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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1990 Sep;87(17):6718–6722. doi: 10.1073/pnas.87.17.6718

Biophysical model of a Hebbian synapse.

A Zador 1, C Koch 1, T H Brown 1
PMCID: PMC54608  PMID: 2168555

Abstract

We present a biophysical model of electrical and Ca(2+) dynamics following activation of N-methyl-D-aspartate (NMDA) receptors located on a dendritic spine. The model accounts for much of the phenomenology of the induction of long-term potentiation at a Hebbian synapse in hippocampal region CA1. Computer simulations suggested four important functions of spines in this Ca(2+)-dependent synaptic modification: (i) compartmentalizing transient changes in [Ca(2+)] to just those synapses that satisfy the conjunctive requirement for synaptic modification; (ii) isolating the spine head from changes in the [Ca(2+)] at the dendritic shaft; (iii) amplifying the concentration changes at those synapses; and (iv) increasing the voltage dependence of the processes underlying long term potentiation induction. This proposed role of spines in the regulation of Ca(2+) dynamics contrasts with traditional approaches to spine function that have stressed electronic properties. This model can be used to explore the computational implications of Hebbian synapses.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Ascher P., Nowak L. The role of divalent cations in the N-methyl-D-aspartate responses of mouse central neurones in culture. J Physiol. 1988 May;399:247–266. doi: 10.1113/jphysiol.1988.sp017078. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Barrionuevo G., Brown T. H. Associative long-term potentiation in hippocampal slices. Proc Natl Acad Sci U S A. 1983 Dec;80(23):7347–7351. doi: 10.1073/pnas.80.23.7347. [DOI] [PMC free article] [PubMed] [Google Scholar]
  3. Bekkers J. M., Stevens C. F. NMDA and non-NMDA receptors are co-localized at individual excitatory synapses in cultured rat hippocampus. Nature. 1989 Sep 21;341(6239):230–233. doi: 10.1038/341230a0. [DOI] [PubMed] [Google Scholar]
  4. Bliss T. V., Lomo T. Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path. J Physiol. 1973 Jul;232(2):331–356. doi: 10.1113/jphysiol.1973.sp010273. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Brown T. H., Chapman P. F., Kairiss E. W., Keenan C. L. Long-term synaptic potentiation. Science. 1988 Nov 4;242(4879):724–728. doi: 10.1126/science.2903551. [DOI] [PubMed] [Google Scholar]
  6. Brown T. H., Fricke R. A., Perkel D. H. Passive electrical constants in three classes of hippocampal neurons. J Neurophysiol. 1981 Oct;46(4):812–827. doi: 10.1152/jn.1981.46.4.812. [DOI] [PubMed] [Google Scholar]
  7. Brown T. H., Johnston D. Voltage-clamp analysis of mossy fiber synaptic input to hippocampal neurons. J Neurophysiol. 1983 Aug;50(2):487–507. doi: 10.1152/jn.1983.50.2.487. [DOI] [PubMed] [Google Scholar]
  8. Brown T. H., Kairiss E. W., Keenan C. L. Hebbian synapses: biophysical mechanisms and algorithms. Annu Rev Neurosci. 1990;13:475–511. doi: 10.1146/annurev.ne.13.030190.002355. [DOI] [PubMed] [Google Scholar]
  9. CHANG H. T. Cortical neurons with particular reference to the apical dendrites. Cold Spring Harb Symp Quant Biol. 1952;17:189–202. doi: 10.1101/sqb.1952.017.01.019. [DOI] [PubMed] [Google Scholar]
  10. Carnevale N. T., Johnston D. Electrophysiological characterization of remote chemical synapses. J Neurophysiol. 1982 Apr;47(4):606–621. doi: 10.1152/jn.1982.47.4.606. [DOI] [PubMed] [Google Scholar]
  11. Collingridge G. L., Kehl S. J., McLennan H. The antagonism of amino acid-induced excitations of rat hippocampal CA1 neurones in vitro. J Physiol. 1983 Jan;334:19–31. doi: 10.1113/jphysiol.1983.sp014477. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Cull-Candy S. G., Usowicz M. M. Multiple-conductance channels activated by excitatory amino acids in cerebellar neurons. Nature. 1987 Feb 5;325(6104):525–528. doi: 10.1038/325525a0. [DOI] [PubMed] [Google Scholar]
  13. Doerner D., Pitler T. A., Alger B. E. Protein kinase C activators block specific calcium and potassium current components in isolated hippocampal neurons. J Neurosci. 1988 Nov;8(11):4069–4078. doi: 10.1523/JNEUROSCI.08-11-04069.1988. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. Dunwiddie T., Lynch G. Long-term potentiation and depression of synaptic responses in the rat hippocampus: localization and frequency dependency. J Physiol. 1978 Mar;276:353–367. doi: 10.1113/jphysiol.1978.sp012239. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Forsythe I. D., Westbrook G. L. Slow excitatory postsynaptic currents mediated by N-methyl-D-aspartate receptors on cultured mouse central neurones. J Physiol. 1988 Feb;396:515–533. doi: 10.1113/jphysiol.1988.sp016975. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Gamble E., Koch C. The dynamics of free calcium in dendritic spines in response to repetitive synaptic input. Science. 1987 Jun 5;236(4806):1311–1315. doi: 10.1126/science.3495885. [DOI] [PubMed] [Google Scholar]
