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Towards a robust algorithm to determine topological domains from colocalization data

1 Department of Applied Mathematics, National Research University Higher School of Economics, 101000, Moscow, Russia;
2 A.N. Nesmeyanov Institute of Organoelement Compounds of the Russian Academy of Sciences, 119991, Moscow, Russia;
3 Chemistry Department, Moscow State University, 119991, Moscow, Russia;
4 Physics Department, Moscow State University, 119991, Moscow, Russia

Special Issues: Chromatin and Epigenetics

One of the most important tasks in understanding the complex spatial organization of the genome consists in extracting information about this spatial organization, the function and structure of chromatin topological domains from existing experimental data, in particular, from genome colocalization (Hi-C) matrices. Here we present an algorithm allowing to reveal the underlying hierarchical domain structure of a polymer conformation from analyzing the modularity of colocalization matrices. We also test this algorithm on several model polymer structures: equilibrium globules, random fractal globules and regular fractal (Peano) conformations. We define what we call a spectrum of cluster borders, and show that these spectra behave strikingly di erently for equilibrium and fractal conformations, allowing us to suggest an additional criterion to identify fractal polymer conformations.
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