Skip to main content

Abstract Modelling of Tethered DNA Circuits

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8727))

Abstract

Sequence-specific DNA interactions are a powerful means of programming nanoscale locomotion. These systems typically use a DNA track that is tethered to a surface, and molecular interactions enable a signal or cargo to traverse this track. Such low copy number systems are highly amenable to mechanized analyses such as probabilistic model checking, which requires a formal encoding. In this paper we present the first general encoding of tethered DNA species into a formal language, which allows the interactions between tethered species to be derived automatically using standard reaction rules. We apply this encoding to a previously published tethered DNA circuit architecture based on hairpin assembly reactions. This work enables automated analysis of large-scale tethered DNA circuits and, potentially, synthesis of optimized track layouts to implement specific logic functions.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   44.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Vale, R.D.: The molecular motor toolbox for intracellular transport. Cell 112(4), 467–480 (2003)

    Article  Google Scholar 

  2. Muscat, R.A., Bath, J., Turberfield, A.J.: A programmable molecular robot. Nano Lett. 11(3), 982–987 (2011)

    Article  Google Scholar 

  3. Wickham, S.F.J., Bath, J., Katsuda, Y., Endo, M., Hidaka, K., Sugiyama, H., Turberfield, A.J.: A DNA-based molecular motor that can navigate a network of tracks. Nature Nanotech. 7, 169–173 (2012)

    Article  Google Scholar 

  4. Gu, H., Chao, J., Xiao, S.-J., Seeman, N.C.: A proximity-based programmable DNA nanoscale assembly line. Nature 465, 202–205 (2010)

    Article  Google Scholar 

  5. Chandran, H., Gopalkrishnan, N., Phillips, A., Reif, J.: Localized hybridization circuits. In: Cardelli, L., Shih, W. (eds.) DNA 17. LNCS, vol. 6937, pp. 64–83. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  6. Muscat, R.A., Strauss, K., Ceze, L., Seelig, G.: DNA-based molecular architecture with spatially localized components. In: Proceedings of ISCA 2013 (2013)

    Google Scholar 

  7. Heath, J., Kwiatkowska, M., Norman, G., Parker, D., Tymchyshyn, O.: Probabilistic model checking of complex biological pathways. Theor. Comput. Sci. 319(3), 239–257 (2008)

    Article  MathSciNet  Google Scholar 

  8. Lakin, M.R., Parker, D., Cardelli, L., Kwiatkowska, M., Phillips, A.: Design and analysis of DNA strand displacement devices using probabilistic model checking. J. R. Soc. Interface 9(72), 1470–1485 (2012)

    Article  Google Scholar 

  9. Dannenberg, F., Kwiatkowska, M., Thachuk, C., Turberfield, A.J.: DNA walker circuits: Computational potential, design, and verification. In: Soloveichik, D., Yurke, B. (eds.) DNA 19. LNCS, vol. 8141, pp. 31–45. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  10. Phillips, A., Cardelli, L.: A programming language for composable DNA circuits. J. R. Soc. Interface 6(suppl. 4), S419–S436 (2009)

    Google Scholar 

  11. Lakin, M.R., Youssef, S., Cardelli, L., Phillips, A.: Abstractions for DNA circuit design. J. R. Soc. Interface 9(68), 470–486 (2012)

    Article  Google Scholar 

  12. Turberfield, A.J., Mitchell, J.C., Yurke, B., Mills Jr., A.P., Blakey, M.I., Simmel, F.C.: DNA fuel for free-running nanomachines. Phys. Rev. Lett. 90(11), 118102 (2003)

    Article  Google Scholar 

  13. Seelig, G., Yurke, B., Winfree, E.: Catalyzed relaxation of a metastable DNA fuel. J. Am. Chem. Soc. 128, 12211–12220 (2006)

    Article  Google Scholar 

  14. Green, S.J., Bath, J., Turberfield, A.J.: Coordinated chemomechanical cycles: A mechanism for autonomous molecular motion. Phys. Rev. Lett. 101, 238101 (2008)

