Skip to main content

Universal Computation and Optimal Construction in the Chemical Reaction Network-Controlled Tile Assembly Model

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9211)

Abstract

Tile-based self-assembly and chemical reaction networks provide two well-studied models of scalable DNA-based computation. Although tile self-assembly provides a powerful framework for describing Turing-universal self-assembling systems, assembly logic in tile self-assembly is localized, so that only the nearby environment can affect the process of self-assembly. We introduce a new model of tile-based self-assembly in which a well-mixed chemical reaction network interacts with self-assembling tiles to exert non-local control on the self-assembly process. Through simulation of multi-stack machines, we demonstrate that this new model is efficiently Turing-universal, even when restricted to unbounded space in only one spatial dimension. Using a natural notion of program complexity, we also show that this new model can produce many complex shapes with programs of lower complexity. Most notably, we show that arbitrary connected shapes can be produced by a program with complexity bounded by the Kolmogorov complexity of the shape, without the large scale factor that is required for the analogous result in the abstract tile assembly model. These results suggest that controlled self-assembly provides additional algorithmic power over tile-only self-assembly, and that non-local control enhances our ability to perform computation and algorithmically self-assemble structures from small input programs.

Keywords

  • Tile Assembly Model
  • Tile-based Self-assembly
  • Abstract Chemical Reaction Networks
  • Ataman
  • Turing-universal Computation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-21999-8_3
  • Chapter length: 21 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   54.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-21999-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   69.99
Price excludes VAT (USA)
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.

References

  1. Adleman, L., Cheng, Q., Goel, A., Huang, M.D.: Running time and program size for self-assembled squares. In: ACM Symposium on Theory of Computing (STOC), pp. 740–748 (2001)

    Google Scholar 

  2. Aggarwal, G., Cheng, Q., Goldwasser, M.H., Kao, M.Y., de Espanes, P.M., Schweller, R.T.: Complexities for generalized models of self-assembly. SIAM J. Comput. 34(6), 1493–1515 (2005)

    MathSciNet  CrossRef  MATH  Google Scholar 

  3. Barish, R.D., Schulman, R., Rothemund, P.W., Winfree, E.: An information-bearing seed for nucleating algorithmic self-assembly. Proc. Natl. Acad. Sci. 106(15), 6054–6059 (2009)

    CrossRef  Google Scholar 

  4. Bennett, C.H.: The thermodynamics of computation - a review. Int. J. Theor. Phys. 21(12), 905–940 (1982)

    CrossRef  Google Scholar 

  5. Cardelli, L., Zavattaro, G.: On the computational power of biochemistry. In: Horimoto, K., Regensburger, G., Rosenkranz, M., Yoshida, H. (eds.) AB 2008. LNCS, vol. 5147, pp. 65–80. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  6. Chen, H.L., Doty, D., Soloveichik, D.: Deterministic function computation with chemical reaction networks. Nat. Comput. 13(4), 517–534 (2014)

    MathSciNet  CrossRef  Google Scholar 

  7. Chen, Y.J., Dalchau, N., Srinivas, N., Phillips, A., Cardelli, L., Soloveichik, D., Seelig, G.: Programmable chemical controllers made from DNA. Nat. Nanotechnol. 8(10), 755–762 (2013)

    CrossRef  Google Scholar 

  8. Condon, A., Hu, A.J., Maňuch, J., Thachuk, C.: Less haste, less waste: on recycling and its limits in strand displacement systems. Interface Focus 2(4), 512–521 (2012)

    CrossRef  Google Scholar 

  9. Cook, M., Fu, Y., Schweller, R.: Temperature 1 self-assembly: deterministic assembly in 3D and probabilistic assembly in 2D. In: ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 570–589. SIAM (2011)

    Google Scholar 

  10. Dirks, R.M., Pierce, N.A.: Triggered amplification by hybridization chain reaction. Proc. Natl. Acad. Sci. 101(43), 15275–15278 (2004)

    CrossRef  Google Scholar 

  11. Doty, D.: Theory of algorithmic self-assembly. Commun. ACM 55(12), 78–88 (2012)

    CrossRef  Google Scholar 

  12. Doty, D., Kari, L., Masson, B.: Negative interactions in irreversible self-assembly. Algorithmica 66, 153–172 (2013)

    MathSciNet  CrossRef  MATH  Google Scholar 

  13. Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22(4), 403–434 (1976)

    MathSciNet  CrossRef  Google Scholar 

  14. Ke, Y., Ong, L.L., Shih, W.M., Yin, P.: Three-dimensional structures self-assembled from DNA bricks. Science 338(6111), 1177–1183 (2012)

    CrossRef  Google Scholar 

  15. Padilla, J.E., Sha, R., Kristiansen, M., Chen, J., Jonoska, N., Seeman, N.C.: A signal-passing DNA-strand-exchange mechanism for active self-assembly of DNA nanostructures. Angew. Chem. Int. Ed. 54(20), 5939–5942 (2015)

    CrossRef  Google Scholar 

  16. Patitz, M.J.: An introduction to tile-based self-assembly and a survey of recent results. Nat. Comput. 13(2), 195–224 (2013)

    MathSciNet  CrossRef  Google Scholar 

  17. 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.) DNA 17 2011. LNCS, vol. 6937, pp. 175–189. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  18. Pinheiro, A.V., Han, D., Shih, W.M., Yan, H.: Challenges and opportunities for structural DNA nanotechnology. Nat. Nanotechnol. 6(12), 763–772 (2011)

    CrossRef  Google Scholar 

  19. Qian, L., Soloveichik, D., Winfree, E.: Efficient turing-universal computation with DNA polymers. In: Sakakibara, Y., Mi, Y. (eds.) DNA 16 2010. LNCS, vol. 6518, pp. 123–140. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  20. Qian, L., Winfree, E.: Scaling up digital circuit computation with DNA strand displacement cascades. Science 332(6034), 1196–1201 (2011)

    CrossRef  Google Scholar 

  21. Rothemund, P.W.K., Papadakis, N., Winfree, E.: Algorithmic self-assembly of DNA Sierpinski triangles. PLoS Biol. 2(12), e424 (2004)

    CrossRef  Google Scholar 

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

    Google Scholar 

  23. Rothemund, P.W., Ekani-Nkodo, A., Papadakis, N., Kumar, A., Fygenson, D.K., Winfree, E.: Design and characterization of programmable DNA nanotubes. J. Am. Chem. Soc. 126(50), 16344–16352 (2004)

    CrossRef  Google Scholar 

  24. Seelig, G., Soloveichik, D., Zhang, D.Y., Winfree, E.: Enzyme-free nucleic acid logic circuits. Science 314(5805), 1585–1588 (2006)

    CrossRef  Google Scholar 

  25. Seeman, N.C.: An overview of structural DNA nanotechnology. Mol. Biotechnol. 37(3), 246–257 (2007)

    CrossRef  Google Scholar 

  26. Sipser, M.: Introduction to the Theory of Computation. Cengage Learning, Boston (2012)

    Google Scholar 

  27. Soloveichik, D., Cook, M., Winfree, E., Bruck, J.: Computation with finite stochastic chemical reaction networks. Nat. Comput. 7(4), 615–633 (2008)

    MathSciNet  CrossRef  MATH  Google Scholar 

  28. Soloveichik, D., Seelig, G., Winfree, E.: DNA as a universal substrate for chemical kinetics. Proc. Natl. Acad. Sci. 107(12), 5393–5398 (2010)

    CrossRef  Google Scholar 

  29. Soloveichik, D., Winfree, E.: Complexity of self-assembled shapes. SIAM J. Comput. 36(6), 1544–1569 (2007)

    MathSciNet  CrossRef  MATH  Google Scholar 

  30. Summers, S.M.: Reducing tile complexity for the self-assembly of scaled shapes through temperature programming. Algorithmica 63(1–2), 117–136 (2011)

    MathSciNet  Google Scholar 

  31. Wei, B., Dai, M., Yin, P.: Complex shapes self-assembled from single-stranded DNA tiles. Nature 485(7400), 623–626 (2012)

    CrossRef  Google Scholar 

  32. Yin, P., Choi, H.M.T., Calvert, C.R., Pierce, N.A.: Programming biomolecular self-assembly pathways. Nature 451(7176), 318–322 (2008)

    CrossRef  Google Scholar 

  33. Zhang, D.Y., Hariadi, R.F., Choi, H.M.T., Winfree, E.: Integrating DNA strand-displacement circuitry with DNA tile self-assembly. Nat. Commun. 4 (2013). Article No. 1965

    Google Scholar 

  34. Zhang, D.Y., Seelig, G.: Dynamic DNA nanotechnology using strand-displacement reactions. Nat. Chem. 3(2), 103–113 (2011)

    CrossRef  Google Scholar 

  35. Zhang, D.Y., Turberfield, A.J., Yurke, B., Winfree, E.: Engineering entropy-driven reactions and networks catalyzed by DNA. Science 318(5853), 1121–1125 (2007)

    CrossRef  Google Scholar 

Download references

Acknowledgements

We acknowledge financial support from National Science Foundation grant CCF-1317694. We also thank Dave Doty, for his helpful comments and suggestions, and Kevin Li, for his useful suggestions on an early draft of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Erik Winfree .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Schiefer, N., Winfree, E. (2015). Universal Computation and Optimal Construction in the Chemical Reaction Network-Controlled Tile Assembly Model. In: Phillips, A., Yin, P. (eds) DNA Computing and Molecular Programming. DNA 2015. Lecture Notes in Computer Science(), vol 9211. Springer, Cham. https://doi.org/10.1007/978-3-319-21999-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21999-8_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21998-1

  • Online ISBN: 978-3-319-21999-8

  • eBook Packages: Computer ScienceComputer Science (R0)