Reachability Bounds for Chemical Reaction Networks and Strand Displacement Systems

  • Anne Condon
  • Bonnie Kirkpatrick
  • Ján Maňuch
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7433)

Abstract

Chemical reaction networks (CRNs) and DNA strand displacement systems (DSDs) are widely-studied and useful models of molecular programming. However, in order for some DSDs in the literature to behave in an expected manner, the initial number of copies of some reagents is required to be fixed. In this paper we show that, when multiple copies of all initial molecules are present, general types of CRNs and DSDs fail to work correctly if the length of the shortest sequence of reactions needed to produce any given molecule exceeds a threshold that grows polynomially with attributes of the system.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Condon, A., Hu, A.J., Maňuch, J., Thachuk, C.: Less haste, less waste: On recycling and its limits in strand displacement systems. J R Soc. Interface (2012)Google Scholar
  2. 2.
    Cardelli, L.: Two-domain DNA strand displacement. In: Proc. of Developments in Computational Models (DCM 2010). Electronic Proceedings in Theoretical Computer Science, vol. 26, pp. 47–61 (2010)Google Scholar
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    Qian, L., Winfree, E.: Scaling up digital circuit computation with DNA strand displacement cascades. Science 332, 1196–1201 (2011)CrossRefGoogle Scholar
  5. 5.
    Qian, L., Winfree, E., Bruck, J.: Neural network computation with DNA strand displacement cascades. Nature 475, 368–372 (2011)CrossRefGoogle Scholar
  6. 6.
    Seelig, G., Soloveichik, D., Zhang, D.Y., Winfree, E.: Enzyme-free nucleic acid logic circuits. Science 314(5805), 1585–1588 (2006)CrossRefGoogle Scholar
  7. 7.
    Soloveichik, D.: Robust stochastic chemical reaction networks and bounded tau-leaping. J. Comput. Biol. 16(3), 501–522 (2009)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Soloveichik, D., Cook, M., Winfree, E., Bruck, J.: Computation with finite stochastic chemical reaction networks. Nat. Comp. 7, 615–633 (2008)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Soloveichik, D., Seelig, G., Winfree, E.: DNA as a universal substrate for chemical kinetics. Proc. Nat. Acad. Sci. USA 107(12), 5393–5398 (2010)CrossRefGoogle Scholar
  10. 10.
    Yurke, B., Mills, A.P.: Using DNA to power nanostructures. Genet. Program. Evolvable Mach. 4(2), 111–122 (2003)CrossRefGoogle Scholar
  11. 11.
    Yurke, B., Turberfield, A.J., Mills Jr., A.P., Simmel, F.C., Neumann, J.L.: A DNA-fuelled molecular machine made of DNA. Nature 406, 605–608 (2000)CrossRefGoogle Scholar
  12. 12.
    Zhang, D.Y.: Cooperative hybridization of oligonucleotides. J. Am. Chem. Soc. 133, 1077–1086 (2011)CrossRefGoogle Scholar
  13. 13.
    Zhang, D.Y., Turberfield, A.J., Yurke, B., Winfree, E.: Engineering entropy-driven reactions and networks catalyzed by DNA. Science 318, 1121–1125 (2007)CrossRefGoogle Scholar
  14. 14.
    Zhang, D.Y., Seelig, G.: Dynamic DNA nanotechnology using strand displacement reactions. Nature Chemistry 3, 103–113 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Anne Condon
    • 1
  • Bonnie Kirkpatrick
    • 1
  • Ján Maňuch
    • 1
    • 2
  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverBritish Columbia
  2. 2.Department of MathematicsSimon Fraser UniversityBurnabyBritish Columbia

Personalised recommendations