Skip to main content
Log in

Neurotransmitter release: Facilitation and three-dimensional diffusion of intracellular calcium

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

Abstract

In order to account for the time courses of both evoked release and facilitation, in the framework of the Ca2+ hypothesis, Fogelson and Zucker (1985,Biophys. J. 48, 1003–1017) suggested treating diffusion of Ca2+, once it enters through the Ca2+ channels, as a three-dimensional process (three-dimensional diffusion model). This model is examined here as a refined version of the “Ca2+-theory” for neurotransmitter release. The three-dimensional model was suggested to account for both the time course of release and that of facilitation. As such, it has been examined here as to its ability to predict the dependence of the amplitude and time course of facilitation under various experimental conditions. It is demonstrated that the three-dimensional diffusion model predicts the time course of facilitation to be insensitive to temperature. It also predicts the amplitude and time course of facilitation to be independent of extracellular Ca2+ concentration. Moreover, it predicts that inhibition of the [Na+]o↔[Ca2+]i exchange does not alter facilitation. These predictions are not upheld by the experimental results. Facilitation is prolonged upon reduction in temperature. The amplitude of facilitation declines and its duration is prolonged upon increase in extracellular Ca2+ concentration. Finally, inhibition of the [Na+]o↔[Ca2+]i exchange prolongs facilitation but does not alter the time course of evoked release after an impulse.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

Literature

  • Arechiga, H., A. Cannone, H. Parnas and I. Parnas. Blockage of synaptic release by brief hyperpolarizing pulses.J. Physiol. (London) in press.

  • Augustine, G. J., M. P. Charlton and S. J. Smith. 1985. Calcium entry and transmitter release at voltage clamp nerve terminals of squid.J. Physiol. (London) 367, 163–181.

    Google Scholar 

  • Barrett, E. F. and C. F. Stevens. 1972. The kinetics of transmitter release at the frog neuromuscular junction.J. Physiol. 227, 691–708.

    Google Scholar 

  • Bittner, G. D. and V. L. Sewell. 1976. Facilitation of crayfish neuromuscular junctions.J. comp. Physiol. 109, 287–308.

    Article  Google Scholar 

  • Bittner, G. D. and R. A. Schatz. 1981. An examination of the residual calcium theory for facilitation of transmitter release.Brain Res. 210, 431–436.

    Article  Google Scholar 

  • Blaustein, M. P. 1988. Calcium transport and buffering in neurons.TINS 11, 438–443.

    Google Scholar 

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

    Google Scholar 

  • Charlton, M. P. and G. D. Bittner. 1978. Facilitation of transmitter release at squid synapses.J. gen. Physiol. 72, 471–486.

    Article  Google Scholar 

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

    Google Scholar 

  • Delaney, K. R., R. S. Zucker and D. W. Tank. 1989. Calcium in motor nerve terminals associated with post tetanic potentiation.J. Neurosci. 9(10), 3558–3567.

    Google Scholar 

  • Dudel, J. 1984. Control of quantal transmitter release at frog's motor nerve terminals. I. Modulation by de- or hyperpolarizing pulses.Pflügers Arch. 402, 235–243.

    Article  Google Scholar 

  • Dudel, J. 1990a. Calcium and depolarization dependence of twin-pulse facilitation of synaptic release at nerve terminals of crayfish and frog muslce.Pflügers Arch., in press.

  • Dudel, J. 1990b. Twin pulse facilitation in dependence on pulse duration and calcium concentration at motor nerve terminals of crayfish and frogs.Pflügers Arch., in press.

  • Dudel, J., I. Parnas and H. Parnas. 1983. Neurotransmitter release and its facilitation in crayfish muscle. VI. Release determined by both intracellular calcium concentration and depolarization of the nerve terminal.Pflügers Arch. 399, 1–10.

    Article  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 

  • Hodgkin, A. L. and R. D. Keynes. 1957. Movement of labelled calcium in squid giant axons.J. Physiol. (London) 138, 153–281.

    Google Scholar 

  • Katz, B. and R. Miledi. 1965. The measurements of synaptic delay and the time course of acetylcholine release at the neuromuscular junction.Proc. R. Soc. Lond. B161, 483–495.

