e106 Nucleic Acids Research, 2007, Vol. 35, No. 16 DNA every time it coils around a core particle and the angle between the ﬂat faces of consecutive nucleosomes around their interconnecting linker DNA. This angle is often referred to as the rotational angle, because the positions of the core particles in the ﬁlament follow the right-handed rotation of the DNA double helix and therefore vary with the linker length. The conformational changes caused by variations in these two angles have been studied by computer models (12–14), but existing models do not take into account the full consequences of the size of the directional change of the DNA at the nucleosome, the asymmetry of rotation around the linker DNA and the conformational limitations imposed by the linker length. The present study shows that these parameters are of major importance for the conforma- tional freedom of the ﬁlament, and explores the possible conformations by means of physical models. It provides a survey of diﬀerent conformations of the nucleosomal ﬁlament and how they are related to each other, as well as to existing models of the chromatin ﬁber. It is shown that repeated or periodic variations in b sequence give rise to diﬀerent types of helical and looped conformations and that helical conformations are able to associate pairwise as a zip, to form double helices, intercalate and contract to a high density. Finally, the irregular conformation of a ﬁlament with a random b sequence is described as well as how it can be converted into a regular helix by chromatin remodeling and limited twisting of the linkers. Although physical models are static and do not account for the linker ﬂexibility, they might be useful in studies of chromatin ultrastructure and serve as reference models for the analysis of transmission electron microscopic images. MATERIALS AND METHODS Models of the nucleosomal ﬁlament were built in the scale 1.25 106:1 using a plastic-coated copper wire with a mean diameter of 2.5 mm. Filaments were folded into pentagonal star- and polygon ﬁbers at b = 08 using a metal block perforated by ﬁve displaceable parallel cylindrical metal rods of 8.5 mm in diameter, placed in the corners of a regular pentagon with a center-to-center distance of 21 mm. These dimensions correspond to a NRL of 86 mm (196 bp) and 98 mm (205 bp) for the star- and the polygon ﬁber, respectively. The ﬁbers were subsequently modiﬁed by hand. In the star ﬁber, the orientation of the linkers of every single nucleosome was ﬁrst adjusted, using Z1 = 98. The nucleosomes were then rotated around the linker DNA in steps of b = 368 corresponding to 10 bp/coil of the DNA. This was done by orienting the dinucleosomes with their connecting linker in the viewing direction, deﬁning b as the angle between the exiting or the entering coils of the nucleoso- mal DNA. In the polygon ﬁber, the orientation of the terminal linkers of the dinucleosomes was adjusted after rotation of the nucleosomes, using Z2 = 108. A number of videos of the models shown on Figures 3–6 are presented at: http://icmm.ku.dk/ansat/personsider/ mogens_engelhardt/choreography/ PAGE 2 OF 15 RESULTS Basic parameters The conformation of a nucleosomal ﬁlament with straight linkers is determined by a number of geometric para- meters, which are shortly introduced in the following (Figure 1-I). The two most important parameters are the angle (a) between the entering and exiting linkers of the nucleosome, caused by the change in the direction of the linker DNA (d = 1808 a) and the angle (b) between the ﬂat faces of consecutive nucleosomes. According to the X-ray crystal structure of the nucleosome, the ends of the 146 bp of nucleosomal DNA are separated by 758 (1) corresponding to a default value of a = 1058. The size of a is sensitive to binding of one molecule of linker histone (H1) (15,16), while b varies with the length of the inter- connecting linker. When a and b are constant the ﬁlament forms a regular ﬁber within a cylindrical space, with an axial symmetry determined by a (for b = 08) or the projection of a (a0) into a plane perpendicular to the ﬁber axis (for b 6¼ 08). Because of the slope of the DNA [g = 4.58 (13)] due to its coiling around the core particle, the two linkers diverge (negative conformation) by an angle (Z1), as deﬁned by their projections into a plane of symmetry formed by the dyad axis and the symmetry axis of the nucleosome. If the linkers are bent so that their projections into this plane cross each other, they are said to be in a positive conformation. Linkers have also been proposed to be able to approach each other as a result of an allosteric change of the nucleosome (nucleosome gaping) in which the coils of the DNA are separated like a local opening of a spring (17). In the following, the signiﬁcance of a and b for the conformation the nucleo- somal ﬁlament will be demonstrated, assuming the linker DNA to be straight, entering and exiting the nucleosomes as tangents to their circular surface. The effect of a on the axial symmetry: star fibers and polygon fibers The conformation of the ﬁlament is determined by the size of a when b = 08 (Figure 1-II). At a = 08 the direction of the DNA is changing 1808 (d) at each nucleosome, placing every second nucleosome on top of each other as two columns parallel to the ﬁber axis, like the edges of a ribbon. The ﬁlament unfolds when is increased, forming a linear string of nucleosomes at a = 1808, and a can be increased either by directing the linkers toward each other (closed conformation) or away from each other (open conformation). A ﬁlament with linkers in the closed conformation uncoils clockwise with a concomitant decrease in the distance between the nucleosomes, as more of the linker DNA becomes associated with the core particles. Conversely, a ﬁlament with linkers in the open conformation uncoils counter-clockwise, increasing the distance between the nucleosomes as the terminals of the nucleosomal DNA are peeled oﬀ the core particles. Thus, at a = 1808 the DNA coils twice around the core particles when linkers are in the closed conformation, but only once if linkers are in the open conformation. The eﬀective linker length, i.e. the fraction of the NRL,