Coherent modeling of double-folded ring polymers and their underlying random tree structure

Area of Science:

• Polymer Physics
• Computational Biology
• Statistical Mechanics

Background:

• Genome-like polymers form complex tree-like structures due to topological constraints.
• These structures can be modeled as either folded ring polymers or underlying random trees.
• Previous work derived configurational entropy for both models with controlled branching.

Purpose of the Study:

• To demonstrate the equivalence between tree and ring polymer models for topologically constrained polymers.
• To establish a unified framework for switching between tree and ring representations.
• To introduce an efficient computational method for simulating these polymer ensembles.

Main Methods:

• Developed a theoretical framework proving the equivalence of tree and ring polymer models.
• Introduced a generalized Amoeba Monte Carlo algorithm for generating tree ensembles.
• Validated the tree algorithm against dynamic simulations of the ring model.

Main Results:

• Established the equivalence of tree and ring polymer models, including for interacting systems.
• The generalized Amoeba Monte Carlo algorithm efficiently samples tree configurations.
• The tree algorithm is computationally faster (O(N)) for static properties compared to ring simulations.

Conclusions:

• A coherent framework for analyzing topologically constrained polymers by switching between tree and ring models is now available.
• The developed Monte Carlo method offers significant speed advantages for static property analysis.
• This work bridges the gap between static and dynamic studies of polymer folding and topological constraints.