Abstract
Here, we show that a problem of forced polymer loops can be mapped to an asymmetric simple exclusion process with reflecting boundary conditions. The dynamics of the particle system can be solved exactly using the Bethe ansatz. We thus can fully describe the relaxation dynamics of forced polymer loops. In the steady state, the conformation of the loop can be approximated by a combination of Fermi–Dirac and Brownian bridge statistics, while the exact solution is found by using the fermion integer partition theory. With the theoretical framework presented here we establish a link between the physics of polymers and statistics of many-particle systems opening new paths of exploration in both research fields. Our result can be applied to the dynamics of the biopolymers which form closed loops. One such example is the active pulling of chromosomal loops during meiosis in yeast cells which helps to align chromosomes for recombination in the viscous environment of the cell nucleus.
Highlights
Simple models in polymer physics capture generic polymer features [1, 2]
The Rouse model, representing a polymer as a chain of beads connected by harmonic springs [4], its extension to account for hydrodynamic interactions between the beads by Zimm [5], and the reptation model [1] were successful in describing various aspects of polymer dynamics, relaxation and rheology [1, 2]
We demonstrate that the one-dimensional version of the forced pinned polymer loop model can be mapped to the asymmetric simple exclusion process (ASEP) model with reflecting boundaries
Summary
Wenwen Huang , Yen Ting Lin1,2 , Daniela Frömberg, Jaeoh Shin , Frank Jülicher and Vasily Zaburdaev. We show that a problem of forced polymer loops can be mapped to an asymmetric simple. We can fully describe the relaxation dynamics of forced author(s) and the title of the work, journal citation polymer loops. With the theoretical framework presented here we establish a link between the physics of polymers and statistics of many-particle systems opening new paths of exploration in both research fields. Our result can be applied to the dynamics of the biopolymers which form closed loops. One such example is the active pulling of chromosomal loops during meiosis in yeast cells which helps to align chromosomes for recombination in the viscous environment of the cell nucleus
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