Ubiquitous nucleosome unwrapping in the yeast genome

Nucleosome core particle is a dynamic structure -- DNA may transiently peel off the histone octamer surface due to thermal fluctuations or the action of chromatin remodeling enzymes. Partial DNA unwrapping enables easier access of DNA-binding factors to their target sites and thus may provide a dominant pathway for effecting rapid and robust access to DNA packaged into chromatin. Indeed, a recent high-resolution map of distances between neighboring nucleosome dyads in \emph{S.cerevisiae} shows that at least 38.7\% of all nucleosomes are partially unwrapped. The extent of unwrapping follows a stereotypical pattern in the vicinity of genes, reminiscent of the canonical pattern of nucleosome occupancy in which nucleosomes are depleted over promoters and well-positioned over coding regions. To explain these observations, we developed a biophysical model which employs a 10-11 base pair periodic nucleosome energy profile. The profile, based on the pattern of histone-DNA contacts in nucleosome crystal structures and the idea of linker length discretization, accounts for both nucleosome unwrapping and higher-order chromatin structure. Our model reproduces the observed genome-wide distribution of inter-dyad distances, and accounts for patterns of nucleosome occupancy and unwrapping around coding regions. At the same time, our approach explains \emph{in vitro} measurements of accessibility of nucleosome-covered binding sites, and of nucleosome-induced cooperativity between DNA-binding factors. We are able to rule out several alternative scenarios of nucleosome unwrapping as inconsistent with the genomic data.Comment: 49 pages; 15 figure

Statistical Physics of Evolutionary Trajectories on Fitness Landscapes

Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role in evolutionary theory. The topography of fitness landscapes and its effect on evolutionary dynamics have been extensively studied in the literature. We will survey the current research knowledge in this field, focusing on a recently developed systematic approach to characterizing path lengths, mean first-passage times, and other statistics of the path ensemble. This approach, based on general techniques from statistical physics, is applicable to landscapes of arbitrary complexity and structure. It is especially well-suited to quantifying the diversity of stochastic trajectories and repeatability of evolutionary events. We demonstrate this methodology using a biophysical model of protein evolution that describes how proteins maintain stability while evolving new functions