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Order From Disorder

David Ruelle1 has written, –Scientists know how hard it is to understand simple phenomena like the boiling and freezing of water, and they are not too astonished to find that many questions related to the … functioning of the brain … are for the time being beyond our understanding.” Wouldn't it be an amazing example of serendipity if the two questions were, at root, the same questions? If the conformational transition of a voltage-sensitive ion channel were really a kind of phase transition? Such ideas were already proposed by Ichiji Tasaki for the excitable membrane in the 1960s.2

We have seen that the concept of a mechanical gate opening to admit ions into a preformed pore is not only inadequate but also inappropriate to the molecular scale of a voltage-sensitive ion channel. An effort to provide a viable alternative will require a more sophisticated approach, based on contemporary physical concepts. This chapter is intended to review some of the background needed for such an approach.s

Keywords

Fractal Dimension Critical Temperature Magnetic Dipole Critical Exponent Dissipative Structure 
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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Notes And References

  1. 1.
    David Ruelle, Chance and Chaos, Princeton University, 1991, 153.Google Scholar
  2. 2.
    Ichiji Tasaki, J. Gen. Physiol.46:755–772, 1963; —, Ferroel. 220:305–316, 1999.CrossRefGoogle Scholar
  3. 3.
    Nigel Goldenfeld, Lectures on Phase Transitions and the Renormalization Group, Addison-Wesley, Reading, MA, 1992.Google Scholar
  4. 4.
    Per Bak, How Nature Works: The Science of Organized Criticality, Springer, New York, 1996.MATHGoogle Scholar
  5. 5.
    Talbot H. Waterman, inTheoretical and Mathematical Biology, edited by Talbot H. Waterman and Harold J. Morowitz, Blaisdell, New York, 1965, 13.Google Scholar
  6. 6.
    Jack A. Tuszynski and Michal Kurzynski, Introduction to Molecular Biophysics, CRC Press, Boca Raton, 2003, 403–407.Google Scholar
  7. 7.
    Goldenfeld, 5–19.Google Scholar
  8. 8.
    Goldenfeld, 229–384.Google Scholar
  9. 9.
    Larry S. Liebovitch, Fractals and Chaos Simplified for the Life Sciences, Oxford University, 1998, 3–15.Google Scholar
  10. 10.
    Liebovitch, 24f.Google Scholar
  11. 11.
    Bak, 20, 6.Google Scholar
  12. 12.
    Liebovitch, 58f.Google Scholar
  13. 13.
    A. M. Churilla, W. A. Gottschalke, L. S. Liebovitch, L. Y. Selector, A. T. Todorov and S. Yeandle, Ann. Biomed. Engr.24:99–108, 1996.CrossRefGoogle Scholar
  14. 14.
  15. 15.
  16. 16.
    B. Sapoval, M. Rosso and J. F. Gouyet, in Amulya L. Laskar and Suresh Chandra, Superionic Solids and Solid Electrolytes: Recent Trends, Academic, Boston, 1989, 473–514.Google Scholar
  17. 17.
    Reprinted from Sapovalet al., 503, Copyright 1989, with permission from Elsevier; J. A. Bruce and M. D. IngramSolid State Ionics9&10:717–723, Copyright 1983, with permission from Elsevier; G. V. Chandrashekhar and L. M. Foster, Solid State Comm.27:269–273, Copyright 1987, with permission from Elsevier.Google Scholar
  18. 18.
    Giorgio Careri, Order and Disorder in Matter, Benjamin/Cummings, 1984.Google Scholar
  19. 19.
    Robert J. Finkelstein, Thermodynamics and Statistical Physics: A Short Introduction, W. H. Freeman, San Francisco, 1969, 148.Google Scholar
  20. 20.
    Figures 15.4 and 15.5 are from Careri, p. 5; 15.6, p. 8, and 15.7, p. 17.Google Scholar
  21. 21.
    I. Prigogine and G. Nicolis, inFrom Theoretical Physics to Biology, edited by M. Marois, Karger, Basel, 1973, 89–109.Google Scholar
  22. 22.
    See, e.g., J. A. Scott Kelso, Dynamic Patterns: The Self-Organization of Brain and Behavior, MIT Press, Cambridge, Mass., 1995, 6–8.Google Scholar
  23. 23.
    Careri, 104.Google Scholar
  24. 24.
    M.-W. Ho, The Rainbow and the Worm: The Physics of Organisms, 2nd edition, World Scientific, Singapore, 1998, 37–60.Google Scholar
  25. 25.
    Lev M. Blinov, Electro-Optical and Magneto-Optical Properties of Liquid Crystals, John Wiley, Chichester 1983, 205.Google Scholar
  26. 26.
    S. A. Pikin, Structural Transformations in Liquid Crystals, Gordon and Breach, 1991, 267–283.Google Scholar
  27. 27.
    Minoru Fujimoto, The Physics of Structural Phase Transitions, Springer, New York, 1997, 28. With kind permission of Springer Science and Business Media.Google Scholar
  28. 28.
    S. K. Ma, Modern Theory of Critical Phenomena, W. A. Benjamin, Inc., 1976, 4.Google Scholar
  29. 29.
    Goldenfeld, 124–127.Google Scholar
  30. 30.
    Goldenfeld, 229–282.Google Scholar
  31. 31.
    Finkelstein, 188.Google Scholar
  32. 32.
    Goldenfeld, 212.Google Scholar
  33. 33.
    Careri, 86.Google Scholar
  34. 34.
    Goldenfeld, 348f.Google Scholar
  35. 35.
    Ilya Prigogine, Gregoire Nicolis and Agnes Babloyantz, Physics Today25 (11):23–28, Nov.1972; 25 (12):38–44, Dec. 1972.CrossRefGoogle Scholar
  36. 36.
    P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations, Wiley-Interscience, London, 1971.MATHGoogle Scholar
  37. 37.
    H. Haken, inCooperative Phenomena, edited by H. Haken and M. Wagner, Springer-Verlag, New York, 1973, 363–372.Google Scholar
  38. 38.
    R. Blumenthal, J. P. Changeux and R. Lefever, J. Membrane Biol.2:351–374, 1970;Compt. Rend.270:389–392, 1970.CrossRefGoogle Scholar
  39. 39.
    Glansdorff and Prigogine, 272–286.Google Scholar

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