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Impossibility of Sufficiently Simple Chemical Reaction Network Implementations in DNA Strand Displacement

  • Robert F. JohnsonEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11493)

Abstract

DNA strand displacement (DSD) has recently become a common technology for constructing molecular devices, with a number of useful systems experimentally demonstrated. To help with DSD system design, various researchers are developing formal definitions to model DNA strand displacement systems. With these models a DSD system can be defined, described by a Chemical Reaction Network, simulated, and otherwise analyzed. Meanwhile, the research community is trying to use DSD to do increasingly complex tasks, while also trying to make DSD systems simpler and more robust. I suggest that formal modeling of DSD systems can be used not only to analyze DSD systems, but to guide their design. For instance, one might prove that a DSD system that implements a certain function must use a certain mechanism. As an example, I show that a physically reversible DSD system with no pseudoknots, no effectively trimolecular reactions, and using 4-way but not 3-way branch migration, cannot be a systematic implementation of reactions of the form \(A \rightleftharpoons B\) that uses a constant number of toehold domains and does not crosstalk when multiple reactions of that type are combined. This result is a tight lower bound in the sense that, for most of those conditions, removing just that one condition makes the desired DSD system possible. I conjecture that a system with the same restrictions using both 3-way and 4-way branch migration still cannot systematically implement the reaction \(A + B \rightleftharpoons C\).

Notes

Acknowledgements

I thank Chris Thachuk, Stefan Badelt, Erik Winfree, and Lulu Qian for helpful discussions on formal verification and on two-stranded DSD systems. I also thank the anonymous reviewers of a rejected previous version of this paper for their suggestions, many of which appear in this version. I thank the NSF Graduate Research Fellowship Program for financial support.

References

  1. 1.
    Badelt, S., Shin, S.W., Johnson, R.F., Dong, Q., Thachuk, C., Winfree, E.: A general-purpose CRN-to-DSD compiler with formal verification, optimization, and simulation capabilities. In: Brijder, R., Qian, L. (eds.) DNA 2017. LNCS, vol. 10467, pp. 232–248. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-66799-7_15CrossRefzbMATHGoogle Scholar
  2. 2.
    Cardelli, L.: Two-domain DNA strand displacement. Math. Struct. Comput. Sci. 23, 247–271 (2013)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Chen, S.X., Zhang, D.Y., Seelig, G.: Conditionally fluorescent molecular probes for detecting single base changes in double-stranded DNA. Nat. Chem. 5(9), 782 (2013)CrossRefGoogle Scholar
  4. 4.
    Chen, Y.J., et al.: Programmable chemical controllers made from DNA. Nat. Nanotechnol. 8, 755–762 (2013)CrossRefGoogle Scholar
  5. 5.
    Dabby, N.L.: Synthetic molecular machines for active self-assembly: prototype algorithms, designs, and experimental study. Ph.D. thesis, California Institute of Technology, February 2013Google Scholar
  6. 6.
    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)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Douglas, S.M., Bachelet, I., Church, G.M.: A logic-gated nanorobot for targeted transport of molecular payloads. Science 335(6070), 831–834 (2012)CrossRefGoogle Scholar
  8. 8.
    Groves, B., et al.: Computing in mammalian cells with nucleic acid strand exchange. Nat. Nanotechnol. 11(3), 287 (2016)CrossRefGoogle Scholar
  9. 9.
    Grun, C., Sarma, K., Wolfe, B., Shin, S.W., Winfree, E.: A domain-level DNA strand displacement reaction enumerator allowing arbitrary non-pseudoknotted secondary structures. CoRR p. http://arxiv.org/abs/1505.03738 (2015)
  10. 10.
    Johnson, R.F., Dong, Q., Winfree, E.: Verifying chemical reaction network implementations: a bisimulation approach. Theoret. Comput. Sci. (2018).  https://doi.org/10.1016/j.tcs.2018.01.002CrossRefzbMATHGoogle Scholar
  11. 11.
    Johnson, R.F., Qian, L.: Simplifying chemical reaction network implementations with two-stranded DNA building blocks, in preparationGoogle Scholar
  12. 12.
    Lakin, M.R., Stefanovic, D., Phillips, A.: Modular verification of chemical reaction network encodings via serializability analysis. Theoret. Comput. Sci. 632, 21–42 (2016)MathSciNetCrossRefGoogle Scholar
  13. 13.
    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, 3211–3213 (2011)CrossRefGoogle Scholar
  14. 14.
    Petersen, R.L., Lakin, M.R., Phillips, A.: A strand graph semantics for DNA-based computation. Theoret. Comput. Sci. 632, 43–73 (2016)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Qian, L., Soloveichik, D., Winfree, E.: Efficient turing-universal computation with DNA polymers. In: Sakakibara, Y., Mi, Y. (eds.) DNA 2010. LNCS, vol. 6518, pp. 123–140. Springer, Heidelberg (2011).  https://doi.org/10.1007/978-3-642-18305-8_12CrossRefzbMATHGoogle Scholar
  16. 16.
    Qian, L., Winfree, E.: Scaling up digital circuit computation with DNA strand displacement cascades. Science 332(6034), 1196–1201 (2011)CrossRefGoogle Scholar
  17. 17.
    Qian, L., Winfree, E.: Parallel and scalable computation and spatial dynamics with DNA-based chemical reaction networks on a surface. In: Murata, S., Kobayashi, S. (eds.) DNA 2014. LNCS, vol. 8727, pp. 114–131. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-11295-4_8CrossRefzbMATHGoogle Scholar
  18. 18.
    Shin, S.W., Thachuk, C., Winfree, E.: Verifying chemical reaction network implementations: a pathway decomposition approach. Theor. Comput. Sci. (2017)  https://doi.org/10.1016/j.tcs.2017.10.011MathSciNetCrossRefGoogle Scholar
  19. 19.
    Soloveichik, D., Seelig, G., Winfree, E.: DNA as a universal substrate for chemical kinetics. Proc. Nat. Acad. Sci. 107, 5393–5398 (2010)CrossRefGoogle Scholar
  20. 20.
    Srinivas, N., Parkin, J., Seelig, G., Winfree, E., Soloveichik, D.: Enzyme-free nucleic acid dynamical systems. Science 358 (2017).  https://doi.org/10.1126/science.aal2052CrossRefGoogle Scholar
  21. 21.
    Thubagere, A.J., et al.: A cargo-sorting DNA robot. Science 357(6356), eaan6558 (2017)CrossRefGoogle Scholar
  22. 22.
    Thubagere, A.J., et al.: Compiler-aided systematic construction of large-scale DNA strand displacement circuits using unpurified components. Nat. Commun. 8, 14373 (2017)CrossRefGoogle Scholar
  23. 23.
    Venkataraman, S., Dirks, R.M., Rothemund, P.W., Winfree, E., Pierce, N.A.: An autonomous polymerization motor powered by DNA hybridization. Nat. Nanotechnol. 2(8), 490 (2007)CrossRefGoogle Scholar
  24. 24.
    Zhang, D.Y., Seelig, G.: Dynamic DNA nanotechnology using strand-displacement reactions. Nat. Chem. 3(2), 103–113 (2011)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.BioengineeringCalifornia Institute of TechnologyPasadenaUSA

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