Exploring Synthetic Mass Action Models

  • Oded MalerEmail author
  • Ádám M. Halász
  • Olivier Lebeltel
  • Ouri Maler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7699)


In this work we propose a model that can be used to study the dynamics of mass action systems, systems consisting of a large number of individuals whose behavior is influenced by other individuals that they encounter. Our approach is rather synthetic and abstract, viewing each individual as a probabilistic automaton that can be in one of finitely many discrete states. We demonstrate the type of investigations that can be carried out on such a model using the Populus toolkit. In particular, we illustrate how sensitivity to initial spatial distribution can be observed in simulation.


Particle Type Aggregate Model Stochastic Simulation Algorithm Input Alphabet Interaction Radius 
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.



We thank Eric Fanchon for many useful comments.


  1. 1.
    Andrews, S.S., Bray, D.: Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Phys. Biol. 1(3), 137 (2004)CrossRefGoogle Scholar
  2. 2.
    Ball, P.: Critical Mass: How One Thing Leads to Another. Macmillan, London (2004) Google Scholar
  3. 3.
    Bortolussi, L., Hillston, J.: Checking individual agent behaviours in markov population models by fluid approximation. In: Bernardo, M., de Vink, E., Di Pierro, A., Wiklicky, H. (eds.) SFM 2013. LNCS, vol. 7938, pp. 113–149. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  4. 4.
    Burrage, K., Burrage, P.M., Leier, A., Marquez-Lago, T., Nicolau Jr., D.V.: Stochastic simulation for spatial modelling of dynamic processes in a living cell. In: Koeppl, H., Setti, G., di Bernardo, M., Densmore, D. (eds.) Design and Analysis of Biomolecular Circuits, pp. 43–62. Springer, New York (2011)CrossRefGoogle Scholar
  5. 5.
    Cardelli, L.: Artificial biochemistry. In: Condon, A., Harel, D., Kok, J.N., Salomaa, A., Winfree, E. (eds.) Algorithmic Bioprocesses, pp. 429–462. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  7. 7.
    Gillespie, D.T.: Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115, 1716 (2001)CrossRefGoogle Scholar
  8. 8.
    Gillespie, D.T.: Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem. 58, 35–55 (2007)CrossRefGoogle Scholar
  9. 9.
    Halász, A.M., Pryor, M.M., Wilson, B.S., Edwards, J.S.: Spatio-temporal modeling of membrane receptors (2015). under reviewGoogle Scholar
  10. 10.
    Julius, A.A., Halász, Á., Sakar, M.S., Rubin, H., Kumar, V., Pappas, G.J.: Stochastic modeling and control of biological systems: the Lactose regulation system of escherichia coli. IEEE Trans. Autom. Control 53, 51–65 (2008)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Le Boudec, J.-Y., McDonald, D., Mundinger, J.: A generic mean field convergence result for systems of interacting objects. In: QEST, IEEE, pp. 3–18 (2007)Google Scholar
  12. 12.
    Maler, O.: Control from computer science. Ann. Rev. Control 26(2), 175–187 (2002)CrossRefGoogle Scholar
  13. 13.
    Maler, O.: On under-determined dynamical systems. In: EMSOFT, pp. 89–96. ACM (2011)Google Scholar
  14. 14.
    Maler, O., Halász, A.M., Lebeltel, O., Maler, O.: Exploring the dynamics of mass action systems. EPTCS 125, 84–91 (2013)CrossRefGoogle Scholar
  15. 15.
    Paz, A.: Introduction to Probabilistic Automata. Academic Press, Orlando (1971)zbMATHGoogle Scholar
  16. 16.
    Samoilov, M.S., Arkin, A.P.: Deviant effects in molecular reaction pathways. Nat. Biotechnol. 24(10), 1235–1240 (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Oded Maler
    • 1
    Email author
  • Ádám M. Halász
    • 2
  • Olivier Lebeltel
    • 1
  • Ouri Maler
    • 2
  1. 1.VERIMAG, CNRS, University of Grenoble-AlpesGrenobleFrance
  2. 2.Department of MathematicsWest Virginia UniversityMorgantownUSA

Personalised recommendations