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. 1999 Feb;76(2):735–750. doi: 10.1016/S0006-3495(99)77240-1

Modeling study of the effects of overlapping Ca2+ microdomains on neurotransmitter release.

R Bertram 1, G D Smith 1, A Sherman 1
PMCID: PMC1300078  PMID: 9929478

Abstract

Although single-channel Ca2+ microdomains are capable of gating neurotransmitter release in some instances, it is likely that in many cases the microdomains from several open channels overlap to activate vesicle fusion. We describe a mathematical model in which transmitter release is gated by single or overlapping Ca2+ microdomains produced by the opening of nearby Ca2+ channels. This model accounts for the presence of a mobile Ca2+ buffer, provided either that the buffer is unsaturable or that it is saturated near an open channel with Ca2+ binding kinetics that are rapid relative to Ca2+ diffusion. We show that the release time course is unaffected by the location of the channels (at least for distances up to 50 nm), but paired-pulse facilitation is greater when the channels are farther from the release sites. We then develop formulas relating the fractional release following selective or random channel blockage to the cooperative relationship between release and the presynaptic Ca2+ current. These formulas are used with the transmitter release model to study the dependence of this form of cooperativity, which we call Ca2+ current cooperativity, on mobile buffers and on the local geometry of Ca2+ channels. We find that Ca2+ current cooperativity increases with the number of channels per release site, but is considerably less than the number of channels, the theoretical upper bound. In the presence of a saturating mobile buffer the Ca2+ current cooperativity is greater, and it increases more rapidly with the number of channels. Finally, Ca2+ current cooperativity is an increasing function of channel distance, particularly in the presence of saturating mobile buffer.

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Selected References

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  1. Adler E. M., Augustine G. J., Duffy S. N., Charlton M. P. Alien intracellular calcium chelators attenuate neurotransmitter release at the squid giant synapse. J Neurosci. 1991 Jun;11(6):1496–1507. doi: 10.1523/JNEUROSCI.11-06-01496.1991. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Aharon S., Bercovier M., Parnas H. Parallel computation enables precise description of Ca2+ distribution in nerve terminals. Bull Math Biol. 1996 Nov;58(6):1075–1097. doi: 10.1007/BF02458384. [DOI] [PubMed] [Google Scholar]
  3. Aharon S., Parnas H., Parnas I. The magnitude and significance of Ca2+ domains for release of neurotransmitter. Bull Math Biol. 1994 Nov;56(6):1095–1119. doi: 10.1007/BF02460288. [DOI] [PubMed] [Google Scholar]
  4. Allbritton N. L., Meyer T., Stryer L. Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate. Science. 1992 Dec 11;258(5089):1812–1815. doi: 10.1126/science.1465619. [DOI] [PubMed] [Google Scholar]
  5. Augustine G. J., Adler E. M., Charlton M. P. The calcium signal for transmitter secretion from presynaptic nerve terminals. Ann N Y Acad Sci. 1991;635:365–381. doi: 10.1111/j.1749-6632.1991.tb36505.x. [DOI] [PubMed] [Google Scholar]
  6. Augustine G. J., Charlton M. P. Calcium dependence of presynaptic calcium current and post-synaptic response at the squid giant synapse. J Physiol. 1986 Dec;381:619–640. doi: 10.1113/jphysiol.1986.sp016347. [DOI] [PMC free article] [PubMed] [Google Scholar]
