The Cerebellum

, Volume 2, Issue 1, pp 44–54 | Cite as

Time windows and reverberating loops: a reverse-engineering approach to cerebellar function

  • Werner M. KistlerEmail author
  • Chris I. De Zeeuw


We review a reverse-engineering approach to cerebellar function that pays particular attention to temporal aspects of neuronal interactions. This approach offers new vistas on the role of GABAergic synapses and reverberating projections within the olivocerebellar system. More specifically, our simulations show that Golgi cells can control the ring time of granule cells rather than their ring rate and that Purkinje cells can trigger precisely timed rebound spikes in neurons of the deep cerebellar nuclei. This rebound activity can reverberate back to the cerebellar cortex giving rise to a complex oscillatory dynamics that may have interesting functional implications for working memory and timed-response tasks.


theoretical model cerebellum olivary nucleus cerebellar nuclel 


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  1. 1.
    Thach WT, Goodkin HP, Keating JG. The cerebellum and the adaptive coordination of movement. Annu Rev Neurosci 1992; 15: 403–442.PubMedCrossRefGoogle Scholar
  2. 2.
    Houk JC, Buckingham JT, Barto AG. Models of the cerebellum and motor learning. Behav Brain Sci 1996; 19: 368–383.Google Scholar
  3. 3.
    Marr D. A theory of cerebellar cortex. J Physiol (Lond) 1969; 202: 437–470.Google Scholar
  4. 4.
    Bower JM. The cerebellum and the control of sensory data aquisition. In: Schmahmann J, editor, International Review of Neurobiology, vol. 41. San Diego: Academic Press, 1997: 489–513.Google Scholar
  5. 5.
    Bell C, Bodznick D, Montgommery J, Bastian J. The generation and subtraction of sensory expectations within cerebellum-like structures. Brain Behav Evol 1997; 50(suppl. 1): 17–31.PubMedCrossRefGoogle Scholar
  6. 6.
    Hartmann MJ, Bower JM. Tactile responses in the granule cell layer of cerebellar folium crus IIa of freely behaving rats. J Neurosci 2001; 21: 3549–3563.PubMedGoogle Scholar
  7. 7.
    Leiner HC, Leiner AL, Dow RS. Cognitive and language functions of the human cerebellum. Trends Neurosci 1993; 16: 444–447.PubMedCrossRefGoogle Scholar
  8. 8.
    Daum I, Ackermann H. Cerebellar contributions to cognition. Behav Brain Res 1995; 67: 201–210.PubMedCrossRefGoogle Scholar
  9. 9.
    Townsend J, Courchesne E, Covington J, Westerfield M, Harris NS, Lyden P, Lowry TP, Press GA. Spatial attention deficits in patients with acquired or developmental cerebellar abnormality. J Neurosci 1999; 19: 5632–5643.PubMedGoogle Scholar
  10. 10.
    Albus JS. A theory of cerebellar function. Math Biosci 1971; 10: 25–61.CrossRefGoogle Scholar
  11. 11.
    Braitenberg V. Is the cerebellar cortex a biological clock in the millisecond range? In: Fox CA, Snider RS, editors, Progress in Brain Research, volume 25. Amsterdam: Elsevier Publishing Company, 1967: 334–346.Google Scholar
  12. 12.
    Fujita M. Adaptive filter model of the cerebellum. Biol Cybern 1982; 45: 195–206.PubMedCrossRefGoogle Scholar
  13. 13.
    Braitenberg V. The cerebellar network: attempt at a formalization of its structure. Network 1993; 4: 11–17.Google Scholar
  14. 14.
    Kistler WM, van Hemmen JL. Delayed reverberation through time windows as a key to cerebellar function. Biol Cybern 1999; 81: 373–380.PubMedCrossRefGoogle Scholar
  15. 15.
    Schulman JA, Bloom FE. Golgi cells of the cerebellum are inhibited by inferior olive activity. Brain Res 1981; 210: 350–355.PubMedCrossRefGoogle Scholar
  16. 16.
