e106 Nucleic Acids Research, 2007, Vol. 35, No. 16 compressed at b(+3) into the triple helix model (21), named after its three left-hand rotating columns of every third nucleosome (data not shown). At b(+4) a can be reduced to 808, accompanied by intercalation of the every second nucleosome and a slight rotation, until the linkers are aligned side-by-side in the interior of the ﬁber (Figure 2E). This is an example of the double- helical crossed linker model (6), which has recently been found to correspond to the crystal structure of the tetranucleosome (22). Much less compaction is possible at b( 4) (Figure 2F). Asymmetries of clockwise and counter-clockwise rotations The asymmetry of clockwise and counter-clockwise rotations can be seen by considering a dinucleosome with a deﬁned direction of the DNA from nucleosome no. 1 to no. 2, in which nucleosome no. 2 is rotated either clockwise or counter-clockwise around the interconnect- ing linker from b = 08 to 1808 (Figure 1-IIIC, D). In both cases the pitch (p) of the dinucleosomes is reduced to zero. However, as the entry and exit sites of the terminal linkers are not diametrically positioned relative to the axis of rotation at b = 08 the changes in p are diﬀerent for clockwise and counter-clockwise rotation. Thus, by clock- wise rotation p goes through a slightly negative minimum, and by counter-clockwise rotation, p increases to a maximum before reaching zero at b = 1808 (Figure 1-IIID). For the same value of |b| the axial symmetry of nucleosomal ﬁlaments therefore diﬀer for b(+) and b( ), the former being more compact than the latter, which has a larger diameter with a hole in the middle (Figure 2G). Another asymmetry of clockwise and counter-clockwise rotation is due to variations in the angle (Z) between the terminal linkers of the dinucleosomes, as deﬁned by their projections into a plane perpendicular to the interconnect- ing linker (Figure 1-IIID). As the two linkers are not parallel to each other at b = 08, but diverge by a small angle (Z2), jZj will be larger for clockwise rotations (Z2 + b) than for counter-clockwise rotations (Z2 b) of the same size. The diﬀerence in Z is greatest for small values of b as seen from the diﬀerence in axial symmetry of ﬁbers with Z2 = 10 and 08 (Figure 2G). Variations in a and linker conformation caused by binding of linker histone H1 The wire models could only be made with straight linkers leaving the nucleosomes as tangents to their curved surface, because bent linkers cannot be folded with any precision. As the linkers in the nucleosomal ﬁlament are PAGE 6 OF 15 in fact bent as a result of the binding of histone H1, this represents a major simpliﬁcation of the geometry. Thus, the size of a is to a large extent determined by binding of H1, which bridges the linkers close to their entry/exit sites and inhibits their ﬂuctuation (16). This makes the entry and exit sites approach each other, so that the DNA makes two full coils around the core particle (as for a = 1808, see Figure 1-IVA), thereby decreasing the eﬀective linker length. However, binding of H1 stabilizes at a value below 1808 by bending of the linkers close to their entry/exit sites, causing the nucleosomes to rotate away from each other around the linker entry/exit sites (Figure 1-IVB). A conformation of the linkers at a = 08 has been reported, in which the two linker DNA segments are juxtaposed 8 nm from the nucleosome center and remain apposed for 3–5 nm before diverging, forming a so-called stem motive (23–25) (Figure 1-IVC). As the stem takes up 25–30 bp of the linker, a NRL of more than 200 bp is required to accommodate a stem at each nucleosome plus an additional linker DNA segment between the stems to provide a pitch of the dinucleosome 6¼ 08 and to make a > 08 at the entry/exit of the stem. Bending of the linkers at their entry/exit sites by binding of H1 may also change the slope of the linker DNA, reducing the pitch of the dinucleosomes (Figure 1-IVD and E). Moreover, bent linkers may introduce a tilt angle between the ﬂat faces of the core particles (Figure 1-IVF). Although the wire models do not reﬂect the path of the linker as aﬀected by histone H1 they can, by minor adjustments of NRL, Z1 and Z2, imitate changes in the distance between the nucleosomes that may be caused by eﬀects of linker histone binding on the eﬀective linker length and on the pitch of the dinucleosomes. Regular fibers with repeated variations in b: helices and loops Repeated b sequences along the nucleosomal ﬁlament give rise to a large number of diﬀerent conformations, some of which are described below using the following nomencla- ture: Values of b are numbered according to the conven- tion in Figure 2, b( 1) b( 4) being underlined and in italics. b Angles without speciﬁed values are indicated only by (+) and ( ) and nucleosomes are indicated by a dot, when convenient. A ﬁber with alternating positive and negative values of b can thus be written as (+ )n or ( + )n . Star- and polygon ﬁbers have been folded with a = 36 and 1088, respectively, unless stated otherwise. Star ﬁbers retain the axial symmetry of a star ﬁber for all sterically allowed combinations of b(+) and b( ) and little variation in b is allowed owing to the small value Figure 2. The inﬂuence of b on the conformation of a star ﬁber (A) and a polygon ﬁber (B) with pentagonal axial symmetry (a = 36 and 1088, respectively). Each ﬁber contains 10 nucleosomes. The ﬁrst nucleosome in each ﬁber is indicated by an asterisk. The nucleosomal repeat length [205 bp (A) and 196 bp (B)] is kept independent of b, which is varied in steps of 368, corresponding to 10 bp/turn of the DNA, and numbered according to the number of increments of 368. Large, black arrowheads point towards values of b that are not allowed for sterical reasons. Circular, white arrows indicate the coiling direction. The ﬁbers in A and B are oriented with the connecting linker of the ﬁrst dinucleosome in the viewing direction (y-axis). As the shifting directions of the ﬁbers do not follow the plane of the paper, as indicated by the thick ﬁbers in gray scale, except for b = 08, their true length cannot be inferred from the ﬁgure. (C) Polygon ﬁber with NRL 210 bp at b( 1). (D) Stacking of nucleosomes at b(5) into two columns with alternating positive and negative linker orientations by reducing the size of a. The ﬁber in (D) has NRL = 230 bp and a = 368. (E and F) Compressed polygon ﬁbers formed by reducing the size of a. (E) b(+4) is shown from the end (top) and from the side as seen from two diﬀerent angles. (F) b( 4) seen from the end (top) and from the side. (G) Axial symmetries of the polygon ﬁber as a function of b at Z2 = 10 and 08. Bar = 30 nm.