One-dimensional lattice gasses with soft interaction
Eukaryotic DNA must undergo several levels of organized compaction in order to be packaged within the spatial confines of the cell nucleus. The first level of this packaging involves the formation of nucleosomes by wrapping DNA around histone-octamers. The arrangement of nucleosomes along the length of the DNA has important influences on the way higher levels of packaging are organized. In addition to this structural role, the positioning of nucleo- somes along the genome \u2013and in relation to one-another\u2013 has important implications for the regulation of genes. Tightly-packaged nucleosomes tend to occlude promoter regions from transcription machinery, while looser configurations tend to be up-regulated.\n\nAt this level, nucleosome positioning can be treated as an effective one-dimensional system. Many factors contribute to the positioning of nucleosomes along the DNA: genetic sequence, active remodellers, and competition for binding sites with other binding proteins and with one-another all play a role. How to disentangle these effects is a central question that will be explored in this work using yeast as a model organism. In the process, however, more general physical questions will arise regarding the kinetics of one-dimensional adsorption/desorption processes. The over-arching goal is to provide a bridge from biophysical, data-driven work to more pure statistical physics; thus the work is comprised mainly of 5 somewhat separate, but related projects.\n\nThis thesis will begin with an overview of background information and introductory observa- tions in Chapter 1 to provide context. Chapter 2 will then focus on equilibrium properties of nucleosome positioning. Experimental nucleosome data from a dozen different species of yeast will be used to model the pattern of nucleosome formation near a \u2018barrier\u2019 \u2013in this case, the strongly positioned +1 nucleoseome nearest (downstream) to the transcription start site. It will be shown that accounting for \u2018softness\u2019 in nucleosomes, due to known biophysical effects, allows for a unified model of nucleosome positioning. Since nucleosomes are rela- tively structurally consistent across very different species, this represents a model that is both parsimonious and physically sound. The published work studying the nucleosome po- sitioning patterns of a dozen species of yeast is included and relies on equilibrium statistical mechanics, as well as a Monte Carlo numeric scheme to account for active processes.\n\nWhile histones clearly dominate the landscape of DNA binding positions, important loci ad- mit binding by other proteins such as transcription factors which serve to regulate genetic transcription and influence nucleosomal patterning. In Chapter 3, we consider the interac- tion of small transcription factors which bind specifically to loci on the DNA and shift the positioning of the neighboring nucleosome, with a corresponding domino effect on other nu- cleosomes in the vicinity. Such shifts in nucleosome patterns can create nucleosome-mediated cooperativity between transcription factors, even when separated by intervening nucleosomes.\n\nNext, in Chapter 4, we will consider the role of the genetic sequence in nucleosome positioning, an effect which has also been the subject of considerable research. We will refer to this as the energetic \u2018landscape\u2019 of the genome and present a new way of inferring this sequence- preference from nucleosome positioning data. We will see that the experimentally observed density patterns in yeast, together with the interaction-energy of neighboring nucleosomes that was derived in Chapter 2, can be used to quantify this sequence preference. This effort, however, is complicated by the lack of specific data characterizing the 2-body correlation between neighboring nucleosomes. For this reason, the \u2018amoeba\u2019 optimization algorithm is adapted to fit the available data, as described in Chapter 4.\n\nIn Chapter 5, the focus will shift to the dynamics of one-dimensional filling. It will be shown that the kinetic process of equilibration through one-dimensional reversible adsorption is qualitatively different, and much faster, when one allows for soft-interaction of neighboring particles. It has long been known that \u2018hard rods\u2019 adsorbing randomly in 1 dimension undergo a jamming phenomenon which can only be resolved into densely packed arrays through very slow collective rearrangement processes. Upon introduction of softness to the nucleosome model, however, jamming is circumvented by a new phase we term \u2018cramming\u2019; equilibration can then proceed orders of magnitude faster. This will be reviewed with specific application to the problem of nucleosome adsorption which has been of interest recently in light of new experimental work and the attached publication highlights the main findings.\n\nFinally, the dynamics of one-dimensional adsorption-desorption with soft-interacting particles are considered in a more general way. With finite neighbor interactions, a rich new set of dynamics emerges, including a curious non-monotonic density trace in time. The theoretical underpinnings of this effect will be provided in a manuscript, accepted for publication, that concludes this text.