    Vos BP, Maex R, Volny-Luraghi A, De Schutter E. Parallel fibers synchronize spontaneous activity in cerebellar Golgi cells. J Neurosci 1999; 19(RC6): 1–5.Google Scholar
  17. 17.
    Vos BP, Volny-Luraghi A, Maex R, De Schutter E. Precise spike timing of tactile-evoked cerebellar Golgi cell responses: a re ection of combined mossy fiber and parallel fiber activation. In: Gerrits NM, Ruigrok TJH, De Zeeuw CI, editors, Cerebellar Modules: Molecules, Morphology, and Function, Progress in Brain Research. Amsterdam: Elsevier, 2000.Google Scholar
  18. 18.
    Gabbiani F, Midtgaard J, Knoep T. Synaptic integration in a model of cerebellar granule cells. J Neurophysiol 1994; 72: 999–1009 [Corrigenda have been published in J Neurophysiol 1996; 75(6), without covering, however, all typing errors].PubMedGoogle Scholar
  19. 19.
    Kistler WM, van Hemmen JL, De Zeeuw CI. Time window control: a model for cerebellar function based on synchronization, reverberation, and time slicing. Prog Brain Res 2000; 124: 275–297.PubMedCrossRefGoogle Scholar
  20. 20.
    Kistler WM. Time-slicing: a model for cerebellar function based on synchronization, reverberation, and time windows. Neurocomputing 2001; 38-40: 1367–1372.CrossRefGoogle Scholar
  21. 21.
    Ito M, Yoshida M. The cerebellar-invoked monosynaptic inhibition of Deiters’ neurones. Experientia 1964; 20: 515–516.PubMedCrossRefGoogle Scholar
  22. 22.
    Ito M, Yoshida M, Obata K. Monosynaptic inhibition of the intracerebellar nuclei induced from the cerebellar cortex. Experientia 1964; 20: 575–576.PubMedCrossRefGoogle Scholar
  23. 23.
    Jahnsen H. Electrophysiological characteristics of neurones in the guinea-pig deep cerebellar nuclei in vitro. J Physiol (Lond) 1986; 372: 129–147.Google Scholar
  24. 24.
    Llinás R, Mühlethaler M. Electrophysiology of guinea-pig cerebellar nuclear cells in the in vitro brain stem-cerebellar preparation. J Physiol (Lond) 1988; 404: 241–258.Google Scholar
  25. 25.
    Aizenman CD, Manis PB, Linden DJ. Polarity of long-term synaptic gain change is related to postsynaptic spike firing at a cerebellar inhibitory synapse. Neuron 1998; 21: 827–835.PubMedCrossRefGoogle Scholar
  26. 26.
    Aizenman CD, Linden DJ. Regulation of the rebound depolarization and spontaneous firing patterns of deep nuclear neurons in slices of rat cerebellum. J Neurophysiol 1999; 82: 1697–1709.PubMedGoogle Scholar
  27. 27.
    Gauck V, Jaeger D. The control of rate and timing of spikes in the deep cerebellar nuclei by inhibition. J Neurosci 2000; 20: 3006–3016.PubMedGoogle Scholar
  28. 28.
    Anchisi D, Scelfo B, Tempia F. Postsynaptic currents in deep cerebellar nuclei. J Neurophysiol 2001; 85: 323–331.PubMedGoogle Scholar
  29. 29.
    Ito M The Cerebellum and Neural Control. New York: Raven Press 1984.Google Scholar
  30. 30.
    De Zeeuw C, Ruigrok TJ. Olivary projecting neurons in the nucleus of darkschewitsch in the cat receive excitatory monosynaptic input from the cerebellar nuclei. Brain Res 1994; 653: 345–350.PubMedCrossRefGoogle Scholar
  31. 31.
    De Zeeuw CI, Alphen AM, Hawkins RK, Ruigrok TJH. Climbing fiber collaterals contact neurons in the cerebellar nuclei that provide a GABAergic feedback to the inferior olive. Neurosci 1997; 80: 981–986.CrossRefGoogle Scholar
  32. 32.
