Measuring the three-dimensional structural properties of topologically associating domains

Genome topologically associating domains (TADs) are mega base pair (Mbp) sized genomic regions that may be the structural and functional units of the genome. To better understand their structural properties and the relationship between structural properties and genetic and epigenetic features, we designed and benchmarked two measures to capture the three-dimensional structural signature of TADs. We modified the original definition of radius of gyration so that it could measure the spatial compactness of TADs weighted by one or more genetic or epigenetic feature(s). Another structural measure we have benchmarked is folding degree. We found correlations between structural measures and genetic and epigenetic features. We obtained similar correlations if considering the spatial compactness of the DNA segments containing transcription start sites, RNA polymerase II, and H3K4me3 peaks. Moreover, we designed a new objective function for reconstructing chromosome 3D structures using multidimensional scaling and compared it with two existent objective functions. The three objective functions have been implemented as web-based and standalone tools. The web server and source code are available at http://dna.cs.miami.edu/3DChrom/.