Program Size and Temperature in Self-Assembly

  • Ho-Lin Chen
  • David Doty
  • Shinnosuke Seki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7074)

Abstract

Winfree’s abstract Tile Assembly Model (aTAM) is a model of molecular self-assembly of DNA complexes known as tiles, which float freely in solution and attach one at a time to a growing “seed” assembly based on specific binding sites on their four sides. We show that there is a polynomial-time algorithm that, given an n ×n square, finds the minimal tile system (i.e., the system with the smallest number of distinct tile types) that uniquely self-assembles the square, answering an open question of Adleman, Cheng, Goel, Huang, Kempe, Moisset de Espanés, and Rothemund (Combinatorial Optimization Problems in Self-Assembly, STOC 2002). Our investigation leading to this algorithm reveals other positive and negative results about the relationship between the size of a tile system and its “temperature” (the binding strength threshold required for a tile to attach)

Keywords

Tile System Strength Function Tile Type Program Size Tile Assembly System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Adleman, L.M., Cheng, Q., Goel, A., Huang, M.-D.: Running time and program size for self-assembled squares. In: STOC 2001: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, Hersonissos, Greece, pp. 740–748. ACM (2001)Google Scholar
  2. 2.
    Adleman, L.M., Cheng, Q., Goel, A., Huang, M.-D.A., Kempe, D., de Espanés, P.M., Rothemund, P.W.K.: Combinatorial optimization problems in self-assembly. In: STOC 2002: Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, pp. 23–32 (2002)Google Scholar
  3. 3.
    Barish, R.D., Schulman, R., Rothemund, P.W., Winfree, E.: An information-bearing seed for nucleating algorithmic self-assembly. Proceedings of the National Academy of Sciences 106(15), 6054–6059 (2009)CrossRefGoogle Scholar
  4. 4.
    Evans, C.: Personal communicationGoogle Scholar
  5. 5.
    Fujibayashi, K., Hariadi, R., Park, S.H., Winfree, E., Murata, S.: Toward reliable algorithmic self-assembly of DNA tiles: A fixed-width cellular automaton pattern. Nano Letters 8(7), 1791–1797 (2007)CrossRefGoogle Scholar
  6. 6.
    Rothemund, P.W.K., Winfree, E.: The program-size complexity of self-assembled squares (extended abstract). In: STOC 2000: Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, pp. 459–468 (2000)Google Scholar
  7. 7.
    Rothemund, P.W.K., Papadakis, N., Winfree, E.: Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biology 2(12), 2041–2053 (2004)CrossRefGoogle Scholar
  8. 8.
    Seeman, N.C.: Nucleic-acid junctions and lattices. Journal of Theoretical Biology 99, 237–247 (1982)CrossRefGoogle Scholar
  9. 9.
    Wang, H.: Proving theorems by pattern recognition – II. The Bell System Technical Journal XL(1), 1–41 (1961)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Wang, H.: Dominoes and the AEA case of the decision problem. In: Proceedings of the Symposium on Mathematical Theory of Automata, New York, pp. 23–55 (1962); Polytechnic Press of Polytechnic Inst. of Brooklyn, Brooklyn, N.Y. (1963)Google Scholar
  11. 11.
    Winfree, E.: Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology (June 1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Ho-Lin Chen
    • 1
  • David Doty
    • 1
  • Shinnosuke Seki
    • 2
  1. 1.Department of Computing and Mathematical SciencesCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of System Sciences for Drug DiscoveryKyoto UniversityKyotoJapan

Personalised recommendations