Abstraction of Graph-Based Models of Bio-molecular Reaction Systems for Efficient Simulation

  • Ibuki Kawamata
  • Nathanael Aubert
  • Masahiro Hamano
  • Masami Hagiya
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7605)


We propose a technique to simulate molecular reaction systems efficiently by abstracting graph models. Graphs (or networks) and their transitions give rise to simple but powerful models for molecules and their chemical reactions. Depending on the purpose of a graph-based model, nodes and edges of a graph may correspond to molecular units and chemical bonds, respectively. This kind of model provides naive simulations of molecular reaction systems by applying chemical kinetics to graph transition. Such naive models, however, can immediately cause a combinatorial explosion of the number of molecular species because combination of chemical bonds is usually unbounded, which makes simulation intractable. To overcome this problem, we introduce an abstraction technique to divide a graph into local structures. New abstracted models for simulating DNA hybridization systems and RNA interference are explained as case studies to show the effectiveness of our abstraction technique. We then discuss the trade-off between the efficiency and exactness of our abstracted models from the aspect of the number of structures and simulation error. We classify molecular reaction systems into three groups according to the assumptions on reactions. The first one allows efficient and exact abstraction, the second one allows efficient but approximate abstraction, and the third one does not reduce the number of structures by abstraction. We conclude that abstraction is a useful tool to analyze complex molecular reaction systems and measure their complexity.


