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 –and in relation to one-another– 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. At 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. This 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 ‘barrier’ –in this case, the
strongly positioned +1 nucleoseome nearest (downstream) to the
transcription start site. It will be shown that accounting for
‘softness’ 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. While
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. Next, 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
‘landscape’ 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 ‘amoeba’ optimization
algorithm is adapted to fit the available data, as described in
Chapter 4. In 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 ‘hard rods’ 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 ‘cramming’; 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.
Finally, 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.