Skip to main content
SpringerLink
Log in

Polyomino-Safe DNA Self-assembly via Block Replacement

  • Conference paper
DNA Computing (DNA 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5347))

Included in the following conference series:

Abstract

The standard abstract model for analyzing DNA self- assembly, aTAM, assumes that single tiles attach one by one to a larger structure. In practice, tiles may attach to each other forming structures called polyominoes and then attach to the assembly using bonds from multiple tiles. Such polyominoes may cause errors in systems designed with only aTAM in mind. In this paper, we first present a formal definition of when one tile system is a “block replacement” of another. Then we present a block replacement scheme for making any system that admits non-trivial block replacement polyomino-safe. In addition, we present a smaller block replacement scheme that makes the Chinese Remainder counter polyomino-safe and prove that the question of whether a system is polyomino-safe (or other similar properties) is undecidable. Finally, we show that applying our polyomino-safe system produces self-healing systems when applied to most self-healing systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barish, R., Rothemund, P., Winfree, E.: Two computational primitives for algorithmic self-assembly: Copying and counting. Nano Lett. 5, 2586–2592 (2005)

    Article  Google Scholar 

  2. Winfree, E., Yang, X., Seeman, N.: Universal computation via self-assembly of DNA: Some theory and experiments. In: Landweber, L.F., Baum, E.B. (eds.) DNA Based Computers II. DIMACS, vol. 44, pp. 191–213. American Mathematical Society, Providence (1998)

    Google Scholar 

  3. Winfree, E.: Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology, Computation and Neural Systems Option (1998)

    Google Scholar 

  4. Rothemund, P.: Folding DNA to create nanoscale shapes and patterns. Nature 440, 297–302 (2006)

    Article  Google Scholar 

  5. 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)

    Chapter  Google Scholar 

  6. Yurke, B., Turberfield, A., Mills Jr., A., Simmel, F., Neumann, J.: A DNA-fuelled molecular machine made of DNA. Nature (406), 605–608 (2000)

    Article  Google Scholar 

  7. Shin, J.S., Pierce, N.: A synthetic DNA walker for molecular transport. J. Am. Chem. Soc. 126, 10834–10835 (2004)

    Article  Google Scholar 

  8. Sherman, W., Seeman, N.: A precisely controlled DNA biped walking device. Nano Letters 4, 1203–1207 (2004)

    Article  Google Scholar 

  9. Yin, P., Yan, H., Daniel, X., Turberfield, A., Reif, J.: A unidirectional DNA walker moving autonomously along a linear track. Angewandte Chemie 43, 4906–4911 (2004)

    Article  Google Scholar 

  10. Tian, Y., He, Y., Chen, Y., Yin, P., Mao, C.: A DNAzyme that walks processively and autonomously along a one-dimensional track. Angewandte Chemie 117, 4429–4432 (2005)

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Rothemund, P., Winfree, E.: The program-size complexity of self-assembled squares. In: Symposium on Theory of Computing (STOC), Portland, Oregon, United States, pp. 459–468. ACM Press, New York (2000)

    Google Scholar 

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

    Google Scholar 

  14. Cheng, Q., Goel, A., Moisset, P.: Optimal self-assembly of counters at temperature two. In: Proceedings of the first Conference on Foundations of nanoscience: self-assembled architectures and devices (April 2004)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Lagoudakis, M., LaBean, T.: 2-D DNA self-assembly for satisfiability. In: Winfree, E., Gifford, D.K. (eds.) DNA Based Computers V. DIMACS, vol. 54, pp. 141–154. American Mathematical Society, Providence (2000)

    Google Scholar 

  17. Baryshnikov, Y., Coffman, E., Momcilovic, P.: DNA-based computation times. In: Proceedings of the Tenth International Meeting on DNA Based Computers, Milano, Italy (June 2004)

    Google Scholar 

  18. 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 

  19. Chen, H., Goel, A.: Error free self-assembly using error prone tiles. In: [27], pp. 62–75

    Google Scholar 

  20. Reif, J., Sahu, S., Yin, P.: Compact error-resilient computational DNA tiling assemblies. In: [27], pp. 293–307

    Google Scholar 

  21. Schulman, R., Winfree, E.: Programmable control of nucleation for algorithmic self-assembly. In: [27], pp. 319–328 (Extended abstract; preprint of the full paper is cond.mat/0607317 on arXiv.org)

    Google Scholar 

  22. Chen, H., Cheng, Q., Goel, A., Huang, M., Moisset, P.: Invadable self-assembly: Combining robustness with efficiency. In: ACM-SIAM Symposium on Discrete Algorithms (SODA) (2004)

    Google Scholar 

  23. Chen, H., Goel, A., Luhrs, C.: Dimension augmentation and combinatorial criteria for efficient error-resistant DNA self-assembly. In: Symposium on Discrete Algorithms (2008)

    Google Scholar 

  24. Winfree, E.: Self-healing tile sets. Nanotechnology: Science and Computation, 55–78 (2006)

    Google Scholar 

  25. Chen, H., Goel, A., Luhrs, C., Winfree, E.: Self-assembling tile systems that heal from small fragments. In: DNA 13 (2007)

    Google Scholar 

  26. 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. In: Garzon, M.H., Yan, H. (eds.) DNA 2007. LNCS, vol. 4848, pp. 1–14. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  27. Ferretti, C., Mauri, G., Zandron, C. (eds.): DNA 2004. LNCS, vol. 3384. Springer, Heidelberg (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Stanford University, USA

    Chris Luhrs

Authors
  1. Chris Luhrs
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Management Science and Engineering and (by courtesy) Computer Science, Stanford University, Terman 311, Stanford, 94305, CA, USA

    Ashish Goel

  2. Physics Department, TU Munich, Garching, Germany

    Friedrich C. Simmel

  3. Institute of Computer Science, Faculty of Philosophy and Science, Silesian University, Bezručovo nám. 13, 74601, Opava, Czech Republic

    Petr Sosík

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Luhrs, C. (2009). Polyomino-Safe DNA Self-assembly via Block Replacement. In: Goel, A., Simmel, F.C., Sosík, P. (eds) DNA Computing. DNA 2008. Lecture Notes in Computer Science, vol 5347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03076-5_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-03076-5_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03075-8

  • Online ISBN: 978-3-642-03076-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation