Paradox Regained: a Topological Coupling of Nuclesomal DNA Wrapping and Chromatin Fibre Coiling

  • Andrew Travers
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 150)

The folding and unfolding of the chromatin fibre is a fundamental control point for the regulation of eukaryotic transcription. Although recent efforts have elucidated many of the mechanistic elaborations that regulate this process, the underlying mechanical basis of the folding transitions is poorly understood. Here I present a novel solution to the so-called 'linking number paradox' problem (Finch et al., 1977) and show that this solution implies that the chromatin fibre acts a tunable coil. The folding/unfolding process is essentially a topological transition in which the wrapping of DNA around the nucleosome core particle is directly coupled to degree of compaction of the coil.


Core Particle Histone Tail Linker Histone Nucleosome Core Particle Coiled Form 


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I am most grateful to Ernesto Di Mauro for suggesting the term 'tunable' and especially to the organisers of a recent workshop on the Mathematics of DNA Structure, Function and Interac- tions held at the Institute of Mathematics and its Applications at the University of Minnesota in Minneapolis for bringing this problem to my attention again.


  1. Angelov D., Vitolo J.M., Mutskov V., Dimitrov S., and Hayes J.J. (2001). Preferential interaction of the core histone tail domains with linker DNA. Proc. Nat. Acad. Sci. USA 98: 6599–6599.CrossRefGoogle Scholar
  2. Athey B.D., Smith M.F., Rankert D.A., Williams S.P., and Langmore J.P. (1990). The diameters of frozen-hydrated chromatin fibers increase with DNA linker length: evidence in support of variable diameter models for chromatin. J. Cell Biol. 111: 795–795.CrossRefGoogle Scholar
  3. Bauer W.R., Hayes J.J., White J.H., and Wolffe A.P. (1994). Nucleosome structural changes due to acetylation. J. Mol. Biol. 236: 685–690.CrossRefGoogle Scholar
  4. Bednar J., Horowitz R.A., Dubochet J., and Woodcock C.L. (1995). Chromatin conformation and salt-induced compaction: three-dimensional structural information from cryoelectron microscopy. J. Cell Biol. 131: 1365–1376.CrossRefGoogle Scholar
  5. Butler P.J. and Thomas J.O. (1980). Changes in chromatin folding in solution. J. Mol. Biol. 140: 505–529.CrossRefGoogle Scholar
  6. De Lucia F., Alilat M., Sivolob A., and Prunell A. (1999). Nucleosome dynamics. III. Histone tail-dependent fluctuation of nucleosomes between open and closed DNA conformations. Implications for chromatin dynamics and the linking number paradox. A relaxation study of mononucleosomes on DNA minicircles. J. Mol. Biol. 285: 1101–1119.Google Scholar
  7. Dimitrov S.I., Makarov V.L., and Pashev I.G. (1990). The chromatin fiber: structure and conformational transitions as revealed by optical anisotropytudies. J. Biomol. Struct. Dynam. 8: 23–23.Google Scholar
  8. Dorigo B.,Schalch T., Kulangara A., Duda S., Schroeder R.R., and Richmond T.J. (2004) Nucleosome arrays reveal a two-start organisation of the chromatin fiber. Science 306: 1571–1573.CrossRefGoogle Scholar
  9. Finch J.T., Lutter L.C., Rhodes D., Brown R.S., Rushton B., Levitt M., and Klug A. (1977). Structure of nucleosome core particles of chromatin. Nature 269: 29–36.CrossRefGoogle Scholar
  10. Gasser S.M., Laroche T., Falquet J., Boy de la Tour E., and Laemmli U.K. (1986).Metaphase chromosome structure. Involvement of topoisomerase II. J. Mol. Biol. 188: 613–629.Google Scholar
  11. Gerchman S.E. and Ramakrishnan V. (1987). Chromatin higher-order structure studied by neutron scattering and scanning transmission electron microscopy. Proc. Nat. Acad. Sci. USA 84: 7802–7806.CrossRefGoogle Scholar
  12. Germond J.E., Hirt B., Oudet P., Gross-Bellark M., and Chambon P. (1975). Folding of the DNA double helix in chromatin-like structures from simian virus 40. Proc. Nat. Acad. Sci. USA 72: 1843–1847.CrossRefGoogle Scholar
  13. Ghirlando R. and Felsenfeld G. (2008). Hydrodynamic studies on defined heterochromatin fragments support a 30 nm fiber having 6 nucleosomes per turn. J. Mol. Biol. epub. 3 Jan. 2008.Google Scholar
  14. Ghirlando R., Litt M.D., Prioleau M.N., Recillas-Targa F., and Felsenfeld G. (2004). Physical properties of a genomic condensed chromatin fragment. J. Mol. Biol. 336:597–605.CrossRefGoogle Scholar
