PAGE 13 OF 15 to a density corresponding to metaphase chromosomes. This high density is so far only exceeded by two other models in which the compaction was caused by bending of the linkers (18) and by nucleosome gaping (17,37). Energy analyses have indicated that the balance between repulsion among linker DNA and internucleo- some interactions determines the salt-dependent conden- sation of the nucleosomal ﬁlament (38), and positively charged core histone N-terminal tails are important in this process by mediating favorable internucleosomal interac- tions and screening DNA repulsion (39). Compaction of the ﬁber would seem to require a high degree of charge neutralization, as linker DNA and nucleosomal DNA are brought very close to each other, while face-to-face internucleosomal interactions are only involved in inter- digitation of the ﬁbers and in apposition of layers of interdigitated ﬁbers. Since a regular spacing of nucleosomes is rare, it is noteworthy that repeated b sequences required for double ﬁber formation and compaction can also be formed by ﬁbers with a random distribution of b values after displacement of nucleosomes and limited twisting of the linkers. This supports speculations that the nucleosome repositioning activity of chromatin remodeling factors may provide the chromatin ﬁber with dynamic properties at the supra-nucleosomal level (40). It furthermore shows that variations in b may not only be caused by diﬀerences in linker length but also by twisting of the linker. There is therefore no unambiguous correlation between b and linker length. In addition, linkers of the same length can diﬀer slightly in their b values owing to sequence- dependent variations in the helical twist angle of base pairs in the linker DNA. An important consequence of the polygon ﬁber geometry is the ability of the ﬁlament to form loops in response to variations in b. Closed and locked loops formed by periodic variations in b(0), b(+), b(5) and b( ) remained compact at many diﬀerent combinations of b values, and the ﬂexibility of the ﬁlament was caused only by the interconnecting linkers. The fact that some of these types of loops required the addition of one nucleosome at each terminal linker to provide space for being serially connected is reminiscent of the supranucleosomal organi- zation of the chromatin. The size of supranucleosomes isolated by nuclease digestion thus varies from a minimum of 6 or 8 nucleosomes up to 40 nucleosomes (3). Filaments with random variations in b sequence also seem to be able to attain a supranucleosomal organization by the forma- tion of relatively stable loop clusters separated by more ﬂexible segments. It is generally recognized that the nucleosome ﬁlament is highly dynamic owing to limited twisting of the linkers within the twist constraints and a rapid exchange between free and bound histone H1 (41). The major signiﬁcance of static models may well be to show conformations that have the potential to be stabilized, either by double ﬁber formation, by the presence of closed and locked loops, or by cross linking of nucleosomes by nuclear proteins (42). The stability of loop clusters in ﬁlaments with a random distribution of b may thus be increased by cross-linking of nearby nucleosomes. Nucleic Acids Research, 2007, Vol. 35, No. 16 e106 In light of the importance of a, b and the linker length for the conformation of the nucleosomal ﬁlament, what is then the role of these parameters for the organization of chromatin in the nucleus? A discussion of this question has to take into account that the geometry of the linker can be aﬀected by bending. Stretches of poly(dAdT) are often bent and have an increased likelihood of being present in linkers (43) and linkers may also bend as a result of binding of H1. Moreover, theoretical calculations do not exclude that electrostatic interactions with core histone tail domains (44) can bend the linker DNA, despite the known large persistence length of the DNA (45). Mesoscopic computer models have indeed shown that when chromatin ﬁber models include real DNA ﬂexibility and charge, then the internucleosome interac- tions overcome the pre-designed linker DNA geometry and result in establishing new nucleosome chain conﬁg- urations. However, the internucleosomal interactions appeared to be relatively weak and probably insuﬃcient to maintain highly bent linker DNA (39). Bending and twisting of linker DNA may be the result of aggregation of nucleosomes (28), which have a prop- ensity to aggregate at high concentration and in high salt, and the sequence of aggregation of newly synthesized nucleosomes to their nearest neighbors, might in fact function as a folding path for nucleosomal ﬁlaments in the nucleus. The potential importance of a folding path is seen from models of ﬁbers consisting of hexanucleosomal loops, some of which needed an extra nucleosome at the terminals to give space for being serially connected. Such sequences of eight nucleosomes could not be folded from preformed ﬁlaments and are therefore unlikely to be generated from pre-existing ﬁlaments as a result of a thermodynamic equilibrium. The narrow distribution of NRLs in every cell type and organism around a single mean value suggests that there is a range of preferred b values in the chromatin. 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 (27), suggesting that preferred b values might be the same for these organisms. However, as the NRL can be changed experimentally by up to 15 bp without fatal eﬀects (46,47), it seems that chromatin higher order structure can accommodate to a wide range of b values. This is in fact the case for the closed and locked hexanucleosomal looping of the ﬁlament, which depends more on the distribution of (+)- and ( )-linkers than on the actual values of b(+) and b( ). While looping appears to be an inherent property of the ﬁlament, occurring even as a result of a stochastic distribution of linker lengths, the location, conformation and length of the loops depend on the actual b sequence. This suggests that for a supranucleosomal organization of the chroma- tin, changes in linker lengths have a modulating eﬀect on the conformation of the ﬁlament, leaving some loops unaltered, changing the conformation of others, destroy- ing some loops and creating new ones, thus leaving the principal structure of the ﬁber roughly unaltered and within the same average dimensions.