Compact Error-Resilient Computational DNA Tiling Assemblies

  • John H. Reif
  • Sudheer Sahu
  • Peng Yin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3384)


The self-assembly process for bottom-up construction of nanostructures is of key importance to the emerging scientific discipline Nanoscience. However, self-assembly at the molecular scale is prone to a quite high rate of error. Such high error rate is a major barrier to large-scale experimental implementation of DNA tiling. The goals of this paper are to develop theoretical methods for compact error-resilient self-assembly and to analyze these methods by stochastic analysis and computer simulation. Prior work by Winfree provided an innovative approach to decrease tiling self-assembly errors without decreasing the intrinsic error rate ε of assembling a single tile. However, his technique resulted in a final structure that is four times the size of the original one. This paper describes various compact error-resilient tiling methods that do not increase the size of the tiling assembly. These methods apply to assembly of boolean arrays which perform input sensitive computations (among other computations). Our 2-way (3-way) overlay redundancy construction drops the error rate from ε to approximately ε 2 (ε 3), without increasing the size of the assembly. These results were further validated using stochastic analysis and computer simulation.


Tile Type Binary Counter Single Mismatch Adjacent Tile Neighborhood Tile 
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  1. 1.
    Bondarenko, B.A.: Generalized Pascal Triangles and Pyramids, Their Fractals, Graphs and Applications. The Fibonacci Association (1993); Translated from Russian and edited by R. C. BollingerGoogle Scholar
  2. 2.
    Chen, H.L., Cheng, Q., Goel, A., Huang, M.D., de Espanes, P.M.: Invadable self-assembly: Combining robustness with efficiency. In: ACM-SIAM Symposium on Discrete Algorithms, SODA (2004)Google Scholar
  3. 3.
    LaBean, T.H., Yan, H., Kopatsch, J., Liu, F., Winfree, E., Reif, J.H., Seeman, N.C.: The construction, analysis, ligation and self-assembly of DNA triple crossover complexes. J. Am. Chem. Soc. 122, 1848–1860 (2000)CrossRefGoogle Scholar
  4. 4.
    Lagoudakis, M.G., LaBean, T.H.: 2-D DNA self-assembly for satisfiability. In: DNA Based Computers V. DIMACS, vol. 54, pp. 141–154. American Mathematical Society (2000)Google Scholar
  5. 5.
    Mao, C., Sun, W., Seeman, N.C.: Designed two-dimensional DNA holliday junction arrays visualized by atomic force microscopy. J. Am. Chem. Soc. 121, 5437–5443 (1999)CrossRefGoogle Scholar
  6. 6.
    Reif, J.H.: Local parallel biomolecular computation. In: Rubin, H., Wood, D.H. (eds.) DNA-Based Computers 3. DIMACS, vol. 48, pp. 217–254. American Mathematical Society (1999)Google Scholar
  7. 7.
    Reif, J.H., Sahu, S., Yin, P.: Compact error-resilient computational DNA tiling assemblies. Technical Report CS-2004-08, Duke University, Computer Science Department (2004)Google Scholar
  8. 8.
    Seeman, N.C.: DNA in a material world. Nature 421, 427–431 (2003)CrossRefMathSciNetGoogle Scholar
  9. 9.
    von Neumann, J.: Probabilistic logics and the synthesis of reliable organisms from unreliable components. Autonomous Studies, 43–98 (1956)Google Scholar
  10. 10.
    Winfree, E.: On the computational power of DNA annealing and ligation. In: Lipton, R.J., Baum, E.B. (eds.) DNA Based Computers 1. DIMACS, vol. 27, pp. 199–221. American Mathematical Society (1996)Google Scholar
  11. 11.
    Winfree, E.: Simulation of computing by self-assembly. Technical Report 1988.22, Caltech (1998)Google Scholar
  12. 12.
    Winfree, E., Bekbolatov, R.: Proofreading tile sets: logical error correction for algorithmic self-assembly. In: Chen, J., Reif, J.H. (eds.) DNA 2003. LNCS, vol. 2943, pp. 126–144. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Winfree, E., Liu, F., Wenzler, L.A., Seeman, N.C.: Design and self-assembly of two-dimensional DNA crystals. Nature 394, 539–544 (1998)CrossRefGoogle Scholar
  14. 14.
    Winfree, E., Yang, X., Seeman, N.C.: Universal computation via self-assembly of DNA: Some theory and experiments. In: Landweber, L.F., Baum, E.B. (eds.) DNA Based Computers II. DIMACS, vol. 44, pp. 191–213. American Mathematical Society (1999)Google Scholar
  15. 15.
    Yan, H., Park, S.H., Finkelstein, G., Reif, J.H., LaBean, T.H.: DNA-templated self-assembly of protein arrays and highly conductive nanowires. Science 301, 1882–1884 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

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

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