Skip to main content
SpringerLink
Log in

A kinetic model unifying presynaptic short-term facilitation and depression

  • Published:
Journal of Computational Neuroscience Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • 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.

    Article  Google Scholar 

  • 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.

    PubMed  CAS  Google Scholar 

  • 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.

    PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Bertram, R., Sherman, A., & Stanley, E. F. (1996). Single-domain/bound calcium hypothesis of transmitter release and facilitation. Journal of Neurophysiology, 75, 1919–1931.

    PubMed  CAS  Google Scholar 

  • Betz, W. (1970). Depression of transmitter release at the neuromuscular junction of the frog. The Journal of Physiology, 206, 629–644.

    PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Byrne, J. H. (1982). Analysis of synaptic depression contributing to habituation of gill-withdrawal reflex in Aplysia californica. Journal of Neurophysiology, 48, 431–438.

    PubMed  CAS  Google Scholar 

  • Byrne, J. H., & Kandel, E. R. (1996). Presynaptic facilitation revisited: State and time dependence. The Journal of Neuroscience, 16, 425–435.

    PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • Del Castillo, J., & Katz, B. (1954). Statistical factors involved in neuromuscular facilitation and depression. The Journal of Physiology, 124, 574–585.

    PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    PubMed  CAS  Google Scholar 

  • 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.

    PubMed  CAS  Google Scholar 

  • 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.

    PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Fuhrmann G., Segev I., Markram H., Tsodyks M. (2002). Coding of temporal information by activity-dependent synapses. J Neurophysiol, 87, 140–148.

    PubMed  Google Scholar 

  • 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.

    PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Kandel, E. R., Schwartz, J. H., & Jessell, T. M. (2000). Principles of neural science. New York, NY: McGraw-Hill.

    Google Scholar 

  • Katz, B., & Miledi, R. (1968). The role of calcium in neuromuscular facilitation. The Journal of Physiology, 195, 481–492.

    PubMed  CAS  Google Scholar 

  • Korn, H., Faber, D. S., Burnod, Y., & Triller, A. (1984). Regulation of efficacy at central synapses. The Journal of Neuroscience, 4, 125–130.

    PubMed  CAS  Google Scholar 

  • Kusano, K., & Landau, E. M. (1975). Depression and recovery of transmission at the squid giant synapse. The Journal of Physiology, 245, 13–32.

    PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    PubMed  CAS  Google Scholar 

  • Mongillo, G., Barak, O., & Tsodyks, M. (2008). Synaptic theory of working memory. Science, 319, 1543–1546. doi:10.1126/science.1150769.

    Article  PubMed  CAS  Google Scholar 

  • Neher, E., & Augustine, G. J. (1992). Calcium gradients and buffers in bovine chromaffin cells. The Journal of Physiology, 450, 273–301.

    PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Schneggenburger R., Neher E. (2000). Intracellular calcium dependence of transmitter release rates at a fast central synapse. Nature, 406, 889–893.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Südhof, T. C. (2004). The synaptic vesicle cycle. Annual Review of Neuroscience, 27, 509–547. doi:10.1146/annurev.neuro.26.041002.131412.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Thies, R. E. (1965). Neuromuscular depression and the apparent depletion of transmitter in mammalian muscle. Journal of Neurophysiology, 28, 427–442.

    Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • Ulrich, D. (2002). Dendritic resonance in rat neocortical pyramidal cells. Journal of Neurophysiology, 87, 2753–2759.

    PubMed  Google Scholar 

  • 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.

    Article  CAS  Google Scholar 

  • 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 

  • Weimer, R. M., & Jorgensen, E. M. (2003). Controversies in synaptic vesicle exocytosis. Journal of Cell Science, 116, 3661–3666. doi:10.1242/jcs.00687.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    PubMed  CAS  Google Scholar 

  • Zucker, R. S. (1989). Short-term synaptic plasticity. Annual Review of Neuroscience, 12, 13–31. doi:10.1146/annurev.ne.12.030189.000305.

    Article  PubMed  CAS  Google Scholar 

  • 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.

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

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

Author information

Authors and Affiliations

  1. Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Room 66-372, Cambridge, MA, 02139-4307, USA

    Chuang-Chung J. Lee, Mihai Anton & Gregory J. McRae

  2. Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Chi-Sang Poon

Authors
  1. Chuang-Chung J. Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mihai Anton
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chi-Sang Poon
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gregory J. McRae
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gregory J. McRae.

Additional information

Action Editor: Carson C. Chow

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lee, CC.J., Anton, M., Poon, CS. et al. A kinetic model unifying presynaptic short-term facilitation and depression. J Comput Neurosci 26, 459–473 (2009). https://doi.org/10.1007/s10827-008-0122-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-008-0122-6

Keywords

Search

Navigation