Letter | Published:

Logical computation using algorithmic self-assembly of DNA triple-crossover molecules

Nature volume 407, pages 493496 (28 September 2000) | Download Citation


  • An Erratum to this article was published on 07 December 2000


Recent work1,2,3 has demonstrated the self-assembly of designed periodic two-dimensional arrays composed of DNA tiles, in which the intermolecular contacts are directed by ‘sticky’ ends. In a mathematical context, aperiodic mosaics may be formed by the self-assembly of ‘Wang’ tiles4, a process that emulates the operation of a Turing machine. Macroscopic self-assembly has been used to perform computations5; there is also a logical equivalence between DNA sticky ends and Wang tile edges6,7. This suggests that the self-assembly of DNA-based tiles could be used to perform DNA-based computation8. Algorithmic aperiodic self-assembly requires greater fidelity than periodic self-assembly, because correct tiles must compete with partially correct tiles. Here we report a one-dimensional algorithmic self-assembly of DNA triple-crossover molecules9 that can be used to execute four steps of a logical (cumulative XOR) operation on a string of binary bits.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1.

    , , & Design and self-assembly of two-dimensional DNA crystals. Nature 394, 539–544 (1998).

  2. 2.

    , & Modifying the surface features of two-dimensional DNA crystals. J. Am. Chem. Soc. 121, 917– 922 (1999).

  3. 3.

    , & Seeman N. C. Designed two-dimensional DNA Holliday junction arrays visualized by atomic force microscopy. J. Am. Chem. Soc. 121, 5437–5443 (1999).

  4. 4.

    in Proceedings of a Symposium in the Mathematical Theory of Automata 23–26 (Polytechnic Press, New York, 1963).

  5. 5.

    K. Using lateral capillary forces to compute by self-assembly. Proc. Nat. Acad. Sci. USA 97, 984– 989 (2000).

  6. 6.

    in DNA Based Computers: Proceedings of a DIMACS Workshop, April 4, 1995, Princeton University (eds Lipton, R. J. & Baum, E. B.) 199– 221 (American Mathematical Society, Providence, RI, 1996).

  7. 7.

    Algorithmic Self-Assembly of DNA. PhD Thesis, Caltech ( 1998).

  8. 8.

    Molecular computation of solutions to combinatorial problems. Science 266, 1021–1024 ( 1994).

  9. 9.

    et al. The construction, analysis, ligation and self-assembly of DNA triple crossover complexes. J. Am. Chem. Soc. 122, 1848–1860 (2000).

  10. 10.

    Nucleic acid nanostructures and topology. Angew. Chem. Int. Edn Engl. 37, 3220–3238 ( 1998).

  11. 11.

    , , & Molecular computation: RNA solutions to chess problems. Proc. Natl Acad. Sci. USA 97, 1385–1389 (2000).

  12. 12.

    & Unexpected substrate specificity of T4 DNA ligase revealed by in vitro selection. Nucleic Acids Res. 21, 2287–2291 (1993).

  13. 13.

    , & in DNA Based Computers: II Proceedings of a DIMACS Workshop, June 10–12, 1996, Princeton University (eds Landweber, L. F. & Baum, E. B.) 217–254 (American Mathematical Society, Providence, RI, 1999).

  14. 14.

    et al. DNA computing on surfaces. Nature 403, 175–179 (2000).

  15. 15.

    et al. The arrayed primer extension method for DNA microchip analysis. Molecular computation of satisfaction problems. J. Am. Chem. Soc. 122, 1873–1882 ( 2000).

  16. 16.

    et al. Molecular computation by DNA hairpin formation. Science 288, 1223–1226 ( 2000).

  17. 17.

    , & in DNA Based Computers: Proceedings of a DIMACS Workshop, June 1999, MIT (ed. E. Winfree) (DIMACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, Providence, RI, in the press).

  18. 18.

    in DNA Based Computers: III Proceedings of a DIMACS Workshop, June 23–25, 1997, University of Pennsylvania (eds Rubin, H. & Wood D. H.) 217–254 (American Mathematical Society, Providence, RI, 1999).

Download references


We thank E. Winfree and A. Carbone for valuable discussions. This work has been supported by grants from DARPA and the National Science Foundation to J.H.R. and N.C.S.; ONR, USAF, NSF and NIH grants to N.C.S.; and NSF and ARO grants to J.H.R.

Author information


  1. *Department of Chemistry, New York University, New York, 10003, USA &

    • Chengde Mao
    •  & Nadrian C. Seeman
  2. †Department of Computer Science, Duke University, Durham, North Carolina 27707, USA

    • Thomas H. LaBean
    •  & John H. Reif


  1. Search for Chengde Mao in:

  2. Search for Thomas H. LaBean in:

  3. Search for John H. Reif in:

  4. Search for Nadrian C. Seeman in:

Corresponding author

Correspondence to Nadrian C. Seeman.

Supplementary information

PDF files

  1. 1.

    Figure 1

Image files

  1. 1.

    Figure 2

Word documents

  1. 1.


About this article

Publication history






Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.