  15. Hamiche A., Schultz P., Ramakrishnan V., Oudet P., and Prunell A. (1996). Linker histone-dependent DNA structure in linear mononucleosomes. J. Mol. Biol. 257:30–42.CrossRefGoogle Scholar
  16. Hizume K., Araki S., Yoshikawa K., and Takeyasu K. (2007). Topoisomerase II, scaffold component,promotes chromatin compaction in vitro in a linker-histone H1-dependent manner. Nucleic Acids Res. 35:2787–2799.CrossRefGoogle Scholar
  17. Hizume K., Yoshimura S.H., and TakeyasuK. (2005). Linker histone H1perse can induce three-dimensional folding of chromatin fiber. Biochemistry 44:12978–12989.CrossRefGoogle Scholar
  18. Keller W., Müller U., Eicken I., Wendel I., and Zentgraf H. ¨(1978). Biochemical and ultrastructural analysis of SV40 chromatin. Cold Spring Harb. Symp. Quant. Biol. 42: 227–244.Google Scholar
  19. Klug A. and Lutter L.C. (1981). The helical periodicity of DNA on the nucleosome. Nucleic Acids Res. 9: 4267–4267.CrossRefGoogle Scholar
  20. Luger K., Mader A.W., Richmond R.K., Sargent D.F., and Richmond T.J. (1997). Crystal structure of the nucleosome core particle at 2.8 A resolution. Nature 389: 251–260.CrossRefGoogle Scholar
  21. Norton V.G., Imai B.S., Yau P., and Bradbury E.M. (1989). Histone acetylation reduces nucleosome core particle linking number change. Cell 57: 449–457.CrossRefGoogle Scholar
  22. Richmond T.J. and Davey C.A. (2003). The structure of DNA in the nucleosome core. Nature 423: 145–150.CrossRefGoogle Scholar
  23. Robinson P.J., Fairall L., Huynh V.A., and Rhodes D. (2006). EM measurements define the dimensions of the "30-nm"chromatin fiber: evidence for a compact, interdigitated structure. Proc. Nat. Acad. Sci. USA 103: 6506–6511.CrossRefGoogle Scholar
  24. Satchwell S.C., Drew H.R., and Travers A.A. (1986). Sequence periodicities in chicken nucleosome core DNA. J. Mol. Biol. 191: 659–675.CrossRefGoogle Scholar
  25. Schalch T., Duda S., Sargent D.F., and Richmond T.J. (2005). X-ray structure of a tetranucleosome and its implications for the chromatin fibre. Nature 436: 138–141.CrossRefGoogle Scholar
  26. Shogren-Knaak M., Ishii H., Sun J.M., Pazin M.J., Davie J.R., and Peterson C.L. (2006). Histone H4-K16 acetylation controls chromatin structure and protein interactions. Science 311: 844–847.CrossRefGoogle Scholar
  27. Stein A. (1980). DNA wrapping in nucleosomes. The linking number problem re-examined. Nucleic Acids Res. 8: 4803–4803.CrossRefGoogle Scholar
  28. Thoma F., Koller T., and Klug A. (1979). Involvement of histone H1 in the organization of the nucleosome and of the salt-dependent superstructures of chromatin. J. Cell Biol. 83: 403–403.CrossRefGoogle Scholar
  29. Travers A. A. and Klug A. (1987). The bending of DNA in nucleosomes and its wider implications. Phil. Trans. Roy. Soc. (London) B 317: 537–561.CrossRefGoogle Scholar
  30. Tse C., Sera T., Wolffe A.P., and Hansen J.C. (1998). Disruption of higher-order folding by core histone acetylation dramatically enhances transcription of nucleo-somal arrays by RNA polymerase III. Mol. Cell. Biol. 18: 4629–4629.Google Scholar
  31. Wang J.C. (1979). Helical repeat of DNA in solution. Proc. Nat. Acad. Sci. USA 76: 200–203.CrossRefGoogle Scholar
  32. White J.H., Cozzarelli N.R., and Bauer W.R. (1988). Helical repeat and linking number of surface-wrapped DNA. Science 241: 323–327.CrossRefMathSciNetGoogle Scholar
  33. Widom J. (1992). A relationship between the helical twist of DNA and the ordered positioning of nucleosomes in all eukaryotic cells. Proc. Nat. Acad. Sci. USA 89: 1095–1095.CrossRefGoogle Scholar
  34. Wu C., Bassett A., and Travers A.A. (2007). A variable topology for the '30 nm' chromatin fibre. EMBO Rep. 8: 1129–1129.CrossRefGoogle Scholar
  35. Zivanovic Y.,Duband-Goulet I.,S Chultz P., Stofer E.,Oudet P., and Prunell A. (1990).Chromatin reconstitution on small DNA rings. III. Histone H5 dependence of DNA supercoiling in the nucleosome. J. Mol. Biol. 214: 479–495.CrossRefGoogle Scholar
  36. Zivanovic Y., Goulet I., Revet B., Le Bret M., and Prunell A. (1988). Chromatin reconstitution on small DNA rings. II. DNA supercoiling on the nucleosome. J. Mol. Biol. 200: 267–290.CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Andrew Travers
    • 1
  1. 1.MRC Laboratory of Molecular BiologyCambridgeU.K

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