Synthesizing Small and Reliable Tile Sets for Patterned DNA Self-assembly
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.
KeywordsMinimal Solution Full Adder Tile Type Wall Clock Time Input Edge
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- 1.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)Google Scholar
- 5.Lifschitz, V.: What is answer set programming? In: Proc. 23rd Natl. Conf. Artificial Intelligence, pp. 1594–1597 (2008)Google Scholar
- 11.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)Google Scholar
- 13.Syrjänen, T., Niemelä, I.: The Smodels system. In: Logic Programming and Nonmonotonic Reasoning, pp. 434–438. Springer, Heidelberg (2001)Google Scholar
- 14.Winfree, E., Liu, F., Wenzler, L.A., Seeman, N.C.: Design and self-assembly of two-dimensional DNA crystals. Nature 394 (1998)Google Scholar
- 15.Winfree, E.: Simulations of Computing by Self-Assembly. Technical Report CSTR 1998.22, California Institute of Technology (1998)Google Scholar
- 16.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)Google Scholar