Topologically associating domain boundaries that are stable across diverse cell types are evolutionarily constrained and enriched for heritability.

Topologically associating domains (TADs) are fundamental units of three-dimensional (3D) nuclear organization. The regions bordering TADs-TAD boundaries-contribute to the regulation of gene expression by restricting interactions of cis-regulatory sequences to their target genes. TAD and TAD-boundary disruption have been implicated in rare-disease pathogenesis; however, we have a limited framework for integrating TADs and their variation across cell types into the interpretation of common-trait-associated variants. Here, we investigate an attribute of 3D genome architecture-the stability of TAD boundaries across cell types-and demonstrate its relevance to understanding how genetic variation in TADs contributes to complex disease. By synthesizing TAD maps across 37 diverse cell types with 41 genome-wide association studies (GWASs), we investigate the differences in disease association and evolutionary pressure on variation in TADs versus TAD boundaries. We demonstrate that genetic variation in TAD boundaries contributes more to complex-trait heritability, especially for immunologic, hematologic, and metabolic traits. We also show that TAD boundaries are more evolutionarily constrained than TADs. Next, stratifying boundaries by their stability across cell types, we find substantial variation. Compared to boundaries unique to a specific cell type, boundaries stable across cell types are further enriched for complex-trait heritability, evolutionary constraint, CTCF binding, and housekeeping genes. Thus, considering TAD boundary stability across cell types provides valuable context for understanding the genome's functional landscape and enabling variant interpretation that takes 3D structure into account.