Synchronous Balanced Analysis

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9957)

Abstract

When modeling Chemical Reaction Networks, a commonly used mathematical formalism is that of Petri Nets, with the usual interleaving execution semantics. We aim to substitute to a Chemical Reaction Network, especially a “growth” one (i.e., for which an exponential stationary phase exists), a piecewise synchronous approximation of the dynamics: a resource-allocation-centered Petri Net with maximal-step execution semantics. In the case of unimolecular chemical reactions, we prove the correctness of our method and show that it can be used either as an approximation of the dynamics, or as a method of constraining the reaction rate constants (an alternative to flux balance analysis, using an emergent formally defined notion of “growth rate” as the objective function), or a technique of refuting models.

Keywords

Chemical Reaction Networks Approximation Resource allocation Max-parallel execution of Petri Nets Flux balance analysis 

References

  1. 1.
    Garey, M.R., Johnson, D.S., Sethi, R.: The complexity of flowshop and jobshop scheduling. Math. Oper. Res. 1, 117–129 (1976)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Sinnen, O.: Task Scheduling for Parallel Systems. Wiley-Interscience, Hoboken (2007)CrossRefGoogle Scholar
  3. 3.
    Pugatch, R.: Greedy scheduling of cellular self-replication leads to optimal doubling times with a log-Frechet distribution. PNAS 112(8), 2611–2616 (2015)CrossRefGoogle Scholar
  4. 4.
    Weiße, A.Y., Oyarzún, D.A., Danos, V., Swain, P.S.: Mechanistic links between cellular trade-offs, gene expression, and growth. PNAS 112(9), E1038–E1047 (2015)CrossRefGoogle Scholar
  5. 5.
    Pãun, G., Rozenberg, G.: A guide to membrane computing. Theor. Comput. Sci. 287(1), 73–100 (2002). doi:10.1016/S0304-3975(02)00136-6 MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Lévy, J.-J.: Réductions correctes et optimales dans le lambda-calcul. Ph.D. thesis, Université Paris 7, January 1978Google Scholar
  7. 7.
    Krepska, E., Bonzanni, N., Feenstra, A., Fokkink, W., Kielmann, T., Bal, H., Heringa, J.: Design issues for qualitative modelling of biological cells with petri nets. In: Fisher, J. (ed.) FMSB 2008. LNCS (LNBI), vol. 5054, pp. 48–62. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  8. 8.
    Fisher, J., Henzinger, T.A., Mateescu, M., Piterman, N.: Bounded asynchrony: concurrency for modeling cell-cell interactions. In: Fisher, J. (ed.) FMSB 2008. LNCS (LNBI), vol. 5054, pp. 17–32. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Picard, V.: Réseaux de réactions: de l’analyse probabiliste à la réfutation. Ph.D. thesis, Université de Rennes 1, December 2015Google Scholar
  10. 10.
    Kurtz, T.G.: Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. J. Appl. Probab. 8(2), 344–355 (1971)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Orth, J.D., Thiele, I., Palsson, B.Ø.: What is flux balance analysis? Nat. Biotechnol. 28(3), 245–248 (2010). http://doi.org/10.1038/nbt.1614 CrossRefGoogle Scholar
  12. 12.
    Karr, J.R., et al.: A whole-cell computational model predicts phenotype from genotype. Cell 150(2), 389–401 (2012). http://dx.doi.org/10.1016/j.cell.2012.05.044 CrossRefGoogle Scholar
  13. 13.
    Gillespie, D.T.: Approximate accelerated stochastic simulation of chemically reacting systems. J. Chem. Phys. 115(4), 1716 (2001). doi:10.1063/1.1378322 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.École Normale SupérieureParisFrance

Personalised recommendations