    Article  Google Scholar 

  15. Genot, A.J., Zhang, D.Y., Bath, J., Turberfield, A.J.: Remote toehold: A mechanism for flexible control of DNA hybridization kinetics. J. Am. Chem. Soc. 133(7), 2177–2182 (2011)

    Article  Google Scholar 

  16. Lakin, M.R., Youssef, S., Polo, F., Emmott, S., Phillips, A.: Visual DSD: a design and analysis tool for DNA strand displacement systems. Bioinformatics 27(22), 3211–3213 (2011)

    Article  Google Scholar 

  17. Douglas, S.M., Marblestone, A.H., Teerapittayanon, S., Vazquez, A., Church, G.M., Shih, W.M.: Rapid prototyping of three-dimensional DNA-origami shapes with caDNAno. Nucleic Acids Res. 37, 5001–5006 (2009)

    Article  Google Scholar 

  18. Priami, C., Regev, A., Shapiro, E., Silverman, W.: Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Inform Process Lett. 80, 25–31 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  19. Phillips, A., Cardelli, L.: Efficient, correct simulation of biological processes in the stochastic pi-calculus. In: Calder, M., Gilmore, S. (eds.) CMSB 2007. LNCS (LNBI), vol. 4695, pp. 184–199. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  20. Li, Y., Breaker, R.R.: Deoxyribozymes: new players in the ancient game of biocatalysis. Curr. Opin. Struct. Biol. 9, 315–323 (1999)

    Article  Google Scholar 

  21. Lund, K., Manzo, A.J., Dabby, N., Michelotti, N., Johnson-Buck, A., Nangreave, J., Taylor, S., Pei, R., Stojanovic, M.N., Walter, N.G., Winfree, E., Yan, H.: Molecular robots guided by prescriptive landscapes. Nature 465, 206–210 (2010)

    Article  Google Scholar 

  22. Pei, R., Taylor, S.K., Stefanovic, D., Rudchenko, S., Mitchell, T.E., Stojanovic, M.N.: Behavior of polycatalytic assemblies in a substrate-displaying matrix. J. Am. Chem. Soc. 128(39), 12693–12699 (2006)

    Article  Google Scholar 

  23. Olah, M.J.: Multivalent Random Walkers: A computational model of superdiffusion at the nanoscale. PhD thesis, University of New Mexico (2012)

    Google Scholar 

  24. Olah, M.J., Stefanovic, D.: Superdiffusive transport by multivalent molecular walkers moving under load. Phys. Rev. E 87, 62713 (2013)

    Article  Google Scholar 

  25. Semenov, O.: Abstract Models of Molecular Walkers. PhD thesis, University of New Mexico (2013)

    Google Scholar 

  26. Semenov, O., Mohr, D., Stefanovic, D.: First passage properties of molecular spiders. Phys. Rev. E 88, 012724 (2013)

    Google Scholar 

  27. Semenov, O., Olah, M.J., Stefanovic, D.: Cooperative linear cargo transport with molecular spiders. Natural Computing 12(2), 259–276 (2013)

    Article  MathSciNet  Google Scholar 

  28. Stefanovic, D.: Maze exploration with molecular-scale walkers. In: Dediu, A.-H., Martín-Vide, C., Truthe, B. (eds.) TPNC 2012. LNCS, vol. 7505, pp. 216–226. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Lakin, M.R., Petersen, R., Gray, K.E., Phillips, A. (2014). Abstract Modelling of Tethered DNA Circuits. In: Murata, S., Kobayashi, S. (eds) DNA Computing and Molecular Programming. DNA 2014. Lecture Notes in Computer Science, vol 8727. Springer, Cham. https://doi.org/10.1007/978-3-319-11295-4_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-11295-4_9

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11294-7

  • Online ISBN: 978-3-319-11295-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics