Modelling Electrostatic Interactions and Solvation in Chromatin: from the single nucleosome towards the chromatin fibre

Chromatin is a complex of proteins and DNA found in the nuclei of eukaryotic cells. It reinforces the DNA and its topology tunes DNA transcription and gene expression. It is formed by nucleosomes, structures composed of an octameric protein core and approximately 147 base pairs of DNA. Chromatin is an extremely complex system, the behaviour of which is ruled by both mechanical and electrostatic factors that are depend on its structure, and biomolecular interactions occurring in the cell nucleus. In this thesis, I analyse chromatin compaction from an electrostatic perspective and focus on the role of electrostatics and solvation as determinants of the topology of chromatin. I examine the effect of the histone tails and propose a methodology to connect electrostatic calculations to the structural and functional features of protein-DNA systems. This methodology can also be combined with coarse-grained representations. I study the electrostatic forces acting on the phosphate atoms of the DNA backbone. I investigate the electrostatic origins of effects such as different stages in DNA unwrapping, nucleosome destabilisation upon histone tail truncation, and the role of specific arginines and lysines undergoing Post - Translational Modifications. I find that the positioning of the histone tails can oppose the attractive pull of the histone core, locally deform the DNA, and tune DNA unwrapping. I conduct an analysis of the porosity of nucleosomes and related to the importance of solvation phenomena. I complement and support my computational findings on nucleosome electrostatic interactions experimental Zeta Potential and Dynamic Light Scattering measurements on single nucleosomes under varying ionic concentrations, providing information on the surface charge and the size of nucleosomes. I present a comprehensive study of the electrostatic interactions between nucleosome pairs sampling different translations and rotations. My analysis aims to provide a cohesive description of nucleosome electrostatic interactions in the chromatin fibre, combining information on the energetics of different relative positions of nucleosomes, especially in very tight packing situations. In addition to numerical estimates of electrostatic interaction energy of nucleosomes at different relative distances and orientations, obtained within the Poisson-Boltzmann framework, I present their approximation by analytical asymptotic expressions, where nucleosomes are approximated as monopoles and dipoles centred in dielectric spheres immersed in an electrolytic solution. I am able to identify a non-linearity region around the nucleosomes, and to exploit the fact that that in points outside that region the electrostatic potential can be described by the linearised Poisson-Boltzmann Equation.