A kinetic model unifying presynaptic short-term facilitation and depression

  • Chuang-Chung J. Lee
  • Mihai Anton
  • Chi-Sang Poon
  • Gregory J. McRaeEmail author


Short-term facilitation and depression refer to the increase and decrease of synaptic strength under repetitive stimuli within a timescale of milliseconds to seconds. This phenomenon has been attributed to primarily presynaptic mechanisms such as calcium-dependent transmitter release and presynaptic vesicle depletion. Previous modeling studies that aimed to integrate the complex short-term facilitation and short-term depression data derived from varying synapses have relied on computer simulation or abstract mathematical approaches. Here, we propose a unified theory of synaptic short-term plasticity based on realistic yet tractable and testable model descriptions of the underlying intracellular biochemical processes. Analysis of the model equations leads to a closed-form solution of the resonance frequency, a function of several critical biophysical parameters, as the single key indicator of the propensity for synaptic facilitation or depression under repetitive stimuli. This integrative model is supported by a broad range of transient and frequency response experimental data including those from facilitating, depressing or mixed-mode synapses. Specifically, the theory predicts that high calcium initial concentration and large gain of calcium action result in low resonance frequency and hence depressing behavior. In contrast, for synapses that are less sensitive to calcium or have higher recovery rate, resonance frequency becomes higher and thus facilitation prevails. The notion of resonance frequency therefore allows valuable quantitative parametric assessment of the contributions of various presynaptic mechanisms to the directionality of synaptic short-term plasticity. Thus, the model provides the reasons behind the switching behavior between facilitation and depression observed in experiments. New experiments are also suggested to control the short-term synaptic signal processing through adjusting the resonance frequency and bandwidth.


Short-term depression/facilitation Transmitter release Frequency response Resonance frequency 



Chi-Sang Poon was supported by NIH grants HL067966, HL072848, and EB005460


  1. Abbott, L. F., Varela, J. A., Sen, K., & Nelson, S. B. (1997). Synaptic depression and cortical gain control. Science, 275, 221–224. doi: 10.1126/science.275.5297.221.CrossRefGoogle Scholar
  2. Akopian, G., & Walsh, J. P. (2002). Corticostriatal paired-pulse potentiation produced by voltage-dependent activation of NMDA receptors and L-type Ca2+ channels. Journal of Neurophysiology, 87, 157–165.PubMedGoogle Scholar
  3. Atluri, P. P., & Regehr, W. G. (1996). Determinants of the time course of facilitation at the granule cell to purkinje cell synapse. The Journal of Neuroscience, 16, 5661–5671.PubMedGoogle Scholar
  4. Augustine, G. J. (2001). How does calcium trigger neurotransmitter release. Current Opinion in Neurobiology, 11, 320–326. doi: 10.1016/S0959-4388(00)00214-2.PubMedCrossRefGoogle Scholar
  5. Bertram, R., Sherman, A., & Stanley, E. F. (1996). Single-domain/bound calcium hypothesis of transmitter release and facilitation. Journal of Neurophysiology, 75, 1919–1931.PubMedGoogle Scholar
  6. Betz, W. (1970). Depression of transmitter release at the neuromuscular junction of the frog. The Journal of Physiology, 206, 629–644.PubMedGoogle Scholar
