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

Biophysical Fitness Landscapes for Transcription Factor Binding Sites

Evolutionary trajectories and phenotypic states available to cell populations are ultimately dictated by intermolecular interactions between DNA, RNA, proteins, and other molecular species. Here we study how evolution of gene regulation in a single-cell eukaryote S. cerevisiae is affected by the interactions between transcription factors (TFs) and their cognate genomic sites. Our study is informed by high-throughput in vitro measurements of TF-DNA binding interactions and by a comprehensive collection of genomic binding sites. Using an evolutionary model for monomorphic populations evolving on a fitness landscape, we infer fitness as a function of TF-DNA binding energy for a collection of 12 yeast TFs, and show that the shape of the predicted fitness functions is in broad agreement with a simple thermodynamic model of two-state TF-DNA binding. However, the effective temperature of the model is not always equal to the physical temperature, indicating selection pressures in addition to biophysical constraints caused by TF-DNA interactions. We find little statistical support for the fitness landscape in which each position in the binding site evolves independently, showing that epistasis is common in evolution of gene regulation. Finally, by correlating TF-DNA binding energies with biological properties of the sites or the genes they regulate, we are able to rule out several scenarios of site-specific selection, under which binding sites of the same TF would experience a spectrum of selection pressures depending on their position in the genome. These findings argue for the existence of universal fitness landscapes which shape evolution of all sites for a given TF, and whose properties are determined in part by the physics of protein-DNA interactions

Single temperature for Monte Carlo optimization on complex landscapes

We propose a new strategy for Monte Carlo (MC) optimization on rugged multidimensional landscapes. The strategy is based on querying the statistical properties of the landscape in order to find the temperature at which the mean first passage time across the current region of the landscape is minimized. Thus, in contrast to other algorithms such as simulated annealing (SA), we explicitly match the temperature schedule to the statistics of landscape irregularities. In cases where this statistics is approximately the same over the entire landscape, or where non-local moves couple distant parts of the landscape, single-temperature MC will outperform any other MC algorithm with the same move set. We also find that in strongly anisotropic Coulomb spin glass and traveling salesman problems, the only relevant statistics (which we use to assign a single MC temperature) is that of irregularities in low-energy funnels. Our results may explain why protein folding in nature is efficient at room temperatures.Comment: 5 pages, 3 figure

An adaptive Bayesian approach to gradient-free global optimization

Many problems in science and technology require finding global minima or maxima of various objective functions. The functions are typically high-dimensional; each function evaluation may entail a significant computational cost. The importance of global optimization has inspired development of numerous heuristic algorithms based on analogies with physical, chemical or biological systems. Here we present a novel algorithm, SmartRunner, which employs a Bayesian probabilistic model informed by the history of accepted and rejected moves to make a decision about the next random trial. Thus, SmartRunner intelligently adapts its search strategy to a given objective function and moveset, with the goal of maximizing fitness gain (or energy loss) per function evaluation. Our approach can be viewed as adding a simple adaptive penalty to the original objective function, with SmartRunner performing hill ascent or descent on the modified landscape. This penalty can be added to many other global optimization algorithms. We explored SmartRunner's performance on a standard set of test functions, finding that it compares favorably against several widely-used alternatives: simulated annealing, stochastic hill climbing, evolutionary algorithm, and taboo search. Interestingly, adding the adaptive penalty to the first three of these algorithms considerably enhances their performance. We have also employed SmartRunner to study the Sherrington-Kirkpatrick (SK) spin glass model and Kauffman's NK fitness model - two NP-hard problems characterized by numerous local optima. In systems with quenched disorder, SmartRunner performs well compared to the other global optimizers. Moreover, in finite SK systems it finds close-to-optimal ground-state energies averaged over disorder.Comment: 25 pages, 7 figures, 2 tables in the main text; 22 pages, 18 figures in the supplemen