Optimizing Tile Set Size While Preserving Proofreading with a DNA Self-assembly Compiler

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11145)


Algorithmic DNA tile systems have the potential to allow the construction by self-assembly of large structures with complex nanometer-scale details out of relatively few monomer types, but are constrained by errors in growth and the limited sequence space of orthogonal DNA sticky ends that program tile interactions. We present a tile set optimization technique that, through analysis of algorithmic growth equivalence, potentially sensitive error pathways, and potential lattice defects, can significantly reduce the size of tile systems while preserving proofreading behavior that is essential for obtaining low error rates. Applied to systems implementing multiple algorithms that are far beyond the size of currently feasible implementations, the optimization technique results in systems that are comparable in size to already-implemented experimental systems.



We thank Chigozie Nri, Philip Petersen, Lulu Qian, and Grigory Tikhomirov for discussions and collaboration on physical implementations and the Alhambra compiler, and Robert Johnson and William Poole for discussions on aTAM equivalence. This work was partially supported by the Evans Foundation and National Science Foundation award CCF-1317694.


  1. 1.
  2. 2.
    Barish, R.D., Schulman, R., Rothemund, P.W.K., Winfree, E.: An information-bearing seed for nucleating algorithmic self-assembly. PNAS 106(15), 6054–6059 (2009). Scholar
  3. 3.
    Cannon, S., et al.: Two hands are better than one (up to constant factors): self-assembly in the 2HAM vs. aTAM. In: Portier, N., Wilke, T. (eds.) STACS 2013. LIPIcs, vol. 20, pp. 172–184. Dagstuhl (2013).
  4. 4.
    Chen, H.-L., Goel, A.: Error free self-assembly using error prone tiles. In: Ferretti, C., Mauri, G., Zandron, C. (eds.) DNA 2004. LNCS, vol. 3384, pp. 62–75. Springer, Heidelberg (2005). Scholar
  5. 5.
    Chen, H.L., Schulman, R., Goel, A., Winfree, E.: Reducing facet nucleation during algorithmic self-assembly. Nano Lett. 7, 2913–2919 (2007). Scholar
  6. 6.
    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 (2018). Scholar
  7. 7.
    Doty, D.: Theory of algorithmic self-assembly. Commun. ACM 55(12), 78–88 (2012). Scholar
  8. 8.
    Doty, D., Patitz, M.J., Summers, S.M.: Limitations of self-assembly at temperature 1. Theor. Comput. Sci. 412(1–2), 145–158 (2011). Scholar
  9. 9.
    Evans, C.G.: Crystals that count! Physical principles and experimental investigations of DNA tile self-assembly. Ph.D. thesis, California Institute of Technology (2014).
  10. 10.
    Evans, C.G., Winfree, E.: DNA sticky end design and assignment for robust algorithmic self-assembly. In: Soloveichik, D., Yurke, B. (eds.) DNA 2013. LNCS, vol. 8141, pp. 61–75. Springer, Cham (2013). Scholar
  11. 11.
    Evans, C.G., Winfree, E.: Physical principles for DNA tile self-assembly. Chem. Soc. Rev. 46(12), 3808–3829 (2017). Scholar
  12. 12.
    Fu, T.J., Seeman, N.C.: DNA double-crossover molecules. Biochemistry 32, 3211–3220 (1993). Scholar
  13. 13.
    Fujibayashi, K., Hariadi, R., Park, S.H., Winfree, E., Murata, S.: Toward reliable algorithmic self-assembly of DNA tiles: a fixed-width cellular automaton pattern. Nano Lett. 8(7), 1791–1797 (2008). Scholar
  14. 14.
    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). Scholar
  15. 15.
    Jacobs, W.M., Reinhardt, A., Frenkel, D.: Rational design of self-assembly pathways for complex multicomponent structures. PNAS 112(20), 6313–6318 (2015). Scholar
  16. 16.
