Statistical Properties of a Polymer Globule Formed during Collapse with the Irreversible Coalescence of Units

TL;DR

This study investigates the collapse of polymer chains into globules with irreversible crosslinks, revealing hierarchical packing structures similar to chromatin organization through computer simulations and statistical analysis.

Contribution

It introduces a model of polymer collapse with irreversible coalescence, linking contact probabilities to hierarchical packing features observed in chromatin.

Findings

Contact probability dependence matches experimental chromatin data

Hierarchical levels in polymer packing are identified

Discrete statistical features relate to number-theoretic properties

Abstract

Collapse of the polymer chain upon the sharp decrease of solvent quality is studied. During collapse, any pair of polymer units appearing in a sufficiently close vicinity in space has the possibility with a certain probability to form an irreversible crosslink, thereby preventing the interpenetration of chain material between the forming clusters. Globular structures having different spatial chain packing at various scales are obtained by computer simulations. It is shown that the dependence of probability of contact between two monomers in space , where s is a distance between monomers along chain, reproduces a number of characteristic features observed previously in experiments on the analysis of three-dimensional chromatin packing. The cluster analysis of intramolecular contact maps makes it possible to express the hypothesis that there are characteristic discrete hierarchical levels in polymer packing associated with the number-theoretic origin of rare-event statistics and inherent to individual maps of intra- and interchromosomal contacts.