Predicting nucleosome positions on the DNA: combining intrinsic sequence preferences and remodeler activities

Abstract

Nucleosome positions on the DNA are determined by the intrinsic affinities of histone proteins to a given DNA sequence and by the ATP-dependent activities of chromatin remodeling complexes that can translocate nucleosomes with respect to the DNA. Here, we report a theoretical approach that takes into account both contributions. In the theoretical analysis two types of experiments have been considered: in vitro experiments with a single reconstituted nucleosome and in vivo genome-scale mapping of nucleosome positions. The effect of chromatin remodelers was described by iteratively redistributing the nucleosomes according to certain rules until a new steady state was reached. Three major classes of remodeler activities were identified: (i) the establishment of a regular nucleosome spacing in the vicinity of a strong positioning signal acting as a boundary, (ii) the enrichment/depletion of nucleosomes through amplification of intrinsic DNA-sequence-encoded signals and (iii) the removal of nucleosomes from high-affinity binding sites. From an analysis of data for nucleosome positions in resting and activated human CD4(+) T cells [Schones et al., Cell 132, p. 887] it was concluded that the redistribution of a nucleosome map to a new state is greatly facilitated if the remodeler complex translocates the nucleosome with a preferred directionality.

Figure 1.

A schematic view of the remodeler action and the corresponding theoretical models. (A) Once a remodeler encounters a nucleosome, it removes it with a probability P_m, which may depend on the nucleosome and remodeler type and the DNA sequence. Nucleosome remodeling may be realized either as a sliding left/right without dissociation, or as a complete nucleosome eviction. (B) Nucleosome positioning may be viewed as an equilibrium thermodynamic process allowing nucleosome dissociation and rebinding to a one-dimensional DNA lattice of elementary units (base pairs) numbered by the index n. Nucleosome binding is characterized by the effective affinity K_n = K(n) and the nucleosome length m = 147 bp. (C) A single-nucleosome translocation model considers one nucleosome on a short DNA segment as studied in in vitro experiments with reconstituted nucleosomes. Nucleosome dissociation and sliding off from the DNA ends is prohibited. The model has four parameters: the remodeling probability P_m, the elementary remodeler step s and the probabilities to move the nucleosome to the left (P_–s) and to the right (P_+s). (D) A multi-nucleosome translocation model describes nucleosome repositioning in vivo. It is based on the model (C), but the probabilities to move the nucleosome to the left and to the right now depend on the occupancy of the target site by other nucleosomes.

Figure 2.

Nucleosome positioning in vitro at the Drosophila hsp70 promoter region (359 bp). (A) Nucleosome positions determined by footprinting (37). (B) Relative intensities of nucleosome positioning peaks determined from our scan of the electrophoresis experiments (16). The black line shows nucleosome start site probabilities, and the red line is a calculated probability that a given DNA base pair is occupied by a nucleosome. The blue line shows a predicted start site probability assuming that the positioning is determined solely by the DNA sequence according to the algorithm by Segal, Widom and co-workers (25,45).

Figure 3.

Experimental nucleosome occupancy scores in the resting (black lines) and activated (red lines) human CD4P^+P T cells (33) compared with the predictions for nucleosome positioning based on the DNA sequence (blue lines) according to the algorithm by Segal, Widom and coworkers (25,45). (A) Nucleosome occupancies for a 2-kb enhancer region, which is involved in the IL-4 and IL-13 gene regulation during T-cell activation (Chr5: 132 026 342 to 132 1028 342). (B) Autocorrelation functions calculated for a 40-kb interval including the enhancer region above.

Figure 4.

Probabilities that a nucleosome starts at the DNA site n, calculated in the frame of the single-nucleosome translocation model in the absence of remodelers (red lines) and in the presence of remodelers (blue lines), 10 000 iterations. (A) Repositioning probabilities are equal for all sites: P_m = 1, s = 50. (B) Repositioning probabilities correlate with thermal nucleosome positioning probabilities: P_m = 1/K², s = 10. (C) The initial map is calculated assuming that there is no specific binding at the distal DNA sites. The remodeler can move nucleosomes from any site but the DNA ends [P_m (1 < n < N) = 1, P_m (n = 1, N) = 1, s = 10]. (D and E) Remodeler-positioner does not translocate a nucleosome from a position n = 110 [P_m (n = 110) = 0, P_m (n ≠ 110) = 1, s = 50] (D) and s = 10 (E). (F) Remodeler removes a nucleosome from site n = 110 [P_m (n = 110) = 1, P_m (n ≠ 110) = 1/K, s = 10].

Figure 5.

A quantitative analysis of in vivo data using the equilibrium-binding model. The experimental nucleosome occupancy scores for the resting (black) and activated (red) CD4⁺ T cell reported by Schones et al. (33) (A) were transformed into the nucleosome start site probabilities (B). Then, relative binding affinities were assigned as K(n) = P(n)/(1 – P(n) and used to calculate equilibrium binding maps shown in the (C). Three main remodeler activities predicted from single-nucleosome modeling (Figure 4) are observed at this genomic region as indicated by the arrows. The nucleosomes 4 and 10 are removed, the occupancies of nucleosomes 6, 8 and 9 and the nucleosomes between these sites are amplified and shifted due to the change of their local boundary conditions as imposed by the flanking nucleosomes.

Figure 6.

Modeling multi-nucleosome redistribution by a remodeler-spacer. (Bottom) Shows nucleosome start site probabilities predicted from the intrinsic affinities according to the algorithm by Segal, Widom and coworkers (25,45). (Top) Shows the nucleosome maps recalculated iteratively according to Equations (7–9) for the remodeler-spacer starting from the thermal equilibrium distribution. The number of iterations is indicated in the Figure. (A) The remodeling probability is equal for all sites (P_m = 1, s = 10). (B) The remodeling probability is negatively correlated with intrinsic histone-DNA affinities [P_m(n) = 1/exp(K(n)), s = 10].

Figure 7.

Calculating multi-nucleosome redistribution patterns by a sequence-specific remodeler. The two plots at the bottom show experimental nucleosome start site probabilities in the resting (black) and activated (red) CD4⁺ T cells from the data of Schones et al. (33). Above them the theoretical nucleosome maps calculated iteratively starting from the resting state as an initial distribution are depicted. The remodeling probability depends on the activated state pattern [P_m(n) = 1/exp(P_a(n)], where P_a(n) is the nucleosome start site probability in the activated state and the step size is s = 10. The number of iterations is indicated in the Figure. (A) The probabilities to move the nucleosome to the left and to the right were determined only by the occupancies of the corresponding target sites according to Equations (8) and (9). Arrows point to the nucleosome locations where the discrepancy between the observed and expected distributions is especially large. (B) The probabilities to move the nucleosomes to the left and to the right were determined not only by the occupancies of the target sites, but also included a preferred directionality calculated using the nucleosome preferences given by P_a(n) according to Equations (10) and (11).