Skip to main content

Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 12))

  • 197 Accesses

Abstract

The models discussed in sections 3–10 all deal with stochastic trains of action potentials: in this section I will deal with models of the processes which occur when an action potential reaches the axonal termination and produces electrical changes in a post-synaptic cell. There are two types of specific mechanism for the transmission of electrical activity between excitable cells — these are electrical transmission and chemical transmission. Eccles (1964) has given an extensive review of the basic physiology of these transmission mechanisms in the nervous system.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anderson, C.R. and Stevens, C.F.: Voltage clamp analysis of acetylcholine produced end-plate current fluctuations at frog neuromuscular junction. J. Physiol. 235 655–691 (1973).

    Google Scholar 

  • Bayly, E.J.: Spectral analysis of pulse frequency modulation in the nervous system. I.E.E.E. Trans. Bio-Med Engng. 15 257–265 (1968).

    Google Scholar 

  • Bayly, E.J.: Spectral Analysis of pulse frequency modulation. In: Systems analysis in Neurophysiology, ed. C.A.Terzuolo. Univ. of Minnesota 48–60 (1969).

    Google Scholar 

  • Bennett, M.V.L.: Physiology of Electrotonic junctions. Ann. N.Y. Acad. Sci. 137 509–539 (1966).

    Article  Google Scholar 

  • Boyd, I.A. and Martin, A.R.: Spontaneous subthreshold activity at mammalian neuromuscular junctions. J. Physiol. 132 61–73 (1956).

    Google Scholar 

  • Braun, M. and Schmidt, R.F.: Potential changes recorded from the frog motor nerve terminal during its activation. Pflugers Arch. ges. Physiol. 28 756–80 (1966).

    Google Scholar 

  • Brillinger, D.R.: Cross-spectral analysis of processes with stationary increments including the G/G/.0 queue. Annals of Prob. 2 815–827 (1974).

    Article  MathSciNet  MATH  Google Scholar 

  • Brillinger, D.R.: The identification of point process sustems. Annals of Prob. 3 909–929 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  • Brillinger, D.R., Bryant, H.L. and Segundo, J.P.: Identification of synaptic interactions. Biological Cybernetics (1976)

    Google Scholar 

  • Bryant, H.L., Marios, A.R. and Segundo, J.P.: Correlations of neuronal spike discharges produced by monosynaptic connections and by common inputs. J. Neurophysiol. 36 205–225 (1973).

    Google Scholar 

  • Bullock, T.H.: Transfer functions at synaptic junctions. In: Information processing in the nervous system. Proc. I.U.P.S. XXII Congress, Leiden 1962. ed. R.W.Gerard and J.W.Duyff. Excerpta Medica (1964).

    Google Scholar 

  • Cohen, I., Kita, H. and van der Kloot, W.: Miniature endplate potentials: evidence that the intervals are not fit by a Poisson distribution. Brain Research 54 318–323 (1973).

    Article  Google Scholar 

  • Cohen, I., Kita, H. and van der Kloot, W.: The intervals between miniature endplate potentials in the frog are unlikely to be exponentially distributed. J. Physiol. 236 327–339 (1974a).

    Google Scholar 

  • Cohen, I., Kita, H. and van der Kloot, W.: The stochastic properties of spontaneous quantal release of transmitter at the frog neuromuscular junction. J. Physiol. 236 341–361 (1974b).

    Google Scholar 

  • Cohen, I., Kita, H. and van der Kloot, W.: Stochastic properties of spontaneous release at the crayfish neuromuscular junction. J. Physiol. 236 363–371 (1974c).

    Google Scholar 

  • Cox, D.R. and Lewis, P.A.W.: The Statistical Analysis of Series of Events. Methuen, London (1966).

    MATH  Google Scholar 

  • Crow, J.F. and Kimura, M.: An Introduction to Population Genetics Theory. Harper and Row, New York. (1970).

    MATH  Google Scholar 

  • del Castillo, J. and Katz, B.: Changes in endplate activity produced by presynaptic polarization. J.Physiol. 124 586–604 (1954).

    Google Scholar 

  • del Castillo, J. and Katz, B.: Quantal components of the endplate potential. J. Physiol. 124 560–573 (1954).

    Google Scholar 

  • del Castillo, J. and Katz, B.: Statistical factors involved in neuromuscular facilitation and depression. J. Physiol. 124 574–585 (1954).

    Google Scholar 

  • del Castillo, J. and Katz, B.: Local activity at a depolarized nerve-muscle junction. J. Physiol. 128 396–411 (1955).

    Google Scholar 

  • Eccles, J.C.: The Physiology of Synapses. Springer-Verlag, Berlin (1964).

    Book  Google Scholar 

  • Fatt, P. and Katz, B.: Some observations on biological noise. Nature 166 597–598 (1950).

    Article  Google Scholar 

  • Fatt, P. and Katz, B.: Spontaneous subthreshold activity at motor nerve endings. J. Physiol. 117 109–128 (1952).

