Embryogenic remodeling of global chromatin and its role on structure of corresponding lattice representation

Abstract

Recent findings demonstrate that chromatin is functionally compartmentalized and packed into three dimensional multi-hierarchical structures that influence gene expression patterns. Using lattice theory tools we compare lattice representation of unstructured DNA, as identified in early-embryo phase, with compartmentalized DNA, as found in later embryo phases and in differentiated cells. By comparing these two representations we show that corresponding contact maps have elementary diagonal structure (unstructured DNA) and block diagonal structure (compartmentalized DNA). We show that a lattice corresponding to the binary relation with block diagonal structure is a product of so called Chinese lantern lattice. In contrast to Boolean lattice, formation of words in Chinese lantern lattice is highly restricted which is comparable to emergence of DNA compartmentalization during embryogenesis.

Keywords: Boolean lattice; DNA; Embryogenesis; Equivalence class; Rough set; TAD.