# Non-Markovian dynamics of reaction coordinate in polymer folding

## TL;DR

This paper presents a theoretical framework for understanding the non-Markovian, subdiffusive dynamics of polymer zipping at critical temperature, combining tension propagation theory with generalized Langevin equations, validated by simulations.

## Contribution

It introduces a novel theoretical approach to describe the critical zipping dynamics of polymers, including estimates of anomalous exponents and correction terms, aligning well with numerical data.

## Key findings

- Subdiffusive motion of closed base pairs with variance $
ightarrow t^eta$
- Theoretical estimates of anomalous exponent $
ightarrow eta$
- Excellent agreement between theory and simulations

## Abstract

We develop a theoretical description of the critical zipping dynamics of a self-folding polymer. We use tension propagation theory and the formalism of the generalized Langevin equation applied to a polymer that contains two complementary parts which can bind to each other. At the critical temperature, the (un)zipping is unbiased and the two strands open and close as a zipper. The number of closed base pairs $n(t)$ displays a subdiffusive motion characterized by a variance growing as $\langle \Delta n^2(t) \rangle \sim t^\alpha$ with $\alpha < 1$ at long times. Our theory provides an estimate of both the asymptotic anomalous exponent $\alpha$ and of the subleading correction term, which are both in excellent agreement with numerical simulations. The results indicate that the tension propagation theory captures the relevant features of the dynamics and shed some new insights on related polymer problems characterized by anomalous dynamical behavior.