    Google Scholar 

  • French, A.S. and DiCaprio, R.A.: The dynamic electrical behaviour of the electrotonic junction between Retzius cells in the Leech. Biological Cybernetics 17 129–135 (1975).

    Article  Google Scholar 

  • French, A.S. and Holden, A.V.: Alias-free sampling of neuronal spike trains. Kybernetik 8 165–171 (1971).

    Article  Google Scholar 

  • Furshpan, E.J. and Potter, D.D.: Transmission at the giant synapses of the crayfish. J. Physiol. 145 289–325 (1959).

    Google Scholar 

  • Furukawa, T. and Furshpan, E.J.: Two inhibitory mechanisms in the Mauthner neurons of goldfish. J. Neurophysiol. 26 140–176 (1963).

    Google Scholar 

  • Hubbard, J.I.: Repetitive stimulation at the mammalian neuromuscular junction, and the mobilization of transmitter. J. Physiol. 169 641–662 (1963).

    Google Scholar 

  • Jack, J.J.B., Noble, D. and Tsien, R.W.: Electric Current Flow in Excitable Cells. Clarendon Press, Oxford. 502pp. (1975).

    Google Scholar 

  • Katz, B.: Nerve, Muscle and Synapse. McGraw-Hill, New York. 193pp (1966).

    Google Scholar 

  • Katz, B. and Miledi, R.: The measurement of synaptic delay, and the time course of acetylcholine release at the neuromuscular junction. Proc. Roy. Soc. (London) B 161 483–495 (1964).

    Article  Google Scholar 

  • Katz, B. and Miledi, R.: The release of acetylcholine from nerve endings by graded electrical pulses. Proc. Roy. Soc. (London) B 167 23–38 (1967).

    Article  Google Scholar 

  • Katz, B. and Miledi, R.: Membrane noise produced by acetylcholine. Nature 226 962–963 (1970).

    Article  Google Scholar 

  • Katz, B. and Miledi, R.: Further observations on acetylcholine noise. Nature, New Biology 232 124–126 (1971).

    Article  Google Scholar 

  • Katz, B. and Miledi, R.: The statistical nature of the acetylcholine potential and its components. J. Physiol. 224 665–699 (1972).

    Google Scholar 

  • Katz, B. and Miledi, R.: The characteristics of endplate noise produced by different depolarizing drugs. J. Physio1. 230 707–717 (1973a).

    Google Scholar 

  • Katz, B. and Miledi, R.: The binding of acetylcholine to receptors and its removal from the synaptic cleft. J. Physiol. 231 549–574 (1973b).

    Google Scholar 

  • Knox, C.K.: Cross-correlation functions for a neuronal model. Biophysical J. 14 567–582 (1974).

    Article  Google Scholar 

  • Knox, C.K. and Poppele, R.E.: Response of neuronal syatems to random pulse trains. Proc. of the First Symposium on Testing and Identification of Nonlinear Systems. Ed. G.D.McCann and P.Z.Marmarelis. 227–235 (1975).

    Google Scholar 

  • Krausz, H.I.: Identification of nonlinear systems using random impulse train inputs. Biological Cybernetics 19 217–230 (1975).

    Article  MATH  Google Scholar 

  • Krausz, H.I. and Friesen, W.O.: Identification of discrete input nonlinear systems using Poisson impulse trains. Proc. of the First Symposium on Testing and Identification of Nonlinear Systems, Pasedena, California, March 1975. Ed. G.D.McCann and P.Z.Marmarelis.125–146 (1975)

    Google Scholar 

  • Kubo, R.: Statistical mechanical theory of irreversible processes. I.General theory and application to magnetic and conduction problems. J. Phys. Soc. Japan 12 570–586 (1957).

    MathSciNet  Google Scholar 

  • Kubo, R.: In: Some Aspects of the Statistical-Mechanical Theory of Irreversible Processes. Lectures in Theoretical Physics Vol I. Ed. Brittin and Dunham. Interscience Publ., New York (1959).

    Google Scholar 

  • Lewis, P.A.W.: Some results on tests for Poisson processes. Biometrika 52 67–78 (1965).

    MathSciNet  MATH  Google Scholar 

  • Liley, A.W.: The effects of presynaptic polarization on the spontaneous activity at the mammalian neuromuscular junction. J. Physiol 134 427–443 (1956).

    Google Scholar 

  • Liley, A.W.: Spontaneous release of transmitter substance in multi-quantal units. J. Physiol. 136 595–605 (1957).

    Google Scholar 

  • Liley, A.W. and North, K.A.K.: An electrical investigation of the effects of repetitive stimulation on mammalian neuromuscular junctions. J. Neurophysiol. 16 509–527 (1953).

    Google Scholar 

  • Magleby, K.L. and Stevens, C.F.: The effect of voltage on the time course of endplate currents. J. Physiol. 223 151–171 (1972).

    Google Scholar 

  • Magleby, K.L. and Stevens, C.F.: A quantitative description of endplate current. J. Physiol. 223 173–197 (1972).

