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Entropic Tug of War: Topological Constraints Spontaneously Rectify the Dynamics of a Polymer with Heterogeneous Fluctuations

Adam H. T. P. Höfler, Iurii Chubak, Christos N. Likos, and Jan Smrek*

  • *Contact author: jan.smrek@univie.ac.at
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Phys. Rev. X 16, 011046 – Published 4 March, 2026

DOI: https://doi.org/10.1103/rkms-2v1l

Abstract

Polymers with active segments constitute prospective future materials and are used as a model for some biological systems such as chromatin. The directions of the active forces are typically introduced with temporal or spatial correlations to establish directional motion of the chain and corresponding active dynamics. Instead, here we consider an active-passive copolymer, where the two segments differ only by the magnitude of their fluctuations and feature no artificial correlations. Here we show that although the model itself does not possess directional dynamics, if the chains are concentrated, directional persistent motion spontaneously arises as a consequence of the broken translational symmetry owing to the topological constraints. Using scaling arguments and simulations, we explain the phenomenon and describe the ensuing dynamics. Our work has thus far-reaching consequences for the mechanical properties of all dense active polymeric systems with heterogeneous fluctuations and in particular for chromatin conformation and dynamics that are crucial for biological functionality.

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Polymers in biological systems, like chromatin in cell nuclei, can experience heterogeneous activity where some regions fluctuate more vigorously than others. We discovered that even when these fluctuations are completely isotropic—lacking any built-in directional bias—concentrated polymers spontaneously develop persistent directional motion. This surprising behavior emerges from an imbalance of entropic forces at chain ends caused by topological constraints that prevent chains from crossing each other. Using computer simulations and scaling theory, we show that the “hotter” segment pulls the rest of the chain through the entangled mesh, creating superdiffusive dynamics where segments move faster than normal diffusion would predict. This mechanism provides new insight into chromatin dynamics in living cells, where active processes create localized fluctuations. Our findings suggest that topological constraints play a crucial role in converting nondirectional activity into directed motion, with implications for understanding genome organization and designing functional active polymeric materials.

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Phys. Rev. X 16, 011046– Published 4 March, 2026
  • Received 27 January 2025
  • Revised 31 October 2025
  • Accepted 29 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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