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The consequences of imperfect mixing in autocatalytic chemical and biological systems

Abstract

When chemical reactions whose rate increases with the concentration of a product species are carried out in imperfectly mixed systems, a variety of complex behaviours can occur. These phenomena, which have relevance for biological processes as well, include chaotic and stochastic behaviour and selection of one final state over an equally probable alternative.

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References

  1. May, R. M. Nature 261, 459–467 (1976).

    Article  ADS  CAS  Google Scholar 

  2. Jahnke, W. & Winfree, A. T. J. chem. Educ. 68, 320–324 (1991).

    Article  CAS  Google Scholar 

  3. Devreotes, P., Fontana, D., Klein, P., Sherring J. & Theibert A. Meth. Cell. Biol. 28, 299–331 (1987).

    Article  CAS  Google Scholar 

  4. Lechleiter, J., Girard, S. E., Peralta, E. G. & Clapham, D. Science 252, 123–126 (1991).

    Article  ADS  CAS  Google Scholar 

  5. Turing, A. M. Phil. Trans. R. Soc. B237, 37–72 (1952).

    Article  Google Scholar 

  6. Castets, V., Dulos, E., Boissonade, J. & De Kepper, P. Phys. Rev. Lett. 64, 2953–2956 (1990).

    Article  ADS  CAS  Google Scholar 

  7. Malthus, T. R. An Essay on the Principle of Population 14 (Oxford Univ. Press, London, 1798).

    Google Scholar 

  8. Epstein, I. R. J. chem. Educ. 66, 191–195 (1989).

    Article  CAS  Google Scholar 

  9. Villermaux, J. Rev. chem. Engng. 7, 51–108 (1991).

    CAS  Google Scholar 

  10. Roux, J. C., De Kepper, P. & Boissonade, J. J. Phys. 97A, L168–L170 (1983).

    Google Scholar 

  11. De Kepper, P., Boissonade, J. & Epstein, I. R. J. phys. Chem. 94, 6525–6536 (1990).

    Article  CAS  Google Scholar 

  12. Luo, Y. & Epstein, I. R. J. chem. Phys. 85, 5733–5740 (1986).

    Article  ADS  CAS  Google Scholar 

  13. Kumpinsky, E. & Epstein, I. R. J. chem. Phys. 82, 53–57 (1985).

    Article  ADS  CAS  Google Scholar 

  14. Menzinger, M. & Dutt, A. K. J. phys. Chem. 94, 4510–4514 (1990).

    Article  CAS  Google Scholar 

  15. Schmitz, R. A., Graziani, K. R. & Hudson, J. L. J. chem. Phys. 67, 3040–3044 (1977).

    Article  ADS  CAS  Google Scholar 

  16. Roux, J. C., Rossi, A., Bachelart, S. & Vidal, C. Phys. Lett. A77, 391–393 (1980).

    Article  MathSciNet  Google Scholar 

  17. Roux, J. C., Simoyi, R. H. & Swinney, H. L. Physica D8, 257–266 (1983).

    MathSciNet  Google Scholar 

  18. Györgyi, L. & Field, R. J. J. chem. Phys. 91, 6131–6141 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  19. Field, R. J. & Noyes, R. M. J. chem. Phys. 60, 1877 (1974).

    Article  ADS  CAS  Google Scholar 

  20. Györgyi, L. & Field, R. J. J. phys. Chem. 95, 6594–6602 (1991).

    Article  Google Scholar 

  21. Györgyi, L. & Field, R. J. Nature 355, 808–810 (1992).

    Article  ADS  Google Scholar 

  22. Maselko, J. & Epstein, I. R. J. chem. Phys. 80, 3175–3178 (1984).

    Article  ADS  CAS  Google Scholar 

  23. Alamgir, M. & Epstein, I. R. Int. J. chem. Kinet 17, 429–439 (1985).

    Article  CAS  Google Scholar 

  24. Olsen, L. F. & Degn, H. Nature 267, 177–178 (1977).

    Article  ADS  CAS  Google Scholar 

  25. Aguda, B. D. & Larter, R. J. Am. chem. Soc. 113, 7913–7916 (1991).

    Article  CAS  Google Scholar 

  26. Kondepudi, D. K., Kaufman, R. J. & Singh, N. Science 250, 975–976 (1990).

    Article  ADS  CAS  Google Scholar 

  27. Kondepudi, D. K. & Sabanayagam, C. Chem. Phys. Lett. 217, 364–368 (1994).

    Article  ADS  CAS  Google Scholar 

  28. Metcalfe, G. & Ottino, J. M. Phys. Rev. Lett. 72, 2875–2878 (1994).

    Article  ADS  CAS  Google Scholar 

  29. Swanson, P. D. & Ottino, J. M. J. Fluid Mech. 213, 227–249 (1990).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  30. Nagypál, I. & Epstein, I. R. J. phys. Chem. 90, 6285–6292 (1986).

    Article  Google Scholar 

  31. Nagypál, I. & Epstein, I. R. J. chem. Phys. 89, 6925–6928 (1988).

    Article  ADS  Google Scholar 

  32. Ferrone, F. A., Hofrichter, J. & Eaton, W. A. J. molec. Biol. 183, 591–610, 611–631 (1985).

    Article  CAS  Google Scholar 

  33. Hofrichter, J. J. molec. Biol. 189, 533–571 (1986).

    Article  Google Scholar 

  34. Lemarchand, A., Ben Aim, R. I. & Nicolis, G. Chem. Phys. Lett. 162, 92–98 (1989).

    Article  ADS  CAS  Google Scholar 

  35. Szabo, A. J. molec. Biol. 199, 539–542 (1988).

    Article  CAS  Google Scholar 

  36. Sagués, F., Ramirez-Piscina, L. & Sancho, J. M. J. chem. Phys. 92, 4786–4792 (1990).

    Article  ADS  Google Scholar 

  37. Eigen, M. & Schuster, P. The Hypercycle. A Principle of Natural Self-Organization (Springer, Berlin, 1979).

    Google Scholar 

  38. Kareiva, P. & Wennergren, U. Nature (in the press).

Download references

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Epstein, I. The consequences of imperfect mixing in autocatalytic chemical and biological systems. Nature 374, 321–327 (1995). https://doi.org/10.1038/374321a0

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