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 Saccharomyces 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 ∼1,000 bp to each side.Author Summary: Within the last five years, knowledge about nucleosome organization on the genome has grown dramatically. To a large extent, this has been achieved by an increasing number of experimental studies determining nucleosome positions at high resolution over entire genomes. Particular attention has been paid to promoter regions, where a canonical pattern has been established: a nucleosome-free region with pronounced adjacent oscillations in the nucleosome density. Here we tested to what extent this pattern may be quantitatively described by a minimal physical model, a one-dimensional gas of impenetrable particles, commonly referred to as the “Tonks gas.” In this model, density oscillations occur close to a boundary at dense packing. Our systematic quantitative analysis reveals that, in an average over many promoters, a Tonks gas model can indeed account for the nucleosome organization to both sides of the nucleosome-free region, if one allows for different boundary conditions at the two edges. On the downstream side, a single nucleosome is typically directly positioned such that it forms an obstacle for the neighboring nucleosomes, while such a barrier nucleosome is typically missing on the upstream side.