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Chemical Organizations at Different Spatial Scales

  • Pietro Speroni di Fenizio
  • Peter Dittrich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4648)

Abstract

The dynamics of spatial reaction systems that consists of many molecular species can be difficult to understand. Here we introduce a method that allows to observe the dynamics of a diverse spatial reaction system at different spatial scales. Using chemical organization theory we define for a given spatial location its so called spatial organization, which is the organization generated by the molecular species present in the neighborhood of this location. The scale determines the size of that neighborhood. We show that at one scale, patterns become visible that can not be seen at a different scale. Furthermore, different scales tend to map to different parts of the lattice of organizations; at small scales spatial organizations tend to be small (lower part of the lattice of organizations) while at large scales spatial organizations tend to be large (upper part of the lattice of organizations). Finally we show how the right scale can be selected by comparing the spatial reactor with its well-stirred counterpart. The method is illustrated using an artificial chemistry.

Keywords

Spatial Scale Molecular Species Actual Experiment Spatial Organization Reaction Network 
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.

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References

  1. 1.
    Lehmann, R.: Determination of dominant pathways in chemical reaction systems: An algorithm and its application to stratospheric chemistry. J. Atmos. Chem. 41, 297–314 (2002)CrossRefGoogle Scholar
  2. 2.
    Puchalka, J., Kierzek, A.: Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys. J. 86(3), 1357–1372 (2004)CrossRefGoogle Scholar
  3. 3.
    Moreac, G., Blurock, E., Mauss, F.: Automatic generation of a detailed mechanism for the oxidation of n-decane. Combust. Sci. Technol. 178(10-11), 2025–2038 (2006)CrossRefGoogle Scholar
  4. 4.
    Dittrich, P., Speroni di Fenizio, P.: Chemical organization theory. Bull. Math. Biol. 69(4), 1199–1231 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Banzhaf, W.: Self-replicating sequences of binary numbers. Comput. Math. Appl. 26, 1–8 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Speroni di Fenizio, P., Dittrich, P., Ziegler, J., Banzhaf, W.: Towards a theory of organizations. In: German Workshop on Artificial Life (GWAL 2000), Bayreuth, 5.-7. April, 2000 (in print)Google Scholar
  7. 7.
    Eigen, M., Schuster, P.: The hypercycle: a principle of natural self-organisation, part A. Naturwissenschaften 64(11), 541–565 (1977)CrossRefGoogle Scholar
  8. 8.
    Schuster, P., Sigmund, K.: Replicator dynamics. J. Theor. Biol. 100, 533–538 (1983)CrossRefMathSciNetGoogle Scholar
  9. 9.
    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
  10. 10.
    Fontana, W.: Algorithmic chemistry. In: Langton, C.G., Taylor, C., Farmer, J.D., Rasmussen, S. (eds.) Proc. Artificial Life II, Redwood City, CA, pp. 159–210. Addison-Wesley, Reading (1992)Google Scholar
  11. 11.
    Lindgren, K., Eriksson, A., Eriksson, K.E.: Flows of information in spatially extended chemical dynamics. In: Pollack, J., Bedau, M., Husbands, P., Ikegami, T., Watson, R.A. (eds.) Proc. Artififical Life IX, pp. 456–460. MIT Press, Boston (2004)Google Scholar
  12. 12.
    Centler, F., Dittrich, P.: Chemical organizations in atmospheric photochemistries: a new method to analyze chemical reaction networks. Planet. Space Sci. 55(4), 413–428 (2007)CrossRefGoogle Scholar
  13. 13.
    Matsumaru, N., Centler, F., Speroni di Fenizio, P., Dittrich, P.: Chemical organization theory applied to virus dynamics. it - Information Technology 48(3), 154–160 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Pietro Speroni di Fenizio
    • 1
    • 2
  • Peter Dittrich
    • 2
  1. 1.ProtoLife, Parco Vega Via della Liberta’ 12, 30175, Marghera, VeneziaItalia
  2. 2.Bio Systems Analysis Group, Department of Mathematics and Computer Science, Friedrich Schiller University Jena, D-07743 JenaGermany

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