Natural Computing

, Volume 7, Issue 2, pp 203–218 | Cite as

Combining self-healing and proofreading in self-assembly

  • David SoloveichikEmail author
  • Matthew Cook
  • Erik Winfree


Molecular self-assembly is a promising approach to bottom-up fabrication of complex structures. A major impediment to the practical use of self-assembly to create complex structures is the high rate of error under existing experimental conditions. Recent theoretical work on algorithmic self-assembly has shown that under a realistic model of tile addition and detachment, error correcting tile sets are possible that can recover from the attachment of incorrect tiles during the assembly process. An orthogonal type of error correction was recently considered as well: whether damage to a completed structure can be repaired. It was shown that such self-healing tile sets are possible. However, these tile sets are not robust to the incorporation of incorrect tiles. It remained an open question whether it is possible to create tile sets that can simultaneously resist wholesale removal of tiles and the incorporation of incorrect ones. Here we present a method for converting a tile set producing a pattern on the quarter plane into a tile set that makes the same pattern (at a larger scale) but is able to withstand both of these types of errors.


DNA nanotechnology Error-correction Proofreading Self-assembly Self-healing Tile Assembly Model 



We thank Ho-Lin Chen and Ashish Goel for insightful conversations and suggestions. This work was supported by NSF Grant No. 0523761.


  1. Adleman LM, Cheng Q, Goel A, Huang M-DA (2001) Running time and program size for self-assembled squares. In ACM Symposium on theory of computing (STOC), 740–748Google Scholar
  2. Aggarwal G, Cheng Q, Goldwasser MH, Kao M-Y, de Espanés PM, Schweller RT (2005) Complexities for generalized models of self-assembly. SIAM J Comput 34:1493–1515zbMATHCrossRefMathSciNetGoogle Scholar
  3. Barish RD, Rothemund PWK, Winfree E (2005) Two computational primitives for algorithmic self-assembly: Copying and counting. Nano Lett 5:2586–2592CrossRefGoogle Scholar
  4. Chen HL, Goel A (2005) Error free self-assembly using error prone tiles. In: Ferretti C, Mauri G, Zandron C (eds) DNA Computing 10, LNCS vol 3384. Berlin, Springer-Verlag, pp 62–75Google Scholar
  5. Cook M, Rothemund PWK, Winfree E (2004) Self-assembled circuit patterns. In: Chen J, Reif J (eds) DNA Computing 9, LNCS vol 2943. Berlin, Springer-Verlag, pp 91–107Google Scholar
  6. Feller W (1968) An introduction to probability theory and its applications, vol 1. New York, WileyGoogle Scholar
  7. Rothemund PWK, Papakakis N, Winfree E (2004) Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biol 2:e424CrossRefGoogle Scholar
  8. Rothemund PWK, Winfree E (2000) The program-size complexity of self-assembled squares. In: ACM symposium on theory of computing (STOC), pp 459–468Google Scholar
  9. LaBean TH, Yan H, Kopatsch J, Liu F, Winfree E, Reif JH, Seeman NC (2000) Construction, analysis, ligation, and self-assembly of DNA triple crossover complexes. J Am Chem Soc 122:1848–1860CrossRefGoogle Scholar
  10. Lagoudakis MG, LaBean TH (2000) 2-D DNA self-assembly for satisfiability. In: Winfree E, Gifford DK (eds) DNA Based Computers V, DIMACS vol 54. Providence, RI, American Mathematical Society, pp 141–154Google Scholar
  11. Mao C, LaBean TH, Reif JH, Seeman NC (2000) Logical computation using algorithmic self-assembly of DNA triple-crossover molecules. Nature 407:493–496CrossRefGoogle Scholar
  12. Mao C, Sun W, Seeman NC (1999) Designed two-dimensional DNA holliday junction arrays visualized by atomic force microscopy. J Am Chem Soc 121:5437–5443CrossRefGoogle Scholar
  13. Reif J (1999) Local parallel biomolecular computing. In: Rubin H, Wood DH (eds) DNA Based Computers III, DIMACS vol 48. Providence, RI, American Mathematical Society, pp 217–254Google Scholar
  14. Reif JH, Sahu S, Yin P (2005) Compact error-resilient computational DNA tiling assemblies. In: Ferretti C, Mauri G, Zandron C (eds) DNA Computing 10, LNCS vol 3384. Berlin, Springer-Verlag, pp 293–307Google Scholar
  15. Schulman R, Winfree E (2005a) Programmable control of nucleation for algorithmic self-assembly. In: Ferretti C, Mauri G, Zandron C (eds) DNA Computing 10, LNCS vol 3384. Berlin, Springer-Verlag, pp 319–328. Extended abstract in DNA Computing 10; preprint of the full paper is cond-mat/0607317 on arXiv.orgGoogle Scholar
  16. Schulman R, Winfree E (2005b) Self-replication and evolution of DNA crystals. In: Capcarrere MS, Freitas AA, Bentley PJ, Johnson CG, Timmis J (eds) Advances in Artificial Life: 8th European Conference (ECAL), LNCS vol 3630. Berlin, Springer-Verlag, pp 734–743Google Scholar
  17. Soloveichik D, Winfree E (2005) Complexity of compact proofreading for self-assembled patterns. In: DNA Computing 11. Berlin, Springer-VerlagGoogle Scholar
  18. Soloveichik D, Winfree E (2007) Complexity of self-assembled shapes. SIAM J Comput 36:1544–1569zbMATHCrossRefMathSciNetGoogle Scholar
  19. Winfree E (1996) On the computational power of DNA annealing and ligation. In: Lipton RJ, Baum E B (eds) DNA Based Computers, DIMACS vol 27. Providence, RI, American Mathematical Society, pp 199–221Google Scholar
  20. Winfree E (1998a) Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology, PasadenaGoogle Scholar
  21. Winfree E (1998b) Simulations of computing by self-assembly. Technical Report CS-TR:1998.22, CaltechGoogle Scholar
  22. Winfree E (2006) Self-healing tile sets. In: Chen J, Jonoska N, Rozenberg G (eds) Nanotechnology: science and computation. Springer-Verlag, Berlin, pp 55–78CrossRefGoogle Scholar
  23. Winfree E, Bekbolatov R (2004) Proofreading tile sets: error-correction for algorithmic self-assembly. In: Chen J, Reif J (eds) DNA Computing 9, LNCS vol 2943. Berlin, Springer-Verlag, pp 126–144Google Scholar
  24. Winfree E, Liu F, Wenzler LA, Seeman NC (1998) Design and self-assembly of two dimensional DNA crystals. Nature 394:539–544CrossRefGoogle Scholar
  25. Winfree E, Yang X, Seeman NC (1998) Universal computation via self-assembly of DNA: some theory and experiments. In: Landweber LF, Baum EB (eds) DNA Based Computers II, DIMACS vol 44. Providence, RI, American Mathematical Society, pp 191–213Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Department of CNSCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Institute of NeuroinformaticsZurichSwitzerland
  3. 3.Department of CNS and CSCalifornia Institute of TechnologyPasadenaUSA

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