    De Zeeuw CI, Simpson JI, Hoogenraad CC, Galjart N, Koekkoek SKE, Ruigrok TJH. Microcircuitry and function of the inferior olive. Trends Neurosci 1998; 21: 391–400.PubMedCrossRefGoogle Scholar
  33. 33.
    Tsukahara N, Bando T, Kitai ST, Kiyohara T. Cerebello-pontine reverberating circuit. Brain Res 1971; 33: 233–237.PubMedCrossRefGoogle Scholar
  34. 34.
    Murakami F, Ozawa NN, Katsumaru H, Tsukahara H. Reciprocal connections between the nucleus interpositus of the cerebellum and precerebellar nuclei. Neurosci Lett 1981; 25: 209–213.PubMedCrossRefGoogle Scholar
  35. 35.
    Tsukahara N, Bando T, Murakami F, Oda Y. Properties of cerebello-precerebellar reverberating circuits. Brain Res 1983; 274: 249–259.PubMedCrossRefGoogle Scholar
  36. 36.
    Verveer C, Hawkins RK, Ruigrok TJH, De Zeeuw CI. Ultrastructural study of the GABAergic and cerebellar input to the nucleus reticularis tegmenti pontis. Brain Res 1997; 766: 289–296.PubMedCrossRefGoogle Scholar
  37. 37.
    Gould BB, Graybiel AM. Afferents to the cerebellar cortex in the cat: evidence for an intrinsic pathway leading from the deep nuclei to the cortex. Brain Res 1976; 110: 601–611.PubMedCrossRefGoogle Scholar
  38. 38.
    Tolbert DL, Bantli H, Bloedel JR. Anatomical and physiological evidence for a cerebellar nucleocortical projection in the cat. Neurosci 1976; 1: 205–217.CrossRefGoogle Scholar
  39. 39.
    Umetani T. Topographic organization of the cerebellar nucleocortical projection in the albino rat: an autoradiographic orthograde study. Brain Res 1990; 507: 216–224.PubMedCrossRefGoogle Scholar
  40. 40.
    Trott JR, Apps R, Armstrong DM. Topographic organisation within the cerebellar nucleocortical projection to the paravermal cortex of lobule Vb/c in the cat. Exp Brain Res 1990; 80: 415–428.PubMedCrossRefGoogle Scholar
  41. 41.
    Farrant M, Cull-Candy S. GABA receptors, granule cells and genes. Nature 1993; 361: 302–303.PubMedCrossRefGoogle Scholar
  42. 42.
    Tia S, Wang JF, Kotchabhakdi N, Vicini S. Developmental changes of inhibitory synaptic currents in cerebellar granule cells: role of GABAA receptor α6 subunit. J Neurosci 1996; 16: 3630–3640.PubMedGoogle Scholar
  43. 43.
    Mathews GC, Bolos-Sy AM, Holland KD, Isenberg KE, Covey DF, Ferrendelli JA, Rothman SM. Developmental alteration in GABAA receptor structure and physiological properties in cultured cerebellar granule cells. Neuron 1994; 13: 149–158.PubMedCrossRefGoogle Scholar
  44. 44.
    Ueno S, Zempel JM, Steinbach JH. Differences in the expression of GABAA receptors between functionally innervated and noninnervated granule neurons in neonatal cerebellar cultures. Brain Res 1996; 714: 49–56.PubMedCrossRefGoogle Scholar
  45. 45.
    Carlson BX, Belhage B, Hansen GH, Elster L, Olsen RW, Schousboe A. Expression of the GABAA receptorα6 subunit in cultured cerebellar granule cells is developmentally regulated by activation of GABAA receptors. J Neurosci Res 1997; 50: 1053–1062.PubMedCrossRefGoogle Scholar
  46. 46.
