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Abstract

With the rapid development of modern computational techniques, more complex systems have been found to have their global organization principles. In this thesis, we aim to establish a method to systematically unravel chromosome organization principles, which can serve as a general framework for the analysis of 3D genome architecture and other systems.

We start the analysis with crucial physical properties. We compute the contact probability curve for different polymer models and conclude that the asymptotic behavior of the contact probability curve does not depend on the definition of contact. Moreover, the effect of bending rigidity and compartmentalization is examined. The persistence lengths for homogeneous and heterogeneous semi-flexible self-avoiding walks are computed, and it is observed that the persistence length in the heterogeneous case is systematically smaller than in the homogeneous case.

To access genome-wide organizational patterns, experimental nucleosome positioning data for Candida albicans are investigated. Specifically, by performing hierarchical clustering on the auto-correlation function of the data, repeated patterns are observed across the entire genome, which supports a classification beyond the typical categories of heterochromatin and euchromatin.

In addition to observing the patterns, we successfully develop a quantitative characterization of intra-chromosomal organizational structure by extracting the inter-nucleosomal potential. These effective potentials capture the interaction between nucleosomes that incorporates the dynamics of related complexes.Moreover, an essential thermodynamic property, namely isothermal compressibility, is computed from the potential. By applying k-means clustering to potential parameters and thermodynamic compressibility, genome-wide clustering result is obtained, and information that leads to the genomic mechanical code is collected.

Finally, we focus on patterns of local structures. The organization principles of the CTCF (abbreviation for nucleotide sequence CCCTC-binding factor) are revealed. The averaged nucleosome frequency near CTCF binding sites is computed, and the corresponding spatial structure is observed for the first time.