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)

Abstract

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 ε2 (ε3), without increasing the size of the assembly. These results were further validated using stochastic analysis and computer simulation.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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

Personalised recommendations