Topological Data Analysis of Single-Cell Hi-C Contact Maps
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Due to recent breakthroughs in high-throughput sequencing, it is now possible to use chromosome conformation capture (CCC) to understand the three dimensional conformation of DNA at the whole genome level, and to characterize it with the so-called contact maps. This is very useful since many biological processes are correlated with DNA folding, such as DNA transcription. However, the methods for the analysis of such conformations are still lacking mathematical guarantees and statistical power. To handle this issue, we propose to use the Mapper, which is a standard tool of Topological Data Analysis (TDA) that allows one to efficiently encode the inherent continuity and topology of underlying biological processes in data, in the form of a graph with various features such as branches and loops. In this article, we show how recent statistical techniques developed in TDA for the Mapper algorithm can be extended and leveraged to formally define and statistically quantify the presence of topological structures coming from biological phenomena, such as the cell cyle, in datasets of CCC contact maps.
This work has been funded by NIH grants (U54 CA193313 and U54 CA209997) and Chan Zuckerberg Initiative pilot grant.
- 1.Alan Agresti. Categorical data analysis, 3rd edition. Wiley, 2012.Google Scholar
- 6.Mathieu Carrière and Steve Oudot. Structure and Stability of the 1-Dimensional Mapper. Foundations of Computational Mathematics, 2017.Google Scholar
- 9.Tamal Dey, Facundo Mémoli, and Yusu Wang. Multiscale Mapper: Topological Summarization via Codomain Covers. In Proceedings of the 27th Symposium on Discrete Algorithms, pages 997–1013, 2016.Google Scholar
- 10.Josée Dostie, Todd Richmond, Ramy Arnaout, Rebecca Selzer, William Lee, Tracey Honan, Eric Rubio, Anton Krumm, Justin Lamb, Chad Nusbaum, Roland Green, and Job Dekker. Chromosome Conformation Capture Carbon Copy (5C): A massively parallel solution for mapping interactions between genomic elements. Genome Research, 16(10):1299–1309, 2006.CrossRefGoogle Scholar
- 14.Erez Lieberman-Aiden, Nynke van Berkum, Louise Williams, Maxim Imakaev, Tobias Ragoczy, Agnes Telling, Ido Amit, Bryan Lajoie, Peter Sabo, Michael Dorschner, Richard Sandstrom, Bradley Bernstein, Michael Bender, Mark Groudine, Andreas Gnirke, John Stamatoyannopoulos, Leonid Mirny, Eric Lander, and Job Dekker. Comprehensive Mapping of Long-Range Interactions Reveals Folding Principles of the Human Genome. Science, 326(5950):289–293, 2009.CrossRefGoogle Scholar
- 17.Fionn Murtagh and Pedro Contreras. Algorithms for hierarchical clustering: an overview. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 2(1):86–97, 2012.Google Scholar
- 18.Elizabeth Munch and Bei Wang. Convergence between Categorical Representations of Reeb Space and Mapper. In Proceedings of the 32nd Symposium on Computational Geometry, volume 51, pages 53:1–53:16, 2016.Google Scholar
- 20.Steve Oudot. Persistence Theory: From Quiver Representations to Data Analysis. Number 209 in Mathematical Surveys and Monographs. American Mathematical Society, 2015.Google Scholar
- 22.Marieke Simonis, Petra Klous, Erik Splinter, Yuri Moshkin, Rob Willemsen, Elzo de Wit, Bas van Steensel, and Wouter de Laat. Nuclear organization of active and inactive chromatin domains uncovered by chromosome conformation capture-on-chip (4C). Nature Genetics, 38:1348–1354, 2006.CrossRefGoogle Scholar
- 23.Gurjeet Singh, Facundo Mémoli, and Gunnar Carlsson. Topological Methods for the Analysis of High Dimensional Data Sets and 3D Object Recognition. In Symposium on Point Based Graphics, pages 91–100, 2007.Google Scholar