  7. Blitz, D. M., Foster, K. A., & Regehr, W. G. (2004). Short-term synaptic plasticity: A comparison of two synapses. Nature Reviews Neuroscience, 5, 630–640. doi: 10.1038/nrn1475.PubMedCrossRefGoogle Scholar
  8. Byrne, J. H. (1982). Analysis of synaptic depression contributing to habituation of gill-withdrawal reflex in Aplysia californica. Journal of Neurophysiology, 48, 431–438.PubMedGoogle Scholar
  9. Byrne, J. H., & Kandel, E. R. (1996). Presynaptic facilitation revisited: State and time dependence. The Journal of Neuroscience, 16, 425–435.PubMedGoogle Scholar
  10. Dekay, J. G., Chang, T. C., Mills, N., Speed, H. E., & Dobrunz, L. E. (2006). Responses of excitatory hippocampal synapses to natural stimulus patterns reveal a decrease in short-term facilitation and increase in short-term depression during postnatal development. Hippocampus, 16, 66–79. doi: 10.1002/hipo.20132.PubMedCrossRefGoogle Scholar
  11. Del Castillo, J., & Katz, B. (1954). Statistical factors involved in neuromuscular facilitation and depression. The Journal of Physiology, 124, 574–585.PubMedGoogle Scholar
  12. Destexhe, A., Mainen, Z. F., & Sejnowski, T. J. (1994). Synthesis of models for excitable membranes, synaptic transmission and neuromodulation using a common kinetic formalism. Journal of Computational Neuroscience, 1, 195–230. doi: 10.1007/BF00961734.PubMedCrossRefGoogle Scholar
  13. Dittman, J. S., & Regehr, W. G. (1998). Calcium dependence and recovery kinetics of presynaptic depression at the climbing fiber to Purkinje cell synapse. The Journal of Neuroscience, 18, 6147–6162.PubMedGoogle Scholar
  14. Dittman, J. S., Kreitzer, A. C., & Regehr, W. G. (2000). Interplay between facilitation, depression, and residual calcium at three presynaptic terminals. The Journal of Neuroscience, 20, 1374–1385.PubMedGoogle Scholar
  15. Dodge, F. A., Jr., & Rahamimoff, R. (1967). Co-operative action a calcium ions in transmitter release at the neuromuscular junction. The Journal of Physiology, 193, 419–432.PubMedGoogle Scholar
  16. Fernández-Chacón, R., Königstorfer, A., Gerber, S. H., García, J., Matos, M. F., Stevens, C. F., et al. (2001). Synaptotagmin I functions as a calcium regulator of release probability. Nature, 410, 41–49. doi: 10.1038/35065004.PubMedCrossRefGoogle Scholar
  17. Fortune, E. S., & Rose, G. J. (2001). Short-term synaptic plasticity as a temporal filter. Trends in Neurosciences, 24, 381–385. doi: 10.1016/S0166-2236(00)01835-X.PubMedCrossRefGoogle Scholar
  18. Fuhrmann G., Segev I., Markram H., Tsodyks M. (2002). Coding of temporal information by activity-dependent synapses. J Neurophysiol, 87, 140–148.PubMedGoogle Scholar
  19. Gingrich, K. J., & Byrne, J. H. (1985). Simulation of synaptic depression, posttetanic potentiation, and presynaptic facilitation of synaptic potentials from sensory neurons mediating gill-withdrawal reflex in Aplysia. Journal of Neurophysiology, 53, 652–669.PubMedGoogle Scholar
  20. Goda, Y., & Stevens, C. F. (1994). Two components of transmitter release at a central synapse. Proceedings of the National Academy of Sciences of the United States of America, 91, 12942–12946. doi: 10.1073/pnas.91.26.12942.PubMedCrossRefGoogle Scholar
  21. Han, J., Mark, M. D., Li, X., Xie, M., Waka, S., Rettig, J., et al. (2006). RGS2 determines short-term synaptic plasticity in hippocampal neurons by regulating Gi/o-mediated inhibition of presynaptic Ca2+ channels. Neuron, 51, 575–586. doi: 10.1016/j.neuron.2006.07.012.PubMedCrossRefGoogle Scholar
