A wavelet-based approach generates quantitative, scale-free and hierarchical descriptions of 3D genome structures and new biological insights.

Eukaryotic genomes are organized within nuclei in three-dimensional space, forming structures such as loops, topologically associating domains (TADs), and chromosome territories. This 3D architecture impacts gene regulation and development, stress responses, and disease. However, current methods to infer these 3D structures from genomic data have multiple drawbacks, including varying outcomes depending on the resolution of the analysis and sequencing depth, qualitative outputs that limit statistical comparisons, and insufficient insight into structure frequency within samples. These challenges hinder rigorous comparisons of 3D properties across genomes, conditions, or species. To overcome these issues, we developed WaveTAD, a wavelet transform-based method that provides a resolution-free, probabilistic, and hierarchical description of 3D organization. WaveTAD generates TAD strengths, capturing the variable frequency of intrachromosomal interactions within samples, and shows increased accuracy and sensitivity over existing methods. We applied WaveTAD to multiple datasets from Drosophila, mouse, and humans to illustrate new biological insights that our more sensitive and quantitative approach provides, such as the widespread presence of embryonic 3D organization before zygotic genome activation, the effect of multiple CTCF units on the stability of loops and TADs, and the association between gene expression and TAD structures in COVID-19 patients or sex-specific transcription in Drosophila.