, Volume 46, Issue 1, pp 25–32 | Cite as

Analysis of Long-Term Depression in the Purkinje Cell Circuit (a Model Study)


In the cerebellum, long-term depression (LTD) plays a key function in sculpting neuronal circuits to store information, since motor learning and memory are thought to be associated with such long-term changes in synaptic efficacy. To better understand the principles of transmission of information in the cerebellum, we, in our model, distinguished different types of neurons (type 1- and type 2-like) to examine the neuronal excitability and analyze the interspike interval (ISI) bifurcation phenomenon in these units, and then built a Purkinje cell circuit to study the impact of external stimulation on LTD in this circuit. According to the results of computational analysis, both climbing fiber-Purkinje cell and granule cell-Purkinje cell circuits were found to manifest LTD; the external stimuli would influence LTD by changing both depression time and depression intensity. All of the simulated results showed that LTD is a very significant factor in the Purkinje circuit networks. Finally, to deliver the learning regularities, we simulated spike timing-dependent plasticity (STDP) by increasing the CaP conductance.


long-term depression (LTD) interspike interval (ISI) ion currents depression time depression intensity spike timing-dependent plasticity (STDP) 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. V. Massey and Z. I. Bashir, “Long-term depression: multiple forms and implications for brain function,” Trends Neurosci., 30, No. 4, 176-84 (2007).PubMedCrossRefGoogle Scholar
  2. 2.
    D. Purves, G. J. Augustine, D. Fitzpatrick, et al., Neuroscience (4th edition), Sinauer Associates, Sunderland (MA) (2008).Google Scholar
  3. 3.
    M. Ito and M. Kano, “Long-lasting depression of parallel fiber-Purkinje cell transmission induced by conjunctive stimulation of parallel fibers and climbing fibers in the cerebellar cortex,” Neurosci. Lett., 33, 253-2589 (1982).PubMedCrossRefGoogle Scholar
  4. 4.
    M. Ito, M. Sakurai, and P. Tongroach, “Climbing fiber induced depression of both mossy fiber responsiveness and glutamate sensitivity of cerebellar Purkinje cells,” J. Physiol., 324,113-134 (1982).PubMedCentralPubMedGoogle Scholar
  5. 5.
    A. Konnerth, J. Dreessen, and G. J. Augustine, “Brief dendritic calcium signals initiate long-lasting synaptic depression in cerebellar Purkinje cells,” Neurobiology, 89, No. 15, 7051-7055 (1992).Google Scholar
  6. 6.
    A. Aiba, M. Kano, C. Chen, et al., “Deficient cerebellar long-term depression and impaired motor learning in mGluR1 mutant mice,” Cell, 79, 377-388 (1994).PubMedCrossRefGoogle Scholar
  7. 7.
    D. J. Krupa, J. K. Thompson, and R. F. Thompson. “Localization of a memory trace in the mammalian brain,” Science, 260, 989-991 (1993).PubMedCrossRefGoogle Scholar
  8. 8.
    C. Hansel and D. J. Linden, “Long-term depression of the cerebellar climbing fiber–Purkinje neuron synapse,” Neuron, 26, 473-482 (2000).PubMedCrossRefGoogle Scholar
  9. 9.
    C. Chen and R. F. Thompson. “Temporal specificity of long-term depression in parallel fiber-Purkinje synapses in rat cerebellar slices,” Learning Memory, 2, 185-198 (1995).PubMedCrossRefGoogle Scholar
  10. 10.
    M. F. Bear, B. W. Connors, and M. A. Paradios, Neuroscience: Exploring the Brain, Lippincott Williams & Wilkins, Maryland (2001).Google Scholar
  11. 11.
    A. Longstaff, Instant Notes in Neuroscience, Springer-Verlag, New York (2000).Google Scholar
  12. 12.
    F. Fabbro, “Introduction to language and cerebellum,” J. Neurolinguistics, 13, 83-94 (2000).CrossRefGoogle Scholar
  13. 13.
    J. T. Davie, B. A. Clark, and M. Häusser, “The origin of the complex spike in cerebellar Purkinje cells,” J. Neurosci., 28, No. 30, 7599-7609 (2003).CrossRefGoogle Scholar
  14. 14.
    S. Solinas, L. Forti, E. Cesana, et al., “Fast-reset of pacemaking and theta-frequency resonance patterns in cerebellar Golgi cells: Simulations of their impact in vivo,Front. Cell Neurosci., 1, No. 4, 1-9 (2007).Google Scholar
  15. 15.
    W. M. Yamada, C. Koch, and P. R. Adams, Methods in Neuronal Modeling, MIT Press, Cambridge (Massachusetts) (1987).Google Scholar
  16. 16.
    M. Migliore and G. M. Shepherd, “Dendritic action potentials connect distributed dendrodendritic microcircuits,” J. Comput. Neurosci., 24, 207-221 (2008).PubMedCentralPubMedCrossRefGoogle Scholar
  17. 17.
    W. Akemann and T. Knopfel, “Interaction of Kv3 potassium channels and resurgent sodium current influences the rate of spontaneous firing of Purkinje neurons,” J. Neurosci., 26, No. 17, 4602-4612 (2006).PubMedCrossRefGoogle Scholar
  18. 18.
    L. Wang and S. Q. Liu, “Neural circuit and its functional roles in cerebellar cortex,” Neurosci. Bull., 27, No. 3, 173-184 (2011).PubMedCrossRefGoogle Scholar
  19. 19.
    J. C. Eccles, R. Llinis, and K. Sasaki, “The excitatory synaptic action of climbing fibers on the Purkinje cells of the cerebellum,” J. Physiol., 182, 268-296 (1966).PubMedCentralPubMedGoogle Scholar
  20. 20.
    S. L. Palay and V. Chan-Palay, Cerebellar Cortex: Cytology and Organization, Springer-Verlag, Berlin, Heidelberg, New York (1974).CrossRefGoogle Scholar
  21. 21.
    N. Kashiwabuchi, K. Ikeda, K. Araki, et al., “Impairment of Motor Coordination, Purkinje Cell Synapse Formation, and Cerebellar Long-Term Depression in GluR &2 Mutant Mice,” Cell, 81, 245-252 (1995).PubMedCrossRefGoogle Scholar
  22. 22.
    T. Tateno, A. Harsch, and H. Robinson, “Threshold firing frequency–current relationships of neurons in rat somatosensory cortex: type 1 and type 2 dynamics,” J. Neurophysiol., 92, 2283-2294 (2004).PubMedCrossRefGoogle Scholar
  23. 23.
    A. M. Swensen and B. P. Bean, “Ionic mechanisms of burst firing in dissociated Purkinje neurons,” J. Neurosci., 23, No. 29, 9650-9663 (2003).PubMedGoogle Scholar
  24. 24.
    J. C. Eccles, M. Ito, and J. Szentagothal, The Cerebellum as a Neuronal Machine, Springer-Verlag, Berlin, Heidelberg & New York (1967).CrossRefGoogle Scholar
  25. 25.
    J. R. Hughes, “Post-tetanic potentiation,” Physiol. Rev., 38, No. 4, 91-113 (1958).PubMedGoogle Scholar
  26. 26.
    D. L. Cook, P. C. Schwindt, L. A. Grande, and W. J. Spain, “Synaptic depression in the localization of sound,” Nature, 421, 66-70 (2003).PubMedCrossRefGoogle Scholar
  27. 27.
    G. Q. Bi and M. M. Poo, “Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type,” J. Neurosci., 18, 10464-10472 (1998).PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsSouth China University of TechnologyGuangzhouChina
  2. 2.Biomedical Engineering CenterBeijing University of TechnologyBeijingChina

Personalised recommendations