  22. Hashimoto, K., & Kano, M. (1998). Presynaptic origin of paired-pulse depression at climbing fibre-Purkinje cell synapses in the rat cerebellum. The Journal of Physiology, 506, 391–405. doi: 10.1111/j.1469-7793.1998.391bw.x.PubMedCrossRefGoogle Scholar
  23. Holmgren, C., Harkany, T., Svennenfors, B., & Zilberter, Y. (2003). Pyramidal cell communication within local networks in layer 2/3 of rat neocortex. The Journal of Physiology, 551, 139–153. doi: 10.1113/jphysiol.2003.044784.PubMedCrossRefGoogle Scholar
  24. Hosoi, N., Sakaba, T., & Neher, E. (2007). Quantitative analysis of calcium-dependent vesicle recruitment and its functional role at the calyx of Held synapse. The Journal of Neuroscience, 27, 14286–14298. doi: 10.1523/JNEUROSCI.4122-07.2007.PubMedCrossRefGoogle Scholar
  25. Izhikevich, E. M., Desai, N. S., Walcott, E. C., & Hoppensteadt, F. C. (2003). Bursts as a unit of neural information: Selective communication via resonance. Trends in Neurosciences, 26, 161–167. doi: 10.1016/S0166-2236(03)00034-1.PubMedCrossRefGoogle Scholar
  26. Kandel, E. R., Schwartz, J. H., & Jessell, T. M. (2000). Principles of neural science. New York, NY: McGraw-Hill.Google Scholar
  27. Katz, B., & Miledi, R. (1968). The role of calcium in neuromuscular facilitation. The Journal of Physiology, 195, 481–492.PubMedGoogle Scholar
  28. Korn, H., Faber, D. S., Burnod, Y., & Triller, A. (1984). Regulation of efficacy at central synapses. The Journal of Neuroscience, 4, 125–130.PubMedGoogle Scholar
  29. Kusano, K., & Landau, E. M. (1975). Depression and recovery of transmission at the squid giant synapse. The Journal of Physiology, 245, 13–32.PubMedGoogle Scholar
  30. Macleod, K. M., Horiuchi, T. K., & Carr, C. E. (2007). A role for short-term synaptic facilitation and depression in the processing of intensity information in the auditory brain stem. Journal of Neurophysiology, 97, 2863–2874. doi: 10.1152/jn.01030.2006.PubMedCrossRefGoogle Scholar
  31. Markram, H., Wang, Y., & Tsodyks, M. (1998). Differential signaling via the same axon of neocortical pyramidal neurons. Proceedings of the National Academy of Sciences of the United States of America, 95, 5323–5328. doi: 10.1073/pnas.95.9.5323.PubMedCrossRefGoogle Scholar
  32. Matveev, V., & Wang, X. J. (2000). Implications of all-or-none synaptic transmission and short-term depression beyond vesicle depletion: A computational study. The Journal of Neuroscience, 20, 1575–1588.PubMedGoogle Scholar
  33. Mongillo, G., Barak, O., & Tsodyks, M. (2008). Synaptic theory of working memory. Science, 319, 1543–1546. doi: 10.1126/science.1150769.PubMedCrossRefGoogle Scholar
  34. Neher, E., & Augustine, G. J. (1992). Calcium gradients and buffers in bovine chromaffin cells. The Journal of Physiology, 450, 273–301.PubMedGoogle Scholar
  35. Otsu Y., Shahrezaei V., Li B., Raymond L. A., Delaney K. R., Murphy T. H. (2004). Competition between phasic and asynchronous release for recovered synaptic vesicles at developing hippocampal autaptic synapses. J Neurosci, 24, 420–433.PubMedCrossRefGoogle Scholar
  36. Parnas, H., & Segel, L. A. (1981). A theoretical study of calcium entry in nerve terminals, with application to neurotransmitter release. Journal of Theoretical Biology, 91, 125–169. doi: 10.1016/0022-5193(81)90378-7.PubMedCrossRefGoogle Scholar
