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Design of a Minimal System for Self-replication of Rectangular Patterns of DNA Tiles

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Theory and Practice of Natural Computing (TPNC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8890))

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Abstract

Complex nanostructures assembled from DNA tiles cannot be manufactured in large volumes without extensive wet-lab efforts. Self-replication of tile structures would offer a low-cost and efficient nanomanufacturing if it would be based on an automated dynamically controlled assembly and disassembly of tiles — an attribute that is lacking in existing tile self-assembly framework. Here we propose self-replication of rectangular two-dimensional patterns based on the abstract Tile Assembly Model, by designing a system of tiles which replicate a target pattern by replicating its “L”-shaped seed. Self-replication starts by the formation of a mold structure from a “L”-shaped seed of a target pattern. The mold consists of switch-enabled tiles that can be dynamically triggered to dissociate the seed and the mold templates. The dissociated mold and seed structures each further catalyse assembly of new templates of seed and mold structures, respectively, forming the basis of a cross-catalytic exponential replication cycle.

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References

  1. Abel, Z., Benbernou, N., Damian, M., Demaine, E.D., Demaine, M.L., Flatland, R.Y., Kominers, S.D., Schweller, R.T.: Shape replication through self-assembly and RNase enzymes. In: SODA, pp. 1045–1064. SIAM (2010)

    Google Scholar 

  2. Czeizler, E., Popa, A.: Synthesizing minimal tile sets for complex patterns in the framework of patterned DNA self-assembly. Theor. Comput. Sci. 499, 23–37 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  3. Field, R.J., Niyes, R.M.: Oscillations in chemical systems iv. limit cycle behavior in a model of a real chemical reaction. Journal of Chemical Physics 60, 1877–1884 (1974)

    Article  Google Scholar 

  4. Gautam, V.K., Haddow, P.C., Kuiper, M.: Reliable self-assembly by self-triggered activation of enveloped DNA tiles. In: Dediu, A.-H., Martín-Vide, C., Truthe, B., Vega-Rodríguez, M.A. (eds.) TPNC 2013. LNCS, vol. 8273, pp. 68–79. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  5. Göös, M., Lempiäinen, T., Czeizler, E., Orponen, P.: Search methods for tile sets in patterned DNA self-assembly. J. Comput. Syst. Sci. 80(1), 297–319 (2014)

    Article  MATH  Google Scholar 

  6. Hoops, S., et al.: COPASI - a complex pathway simulator. Bioinformatics 22(24), 3067–3074 (2006)

    Article  Google Scholar 

  7. Keenan, A., Schweller, R., Zhong, X.: Exponential replication of patterns in the signal tile assembly model. In: Soloveichik, D., Yurke, B. (eds.) DNA 2013. LNCS, vol. 8141, pp. 118–132. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  8. von Kiedrowski, G.: A self-replicating hexadeoxynucleotide. Angewandte Chemie International Edition in English 25(10), 932–935 (1986)

    Article  Google Scholar 

  9. Liu, W., Zhong, H., Wang, R., Seeman, N.C.: Crystalline two-dimensional DNA-origami arrays. Angewandte Chemie International Edition 50(7082), 264–267 (2011)

    Article  Google Scholar 

  10. Majumder, U., LaBean, T.H., Reif, J.H.: Activatable tiles: Compact, robust programmable assembly and other applications. In: Garzon, M.H., Yan, H. (eds.) DNA 2007. LNCS, vol. 4848, pp. 15–25. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  11. Morrison, L.E., Stols, L.M.: Sensitive fluorescence-based thermodynamic and kinetic measurements of DNA hybridization in solution. Biochemistry 32(12), 3095–3104 (1993)

    Article  Google Scholar 

  12. 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. In: UCNC, pp. 174–185 (2013)

    Google Scholar 

  13. Padilla, J., Liu, W., Seeman, N.C.: Hierarchical self assembly of patterns from the robinson tilings: DNA tile design in an enhanced tile assembly model. Natural Computing 11(2), 323–338 (2012)

    Article  MathSciNet  Google Scholar 

  14. Rothemund, P.W.K., Winfree, E.: The program-size complexity of self-assembled squares. In: Proceedings of the Thirty-second Annual ACM Symposium on Theory of Computing, STOC 2000, pp. 459–468. ACM (2000)

    Google Scholar 

  15. Schulman, R., Winfree, E.: Self-replication and evolution of DNA crystals. In: Capcarrère, M.S., Freitas, A.A., Bentley, P.J., Johnson, C.G., Timmis, J. (eds.) ECAL 2005. LNCS (LNAI), vol. 3630, pp. 734–743. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. Schulman, R., Yurke, B., Winfree, E.: Robust self-replication of combinatorial information via crystal growth and scission. Proceedings of the National Academy of Sciences 109(17), 6405–6410 (2012)

    Article  Google Scholar 

  17. Seki, S.: Combinatorial optimization in pattern assembly. In: Mauri, G., Dennunzio, A., Manzoni, L., Porreca, A.E. (eds.) UCNC 2013. LNCS, vol. 7956, pp. 220–231. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  18. Soloveichik, D., Seelig, G., Winfree, E.: DNA as a universal substrate for chemical kinetics. Proceedings of the National Academy of Sciences 107(12), 5393–5398 (2010)

    Article  Google Scholar 

  19. Winfree, E.: Algorithmic Self-Assembly of DNA. Ph.D. thesis, California Institute of Technology, Pasadena, USA (1998)

    Google Scholar 

  20. 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 

  21. Winfree, E., Liu, F., Wenzler, L., Seeman, N.C.: Design and self-assembly of two-dimensional DNA crystals. Nature 394(6693), 539–544 (1998)

    Article  Google Scholar 

  22. Zhang, D.Y., Hariadi, R.F., Choi, H.M., Winfree, E.: Integrating DNA strand-displacement circuitry with DNA tile self-assembly. Nature Communications 4 (2013)

    Google Scholar 

  23. Zhang, D.Y., Winfree, E.: Control of DNA strand displacement kinetics using toehold exchange. Journal of the American Chemical Society (2009)

    Google Scholar 

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Gautam, V.K., Czeizler, E., Haddow, P.C., Kuiper, M. (2014). Design of a Minimal System for Self-replication of Rectangular Patterns of DNA Tiles. In: Dediu, AH., Lozano, M., Martín-Vide, C. (eds) Theory and Practice of Natural Computing. TPNC 2014. Lecture Notes in Computer Science, vol 8890. Springer, Cham. https://doi.org/10.1007/978-3-319-13749-0_11

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  • DOI: https://doi.org/10.1007/978-3-319-13749-0_11

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13748-3

  • Online ISBN: 978-3-319-13749-0

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