behavior of topologically constrained polymer systems.
- Contact matrix visualization offers a powerful tool for identifying and characterizing different phases of polymers.
- This approach enhances the understanding of structural rearrangements in complex polymer architectures, particularly during phase transitions.
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