Feasibility of Organizations – A Refinement of Chemical Organization Theory with Application to P Systems

  • Stephan Peter
  • Tomas Veloz
  • Peter Dittrich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6501)


In membrane computing, a relatively simple set of reaction rules usually implies a complex “constructive” dynamics, in which novel molecular species appear and present species vanish. Chemical organization theory is a new approach that deals with such systems by describing chemical computing as a transition between organizations, which are closed and self-maintaining sets of molecular species. In this paper we show that for the case of mass-action kinetics some organizations are not feasible in the space of concentrations and thus need not to be considered in the analysis. We present a theorem providing criteria for an unfeasible organization. This is a refinement of organization theory making its statements more precise. In particular it follows for the design of a membrane computing system that the desired resulting organization of a chemical computing process should be a feasible organization. Nevertheless we show that due to the membranes in a P system unfeasible organizations can be observed, suggesting a strong link between the two approaches.


Reaction Network Organization Theory Oscillatory Regime Stoichiometric Matrix Reaction Rule 
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.
    National Center for Biotechnology Information,
  2. 2.
    Centler, F., Dittrich, P.: Chemical Organizations in Atmospheric Photochemistries: A New Method to Analyze Chemical Reaction Networks. Planet. Space Sci. 55, 413–428 (2007)CrossRefGoogle Scholar
  3. 3.
    Centler, F., Kaleta, C., Speroni di Fenizio, P., Dittrich, P.: Computing Chemical Organizations in Biological Networks. Bioinformatics 24, 1611–1618 (2008)CrossRefGoogle Scholar
  4. 4.
    Dittrich, P., Speroni di Fenizio, P.: Chemical Organization Theory. Bull. Math. Biol. 69, 1199–1231 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Feinberg, M., Horn, F.J.M.: Dynamics of Open Chemical Systems and the Algebraic Structure of the Underlying Reaction Network. Chem. Eng. Sci. 29, 775–787 (1974)CrossRefGoogle Scholar
  6. 6.
    Fontana, W., Buss, L.W.: The Arrival of the Fittest: Toward a Theory of Biological Organization. Bull. Math. Biol. 56, 1–64 (1994)zbMATHGoogle Scholar
  7. 7.
    Luhmann, N.: Soziale Systeme. Suhrkamp, Frankfurt a.M (1984)Google Scholar
  8. 8.
    Matsumaru, N., Centler, F., di Fenizio, P.S., Dittrich, P.: Chemical Organization Theory as a Theoretical Base for Chemical Computing. Int. Jour. on Unconventional Computing 3, 285–309 (2007)Google Scholar
  9. 9.
    Matsumaru, N., Centler, F., di Fenizio, P.S., Dittrich, P.: Chemical Organization Theory Applied to Virus Dynamics. Information Technology 48, 154–160 (2006)Google Scholar
  10. 10.
    Murray, J.D.: Mathematical Biology I: An Introduction. Springer, New York (2002)zbMATHGoogle Scholar
  11. 11.
    Peter, S.: Chemische Organisationen und kontinuierliche Dynamik. Diploma Thesis (2008)Google Scholar
  12. 12.
    Petri, C.A.: Kommunikation mit Automaten. Ph.D. thesis, University of Bonn, Bonn (1962)Google Scholar
  13. 13.
    Schilling, C.H., Schuster, S., Palsson, B.O., Heinrich, R.: Metabolic Pathway Analysis: Basic Concepts and Scientific Applications in the Post-genomic Era. Biotechnol. Prog. 15, 296–303 (1999)CrossRefGoogle Scholar
  14. 14.
    Schuster, S., Dandekar, T., Fell, D.A.: Detection of Elementary Flux Modes in Biochemical Networks: A Promising Tool for Pathway Analysis and Metabolic Engineering. Trends Biotechnol. 17, 53–60 (1999)CrossRefGoogle Scholar
  15. 15.
    Sensse, A.: Convex and Toric Geometry to Analyze Complex Dynamics in Chemical Reaction Systems. Ph.D. thesis, Otto-von-Guericke University Magdeburg, Magdeburg (2005)Google Scholar
  16. 16.
    Sensse, A., Eiswirth, M.: Feedback Loops for Chaos in Activator-inhibitor Systems. Jour. Chem. Phys. 122, 044516–044516-9 (2005)Google Scholar
  17. 17.
    Sensse, A., Hauser, M.J.B., Eiswirth, M.: Feedback Loops for Shilnikov Chaos: The Peroxidase-oxidase Reaction, Jour. Chem. Phys. 125, 014901–014901-12 (2006)Google Scholar
  18. 18.
    Strogatz, S.H.: Nonlinear Dynamics and Chaos. Westview Press, Cambridge (2000)Google Scholar
  19. 19.
    Paun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)CrossRefzbMATHGoogle Scholar
  20. 20.
    Bernardini, F., Manca, V.: Dynamical aspects of P systems. Biosystems 70, 85–93 (2003)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Stephan Peter
    • 1
  • Tomas Veloz
    • 2
  • Peter Dittrich
    • 1
  1. 1.Department for Mathematics and Computer Sciences, Bio Systems Analysis GroupFriedrich Schiller University of JenaJenaGermany
  2. 2.Departamento de Ciencias de la ComputacionUniversity of ChileSantiagoChile

Personalised recommendations