Bulletin of Mathematical Biology

, Volume 69, Issue 4, pp 1199–1231 | Cite as

Chemical Organisation Theory

Original Article

Abstract

Complex dynamical reaction networks consisting of many components that interact and produce each other are difficult to understand, especially, when new component types may appear and present component types may vanish completely. Inspired by Fontana and Buss (Bull. Math. Biol., 56, 1–64) we outline a theory to deal with such systems. The theory consists of two parts. The first part introduces the concept of a chemical organisation as a closed and self-maintaining set of components. This concept allows to map a complex (reaction) network to the set of organisations, providing a new view on the system’s structure. The second part connects dynamics with the set of organisations, which allows to map a movement of the system in state space to a movement in the set of organisations. The relevancy of our theory is underlined by a theorem that says that given a differential equation describing the chemical dynamics of the network, then every stationary state is an instance of an organisation. For demonstration, the theory is applied to a small model of HIV-immune system interaction by Wodarz and Nowak (Proc. Natl. Acad. USA, 96, 14464–14469) and to a large model of the sugar metabolism of E. Coli by Puchalka and Kierzek (Biophys. J., 86, 1357–1372). In both cases organisations where uncovered, which could be related to functions.

Keywords

Reaction networks Constraint based network analysis Hierarchical decomposition Constructive dynamical systems 

