Skip to main content
SpringerLink
Log in

Stability of complex spike timing-dependent plasticity in cerebellar learning

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

Abstract

Dynamics of spike-timing dependent synaptic plasticity are analyzed for excitatory and inhibitory synapses onto cerebellar Purkinje cells. The purpose of this study is to place theoretical constraints on candidate synaptic learning rules that determine the changes in synaptic efficacy due to pairing complex spikes with presynaptic spikes in parallel fibers and inhibitory interneurons. Constraints are derived for the timing between complex spikes and presynaptic spikes, constraints that result from the stability of the learning dynamics of the learning rule. Potential instabilities in the parallel fiber synaptic learning rule are found to be stabilized by synaptic plasticity at inhibitory synapses if the inhibitory learning rules are stable, and conditions for stability of inhibitory plasticity are given. Combining excitatory with inhibitory plasticity provides a mechanism for minimizing the overall synaptic input. Stable learning rules are shown to be able to sculpt simple-spike patterns by regulating the excitability of neurons in the inferior olive that give rise to climbing fibers.

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

Similar content being viewed by others

References

  • Abbott LF, Blum KI (1996) Functional significance of long-term potentiation for sequence learning and prediction. Cerebral Cortex 6: 406–416.

    Google Scholar 

  • Abbott LF, Kepler TB (1990) Model neurons: From Hodgkin-Huxley to Hopfield. In: Garrido L (ed.) Statistical Mechanics of Neural Networks, Springer-Verlag, Berlin, pp. 5–18.

  • Albus JS (1971) A theory of cerebellar function. Math. Biosci. 10: 25–61.

    Google Scholar 

  • Barbour B (1993) Synaptic currents evoked in purkinje cells by stimulating individual granule cells. Neuron 11: 759–769.

    Google Scholar 

  • Barmack NH, Shojaku H (1995) Vestibular and visual climbing fiber signals evoked in the uvula-nodulus of the rabbit cerebellum by natural stimulation. J. Neurophysiol. 74: 2573–2589.

    Google Scholar 

  • Bell CC, Bodznick D, Montgomery J, Bastian J (1997a) The generation and subtraction of sensory expectations within cerebellum-like structures. Brain. Beh. Evol. 50(Suppl 1): 17–31.

    Google Scholar 

  • Bell CC, Han V, Sugawara Y, Grant K (1997b) Direction of change in synaptic efficacy following pairing depends on the temporal relation of presynaptic input and postsynaptic spike during pairing. Soc. Neurosci. Abstr. 23: 1840.

    Google Scholar 

  • Bell CC, Han V, Sugawara Y, Grant K (1997c) Synaptic plasticity in a cerebellum-like structure depends on temporal order. Nature 387: 278–281.

    Google Scholar 

  • Brunel N, Hakim V, Isope P, Nadal JP, Barbour B (2004) Optimal information storage and the distribution of synaptic weights: perceptron versus purkinje cell. Neuron 43(5): 745–757.

    Google Scholar 

  • Buonomano DV, Mauk MD (1994) Neural network model of the cerebellum: Temporal discrimination and the timing of motor responses. Neural Comp. 6: 38–55.

    Google Scholar 

  • Callaway JC, Lasser-Ross N, Ross WN (1995) Ipsps strongly inhibit climbing fiber-activated [Ca2+]\(_i\) increases in the dendrites of cerebellar Purkinje neurons. J. Neurosci. 15: 2777–2787.

    Google Scholar 

  • Chadderton P, Margrie TW, Hausser M (2004) Integration of quanta in cerebellar granule cells during sensory processing. Nature 428: 856–860.

    Google Scholar 

  • Chen C, Thompson RF (1995) Temporal specificity of long-term depression in parallel fiber-Purkinje synapses in rat cerebellar slices. Learn. Memory 2: 185–198.

    Google Scholar 

  • Coesmans M, Weber JT, De Zeeuw CI, Hansel C (2004) Bidirectional parallel fiber plasticity in the cerebellum under climbing fiber control. Neuron 44(4): 691–700.

    Google Scholar 

  • Crepel F, Jaillard D (1991) Pairing of pre- and postsynaptic activities induces long-term changes in synaptic efficacy in vitro. J. Physiol. 432: 123–141.

    Google Scholar 

  • de Vries B, Principe J (1992) The gamma model—A new neural network for temporal processing. Neural Netw. 5: 565–576.

