Diffusion-reaction approach applied to the ionic wave propagation through biomembrane channels

• Autorzy: Gadomski A.
• Języki publikacji: EN

Abstrakty

EN

A one-dimensional diffusion-reaction equation for the probability of finding of a random walker (ion) in a space-time domain (protein channel) is proposed to model the process of ionic wave propagation through membranes. The diffusion process stands here for a kind of kinetic hindrance or perturbation because it is assumed to be very slow. The chemical reaction, in turn, proceeds in an usual way rather, but is presumed to be considered in the fractal-like chemical reaction kinetics regime. The damped pendulum theory is effectively applied to get the solution to the problem studied. This solution has been found to reflect the Kohlrausch-Williams-Watts behaviour characteristic of the slow relaxation kinetics, e g. in spin glasses or fragile liquids. As a quite specific result, the Weibull function stated in the work of L.S. Liebovitch and J.M. Sullivan, Biophys.J. 52 (1987) 979- 988, and describing the channel kinetics in cultured mouse hippocampal neurons has been gained.

Słowa kluczowe

EN

damped pendulum; mouse; hippocampal neuron; mice; ionic wave; diffusion process; propagation; biomembrane channel

• Wydawca: -
• Czasopismo: Cellular and Molecular Biology Letters
• Rocznik: 1996
• Tom: 01
• Numer: 3
• Opis fizyczny: p.273-289,fig.

Twórcy

autor

Gadomski A.

• Technical University for Technology and Agriculture, Kaliskiego-Street 7, Building 2.7, 85-796 Bydgoszcz, Poland

Bibliografia

• 1. Hille, B. Ionic Channels of Excitable Membranes, Sinauer Inc., Sunderland, MA, 1992.
• 2. Starzak, M E. The Physical Chemistry of Membranes, Academic Press, Orlando, 1984, Chap. 12.
• 3. Hodgkin, A.L. and Huxley, A.F. J. Physiol. (London) 116 (1952) 449-472.
• 4. Hodgkin, A.L. and Huxley, A.F. J. Physiol. (London) 116 (1952) 473-496; 497- 506.
• 5. De Felice, L.J. Introduction to Membrane Noise, Plenum Press, New York, 1981; Verveen, A.A. and De Felice, L.J. Prog. Biophys. Mol. Biol. 28 (1974) 189-265.
• 6. Liebovitch, L.S. and Sullivan, J.M. Biophys. J. 52 (1987) 979-988.
• 7. Dewey, T.G. and Datta, M.M. Biophys. J. 56 (1989) 415-420.
• 8. Mandelbrot, B.B. The Fractal Geometry of Nature, Freeman, San Francisco, 1982.
• 9. Kopelman, R. Science 241 (1988) 1620-1626; Prasad, J. and Kopelman, R. Phys. Rev. Lett. 59 (1987) 2103-2105.
• 10. Bassingthwaighte J.B., Liebovitch, L.S. and West, B.J. Fractal Physiology, Oxford University Press, New York, 1995.
• 11. Berg, H.C. Random Walks in Biology, Princeton University Press, Princeton, New Jersey, 1993.
• 12. Grzywna, Z. J. and Siwy, Z. Int. J. Bifurcation and Chaos, accepted; Grzywna, Z.J. Chem. Engng Sci., in press.
• 13. Liebovitch, L.S. and Toth, T.I. J. Theor. Biol. 148 (1991) 243-267.
• 14. Nicolis, G. and Prigogine, I. Self-Organization in Nonequilibrium Systems, Wiley, New York, 1977.
• 15. Fricke, T. and Wendt, D. Inter. J. Mod. Phys. 6 (1995) 277-306.
• 16. Liebovitch, L.S., Fischbarg, J., Koniarek, J.P., Todorova, I. and Wang, M. Biochim. Biophys. Acta 896 (1987) 173-180.
• 17. Shlesinger, M.F. Ann. Rev. Phys. Chem. 39 (1988) 269-290; Clay, JR and Shlesinger, M.F. Biophys.J. 37 (1982) 677-680.
• 18. Schimansky-Geier, L. in: Far-From-Equilibrium Dynamics of Chemical Systems, (Popielawski, J. and Górecki, J., Eds.), World Scientific, Singapore, 1991, 226-256.
• 19. Leja, F. Differential and Integral Calculus, PWN (Polish Edition), Warsaw, 1975, 487-489; Kittel, C., Knight, W.D. and Ruderman, M.A. Mechanics. Berkeley Physics Course - Volume 1, Mc Graw-Hill Book Company, New Berkeley Physics Course - Volume 1, Mc Graw-Hill Book Company, New York, 1965, Chap. 7.
• 20. Havlin, Sh. in: Fractal Approach to Heterogeneous Chemistry, (Avnir, D., Ed ), Wiley, Chichester, West Sussex, 1989, 249-269; Havlin, S., Araujo, M., Lereah, J., Larralde, H., Shehter, A., Stanley, HE., Trunfio, P. and Vilensky, B. Phvsica A 221 (1995) 1-14.
• 21. Gadomski, A. Philos. Mag. Lett. 70 (1994) 335-343; Ber. Bunsengesell. Chem.Phys. 100 (1996) 134-137; Chem. Phys. Lett., in press.
• 22. Angell, C.A. , Poole, P.H. and Shao, J. Nuovo Cim. D 16 (1994) 993-1025.
• 23. Gadomski, A., Kriechbaum, M., Laggner, P. and Łuczka, J. Phys. Lett. A 203 (1995) 367-372.
• 24. Hille, B. Progr. Biophys. Mol. Biol. 21 (1970) 1-32; Läuger P. Biophys. Biochem. Acta 413 (1975) 1-10.
• 25. Voss, R.F. Physica D 38 (1989) 362-371.
• 26. Fuliński, A. Phys. Lett. A 193 (1994) 267-273.
• 27. Liebovitch, L.S., Polish-British Workshop „Fractals, Nonlinear Dynamics and Chaos in Biophysics”, Zakopane, May 6-10, 1996; key note lecture on „Using Fractals and Chaos to Understand the Physical Properties of Ion Channels”.
• 28. Privman, V. and Grynberg, M. D. J. Phys. A: Math. Gen 25 (1992) 6567- 6575; Nielaba, P. and Privman, V. Mod. Phys. Lett. B 6 (1992) 533-539.
• 29. Fife, P. C. Mathematical Aspects of Reacting and Diffusing Systems, Springer-Verlag, Berlin, 1979; Malchow, H. and Schimansky-Geier, L. Noise and Diffusion in Bistable Nonequilibrium Systems, Teubner, Berlin, 1985, Chap.2.2.3.
• 30. Kumpf, R.A. and Dougherty, D A. Science 261 (1993) 1708-1710; Teisseyre, A., private communication.
• 31. Sansom, M. S. P., Ball, F.G., Kerry, J. , Mc Gee, R, Ramsey, R.L. and Usherwood P.N.L. Biophys.J. 56 (1989) 1229-1243; Mc Manus, OB, Weiss, D. C., Spivak, C.E., Blatz, A. L. and Magleby, K. L. Biophys.J. 54 (1988) 859-870.
• 32. Chvosta, P. , Aslangul, C., Pottier, N. and Saint-James, D. Physica A 184 (1992) 143-168; Aslangul, C. Physica A, to appear.
• 33. Amitrano, C., Bunde, A. and Stanley, H. E. J. Phys. A: Math. Gen 18 (1985) L923- L929.