Compact Error-Resilient Computational DNA Tilings

  • John H. Reif
  • Sudheer Sahu
  • Peng Yin
Part of the Natural Computing Series book series (NCS)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Barish, P. W.K. Rothemund, and E. Winfree. Algorithmic self-assembly of a binary counter using DNA tiles. 2005. In preparation.Google Scholar
  2. 2.
    B.A. Bondarenko. Generalized Pascal Triangles and Pyramids, Their Fractals, Graphs and Applications. The Fibonacci Association, 1993. Translated from Russion and edited by R.C. Bollinger.Google Scholar
  3. 3.
    N. Chelyapov, Y. Brun, M. Gopalkrishnan, D. Reishus, B. Shaw, and L. Adleman. DNA triangles and self-assembled hexagonal tilings. J. Am. Chem. Soc., 126:13924–13925, 2004.CrossRefGoogle Scholar
  4. 4.
    H.L. Chen, Q. Cheng, A. Goel, M.D. Huang, and P.M. de Espanes. Invadable self-assembly: Combining robustness with efficiency. In Proceedings of the 15th annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 890–899, 2004.Google Scholar
  5. 5.
    H.L. Chen and A. Goel. Error free self-assembly using error prone tiles. In DNA Based Computers 10, pages 274–283, 2004.Google Scholar
  6. 6.
    K. Fujibayashi and S. Murata. A method for error suppression for self-assembling DNA tiles. In DNA Based Computing 10, pages 284–293, 2004.Google Scholar
  7. 7.
    T.H. LaBean, H. Yan, J. Kopatsch, F. Liu, E. Winfree, J.H. Reif, and N.C. Seeman. The construction, analysis, ligation and self-assembly of DNA triple crossover complexes. J. Am. Chem. Soc., 122:1848–1860, 2000.CrossRefGoogle Scholar
  8. 8.
    M.G. Lagoudakis and T.H. LaBean. 2-D DNA self-assembly for satisfiability. In DNA Based Computers V, volume 54 of DIMACS, pages 141–154. American Mathematical Society, 2000.MathSciNetGoogle Scholar
  9. 9.
    D. Liu, M.S. Wang, Z.X. Deng, R. Walulu, and C.D. Mao. Tensegrity: Construction of rigid DNA triangles with flexible four-arm DNA junctions. J. Am. Chem. Soc., 126:2324–2325, 2004.CrossRefGoogle Scholar
  10. 10.
    D. Liu, S.H. Park, J.H. Reif, and T.H. LaBean. DNA nanotubes self-assembled from triple-crossover tiles as templates for conductive nanowires. Proc. Natl. Acad. Sci. USA, 101:717–722, 2004.CrossRefGoogle Scholar
  11. 11.
    C. Mao, T.H. LaBean, J.H. Reif, and N.C. Seeman. Logical computation using algorithmic self-assembly of DNA triple-crossover molecules. Nature, 407:493–496, 2000.CrossRefGoogle Scholar
  12. 12.
    C. Mao, W. Sun, and N.C. Seeman. Designed two-dimensional DNA Holliday junction arrays visualized by atomic force microscopy. J. Am. Chem. Soc., 121:5437–5443, 1999.CrossRefGoogle Scholar
  13. 13.
    J.H. Reif. Local parallel biomolecular computation. In H. Rubin and D. H. Wood, editors, DNA-Based Computers 3, volume 48 of DIMACS, pages 217–254. American Mathematical Society, 1999.Google Scholar
  14. 14.
    P.W.K. Rothemund and E. Winfree. The program-size complexity of self-assembled squares (extended abstract). In Proceedings of the thirty-second annual ACM symposium on Theory of computing, pages 459–468. ACM Press, 2000.Google Scholar
  15. 15.
    P.W.K. Rothemund, A. Ekani-Nkodo, N. Papadakis, A. Kumar, D.K. Fygenson, and E. Winfree. Design and characterization of programmable DNA nanotubes. J. Am. Chem. Soc., 126:16344–16353, 2004.CrossRefGoogle Scholar
  16. 16.
    P.W.K. Rothemund, N. Papadakis, and E. Winfree. Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biology 2 (12), 2:e424, 2004.CrossRefGoogle Scholar
  17. 17.
    R. Schulman and E. Winfree. Programmable control of nucleation for algorithmic self-assembly. In DNA Based Computers 10, LNCS, 2005.Google Scholar
  18. 18.
    N.C. Seeman. DNA in a material world. Nature, 421:427–431, 2003.MathSciNetCrossRefGoogle Scholar
  19. 19.
    J. von Neumann. Probabilistic logics and the synthesis of reliable organisms from unreliable components. Autonomous Studies, pages 43–98, 1956.Google Scholar
  20. 20.
    H. Wang. Proving theorems by pattern recognition II. Bell Systems Technical Journal, 40:1–41, 1961.Google Scholar
  21. 21.
    E. Winfree. Complexity of restricted and unrestricted models of molecular computation. In R. J. Lipton and E. B. Baum, editors, DNA Based Computers 1, volume 27 of DIMACS, pages 187–198. American Mathematical Society, 1996.Google Scholar
  22. 22.
    E. Winfree. On the computational power of DNA annealing and ligation. In R. J. Lipton and E. B. Baum, editors, DNA Based Computers 1, volume 27 of DIMACS, pages 199–221. American Mathematical Society, 1996.Google Scholar
  23. 23.
    E. Winfree. Algorithmic Self-Assembly of DNA. PhD thesis, 1998.Google Scholar
  24. 24.
    E. Winfree. Simulation of computing by self-assembly. Technical Report 1998.22, Caltech, 1998.Google Scholar
  25. 25.
    E. Winfree and R. Bekbolatov. Proofreading tile sets: Error correction for algorithmic self-assembly. In DNA Based Computers 9, volume 2943 of LNCS, pages 126–144, 2004.MathSciNetGoogle Scholar
  26. 26.
    E. Winfree, F. Liu, L.A. Wenzler, and N.C. Seeman. Design and self-assembly of two-dimensional DNA crystals. Nature, 394(6693):539–544, 1998.CrossRefGoogle Scholar
  27. 27.
    E. Winfree, X. Yang, and N.C. Seeman. Universal computation via self-assembly of DNA: Some theory and experiments. In L.F. Landweber and E.B. Baum, editors, DNA Based Computers II, volume 44 of DIMACS, pages 191–213. American Mathematical Society, 1999.Google Scholar
  28. 28.
    H. Yan, L. Feng, T.H. LaBean, and J.H. Reif. Parallel molecular computation of pair-wise XOR using DNA string tile. J. Am. Chem. Soc., 125(47), 2003.Google Scholar
  29. 29.
    H. Yan, T.H. LaBean, L. Feng, and J.H. Reif. Directed nucleation assembly of DNA tile complexes for barcode patterned DNA lattices. Proc. Natl. Acad. Sci. USA, 100(14):8103–8108, 2003.CrossRefGoogle Scholar
  30. 30.
    H. Yan, S.H. Park, G. Finkelstein, J.H. Reif, and T.H. LaBean. DNA-templated self-assembly of protein arrays and highly conductive nanowires. Science, 301(5641):1882–1884, 2003.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • John H. Reif
    • 1
  • Sudheer Sahu
    • 1
  • Peng Yin
    • 1
  1. 1.Department of Computer ScienceDuke UniversityDurhamUSA

Personalised recommendations