# Modeling the Copy Number of HSATII Repeats in Human Pericentromere

## TL;DR

This paper presents a mathematical model showing how human pericentromeric repeats dynamically change in copy number based on chromatin regulation.

## Contribution

The novelty lies in developing a mathematical and spatial model to explain copy number dynamics of pericentromeric satellite repeats.

## Key findings

- Chromatin factors can facilitate copy gain in satellite repeats.
- The system can be bistable, allowing coexistence of cells with different repeat copy numbers.
- Local chromatin domains may regulate satellite copy number through methylation.

## Abstract

Tandemly repeated DNA fragments are major components of centromeres and pericentromeric heterochromatin, which is responsible for chromosomal stability and segregation. Recent evidence suggests that transcripts from these repeats play a key role in heterochromatin maintenance, and these repeats can be highly dynamic with various copy numbers. Here, we developed a mathematical model for human satellite repeats, which tracks the silenced and desilenced repeats, lncRNA, and copy number. Our model shows that chromatin factors for silencing and RNA stability can facilitate copy gain in satellites. Also, the system can be bistable, and cells with different copy numbers, silenced repeats with a small copy number, and desilenced repeats with a large copy number may coexist. To incorporate the cooperative methylation by neighboring repeats and the local chromatin environment, we also developed a spatial model where the local chromatin environment facilitates methylation locally. This model suggests that a local domain of silenced repeats may be an important feature of copy number regulation. Our models suggest that pericentromeric repeats are highly dynamic, and small changes in chromatin regulation can lead to large changes in satellite copy numbers.