Local Structure Combinatorial Explosion Reaction Rule Abstracted Model Supplementary Document 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bath, J., Turberfield, A.J.: DNA nanomachines. Nat. Nanotechnol. 2(5), 275–284 (2007)CrossRefGoogle Scholar
  2. 2.
    Baulcombe, D.C.: Amplified Silencing. Science 315(5809), 199–200 (2007)CrossRefGoogle Scholar
  3. 3.
    Bergstrom, C.T., McKittrick, E., Antia, R.: Mathematical models of RNA silencing: unidirectional amplification limits accidental self-directed reactions. Proc. Natl. Acad. Sci. USA 100(20), 11511–11516 (2003)CrossRefGoogle Scholar
  4. 4.
    Borisov, N.M., Chistopolsky, A.S., Faeder, J.R., Kholodenko, B.N.: Domain-oriented reduction of rule-based network models. IET Syst. Biol. 2(5), 342–351 (2008)CrossRefGoogle Scholar
  5. 5.
    Brodersen, P., Voinnet, O.: The diversity of RNA silencing pathways in plants. TRENDS in Genettics 22(5), 268–280 (2006)CrossRefGoogle Scholar
  6. 6.
    Conzelmann, H., Fey, D., Gilles, E.D.: Exact model reduction of combinatorial reaction networks. BMC Syst. Biol. 2, 78 (2008)CrossRefGoogle Scholar
  7. 7.
    Conzelmann, H., Saez-Rodriguez, J., Sauter, T., Kholodenko, B.N., Gilles, E.D.: A domain-oriented approach to the reduction of combinatorial complexity in signal transduction networks. BMC Bioinformatics 7, 34 (2006)CrossRefGoogle Scholar
  8. 8.
    Cuccato, G., Polynikis, A., Siciliano, V., Graziano, M., di Bernardo, M., di Bernardo, D.: Modeling RNA interference in mammalian cells. BMC Syst. Biol. 5, 19 (2011)CrossRefGoogle Scholar
  9. 9.
    Danos, V., Feret, J., Fontana, W., Harmer, R., Krivine, J.: Abstracting the differential semantics of rule-based models: exact and automated model reduction. In: Proceedings of the Twenty-Fifth Annual IEEE Symposium on Logic in Computer Science, pp. 362–381. IEEE (2010)Google Scholar
  10. 10.
    Danos, V., Feret, J., Fontana, W., Krivine, J.: Abstract Interpretation of Cellular Signalling Networks. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 83–97. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. 11.
    Dirks, R.M., Pierce, N.A.: Triggered amplification by hybridization chain reaction. Proc. Natl. Acad. Sci. USA 101(43), 15275–15278 (2004)CrossRefGoogle Scholar
  12. 12.
    Fehlberg, E.: Klassische Runge-Kutta-Formeln vierter und niedrigerer ordnung mit schrittweiten-kontrolle und ihre Anwendung auf wärmeleitungsprobleme. Computing 6(1), 61–71 (1970)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Feret, J., Danos, V., Krivine, J., Harmer, R., Fontana, W.: Internal coarse-graining of molecular systems. Proc. Natl. Acad. Sci. USA 106(16), 6453–6458 (2009)CrossRefGoogle Scholar
  14. 14.
    Groenenboom, M.A.C., Marée, A.F.M., Hogeweg, P.: The RNA Silencing Pathway: The Bits and Pieces That Matter. PLoS Comput. Biol. 1(2), 155–165 (2005)CrossRefGoogle Scholar
  15. 15.
    Han, D., Pal, S., Nangreave, J., Deng, Z., Liu, Y., Yan, H.: DNA Origami with Complex Curvatures in Three-Dimensional Space. Science 332(6027), 342–346 (2011)CrossRefGoogle Scholar
  16. 16.
    Harmer, R., Danos, V., Feret, J., Krivine, J., Fontana, W.: Intrinsic Information Carriers in Combinatorial Dynamical Systems. Chaos 20(3), 037108 (2010)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Kawamata, I.: Formal Definition of the ODE of RNAi and Experimental Results for Approximate Abstraction: supplementary documents (2012),
  18. 18.
    Kawamata, I., Tanaka, F., Hagiya, M.: Automatic Design of DNA Logic Gates Based on Kinetic Simulation. In: Deaton, R., Suyama, A. (eds.) DNA 15. LNCS, vol. 5877, pp. 88–96. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  19. 19.
    Kawamata, I., Tanaka, F., Hagiya, M.: Abstraction of DNA Graph Structures for Efficient Enumeration and Simulation. In: International Conference on Parallel and Distributed Processing Techniques and Applications, pp. 800–806 (2011)Google Scholar
  20. 20.
    Kitano, H.: Systems Biology: A Brief Overview. Science 295(5560), 1662–1664 (2002)CrossRefGoogle Scholar
  21. 21.
    Kobayashi, S.: A New Approach to Computing Equilibrium State of Combinatorial Hybridization Reaction Systems. In: Proc. of Workshop on Computing and Communications from Biological Systems: Theory and Applications, pp. 330–335 (2007)Google Scholar
  22. 22.
    Kobayashi, S.: Symmetric Enumeration Method: A New Approach to Computing Equilibria. Technical Report of Dept. of Computer Science, University of Electro-Communications (2008)Google Scholar
  23. 23.
    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)CrossRefGoogle Scholar
  24. 24.
    Marshall, W.F.: Modeling recursive RNA interference. PLoS Comput. Biol. 4(9), e1000183 (2008)Google Scholar
  25. 25.
    Pak, J., Fire, A.: Distinct Populations of Primary and Secondary Effectors During RNAi in C. elegans. Science 315(5809), 241–244 (2007)CrossRefGoogle Scholar
  26. 26.
    Pinheiro, A.V., Han, D., Shih, W.M., Yan, H.: Challenges and opportunities for structural DNA nanotechnology. Nat. Nanotechnol. 6(12), 763–772 (2011)CrossRefGoogle Scholar
  27. 27.
    Qian, L., Winfree, E.: Scaling Up Digital Circuit Computation with DNA Strand Displacement Cascades. Science 332(6034), 1196–1201 (2011)CrossRefGoogle Scholar
  28. 28.
    Seelig, G., Soloveichik, D., Zhang, D.Y., Winfree, E.: Enzyme-Free Nucleic Acid Logic Circuits. Science 314(5805), 1585–1588 (2006)CrossRefGoogle Scholar
  29. 29.
    Venkataraman, S., Dirks, R.M., Ueda, C.T., Pierce, N.A.: Selective cell death mediated by small conditional RNAs. Proc. Natl. Acad. Sci. USA 107(39), 16777–16782 (2010)CrossRefGoogle Scholar
  30. 30.
    Win, M.N., Smolke, C.D.: Higher-Order Cellular Information Processing with Synthetic RNA Devices. Science 322(5900), 456–460 (2008)CrossRefGoogle Scholar
  31. 31.
    Winfree, E.: Algorithmic self-assembly of DNA. Ph.D. thesis, California Institute of Technology (1998)Google Scholar
  32. 32.
    Yin, P., Choi, H.M.T., Calvert, C.R., Pierce, N.A.: Programming biomolecular self-assembly pathways. Nature 451(7176), 318–322 (2008)CrossRefGoogle Scholar
  33. 33.
    Zhang, D.Y., Seelig, G.: Dynamic DNA nanotechnology using strand-displacement reactions. Nat. Chem. 3(2), 103–113 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ibuki Kawamata
    • 1
  • Nathanael Aubert
    • 1
  • Masahiro Hamano
    • 1
  • Masami Hagiya
    • 1
  1. 1.Graduate School of Information Science and TechnologyUniversity of TokyoBunkyo-kuJapan

Personalised recommendations