# Statistical modeling and significance estimation of multi-way chromatin contacts with HyperloopFinder

## TL;DR

This paper introduces HyperloopFinder, a new method to identify and analyze complex chromatin interactions involving multiple genes and regulatory elements.

## Contribution

HyperloopFinder jointly models random polymer looping and technical biases to accurately estimate the significance of multi-way chromatin contacts.

## Key findings

- Most multi-way chromatin contacts can be explained by random linking of adjacent pairwise contacts.
- Hyperloops spatially colocalize and may act as scaffolds for gene and regulatory element cooperation.
- The method improves understanding of higher-order chromatin structures and transcriptional regulation.

## Abstract

Recent advances in chromatin conformation capture technologies, such as SPRITE and Pore-C, have enabled the detection of simultaneous contacts among multiple chromatin loci. This has made it possible to investigate the cooperative transcriptional regulation involving multiple genes and regulatory elements at the resolution of a single molecule. However, these technologies are unavoidably subject to the random polymer looping effect and technical biases, making it challenging to distinguish genuine regulatory relationships directly from random polymer interactions. Here, we present HyperloopFinder, a method for identifying regulatory multi-way chromatin contacts (hyperloops) by jointly modeling the random polymer looping effect and technical biases to estimate the statistical significance of multi-way contacts. The results show that our model can accurately estimate the expected interaction frequency of multi-way contacts based on the distance distribution of pairwise contacts, revealing that most multi-way contacts can be formed by randomly linking the pairwise contacts adjacent to each other. Moreover, we observed the spatial colocalization of the interaction sites of hyperloops from image-based data. Our results also revealed that hyperloops can function as scaffolds for the cooperation among multiple genes and regulatory elements. In summary, our work contributes novel insights into higher-order chromatin structures and functions and has the potential to enhance our understanding of transcriptional regulation and other cellular processes.