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Updated: Feb 24, 2026
06:55
Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
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Configurational entropy of randomly double-folding ring polymers.
Pieter H W van der Hoek1, Angelo Rosa1, Elham Ghobadpour2
1SISSA - Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, 34136 Trieste, Italy.
The Journal of Chemical Physics
|February 23, 2026
Summary
We calculated the exact number of ways a ring polymer can form tree-like structures. This finding helps understand genome folding and polymer physics, crucial for topological polymer science.
Area of Science:
- Polymer Physics
- Computational Biology
- Statistical Mechanics
Background:
- Genome-like polymers, when topologically constrained, frequently adopt tree-like configurations through double-folding.
- Understanding these complex folding patterns is essential for deciphering genome organization and polymer behavior under topological constraints.
Purpose of the Study:
- To determine the precise number of possible tightly double-folded configurations for a ring polymer under ideal conditions.
- To develop a theoretical framework for quantifying the topological complexity of polymer folding.
Main Methods:
- Introduction of a novel coding scheme to represent how a ring polymer wraps a branching tree structure.
- Application of a variant of Bertrand's ballot theorem to enumerate the number of admissible wrapping codes.
- Validation using Monte Carlo simulations of an elastic lattice model for double-folded rings.
Main Results:
- Derived an exact expression for the number of admissible configurations (ring entropy) for tightly double-folded ring polymers.
- Monte Carlo simulations confirmed the theoretical predictions for branch-node and tree size statistics.
- Demonstrated excellent agreement between simulation data and exact theoretical expressions.
Conclusions:
- The study provides an exact mathematical solution for the enumeration of topologically constrained ring polymer configurations.
- The findings offer a fundamental contribution to understanding polymer folding, with implications for genome organization and topological polymer physics.
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