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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adam, G.: Ionenstrom nach einem depolarisierenden Sprung im Membranpotential. Z.f. Naturforsch. 23b, 181–197 (1968)
Baker, P. F.: The regulation of intracellular calcium. In: Calcium in biological systems (C.J. Duncan, ed.), pp. 67–88, Cambridge: Univ. Press, 1976
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
Bass, L., McIlroy, D. K.: Enzyme activities in polarized cell membranes. Biophys. J. 8, 99–109 (1968)
Brehm, P., Eckert, R.: Calcium entry leads to inactivation of calcium channel in Paramecium. Science 202, 1203–1206 (1978)
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)
Dunlap, K.: Localization of calcium channels in Paramecium caudatum. J. Physiol. (Lond.) 271, 119–133 (1977)
Eckert, R.: Bioelectric control of ciliary activity. Science 176, 473–481 (1972)
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
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)
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)
Hildebrand, E.: Ciliary reversal in Paramecium: Temperature dependence of K+-induced excitability decrease and of recovery. J. comp. Physiol. 127, 39–44 (1978)
Hildebrand, E., Dryl, S.: Significance of Ca2+ and K+ ions for the excitation of the protozoan membrane. Bioelectrochem. Bioenerg. 3, 543–544 (1976)
Hill, T. L.: Studies in irreversible thermodynamics. J. theor. Biol. 10, 442–459 (1966)
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)
Hodgkin, A. L.: Ionic movements and electrical activity in giant nerve fibres. Proc. Roy. Soc. B. 148, 1–37 (1958)
Jahn, T. L.: The mechanism of ciliary movement. II. Ion antagonism and ciliary reversal. J. cell. comp. Physiol. 60, 217–228 (1962)
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)
Machemer, H., Eckert, R.: Ciliary frequency and orientational responses to clamped voltage steps in Paramecium. J. comp. Physiol. 104, 247–260 (1975)
McIlroy, D. K.: A mathematical model of the nerve impulse at the molecular level. Math. Biosci. 7, 313–328 (1970)
McLaughlin, S., Harary, H.: Phospholipid flip-flop and the distribution of surface charges in excitable membranes. Biophys. J. 14, 200–208 (1974)
Meech, R. W.: Intracellular calcium injection causes increased potassium conductance in Aplysia nerve cells. Comp. Biochem. Physiol. 42A, 493–499 (1972)
Naitoh, Y.: Ionic control of the reversal response of cilia in Paramecium caudatum. A calcium hypothesis. J. gen. Physiol. 51, 85–103 (1968)
Naitoh, Y., Eckert, R.: Electrical properties of Paramecium caudatum: All-or-none electrogenesis. Z. vergl. Physiol. 61, 453–472 (1968)
Naitoh, Y., Kaneko, H.: Reactivated triton-extracted models of Paramecium: Modification of ciliary movement by calcium ions. Science 176, 523–524 (1972)
Naitoh, Y., Eckert, R., Friedman, K.: A regenerative calcium response in Paramecium. J. exp. Biol. 56, 667–681 (1972)
Nonner, W., Rojas, E., Stämpfli, R.: Displacement currents in the node of Ranvier. Pflügers Arch. 354, 1–18 (1975)
Oertel, D., Schein, S. J., Kung, C.: Separation of membrane currents using a Paramecium mutant. Nature 268, 120–124 (1977)
Ogura, A., Takahashi, K.: Artificial deciliation causes loss of calcium-dependent responses in Paramecium. Nature 264, 170–172 (1976)
Satow, Y.: Internal calcium concentration and potassium permeability in Paramecium. J. Neurobiol. 9, 81–91 (1978)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hook, C., Hildebrand, E. Excitation of paramecium . J. Math. Biology 8, 197–214 (1979). https://doi.org/10.1007/BF00279722
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00279722