Using DNA mechanics to predict in vitro nucleosome positions and formation energies

Abstract

In eukaryotic genomes, nucleosomes function to compact DNA and to regulate access to it both by simple physical occlusion and by providing the substrate for numerous covalent epigenetic tags. While competition with other DNA-binding factors and action of chromatin remodeling enzymes significantly affect nucleosome formation in vivo, nucleosome positions in vitro are determined by steric exclusion and sequence alone. We have developed a biophysical model, DNABEND, for the sequence dependence of DNA bending energies, and validated it against a collection of in vitro free energies of nucleosome formation and a set of in vitro nucleosome positions mapped at high resolution. We have also made a first ab initio prediction of nucleosomal DNA geometries, and checked its accuracy against the nucleosome crystal structure. We have used DNABEND to design both strong and weak histone- binding sequences, and measured the corresponding free energies of nucleosome formation. We find that DNABEND can successfully predict in vitro nucleosome positions and free energies, providing a physical explanation for the intrinsic sequence dependence of histone-DNA interactions.

Figure 1.

(a) DNA mechanics model of histone–DNA interactions. Conformation of a single DNA basestep (defined as two consecutive DNA base pairs in the 5′ → 3′ direction) is described by six geometric degrees of freedom: rise, shift, slide, twist, roll and tilt. (11) DNA base pairs are shown as rectangular blocks. The minimized nucleosome energy (a weighted sum of the elastic energy E_el and the restraint energy E_sh which penalizes deviations of the DNA conformation from the ideal superhelix, see Methods section) is computed for each position along the DNA sequence. (b) Schematic illustration of a single dinucleotide (basestep) geometry. Coordinate frames attached to base pairs i and i + 1 are shown in blue, and the MST coordinate frame is shown in green. For illustrative purposes, only rise D_z and twist Ω are set to nonzero values. The origin of the MST frame is at the midpoint of the line connecting the origins of two base pair frames (which are separated by D_z Å along the z-axis); the MST frame is rotated through Ω/2 with respect to the frame i.

Figure 2.

DNABEND-predicted and experimentally observed DNA geometries. Six dinucleotide degrees of freedom in the crystal structure of the nucleosome core particle [(2); PDB code: 1kx5] (blue), in the minimum energy structure obtained using 1kx5 DNA sequence as input to DNABEND (red) and in the ideal superhelix with no energy relaxation (green). The 2-fold nucleosome symmetry axis is shown as a dashed vertical line. Mean values of the geometric degrees of freedom in the ideal superhelix are shown as dashed horizontal lines. Correlation coefficients between the degrees of freedom from the native and the minimized structures are: (r_twist, r_roll, r_tilt, r_slide, r_shift, r_rise) = (0.489, 0.709, 0.539, 0.536, 0.247, 0.238) (〈r〉 = 0.460). Correlation coefficients between the degrees of freedom from the native structure and the ideal superhelix are: (r_twist, r_roll, r_tilt, r_slide, r_shift, r_rise) = (−0.066, 0.669, 0.322, −0.550, 0.027, 0.021) (〈r〉 = 0.071).

Figure 3.

Elastic energy analysis of the nucleosome crystal structure. (a) Position-dependent sequence specificity in the nucleosomal DNA revealed by the energetic analysis of dinucleotides substituted into the crystal structure of the nucleosome core particle [PDB code: 1kx5; (2)] All possible dinucleotides were introduced at every position into the 147 bp nucleosomal site using DNA dihedral angles from the native dinucleotide, and DNA elastic energy was computed for every sequence variant. Upper panel: the difference between the energy of the most favorable dinucleotide and the average energy of all dinucleotides at this position. Lower panel: information entropy, defined as , where , and E_i^s is the elastic energy change which results from introducing a dinucleotide of type i = 1, … , 16 at position s: E_i^s = E_i^s(mut) − E_i^s(wt). To enforce the 2-fold symmetry of the nucleosome core particle, all dinucleotide energies were symmetrized around the middle of the DNA site, shown as a dashed vertical line. Middle panel: roll angle of the ideal superhelix showing DNA geometry in relation to the histone octamer. Negative roll angles correspond to the minor groove facing the histone surface. (b) Elastic energy components for all possible dinucleotides substituted into the 1kx5 crystal structure at position 109 where the DNA conformation is kinked (Figure 2) (2). Dinucleotides are ranked by their total energy as shown in the legend (best to worst energy from top to bottom). TA is the lowest energy dinucleotide (thick golden line). The energy component analysis reveals that it is the degrees of freedom related to slide (slide–slide and slide–twist components) and roll (roll–roll component) that make the TA dinucleotide most favorable, although the slide–slide component is slightly better in the native CA/TG dinucleotide (red/brown dots). In contrast, the AT dinucleotide (black lines) has the highest energy due to its low flexibility with respect to roll, slide and twist (Supplementary Table 2).

Figure 4.

DNABEND accurately ranks free energies of nucleosome formation and sets of nucleosome sequences. (a) Prediction of in vitro free energies of nucleosome formation measured using nucleosome dialysis (red circles) (31) and nucleosome exchange (green circles) (32,33). High affinity sequence 601 (25,31) is shown in black. Free energies were computed using only the central 71 bp of the 147 bp nucleosomal site, because competitive nucleosome reconstitution on DNAs with any lengths between 71 and 147 bp gives identical apparent free energies, and quantitatively equivalent free energies are obtained using either the full histone octamer or just the core histone tetramer (5,25). (b) Ranking of the nucleosome free energies shown in (a). Blue triangles: nucleosome dialysis (31). Black triangles: nucleosome exchange (32,33). (c) Histograms of DNA elastic energies (in arbitrary units) computed using the 147 bp nucleosomal site, consistent with the sequence lengths found in the in vitro selection on the yeast genome. (5) Yeast genomic sequences are compared with three sets of sequences selected for their nucleosome positioning ability. Blue: energies of all 147-bp long sequences from Saccharomyces cerevisiae chromosome III, green: energies of sequences from a genome-wide in vivo mononucleosome extraction assay (5), red: energies of sequences from an in vitro selection assay on yeast genomic DNA (5), black: energies of sequences from a SELEX experiment on a large pool of chemically synthesized random DNA molecules (27). Sequences shorter than 147 bp were omitted from all selected sequence sets; in sequences longer than 147 bp the most favorable energy was reported, taking both forward and reverse strands into account. (d) Histograms of DNA elastic energies for the mouse genome sequences selected for their ability to position nucleosomes (red) (34), or to impair nucleosome formation (blue) (35). Because most of these sequences are shorter than 147 bp, it was assumed that selective pressure was exerted mainly on the central 71 bp stretch of the nucleosomal DNA which interacts with the H3₂H4₂ tetramer. In sequences longer than 71 bp the most favorable energy of binding with the tetramer was computed, taking both forward and reverse strands into account.

Figure 5.

DNABEND predictions of in vitro nucleosome positions. Probability of a nucleosome to start at each base pair (green), nucleosome occupancy (blue) and nucleosome formation energy (violet). Vertical lines: experimentally known nucleosome starting positions, with base pair coordinates listed in parentheses below. (a) The 180 bp sequence from the sea urchin 5S rRNA gene (bps 8,26) (36). (b) The 183 bp sequence from the pGUB plasmid (bps 11,31) (37). (c) The 215 bp fragment from the sequence of the chicken β–globin^A gene (bp 52) (38). (d,e,f) Synthetic high-affinity sequences (27) 601 (bp 61), 603 (bp 81) and 605 (bp 59). Nucleosomes on sequences 601, 603 and 605 were mapped by hydroxyl radical footprinting (Supplementary Figures 2 and 3). All DNA sequences used in this calculation are available on the Nucleosome Explorer web site: http://nucleosome.rockefeller.edu.

Figure 5.

DNABEND predictions of in vitro nucleosome positions. Probability of a nucleosome to start at each base pair (green), nucleosome occupancy (blue) and nucleosome formation energy (violet). Vertical lines: experimentally known nucleosome starting positions, with base pair coordinates listed in parentheses below. (a) The 180 bp sequence from the sea urchin 5S rRNA gene (bps 8,26) (36). (b) The 183 bp sequence from the pGUB plasmid (bps 11,31) (37). (c) The 215 bp fragment from the sequence of the chicken β–globin^A gene (bp 52) (38). (d,e,f) Synthetic high-affinity sequences (27) 601 (bp 61), 603 (bp 81) and 605 (bp 59). Nucleosomes on sequences 601, 603 and 605 were mapped by hydroxyl radical footprinting (Supplementary Figures 2 and 3). All DNA sequences used in this calculation are available on the Nucleosome Explorer web site: http://nucleosome.rockefeller.edu.

Figure 6.

Comparison of four alternative methods for predicting nucleosome positions. For each experimentally mapped nucleosome position, we compute a sum over all predicted probabilities to start a nucleosome (green curves in Figure 5 and Supplementary Figures 5–7) that are separated by ≤D bp from the experimental position. Shown are the averages over all experimental positions for a given method, as a function of D. Blue—DNABEND, green—DNABEND with geometries from the nucleosome crystal structure, red—DNABEND with geometries from the ideal superhelix, cyan—an alignment-based method from Kaplan et al. (9). Alignment-based nucleosome positioning software was downloaded from http://genie.weizmann.ac.il/pubs/nucleosomes08/ and run with default parameters. Note that the provided software does not output nucleosome energies or scores.

Figure 7.

Nucleosome positioning explains background gene expression levels observed in reporter plasmids. Panel I (from top). Blue: nucleosome energies (in arbitrary units, au) in the CYC1 promoter region from the lacI::lacZ reporter plasmid (42). Note the 10-11 bp periodicity due to DNA helical twist. Panel II. Probability of a nucleosome to start at each base pair, in the absence (blue) and presence (maroon) of TBP. Some of the latter nucleosomes are also shown as orange ovals (note that in general nucleosome positions with P < 0.5 may overlap). Green: probability of a TBP to bind a TATA box. Panel III. Nucleosome occupancy in the absence (blue) and presence (maroon) of TBP. Green: TBP occupancy, red vertical lines: known TATA box positions. Arrows on the right correspond to the order of calculations. Panel IV. Nucleosome occupancy of the MEL1 promoter region from the DIT1::GFP reporter vector [(39); see CYC1 legend above for the color scheme]. Red vertical lines: known TATA box positions. Note that blue and maroon occupancy profiles completely overlap. TBP DNA-binding energies were computed as weight matrix log scores. The weight matrix was constructed using the alignment of TATA box sites from Basehoar et al. (43). From left to right the TBP binding energies were set to −5.819 au (TATATATA site) and −5.327 au (TATATAAA site) for CYC1, and to −4.726 au for both MEL1 sites (TATAAAAA).