Skip to main content
SpringerLink
Log in

The magnitude and significance of Ca2+ domains for release of neurotransmitter

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

It is now widely accepted that localized high concentrations of Ca2+ (Ca2+ domains) play a major role in controlling the time course of neurotransmitter release. In the present work we calculate the magnitude and the time course of Ca2+ domains that evolve in the vicinity of a Ca2+ channel and an adjacent release site. In the calculations we consider a accurately dimensioned Ca2+ channel. Moreover, the Ca2+ current is continuously adjusted with regard to the accumulated intracellular Ca2+ and, in addition, endogenous buffers are considered. The calculations, carried out by the software FIDAP, based on finite element method, show that the Ca2+ concentrations achieved near the release sites are significantly lower than claimed by other investigators. Furthermore, we present arguments indicating that the Ca2+ domains, regardless of their magnitude, do not play a role in controlling the time course of release of neurotransmitter.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Aharon, S. and M. Bercovier. 1993. Semi-automatic computer construction of three-dimensional shapes for the finite element method.Comput. Meth. Programs Biomed. 41, 135–146.

    Article  Google Scholar 

  • Andrew, R. and E. F. Barrett. 1980. Calcium dependence of evoked transmitter release at very low quantal contents at the frog neuromuscular junction.J. Physiol. (Lond.) 308, 79–97.

    Google Scholar 

  • Arechiga, H., A. Cannone, H. Parnas and I. Parnas. 1990. Blockage of synaptic release by brief hyperpolarizing pulses in the neuromuscular junction of the crayfish.J. Physiol. (Lond.) 430, 119–133.

    Google Scholar 

  • Connor, J. A., R. Kretz and E. Shapiro. 1986. Calcium levels measured in a presynaptic neuron of Aplysia under conditions that modulate transmitter release.J. Physiol. (Lond.) 375, 625–642.

    Google Scholar 

  • Crank, J. 1975.The Mathematics of Diffusion. 2nd edn. Oxford: Clarendon Press.

    Google Scholar 

  • Datyner, N. B. and P. W. Gage. 1980. Phasic secretion of acetylcholine at a mammalian neuromuscular junction.J. Physiol. (Lond.) 303, 299–314.

    Google Scholar 

  • Delaney, K. R., R. S. Zucker and D. W. Tank. 1989. Calcium in motor nerve terminals associated with posttetanic potentiation.J. Neurosci. 9, 3558–3567.

    Google Scholar 

  • Dudel, J., I. Parnas and H. Parnas. 1983. Neurotransmitter release and its facilitation in crayfish muscle.Pflügers Arch. 399, 1–10.

    Article  Google Scholar 

  • Dudel, J. 1984. Control of quantal transmitter release at frog's motor nerve terminal. [I] Dependence on amplitude and duration of depolarization.Pflügers Arch. 402, 225–234.

    Article  Google Scholar 

  • Engelman, M. 1991.FIDAP Theoretical Manual, version 6.02. FDI, 500 Davis Street, Suite 600, Evanston, Illinois 60201, U.S.A.

    Google Scholar 

  • Fogelson, A. L. and R. S. Zucker. 1985. Presynaptic calcium diffusion from various arrays of single channels.Biophys. J. 48, 1003–1017.

    Google Scholar 

  • Goldman, D. E. 1943. Potential impedance, and rectification in membranes.J. Gen. Physiol. 27, 37–60.

    Article  Google Scholar 

  • Hodgkin, A. L. and B. Katz. 1949. The effect of sodium ions on the electrical activity of the giant axon of the squid.J. Physiol. (Lond.) 108, 37–77.

    Google Scholar 

  • Hochner, B., H. Parnas and I. Parnas. 1991. Effects of intra-axonal injection of Ca2+ buffers on evoked release and on facilitation in crayfish neuromuscular junction.Neurosci. Lett 125, 215–218.

    Article  Google Scholar 

  • Lustig, C., H. Parnas and L. A. Segel. 1990. Release kinetics as a tool to describe drug effects on neurotransmitter release.J. theor. Biol. 144, 225–248.

    Google Scholar 

  • Lux, H. D. and A. M. Brown. 1984. Patch and whole cell calcium currents recorded simultaneously in snail neurons.J. Gen. Physiol. 83, 727–750.

    Article  Google Scholar 

  • McCleskey, E. W. and W. Almers. 1985. The Ca channel in skeletal muscle is a large pore.Proc. Natn. Acad. Sci., U.S.A. 82, 7149–7153.

    Article  Google Scholar 

  • Nasi, E. and D. Tillotson. 1985. The rate of diffusion of Ca2+ and Ba2+ in a nerve cell body.Biophys. J. 47, 735–738.

    Google Scholar 

  • Neher, E. and G. J. Augustine. 1992. Calcium gradients and buffers in bovine chromaffin cells.J. Physiol. (Lond. 450, 273–301.

    Google Scholar 

  • Nernst, W. 1988. On the kinetics of substances in solution (Translated fromZ. Physik. Chemie 2, 613–622, 634–637). In G. R. Kepnor (ed.)Cell Membrane Permability and Transport. Stroundsburg, PA. Downon: Hutchinson and Ross, 1979, pp. 174–183.

    Google Scholar 

  • Parnas, H., J. Dudel and I. Parnas (1986). Neurotransitter release and its facilitation in crayfish. [VII] Another voltage dependent beside Ca entry controls the time course of phasic release.Pflügers Arch. 406, 121–130.

    Article  Google Scholar 

  • Parnas, H., G. Hovav and I. Parnas. 1989. Effect of Ca2+ diffusion on the time course of neurotransmitter release.Biophys. J. 53, 859–874.

    Google Scholar 

  • Parnas, H., I. Parnas and L. A. Segel. 1990. On the contribution of mathematical models to the understanding of neurotransmitter release.Inter. Rev. Neuro. Sci. 32, 1–50.

    Article  Google Scholar 

  • Parnas, I., H. Parnas and J. Dudel. 1986. Neurotransmitter release and its facilitation in crayfish. [VIII] Modulation of release by hyperpolarizing pulses.Pflügers Arch. 406, 131–137.

    Article  Google Scholar 

  • Parnas, I., R. Ravin, B. Hochner, H. Parnas, N. Ziv and M. E. Spira. 1994. Evoked neurotransmitter release from crayfish neuromuscular junction in micromolar Ca2+ concentration, Unpublished work.

  • Pumplin, D. W., T. S. Reese and R. Llinas. 1981. Are the presynaptic membrane particles the calcium channels?Proc. Natn. Acad. Sci., U.S.A. 78, 7210–7213.

    Article  Google Scholar 

  • Sherman, A., J. Keizer and J. Rinzel. 1990. Domain model for Ca2+ inactivation of Ca2+ chennels at low channel density.Biophys. J. 58, 985–995.

    Google Scholar 

  • Simon, S. M. and R. Llinas. 1985. Compartmentalization of the submembrane calcium activity during calcium influx and its significance in transmitter release.Biophys. J. 48, 485–498.

    Google Scholar 

  • Smith, S. J. and G. J. Augustine. 1988. Calcium ions, active zones and synaptic transmitter release.TINS 11, 458–464.

    Google Scholar 

  • Strang, G. and G. J. Fix. 1973.An Analysis of the Finite Element Method. Englewood Cliffs, NJ: Prentice Hall (Series in Automatic Computation)

    MATH  Google Scholar 

  • Tsien, R. W., L. D. Ipsocmbe, D. V. Madison, K. R. Bley and A. P. Fox. 1988. Multiple types of neuronal calcium channels and their selective modulation.TINS 11, 431–438.

    Google Scholar 

  • Yamada, W. M. and R. S. Zucker. 1992. Time course of transmitter release calculated from simulation of a calcium diffusion model.Biophys. J. 61, 671–682.

    Article  Google Scholar 

  • Yue, D. T. and E. Marban. 1990. Permeation in the dihydropyridine-sensitive calcium channel.J. Gen. Physiol. 95, 911–939.

    Article  Google Scholar 

  • Zienkiewicz, O. C. 1977.The Finite Element Method, 3rd edn. London: McGraw Hill.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Neurobiology and the Otto Loewi Center for Cellular and Molecular Neurobiology, Hebrew University, Givat Ram, Jerusalem, Israel

    S. Aharon, H. Parnas & I. Parnas

Authors
  1. S. Aharon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Parnas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. I. Parnas
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Also belongs to the Center for Neural Computation.

Parnas is the Greenfield Professor of Neurobiology.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aharon, S., Parnas, H. & Parnas, I. The magnitude and significance of Ca2+ domains for release of neurotransmitter. Bltn Mathcal Biology 56, 1095–1119 (1994). https://doi.org/10.1007/BF02460288

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02460288

Keywords

Search

Navigation