Synthesising topological links
- 316 Downloads
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.
KeywordsSynthetic DNA topology of links Brunnian links Carpets and solids Hopf links Synthesizing double stranded DNA nodes
Mathematics Subject Classification57M25
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.
- 3.N.A. Baas, New structures in complex systems. Eur. Phys. J. 178, 25–44 (2009)Google Scholar
- 5.The Knot Atlas. Rubber band links. http://katlas.org/wiki/‘‘Rubberband’’_Brunnian_Links
- 8.Y. Weizmann, Private communicationGoogle Scholar
- 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.N.C. Seeman, DNA nicks and nodes and nanotechnology. NanoLetters 1, 22–26 (2001)Google Scholar
- 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
- 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