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References

  1. Adleman, L.M., 1994. Molecular computation of solutions to combinatorial problems. Science 266(5187), 1021–1024.Google Scholar
  2. Banâtre, J.-P., Métayer, D.L., 1990. The GAMMA model and its discipline of programming. Sci. Comput. Program. 15(1), 55–77.MATHCrossRefGoogle Scholar
  3. Banzhaf, W., 1993. Self-replicating sequences of binary numbers – foundations I and II: General and strings of length n = 4. Biol. Cybern. 69, 269–281.MATHCrossRefGoogle Scholar
  4. et al., 1996]ped:BDR1996nanotech Banzhaf, W., Dittrich, P., and Rauhe, H., 1996. Emergent computation by catalytic reactions. Nanotechnology 7(1):307–314.CrossRefGoogle Scholar
  5. Benkö, G., Flamm, C., Stadler, P. F., 2002. A graph-based toy model of chemistry. J. Chem. Inf. Comput. Sci. 43(4), 1085–1093.CrossRefGoogle Scholar
  6. Borisov, N., Markevich, N., J.B., H., and B.N., K., 2005. Signaling through receptors and scaffolds: independent interactions reduce combinatorial complexity. Biophys. J. 89(2), 951–966.CrossRefGoogle Scholar
  7. Dittrich, P., Kron, T., Banzhaf, W., 2003. On the formation of social order – modeling the problem of double and multi contingency following luhmann. J. Artif. Soc. Soc. Simul. 6(1).Google Scholar
  8. Ebenhöh, O., Handorf, T., Heinrich, R., 2004. Structural analysis of expanding metabolic network. Genome Inform. 15(1), 35–45.Google Scholar
  9. Eigen, M., 1971. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 58(10), 465–523.CrossRefGoogle Scholar
  10. Eigen, M., Schuster, P., 1977. The hypercycle: a principle of natural self-organisation, part A. Naturwissenschaften 64(11), 541–565.CrossRefGoogle Scholar
  11. Érdi, P., Tóth, J., 1989. Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models. Pinceton University Press, Princeton, NJ.Google Scholar
  12. Espinosa-Soto, C., Padilla-Longoria, P., Alvarez-Buylla, E.R., 2004. A gene regulatory network model for cell-fate determination during Arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles. Plant Cell 16(11), 2923–2939.CrossRefGoogle Scholar
  13. Feinberg, M., Horn, F.J.M., 1973. Dynamics of open chemical systems and the algebraic structure of the underlying reaction network. Chem. Eng. Sci. 29(3), 775–787.Google Scholar
  14. Fontana, W., 1992. Algorithmic chemistry. In: Langton, C.G., Taylor, C., Farmer, J.D., Rasmussen, S. (Eds.), Artificial Life II, Addison-Wesley, Redwood City, CA, pp. 159–210.Google Scholar
  15. Fontana, W., and Buss, L.W., 1994. ‘The arrival of the fittest’: Toward a theory of biological organization. Bull. Math. Biol. 56(1), 1–64.MATHGoogle Scholar
  16. Gothelf, K.V., Brown, R.S., 2005. A modular approach to DNA-programmed self-assembly of macromolecular nanostructures. Chemistry 11(4), 1062–1069.CrossRefGoogle Scholar
  17. Heij, C., Ran, A.C., Schagen, F.v., 2006. Introduction to Mathematical Systems Theory Linear Systems, Identification and Control. Birkhäuser.Google Scholar
  18. Heinrich, R., Schuster, S., 1996. The Regulation of Cellular Systems. Chapman and Hall, New York, NY.Google Scholar
  19. Jain, S., Krishna, S., 2001. A model for the emergence of cooperation, interdependence, and structure in evolving networks. Proc. Natl. Acad. Sci. U. S. A. 98(2), 543–547.CrossRefGoogle Scholar
  20. Kauffman, S.A., 1971. Cellular homeostasis, epigenesis and replication in randomly aggregated macromolecular systems. J. Cybernetics 1, 71–96.Google Scholar
  21. Luhmann, N., 1984. Soziale Systeme. Suhrkamp, Frankfurt a.M.Google Scholar
  22. Matsumaru, N., Centler, F., and Klaus-Peter Zauner, P.D., 2004. Self-adaptive scouting - autonomous experimentation for systems biology. In: Raidl, G.R., Cagnoni, S., Branke, J., Corne, D., Drechsler, R., Jin, Y., Johnson, C.G., Machado, P., Marchiori, E., Rothlauf, F., Smith, G.D., Squillero, G. (Eds.), Applications of Evolutionary Computing, EvoWorkshops 2004, vol. 3005 of LNAI. Springer, Berlin, pp. 52–62.Google Scholar
  23. Murray, J.D., 2004. Mathematical Biology I. An Introduction, vol. 17 of Interdisciplinary Applied Mathematics. Springer, 3rd, 2nd printing edition.Google Scholar
  24. Papin, J.A., Stelling, J., Price, N.D., Klamt, S., Schuster, S., Palsson, B.O., 2004. Comparison of network-based pathway analysis methods. Trends Biotechnol. 22(8), 400–405.CrossRefGoogle Scholar
  25. Petri, C.A., 1962. Kommunikation mit automaten. Ph.D. thesis, University of Bonn, Bonn.Google Scholar
  26. Pinkas-Kramarski, R., Alroy, I., Yarden, Y., 1997. Erbb receptors and egf-like ligands: cell lineage determination and oncogenesis through combinatorial signaling. J. Mammary. Gland. Biol. Neoplasia 2(2), 97–107.CrossRefGoogle Scholar
  27. Puchalka, J., Kierzek, A., 2004. Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys. J. 86(3), 1357–1372.CrossRefGoogle Scholar
  28. Rössler, O.E., 1971. A system theoretic model for biogenesis (in German). Z. Naturforsch. B 26(8), 741–746.Google Scholar
  29. Schuster, P., Sigmund, K., 1983. Replicator dynamics. J. Theor. Biol. 100, 533–538.CrossRefMathSciNetGoogle Scholar
  30. Segré, D., Lancet, D., Kedem, O., Pilpel, Y., 1998. Graded autocatalysis replication domain (GARD): Kinetic analysis of self-replication in mutually catalytic sets. Orig. Life Evol. Biosph. 28(4–6), 501–514.CrossRefGoogle Scholar
  31. Wikipedia, 2004. Lattice (order). Wikipedia, http://en.wikipedia.org/wiki/Lattice_%28order%29, modified: 15 Nov 2004, visited: 16 Nov 2004.Google Scholar
  32. Wodarz, D., Nowak, M.A., 1999. Specific therapy regimes could lead to long-term immunological control of hiv. Proc. Nat. Acad. Sci. USA 96(25), 14464–14469.CrossRefGoogle Scholar
  33. Yung, Y.L., DeMore, W.B., 1999. Photochemistry of Planetary Athmospheres. Oxford University Press, New York.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Bio Systems Analysis Group, Jena Centre for Bioinformatics and Department of Mathematics and Computer ScienceFriedrich Schiller University JenaJenaGermany

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