Regulation of the nucleosome repeat length in vivo by the DNA sequence, protein concentrations and long-range interactions

Abstract

The nucleosome repeat length (NRL) is an integral chromatin property important for its biological functions. Recent experiments revealed several conflicting trends of the NRL dependence on the concentrations of histones and other architectural chromatin proteins, both in vitro and in vivo, but a systematic theoretical description of NRL as a function of DNA sequence and epigenetic determinants is currently lacking. To address this problem, we have performed an integrative biophysical and bioinformatics analysis in species ranging from yeast to frog to mouse where NRL was studied as a function of various parameters. We show that in simple eukaryotes such as yeast, a lower limit for the NRL value exists, determined by internucleosome interactions and remodeler action. For higher eukaryotes, also the upper limit exists since NRL is an increasing but saturating function of the linker histone concentration. Counterintuitively, smaller H1 variants or non-histone architectural proteins can initiate larger effects on the NRL due to entropic reasons. Furthermore, we demonstrate that different regimes of the NRL dependence on histone concentrations exist depending on whether DNA sequence-specific effects dominate over boundary effects or vice versa. We consider several classes of genomic regions with apparently different regimes of the NRL variation. As one extreme, our analysis reveals that the period of oscillations of the nucleosome density around bound RNA polymerase coincides with the period of oscillations of positioning sites of the corresponding DNA sequence. At another extreme, we show that although mouse major satellite repeats intrinsically encode well-defined nucleosome preferences, they have no unique nucleosome arrangement and can undergo a switch between two distinct types of nucleosome positioning.

Figure 1. Lattice models to calculate nucleosome/TF binding landscapes in chromatin.

A) All-or-none models require that a DNA region is either within a nucleosome or bound by a transcription factor. B) Advanced view on co-binding of a TF and histone octamer to the same DNA region (top), and the corresponding lattice model (bottom), which takes into account the possibility of partial nucleosome unwrapping. C) Taking into account linker histones requires the introduction of long-range interactions between DNA-bound proteins. D), E) The scheme of the method of NRL calculation. Firstly, the oscillations of the nucleosome density are plotted around the boundary of interest (for example, an end of the DNA segment would be appropriate as a boundary). Then the coordinates of the peaks from (D) are collected and fitted with a linear function. The slope of the line in (E) determines the NRL.

Figure 2. NRL as a function of thermodynamic parameters such as the concentration of bound nucleosome core particles (A), maximum allowed length of DNA unwrapping from the nucleosome (B), contact cooperativity between nucleosomes (C), long-range anti-cooperativity between neighboring nucleosomes (D), ratio of linker histone per nucleosome (with m(linker) = 15 bp) (E), and the effective size of the linker protein in terms of covered DNA base pairs (F).

Unless stated otherwise in the figure, the following parameters were used: K _NCP* c ₀(NCP) = 0.7; K _linker = 2·10⁹ M⁻¹.

Figure 3. Nucleosome occupancy patterns around TSS in S. cerevisiae explained by the lattice binding model.

Dots correspond to the experimental data ; straight lines are the nucleosome density patterns estimated by TFnuc algorithm with the following model parameters: A) “Tonks gas” model: N = 4000 bp, K _NCP = 3·10⁶ M⁻¹; c ₀(NCP) = 10⁻⁶ M; B) Nucleosome unwrapping model: K _NCP = 3·10⁶ M⁻¹; c ₀(NCP) = 10⁻⁶ M; h _max = 40; C) Linker histone model: K _NCP = 1·10⁵ M⁻¹; c ₀(NCP) = 10⁻⁶ M; K _linker = 9·10⁵ M⁻¹; c ₀(linker) = 10⁻⁶ M; m(linker) = 15 bp; h _max = 15 bp; D) Long-range interaction model: K _NCP = 3·10⁶ M⁻¹; c ₀(NCP) = 10⁻⁶ M; h _max = 40 bp; w(0:30, NCP, NCP) = 0.

Figure 4. NRL dependence on the concentration of linker histones.

A) Experimentally determined NRL as a function of the concentration of histone hH1.4 . B) Theoretically predicted NRL as a function of H1 activity. K _H1 – binding constant; [H1] – concentration of free H1 in solution; m(H1) = 15 bp. C) A scheme illustrating the refined model for nucleosome-H1 arrangement: different configurations of bound H1 around nucleosome are allowed, but not more than a critical number of H1 per nucleosome. D) Dots - experimental NRL data from Woodcock et al. for different mouse cell types. Solid line - theoretical prediction. m(H1) = 15 bp, K _H1* c ₀(H1) = 0.0035, w(0, NCP, NCP) = 11.

Figure 5. Nucleosome oscillations around CTCF and Pol2 ChIP-seq peaks reveal DNA sequence modulation.

A) Red and green lines - experimental nucleosomes in ESCs around Pol2 sites using MNase-seq data from and , correspondingly. Black and blue lines - average nucleosome occupancies around Pol2 ChIP-seq peaks predicted from the DNA sequence without competition with Pol2, at different core histone concentrations: K _NCP*c ₀(NCP) = 1.4·10⁻⁶ and K _NCP*c ₀(NCP) = 1.5 respectively. B) Heat map of the nucleosome density for all individual genomic regions used in the calculation of the average profile in panel A. C) Raw energy of nucleosome formation averaged for the same genomic regions as in A using the method of Kaplan et al (black line), and the difference between the raw energy and its fit with the 90^th power polynomial regression, followed by the Fourier transformation. Changing the power of the polynomial regression in the range >50 did not affect the calculated NRL. D) Theoretical nucleosome occupancies in ESCs around CTCF sites predicted from sequence as in (A), black line: K _NCP*c₀(NCP) = 1.4·10⁻⁶, blue line: K _NCP*c₀(NCP) = 1.5. E) Red line - experimental nucleosome occupancies in ESCs around CTCF sites. Black line - theoretical nucleosome occupancies predicted from DNA sequence including competition with CTCF. h _max = 40 bp; V = 40 bp K _NCP*c ₀(NCP) = 0.2; K _CTCF*c ₀(CTCF) = 0.5. F) The probability to find a strong Trifonov's nucleosome determined by the (R₅Y₅)₁₁ pattern, as a function of the distance from CTCF.

Figure 6. The NRL in mouse pericentric heterochromatin is not determined by the sequence of the major satellite repeats.

A) Regular nucleosome positioning around tandems of repeating 234-bp major satellite repeats predicted from the DNA sequence. B) Frequency of the left and right ends of nucleosomal DNA fragments obtained with paired-end MNase-seq . C) Autocorrelation of the nucleosome start site positions from Panel B reveals a 10-bp periodicity. D) Frequency of the left and right ends of MNase-seq nucleosomal DNA fragments size-selected in the interval [145 bp; 150 bp].