DNA as a Universal Substrate for Chemical Kinetics

(Extended Abstract)
  • David Soloveichik
  • Georg Seelig
  • Erik Winfree
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5347)

Abstract

We show that a DNA-based chemical system can be constructed such that it closely approximates the dynamic behavior of an arbitrary system of coupled chemical reactions. Using strand displacement reactions as a primitive we explicitly construct reaction cascades with effectively unimolecular and bimolecular kinetics. Our construction allows for individual reactions to be coupled in arbitrary ways such that reactants can participate in multiple reactions simultaneously, correctly reproducing the desired dynamical properties. Thus arbitrary systems of chemical equations can be compiled into chemistry. We illustrate our method on a chaotic Rössler attractor; simulations of the attractor and of our proposed DNA-based implementation show good agreement.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Gavalas, G.R.: Nonlinear Differential Equations of Chemically Reacting Systems. Springer, Heidelberg (1968)CrossRefMATHGoogle Scholar
  2. 2.
    Scott, S.K.: Chemical Chaos. Oxford University Press, Oxford (1991)Google Scholar
  3. 3.
    Epstein, I.R., Pojman, J.A.: An Introduction to Nonlinear Chemical Dynamics: Oscillations, Waves, Patterns, and Chaos. Oxford University Press, Oxford (1998)Google Scholar
  4. 4.
    Willamowski, K.D., Rössler, O.E.: Irregular oscillations in a realistic abstract quadratic mass action system. Z. Naturforsch A 35, 317–318 (1980)CrossRefGoogle Scholar
  5. 5.
    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(6796), 605–608 (2000)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.
    Seelig, G., Yurke, B., Winfree, E.: Catalyzed relaxation of a metastable DNA fuel. Phys. Rev. Lett. 90, 118102–118111 (2006)Google Scholar
  8. 8.
    Zhang, D.Y., Turberfield, A.J., Yurke, B., Winfree, E.: Engineering entropy-driven reactions and networks catalyzed by DNA. Science 318(5853), 1121 (2007)CrossRefGoogle Scholar
  9. 9.
    Green, C., Tibbetts, C.: Reassociation rate limited displacement of DNA strands by branch migration. Nucleic Acids Research 9, 1905–1918 (1981)CrossRefGoogle Scholar
  10. 10.
    Yurke, B., Mills, A.P.: Using DNA to Power Nanostructures. Genetic Programming and Evolvable Machines 4(2), 111–122 (2003)CrossRefGoogle Scholar
  11. 11.
    Gaspard, P.: Encyclopedia of Nonlinear Science. In: “Rössler Systems”, pp. 808–811. Routledge (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • David Soloveichik
    • 1
  • Georg Seelig
    • 1
  • Erik Winfree
    • 1
  1. 1.California Institute of TechnologyPasadenaUSA

Personalised recommendations