Skip to main content
Log in

Chemical Organisation Theory

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Adleman, L.M., 1994. Molecular computation of solutions to combinatorial problems. Science 266(5187), 1021–1024.

    Google Scholar 

  • Banâtre, J.-P., Métayer, D.L., 1990. The GAMMA model and its discipline of programming. Sci. Comput. Program. 15(1), 55–77.

    Article  MATH  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • et al., 1996]ped:BDR1996nanotech Banzhaf, W., Dittrich, P., and Rauhe, H., 1996. Emergent computation by catalytic reactions. Nanotechnology 7(1):307–314.

    Article  Google Scholar 

  • Benkö, G., Flamm, C., Stadler, P. F., 2002. A graph-based toy model of chemistry. J. Chem. Inf. Comput. Sci. 43(4), 1085–1093.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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).

  • Ebenhöh, O., Handorf, T., Heinrich, R., 2004. Structural analysis of expanding metabolic network. Genome Inform. 15(1), 35–45.

    Google Scholar 

  • Eigen, M., 1971. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften 58(10), 465–523.

    Article  Google Scholar 

  • Eigen, M., Schuster, P., 1977. The hypercycle: a principle of natural self-organisation, part A. Naturwissenschaften 64(11), 541–565.

    Article  Google Scholar 

  • Érdi, P., Tóth, J., 1989. Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models. Pinceton University Press, Princeton, NJ.

  • 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.

    Article  Google Scholar 

  • 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 

  • 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.

  • 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.

    MATH  Google Scholar 

  • Gothelf, K.V., Brown, R.S., 2005. A modular approach to DNA-programmed self-assembly of macromolecular nanostructures. Chemistry 11(4), 1062–1069.

    Article  Google Scholar 

  • Heij, C., Ran, A.C., Schagen, F.v., 2006. Introduction to Mathematical Systems Theory Linear Systems, Identification and Control. Birkhäuser.

  • Heinrich, R., Schuster, S., 1996. The Regulation of Cellular Systems. Chapman and Hall, New York, NY.

  • 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.

    Article  Google Scholar 

  • Kauffman, S.A., 1971. Cellular homeostasis, epigenesis and replication in randomly aggregated macromolecular systems. J. Cybernetics 1, 71–96.

    Google Scholar 

  • Luhmann, N., 1984. Soziale Systeme. Suhrkamp, Frankfurt a.M.

  • 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.

  • Murray, J.D., 2004. Mathematical Biology I. An Introduction, vol. 17 of Interdisciplinary Applied Mathematics. Springer, 3rd, 2nd printing edition.

  • 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.

    Article  Google Scholar 

  • Petri, C.A., 1962. Kommunikation mit automaten. Ph.D. thesis, University of Bonn, Bonn.

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Rössler, O.E., 1971. A system theoretic model for biogenesis (in German). Z. Naturforsch. B 26(8), 741–746.

    Google Scholar 

  • Schuster, P., Sigmund, K., 1983. Replicator dynamics. J. Theor. Biol. 100, 533–538.

    Article  MathSciNet  Google Scholar 

  • 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.

    Article  Google Scholar 

  • Wikipedia, 2004. Lattice (order). Wikipedia, http://en.wikipedia.org/wiki/Lattice_%28order%29, modified: 15 Nov 2004, visited: 16 Nov 2004.

  • 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.

    Article  Google Scholar 

  • Yung, Y.L., DeMore, W.B., 1999. Photochemistry of Planetary Athmospheres. Oxford University Press, New York.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Peter Dittrich.

Additional information

Both authors contributed equally.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dittrich, P., di Fenizio, P.S. Chemical Organisation Theory. Bull. Math. Biol. 69, 1199–1231 (2007). https://doi.org/10.1007/s11538-006-9130-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-006-9130-8

Keywords

Navigation