    Google Scholar 

  • Katz, B. and R. Miledi. 1968. The role of calcium in neuromuscular facilitation.J. Physiol. (London)195, 481–492.

    Google Scholar 

  • Katz, B. and R. Miledi. 1977. Suppression of transmitter release at the neuromuscular junction.Proc. R. Soc. Lond. B196, 465–469.

    Article  Google Scholar 

  • Llinas, R., I. Z. Steinberg and K. Walton. 1981. Relationship between presynaptic calcium current and post synaptic potential in squid giant synapse.Biophys. J. 33, 323–352.

    Google Scholar 

  • Lustig, C., H. Parnas and L. A. Segel. 1989. Neurotransmitter release: Development of a theory for total release based on kinetics.J. theor. Biol. 136, 151–170.

    Article  MathSciNet  Google Scholar 

  • Magleby, K. L. 1973. The effect of repetitive stimulation on facilitation of transmitter release at the frog neuromuscular junction.J. Physiol (London) 234, 327–352.

    Google Scholar 

  • Mallart, A. and A. R. Martin. 1967. An analysis of facilitation of transmitter release at the neuromuscular junction of the frog.J. Physiol. (London) 193, 679–694.

    Google Scholar 

  • Parnas, H. and L. Segel. 1980. A theoretical explanation for some effects of calcium on the facilitation of neurotransmitter release.J. theor. Biol. 84, 3–29.

    Article  Google Scholar 

  • Parnas, H., J. Dudel and I. Parnas. 1982. Neurotransmitter release and its facilitation in crayfish. I. Saturation kinetics of release and of entry and removal of calcium.Pflügers Arch. 393, 1–14.

    Article  Google Scholar 

  • Parnas, H. and L. A. Segel. 1989. Facilitation as a tool to study the entry of calcium and the mechanism of neurotransmitter release.Prog. Neurobiol. 32, 1–9.

    Article  Google Scholar 

  • Parnas, H., I. Parnas and L. A. Segel. 1990. On the contribution of mathematical models to the understanding of neurotransmitter release.Int. rev. Neurobiol. 32, 1–50.

    Google Scholar 

  • Parnas, I., H. Parnas and J. Dudel. 1982. Neurotransmitter release and its facilitation in crayfish. II. Duration of facilitation and removal processes of calcium from, the terminal.Pflügers Arch. 393, 232–236.

    Article  Google Scholar 

  • Parnas, I. and H. Parnas. 1986. Calcium is essential but insufficient for neurotransmitter release: The calcium-voltage hypothesis.J. Physiol. (Paris)81, 289–305.

    Google Scholar 

  • Rahamimoff, R. 1968. A dual effect of calcium ions on neuromuscular facilitation.J. Physiol. (London) 195, 471–480.

    Google Scholar 

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

    Article  Google Scholar 

  • Stockbridge, N. and J. W. Moore. 1984. Dynamics of intracellular calcium and its possible relationship to phasic transmitter release and facilitation at the frog neuromuscular junction.J. Neurosci. 4, 803–811.

    Google Scholar 

  • Zengel, J. E., K. L. Magleby, J. P. Horn, D. A. McAfee and P. J. Yarowsky. 1980. Facilitation, augmentation and potentiation of synaptic transmission at the superior cervical ganglion of the rabbit.J. gen Physiol. 76, 213–231.

    Article  Google Scholar 

  • Zucker, R. S. and L. Lando. 1986. Mechanisms of transmitter release: voltage hypothesis and calcium hypothesis.Science 231, 574–579.

    Google Scholar 

  • Zucker, R. S. and N. Stockbridge. 1983. Presynaptic calcium diffusion and the time courses of transmitter release and synaptic facilitation at the squid giant synapse.J. Neurosci. 3, 1263–1269.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hovav, G., Parnas, H. & Parnas, I. Neurotransmitter release: Facilitation and three-dimensional diffusion of intracellular calcium. Bltn Mathcal Biology 54, 875–894 (1992). https://doi.org/10.1007/BF02459934

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02459934

Keywords

Navigation