# Folding and cytoplasm viscoelasticity contribute jointly to chromosome dynamics

## TL;DR

This paper develops a theoretical framework to understand how chromosome folding and the viscoelastic properties of the cytoplasm jointly influence chromosome dynamics, providing methods to infer folding from dynamical data.

## Contribution

It introduces a novel theoretical model linking chromosome folding, cytoplasm viscoelasticity, and dynamics, with analytical estimates and a scaling analysis for stress-propagation.

## Key findings

- Stress-propagation time scales with chromosomal arclength distance.
- Dynamical coupling reveals folding information.
- Analytical estimates of correlation functions in a viscoelastic medium.

## Abstract

The chromosome is a key player of cell physiology, and its dynamics provides valuable information about its physical organization. In both prokaryotes and eukaryotes, the short-time motion of chromosomal loci has been described as a Rouse model in a simple or viscoelastic medium. However, little emphasis has been put on the role played by the folded organization of chromosomes on the local dynamics. Clearly, stress-propagation, and thus dynamics, must be affected by such organization, but a theory allowing to extract such information from data, e.g.\ of two-point correlations, is lacking. Here, we describe a theoretical framework able to answer this general polymer dynamics question, and we provide a general scaling analysis of the stress-propagation time between two loci at a given arclength distance along the chromosomal coordinate. The results suggest a precise way to detect folding information from the dynamical coupling of chromosome segments. Additionally, we realize this framework in a specific theoretical model of a polymer with variable-range interactions in a viscoelastic medium characterized by a tunable scaling exponent, where we derive analytical estimates of the correlation functions.