Multi-scale phase separation by explosive percolation with single chromatin loop resolution

The 2m-long human DNA is tightly intertwined into the cell nucleus of the size of 10μm. The DNA packing is explained by folding of chromatin fiber. This folding leads to the formation of such hierarchical structures as: chromosomal territories, compartments; densely packed genomic regions known as Chromatin Contact Domains (CCDs), and loops. We propose models of dynamical genome folding into hierarchical components in human lymphoblastoid, stem cell, and fibroblast cell lines. Our models are based on explosive percolation theory. The chromosomes are modeled as graphs where CTCF chromatin loops are represented as edges. The folding trajectory is simulated by gradually introducing loops to the graph following various edge addition strategies that are based on topological network properties, chromatin loop frequencies, compartmentalization, or epigenomic features. Finally, we propose the genome folding model - a biophysical pseudo-time process guided by a single scalar order parameter. The parameter is calculated by Linear Discriminant Analysis. We simulate the loop formation by using Loop Extrusion Model (LEM) while adding them to the system. The chromatin phase separation, where fiber folds into topological domains and compartments, is observed when the critical number of contacts is reached. We also observe that 80% of the loops are needed for chromatin fiber to condense in 3D space, and this is constant through various cell lines. Overall, our in-silico model integrates the high-throughput 3D genome interaction experimental data with the novel theoretical concept of phase separation, which allows us to model event-based time dynamics of chromatin loop formation and folding trajectories. ### Competing Interest Statement The authors have declared no competing interest.