Influence Systems vs Reaction Systems

  • François FagesEmail author
  • Thierry Martinez
  • David A. Rosenblueth
  • Sylvain Soliman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9859)


In Systems Biology, modelers develop more and more reaction-based models to describe the mechanistic biochemical reactions underlying cell processes. They may also work, however, with a simpler formalism of influence graphs, to merely describe the positive and negative influences between molecular species. The first approach is promoted by reaction model exchange formats such as SBML, and tools like CellDesigner, while the second is supported by other tools that have been historically developed to reason about boolean gene regulatory networks. In practice, modelers often reason with both kinds of formalisms, and may find an influence model useful in the process of building a reaction model. In this paper, we introduce a formalism of influence systems with forces, and put it in parallel with reaction systems with kinetics, in order to develop a similar hierarchy of boolean, discrete, stochastic and differential semantics. We show that the expressive power of influence systems is the same as that of reaction systems under the differential semantics, but weaker under the other interpretations, in the sense that some discrete behaviours of reaction systems cannot be expressed by influence systems. This approach leads us to consider a positive boolean semantics which we compare to the asynchronous semantics of gene regulatory networks à la Thomas. We study the monotonicity properties of the positive boolean semantics and derive from them an efficient algorithm to compute attractors.



We are grateful to Paul Ruet for interesting discussions on Thomas’s framework, and to the reviewers for their comments. This work was partially supported by ANR project Hyclock under contract ANR-14-CE09-0011, and PASPA-DGAPA-UNAM, Conacyt grants 221341 and 261225.