    Google Scholar 

  • DeSchutter E, Bower JM (1994) An active membrane model of the cerebellar Purkinje cell: II. Simulation of synaptic responses. J. Neurophysiol. 71: 401–419.

    Google Scholar 

  • Doi T, Kuroda S, Michikawa T, Kawato M (2005) Inositol 1,4,5-trisphosphate-dependent Ca2+ threshold dynamics detect spike timing in cerebellar purkinje cells. J. Neurosci. 25(4): 950–961.

    Google Scholar 

  • Ekerot CF, Jorntell H (2003) Parallel fiber receptive fields: a key to understanding cerebellar operation and learning. Cerebellum 2(2): 101–109.

    Google Scholar 

  • Ekerot CF, Kano M (1985) Long-term depression of parallel fibre synapses following stimulation of climbing fibres. Brain Res. 342: 357–360.

    Google Scholar 

  • Fiala JC, Grossberg S, Bullock D (1996) Metabotropic glutamate receptor activation in cerebellar Purkinje cells as substrate for adaptive timing of the classically conditioned eye-blink response. J. Neurosci. 16: 3760–3774.

    Google Scholar 

  • Gerstner W (1998) Spiking neurons. In: Maass W, Bishop CM (eds.) Pulsed Neural Networks, MIT Press, Cambridge, pp. 3–54.

  • Gerstner W, Ritz R, Leo Hemmen J (1993) Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns. Biol. Cybern. 69: 503–515.

    Google Scholar 

  • Gerstner W, Leo Hemmen J (1992) Associative memory in a network of ‘spiking’ neurons. Network 3: 139–164.

    Google Scholar 

  • Haas JS, Selverston AI, Abarbanel HDI (2004) Spike-timing-dependent plasticity of inhibition in the entorhinal cortex. Soc. Neurosci. Abstr./Online Abstract Viewer. 57: 13.

  • Han V, Bell CC, Grant K, Sugawara Y (1999) Mormyrid electrosensory lobe in vitro: I. Morphology of cells and circuits. J. Comp. Neurol. 404: 359–374.

    Google Scholar 

  • Han V, Grant K, Bell CC (2000) Reversible associative depression and nonassociative potentiation at a parallel fiber synapse. Neuron 27: 611–622.

    Google Scholar 

  • Hansel C, Linden DJ, D’Angelo E (2001) Beyond parallel fiber ltd: the diversity of synaptic and nonsynaptic plasticity in the cerebellum. Nature Neurosci. 4: 467–475.

    Google Scholar 

  • Hirano T (1991) Differential of pre- and postsynaptic mechanisms for synaptic potentiation and depression between granule cell and a Purkinje cell in rat cerebellar culture. Synapse 7: 321–323.

    Google Scholar 

  • Houk JC, Alford S (1996) Computational significance of the cerebellar mechanism for synaptic plasticity in Purkinje cells. Beh. Brain Sci. 19: 457–461.

    Google Scholar 

  • Isope P, Barbour B (2002) Properties of unitary granule cell \({{\to}}\) purkinje cell synapses in adult rat cerebellar slices. J. Neurosci. 22(22): 9668–9678.

    Google Scholar 

  • Isope P, Dieudonne S, Barbour B (2002) Temporal organization of activity in the cerebellar cortex: a manifesto for synchrony. Ann. NY Acad. Sci. 978: 164–174.

    Google Scholar 

  • Ito M (1989) Long-term depression. Ann. Rev. Neurosci. 12: 85–102.

    Google Scholar 

  • Ito M (1990) Long-term depression in the cerebellum. Seminars Neurosci. 2: 381–390.

    Google Scholar 

  • Ito M, Sakurai M, Tongroach P (1982) Climbing fibre induced depression of both mossy fiber responsiveness and glutamate sensitivity of cerebellar Purkinje cells. J. Physiol. (London) 5: 275–289.

    Google Scholar 

  • Jack JJB, Noble D, Tsien RW (1975) Electric Current Flow in Excitable Cells. Clarendon Press, Oxford.

  • Jörntell H, Ekerot CF (2002) Reciprocal bidirectional plasticity of parallel fiber receptive fields in cerebellar purkinje cells and their afferent interneurons. Neuron 34(5): 797–806.

