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arXiv · 2512.18070

Configurational entropy of randomly double-folding ring polymers

Pieter H. W. van der Hoek·Angelo Rosa·Elham Ghobadpour·Ralf Everaers
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Abstract

Topologically constrained genome-like polymers often double-fold into tree-like configurations. Here we calculate the exact number of tightly double-folded configurations available to a ring polymer in ideal conditions. For this purpose, we introduce a scheme which allows us to define a ``code'' specifying how a ring wraps a randomly branching tree and calculate the number of admissible wrapping codes via a variant of Bertrand's ballot theorem. As a validation, we demonstrate that data from Monte Carlo simulations of an elastic lattice model of non-interacting tightly double-folded rings with controlled branching activity are in excellent agreement with exact expressions for branch-node and tree size statistics that can be derived from our expression for the ring entropy.

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Pieter H. W. van der Hoek, Angelo Rosa, Elham Ghobadpour, Ralf Everaers. 2025-12-19. Configurational entropy of randomly double-folding ring polymers. https://doi.org/10.1063/5.0318212

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