  17. Harris K. M., Stevens J. K. Dendritic spines of CA 1 pyramidal cells in the rat hippocampus: serial electron microscopy with reference to their biophysical characteristics. J Neurosci. 1989 Aug;9(8):2982–2997. doi: 10.1523/JNEUROSCI.09-08-02982.1989. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Hopfield J. J. Neurons with graded response have collective computational properties like those of two-state neurons. Proc Natl Acad Sci U S A. 1984 May;81(10):3088–3092. doi: 10.1073/pnas.81.10.3088. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. Jahr C. E., Stevens C. F. A quantitative description of NMDA receptor-channel kinetic behavior. J Neurosci. 1990 Jun;10(6):1830–1837. doi: 10.1523/JNEUROSCI.10-06-01830.1990. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Jahr C. E., Stevens C. F. Glutamate activates multiple single channel conductances in hippocampal neurons. Nature. 1987 Feb 5;325(6104):522–525. doi: 10.1038/325522a0. [DOI] [PubMed] [Google Scholar]
  21. Kelso S. R., Brown T. H. Differential conditioning of associative synaptic enhancement in hippocampal brain slices. Science. 1986 Apr 4;232(4746):85–87. doi: 10.1126/science.3952501. [DOI] [PubMed] [Google Scholar]
  22. Kelso S. R., Ganong A. H., Brown T. H. Hebbian synapses in hippocampus. Proc Natl Acad Sci U S A. 1986 Jul;83(14):5326–5330. doi: 10.1073/pnas.83.14.5326. [DOI] [PMC free article] [PubMed] [Google Scholar]
  23. Kennedy M. B. Regulation of synaptic transmission in the central nervous system: long-term potentiation. Cell. 1989 Dec 1;59(5):777–787. doi: 10.1016/0092-8674(89)90601-6. [DOI] [PubMed] [Google Scholar]
  24. Koch C., Poggio T. A theoretical analysis of electrical properties of spines. Proc R Soc Lond B Biol Sci. 1983 Jul 22;218(1213):455–477. doi: 10.1098/rspb.1983.0051. [DOI] [PubMed] [Google Scholar]
  25. Larson J., Lynch G. Theta pattern stimulation and the induction of LTP: the sequence in which synapses are stimulated determines the degree to which they potentiate. Brain Res. 1989 Jun 5;489(1):49–58. doi: 10.1016/0006-8993(89)90007-3. [DOI] [PubMed] [Google Scholar]
  26. Lynch G., Larson J., Kelso S., Barrionuevo G., Schottler F. Intracellular injections of EGTA block induction of hippocampal long-term potentiation. Nature. 1983 Oct 20;305(5936):719–721. doi: 10.1038/305719a0. [DOI] [PubMed] [Google Scholar]
  27. MacDermott A. B., Mayer M. L., Westbrook G. L., Smith S. J., Barker J. L. NMDA-receptor activation increases cytoplasmic calcium concentration in cultured spinal cord neurones. 1986 May 29-Jun 4Nature. 321(6069):519–522. doi: 10.1038/321519a0. [DOI] [PubMed] [Google Scholar]
  28. Malenka R. C., Kauer J. A., Zucker R. S., Nicoll R. A. Postsynaptic calcium is sufficient for potentiation of hippocampal synaptic transmission. Science. 1988 Oct 7;242(4875):81–84. doi: 10.1126/science.2845577. [DOI] [PubMed] [Google Scholar]
  29. Malinow R., Miller J. P. Postsynaptic hyperpolarization during conditioning reversibly blocks induction of long-term potentiation. Nature. 1986 Apr 10;320(6062):529–530. doi: 10.1038/320529a0. [DOI] [PubMed] [Google Scholar]
  30. Regehr W. G., Connor J. A., Tank D. W. Optical imaging of calcium accumulation in hippocampal pyramidal cells during synaptic activation. Nature. 1989 Oct 12;341(6242):533–536. doi: 10.1038/341533a0. [DOI] [PubMed] [Google Scholar]
  31. Richardson T. L., Turner R. W., Miller J. J. Action-potential discharge in hippocampal CA1 pyramidal neurons: current source-density analysis. J Neurophysiol. 1987 Nov;58(5):981–996. doi: 10.1152/jn.1987.58.5.981. [DOI] [PubMed] [Google Scholar]
  32. Stanton P. K., Sejnowski T. J. Associative long-term depression in the hippocampus induced by hebbian covariance. Nature. 1989 May 18;339(6221):215–218. doi: 10.1038/339215a0. [DOI] [PubMed] [Google Scholar]
  33. Traub R. D. Simulation of intrinsic bursting in CA3 hippocampal neurons. Neuroscience. 1982 May;7(5):1233–1242. doi: 10.1016/0306-4522(82)91130-7. [DOI] [PubMed] [Google Scholar]
  34. Wickens J. Electrically coupled but chemically isolated synapses: dendritic spines and calcium in a rule for synaptic modification. Prog Neurobiol. 1988;31(6):507–528. doi: 10.1016/0301-0082(88)90013-5. [DOI] [PubMed] [Google Scholar]
  35. Wigström H., Gustafsson B., Huang Y. Y., Abraham W. C. Hippocampal long-term potentiation is induced by pairing single afferent volleys with intracellularly injected depolarizing current pulses. Acta Physiol Scand. 1986 Feb;126(2):317–319. doi: 10.1111/j.1748-1716.1986.tb07822.x. [DOI] [PubMed] [Google Scholar]
  36. Wilson C. J. Passive cable properties of dendritic spines and spiny neurons. J Neurosci. 1984 Jan;4(1):281–297. doi: 10.1523/JNEUROSCI.04-01-00281.1984. [DOI] [PMC free article] [PubMed] [Google Scholar]

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