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Model of multifractal gating of single ionic channels in biological membranes

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Biochemistry (Moscow) Supplement Series A: Membrane and Cell Biology Aims and scope

Abstract

A physico-mathematical model of the gating machinery of single ionic channels in biological membranes has been developed. In the paradigm of this model, gating particles are subjected to: (i) deterministic friction force responsible for interactions of gating particles with the surrounding solution; (ii) deterministic potential force depending on the structure and conformational state of the channel pore (the latter is controlled by the transmembrane voltage V and regulates the motion of particles overcoming potential barriers on going from the closed (open) to the open (closed) state of the channel); (iii) deterministic force responsible for interactions of water molecules with hydrophobic sites in the channel pore, and, finally, (iv) stochastic thermal fluctuation force. The model affords adequate approximation of experimental data.

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References

  1. Kazachenko, V.N. and Kochetkov, K.V., Maxi-Ca2+-Activated K+ Channels: Structure and Gating Machinery, Biologicheskie Membrany (Rus.), 2003, vol. 20, pp. 99–120.

    CAS  Google Scholar 

  2. Liebovitch, L.S., Fischbarg, J., and Koniarek, J., Ion Channel Kinetics: A Model Based on Fractal Scaling Rather than Multistate Markov Process, Math. Biosci., 1987, vol. 84, pp. 37–68.

    Article  Google Scholar 

  3. Liebovitch, L.S. and Lullivan, J.M., Fractal Analysis of a Voltage-Dependent Potassium Channel from Cultured Mouse Hippocampal Neurons, Biophys. J., 1987, vol. 52, pp. 979–988.

    PubMed  CAS  Google Scholar 

  4. Liebovitch, L.S. and Krekora, P., The Physical Basis of Ion Channel Kinetics: The Impotance of Dynamics, Proc. Inst. Math. And Its Appl. Univer. Minnessota, 2002, vol. 129, pp. 27–52.

    CAS  Google Scholar 

  5. Mcmanus, O.B., Blatz, A.L., and Magleby, K.L., Inverse Relationship of the Durations of Adjacent Open and Shut Intervals for Cl− and K+ Channels, Nature (Lond.), 1985, vol. 317, pp. 625–627.

    Article  CAS  Google Scholar 

  6. Varanda, W.A., Liebovitch, L.S., Figueiroa, J.N., and Nogueira, R.A., Hurst Analysis Applied to the study of Single Calcium-Activated Potassium Channel Kinetics, J. Theor. Biol., 2000, vol. 206, pp. 343–353.

    Article  PubMed  CAS  Google Scholar 

  7. Nogueira, R.A., Varanda, W.A., and Liebovitch, L.S., Hurst Analysis in the Study of Ion Current Kinetics, Brasilian J. Med. Biol., 1995, vol. 28, pp. 491–496.

    CAS  Google Scholar 

  8. Kochetkov, K.V., Kazachenko, V.N., Aslanidi, O.V., Chemeris, N.K., and Gapeev, A.B., Non-Markovian Gating of Ca2+-Activated K+-Channels Kidney Cells Vero. Rescaled Range Analysis, J. Biol. Phys., 1999, vol. 25, pp. 211–222.

    Article  CAS  Google Scholar 

  9. Kochetkov, K.V., Kazachenko, V.N., and Aslanidi, O.V., Time Course of Reactions Related to Gating Activity of Ionic Channels as Established by the Rescaled Range Method, Biologicheskie Membrany (Rus.), 2001, vol. 18, pp. 51–66.

    CAS  Google Scholar 

  10. Kazachenko, V.N., Kochetkov, K.V., Astashev, M.E., and Grinevich, A.A., Fractal Characteristics of the Gating Machinery of Voltage-Dependent K+ Channels in L. stagnalis Neurons, Biofizika (Rus.), 2004, vol. 49, pp. 852–865.

    CAS  Google Scholar 

  11. Kazachenko, V.N., Kochetkov, K.V., Aslanidi, O.V., and Grinevich, A.A., Analysis of Fractal Characteristics of the “Gating” Machinery of Single Ionic Channels Using Fast Fourier Transform, Biofizika (Rus.), 2001, vol. 46, pp. 1062–1070.

    CAS  Google Scholar 

  12. Kochetkov, K.V., Kazachenko, V.N., and Aslanidi, O.V., Wavelet Transform As a Method of Choice for the Study of Single Ionic Channel Activity, Biologicheskie Membrany (Rus.), 2003, vol. 20, pp. 359–368.

