# A minimal G$\bar{\textrm{o}}$-model for rebuilding whole genome structures from haploid single-cell Hi-C data

## TL;DR

This paper introduces a fast, minimal computational model for reconstructing 3D haploid genome structures from single-cell Hi-C data, highlighting the importance of specific modeling choices for realistic conformations.

## Contribution

The authors develop a minimal, GPU-accelerated model that efficiently reconstructs genome structures from Hi-C data, emphasizing the role of excluded volume and contact map limitations.

## Key findings

- Contact map fulfillment alone is insufficient for realistic structures.
- Excluded volume is crucial for chromosome territory formation.
- Knots are consistently present across reconstructed structures.

## Abstract

We present a minimal computational model, which allows very fast, on-the-fly construction of three dimensional haploid interphase genomes from single cell Hi-C contact maps using the HOOMD-blue molecular dynamics package on graphics processing units. Chromosomes are represented by a string of connected beads, each of which corresponds to 100,000 base pairs, and contacts are mediated via a structure-based harmonic potential. We suggest and test two minimization protocols which consistently fold into conformationally similar low energy states. The latter are similar to previously published structures but are calculated in a fraction of the time. We find evidence that mere fulfillment of contact maps is insufficient to create experimentally relevant structures. Particularly, an excluded volume term is required in our model to induce the formation of chromosome territories. We also observe empirically that contact maps do not capture the chirality of the underlying structures. Depending on starting configurations and protocol details, one of two mirror images emerges. Finally, we analyze the occurrence of knots in a particular chromosome. The same knot appears in (almost) all structures irrespective of minimization protocols or even details of underlying potentials providing further evidence for the existence of knots in interphase chromatin.