Journal of Mathematical Chemistry

, Volume 53, Issue 1, pp 183–199 | Cite as

Synthesising topological links

  • Nils A. Baas
  • Nadrian C. SeemanEmail author
  • Andrew Stacey
Original Paper


We discuss the chemical synthesis of topological links, in particular higher order links which have the Brunnian property (namely that removal of any one component unlinks the entire system). Furthermore, we suggest how to obtain both two dimensional and three dimensional objects (surfaces and solids, respectively) which also have this Brunnian property.


Synthetic DNA topology of links Brunnian links Carpets and solids Hopf links Synthesizing double stranded DNA nodes 

Mathematics Subject Classification




N.A.B. would like to thank The Institute for Advanced Study, Princeton, USA for their kind hospitality during part of the period when this research was done. This research has been supported by the following Grants to NCS: GM-29554 from NIGMS, Grants CMMI-1120890, EFRI-1332411, and CCF-1117210 from the NSF, MURI W911NF-11-1-0024 from ARO, Grants N000141110729 and N000140911118 from ONR, DE-SC0007991 from DOE for DNA synthesis and partial salary support, and Grant 3849 from the Gordon and Betty Moore Foundation. A.S. acknowledges partial support of the Research Council of Norway, Grant 213458 Topology in Norway.


  1. 1.
    N.A. Baas, N.C. Seeman, On the chemical synthesis of new topological structures. J. Math. Chem. 50(1), 220–232 (2012)CrossRefGoogle Scholar
  2. 2.
    N.A. Baas, New states of matter suggested by new topological structures. Int. J. Gen. Syst. 42(2), 170–196 (2013)CrossRefGoogle Scholar
  3. 3.
    N.A. Baas, New structures in complex systems. Eur. Phys. J. 178, 25–44 (2009)Google Scholar
  4. 4.
    N.A. Baas, On structure and organization: an organizing principle. Int. J. Gen. Syst. 42(2), 170–196 (2013)CrossRefGoogle Scholar
  5. 5.
  6. 6.
    C. Mao, W. Sun, N.C. Seeman, Assembly of Borromean rings from DNA. Nature 386, 137–138 (1997)CrossRefGoogle Scholar
  7. 7.
    K.S. Chicack, S.J. Cantrill, A.R. Pease, S.H. Chiu, G.W.V. Cave, J.L. Atwood, J.F. Stoddart, Molecular Borromean rings. Science 304, 1308–1312 (2004)CrossRefGoogle Scholar
  8. 8.
    Y. Weizmann, Private communicationGoogle Scholar
  9. 9.
    H.K. Moffatt, The energy spectrum of knots and links. Nature 347, 367–369 (1990)CrossRefGoogle Scholar
  10. 10.
    L. Zhu, P.S. Lukeman, J. Canary, N.C. Seeman, Nylon/DNA: single-stranded DNA with covalently stitched nylon lining. J. Am. Chem. Soc. 125, 10178–10179 (2003)Google Scholar
  11. 11.
    N.C. Seeman, DNA nicks and nodes and nanotechnology. NanoLetters 1, 22–26 (2001)Google Scholar
  12. 12.
    H.L. Frisch, E. Wasserman, Chemical topology. J. Am. Chem. Soc. 83, 3789–3795 (1961)CrossRefGoogle Scholar
  13. 13.
    N.C. Seeman, J. Chen, S.M. Du, J.E. Mueller, Y. Zhang, T.-J. Fu, H. Wang, Y. Wang, S. Zhang, Synthetic DNA knots and catenanes. New J. Chem. 17, 739–755 (1993)Google Scholar
  14. 14.
    N.C. Seeman, The design of single-stranded nucleic acid knots. Mol. Eng. 2, 297307 (1992)CrossRefGoogle Scholar
  15. 15.
    J.H. White, K.C. Millett, N.R. Cozzarelli, Description of the topological entanglement of DNA catenanes and knots by a powerful method involving strand passage and recombination. J. Mol. Biol 197, 585–603 (1987)CrossRefGoogle Scholar
  16. 16.
    J.D. Watson, F.H.C. Crick, Molecular structure of nucleic acids—a structure for deoxyribose nucleic acid. Nature 171, 737–738 (1953)CrossRefGoogle Scholar
  17. 17.
    A. Rich, A. Nordheim, A.H.-J. Wang, The chemistry and biology of left-handed Z-DNA. Annu. Rev. Biochem. 53, 791–846 (1984)CrossRefGoogle Scholar
  18. 18.
    T. Ciengshin, R. Sha, N.C. Seeman, Automatic molecular weaving prototyped using single-stranded DNA. Angew. Chem. Int. Ed. 50, 4419–4422 (2011)CrossRefGoogle Scholar
  19. 19.
    Z. Shen, H. Yan, T. Wang, N.C. Seeman, Paranemic crossover DNA: a generalized holliday structure with applications in nanotechnology. J. Am. Chem. Soc. 126, 16661674 (2004)Google Scholar
  20. 20.
    N.C. Seeman, DNA in a material world. Nature 421, 427–431 (2003)CrossRefGoogle Scholar
  21. 21.
    J.E. Mueller, S.M̃. Du, N.C. Seeman, The design and synthesis of a knot from single-stranded DNA. J. Am. Chem. Soc. 113, 6306–6308 (1991)CrossRefGoogle Scholar
  22. 22.
    S.M. Du, B.D. Stollar, N.C. Seeman, A synthetic DNA molecule in three knotted topologies. J. Am. Chem. Soc. 117, 1194–1200 (1995)CrossRefGoogle Scholar
  23. 23.
    J. Zheng, J.J. Birktoft, Y. Chen, T. Wang, R. Sha, P.E. Constantinou, S.L. Ginell, C. Mao, N.C. Seeman, From molecular to macroscopic via the rational design of a selfassembled 3D DNA crystal. Nature 461, 74–77 (2009)CrossRefGoogle Scholar
  24. 24.
    N.C. Seeman, Nucleic acid junctions and lattices. J. Theor. Biol. 99, 237–247 (1982)CrossRefGoogle Scholar
  25. 25.
    Y. Inokuma, S. Yoshioka, J. Arioshi, T. Arai, Y. Hitori, K. Takada, S. Matsunaga, K. Rissanen, M. Fujita, X-ray analysis on the nanogram to microgram scale using porous complexes. Nature 495, 461–467 (2013)CrossRefGoogle Scholar
  26. 26.
    H. Wang, S.M. Du, N.C. Seeman, Tight single-stranded DNA knots. J. Biomol. Struct. Dyns 10, 853–863 (1993)CrossRefGoogle Scholar
  27. 27.
    I. McNulty, J. Kirz, C. Jacobsen, E.H. Andersen, M.R. Howells, D.P. Kern, High resolution imaging by Fourier transform X-ray holography. Science 256, 1009–1012 (1992)CrossRefGoogle Scholar
  28. 28.
    S. Eisebitt, J. Lning, W.F. Schlotter, M. Lrgen, O. Hellwig, W. Eberhardt, J. Sthr, Lensless imaging of magnetic nanostructures by X-ray spectro-holography. Nature 432, 885–888 (2004)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Nils A. Baas
    • 1
  • Nadrian C. Seeman
    • 2
    Email author
  • Andrew Stacey
    • 1
  1. 1.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway
  2. 2.Department of ChemistryNew York UniversityNew YorkUSA

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