  1. 1.
    Abou-Jaoudé, W., Ouattara, D.A., Kaufman, M.: From structure to dynamics: frequency tuning in the p53-Mdm2 network: I. logical approach. J. Theor. Biol. 258(4), 561–577 (2009)CrossRefGoogle Scholar
  2. 2.
    Abou-Jaoudé, W., Ouattara, D.A., Kaufman, M.: From structure to dynamics: frequency tuning in the p53-Mdm2 network: II differential and stochastic approaches. J. Theor. Biol. 264, 1177–1189 (2010)CrossRefGoogle Scholar
  3. 3.
    Angeli, D., Sontag, E.D.: Monotone control systems. IEEE Trans. Autom. Control 48(10), 1684–1698 (2003)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Batt, G., et al.: Genetic Network Analyzer: a tool for the qualitative modeling and simulation of bacterial regulatory networks. In: van Helden, J., Toussaint, A., Thieffry, D. (eds.) Bacterial Molecular Networks. Methods in Molecular Biology, vol. 804, pp. 439–462. Springer, New York (2012)CrossRefGoogle Scholar
  5. 5.
    Bernot, G., Comet, J.P., Khalis, Z.: Gene regulatory networks wih multiplexes. In: Proceedings of European Simulation and Modelling Conference, ESM 2008. pp. 423–432 (2008)Google Scholar
  6. 6.
    Chaouiya, C.: Petri net modelling of biological networks. Brief. Bioinform. 8, 210 (2007)CrossRefGoogle Scholar
  7. 7.
    Chazelle, B.: Natural algorithms and influence systems. Commun. ACM 55(12), 101–110 (2012)CrossRefGoogle Scholar
  8. 8.
    Ciliberto, A., Capuani, F., Tyson, J.J.: Modeling networks of coupled enzymatic reactions using the total quasi-steady state approximation. PLOS Comput. Biol. 3(3), e45 (2007)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Comet, J.P., Bernot, G., Das, A., Diener, F., Massot, C., Cessieux, A.: Simplified models for the mammalian circadian clock. Procedia Comput. Sci. 11, 127–138 (2012)CrossRefGoogle Scholar
  10. 10.
    Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proceedings of the 6th ACM Symposium on Principles of Programming Languages, POPL1977, pp. 238–252, Los Angeles. ACM, New York (1977)Google Scholar
  11. 11.
    Fages, F., Gay, S., Soliman, S.: Inferring reaction systems from ordinary differential equations. Theor. Comput. Sci. 599, 64–78 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Fages, F., Soliman, S.: Abstract interpretation and types for systems biology. Theor. Comput. Sci. 403(1), 52–70 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Fages, F., Soliman, S.: From reaction models to influence graphs and back: a theorem. In: Fisher, J. (ed.) FMSB 2008. LNCS (LNBI), vol. 5054, pp. 90–102. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  14. 14.
    Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  15. 15.
    Glass, L., Kauffman, S.A.: The logical analysis of continuous, non-linear biochemical control networks. J. Theor. Biol. 39(1), 103–129 (1973)CrossRefGoogle Scholar
  16. 16.
    González, A.G., Chaouiya, C., Thieffry, D.: Qualitative dynamical modelling of the formation of the anterior-posterior compartment boundary in the drosophila wing imaginal disc. Bioinformatics 24, 234–240 (2008)CrossRefGoogle Scholar
  17. 17.
    Grieco, L., Calzone, L., Bernard-Pierrot, I., Radvanyi, F., Kahn-Perlès, B., Thieffry, D.: Integrative modelling of the influence of mapk network on cancer cell fate decision. PLOS Comput. Biol. 9(10), e1003286 (2013)CrossRefGoogle Scholar
  18. 18.
    Hucka, M., et al.: The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics 19(4), 524–531 (2003). CrossRefGoogle Scholar
  19. 19.
    Katsumata, M.: Graphic representation of Botts-Morales equation for enzyme-substrate-modifier system. J. Theor. Biol. 36(2), 327–338 (1972)CrossRefGoogle Scholar
  20. 20.
    Klarner, H., Bockmayr, A., Siebert, H.: Computing symbolic steady states of Boolean networks. In: Wąs, J., Sirakoulis, G.C., Bandini, S. (eds.) ACRI 2014. LNCS, vol. 8751, pp. 561–570. Springer, Heidelberg (2014)Google Scholar
  21. 21.
    Leloup, J.C., Goldbeter, A.: Toward a detailed computational model for the mammalian circadian clock. Proc. Nat. Acad. Sci. 100, 7051–7056 (2003)CrossRefGoogle Scholar
  22. 22.
    Naldi, A., Berenguier, D., Fauré, A., Lopez, F., Thieffry, D., Chaouiya, C.: Logical modelling of regulatory networks with GINsim 2.3. Biosystems 97(2), 134–139 (2009)CrossRefGoogle Scholar
  23. 23.
    Naldi, A., Remy, E., Thieffry, D., Chaouiya, C.: A reduction of logical regulatory graphs preserving essential dynamical properties. In: Degano, P., Gorrieri, R. (eds.) CMSB 2009. LNCS, vol. 5688, pp. 266–280. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  24. 24.
    Naldi, A., Carneiro, J., Chaouiya, C., Thieffry, D.: Diversity and plasticity of th cell types predicted from regulatory network modelling. PLoS Comput. Biol. 6(9), e1000912 (2010)CrossRefGoogle Scholar
  25. 25.
    le Novère, N., Bornstein, B., Broicher, A., Courtot, M., Donizelli, M., Dharuri, H., Li, L., Sauro, H., Schilstra, M., Shapiro, B., Snoep, J.L., Hucka, M.: BioModels database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems. Nucleic Acid Res. 1(34), D689–D691 (2006)CrossRefGoogle Scholar
  26. 26.
    le Novere, N., Hucka, M., Mi, H., Moodie, S., Schreiber, F., Sorokin, A., Demir, E., Wegner, K., Aladjem, M.I., Wimalaratne, S.M., Bergman, F.T., Gauges, R., Ghazal, P., Kawaji, H., Li, L., Matsuoka, Y., Villeger, A., Boyd, S.E., Calzone, L., Courtot, M., Dogrusoz, U., Freeman, T.C., Funahashi, A., Ghosh, S., Jouraku, A., Kim, S., Kolpakov, F., Luna, A., Sahle, S., Schmidt, E., Watterson, S., Wu, G., Goryanin, I., Kell, D.B., Sander, C., Sauro, H., Snoep, J.L., Kohn, K., Kitano, H.: The systems biology graphical notation. Nat. Biotechnol. 27(8), 735–741 (2009)CrossRefGoogle Scholar
  27. 27.
    Remy, E., Ruet, P., Thieffry, D.: Graphic requirements for multistability and attractive cycles in a Boolean dynamical framework. Adv. Appl. Math. 41(3), 335–350 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Rosenblueth, D.A., Muñoz, S., Carrillo, M., Azpeitia, E.: Inference of Boolean networks from gene interaction graphs using a SAT solver. In: Dediu, A.-H., Martín-Vide, C., Truthe, B. (eds.) AlCoB 2014. LNCS, vol. 8542, pp. 235–246. Springer, Heidelberg (2014)Google Scholar
  29. 29.
    Ruet, P.: Local cycles and dynamical properties of Boolean networks. Math. Found. Comput. Sci. 26(4), 702–718 (2016)MathSciNetzbMATHGoogle Scholar
  30. 30.
    Thomas, R.: Boolean formalisation of genetic control circuits. J. Theor. Biol. 42, 565–583 (1973)CrossRefGoogle Scholar
  31. 31.
    Thomas, R., D’Ari, R.: Biological Feedback. CRC Press, Boca Raton (1990)zbMATHGoogle Scholar
  32. 32.
    Traynard, P., Fauré, A., Fages, F., Thieffry, D.: Logical model specification aided by model- checking techniques: application to the mammalian cell cycle regulation. Bioinformatics, Special issue of ECCB (2016)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • François Fages
    • 1
    Email author
  • Thierry Martinez
    • 2
  • David A. Rosenblueth
    • 1
    • 3
  • Sylvain Soliman
    • 1
  1. 1.Inria Saclay-Île-de-France, Team LifewarePalaiseauFrance
  2. 2.Inria Paris, SEDParisFrance
  3. 3.Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas (IIMAS)Universidad Nacional Autónoma de México (UNAM)Mexico, D.F.Mexico

Personalised recommendations