Abstract
We propose a new computational method for exploring chromatin structural organization based on Markov State Modelling of Hi-C data represented as an interaction network between genomic loci. A Markov process describes the random walk of a traveling probe in the corresponding energy landscape, mimicking the motion of a biomolecule involved in chromatin function. By studying the metastability of the associated Markov State Model upon annealing, the hierarchical structure of individual chromosomes is observed, and corresponding set of structural partitions is identified at each level of hierarchy. Then, the notion of effective interaction between partitions is derived, delineating the overall topology and architecture of chromosomes. Mapping epigenetic data on the graphs of intra-chromosomal effective interactions helps in understanding how chromosome organization facilitates its function. A sketch of whole-genome interactions obtained from the analysis of 539 partitions from all 23 chromosomes, complemented by distributions of gene expression regulators and epigenetic factors, sheds light on the structure-function relationships in chromatin, delineating chromosomal territories, as well as structural partitions analogous to topologically associating domains and active / passive epigenomic compartments. In addition to the overall genome architecture shown by effective interactions, the affinity between partitions of different chromosomes was analyzed as an indicator of the degree of association between partitions in functionally relevant genomic interactions. The overall static picture of whole-genome interactions obtained with the method presented in this work provides a foundation for chromatin structural reconstruction, for the modelling of chromatin dynamics, and for exploring the regulation of genome function. The algorithms used in this study are implemented in a freely available Python package ChromaWalker (https://bitbucket.org/ZhenWahTan/chromawalker).
Highlights
The packing of two meters of DNA in the few-micrometer nucleus results in a structure that performs multiple roles, from forming a structural scaffold of chromatin to facilitating active expression and silencing of genetic material [1, 2]
We interpret the Hi-C frequencies of chromatin interactions in terms of pairwise contact energies, obtaining corresponding energy landscape that represents the structure and interactions in chromatin. The ruggedness of this landscape is explored by the random walk of a travelling probe, which is formalized in the framework of a Markov State Model
Structural partitions determined by the basins in the energy landscape are, naturally obtained at different levels of hierarchy without any preliminary assumptions
Summary
The packing of two meters of DNA in the few-micrometer nucleus results in a structure that performs multiple roles, from forming a structural scaffold of chromatin to facilitating active expression and silencing of genetic material [1, 2]. With the development of the chromosome conformation capture (3C) protocol [8], it has become possible to study chromatin interactions between distant genomic loci. In less than a decade, the original 3C protocol evolved from the analysis of selected pairs of genomic loci to the detection of pairwise interactions between loci and the rest of the genome using chromosome conformation capture on-chip (one-to-all, 4C, [20]), carbon copy (many-tomany, 5C, [21]), and high-throughput 3C (all-to-all, Hi-C, [22]). Improvement of the signal-noise ratio was achieved by performing DNA proximity ligation before nuclear lysis, implemented in in-situ Hi-C [23]
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