  7. Augustine G. J., Charlton M. P., Smith S. J. Calcium entry and transmitter release at voltage-clamped nerve terminals of squid. J Physiol. 1985 Oct;367:163–181. doi: 10.1113/jphysiol.1985.sp015819. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Augustine G. J. Regulation of transmitter release at the squid giant synapse by presynaptic delayed rectifier potassium current. J Physiol. 1990 Dec;431:343–364. doi: 10.1113/jphysiol.1990.sp018333. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Bennett M. R., Gibson W. G., Robinson J. Probabilistic secretion of quanta and the synaptosecretosome hypothesis: evoked release at active zones of varicosities, boutons, and endplates. Biophys J. 1997 Oct;73(4):1815–1829. doi: 10.1016/S0006-3495(97)78212-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Bennett M. R., Gibson W. G., Robinson J. Probabilistic secretion of quanta: spontaneous release at active zones of varicosities, boutons, and endplates. Biophys J. 1995 Jul;69(1):42–56. doi: 10.1016/S0006-3495(95)79873-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Bertram R. A simple model of transmitter release and facilitation. Neural Comput. 1997 Apr 1;9(3):515–523. doi: 10.1162/neco.1997.9.3.515. [DOI] [PubMed] [Google Scholar]
  12. Bertram R., Sherman A., Stanley E. F. Single-domain/bound calcium hypothesis of transmitter release and facilitation. J Neurophysiol. 1996 May;75(5):1919–1931. doi: 10.1152/jn.1996.75.5.1919. [DOI] [PubMed] [Google Scholar]
  13. 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]
  14. Brose N., Petrenko A. G., Südhof T. C., Jahn R. Synaptotagmin: a calcium sensor on the synaptic vesicle surface. Science. 1992 May 15;256(5059):1021–1025. doi: 10.1126/science.1589771. [DOI] [PubMed] [Google Scholar]
  15. Charlton M. P., Bittner G. D. Presynaptic potentials and facilitation of transmitter release in the squid giant synapse. J Gen Physiol. 1978 Oct;72(4):487–511. doi: 10.1085/jgp.72.4.487. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Cooper R. L., Winslow J. L., Govind C. K., Atwood H. L. Synaptic structural complexity as a factor enhancing probability of calcium-mediated transmitter release. J Neurophysiol. 1996 Jun;75(6):2451–2466. doi: 10.1152/jn.1996.75.6.2451. [DOI] [PubMed] [Google Scholar]
  17. Datyner N. B., Gage P. W. Phasic secretion of acetylcholine at a mammalian neuromuscular junction. J Physiol. 1980 Jun;303:299–314. doi: 10.1113/jphysiol.1980.sp013286. [DOI] [PMC free article] [PubMed] [Google Scholar]
  18. Davletov B. A., Südhof T. C. A single C2 domain from synaptotagmin I is sufficient for high affinity Ca2+/phospholipid binding. J Biol Chem. 1993 Dec 15;268(35):26386–26390. [PubMed] [Google Scholar]
  19. Delaney K. R., Zucker R. S., Tank D. W. Calcium in motor nerve terminals associated with posttetanic potentiation. J Neurosci. 1989 Oct;9(10):3558–3567. doi: 10.1523/JNEUROSCI.09-10-03558.1989. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Dodge F. A., Jr, Rahamimoff R. Co-operative action a calcium ions in transmitter release at the neuromuscular junction. J Physiol. 1967 Nov;193(2):419–432. doi: 10.1113/jphysiol.1967.sp008367. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Dunlap K., Luebke J. I., Turner T. J. Exocytotic Ca2+ channels in mammalian central neurons. Trends Neurosci. 1995 Feb;18(2):89–98. [PubMed] [Google Scholar]
  22. Falke J. J., Drake S. K., Hazard A. L., Peersen O. B. Molecular tuning of ion binding to calcium signaling proteins. Q Rev Biophys. 1994 Aug;27(3):219–290. doi: 10.1017/s0033583500003012. [DOI] [PubMed] [Google Scholar]