  37. Poon, C. S., & Young, D. L. (2006). Nonassociative learning as gated neural integrator and differentiator in stimulus–response pathways. Behavioral and Brain Functions, 2, 29. doi: 10.1186/1744-9081-2-29.PubMedCrossRefGoogle Scholar
  38. Richardson, M. J. E., Melamed, O., Silberberg, G., Gerstner, W., & Markram, H. (2005). Short-term synaptic plasticity orchestrates the response of pyramidal cells and interneurons to population bursts. Journal of Computational Neuroscience, 18, 323–331. doi: 10.1007/s10827-005-0434-8.PubMedCrossRefGoogle Scholar
  39. Rizzuto, R., & Pozzan, T. (2006). Microdomains of intracellular Ca2+ : Molecular determinants and functional consequences. Physiological Reviews, 86, 369–408. doi: 10.1152/physrev.00004.2005.PubMedCrossRefGoogle Scholar
  40. Rosenmund, C., Sigler, A., Augustin, I., Reim, K., Brose, N., & Rhee, J. S. (2002). Differential control of vesicle priming and short-term plasticity by Munc13 isoforms. Neuron, 33, 411–424. doi: 10.1016/S0896-6273(02)00568-8.PubMedCrossRefGoogle Scholar
  41. Rozov, A., Burnashev, N., Sakmann, B., & Neher, E. (2001). Transmitter release modulation by intracellular Ca2 + buffers in facilitating and depressing nerve terminals of pyramidal cells in layer 2/3 of the rat neocortex indicates a target cell-specific difference in presynaptic calcium dynamics. The Journal of Physiology, 531, 807–826. doi: 10.1111/j.1469-7793.2001.0807h.x.PubMedCrossRefGoogle Scholar
  42. Schlüter, O. M., Basu, J., Südhof, T. C., & Rosenmund, C. (2006). Rab3 superprimes synaptic vesicles for release: Implications for short-term synaptic plasticity. The Journal of Neuroscience, 26, 1239–1246. doi: 10.1523/JNEUROSCI.3553-05.2006.PubMedCrossRefGoogle Scholar
  43. Schneggenburger R., Neher E. (2000). Intracellular calcium dependence of transmitter release rates at a fast central synapse. Nature, 406, 889–893.PubMedCrossRefGoogle Scholar
  44. Schneggenburger, R., Sakaba, T., & Neher, E. (2002). Vesicle pools and short-term synaptic depression: Lessons from a large synapse. Trends in Neurosciences, 25, 206–212. doi: 10.1016/S0166-2236(02)02139-2.PubMedCrossRefGoogle Scholar
  45. Simons-Weidenmaier, N. S., Weber, M., Plappert, C. F., Pilz, P. K., & Schmid, S. (2006). Synaptic depression and short-term habituation are located in the sensory part of the mammalian startle pathway. BMC Neuroscience, 7, 38. doi: 10.1186/1471-2202-7-38.PubMedCrossRefGoogle Scholar
  46. Sippy, T., Cruz-Martin, A., Jeromin, A., & Schweizer, F. E. (2003). Acute changes in short-term plasticity at synapses with elevated levels of neuronal calcium sensor-1. Nature Neuroscience, 6, 1031–1038. doi: 10.1038/nn1117.PubMedCrossRefGoogle Scholar
  47. Stevens, C. F., & Wang, Y. (1995). Facilitation and depression at single central synapses. Neuron, 14, 795–802. doi: 10.1016/0896-6273(95)90223-6.PubMedCrossRefGoogle Scholar
  48. Südhof, T. C. (2004). The synaptic vesicle cycle. Annual Review of Neuroscience, 27, 509–547. doi: 10.1146/annurev.neuro.26.041002.131412.PubMedCrossRefGoogle Scholar
  49. Sun, H. Y., & Dobrunz, L. E. (2006). Presynaptic kainate receptor activation is a novel mechanism for target cell-specific short-term facilitation at Schaffer collateral synapses. The Journal of Neuroscience, 26, 10796–10807. doi: 10.1523/JNEUROSCI.2746-06.2006.PubMedCrossRefGoogle Scholar
  50. Sun, J., Pang, Z. P., Qin, D., Fahim, A. T., Adachi, R., & Südhof, T. C. (2007). A dual-Ca2+-sensor model for neurotransmitter release in a central synapse. Nature, 450, 676–682. doi: 10.1038/nature06308.PubMedCrossRefGoogle Scholar
