Skip to main content
Log in

Coding and geometrical shapes in nanostructures: A fractal DNA-assembly

  • Published:
Natural Computing Aims and scope Submit manuscript

Abstract

Fractal patterns represent an important classof aperiodic arrangements. Generating fractalstructures by self-assembly is a majorchallenge for nanotechnology. The specificityof DNA sticky-ended interactions and thewell-behaved structural nature of DNAparallelogram motifs has previously led to aprotocol that appears likely to be capable ofproducing fractal constructions [A. Carbone andN.C. Seeman, A route to fractal DNAassembly, Natural Computing 1,469–480, 2002]. That protocol dependson gluing the set of tiles with special `gluetiles' to produce the fractal structure. It ispossible to develop a fractal-assembly protocolthat does not require the participation ofgluing components. When designed with similarDNA parallelogram motifs, the protocol involvessixteen specific tiles, sixteen closely relatedtiles, and a series of protecting groups thatare designed to be removed by the introductionof specific strands into the solution. Onenovel aspect of the construction on thetheoretical level is the interplay of bothgeometry and coding in tile design. A secondfeature, related to the implementation, is thenotion of generalized protecting groups.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Carbone A and Seeman NC (2002) A route to fractal DNA assembly. Natural Computing 1: 469–480

    Google Scholar 

  • Caruthers MH (1985) Gene synthesis machines: DNA chemistry and its uses. Science 230: 281–285

    Google Scholar 

  • Churchill MEA, Tullius TD, Kallenbach NR and Seeman NC (1988) A Holliday recombination intermediate is twofold symmetric. Proc. Nat. Acad. Sci. (USA) 85: 4653–4656

    Google Scholar 

  • Cohen SN, Chang ACY, Boyer HW and Helling RB (1973) Construction of biologically functional bacterial plasmids in vitro. Proc. Nat. Acad. Sci. (USA) 70: 3240–3244

    Google Scholar 

  • LaBean T, Yan H, Kopatsch J, Liu F, Winfree E, Reif JH and Seeman NC (2000) The construction, analysis, ligation and self-assembly of DNA triple crossover complexes. J. Am. Chem. Soc. 122: 1848–1860

    Google Scholar 

  • Li X, Yang X, Qi J and Seeman NC (1996) Antiparallel DNA double crossover molecules as components for nanoconstruction. J. Am. Chem. Soc. 118: 6131–6140

    Google Scholar 

  • Liu F, Sha R and Seeman NC (1999) Modifying the surface features of two-dimensional DNA crystals. J. Am. Chem. Soc. 121: 917–922

    Google Scholar 

  • Mao C, Sun W and Seeman NC (1999) Two-dimensional DNA Holliday junction arrays visualized by atomic force microscopy. J. Am. Chem. Soc. 121: 5437–5443

    Google Scholar 

  • Mao C, LaBean T, Reif JH and Seeman NC (2000) Logical computation using algorithmic self-assembly of DNA triple crossover molecules. Nature 407: 493–496

    Google Scholar 

  • Nielsen PE, Egholm M, Berg RH and Buchardt O (1991) Sequence-selective recognition of DNA by strand displacement with a thymine-substituted polyamide. Science 254: 1497–1500

    Google Scholar 

  • Seeman NC (1982) Nucleic acid junctions and lattices. J. Theor. Biol. 99: 237–247

    Google Scholar 

  • Seeman NC (1992) The design of single-stranded nucleic acid knots. Molec. Eng. 2: 297–307

    Google Scholar 

  • Sha R, Liu F, Bruist MF and Seeman NC (1998) Parallel helical domains in DNA branched junctions containing 5', 5' and 3', 3' linkages, Biochemistry 38: 2832–2841

    Google Scholar 

  • Sha R, Liu F, Millar DM and Seeman NC (2000) Atomic force microscopy of parallel DNA branched junction arrays. Chem. & Biol. 7: 743–751

    Google Scholar 

  • Sha R, Liu F and Seeman NC (2002) Atomic force measurement of the interdomain angle in symmetric Holliday junctions. Biochem. 41: 5950–5955

    Google Scholar 

  • Winfree E (1996) On the computational power of DNA annealing and ligation. In: Richard Lipton J and Baum EB (eds) DNA Based Computers: Proceedings of a DIMACS Workshop, April 4, 1995, Princeton University (Volume 27 in DIMACS), pp. 187–198. American Mathematical Society

  • Winfree E (2000) Algorithmic self-assembly of DNA: Theoretical motivations and 2D assembly experiments. J. Biol. Mol. Struct. & Dyns. Conversation 11(2): 263–270

    Google Scholar 

  • Winfree E, Liu F, Wenzler LA and Seeman NC (1998) Design and self-assembly of twodimensional DNA crystals. Nature 394: 539–544

    Google Scholar 

  • Yan H, Zhang X, Shen Z and Seeman NC (2002) A robust DNA mechanical device controlled by hybridization topology. Nature 415: 62–65

    Google Scholar 

  • Yan H and Seeman NC (2002) Edge-sharing motifs in DNA nanotechnology. J. Supramol. Chem., in press

  • Yurke B, Turberfield AJ, Mills AP, Jr., Simmel FC and Neumann JL (2000) A DNA-fuelled molecular machine made of DNA. Nature 406: 605–608

    Google Scholar 

  • Zhang Y and Seeman NC (1992) A solid-support methodology for the construction of geometrical objects from DNA. J. Am. Chem. Soc. 114: 2656–2663

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carbone, A., Seeman, N.C. Coding and geometrical shapes in nanostructures: A fractal DNA-assembly. Natural Computing 2, 133–151 (2003). https://doi.org/10.1023/A:1024943106163

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024943106163

Navigation