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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
. 1994 Apr 26;91(9):3941–3945. doi: 10.1073/pnas.91.9.3941

A model of dendritic spine Ca2+ concentration exploring possible bases for a sliding synaptic modification threshold.

J I Gold 1, M F Bear 1
PMCID: PMC43698  PMID: 8171016

Abstract

We used a biophysical model of an isolated dendritic spine to assess quantitatively the impact of changes in spine geometry, Ca2+ buffer concentration, and channel kinetics on Ca2+ dynamics following high-frequency activation of N-methyl-D-aspartate receptors. We found that varying the buffer concentration in the postsynaptic density from 50 to 500 microM can result in an 8-fold difference in the peak Ca2+ concentration following three pulses at 100 Hz. Similarly, varying the spine neck diameter from 0.1 to 0.55 micron can result in a 15-fold difference in the peak Ca2+ concentration. The amplification of peak Ca2+ concentration also depended on temporal summation of N-methyl-D-aspartate-mediated excitatory postsynaptic currents. Variation of the current duration on the order of 100 msec can significantly affect summation at a given stimulation frequency, resulting in a 10-fold difference in the peak Ca2+ concentration at 100 Hz. It is suggested that activity-dependent modifications of these parameters may be important for the regulation of synaptic plasticity in the brain.

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Selected References

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  1. Baranyi A., Szente M. B. Long-lasting potentiation of synaptic transmission requires postsynaptic modifications in the neocortex. Brain Res. 1987 Oct 13;423(1-2):378–384. doi: 10.1016/0006-8993(87)90867-5. [DOI] [PubMed] [Google Scholar]
  2. Bear M. F., Cooper L. N., Ebner F. F. A physiological basis for a theory of synapse modification. Science. 1987 Jul 3;237(4810):42–48. doi: 10.1126/science.3037696. [DOI] [PubMed] [Google Scholar]
  3. Bienenstock E. L., Cooper L. N., Munro P. W. Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. J Neurosci. 1982 Jan;2(1):32–48. doi: 10.1523/JNEUROSCI.02-01-00032.1982. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Bindman L. J., Murphy K. P., Pockett S. Postsynaptic control of the induction of long-term changes in efficacy of transmission at neocortical synapses in slices of rat brain. J Neurophysiol. 1988 Sep;60(3):1053–1065. doi: 10.1152/jn.1988.60.3.1053. [DOI] [PubMed] [Google Scholar]
  5. Blaustein M. P. Calcium transport and buffering in neurons. Trends Neurosci. 1988 Oct;11(10):438–443. doi: 10.1016/0166-2236(88)90195-6. [DOI] [PubMed] [Google Scholar]
  6. Blaustein M. P. The ins and outs of calcium transport in squid axons: internal and external ion activation of calcium efflux. Fed Proc. 1976 Dec;35(14):2574–2578. [PubMed] [Google Scholar]
  7. 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]
  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. Carafoli E. Intracellular calcium homeostasis. Annu Rev Biochem. 1987;56:395–433. doi: 10.1146/annurev.bi.56.070187.002143. [DOI] [PubMed] [Google Scholar]
  10. Carmignoto G., Vicini S. Activity-dependent decrease in NMDA receptor responses during development of the visual cortex. Science. 1992 Nov 6;258(5084):1007–1011. doi: 10.1126/science.1279803. [DOI] [PubMed] [Google Scholar]
  11. Chang F. L., Greenough W. T. Transient and enduring morphological correlates of synaptic activity and efficacy change in the rat hippocampal slice. Brain Res. 1984 Aug 20;309(1):35–46. doi: 10.1016/0006-8993(84)91008-4. [DOI] [PubMed] [Google Scholar]
  12. Clothiaux E. E., Bear M. F., Cooper L. N. Synaptic plasticity in visual cortex: comparison of theory with experiment. J Neurophysiol. 1991 Nov;66(5):1785–1804. doi: 10.1152/jn.1991.66.5.1785. [DOI] [PubMed] [Google Scholar]
  13. Colino A., Malenka R. C. Mechanisms underlying induction of long-term potentiation in rat medial and lateral perforant paths in vitro. J Neurophysiol. 1993 Apr;69(4):1150–1159. doi: 10.1152/jn.1993.69.4.1150. [DOI] [PubMed] [Google Scholar]
  14. Collingridge G. L., Kehl S. J., McLennan H. Excitatory amino acids in synaptic transmission in the Schaffer collateral-commissural pathway of the rat hippocampus. J Physiol. 1983 Jan;334:33–46. doi: 10.1113/jphysiol.1983.sp014478. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Cooper L. N., Scofield C. L. Mean-field theory of a neural network. Proc Natl Acad Sci U S A. 1988 Mar;85(6):1973–1977. doi: 10.1073/pnas.85.6.1973. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Dunwiddie T. V., Lynch G. The relationship between extracellular calcium concentrations and the induction of hippocampal long-term potentiation. Brain Res. 1979 Jun 15;169(1):103–110. doi: 10.1016/0006-8993(79)90377-9. [DOI] [PubMed] [Google Scholar]
  17. 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]
  18. Gustafsson B., Wigström H. Physiological mechanisms underlying long-term potentiation. Trends Neurosci. 1988 Apr;11(4):156–162. doi: 10.1016/0166-2236(88)90142-7. [DOI] [PubMed] [Google Scholar]
