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. 2001 Oct;81(4):1970–1989. doi: 10.1016/S0006-3495(01)75848-1

Estimating synaptic parameters from mean, variance, and covariance in trains of synaptic responses.

V Scheuss 1, E Neher 1
PMCID: PMC1301672  PMID: 11566771

Abstract

Fluctuation analysis of synaptic transmission using the variance-mean approach has been restricted in the past to steady-state responses. Here we extend this method to short repetitive trains of synaptic responses, during which the response amplitudes are not stationary. We consider intervals between trains, long enough so that the system is in the same average state at the beginning of each train. This allows analysis of ensemble means and variances for each response in a train separately. Thus, modifications in synaptic efficacy during short-term plasticity can be attributed to changes in synaptic parameters. In addition, we provide practical guidelines for the analysis of the covariance between successive responses in trains. Explicit algorithms to estimate synaptic parameters are derived and tested by Monte Carlo simulations on the basis of a binomial model of synaptic transmission, allowing for quantal variability, heterogeneity in the release probability, and postsynaptic receptor saturation and desensitization. We find that the combined analysis of variance and covariance is advantageous in yielding an estimate for the number of release sites, which is independent of heterogeneity in the release probability under certain conditions. Furthermore, it allows one to calculate the apparent quantal size for each response in a sequence of stimuli.

