Studying Phase Separation in the Nucleus

Abstract

The organization of eukaryotic DNA into chromatin and higher order structures through histone proteins serves to be important in packaging DNA inside the nucleus and plays a key role in regulating the expression of genes. Gaining insight into the mechanisms behind the formation of dense, heterochromatic regions can lead to important developments in the study of abnormal gene expression. Phase separation induced by interaction of histones with other proteins has emerged as a potential mechanism governing chromatin condensation. A number of proteins like Heterochromatin = Protein 1 (HP1) have been identified in different organisms which preferentially bind to histones possessing post-translation modifications like methylation to form transient bridges between them. These protein bridges can condense regions of chromatin containing such methylated histones. In this work, we made an attempt to understand the effect of the bridging interaction on the arrangement of histone octamers along the DNA strand. In the following chapters, we present a statistical mechanical model of chromatin as a one dimensional lattice with binding sites for histone octamers. We used transfer matrix formalism to determine the partition function for the system. This was followed by an analysis of quantities like the occupancy of the sites by histone octamers, the proportion of bound histone octamers with post-translation modifications, the correlation function, and the arrangement of histones along the lattice subject to variation in concentration of histones and HP1. We complemented our theoretical analysis with Monte-Carlo simulations. We found that an increase in HP1 concentration led to clustering of methylated histone octamers, which can induce heterochromatin formation. Using Monte Carlo simulations we also found that spatial heterogeneities can localize histone octamers in specific regions of the lattice. The model can be used to study preferential binding of histones to certain loci on the DNA to induce silencing. It can serve as a starting point for the investigation of chromatin condensation through histone interactions. The relationship between protein concentrations and histone occupancy obtained using the one dimensional model could be incorporated into a polymer description of chromatin to investigate phase separation and heterochromatin formation.