Spectral Graph Entropy of Chromatin: A von Neumann Framework for Multiscale Polymer Organization from Hi-C.

Area of Science:

• Genomics
• Biophysics
• Computational Biology

Background:

• Hi-C contact maps offer insights into 3D genome organization but are challenging to interpret quantitatively.
• Extracting physically meaningful descriptors from Hi-C data is difficult due to data limitations like sparsity and varying sequencing depth.
• Understanding multiscale chromatin folding (loops, domains, compartments) requires advanced analytical tools.

Purpose of the Study:

• To introduce VECTOR, a novel graph-spectral framework for quantifying chromatin organization.
• To provide scale-resolved measures of configurational disorder in the genome.
• To establish a physics-grounded method for analyzing multiscale chromatin architecture.

Main Methods:

• Developed VECTOR, a graph-spectral framework utilizing the von Neumann entropy of the normalized contact-map Laplacian.
• Constructed distance-banded egographs for each genomic locus to analyze interactions at different genomic distances.
• Applied the framework to Hi-C data, including sparse single-nucleus Hi-C, and validated with polymer simulations.

Main Results:

• VECTOR quantifies chromatin organization across scales (∼10^2-10^7 bp) by measuring configurational disorder.
• Short-range entropy decreases at topological associating domain (TAD) boundaries, while long-range entropy reflects compartmental organization.
• Entropy scaling analysis revealed shallow exponents and a direct link between compaction and disorder, validated by polymer simulations.

Conclusions:

• VECTOR provides a reproducible, robust, and informative method for analyzing multiscale chromatin architecture.
• The framework offers a compact and physics-grounded approach to interpret complex Hi-C data.
• VECTOR advances our ability to quantitatively describe genome folding and its relationship to function.