  51. Thies, R. E. (1965). Neuromuscular depression and the apparent depletion of transmitter in mammalian muscle. Journal of Neurophysiology, 28, 427–442.Google Scholar
  52. Thomson, A. M. (2000). Facilitation, augmentation and potentiation at central synapses. Trends in Neurosciences, 23, 305–312. doi: 10.1016/S0166-2236(00)01580-0.PubMedCrossRefGoogle Scholar
  53. Trussell, L. O., Zhang, S., & Raman, I. M. (1993). Desensitization of AMPA receptors upon multiquantal neurotransmitter release. Neuron, 10, 1185–1196. doi: 10.1016/0896-6273(93)90066-Z.PubMedCrossRefGoogle Scholar
  54. Tsodyks, M. V., & Markram, H. (1997). The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proceedings of the National Academy of Sciences of the United States of America, 94, 719–723. doi: 10.1073/pnas.94.2.719.PubMedCrossRefGoogle Scholar
  55. Ulrich, D. (2002). Dendritic resonance in rat neocortical pyramidal cells. Journal of Neurophysiology, 87, 2753–2759.PubMedGoogle Scholar
  56. von Gersdorff, H., & Borst, J. G. G. (2002). Short-term plasticity at the calyx of Held. Nature Reviews Neuroscience, 3, 53–64. doi: 10.1038/nrn705.CrossRefGoogle Scholar
  57. von Gersdorff, H., Schneggenburger, R., Weis, S., & Neher, E. (1997). Presynaptic depression at a Calyx synapse: The small contribution of metabotropic glutamate receptors. The Journal of Neuroscience, 17, 8137–8146.Google Scholar
  58. Weimer, R. M., & Jorgensen, E. M. (2003). Controversies in synaptic vesicle exocytosis. Journal of Cell Science, 116, 3661–3666. doi: 10.1242/jcs.00687.PubMedCrossRefGoogle Scholar
  59. Wu, L. G., & Betz, W. J. (1998). Kinetics of synaptic depression and vesicle recycling after tetanic stimulation of frog motor nerve terminals. Biophysical Journal, 74, 3003–3009.PubMedCrossRefGoogle Scholar
  60. Xu, J., & Wu, L. G. (2005). The decrease in the presynaptic calcium current is a major cause of short-term depression at a calyx-type synapse. Neuron, 46, 633–645. doi: 10.1016/j.neuron.2005.03.024.PubMedCrossRefGoogle Scholar
  61. Xu, J., He, L., & Wu, L.-G. (2007). Role of Ca2+ channels in short-term synaptic plasticity. Current Opinion in Neurobiology, 17, 352–359. doi: 10.1016/j.conb.2007.04.005.PubMedCrossRefGoogle Scholar
  62. Yamada, W. M., & Zucker, R. S. (1992). Time course of transmitter release calculated from simulations of a calcium diffusion model. Biophysical Journal, 61, 671–682.PubMedCrossRefGoogle Scholar
  63. Zhou, Z., Champagnat, J., & Poon, C. S. (1997). Phasic and long-term depression in brainstem nucleus tractus solitarius neurons: Differing roles of AMPA receptor desensitization. The Journal of Neuroscience, 17, 5349–5356.PubMedGoogle Scholar
  64. Zucker, R. S. (1989). Short-term synaptic plasticity. Annual Review of Neuroscience, 12, 13–31. doi: 10.1146/ Scholar
  65. Zucker, R. S., & Regehr, W. G. (2002). Short-term synaptic plasticity. Annual Review of Physiology, 64, 355–405. doi: 10.1146/annurev.physiol.64.092501.114547.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Chuang-Chung J. Lee
    • 1
  • Mihai Anton
    • 1
  • Chi-Sang Poon
    • 2
  • Gregory J. McRae
    • 1
    Email author
  1. 1.Department of Chemical EngineeringMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Harvard-MIT Division of Health Sciences and TechnologyMassachusetts Institute of TechnologyCambridgeUSA

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