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Selected References

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  1. Barbour B., Häusser M. Intersynaptic diffusion of neurotransmitter. Trends Neurosci. 1997 Sep;20(9):377–384. doi: 10.1016/s0166-2236(96)20050-5. [DOI] [PubMed] [Google Scholar]
  2. Bekkers J. M., Stevens C. F. Quantal analysis of EPSCs recorded from small numbers of synapses in hippocampal cultures. J Neurophysiol. 1995 Mar;73(3):1145–1156. doi: 10.1152/jn.1995.73.3.1145. [DOI] [PubMed] [Google Scholar]
  3. Borst J. G., Sakmann B. Calcium influx and transmitter release in a fast CNS synapse. Nature. 1996 Oct 3;383(6599):431–434. doi: 10.1038/383431a0. [DOI] [PubMed] [Google Scholar]
  4. Clamann H. P., Mathis J., Lüscher H. R. Variance analysis of excitatory postsynaptic potentials in cat spinal motoneurons during posttetanic potentiation. J Neurophysiol. 1989 Feb;61(2):403–416. doi: 10.1152/jn.1989.61.2.403. [DOI] [PubMed] [Google Scholar]
  5. Clements J. D., Silver R. A. Unveiling synaptic plasticity: a new graphical and analytical approach. Trends Neurosci. 2000 Mar;23(3):105–113. doi: 10.1016/s0166-2236(99)01520-9. [DOI] [PubMed] [Google Scholar]
  6. 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]
  7. Diamond J. S., Jahr C. E. Transporters buffer synaptically released glutamate on a submillisecond time scale. J Neurosci. 1997 Jun 15;17(12):4672–4687. doi: 10.1523/JNEUROSCI.17-12-04672.1997. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Dobrunz L. E., Stevens C. F. Heterogeneity of release probability, facilitation, and depletion at central synapses. Neuron. 1997 Jun;18(6):995–1008. doi: 10.1016/s0896-6273(00)80338-4. [DOI] [PubMed] [Google Scholar]
  9. 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]
  10. Frerking M., Wilson M. Effects of variance in mini amplitude on stimulus-evoked release: a comparison of two models. Biophys J. 1996 May;70(5):2078–2091. doi: 10.1016/S0006-3495(96)79774-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Heinemann S. H., Conti F. Nonstationary noise analysis and application to patch clamp recordings. Methods Enzymol. 1992;207:131–148. doi: 10.1016/0076-6879(92)07009-d. [DOI] [PubMed] [Google Scholar]
  12. Korn H., Mallet A., Triller A., Faber D. S. Transmission at a central inhibitory synapse. II. Quantal description of release, with a physical correlate for binomial n. J Neurophysiol. 1982 Sep;48(3):679–707. doi: 10.1152/jn.1982.48.3.679. [DOI] [PubMed] [Google Scholar]
  13. Korn H., Sur C., Charpier S., Legendre P., Faber D. S. The one-vesicle hypothesis and multivesicular release. Adv Second Messenger Phosphoprotein Res. 1994;29:301–322. doi: 10.1016/s1040-7952(06)80022-4. [DOI] [PubMed] [Google Scholar]
  14. Kraushaar U., Jonas P. Efficacy and stability of quantal GABA release at a hippocampal interneuron-principal neuron synapse. J Neurosci. 2000 Aug 1;20(15):5594–5607. doi: 10.1523/JNEUROSCI.20-15-05594.2000. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Littleton J. T., Bai J., Vyas B., Desai R., Baltus A. E., Garment M. B., Carlson S. D., Ganetzky B., Chapman E. R. synaptotagmin mutants reveal essential functions for the C2B domain in Ca2+-triggered fusion and recycling of synaptic vesicles in vivo. J Neurosci. 2001 Mar 1;21(5):1421–1433. doi: 10.1523/JNEUROSCI.21-05-01421.2001. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Ma L., Zablow L., Kandel E. R., Siegelbaum S. A. Cyclic AMP induces functional presynaptic boutons in hippocampal CA3-CA1 neuronal cultures. Nat Neurosci. 1999 Jan;2(1):24–30. doi: 10.1038/4525. [DOI] [PubMed] [Google Scholar]
  17. Matveev V., Wang X. J. Implications of all-or-none synaptic transmission and short-term depression beyond vesicle depletion: a computational study. J Neurosci. 2000 Feb 15;20(4):1575–1588. doi: 10.1523/JNEUROSCI.20-04-01575.2000. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Murthy V. N., Sejnowski T. J., Stevens C. F. Heterogeneous release properties of visualized individual hippocampal synapses. Neuron. 1997 Apr;18(4):599–612. doi: 10.1016/s0896-6273(00)80301-3. [DOI] [PubMed] [Google Scholar]
  19. Neher E., Sakaba T. Combining deconvolution and noise analysis for the estimation of transmitter release rates at the calyx of held. J Neurosci. 2001 Jan 15;21(2):444–461. doi: 10.1523/JNEUROSCI.21-02-00444.2001. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Neher E. Vesicle pools and Ca2+ microdomains: new tools for understanding their roles in neurotransmitter release. Neuron. 1998 Mar;20(3):389–399. doi: 10.1016/s0896-6273(00)80983-6. [DOI] [PubMed] [Google Scholar]
