Synthesizing Minimal Tile Sets for Patterned DNA Self-assembly

  • Mika Göös
  • Pekka Orponen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6518)


The Pattern self-Assembly Tile set Synthesis (PATS) problem is to determine a set of coloured tiles that self-assemble to implement a given rectangular colour pattern. We give an exhaustive branch-and-bound algorithm to find tile sets of minimum cardinality for the PATS problem. Our algorithm makes use of a search tree in the lattice of partitions of the ambient rectangular grid, and an efficient bounding function to prune this search tree. Empirical data on the performance of the algorithm shows that it compares favourably to previously presented heuristic solutions to the problem.


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  1. 1.
    Adleman, L., Cheng, Q., Goel, A., Huang, M.-D., Kempe, D., de Espanés, P.M., Rothemund, P.W.K.: Combinatorial optimization problems in self-assembly. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC 2002), pp. 23–32. ACM, New York (2002)Google Scholar
  2. 2.
    Göös, M., Orponen, P.: Synthesizing minimal tile sets for patterned DNA self-assembly. A detailed version, arXiv:0911.2924Google Scholar
  3. 3.
    Lathrop, J.I., Lutz, J.H., Summers, S.M.: Strict self-assembly of discrete Sierpinski triangles. Theoretical Computer Science 410(4-5), 384–405 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Lin, C., Liu, Y., Rinker, S., Yan, H.: DNA tile based self-assembly: building complex nanoarchitectures. Chem. Phys. Chem. 7(8), 1641–1647 (2006)Google Scholar
  5. 5.
    Ma, X., Lombardi, F.: Synthesis of tile sets for DNA self-assembly. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 27(5), 963–967 (2008)CrossRefGoogle Scholar
  6. 6.
    Ma, X., Lombardi, F.: On the computational complexity of tile set synthesis for DNA self-assembly. IEEE Transactions on Circuits and Systems II: Express Briefs 56(1), 31–35 (2009)CrossRefGoogle Scholar
  7. 7.
    Park, S.H., Pistol, C., Ahn, S.J., Reif, J.H., Lebeck, A.R., Dwyer, C., LaBean, T.H.: Finite-size, fully addressable DNA tile lattices formed by hierarchical assembly procedures. Angewandte Chemie International Edition 45(5), 735–739 (2006)CrossRefGoogle Scholar
  8. 8.
    Park, S.H., Yan, H., Reif, J.H., LaBean, T.H., Finkelstein, G.: Electronic nanostructures templated on self-assembled DNA scaffolds. Nanotechnology 15, S525–S527 (2004)CrossRefGoogle Scholar
  9. 9.
    Rothemund, P.W.K.: Theory and Experiments in Algorithmic Self-assembly. PhD thesis, University of Southern California (2001)Google Scholar
  10. 10.
    Rothemund, P.W.K.: Folding DNA to create nanoscale shapes and patterns. Nature 440, 297–302 (2006)CrossRefGoogle Scholar
  11. 11.
    Rothemund, P.W.K., Winfree, E.: The program-size complexity of self-assembled squares (extended abstract). In: Proceedings of the 32nd Annual ACM Symposium on Theory of Computing (STOC 2000), pp. 459–468. ACM, New York (2000)Google Scholar
  12. 12.
    Winfree, E.: Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology (1998)Google Scholar
  13. 13.
    Yan, H., Park, S.H., Finkelstein, G., Reif, J.H., LaBean, T.H.: DNA-templated self-assembly of protein arrays and highly conducive nanowires. Science 301, 1882–1884 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Mika Göös
    • 1
  • Pekka Orponen
    • 1
  1. 1.Department of Information and Computer ScienceAalto University School of Science and Technology (TKK)AaltoFinland

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