Abstract
In this paper, we introduce sequence-based multiscale modeling for biomolecular data analysis. We employ spectral clustering method in our modeling and reveal the difference between sequence-based global scale clustering and local scale clustering. Essentially, two types of distances, i.e., Euclidean (or spatial) distance and genomic (or sequential) distance, can be used in data clustering. Clusters from sequence-based global scale models optimize spatial distances, meaning spatially adjacent loci are more likely to be assigned into the same cluster. Sequence-based local scale models, on the other hand, result in clusters that optimize genomic distances. That is to say, in these models, sequentially adjoining loci tend to be cluster together. We propose two sequence-based multiscale models (SeqMMs) for the study of chromosome hierarchical structures, including genomic compartments and topological associated domains (TADs). We find that genomic compartments are determined only by global scale information in the Hi-C data. The removal of all the local interactions within a band region as large as 10 Mb in genomic distance has almost no significant influence on the final compartment results. Further, in TAD analysis, we find that when the sequential scale is small, a tiny variation of diagonal band region in a contact map will result in a great change in the predicted TAD boundaries. When the scale value is larger than a threshold value, the TAD boundaries become very consistent. This threshold value is highly related to TAD sizes. By the comparison of our results with those previously obtained using a spectral clustering model, we find that our method is more robust and reliable. Finally, we demonstrate that almost all TAD boundaries from both clustering methods are local minimum of a TAD summation function.