    CAS  Google Scholar 

  13. Brazhe, A.R., Astashev, M.E., Maximov, G.V., Kazachenko, V.N., and Rubin, A.B., Calculation of Local Hurst Exponents in Lifetime Sequences of Ca2+-Activated K+-Channels, Biofizika (Rus.), 2004, vol. 49, pp. 1075–1083.

    CAS  Google Scholar 

  14. Colquhoun, D. and Hawkes, A.G., Relaxation and Fluctuations of Membrane Currents that Flow through Drug-Operated Channels, Proc. R. Soc. London Ser. B., 1977, vol. 199, pp. 231–262.

    CAS  Google Scholar 

  15. Croxton, T.L., A Model of the Gating of Ion Channels, Biochem. Biophys. Acta, 1988, vol. 946, pp. 19–24.

    Article  PubMed  CAS  Google Scholar 

  16. Horn, R., Statistical Methods for Model Discrimination. Applications to Gating Kinetics and Permeation of the Acetylholine Receptor Channel, Biophys. J., 1987, vol. 51, pp. 255–263.

    PubMed  CAS  Google Scholar 

  17. Mcmanus, O.B. and Magleby, K.L., Accounting for the Ca2+-Depended Kinetics of Single Large-Conductance Ca2+-Activated K+-Channels in Rat Skeletal Muscle, J. Physiol. (London), 1994, vol. 443, pp. 739–777.

    Google Scholar 

  18. Liebovitch, L.S., Analysis of Fractal Ion Channel Gating Kinetics: Kinetics Rates Energy Levels and Activation Energies, Math. Biosci., 1989, vol. 93, pp. 97–115.

    Article  PubMed  CAS  Google Scholar 

  19. Liebovitch, L.S. and Toth, T.I., Fractal Activity in Cell Membrane Ion Channels, Math. Approach. Cardiac. Arrythmias, 1990, vol. 591, pp. 375–391.

    CAS  Google Scholar 

  20. Millhauser, G.L., Salpeter, E.E., and Oswald, R.E., Diffusion Models of Ion Channel Gating and the Origin of Power-Law Distributions from Single Channel Recording, Proc. Natl. Acad. Sci. USA, 1988, vol. 85, pp. 1503–1507.

    Article  PubMed  CAS  Google Scholar 

  21. Oswald, R.E., Millhause, G.L., and Carter, A.A., Diffusion Model in Ion Channel Gating. Extension to Agonist-Activated Ion Channels, Biophys. J., 1991, vol. 59, pp. 1136–1142.

    PubMed  CAS  Google Scholar 

  22. Liebovitch, L.S. and Yang, W., Transition from Persistent to Antipersistent Correlation in Biological Systems, Phys. Rev. E, 1997, vol. 56, pp. 4557–4566.

    Article  CAS  Google Scholar 

  23. Kurzynski, M., Palacz, K., and Chelminiak, P., Time Course of Reactions Controlled and Gated by Intramolecular Dynamics of Proteins: Predictions of the Model of Random Walk on Fractal Lattices, Proc. Natl. Acad. Sci. USA, 1998, vol. 95, pp. 11685–11690.

    Article  PubMed  CAS  Google Scholar 

  24. Liebovitch, L.S. and Toth, T.I., A Model of Ionic Channel Kinetics Using Deterministic Chaotic Rather Than Stochastic Processes, J. Theor. Biol., 1991, vol. 148, pp. 243–267.

    Article  PubMed  CAS  Google Scholar 

  25. Liebovitch, L.S. and Czegledy, F., A Model of Ion Channel Kinetics Based on Deterministic Motion in a Potential with Two Local Minima, Ann. Biomed. Engr., 1992, vol. 84, pp. 37–68.

    Google Scholar 

  26. Cavalcanti, S. and Fontanazzi, F., Deterministic Model of Ion Channel Flipping ith Fractal Scaling of Kinetics Rates, Ann. Biomed. Engr., 1999, vol. 27, pp. 682–695.

    Article  CAS  Google Scholar 

  27. Jiang, Y., Lee, A., Chen, J., Cadene, M., Chalt, B.T., and Mackinnon, R., The Open Pore Conformation of Potassium Channels, Nature, 2002, vol. 417, pp. 523–526.

    Article  PubMed  CAS  Google Scholar 

  28. Gazzarrini, S., Severino, M., Lombardi, M., Morandi, M., Difrancesco, D., Etten, J.L.V., Thiel, G., and Moroni, A., The Viral Potassium Channel Kcv: Structural and Functional Features, FEBS Lett., 2003, vol. 552, pp. 12–16.

