e106 Nucleic Acids Research, 2007, Vol. 35, No. 16 PAGE 10 OF 15 Figure 6. Loops of hexa- and octanucleosomes with diﬀerent b combinations. (A and B) Hexanucleosomal loops formed by b = 08, 908 and 1808 (0, +, , 5). Arrows indicate the direction of the ﬁlament from nucleosome No. 1!6. The ﬂat faces of the core particles nearest to the entering linkers are dark while the faces nearest to the exiting linkers are light. The line diagrams show the orientation of the ﬁve linkers in each loop. (A1–3) Closed loops; (B1–4) locked loops. (C and D) Hexanucleosomes; (23131) (C); (41414) (D). (E) A nucleosome is added to each terminal linker of the loop in (D) (asterisks). (F and G) Loops of six plus two nucleosomes as shown singly and in series of three. (F) A trimer, 1(13132)2, connected by b(2); (G) A trimer, 3(33123)5, connected by b(5). Values of b are approximate. a = 908. Bar = 30 nm (C–G). positive and negative linker conﬁgurations, which are folded from ﬁlaments with an open linker conﬁguration at b(5) (Figure 5J). Looping of polygon fibers with periodic variations in b The ability of the ﬁlament to form longitudinal loops of six nucleosomes (ﬁve linkers) with the b sequence (1111)n (Figure 3G and H) raised the question of whether loops could be formed by other pentameric series of b. This was addressed by folding of loops with six nucleo- somes (a = 908), using b = 08, +908, 1808 and 908, followed by adjusting the b values to integers of 368. Many models of such loops could only be folded from ﬁlaments with b(5), and b values diﬀerent from b(5) often had to be introduced in a speciﬁc folding sequence to avoid collisions between the nucleosomes. The loops could be classiﬁed according to their opening in response to a linear stretch of the ﬁlament, into closed loops, which could be opened after a slight displacement of the terminal nucleosomes, and locked loops, which could only be opened after rotation of the terminal nucleosomes (Figure 6A and B). The loops were relatively independent of the actual b values and could exist in several diﬀerent conformations after adjusting b to integers of 368. Thus, the closed loop (+ + +), which is shown on Figure 6C with the b sequence (23131), underwent no major changes in compaction when the b values were changed correspond- ing to a stepwise increase in linker length up to 10 bp (data not shown). Many of the loops could not be serially connected as the terminal linkers were located too close to each other or to neighboring nucleosomes to provide suﬃcient space, and an extra nucleosome therefore had to be added to each terminal linker (compare Figure 6D and E). Some of these octanucleosomes had highly compact conformations with crossed linkers and linkers and nucleosomes touching each other, as in the ﬁbers shown in Figure 6F and G). Thus, in the octamers in Figure 6G, 6 of the 7 linkers are either crossing another linker or touching a nucleosome. Fibers consisting of such structural motives of octa- nucleosomes were highly stable and stretch resistant with little ﬂexibility, except at the interconnecting linkers. The b sequence of this type of ﬁbers was thus periodic, being divided into segments of six or eight b angles within which the b sequence could vary independently. No folding sequence appeared to exist for models of such octanucleosomal structures, which were made by ﬁrst folding the hexanucleosomal loop and then rolling on a nucleosome on each of the terminal linkers. Characteristics of polygon fiber conformations with random b sequences Random variations in b give rise to irregular conforma- tions which depend on the mean b value, the degree of deviation from the mean value as well as the actual b sequence. NRLs for a large number of diﬀerent organisms and cell types have been shown to be quantized by integral multiples of 10 bp, corresponding to integral multiples of helical turns of linker DNA, with experimentally deter- mined SDs of 2–4 bp (27). It therefore seemed to be most relevant to explore conformations of polygon ﬁbers with b