  19. 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]
  20. Harvey J., Collingridge G. L. Thapsigargin blocks the induction of long-term potentiation in rat hippocampal slices. Neurosci Lett. 1992 May 25;139(2):197–200. doi: 10.1016/0304-3940(92)90551-h. [DOI] [PubMed] [Google Scholar]
  21. Hestrin S. Developmental regulation of NMDA receptor-mediated synaptic currents at a central synapse. Nature. 1992 Jun 25;357(6380):686–689. doi: 10.1038/357686a0. [DOI] [PubMed] [Google Scholar]
  22. Holmes W. R. Is the function of dendritic spines to concentrate calcium? Brain Res. 1990 Jun 11;519(1-2):338–342. doi: 10.1016/0006-8993(90)90098-v. [DOI] [PubMed] [Google Scholar]
  23. Holmes W. R., Levy W. B. Insights into associative long-term potentiation from computational models of NMDA receptor-mediated calcium influx and intracellular calcium concentration changes. J Neurophysiol. 1990 May;63(5):1148–1168. doi: 10.1152/jn.1990.63.5.1148. [DOI] [PubMed] [Google Scholar]
  24. Huang Y. Y., Colino A., Selig D. K., Malenka R. C. The influence of prior synaptic activity on the induction of long-term potentiation. Science. 1992 Feb 7;255(5045):730–733. doi: 10.1126/science.1346729. [DOI] [PubMed] [Google Scholar]
  25. 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]
  26. Kato N., Artola A., Singer W. Developmental changes in the susceptibility to long-term potentiation of neurones in rat visual cortex slices. Brain Res Dev Brain Res. 1991 May 20;60(1):43–50. doi: 10.1016/0165-3806(91)90153-a. [DOI] [PubMed] [Google Scholar]
  27. 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]
  28. Kirkwood A., Bear M. F. Hebbian synapses in visual cortex. J Neurosci. 1994 Mar;14(3 Pt 2):1634–1645. doi: 10.1523/JNEUROSCI.14-03-01634.1994. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Koch C., Zador A. The function of dendritic spines: devices subserving biochemical rather than electrical compartmentalization. J Neurosci. 1993 Feb;13(2):413–422. doi: 10.1523/JNEUROSCI.13-02-00413.1993. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Lee K. S., Schottler F., Oliver M., Lynch G. Brief bursts of high-frequency stimulation produce two types of structural change in rat hippocampus. J Neurophysiol. 1980 Aug;44(2):247–258. doi: 10.1152/jn.1980.44.2.247. [DOI] [PubMed] [Google Scholar]
  31. Lester R. A., Clements J. D., Westbrook G. L., Jahr C. E. Channel kinetics determine the time course of NMDA receptor-mediated synaptic currents. Nature. 1990 Aug 9;346(6284):565–567. doi: 10.1038/346565a0. [DOI] [PubMed] [Google Scholar]
  32. Lowenstein D. H., Miles M. F., Hatam F., McCabe T. Up regulation of calbindin-D28K mRNA in the rat hippocampus following focal stimulation of the perforant path. Neuron. 1991 Apr;6(4):627–633. doi: 10.1016/0896-6273(91)90065-8. [DOI] [PubMed] [Google Scholar]
  33. 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]
  34. 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]
  35. 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]
  36. Mayer M. L., MacDermott A. B., Westbrook G. L., Smith S. J., Barker J. L. Agonist- and voltage-gated calcium entry in cultured mouse spinal cord neurons under voltage clamp measured using arsenazo III. J Neurosci. 1987 Oct;7(10):3230–3244. doi: 10.1523/JNEUROSCI.07-10-03230.1987. [DOI] [PMC free article] [PubMed] [Google Scholar]
  37. Mayer M. L., Westbrook G. L., Guthrie P. B. Voltage-dependent block by Mg2+ of NMDA responses in spinal cord neurones. Nature. 1984 May 17;309(5965):261–263. doi: 10.1038/309261a0. [DOI] [PubMed] [Google Scholar]
  38. Miller J. P., Rall W., Rinzel J. Synaptic amplification by active membrane in dendritic spines. Brain Res. 1985 Jan 28;325(1-2):325–330. doi: 10.1016/0006-8993(85)90333-6. [DOI] [PubMed] [Google Scholar]
  39. Mize R. R., Luo Q. Visual deprivation fails to reduce calbindin 28kD or GABA immunoreactivity in the rhesus monkey superior colliculus. Vis Neurosci. 1992 Aug;9(2):157–168. doi: 10.1017/s0952523800009627. [DOI] [PubMed] [Google Scholar]
  40. Nowak L., Bregestovski P., Ascher P., Herbet A., Prochiantz A. Magnesium gates glutamate-activated channels in mouse central neurones. Nature. 1984 Feb 2;307(5950):462–465. doi: 10.1038/307462a0. [DOI] [PubMed] [Google Scholar]
  41. 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]
  42. Wigström H., Swann J. W., Andersen P. Calcium dependency of synaptic long-lasting potentiation in the hippocampal slice. Acta Physiol Scand. 1979 Jan;105(1):126–128. doi: 10.1111/j.1748-1716.1979.tb06323.x. [DOI] [PubMed] [Google Scholar]
  43. 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]
  44. Zador A., Koch C., Brown T. H. Biophysical model of a Hebbian synapse. Proc Natl Acad Sci U S A. 1990 Sep;87(17):6718–6722. doi: 10.1073/pnas.87.17.6718. [DOI] [PMC free article] [PubMed] [Google Scholar]
  45. Zalutsky R. A., Nicoll R. A. Comparison of two forms of long-term potentiation in single hippocampal neurons. Science. 1990 Jun 29;248(4963):1619–1624. doi: 10.1126/science.2114039. [DOI] [PubMed] [Google Scholar]

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