    Article  PubMed  CAS  Google Scholar 

  29. Beckstein, O.B., Biggin, P.C., Bond, P., Bright, N., Domene, C., Grottesi, A., Holyoake, J., and Sansom, M.S.P., Ion Channel Gating: Insights via Molecular Simulation, FEBS Lett., 2003, vol. 555, pp. 85–90.

    Article  PubMed  CAS  Google Scholar 

  30. Ide, T., Takeuchi, Y., Aoki, T., and Yanagida, T., Simultaneous Optical and Electrical Recording of a Single Ion-Channel, Japan. J. Physical., 2002, vol. 52, pp. 429–434.

    Article  CAS  Google Scholar 

  31. Rubin, A.B., Biofizika (Biophysics) (Moscow: Knizhny Dom Universitet Press, 1999), vol. 1.

    Google Scholar 

  32. Colquhoun, D. and Sigworth, F.J., Processing and Statistic Analysis of the Activity of Single Channels, Recording Single Channel Activity, Sackmann, B. and Neher, E., Eds. (Moscow: Mir Press, 1987), pp. 241–338.

    Google Scholar 

  33. Bassingthwaighte, J.B. and Raymond, G.M., Evaluating Rescaled Range Analysis for Time Series, Ann. Biomed. Eng., 1994, vol. 22, pp. 432–444.

    Article  PubMed  CAS  Google Scholar 

  34. Peng, C.-K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., and Goldberger, A.L., Mosaic Organization of DNA Nucleotides, Phys. Rev., 1994, vol. 49, pp. 1685–1689.

    Article  CAS  Google Scholar 

  35. Kantelhardt, J.W., Zschiegner, S.A., Koscienly-Bunde, E., Bunde, A., Halvin, S., and Stanley, H.E., Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series, Physica A: Stat. Mechanics Appl., 2002, vol. 316, pp. 87–114.

    Article  Google Scholar 

  36. Hurst, H.E., Long-Term Storage: An Experimental Study, Trans. Am. Soc. Civ. Engr., 1951, vol. 116, pp. 770.

    Google Scholar 

  37. Mandelbrot, B.B. and Van Ness, J.W., Fractional Brownian Motions, Fractional Noises and Applications, Siam Rev., 1968, vol. 10, pp. 422–437.

    Article  Google Scholar 

  38. Teich, M.C., Fractal Character of the Auditory Neural Spike Train, IEEE Trans. Biomed. Engr., 1989, vol. 36, pp. 150–160.

    Article  CAS  Google Scholar 

  39. Karplus, M. and Mccammon, J.A., Dynamic of Proteins: Elements and Function, Ann. Rev. Biochem., 1983, vol. 52, pp. 263–300.

    Article  PubMed  CAS  Google Scholar 

  40. Monticelli, L., Robertson, K.M., Maccallum, J.L., and Tieleman, D.P., Computer Simulation of the KvAP Voltage-Gated Potassium Channel: Steered Molecular Dynamics of the Voltage Sensor, FEBS Lett., 2004, vol. 564, pp. 325–332.

    Article  PubMed  CAS  Google Scholar 

  41. Guidoni, L., Torre, V., and Carloni, P., Water and Potassium Dynamics inside the KcsA K Channel, FEBS Lett., 2000, vol. 477, pp. 37–42.

    Article  PubMed  CAS  Google Scholar 

  42. Chung, S., Allen, T.W., and Kuyucak, S., Conducting-State Properties of the KcsA Potassium Channel from Molecular and Brownian Dynamics Simulations, Biophys. J. 2002, vol. 82, pp. 628–645.

    Article  PubMed  CAS  Google Scholar 

  43. Sigg, D. and Bezanilla, F., A Physical Model of Potassium Channel Activation: From Energy Landscape to Gating Kinetics, Biophys. J., 2003, vol. 84, pp. 3703–3716.

    PubMed  CAS  Google Scholar 

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Authors and Affiliations

  1. Institute of Cell Biophysics, Russian Academy of Sciences, Pushchino, Moscow oblast, 142290, Russia

    A. A. Grinevich, M. E. Astashev & V. N. Kazachenko

Authors
  1. A. A. Grinevich
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  2. M. E. Astashev
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  3. V. N. Kazachenko
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Original Russian Text © A.A. Grinevich, M.E. Astashev, V.N. Kazachenko, 2007, published in Biologicheskie Membrany, 2007, Vol. 24, No. 4, pp. 316–332.

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Grinevich, A.A., Astashev, M.E. & Kazachenko, V.N. Model of multifractal gating of single ionic channels in biological membranes. Biochem. Moscow Suppl. Ser. A 1, 253–269 (2007). https://doi.org/10.1134/S1990747807030099

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  • DOI: https://doi.org/10.1134/S1990747807030099

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