Non-backtracking walks reveal compartments in sparse chromatin interaction networks.

Area of Science:

• Genomics
• Computational Biology
• Biophysics

Background:

• Chromatin communities are crucial for gene regulation and the 3D folding of the genome.
• Classical network theories like the stochastic block model (SBM) do not fully capture the linear connectivity of chromatin.

Purpose of the Study:

• To develop a novel model for community detection in polymer networks, specifically for chromatin.
• To establish a new protocol for annotating compartmental domains in sparse single-cell Hi-C data.

Main Methods:

• Proposed the polymer block model (PBM) to account for linear connectivity in chromatin networks.
• Modified the non-backtracking flow operator for community detection.
• Applied the method to sparse single-cell Hi-C matrices and benchmarked against existing operators.
• Demonstrated correspondence to the maximum entropy principle.

Main Results:

• The polymer non-backtracking operator spectrum accurately resolves chromatin compartmental structure, surpassing common operators beyond the detectability threshold.
• Non-backtracking single-cell domains closely match population-averaged compartment sizes.
• Identified domains show significant correlation with gene density and population compartmental masks.

Conclusions:

• The polymer block model and its associated non-backtracking operator provide a robust framework for analyzing chromatin organization.
• This approach offers a biologically significant method for annotating chromatin compartmental domains in single-cell Hi-C data.