Excitation of paramecium

A model analysis

Summary

In a model analysis the excitation mechanism of Paramecium is simulated. The model is based on a specific Ca channel mechanism located in the ciliary part of the membrane. The Ca2+ permeability depends on transmembrane voltage and the binding of cations to channel subunits. Renormalization of intraciliary [Ca2+] following excitation is mediated by active Ca2+ extrusion and diffusion between cilia and cell body. Including the kinetic equations of a. K+ transport system we get a complete description of ionic fluxes and current-voltage relations. The electric responses to injected current pulses of different duration can be simulated as well as voltage-clamp measurements, after introduction of an electrogenic Ca2+ transport system. Allowing Ba2+ to substitute for Ca2+ with slightly different permeability and binding rates, the features of all-or-none action potentials and repetitive firing are reflected by the model. Simulation of membrane responses to varying external [K+] and [Ca2+] leads us to require some additional, slowly changing mechanism to account for processes like slow inactivation and recovery. The possible existence of negative surface charges is discussed.

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References

  1. Adam, G.: Ionenstrom nach einem depolarisierenden Sprung im Membranpotential. Z.f. Naturforsch. 23b, 181–197 (1968)

    Google Scholar 

  2. Baker, P. F.: The regulation of intracellular calcium. In: Calcium in biological systems (C.J. Duncan, ed.), pp. 67–88, Cambridge: Univ. Press, 1976

    Google Scholar 

  3. Barlow, C. A. Jr.: The electrical double layer. In: Physical chemistry, an advanced treatise. Vol. 9A Electrochemistry (H. Eyring, D. Henderson, W. Jost, eds.), pp. 167–246, New York: Academic Press, 1970

    Google Scholar 

  4. Bass, L., McIlroy, D. K.: Enzyme activities in polarized cell membranes. Biophys. J. 8, 99–109 (1968)

    Google Scholar 

  5. Brehm, P., Eckert, R.: Calcium entry leads to inactivation of calcium channel in Paramecium. Science 202, 1203–1206 (1978)

    Google Scholar 

  6. Bretag, A.H., Davis, B. R., Kerr, D. I. B.: Potassium conductance model related to an interactive subunit membrane. J. Memb. Biol. 16, 363–380 (1974)

    Google Scholar 

  7. Dunlap, K.: Localization of calcium channels in Paramecium caudatum. J. Physiol. (Lond.) 271, 119–133 (1977)

    Google Scholar 

  8. Eckert, R.: Bioelectric control of ciliary activity. Science 176, 473–481 (1972)

    Google Scholar 

  9. Eckert, R., Naitoh, Y., Machemer, H.: Calcium in the bioelectric and motor functions of Paramecium. In: Calcium in biological systems (C. J. Duncan, ed.), pp. 233–255, Cambridge: Univ. Press, 1976

    Google Scholar 

  10. Gilbert, D. L., Ehrenstein, G.: Effect of divalent cations on potassium conductance of squid axons: determination of surface charge. Biophys. J. 9, 447–463 (1969)

    Google Scholar 

  11. Hildebrand, E.: Bedeutung der Konkurrenz zwischen Calcium und anderen Kationen für die Steuerung der Leitfähigkeit sensorischer Membranen. Verh. Dtsch. Zool. Ges. 1974, 24–28 (1975)

    Google Scholar 

  12. Hildebrand, E.: Ciliary reversal in Paramecium: Temperature dependence of K+-induced excitability decrease and of recovery. J. comp. Physiol. 127, 39–44 (1978)

    Google Scholar 

  13. Hildebrand, E., Dryl, S.: Significance of Ca2+ and K+ ions for the excitation of the protozoan membrane. Bioelectrochem. Bioenerg. 3, 543–544 (1976)

    Google Scholar 

  14. Hill, T. L.: Studies in irreversible thermodynamics. J. theor. Biol. 10, 442–459 (1966)

    Google Scholar 

  15. Hille, B., Woodhull, A. M., Shapiro, B. I.: Negative surface charge near sodium channel of nerve: divalent ions, monovalent ions, and pH. Phil. Trans. R. Soc. Lond. B 270, 301–318 (1975)

    Google Scholar 

  16. Hodgkin, A. L.: Ionic movements and electrical activity in giant nerve fibres. Proc. Roy. Soc. B. 148, 1–37 (1958)

    Google Scholar 

  17. Jahn, T. L.: The mechanism of ciliary movement. II. Ion antagonism and ciliary reversal. J. cell. comp. Physiol. 60, 217–228 (1962)

    Google Scholar 

  18. Jennings, H. S.: Studies on reactions to stimuli in unicellular organisms. II. The mechanism of motor reactions of Paramecium. Am. J. Physiol. 2, 311–341 (1899)

    Google Scholar 

  19. Machemer, H., Eckert, R.: Ciliary frequency and orientational responses to clamped voltage steps in Paramecium. J. comp. Physiol. 104, 247–260 (1975)

    Google Scholar 

  20. McIlroy, D. K.: A mathematical model of the nerve impulse at the molecular level. Math. Biosci. 7, 313–328 (1970)

    Google Scholar 

  21. McLaughlin, S., Harary, H.: Phospholipid flip-flop and the distribution of surface charges in excitable membranes. Biophys. J. 14, 200–208 (1974)

    Google Scholar 

  22. Meech, R. W.: Intracellular calcium injection causes increased potassium conductance in Aplysia nerve cells. Comp. Biochem. Physiol. 42A, 493–499 (1972)

    Google Scholar 

  23. Naitoh, Y.: Ionic control of the reversal response of cilia in Paramecium caudatum. A calcium hypothesis. J. gen. Physiol. 51, 85–103 (1968)

    Google Scholar 

  24. Naitoh, Y., Eckert, R.: Electrical properties of Paramecium caudatum: All-or-none electrogenesis. Z. vergl. Physiol. 61, 453–472 (1968)

    Google Scholar 

  25. Naitoh, Y., Kaneko, H.: Reactivated triton-extracted models of Paramecium: Modification of ciliary movement by calcium ions. Science 176, 523–524 (1972)

    Google Scholar 

  26. Naitoh, Y., Eckert, R., Friedman, K.: A regenerative calcium response in Paramecium. J. exp. Biol. 56, 667–681 (1972)

    Google Scholar 

  27. Nonner, W., Rojas, E., Stämpfli, R.: Displacement currents in the node of Ranvier. Pflügers Arch. 354, 1–18 (1975)

    Google Scholar 

  28. Oertel, D., Schein, S. J., Kung, C.: Separation of membrane currents using a Paramecium mutant. Nature 268, 120–124 (1977)

    Google Scholar 

  29. Ogura, A., Takahashi, K.: Artificial deciliation causes loss of calcium-dependent responses in Paramecium. Nature 264, 170–172 (1976)

    Google Scholar 

  30. Satow, Y.: Internal calcium concentration and potassium permeability in Paramecium. J. Neurobiol. 9, 81–91 (1978)

    Google Scholar 

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Hook, C., Hildebrand, E. Excitation of paramecium . J. Math. Biology 8, 197–214 (1979). https://doi.org/10.1007/BF00279722

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Key words

  • Cilia
  • Membrane
  • Ca channels
  • Action potential
  • Ion competition
  • Electrogenic pump