DNA combinatorial messages and Epigenomics: The case of chromatin organization and nucleosome occupancy in eukaryotic genomes

Epigenomics is the study of modifications on the genetic material of a cell that do not depend on changes in the DNA sequence, since those latter involve specific proteins around which DNA wraps. The end result is that Epigenomic changes have a fundamental role in the proper working of each cell in Eukaryotic organisms. A particularly important part of Epigenomics concentrates on the study of chromatin, that is, a fiber composed of a DNA-protein complex and very characterizing of Eukaryotes. Understanding how chromatin is assembled and how it changes is fundamental for Biology. In more than thirty years of research in this area, Mathematics and Theoretical Computer Science have gained a prominent role, in terms of modeling and mining, regarding in particular the so-called 10 nm fiber. Starting from some very basic notions of Biology, we briefly illustrate the recent advances obtained via laboratory experiments on the organization and dynamics of chromatin. Then, we mainly concentrate our attention on the contributions given by Combinatorial and Informational Methodologies, that are at the hearth of Theoretical Computer Science, to the understanding of mechanisms determining the 10 nm fiber. We conclude highlighting several directions of investigation that are perceived as important and where Theoretical Computer Science can provide high impact results