  23. Fogelson A. L., Zucker R. S. Presynaptic calcium diffusion from various arrays of single channels. Implications for transmitter release and synaptic facilitation. Biophys J. 1985 Dec;48(6):1003–1017. doi: 10.1016/S0006-3495(85)83863-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Geppert M., Goda Y., Hammer R. E., Li C., Rosahl T. W., Stevens C. F., Südhof T. C. Synaptotagmin I: a major Ca2+ sensor for transmitter release at a central synapse. Cell. 1994 Nov 18;79(4):717–727. doi: 10.1016/0092-8674(94)90556-8. [DOI] [PubMed] [Google Scholar]
  25. Goldman D. E. POTENTIAL, IMPEDANCE, AND RECTIFICATION IN MEMBRANES. J Gen Physiol. 1943 Sep 20;27(1):37–60. doi: 10.1085/jgp.27.1.37. [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. HODGKIN A. L., HUXLEY A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. doi: 10.1113/jphysiol.1952.sp004764. [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Haydon P. G., Henderson E., Stanley E. F. Localization of individual calcium channels at the release face of a presynaptic nerve terminal. Neuron. 1994 Dec;13(6):1275–1280. doi: 10.1016/0896-6273(94)90414-6. [DOI] [PubMed] [Google Scholar]
  28. Heidelberger R., Heinemann C., Neher E., Matthews G. Calcium dependence of the rate of exocytosis in a synaptic terminal. Nature. 1994 Oct 6;371(6497):513–515. doi: 10.1038/371513a0. [DOI] [PubMed] [Google Scholar]
  29. Heuser J. E., Reese T. S., Landis D. M. Functional changes in frog neuromuscular junctions studied with freeze-fracture. J Neurocytol. 1974 Mar;3(1):109–131. doi: 10.1007/BF01111936. [DOI] [PubMed] [Google Scholar]
  30. Issa N. P., Hudspeth A. J. The entry and clearance of Ca2+ at individual presynaptic active zones of hair cells from the bullfrog's sacculus. Proc Natl Acad Sci U S A. 1996 Sep 3;93(18):9527–9532. doi: 10.1073/pnas.93.18.9527. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Katz B., Miledi R. The role of calcium in neuromuscular facilitation. J Physiol. 1968 Mar;195(2):481–492. doi: 10.1113/jphysiol.1968.sp008469. [DOI] [PMC free article] [PubMed] [Google Scholar]
  32. Klingauf J., Neher E. Modeling buffered Ca2+ diffusion near the membrane: implications for secretion in neuroendocrine cells. Biophys J. 1997 Feb;72(2 Pt 1):674–690. doi: 10.1016/s0006-3495(97)78704-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Llinás R., Steinberg I. Z., Walton K. Presynaptic calcium currents in squid giant synapse. Biophys J. 1981 Mar;33(3):289–321. doi: 10.1016/S0006-3495(81)84898-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  34. Llinás R., Steinberg I. Z., Walton K. Relationship between presynaptic calcium current and postsynaptic potential in squid giant synapse. Biophys J. 1981 Mar;33(3):323–351. doi: 10.1016/S0006-3495(81)84899-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Llinás R., Sugimori M., Silver R. B. Microdomains of high calcium concentration in a presynaptic terminal. Science. 1992 May 1;256(5057):677–679. doi: 10.1126/science.1350109. [DOI] [PubMed] [Google Scholar]
  36. Luebke J. I., Dunlap K., Turner T. J. Multiple calcium channel types control glutamatergic synaptic transmission in the hippocampus. Neuron. 1993 Nov;11(5):895–902. doi: 10.1016/0896-6273(93)90119-c. [DOI] [PubMed] [Google Scholar]
  37. Mintz I. M., Sabatini B. L., Regehr W. G. Calcium control of transmitter release at a cerebellar synapse. Neuron. 1995 Sep;15(3):675–688. doi: 10.1016/0896-6273(95)90155-8. [DOI] [PubMed] [Google Scholar]
  38. Naraghi M., Neher E. Linearized buffered Ca2+ diffusion in microdomains and its implications for calculation of [Ca2+] at the mouth of a calcium channel. J Neurosci. 1997 Sep 15;17(18):6961–6973. doi: 10.1523/JNEUROSCI.17-18-06961.1997. [DOI] [PMC free article] [PubMed] [Google Scholar]