    Google Scholar 

  • Kano M, Rexhausen U, Dreessen J, Konnerth A (1992) Synaptic excitation produces a long-lasting rebound potentiation of inhibitory synaptic signals in cerebellar Purkinje cells. Nature 356: 601–604.

    Google Scholar 

  • Karachot L, Kado RT, Ito M (1994) Stimulus parameters for induction of long-term depression in in vitro rat Purkinje cells. Neurosci. Res. 21: 161–168.

    Google Scholar 

  • Lev-Ram V, Makings LR, Keitz PF, Kao JPY, Tsien RY (1995) Long-term depression in cerebellar Purkinje neurons results from coincidence of nitric oxide and depolarization-induced Ca2+ transients. Neuron 15: 407–415.

    Google Scholar 

  • Lev-Ram V, Wong ST, Storm DR, Tsien RY (2002) A new form of cerebellar long-term potentiation is postsynaptic and depends on nitric oxide but not camp. Proc. Natl. Acad. Sci. USA 99(12): 8389–8393.

    Google Scholar 

  • Levine MW (1991) The distribution of the intervals between neural impulses in the maintained discharges of retinal ganglion cells. Biol. Cybern. 65: 459–467.

    Google Scholar 

  • Linden DJ, Dickinson MH, Smeyne M, Connor JA (1991) A long term depression of ampa currents currents in cultured cerebellar Purkinje neurons. Neuron 7: 81–89.

    Google Scholar 

  • Linden DJ, Connor JA (1993) Cellular mechanisms of long-term depression in the cerebellum. Curr. Op. Neurobiol. 3: 401–406.

    Google Scholar 

  • Llinás R, Sugimori M (1980) Electrophysiological properties of in vitro Purkinje cell dendrites in mammalian cerebellar slices. J. Physiol. (London) 395: 197–213.

    Google Scholar 

  • Llinás R (1975) The cortex of the cerebellum. Sci. Am. 232: 56–71.

    Google Scholar 

  • Maex R, DeSchutter E (1998) Synchronization of golgi and granule cell firing in a detailed network model of the cerebellar granule cell layer. J. Neurophysiol. 80: 2521–2537.

    Google Scholar 

  • Marr D (1969) A theory of cerebellar cortex. J. Physiol. 202: 437–470.

    Google Scholar 

  • Mauk MD (1997) Roles of cerebellar cortex and nuclei in motor learning: contradictions or clues? Neuron 18: 343–346.

    Google Scholar 

  • Medina JF, Mauk MD (2000) Computer simulation of cerebellar information processing. Nat. Neurosci. 3(Suppl): 1205–1211.

    Google Scholar 

  • Miyata M, Finch EA, Khiroug L, Hashimoto K, Hayasaka S, Oda SI, Inouye M, Takagishi Y, Augustine GJ, Kano M (2000) Local calcium release in dendritic spines required for long-term synaptic depression. Neuron 28(1): 233–244.

    Google Scholar 

  • Mohr C, Roberts PD, Bell CC (2002) Cells of the mormyrid electrosensory lobe: I. Responses to the electric organ corollary discharge and to electrosensory stimuli. J. Neurophysiol. 90: 1193–1210.

    Google Scholar 

  • Nagano T, Ohmi O (1978) Plausible function of Golgi cells in the cerebellar cortex. Biol Cybern. 29: 75–82.

    Google Scholar 

  • Neale SA, Garthwaite J, Batchelor AM (2001) mglu1 receptors mediate a post-tetanic depression at parallel fibre-purkinje cell synapses in rat cerebellum. Eur. J. Neurosci. 14(8): 1313–1319.

    Google Scholar 

  • Pellionisz A, Szentágothai J (1973) Dynamic single unit simulation of a realistic cerebellar network model. Brain Res. 49: 83–99.

    Google Scholar 

  • Roberts PD (1997) Stochastic recruitment in parallel fiber activity patterns. Beh. Brain Sci. 20: 263–264.

    Google Scholar 

  • Roberts PD (2000a) Dynamics of temporal learning rules. Phys. Rev. E 62: 4077–4082.

    Google Scholar 

  • Roberts PD (2000b). Electrosensory response mechanisms in mormyrid electric fish. Neurocomputing 32–33: 243–248.

    Google Scholar 

  • Roberts PD (2000c) Modeling inhibitory plasticity in the electrosensory system. J. Neurophysiol. 84: 2035–2047.

