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BPscore: an effective metric for meaningful comparisons of structural chromosome segmentations

Studying the 3D structure of chromosomes is an emerging field flourishing in recent years because of rapid development of experimental approaches for studying chromosomal contacts. This has led to numerous studies providing results of segmentation of chromosome sequences of different species into so called Topologically Associating Domains (TADs). As the number of such studies grows steadily and many of them make claims about the perceived differences between TAD structures observed in different conditions, there is a growing need for good measures of similarity (or dissimilarity) between such segmentations. We provide here a BP score, which is a relatively simple distance metric based on the bipartite matching between two segmentations. In this paper, we provide the rationale behind choosing specifically this function and show its results on several different datasets, both simulated and experimental. We show that not only the BP score is a proper metric satisfying the triangle inequality, but that it is providing good granularity of scores for typical situations occuring between different TAD segmentations. We also introduce local variant of the BP metric and show that in actual comparisons between experimental datasets, the local BP score is correlating with the observed changes in gene expression and genome methylation. In summary, we consider the BP score a good foundation for analysing the dynamics of chromosome structures. The methodology we present in this work could be used by many researchers in their ongoing analyses making it a popular and useful tool. Author summary Many researchers are interested in the chromosomal structure, its function and dynamics. Over the recent years, chromosome conformation capture (3C) methods have become the main source of experimental data on the subject and the Topologically Associating Domains (TADs) have become the de-facto standard unit of chromosomal structure. Many methods have been developed for TAD calling and the 3C experiments have been done in multiple conditions giving us a multitude of chromosomal segmentations describing the most atomic differences in chromosomal structure between conditions. Until now, such segmentations were compared mostly by very rough measures, such as the Jaccard coefficient or TAD overlaps or very general metrics like the variation of information coefficient. This has limited the researchers in the analysis of differential TAD segmentations, and practically prevented any proper analysis of TAD dynamics between conditions. Our approach has the potential to facilitate such analyses by providing researchers with mathematically sound metric that is designed specifically for the purpose and tested on both simulated and experimental data. Additionally, we provide a local variant of our measure that is a natural derivative of the BP score that can indicate which parts of the chromosomes are undergoing the most significant structural reorganizations.