Topological data analysis reveals principles of chromosome structure throughout cellular differentiation

Abstract

Topological data analysis (TDA) is a mathematically well-founded set of methods to derive robust information about the structure and topology of data sets, and has been applied successfully in several biological contexts. Derived primarily from algebraic topology, TDA rigorously identifies persistent features in complex data, making it well-suited to better understand the key features of threedimensional chromosome structure. Chromosome structure has a significant influence in many diverse genomic processes and has recently been shown to relate to cellular differentiation. While there exist many methods to study specific substructures of chromosomes, we are still missing a global view of all geometric features of chromosomes. By applying TDA to the study of chromosome structure through differentiation across three cell lines, we provide insight into principles of chromosome folding and looping. We identify persistent connected components and one-dimensional topological features of chromosomes, and characterize them across cell types and stages of differentiation. Availability: Scripts to reproduce the results from this study can be found at https://github.com/Kingsford-Group/hictda

A Topological Data Analysis Approach on Predicting Phenotypes from Gene Expression Data

“…In life sciences, topological data analysis (TDA) has previously been applied in medical imaging [13,29], protein characterization [8,17], describing molecular architecture [24,26], and cancer genomics [3,21]. There have been several studies exploring TDA in genomics [7].…”

Topological Data Analysis of Vascular Disease: A Theoretical Framework

“…The analysis with TDA is based on persistent homology driven by the given topological space. Various forms of data from various applications are actively being used by researchers via TDA for possibly finding new knowledge out of the given data such as those in computational biology [4][5][6][7][8]. The work described in this paper is motivated by the clinical problem of the diagnosis of vascular disease.…”