  21. Oleskevich S., Clements J., Walmsley B. Release probability modulates short-term plasticity at a rat giant terminal. J Physiol. 2000 Apr 15;524(Pt 2):513–523. doi: 10.1111/j.1469-7793.2000.00513.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Otis T. S., Wu Y. C., Trussell L. O. Delayed clearance of transmitter and the role of glutamate transporters at synapses with multiple release sites. J Neurosci. 1996 Mar 1;16(5):1634–1644. doi: 10.1523/JNEUROSCI.16-05-01634.1996. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Otis T., Zhang S., Trussell L. O. Direct measurement of AMPA receptor desensitization induced by glutamatergic synaptic transmission. J Neurosci. 1996 Dec 1;16(23):7496–7504. doi: 10.1523/JNEUROSCI.16-23-07496.1996. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Quastel D. M. The binomial model in fluctuation analysis of quantal neurotransmitter release. Biophys J. 1997 Feb;72(2 Pt 1):728–753. doi: 10.1016/s0006-3495(97)78709-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. 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]
  26. Reid C. A., Clements J. D. Postsynaptic expression of long-term potentiation in the rat dentate gyrus demonstrated by variance-mean analysis. J Physiol. 1999 Jul 1;518(Pt 1):121–130. doi: 10.1111/j.1469-7793.1999.0121r.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Reyes A., Lujan R., Rozov A., Burnashev N., Somogyi P., Sakmann B. Target-cell-specific facilitation and depression in neocortical circuits. Nat Neurosci. 1998 Aug;1(4):279–285. doi: 10.1038/1092. [DOI] [PubMed] [Google Scholar]
  28. Rosenmund C., Clements J. D., Westbrook G. L. Nonuniform probability of glutamate release at a hippocampal synapse. Science. 1993 Oct 29;262(5134):754–757. doi: 10.1126/science.7901909. [DOI] [PubMed] [Google Scholar]
  29. Sakaba T., Neher E. Quantitative relationship between transmitter release and calcium current at the calyx of held synapse. J Neurosci. 2001 Jan 15;21(2):462–476. doi: 10.1523/JNEUROSCI.21-02-00462.2001. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Schikorski T., Stevens C. F. Quantitative ultrastructural analysis of hippocampal excitatory synapses. J Neurosci. 1997 Aug 1;17(15):5858–5867. doi: 10.1523/JNEUROSCI.17-15-05858.1997. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Sigworth F. J. The variance of sodium current fluctuations at the node of Ranvier. J Physiol. 1980 Oct;307:97–129. doi: 10.1113/jphysiol.1980.sp013426. [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. Silver R. A., Momiyama A., Cull-Candy S. G. Locus of frequency-dependent depression identified with multiple-probability fluctuation analysis at rat climbing fibre-Purkinje cell synapses. J Physiol. 1998 Aug 1;510(Pt 3):881–902. doi: 10.1111/j.1469-7793.1998.881bj.x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Tong G., Jahr C. E. Multivesicular release from excitatory synapses of cultured hippocampal neurons. Neuron. 1994 Jan;12(1):51–59. doi: 10.1016/0896-6273(94)90151-1. [DOI] [PubMed] [Google Scholar]
  34. Trussell L. O., Zhang S., Raman I. M. Desensitization of AMPA receptors upon multiquantal neurotransmitter release. Neuron. 1993 Jun;10(6):1185–1196. doi: 10.1016/0896-6273(93)90066-z. [DOI] [PubMed] [Google Scholar]
  35. Waldeck R. F., Pereda A., Faber D. S. Properties and plasticity of paired-pulse depression at a central synapse. J Neurosci. 2000 Jul 15;20(14):5312–5320. doi: 10.1523/JNEUROSCI.20-14-05312.2000. [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Walmsley B., Edwards F. R., Tracey D. J. Nonuniform release probabilities underlie quantal synaptic transmission at a mammalian excitatory central synapse. J Neurophysiol. 1988 Sep;60(3):889–908. doi: 10.1152/jn.1988.60.3.889. [DOI] [PubMed] [Google Scholar]
  37. Weis S., Schneggenburger R., Neher E. Properties of a model of Ca++-dependent vesicle pool dynamics and short term synaptic depression. Biophys J. 1999 Nov;77(5):2418–2429. doi: 10.1016/S0006-3495(99)77079-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  38. Wu L. G., Borst J. G. The reduced release probability of releasable vesicles during recovery from short-term synaptic depression. Neuron. 1999 Aug;23(4):821–832. doi: 10.1016/s0896-6273(01)80039-8. [DOI] [PubMed] [Google Scholar]
  39. Xu T., Binz T., Niemann H., Neher E. Multiple kinetic components of exocytosis distinguished by neurotoxin sensitivity. Nat Neurosci. 1998 Jul;1(3):192–200. doi: 10.1038/642. [DOI] [PubMed] [Google Scholar]
  40. Yamada K. A., Tang C. M. Benzothiadiazides inhibit rapid glutamate receptor desensitization and enhance glutamatergic synaptic currents. J Neurosci. 1993 Sep;13(9):3904–3915. doi: 10.1523/JNEUROSCI.13-09-03904.1993. [DOI] [PMC free article] [PubMed] [Google Scholar]
  41. Zucker R. S. Calcium- and activity-dependent synaptic plasticity. Curr Opin Neurobiol. 1999 Jun;9(3):305–313. doi: 10.1016/s0959-4388(99)80045-2. [DOI] [PubMed] [Google Scholar]
  42. Zucker R. S. Changes in the statistics of transmitter release during facilitation. J Physiol. 1973 Mar;229(3):787–810. doi: 10.1113/jphysiol.1973.sp010167. [DOI] [PMC free article] [PubMed] [Google Scholar]
  43. Zucker R. S. Short-term synaptic plasticity. Annu Rev Neurosci. 1989;12:13–31. doi: 10.1146/annurev.ne.12.030189.000305. [DOI] [PubMed] [Google Scholar]
  44. von Gersdorff H., Schneggenburger R., Weis S., Neher E. Presynaptic depression at a calyx synapse: the small contribution of metabotropic glutamate receptors. J Neurosci. 1997 Nov 1;17(21):8137–8146. doi: 10.1523/JNEUROSCI.17-21-08137.1997. [DOI] [PMC free article] [PubMed] [Google Scholar]

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