Wu C and Travers A (2019), Modelling and DNA topology of compact 2-start a...

ECB-ART-50721

Nucleic Acids Res 2019 Oct 10;4718:9902-9924. doi: 10.1093/nar/gkz495.

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Modelling and DNA topology of compact 2-start and 1-start chromatin fibres.

Wu C , Travers A .

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We have investigated the structure of the most compact 30-nm chromatin fibres by modelling those with 2-start or 1-start crossed-linker organisations. Using an iterative procedure we obtained possible structural solutions for fibres of the highest possible compaction permitted by physical constraints, including the helical repeat of linker DNA. We find that this procedure predicts a quantized nucleosome repeat length (NRL) and that only fibres with longer NRLs (≥197 bp) can more likely adopt the 1-start organisation. The transition from 2-start to 1-start fibres is consistent with reported differing binding modes of the linker histone. We also calculate that in 1-start fibres the DNA constrains more torsion (as writhe) than 2-start fibres with the same NRL and that the maximum constraint obtained is in accord with previous experimental results. We posit that the coiling of the fibre is driven by overtwisting of linker DNA which, in the most compact forms - for example, in echinoderm sperm and avian erythrocytes - could adopt a helical repeat of ∼10 bp/turn. We argue that in vivo the total twist of linker DNA could be modulated by interaction with other abundant chromatin-associated proteins and by epigenetic modifications of the C-terminal tail of linker histones.

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	Figure 1. Defining the path of nucleosomal DNA. The path of the central 129 bp of the nucleosomal DNA (PDB ID: 4LQC) was shown in green, while a theoretical path was generated at the Cartesian origin shown in white. The nucleosome was realigned at the origin by means of transformation such that the y and z axes (z axis being normal to the plane of view) correspond to the nucleosome dyad and superhelical axes respectively. Here the dyad axis is also the 2-fold symmetry axis of the nucleosomal DNA.
	Figure 2. Schematic of the 1-start crossed linker model of the chromatin fibre. The large open circle represents the start of a left-handed helical path rising towards the reader, on which both the odd (red sphere) and even (blue sphere) number nucleosomes reside. The ratio β /α determines the interdigitating pattern of the two series, which, in this example, gives rise to (1 3 5 7 9 2 11 4 13 6…) or alternatively (2 4 6 8 1 10 3 12 5…) because nucleosomes can interdigitate with either those above or below of the neighbouring stacks. The adjacent nucleosomes in this example are identified as (i±7, i, i±9).
	Figure 3. Construction of fibre models. The path of DNA was represented as a smooth tube defined by best fit values of base pair coordinates. The entering and leaving DNAs (the segment between cyan marks) approximate a straight trajectory. The chromatosome structure was used as a geometric unit for model building.
	Figure 4. Calculation of relative twist between consecutive nucleosomes. The green lines lie on the bisecting planes of respective nucleosomes, and are orthogonal to the trajectory of the linker DNA. Consequently, their corresponding vectors are cross products between the linker trajectory and the normals to respective nucleosome discs (defined by their bisecting planes). The relative twist between the nucleosomes are given by the angle between the green lines.
	Figure 5. Diagram adapted from Levitt (21) - computation of writhing number from a polygonal curve. (A) A polygonal curve defined by a series of vertices where the crossovers between individual segments are indicated with (+1) or (-1) signs (depending on handedness). (B) The solid angle (enclosed by four planes) passing through the 2D sphere within which the segments i and j can be seen to cross over. a, b, c, d are normal vectors respectively to the four planes. A, B, C, D are angles between adjacent planes.
	Figure 6. The writhing number of nucleosomal DNA. The DNA paths of three chromatosomes were defined by a series of base pair coordinates shown in black dotted lines. The length of DNA from left to right are 167, 195 and 215 bp, respectively. The writhe values are indicated.
	Figure 7. The topology of 2-start and 1-start fibres is analogous to B- and A-form DNA.
	Figure 8. Predicted chromatin fibres with increasing linker length. Chromatin fibres were built based on both the 2-start and 1-start models over NRLs between ∼177 and ∼237 bp. The number above each structure indicates NRL, which can be uniform or between two alternating lengths.
	Figure 9. Comparison of linker lengths found in vivo and from model predictions. Upper panel: NRL probability distribution derived from measurements of different tissues and organisms (adapted from ref. 39). Lower panel: Occurrence frequency of NRLs (n = 44) in predicted fibres (shown in Figure 8). The labels on x axis are mean values respective of individual bins: 176.3–176.6, 185.9–186.7, 194.8–197.0, 205.0–207.2, 216.0–217.6, 226.8–227.4, 237.0–237.4. Note that the bins are discontinuous. The linker length is modelled continuous although the linker length in terms of bp is an integer.
	Figure 10. The dyad position relative to entering and leaving DNAs. Left: the position of octamer dyad coincides with the symmetry axis of the nucleosome (determined relative to the entering and leaving DNAs). Right: octamer dyad deviates from the symmetry axis (blue line) of the nucleosome. The red line indicates the dyad axis (determined relative to the octamer). Note that the orientation of linker histone in the diagram was based on the chromatosome structure (PDB ID: 4LQC), where the linker histone resides on the DNA minor groove (45). The binding mode of linker histone will be different (which we have not modelled) where octamer dyad deviates from the symmetry axis (44).
	Figure 11. The DNA writhe packaged in compact fibres. The total writhe of fibre DNA was calculated for compact fibres using the 32-mer structures. The writhe per nucleosome was plotted against the pitch angle of nucleosome stack and nucleosome repeat length (NRL) respectively. Data points corresponding to 2-start and 1-start models were indicated in blue and red respectively. The data points include fibres with uniform NRLs and those with mixed NRLs (Table 1).
	Figure 12. Correlation of cation-dependent change in DNA helical repeat adapted from (28) and fibre density (14,15,19,26). These data are plotted according to the X+ and Mg2+ concentrations used. Where appropriate (i.e. when K+ was used instead of Na+) X+ is plotted in terms of Na+ equivalents according to ref. 27). Symbols from ref. 28): open diamonds, filled circles, inverted triangles, squares, triangles, filled diamonds - [Na+] with successively 0, 0.5, 1, 2, 5 mM [Mg2+]; fibre data: filled stars, red circle, green square, blue square from, respectively, (26,19,14,15). Note that the data from (26) indicate a 2-phase folding pathway as further described in Supplementary Figure S3.

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Anderson, Supercoiling in closed circular DNA: dependence upon ion type and concentration. 1978, Pubmed