    Johnsen, A., Kao, M.Y., Seki, S.: A manually-checkable proof for the NP-hardness of 11-color pattern self-assembly tileset synthesis. J. Comb. Optim. 33(2), 496–529 (2017). Scholar
  17. 17.
    Johnsen, A.C., Kao, M.-Y., Seki, S.: Computing minimum tile sets to self-assemble color patterns. In: Cai, L., Cheng, S.-W., Lam, T.-W. (eds.) ISAAC 2013. LNCS, vol. 8283, pp. 699–710. Springer, Heidelberg (2013). Scholar
  18. 18.
    Johnson, R., Dong, Q., Winfree, E.: Verifying chemical reaction network implementations: a bisimulation approach. Theor. Comput. Sci. (2018).
  19. 19.
    Kari, L., Kopecki, S., Meunier, P.É., Patitz, M.J., Seki, S.: Binary pattern tile set synthesis is NP-hard. Algorithmica 78(1), 1–46 (2017). Scholar
  20. 20.
    Kari, L., Kopecki, S., Seki, S.: 3-color bounded patterned self-assembly. Nat. Comput. 14(2), 279–292 (2015). Scholar
  21. 21.
    Ke, Y., Ong, L.L., Shih, W.M., Yin, P.: Three-dimensional structures self-assembled from DNA bricks. Science 338(6111), 1177–1183 (2012). Scholar
  22. 22.
    Lin, C., Liu, Y., Rinker, S., Yan, H.: DNA tile based self-assembly: building complex nanoarchitectures. ChemPhysChem 7(8), 1641–1647 (2006). Scholar
  23. 23.
    Ma, X., Lombardi, F.: Combinatorial optimization problem in designing DNA self-assembly tile sets. In: 2008 IEEE International Workshop on Design and Test of Nano Devices, Circuits and Systems, pp. 73–76 (2008).
  24. 24.
    Ma, X., Lombardi, F.: Synthesis of tile sets for DNA self-assembly. IEEE Trans. Comput.-Aided Des. Integr. Circ. Syst. 27(5), 963–967 (2008). Scholar
  25. 25.
    Milner, R.: Communication and Concurrency. Prentice Hall, Upper Saddle River (1989)zbMATHGoogle Scholar
  26. 26.
    Ong, L.L., et al.: Programmable self-assembly of three-dimensional nanostructures from 10,000 unique components. Nature 552(7683), 72–77 (2017). Scholar
  27. 27.
    Reif, J.H., Sahu, S., Yin, P.: Compact error-resilient computational DNA tiling assemblies. In: Ferretti, C., Mauri, G., Zandron, C. (eds.) DNA 2004. LNCS, vol. 3384, pp. 293–307. Springer, Heidelberg (2005). Scholar
  28. 28.
    Schulman, R., Winfree, E.: Programmable control of nucleation for algorithmic self-assembly. SIAM J. Comput. 39(4), 1581–1616 (2010). Scholar
  29. 29.
    Schulman, R., Yurke, B., Winfree, E.: Robust self-replication of combinatorial information via crystal growth and scission. PNAS 109(17), 6405–6410 (2012). Scholar
  30. 30.
    Seeman, N.C., Sleiman, H.F.: DNA nanotechnology. Nat. Rev. Mater. 3, 17068 (2017). Scholar
  31. 31.
    Soloveichik, D., Winfree, E.: Complexity of compact proofreading for self-assembled patterns. In: Carbone, A., Pierce, N.A. (eds.) DNA 2005. LNCS, vol. 3892, pp. 305–324. Springer, Heidelberg (2006). Scholar
  32. 32.
    Wang, W., Lin, T., Zhang, S., Bai, T., Mi, Y., Wei, B.: Self-assembly of fully addressable DNA nanostructures from double crossover tiles. Nucleic Acids Res. 44(16), 7989–7996 (2016). Scholar
  33. 33.
    Wei, B., Dai, M., Yin, P.: Complex shapes self-assembled from single-stranded DNA tiles. Nature 485(7400), 623–626 (2012). Scholar
  34. 34.
    Winfree, E.: Simulations of computing by self-assembly. Technical report, CaltechCSTR:1998.22, Pasadena, CA (1998).
  35. 35.
    Winfree, E., Bekbolatov, R.: Proofreading tile sets: error correction for algorithmic self-assembly. In: Chen, J., Reif, J. (eds.) DNA 2003. LNCS, vol. 2943, pp. 126–144. Springer, Heidelberg (2004). Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Evans FoundationPasadenaUSA
  2. 2.California Institute of TechnologyPasadenaUSA

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