# Randomly cross-linked polymer models

## TL;DR

This paper introduces a randomly cross-linked polymer model for chromatin, providing analytical formulas for key properties and validating them with simulations, enabling inference of cross-linking from experimental data.

## Contribution

The paper presents a novel RCL polymer model with analytical formulas for chromatin properties, validated by simulations, and applicable to experimental data analysis.

## Key findings

- Derived asymptotic formulas for polymer properties.
- Validated formulas with Brownian simulations.
- Enabled estimation of cross-links from data.

## Abstract

Polymer models are used to describe chromatin, which can be folded at different spatial scales by binding molecules. By folding, chromatin generates loops of various sizes. We present here a randomly cross-linked (RCL) polymer model, where monomer pairs are connected randomly. We obtain asymptotic formulas for the steady-state variance, encounter probability, the radius of gyration, instantaneous displacement and the mean first encounter time between any two monomers. The analytical results are confirmed by Brownian simulations. Finally, the present results can be used to extract the minimum number of cross-links in a chromatin region from {conformation capture} data.