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Thermodynamic Binding Networks

  • David Doty
  • Trent A. Rogers
  • David SoloveichikEmail author
  • Chris Thachuk
  • Damien Woods
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10467)

Abstract

Strand displacement and tile assembly systems are designed to follow prescribed kinetic rules (i.e., exhibit a specific time-evolution). However, the expected behavior in the limit of infinite time—known as thermodynamic equilibrium—is often incompatible with the desired computation. Basic physical chemistry implicates this inconsistency as a source of unavoidable error. Can the thermodynamic equilibrium be made consistent with the desired computational pathway? In order to formally study this question, we introduce a new model of molecular computing in which computation is driven by the thermodynamic driving forces of enthalpy and entropy. To ensure greatest generality we do not assume that there are any constraints imposed by geometry and treat monomers as unstructured collections of binding sites. In this model we design Boolean AND/OR formulas, as well as a self-assembling binary counter, where the thermodynamically favored states are exactly the desired final output configurations. Though inspired by DNA nanotechnology, the model is sufficiently general to apply to a wide variety of chemical systems.

References

  1. 1.
    Barish, R.D., Schulman, R., Rothemund, P.W.K., Winfree, E.: An information-bearing seed for nucleating algorithmic self-assembly. Proc. Natl. Acad. Sci. 106(15), 6054–6059 (2009)CrossRefGoogle Scholar
  2. 2.
    Bennett, C.H.: The thermodynamics of computation—a review. Int. J. Theor. Phys. 21(12), 905–940 (1982)CrossRefGoogle Scholar
  3. 3.
    Breik, K., Prakash, L., Thachuk, C., Heule, M., Soloveichik, D.: Computing properties of stable configurations of thermodynamic binding networks (2017, in preparation)Google Scholar
  4. 4.
    Dirks, R.M., Bois, J.S., Schaeffer, J.M., Winfree, E., Pierce, N.A.: Thermodynamic analysis of interacting nucleic acid strands. SIAM Rev. 49(1), 65–88 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    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)CrossRefGoogle Scholar
  6. 6.
    Gerling, T., Wagenbauer, K.F., Neuner, A.M., Dietz, H.: Dynamic DNA devices and assemblies formed by shape-complementary, non-base pairing 3D components. Science 347(6229), 1446–1452 (2015)CrossRefGoogle Scholar
  7. 7.
    Papadimitriou, C.H.: On the complexity of integer programming. J. ACM (JACM) 28(4), 765–768 (1981)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Phillips, A., Cardelli, L.: A programming language for composable DNA circuits. J. R. Soc. Interface 6(Suppl 4), S419–S436 (2009)CrossRefGoogle Scholar
  9. 9.
    SantaLucia Jr., J., Hicks, D.: The thermodynamics of DNA structural motifs. Annu. Rev. Biophys. Biomol. Struct. 33, 415–440 (2004)CrossRefGoogle Scholar
  10. 10.
    Schulman, R., Winfree, E.: Programmable control of nucleation for algorithmic self-assembly. SIAM J. Comput. 39(4), 1581–1616 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Thachuk, C., Winfree, E., Soloveichik, D.: Leakless DNA strand displacement systems. In: Phillips, A., Yin, P. (eds.) DNA 2015. LNCS, vol. 9211, pp. 133–153. Springer, Cham (2015). doi: 10.1007/978-3-319-21999-8_9 CrossRefGoogle Scholar
  12. 12.
    Winfree, E.: Algorithmic self-assembly of DNA. Ph.D. thesis, California Institute of Technology (1998)Google Scholar
  13. 13.
    Woo, S., Rothemund, P.W.K.: Programmable molecular recognition based on the geometry of DNA nanostructures. Nat. Chem. 3, 620–627 (2011)CrossRefGoogle Scholar
  14. 14.
    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)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • David Doty
    • 1
  • Trent A. Rogers
    • 2
  • David Soloveichik
    • 3
    Email author
  • Chris Thachuk
    • 4
  • Damien Woods
    • 5
  1. 1.University of California, DavisDavisUSA
  2. 2.University of ArkansasFayettevilleUSA
  3. 3.University of Texas at AustinAustinUSA
  4. 4.California Institute of TechnologyPasadenaUSA
  5. 5.InriaParisFrance

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