    Google Scholar 

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

    Google Scholar 

  • Martin, A.R.: A further study of the statistical composition of the endplate potential. J. Physiol. 130 114–122 (1955).

    Google Scholar 

  • Martin, A.R.: Quantal nature of synaptic transmission. Physiol. Reviews 46 51–66 (1966).

    Google Scholar 

  • Perkel, D.H., Schulmam, J., Bullock, T.H., Moore, G.P. and Segundo, J.P.: Pacemaker neurones: effects of regularly spaced synaptic input. Science 145 61–63 (1964).

    Article  Google Scholar 

  • Segundo, J.P., Bryant, H.L. and Brillinger, D.R.: Identification of synaptic operators. Proc. of the First Symposium on Testing and Identification of Nonlinear Systems. Ed. G.D.McCann and P.Z.Marmarelis. California Institute of Technology, California. 221–227 (1975).

    Google Scholar 

  • Segundo, J.P., Moore, G.P., Stensaas, J. and Bullock, T.H.: Sensitivity of neurones in Aplysia to temporal pattern of arriving impulses. J. Expl. Biol. 40 643–667 (1963).

    Google Scholar 

  • Segundo, J.P., Perkel, D.H. and Moore, G.P.: Spike probability in neurones: influence of temporal structure in the train of synaptic events. Kybernetik 3 67–82 (1966).

    Article  Google Scholar 

  • Segundo, J.P., Perkel, D.H., Wyman, H., Hegsted, H. and Moore, G.P.: Input-output relations in computer-simulated nerve cells. Influence of the statistical properties, strength, number and interdependence of excitatory pre-synaptic terminals. Kybernetik 4 157–171 (1968).

    Article  Google Scholar 

  • Soucek, B.: Influence of the latency fluctuations and the quantal process of transmitter release on the endplate potentials amplitude distribution. Biophysical J. 11 127–139 (1971).

    Article  Google Scholar 

  • Stevens, C.F.: Synaptic physiology. Proc. I.E.E.E. 56 916–930 (1968).

    Google Scholar 

  • Stevens, C.F.: Inferences about membrane properties from electrical noise measurements. Biophysical J. 12 1028–1047 (1972).

    Article  Google Scholar 

  • Takeuchi, A.: The longlasting depression in neuromuscular transmission of frog. Japan J. Physiol. 8 102–113 (1958).

    Google Scholar 

  • Terzuolo, C.A.: and Bayly, E.J.: Data transmission between neurones. Kybernetik 5 83–84 (1968).

    Article  Google Scholar 

  • Terzuolo, C.A., McKean, T.A., Poppele, R.E. and Rosenthal, N.P.: Impulse trains, coding and decoding. In: Systems Analysis Approach to Neurophysiological Problems. Ed. C.A.Terzuolo. Univ. of Minnesota, Minneapolis. 86–91 (1969).

    Google Scholar 

  • Terzuolo, C.A., Purple, R.L., Bayly, E. and Handleman, E.: Post-synaptic inhibition - its action upon the transducer and encoder s systems of neurons.In: Structure and Function of Inhibitory Neuronal Mechanisms: Proc. of the 4th International Meeting of Neurobiologists, Stockholm, Sept. 1961. Ed. C. von Euler, S. Skogland and U. Soderberg. Pergamon Press, Oxford. (1968).

    Google Scholar 

  • Theis, R.E.: Neuromuscular depression and the apparent depletion of transmitter in mammalian muscle. J. Neurophysiol. 28 427–442 (1965).

    Google Scholar 

  • Usherwood, P.N.R.: Transmitter release from insect motor nerve terminals. J. Physiol. 227 527–551 (1972).

    Google Scholar 

  • van der Kloot, W., Kita, H. and Cohen, I.: The timing of the appearance of miniature endplate potentials. Progress in Neurobiology 4 269–326 (1975).

    Article  Google Scholar 

  • Verveen, A.A. and DeFelice, L.J.: Membrane noise. Progress in Biophysics and Molecular Biology 28 189–265 (1974).

    Article  Google Scholar 

  • Watanabe, Y.: Responses of an abdominal ganglion of the crayfish to electrical stimulation with a sinusoidal frequency change. J. Fac. Sci. Hokkaido Univ. Ser VI Zool. 15 93–102 (1962).

    Google Scholar 

  • Watanabe, Y.: Statistical measurement of signal transmission in the central nervous system of the crayfish. Kybernetik 6 124–130 (1969).

    Article  Google Scholar 

  • Wernig, A.: Quantum hypothesis of synaptic transmission. J. of Neural Transmission, Suppl. XII 61–74 (1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1976 Springer-Verlag Berlin · Heidelberg

About this chapter

Cite this chapter

Holden, A.V. (1976). Models of Synaptic Transmission. In: Models of the Stochastic Activity of Neurones. Lecture Notes in Biomathematics, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46345-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-46345-7_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07983-5

  • Online ISBN: 978-3-642-46345-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics