Abstract
We consider the problem of finding, for a given 2D pattern of colored tiles, a minimal set of tile types self-assembling to this pattern in the abstract Tile Assembly Model of Winfree (1998). This Patterned self-Assembly Tile set Synthesis (PATS) problem was first introduced by Ma and Lombardi (2008), and subsequently studied by Göös and Orponen (2011), who presented an exhaustive partition-search branch-and-bound algorithm (briefly PS-BB) for it. However, finding the true minimal tile sets is very time consuming, and PS-BB is not well-suited for finding small but not necessarily minimal solutions. In this paper, we modify the basic partition-search framework by using a heuristic to optimize the order in which the algorithm traverses its search space. We find that by running several parallel instances of the modified algorithm PS-H, the search time for small tile sets can be shortened considerably. We also introduce a method for computing the reliability of a tile set, i.e. the probability of its error-free self-assembly to the target tiling, based on Winfree’s analysis of the kinetic Tile Assembly Model (1998). We present data on the reliability of tile sets found by the algorithms and find that also here PS-H constitutes a significant improvement over PS-BB.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Czeizler, E., Lempiäinen, T., Orponen, P.: A design framework for carbon nanotube circuits affixed on DNA origami tiles. In: Proc. 8th Ann. Conf. Foundations of Nanoscience, pp. 186–187 (2011)
Gomes, C.P., Selman, B.: Algorithm portfolios. Artif. Intell. 126, 43–62 (2001)
Göös, M., Orponen, P.: Synthesizing minimal tile sets for patterned DNA self-assembly. In: Sakakibara, Y., Mi, Y. (eds.) DNA 16 2010. LNCS, vol. 6518, pp. 71–82. Springer, Heidelberg (2011)
Kim, K.N., Sarveswaran, K., Mark, L., Lieberman, M.: DNA origami as self-assembling circuit boards. In: Calude, C.S., Hagiya, M., Morita, K., Rozenberg, G., Timmis, J. (eds.) Unconventional Computation. LNCS, vol. 6079, pp. 56–68. Springer, Heidelberg (2010)
Lifschitz, V.: What is answer set programming? In: Proc. 23rd Natl. Conf. Artificial Intelligence, pp. 1594–1597 (2008)
Liu, W., Zhong, H., Wang, R., Seeman, N.C.: Crystalline two-dimensional DNA-origami arrays. Angewandte Chemie International Edition 50(1), 264–267 (2011)
Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of Las Vegas algorithms. Information Processing Letters 47(4), 173–180 (1993)
Ma, X., Lombardi, F.: Synthesis of tile sets for DNA self-assembly. IEEE Trans. CAD of Integrated Circuits and Systems 27, 963–967 (2008)
Maune, H.T., Han, S., Barish, R.D., Bockrath, M., Goddard III, W.A., Rothemund, P.W.K., Winfree, E.: Self-assembly of carbon nanotubes into two-dimensional geometries using DNA origami templates. Nature Nanotechnology 5, 61–66 (2010)
Rajendran, A., Endo, M., Katsuda, Y., Hidaka, K., Sugiyama, H.: Programmed two-dimensional self-assembly of multiple DNA origami jigsaw pieces. ACS Nano 5(1), 665–671 (2011)
Rothemund, P.W.K., Winfree, E.: The program-size complexity of self-assembled squares. In: Proc. 32nd Ann. ACM Theory of Computing, pp. 459–468 (2000)
Rothemund, P.W.K.: Folding DNA to create nanoscale shapes and patterns. Nature 440, 297–302 (2006)
Syrjänen, T., Niemelä, I.: The Smodels system. In: Logic Programming and Nonmonotonic Reasoning, pp. 434–438. Springer, Heidelberg (2001)
Winfree, E., Liu, F., Wenzler, L.A., Seeman, N.C.: Design and self-assembly of two-dimensional DNA crystals. Nature 394 (1998)
Winfree, E.: Simulations of Computing by Self-Assembly. Technical Report CSTR 1998.22, California Institute of Technology (1998)
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 (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lempiäinen, T., Czeizler, E., Orponen, P. (2011). Synthesizing Small and Reliable Tile Sets for Patterned DNA Self-assembly. In: Cardelli, L., Shih, W. (eds) DNA Computing and Molecular Programming. DNA 2011. Lecture Notes in Computer Science, vol 6937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23638-9_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-23638-9_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23637-2
Online ISBN: 978-3-642-23638-9
eBook Packages: Computer ScienceComputer Science (R0)