    Google Scholar 

  • Roberts PD (2004) Recurrent biological neural networks: The weak and noisy limit. Phys. Rev. E 69: 031910.

    Google Scholar 

  • Roberts PD (2005) Recurrent neural network generates a basis for sensory image cancellation. Neurocomputing 65–66: 237–242.

    Google Scholar 

  • Roberts PD, Bell CC (2000) Computational consequences of temporally asymmetric learning rules: II. Sensory image cancellation. J. Comput. Neurosci. 9: 67–83.

    Google Scholar 

  • Roberts PD, Bell CC (2002) Spike timing dependent synaptic plasticity in biological systems. Biol. Cybern. 87: 392–403.

    Google Scholar 

  • Ruigrok TJH, Voogd J (1995) Cerebellar influence on olivary excitability in the cat. Euro. J. Neurosci. 7: 679–693.

    Google Scholar 

  • Rumsey CC, Abbott LF (2004) Equalization of synaptic efficacy by activity- and timing-dependent synaptic plasticity. J. Neurophysiol. 91: 2273–2280.

    Google Scholar 

  • Sakurai M (1989) Depression and potentiation of parallel fiber-Purkinje cell transmission in in vitro cerebellar slices. In: Strata P (ed.) The Olivocerebellar System in Motor Control, Springer-Verlag, Berlin, pp. 221–230.

  • Schreurs BG, Alkon DL (1993) Rabbit cerebellar slice analysis of long-term depression and its role in classical conditioning. Brain Res. 631: 235–240.

    Google Scholar 

  • Schreurs BG, Oh MM, Alkon DL (1996) Pairing-specific long-term depression of Purkinje cell excitatory postsynaptic potentials results from a classical conditioning procedure in the rabbit cerebellar slice. J. Neurophysiol. 75: 1051–1060.

    Google Scholar 

  • Schweighofer N, Doya K, Lay F (2001) Unsupervised learning of granule cell sparse codes enhances cerebellar adaptive control. Neuroscience 103: 35–50.

    Google Scholar 

  • Simpson JI, Hulscher HC, Sabel-Goedknegt E, Ruigrok TJ (2005) Between in and out: linking morphology and physiology of cerebellar cortical interneurons. Prog. Brain Res. 148: 329–340.

    Google Scholar 

  • Stein RB (1967) The frequency of nerve action potentials generated by applied currents. Proc. R. Soc. B (London) 167: 613–635.

    Google Scholar 

  • Steuber V, Willshaw D (2004) A biophysical model of synaptic delay learning and temporal pattern recognition in a cerebellar purkinje cell. J. Comput. Neurosci 17(2): 149–164.

    Google Scholar 

  • Traub RD, Wong RKS, Miles R, Michelson H (1991) A model of a CA3 hippocampal pyramidal neuron incorporating voltage-clamp data on intrinsic conductances. J. Neurophysiol. 66: 635–650.

    Google Scholar 

  • Vos BP, Maex R, Volny-Luraghi A, DeSchutter E (1999) Parallel fibers synchronize spontaneous activity in cerebellar golgi cells. J. Neurosci. 19: 464–476.

    Google Scholar 

  • Wang SS, Denk W, Hausser M (2000) Coincidence detection in single dendritic spines mediated by calcium release. Nat. Neurosci. 3(12): 1266–1273.

    Google Scholar 

  • Williams A, Roberts PD, Leen TK (2003) Stability of negative-image equilibria in spike-timing-dependent plasticity. Phys. Rev. E 68(2/1): 021923.

    Google Scholar 

  • Woodin MA, Ganguly K, Poo (2003) Coincident pre- and postsynaptic activity modifies GABAergic synapses by postsynaptic changes in Cl- transporter activity. Neuron 39: 807–820.

Download references

Author information

Authors and Affiliations

  1. Neurological Sciences Institute, OHSU, 505 N.W. 185th Avenue, Beaverton, OR, 97006, USA

    Patrick D. Roberts

Authors
  1. Patrick D. Roberts
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Patrick D. Roberts.

Additional information

Action Editor:

Nicolas Brunel

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roberts, P.D. Stability of complex spike timing-dependent plasticity in cerebellar learning. J Comput Neurosci 22, 283–296 (2007). https://doi.org/10.1007/s10827-006-0012-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10827-006-0012-8

Keywords

Search

Navigation