  39. Neher E., Augustine G. J. Calcium gradients and buffers in bovine chromaffin cells. J Physiol. 1992 May;450:273–301. doi: 10.1113/jphysiol.1992.sp019127. [DOI] [PMC free article] [PubMed] [Google Scholar]
  40. Parnas H., Dudel J., Parnas I. Neurotransmitter release and its facilitation in crayfish. I. Saturation kinetics of release, and of entry and removal of calcium. Pflugers Arch. 1982 Mar;393(1):1–14. doi: 10.1007/BF00582384. [DOI] [PubMed] [Google Scholar]
  41. Parnas H., Segel L. A. A theoretical study of calcium entry in nerve terminals, with application to neurotransmitter release. J Theor Biol. 1981 Jul 7;91(1):125–169. doi: 10.1016/0022-5193(81)90378-7. [DOI] [PubMed] [Google Scholar]
  42. Pethig R., Kuhn M., Payne R., Adler E., Chen T. H., Jaffe L. F. On the dissociation constants of BAPTA-type calcium buffers. Cell Calcium. 1989 Oct;10(7):491–498. doi: 10.1016/0143-4160(89)90026-2. [DOI] [PubMed] [Google Scholar]
  43. Rahamimoff R. A dual effect of calcium ions on neuromuscular facilitation. J Physiol. 1968 Mar;195(2):471–480. doi: 10.1113/jphysiol.1968.sp008468. [DOI] [PMC free article] [PubMed] [Google Scholar]
  44. Regehr W. G., Mintz I. M. Participation of multiple calcium channel types in transmission at single climbing fiber to Purkinje cell synapses. Neuron. 1994 Mar;12(3):605–613. doi: 10.1016/0896-6273(94)90216-x. [DOI] [PubMed] [Google Scholar]
  45. Reid C. A., Bekkers J. M., Clements J. D. N- and P/Q-type Ca2+ channels mediate transmitter release with a similar cooperativity at rat hippocampal autapses. J Neurosci. 1998 Apr 15;18(8):2849–2855. doi: 10.1523/JNEUROSCI.18-08-02849.1998. [DOI] [PMC free article] [PubMed] [Google Scholar]
  46. Roberts W. M., Jacobs R. A., Hudspeth A. J. Colocalization of ion channels involved in frequency selectivity and synaptic transmission at presynaptic active zones of hair cells. J Neurosci. 1990 Nov;10(11):3664–3684. doi: 10.1523/JNEUROSCI.10-11-03664.1990. [DOI] [PMC free article] [PubMed] [Google Scholar]
  47. Sabatini B. L., Regehr W. G. Timing of neurotransmission at fast synapses in the mammalian brain. Nature. 1996 Nov 14;384(6605):170–172. doi: 10.1038/384170a0. [DOI] [PubMed] [Google Scholar]
  48. Simon S. M., Llinás R. R. Compartmentalization of the submembrane calcium activity during calcium influx and its significance in transmitter release. Biophys J. 1985 Sep;48(3):485–498. doi: 10.1016/S0006-3495(85)83804-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  49. Sinha S. R., Wu L. G., Saggau P. Presynaptic calcium dynamics and transmitter release evoked by single action potentials at mammalian central synapses. Biophys J. 1997 Feb;72(2 Pt 1):637–651. doi: 10.1016/s0006-3495(97)78702-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  50. Smith A. B., Cunnane T. C. Multiple calcium channels control neurotransmitter release from rat postganglionic sympathetic nerve terminals. J Physiol. 1997 Mar 1;499(Pt 2):341–349. doi: 10.1113/jphysiol.1997.sp021931. [DOI] [PMC free article] [PubMed] [Google Scholar]
  51. Smith G. D. Analytical steady-state solution to the rapid buffering approximation near an open Ca2+ channel. Biophys J. 1996 Dec;71(6):3064–3072. doi: 10.1016/S0006-3495(96)79500-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  52. Smith G. D., Wagner J., Keizer J. Validity of the rapid buffering approximation near a point source of calcium ions. Biophys J. 1996 Jun;70(6):2527–2539. doi: 10.1016/S0006-3495(96)79824-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  53. Stanley E. F. Decline in calcium cooperativity as the basis of facilitation at the squid giant synapse. J Neurosci. 1986 Mar;6(3):782–789. doi: 10.1523/JNEUROSCI.06-03-00782.1986. [DOI] [PMC free article] [PubMed] [Google Scholar]
