e106 Nucleic Acids Research, 2007, Vol. 35, No. 16 PAGE 8 OF 15 Figure 4. Swivel-linkers and compaction of a polygon ﬁber (a = 1088). (A) A ﬁber with b sequence (033033)n, in which b(0)-swivel-linkers (arrows) connect trinucleosomes, which alternate between left- ( 3 3 ) and right-handed ( 3 3 ) orientation. (B–H) Compaction of a ﬁber (B) with b sequence (333)n in which (3)-swivel-linkers (arrows) are separating right-handed trinucleosomes ( 3 3 ), two of which are numbered 1–3 and 4–6. The ﬁber is compacted by decreasing a at the terminals of the swivel-linker (C) and in the trinucleosomes (D). (E) Axial view of the compacted ﬁber showing the superposition of linkers of two consecutive trinucleosomes. (F) Compact ﬁber as viewed from the side. Nucleosomes with an orientation close to the ﬁber axis (blue arrows) are stacking edge-to-edge and nucleosomes perpendicular to the ﬁber axis (red arrows) have the potential to interact with nucleosomes in the same orientation in a neighboring ﬁber by interdigitation. (G) Interdigitation of two compact ﬁbers as seen from the end and from the side. (H). Packing of three sheets (red, green, yellow), each consisting of three interdigitated ﬁbers, as seen from the end. Rectangles delineate the cross-section area used for density calculation. Bar = 30 nm. (No. 4) protrudes from the central axis, which consists of groups of three nucleosomes, formed by contacts between one nucleosome from each of three consecutive loops. These nucleosome triplets are located very close to each other and may form dimers. Another conformation, caused by the same periodical shift between b(+) and b( ), but with larger values of b, (3333)n, consists of large loops of 20 nucleosomes (Figure 3I). Swivel-linkers and fiber compaction Linkers with an orientation close to that of the ﬁber axis have the potential of functioning as a swivel between intermittent coils. In the presence of such ‘swivel-linkers’ coiling of the intermittent nucleosome sequences becomes independent of each other, making possible a shift between right- and left-handed coiling, such as (033033)n (Figure 4A) and (03030303)n (data not shown). In some cases, the presence of swivel-linkers makes possible a reduction of a without rotation of the ﬁber. This is shown by the sequence (333)n in which the (3)-linker functions as a swivel-linker, connecting two right-handed trinucleo- somes ( 3 3 ), forming a coil of 6 nucleosomes spanning a little more than 3608 (because Z of the swivel-linker is larger than 1088) (Figure 4B). Reduction of a at the terminals of the swivel-linker makes the trinucleosomes approach each other, and reduction of a in the trinucleo- somes to 728 makes them close like a pair of pincers (Figure 4C and D). As a result of these changes every second linker becomes super positioned (Figure 4E), allowing for compaction of the ﬁber (Figure 4F). The compaction is limited by collision of nucleosomes connected by every second swivel-linker, which stack edge-to-edge in an orientation close to that of the ﬁber axis (blue arrows in Figure 4F). The ﬁber therefore has 6 nucleosomes per 11 nm. If the volume of the ﬁber is calculated as a cylinder with a diameter equal to two times the radius of gyration (32 nm), this corresponds to a density of 0.15 g DNA/ml, which is not diﬀerent from the density of the solenoid model (26). However, the cross- section area is more closely circumscribed by a rectangle of 28 26 nm, corresponding to a density of 0.18 g DNA/ml. These values are within the range of densities calculated from metaphase chromosomes in a variety of organisms (26). The compact ﬁbers can associate by interdigitation between nucleosomes, which are oriented perpendicular to the ﬁber axis (red arrows in Figure 4F) forming sheets, which can be packed into a slightly higher density (Figure 4G and H). Pairwise association of polygon fibers: zip and double helices Separation of coils in a ﬁber by swivel-linkers makes space for interactions with other ﬁbers. Two ﬁbers with the sequence (333)n can align side-by-side and interlock like a zip, in which nucleosomes in each ﬁber ﬁt spatially into a pocket of ﬁve to six nucleosomes ( 3 3 3 3 3 ) in the other ﬁber (Figure 5A). The minimum size of required for the formation of this type of double ﬁber is between 1088 and 908. In a ﬁber with b sequence (3033)n, (3) swivel-linkers separate right-handed coils of four nucleosomes ( 3 0 3 ), providing suﬃcient space for the formation of a double helix in which swivel-linkers in one ﬁlament is alternately located on the inside and outside of swivel-linkers in the other ﬁlament (Figure 5B). This type of double ﬁber can be compressed to 70% of its original size by reducing a to 908.