Kinetic Accessibility of Buried DNA Sites in Nucleosomes

Using a theoretical model for spontaneous partial DNA unwrapping from histones, we study the transient exposure of protein-binding DNA sites within nucleosomes. We focus on the functional dependence of the rates for site exposure and reburial on the site position, which is measurable experimentally and pertinent to gene regulation. We find the dependence to be roughly described by a random walker model. Close inspection reveals a surprising physical effect of flexibility-assisted barrier crossing, which we characterize within a toy model, the "semiflexible Brownian rotor."Comment: final version as published in Phys. Rev. Let

Evolution of populations expanding on curved surfaces

The expansion of a population into new habitat is a transient process that leaves its footprints in the genetic composition of the expanding population. How the structure of the environment shapes the population front and the evolutionary dynamics during such a range expansion is little understood. Here, we investigate the evolutionary dynamics of populations consisting of many selectively neutral genotypes expanding on curved surfaces. Using a combination of individual-based off-lattice simulations, geometrical arguments, and lattice-based stepping-stone simulations, we characterise the effect of individual bumps on an otherwise flat surface. Compared to the case of a range expansion on a flat surface, we observe a transient relative increase, followed by a decrease, in neutral genetic diversity at the population front. In addition, we find that individuals at the sides of the bump have a dramatically increased expected number of descendants, while their neighbours closer to the bump's centre are far less lucky. Both observations can be explained using an analytical description of straight paths (geodesics) on the curved surface. Complementing previous studies of heterogeneous flat environments, the findings here build our understanding of how complex environments shape the evolutionary dynamics of expanding populations.Comment: This preprint has also been posted to http://www.biorxiv.org with doi: 10.1101/406280. Seven pages with 5 figures, plus an appendix containing 3 pages with 1 figur

Connecting the Dots: Range Expansions across Landscapes with Quenched Noise

When biological populations expand into new territory, the evolutionary outcomes can be strongly influenced by genetic drift, the random fluctuations in allele frequencies. Meanwhile, spatial variability in the environment can also significantly influence the competition between sub-populations vying for space. Little is known about the interplay of these intrinsic and extrinsic sources of noise in population dynamics: When does environmental heterogeneity dominate over genetic drift or vice versa, and what distinguishes their population genetics signatures? Here, in the context of neutral evolution, we examine the interplay between a population's intrinsic, demographic noise and an extrinsic, quenched-random noise provided by a heterogeneous environment. Using a multi-species Eden model, we simulate a population expanding over a landscape with random variations in local growth rates and measure how this variability affects genealogical tree structure, and thus genetic diversity. We find that, when the heterogeneity is sufficiently strong, the population front is dominated by genealogical lineages that are pinned to a small number of optimal paths. The landscape-dependent statistics of these optimal paths then supersede those of the population's intrinsic noise as the main determinant of evolutionary dynamics. Remarkably, the statistics for coalescence of genealogical lineages, derived from those deterministic paths, strongly resemble the statistics emerging from demographic noise alone in uniform landscapes. This cautions interpretations of coalescence statistics and raises new challenges for inferring past population dynamics.Comment: 17 pages, 11 figure

Optimal flexibility for conformational transitions in macromolecules

Conformational transitions in macromolecular complexes often involve the reorientation of lever-like structures. Using a simple theoretical model, we show that the rate of such transitions is drastically enhanced if the lever is bendable, e.g. at a localized "hinge''. Surprisingly, the transition is fastest with an intermediate flexibility of the hinge. In this intermediate regime, the transition rate is also least sensitive to the amount of "cargo'' attached to the lever arm, which could be exploited by molecular motors. To explain this effect, we generalize the Kramers-Langer theory for multi-dimensional barrier crossing to configuration dependent mobility matrices.Comment: 4 pages, 4 figure

Quantitative test of the barrier nucleosome model for statistical positioning of nucleosomes up- and downstream of transcription start sites

The positions of nucleosomes in eukaryotic genomes determine which parts of the DNA sequence are readily accessible for regulatory proteins and which are not. Genome-wide maps of nucleosome positions have revealed a salient pattern around transcription start sites, involving a nucleosome-free region (NFR) flanked by a pronounced periodic pattern in the average nucleosome density. While the periodic pattern clearly reflects well-positioned nucleosomes, the positioning mechanism is less clear. A recent experimental study by Mavrich et al. argued that the pattern observed in S. cerevisiae is qualitatively consistent with a `barrier nucleosome model', in which the oscillatory pattern is created by the statistical positioning mechanism of Kornberg and Stryer. On the other hand, there is clear evidence for intrinsic sequence preferences of nucleosomes, and it is unclear to what extent these sequence preferences affect the observed pattern. To test the barrier nucleosome model, we quantitatively analyze yeast nucleosome positioning data both up- and downstream from NFRs. Our analysis is based on the Tonks model of statistical physics which quantifies the interplay between the excluded-volume interaction of nucleosomes and their positional entropy. We find that although the typical patterns on the two sides of the NFR are different, they are both quantitatively described by the same physical model, with the same parameters, but different boundary conditions. The inferred boundary conditions suggest that the first nucleosome downstream from the NFR (the +1 nucleosome) is typically directly positioned while the first nucleosome upstream is statistically positioned via a nucleosome-repelling DNA region. These boundary conditions, which can be locally encoded into the genome sequence, significantly shape the statistical distribution of nucleosomes over a range of up to ~1000 bp to each side.Comment: includes supporting materia

Heterogeneous environments and phage system to study effect of isolated obstacles.

<p><b>(A)</b> Classification of environments composed of regions that permit or prohibit reproduction based on the area fraction of favorable habitat, the fraction of the habitat that allows growth, <i>ρ</i>, and number <i>N</i> of features of linear size <i>L</i>. The features are embedded in the environment accessible to the spreading population. In this work, we focus on the ‘lake scenario’, i.e., regions that prohibit growth (red) distributed in an environment that permits growth (yellow). <b>(B)</b> Bacteriophage as an experimental model for expansion in heterogeneous environments: for bacteriophage T7, a lawn of susceptible <i>E. coli</i> (wild-type, WT) represents an environment of good growth conditions (yellow fluorescent marker), while a region with resistant <i>E. coli</i> (<i>waaC</i>Δ, red fluorescent marker) represents poor growth conditions. <b>(C)</b> Schematic diagram of the assay to observe plaque growth in well-defined reproducible environments. A digital representation serves as input for printing bacterials strains, both wild-type and phage-resistant, on an agar patch using a consumer inkjet printer. After the pattern has grown, phage is added and plaque growth is observed. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004615#sec011" target="_blank">Materials and Methods</a> for details. <b>(D)</b> Snapshots of plaque propagation (dark regions) around a rhombus-shaped area of resistant bacteria (red) printed in a sea of sensitive bacteria (yellow). The plaque front remains flat until it reaches the widest part of the obstacle. There, it curves into a region roughly as wide as the obstacle. Once the front reaches the top of the obstacle, a kink forms, which then slowly heals. This panel also illustrates <i>d</i>(<i>t</i>), the distance the front has traveled beyond the obstacle at time <i>t</i>, where <i>d</i> = 0 at the point of maximal width of the obstacle. See <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004615#pcbi.1004615.s001" target="_blank">S1 Video</a> for the complete time lapse information.</p