  54. Stanley E. F. Single calcium channels and acetylcholine release at a presynaptic nerve terminal. Neuron. 1993 Dec;11(6):1007–1011. doi: 10.1016/0896-6273(93)90214-c. [DOI] [PubMed] [Google Scholar]
  55. Stern M. D. Buffering of calcium in the vicinity of a channel pore. Cell Calcium. 1992 Mar;13(3):183–192. doi: 10.1016/0143-4160(92)90046-u. [DOI] [PubMed] [Google Scholar]
  56. Swandulla D., Hans M., Zipser K., Augustine G. J. Role of residual calcium in synaptic depression and posttetanic potentiation: fast and slow calcium signaling in nerve terminals. Neuron. 1991 Dec;7(6):915–926. doi: 10.1016/0896-6273(91)90337-y. [DOI] [PubMed] [Google Scholar]
  57. Südhof T. C., Rizo J. Synaptotagmins: C2-domain proteins that regulate membrane traffic. Neuron. 1996 Sep;17(3):379–388. doi: 10.1016/s0896-6273(00)80171-3. [DOI] [PubMed] [Google Scholar]
  58. Turner T. J., Adams M. E., Dunlap K. Multiple Ca2+ channel types coexist to regulate synaptosomal neurotransmitter release. Proc Natl Acad Sci U S A. 1993 Oct 15;90(20):9518–9522. doi: 10.1073/pnas.90.20.9518. [DOI] [PMC free article] [PubMed] [Google Scholar]
  59. Wagner J., Keizer J. Effects of rapid buffers on Ca2+ diffusion and Ca2+ oscillations. Biophys J. 1994 Jul;67(1):447–456. doi: 10.1016/S0006-3495(94)80500-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  60. Wheeler D. B., Randall A., Tsien R. W. Roles of N-type and Q-type Ca2+ channels in supporting hippocampal synaptic transmission. Science. 1994 Apr 1;264(5155):107–111. doi: 10.1126/science.7832825. [DOI] [PubMed] [Google Scholar]
  61. Winslow J. L., Duffy S. N., Charlton M. P. Homosynaptic facilitation of transmitter release in crayfish is not affected by mobile calcium chelators: implications for the residual ionized calcium hypothesis from electrophysiological and computational analyses. J Neurophysiol. 1994 Oct;72(4):1769–1793. doi: 10.1152/jn.1994.72.4.1769. [DOI] [PubMed] [Google Scholar]
  62. Wu L. G., Saggau P. Block of multiple presynaptic calcium channel types by omega-conotoxin-MVIIC at hippocampal CA3 to CA1 synapses. J Neurophysiol. 1995 May;73(5):1965–1972. doi: 10.1152/jn.1995.73.5.1965. [DOI] [PubMed] [Google Scholar]
  63. Wu L. G., Saggau P. Pharmacological identification of two types of presynaptic voltage-dependent calcium channels at CA3-CA1 synapses of the hippocampus. J Neurosci. 1994 Sep;14(9):5613–5622. doi: 10.1523/JNEUROSCI.14-09-05613.1994. [DOI] [PMC free article] [PubMed] [Google Scholar]
  64. Wu L. G., Saggau P. Presynaptic inhibition of elicited neurotransmitter release. Trends Neurosci. 1997 May;20(5):204–212. doi: 10.1016/s0166-2236(96)01015-6. [DOI] [PubMed] [Google Scholar]
  65. Xu T., Naraghi M., Kang H., Neher E. Kinetic studies of Ca2+ binding and Ca2+ clearance in the cytosol of adrenal chromaffin cells. Biophys J. 1997 Jul;73(1):532–545. doi: 10.1016/S0006-3495(97)78091-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  66. Yamada W. M., Zucker R. S. Time course of transmitter release calculated from simulations of a calcium diffusion model. Biophys J. 1992 Mar;61(3):671–682. doi: 10.1016/S0006-3495(92)81872-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  67. Yoshikami D., Bagabaldo Z., Olivera B. M. The inhibitory effects of omega-conotoxins on Ca channels and synapses. Ann N Y Acad Sci. 1989;560:230–248. doi: 10.1111/j.1749-6632.1989.tb24100.x. [DOI] [PubMed] [Google Scholar]

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