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. 1997 Feb;72(2 Pt 1):728–753. doi: 10.1016/s0006-3495(97)78709-5

The Binomial Model in Fluctuation Analysis of Quantal Neurotransmitter Release

D M J Quastel 1
PMCID: PMC1185598  PMID: 9017200

Abstract

The mathematics of the binomial model for quantal neurotransmitter release is considered in general terms, to explore what information might be extractable from statistical aspects of data. For an array of N statistically independent release sites, each with a release probability p, the compound binomial always pertains, with <m> = N<p>, p′ ≡ 1 - var(m)/<m> = <p> (1 + cvp2) and n′ ≡ <m>/p′ = N/(1 + cvp2), where m is the output/stimulus and cvp2 is var(p)/<p>2. Unless n′ is invariant with ambient conditions or stimulation paradigms, the simple binomial (cvp = 0) is untenable and n′ is neither N nor the number of “active” sites or sites with a quantum available. At each site p = popA, where po is the output probability if a site is “eligible” or “filled” despite previous quantal discharge, and pA (eligibility probability) depends at least on the replenishment rate, po, and interstimulus time. Assuming stochastic replenishment, a simple algorithm allows calculation of the full statistical composition of outputs for any hypothetical combinations of po's and refill rates, for any stimulation paradigm and spontaneous release. A rise in n′ (reduced cvp) tends to occur whenever po varies widely between sites, with a raised stimulation frequency or factors tending to increase po's. Unlike <m> and var(m) at equilibrium, output changes early in trains of stimuli, and covariances, potentially provide information about whether changes in <m> reflect change in <po> or in <pA>. Formulae are derived for variance and third moments of postsynaptic responses, which depend on the quantal mix in the signals. A new, easily computed function, the area product, gives noise-unbiased variance of a series of synaptic signals and its peristimulus time distribution, which is modified by the unit channel composition of quantal responses and if the signals reflect mixed responses from synapses with different quantal time course.

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Selected References

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  1. Bain A. I., Quastel D. M. Multiplicative and additive Ca(2+)-dependent components of facilitation at mouse endplates. J Physiol. 1992 Sep;455:383–405. doi: 10.1113/jphysiol.1992.sp019307. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Bain A. I., Quastel D. M. Quantal transmitter release mediated by strontium at the mouse motor nerve terminal. J Physiol. 1992 May;450:63–87. doi: 10.1113/jphysiol.1992.sp019116. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Brown T. H., Perkel D. H., Feldman M. W. Evoked neurotransmitter release: statistical effects of nonuniformity and nonstationarity. Proc Natl Acad Sci U S A. 1976 Aug;73(8):2913–2917. doi: 10.1073/pnas.73.8.2913. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. DEL CASTILLO J., KATZ B. Biophysical aspects of neuro-muscular transmission. Prog Biophys Biophys Chem. 1956;6:121–170. [PubMed] [Google Scholar]
  5. DEL CASTILLO J., KATZ B. Quantal components of the end-plate potential. J Physiol. 1954 Jun 28;124(3):560–573. doi: 10.1113/jphysiol.1954.sp005129. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. DEL CASTILLO J., KATZ B. Statistical factors involved in neuromuscular facilitation and depression. J Physiol. 1954 Jun 28;124(3):574–585. doi: 10.1113/jphysiol.1954.sp005130. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Dityatev A. E., Kozhanov V. M., Gapanovich S. O. Modeling of the quantal release at interneuronal synapses: analysis of permissible values of model moments. J Neurosci Methods. 1992 Jul;43(2-3):201–214. doi: 10.1016/0165-0270(92)90030-h. [DOI] [PubMed] [Google Scholar]
  8. Elmqvist D., Quastel D. M. A quantitative study of end-plate potentials in isolated human muscle. J Physiol. 1965 Jun;178(3):505–529. doi: 10.1113/jphysiol.1965.sp007639. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. HUBBARD J. I. REPETITIVE STIMULATION AT THE MAMMALIAN NEUROMUSCULAR JUNCTION, AND THE MOBILIZATION OF TRANSMITTER. J Physiol. 1963 Dec;169:641–662. doi: 10.1113/jphysiol.1963.sp007286. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. KATZ B., MILEDI R. THE MEASUREMENT OF SYNAPTIC DELAY, AND THE TIME COURSE OF ACETYLCHOLINE RELEASE AT THE NEUROMUSCULAR JUNCTION. Proc R Soc Lond B Biol Sci. 1965 Feb 16;161:483–495. doi: 10.1098/rspb.1965.0016. [DOI] [PubMed] [Google Scholar]
  11. Korn H., Faber D. S. Quantal analysis and synaptic efficacy in the CNS. Trends Neurosci. 1991 Oct;14(10):439–445. doi: 10.1016/0166-2236(91)90042-s. [DOI] [PubMed] [Google Scholar]
  12. LILEY A. W., NORTH K. A. An electrical investigation of effects of repetitive stimulation on mammalian neuromuscular junction. J Neurophysiol. 1953 Sep;16(5):509–527. doi: 10.1152/jn.1953.16.5.509. [DOI] [PubMed] [Google Scholar]
  13. MARTIN A. R. A further study of the statistical composition on the end-plate potential. J Physiol. 1955 Oct 28;130(1):114–122. doi: 10.1113/jphysiol.1955.sp005397. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Melkonian D. S. Transient analysis of a chemical synaptic transmission. Biol Cybern. 1993;68(4):341–350. doi: 10.1007/BF00201859. [DOI] [PubMed] [Google Scholar]
  15. Mennerick S., Zorumski C. F. Paired-pulse modulation of fast excitatory synaptic currents in microcultures of rat hippocampal neurons. J Physiol. 1995 Oct 1;488(Pt 1):85–101. doi: 10.1113/jphysiol.1995.sp020948. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Mennerick S., Zorumski C. F. Postsynaptic modulation of NMDA synaptic currents in rat hippocampal microcultures by paired-pulse stimulation. J Physiol. 1996 Jan 15;490(Pt 2):405–417. doi: 10.1113/jphysiol.1996.sp021154. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Quastel D. M., Guan Y. Y., Saint D. A. The relation between transmitter release and Ca2+ entry at the mouse motor nerve terminal: role of stochastic factors causing heterogeneity. Neuroscience. 1992 Dec;51(3):657–671. doi: 10.1016/0306-4522(92)90305-l. [DOI] [PubMed] [Google Scholar]
  18. Redman S. Quantal analysis of synaptic potentials in neurons of the central nervous system. Physiol Rev. 1990 Jan;70(1):165–198. doi: 10.1152/physrev.1990.70.1.165. [DOI] [PubMed] [Google Scholar]

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