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An Introduction to Tile-Based Self-assembly

  • Conference paper
Unconventional Computation and Natural Computation (UCNC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7445))

Abstract

In this tutorial, we give a brief introduction to the field of tile-based algorithmic self-assembly. We begin with a description of Winfree’s abstract Tile Assembly Model (aTAM) and a few basic exercises in designing tile assembly systems. We then survey a series of results in the aTAM. Next, we introduce the more experimentally realistic kinetic Tile Assembly Model (kTAM) and provide an exercise in error correction within the kTAM, then an overview of kTAM results. We next introduce the 2-Handed Assembly Model (2HAM), which allows entire assemblies to combine with each other in pairs, along with an exercise in developing a 2HAM system, and then give overviews of a series of 2HAM results. Finally, we briefly introduce a wide array of more recently developed models and discuss their various tradeoffs in comparison to the aTAM and each other.

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References

  1. Abel, Z., Benbernou, N., Damian, M., Demaine, E., Demaine, M., Flatland, R., Kominers, S., Schweller, R.: Shape replication through self-assembly and RNase enzymes. In: SODA 2010: Proceedings of the Twenty-first Annual ACM-SIAM Symposium on Discrete Algorithms, Austin, Texas. Society for Industrial and Applied Mathematics (2010)

    Google Scholar 

  2. Adleman, L., Cheng, Q., Goel, A., Huang, M.-D.: Running time and program size for self-assembled squares. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing, Hersonissos, Greece, pp. 740–748 (2001)

    Google Scholar 

  3. 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: Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, pp. 23–32 (2002)

    Google Scholar 

  4. Aggarwal, G., Goldwasser, M.H., Kao, M.-Y., Schweller, R.T.: Complexities for generalized models of self-assembly. In: Proceedings of ACM-SIAM Symposium on Discrete Algorithms (2004)

    Google Scholar 

  5. Becker, F., Rapaport, I., Rémila, É.: Self-assemblying Classes of Shapes with a Minimum Number of Tiles, and in Optimal Time. In: Arun-Kumar, S., Garg, N. (eds.) FSTTCS 2006. LNCS, vol. 4337, pp. 45–56. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  6. Cannon, S., Demaine, E.D., Demaine, M.L., Eisenstat, S., Patitz, M.J., Schweller, R., Summers, S.M., Winslow, A.: Two hands are better than one (up to constant factors). Tech. Report 1201.1650, Computing Research Repository (2012)

    Google Scholar 

  7. Chen, H.-L., Doty, D.: Parallelism and time in hierarchical self-assembly. In: SODA 2012: Proceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1163–1182. SIAM (2012)

    Google Scholar 

  8. Chen, H.-L., Goel, A.: Error free self-assembly using error prone tiles. In: Proceedings of the 10th International Meeting on DNA Based Computers, pp. 274–283 (2004)

    Google Scholar 

  9. Chen, H.-L., Kao, M.-Y.: Optimizing Tile Concentrations to Minimize Errors and Time for DNA Tile Self-assembly Systems. In: Sakakibara, Y., Mi, Y. (eds.) DNA16. LNCS, vol. 6518, pp. 13–24. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  10. Chen, H.-L., Schulman, R., Goel, A., Winfree, E.: Reducing facet nucleation during algorithmic self-assembly. Nano Letters 7(9), 2913–2919 (2007)

    Article  Google Scholar 

  11. Cheng, Q., Aggarwal, G., Goldwasser, M.H., Kao, M.-Y., Schweller, R.T., de Espanés, P.M.: Complexities for generalized models of self-assembly. SIAM Journal on Computing 34, 1493–1515 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Cook, M., Fu, Y., Schweller, R.T.: Temperature 1 self-assembly: Deterministic assembly in 3D and probabilistic assembly in 2D. In: SODA 2011: Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms. SIAM (2011)

    Google Scholar 

  13. Demaine, E.D., Demaine, M.L., Fekete, S.P., Ishaque, M., Rafalin, E., Schweller, R.T., Souvaine, D.L.: Staged self-assembly: nanomanufacture of arbitrary shapes with O(1) glues. Natural Computing 7(3), 347–370 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Demaine, E.D., Patitz, M.J., Schweller, R.T., Summers, S.M.: Self-assembly of arbitrary shapes using rnase enzymes: Meeting the kolmogorov bound with small scale factor (extended abstract). In: Schwentick, T., Christoph, D. (eds.) STACS. LIPIcs, vol. 9, pp. 201–212. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2011)

    Google Scholar 

  15. Doty, D.: Randomized self-assembly for exact shapes. SIAM Journal on Computing 39(8), 3521–3552 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. Doty, D., Kari, L., Masson, B.: Negative Interactions in Irreversible Self-assembly. Algorithmica (to appear); In: Sakakibara, Y., Mi, Y. (eds.) DNA16. LNCS, vol. 6518, pp. 37–48. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  17. Doty, D., Lutz, J.H., Patitz, M.J., Schweller, R.T., Summers, S.M., Woods, D.: The tile assembly model is intrinsically universal. In: Proceedings of the 53rd Annual IEEE Symposium on Foundations of Computer Science, FOCS 2012 (to appear, 2012)

    Google Scholar 

  18. Doty, D., Patitz, M.J., Summers, S.M.: Limitations of self-assembly at temperature 1. Theoretical Computer Science 412, 145–158 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  19. Fu, B., Patitz, M.J., Schweller, R.T., Sheline, R.: Self-assembly with Geometric Tiles. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part I. LNCS, vol. 7391, pp. 714–725. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  20. Fujibayashi, K., Zhang, D.Y., Winfree, E., Murata, S.: Error suppression mechanisms for dna tile self-assembly and their simulation. Natural Computing: an International Journal 8(3), 589–612 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Göös, M., Orponen, P.: Synthesizing Minimal Tile Sets for Patterned DNA Self-assembly. In: Sakakibara, Y., Mi, Y. (eds.) DNA16. LNCS, vol. 6518, pp. 71–82. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  22. Jang, B., Kim, Y.-B., Lombardi, F.: Error tolerance of dna self-assembly by monomer concentration control. In: IEEE International Symposium on Defect and Fault-Tolerance in VLSI Systems, pp. 89–97 (2006)

    Google Scholar 

  23. Kao, M.-Y., Schweller, R.T.: Randomized Self-assembly for Approximate Shapes. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 370–384. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  24. Kautz, S.M., Shutters, B.: Self-assembling Rulers for Approximating Generalized Sierpinski Carpets. In: Fu, B., Du, D.-Z. (eds.) COCOON 2011. LNCS, vol. 6842, pp. 284–296. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  25. Lathrop, J.I., Lutz, J.H., Patitz, M.J., Summers, S.M.: Computability and complexity in self-assembly. Theory Comput. Syst. 48(3), 617–647 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  26. Lathrop, J.I., Lutz, J.H., Summers, S.M.: Strict self-assembly of discrete Sierpinski triangles. Theoretical Computer Science 410, 384–405 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  27. Lempiäinen, T., Czeizler, E., Orponen, P.: Synthesizing Small and Reliable Tile Sets for Patterned DNA Self-assembly. In: Cardelli, L., Shih, W. (eds.) DNA17. LNCS, vol. 6937, pp. 145–159. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  28. Lutz, J.H., Shutters, B.: Approximate self-assembly of the sierpinski triangle. Theory Comput. Syst. 51(3), 372–400 (2012)

    Article  MathSciNet  Google Scholar 

  29. Ma, X., Lombardi, F.: Synthesis of tile sets for dna self-assembly. IEEE Trans. on CAD of Integrated Circuits and Systems 27(5), 963–967 (2008)

    Article  Google Scholar 

  30. Majumder, U., LaBean, T.H., Reif, J.H.: Activatable Tiles: Compact, Robust Programmable Assembly and Other Applications. In: Garzon, M.H., Yan, H. (eds.) DNA17. LNCS, vol. 4848, pp. 15–25. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  31. Padilla, J.E., Patitz, M.J., Pena, R., Schweller, R.T., Seeman, N.C., Sheline, R., Summers, S.M., Zhong, X.: Asynchronous signal passing for tile self-assembly: Fuel efficient computation and efficient assembly of shapes. Tech. Report 1202.5012, Computing Research Repository (2012)

    Google Scholar 

  32. Patitz, M.J.: Simulation of self-assembly in the abstract tile assembly model with ISU TAS. In: 6th Annual Conference on Foundations of Nanoscience: Self-Assembled Architectures and Devices, Snowbird, Utah, USA, April 20-24 (2009)

    Google Scholar 

  33. Patitz, M.J., Schweller, R.T., Summers, S.M.: Exact Shapes and Turing Universality at Temperature 1 with a Single Negative Glue. In: Cardelli, L., Shih, W. (eds.) DNA17. LNCS, vol. 6937, pp. 175–189. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  34. Patitz, M.J., Summers, S.M.: Self-assembly of discrete self-similar fractals. Natural Computing 1, 135–172 (2010)

    Article  MathSciNet  Google Scholar 

  35. Patitz, M.J., Summers, S.M.: Self-assembly of decidable sets. Natural Computing 10(2), 853–877 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  36. Reif, J.H., Sahu, S., Yin, P.: Complexity of Graph Self-assembly in Accretive Systems and Self-destructible Systems. In: Carbone, A., Pierce, N.A. (eds.) DNA 2005. LNCS, vol. 3892, pp. 257–274. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  37. Rothemund, P.W.K.: Theory and experiments in algorithmic self-assembly. Ph.D. thesis, University of Southern California (December 2001)

    Google Scholar 

  38. 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, Portland, Oregon, United States, pp. 459–468. ACM (2000)

    Google Scholar 

  39. Seeman, N.C.: Nucleic-acid junctions and lattices. Journal of Theoretical Biology 99, 237–247 (1982)

    Article  Google Scholar 

  40. Soloveichik, D., Cook, M., Winfree, E.: Combining self-healing and proofreading in self-assembly. Natural Computing 7(2), 203–218 (2008)

    Article  MathSciNet  Google Scholar 

  41. Soloveichik, D., Winfree, E.: Complexity of self-assembled shapes. SIAM Journal on Computing 36(6), 1544–1569 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  42. Summers, S.M.: Reducing tile complexity for the self-assembly of scaled shapes through temperature programming. Algorithmica 63(1-2), 117–136 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  43. Wang, H.: Dominoes and the AEA case of the decision problem. In: Proceedings of the Symposium on Mathematical Theory of Automata (New York, 1962), pp. 23–55. Polytechnic Press of Polytechnic Inst. of Brooklyn, Brooklyn (1963)

    Google Scholar 

  44. Winfree, E.: Algorithmic self-assembly of DNA. Ph.D. thesis, California Institute of Technology (June 1998)

    Google Scholar 

  45. Winfree, E.: Self-healing tile sets. In: Chen, J., Jonoska, N., Rozenberg, G. (eds.) Nanotechnology: Science and Computation. Natural Computing Series, pp. 55–78. Springer (2006)

    Google Scholar 

  46. Winfree, E., Bekbolatov, R.: Proofreading Tile Sets: Error Correction for Algorithmic Self-assembly. In: Chen, J., Reif, J.H. (eds.) DNA 2003. LNCS, vol. 2943, pp. 126–144. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science and Computer Engineering, University of Arkansas, Fayetteville, AR, USA

    Matthew J. Patitz

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  1. Matthew J. Patitz
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Editors and Affiliations

  1. Laboratoire d’Informatique, Fondamentale d’Orléan et Départment d’informatique, UFR Sciences, Université d’Orléans, 45067, Orléans Cedex 2, France

    Jérôme Durand-Lose

  2. Department of Mathematics and Statistics, University of South Florida, 33620, Tampa, FL, USA

    Nataša Jonoska

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Patitz, M.J. (2012). An Introduction to Tile-Based Self-assembly. In: Durand-Lose, J., Jonoska, N. (eds) Unconventional Computation and Natural Computation. UCNC 2012. Lecture Notes in Computer Science, vol 7445. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32894-7_6

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  • DOI: https://doi.org/10.1007/978-3-642-32894-7_6

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