    Llinás R, Yarom Y. Oscillatory properties of guinea-pig inferior olivary neurones and their pharmacological modulation: an in vitro study. J Physiol (Lond) 1986; 376: 163–182.Google Scholar
  47. 47.
    Lampl I, Yarom Y. Subthreshold oscillations of the membrane potential: a functional synchronizing and timing device. J Neurophysiol 1993; 70: 2181–2186.PubMedGoogle Scholar
  48. 48.
    Bal T, McCormick DA. Synchronized oscillations in the inferior olive are controlled by the hyperpolarization-activated cation current I h. J Neurophysiol 1997; 77: 3145–3156.PubMedGoogle Scholar
  49. 49.
    Llinás R, Sasaki K. The functional organization of the olivocerebellar system as examined by multiple Purkinje cell recordings. Eur J Neurosci 1989; 1: 587–602.PubMedCrossRefGoogle Scholar
  50. 50.
    Lang EJ, Sugihara I, Llinás R. GABAergic modulation of complex spike activity by the cerebellar nucleoolivary pathway in rat. J Neurophysiol 1996; 76: 255–275.PubMedGoogle Scholar
  51. 51.
    Bell CC, Kawasaki T. Relations among climbing fiber responses of nearby Purkinje cells. J Neurophysiol 1972; 35: 155–169.PubMedGoogle Scholar
  52. 52.
    Aggelopulos NC, Duke C, Edgley SA. Non-uniform conduction time in the olivocerebellar pathway in the anaesthetized cat. J Physiol (Lond) 1995; 486: 763–768.Google Scholar
  53. 53.
    Sotelo C, Llinás R, Baker R. Structural study of inferior olivary nucleus of the cat: morphological correlations of electrotonic coupling. J Neurophysiol 1974; 37: 541–559.PubMedGoogle Scholar
  54. 54.
    De Zeeuw CI, Lang EJ, Sugihara I, Ruigrok TJH, Eisenman LM, Mugnaini E, Llinás R. Morphological correlates of bilateral synchrony in the rat cerebellar cortex. J Neurosci 1996; 16: 3412–3426.PubMedGoogle Scholar
  55. 55.
    Kistler WM, De Zeeuw CI. Dynamical working memory and timed responses: the role of reverberating loops in the olivo-cerebellar system. Neural Comput 2002.Google Scholar
  56. 56.
    Gerstner W, Kempter R, van Hemmen JL, Wagner H. A neuronal learning rule for sub-millisecond temporal coding. Nature 1996; 384: 76–78.CrossRefGoogle Scholar
  57. 57.
    Song S, Miller K, Abbott L. Competitive hebbian learning through spike-time-dependent synaptic plasticity. Nature Neuroscience 2000; 3: 919–926.PubMedCrossRefGoogle Scholar
  58. 58.
    Kistler WM, van Hemmen JL. Modeling synaptic plasticity in conjunction with the timing of pre- and postsynaptic action potentials. Neural Comput 2000; 12: 385–405.PubMedCrossRefGoogle Scholar
  59. 59.
    Kistler WM. Spike-timing dependent synaptic plasticity: a theoretical framework. Biol Cybern 2002 submitted.Google Scholar
  60. 60.
    Hirano T. Synaptic formations and modulations of synaptic transmissions between identified cerebellar neurons in culture. J Physiol (Paris) 1991; 85: 145–153.Google Scholar
  61. 61.
    Schreurs BG, Oh MM, Alkon DL. Pairing-specific long-term depression of Purkinje cell excitatory postsynaptic potentials results from a classical conditioning procedure in the rabbit cerebellar slice. J Neurophysiol 1996; 75: 1051–1060.PubMedGoogle Scholar
  62. 62.
    Lev-Ram V, Jiang T, Wood J, Lawrence DS, Tsien RY. Synergies and coincidence requirements between NO, cGMP, and Ca++ in the induction of cerebellar long-term depression. Neuron 1997; 18: 1025–1038.PubMedCrossRefGoogle Scholar
  63. 63.
    Bell CC, Han VZ, Sugawara Y, Grant K. Synaptic plasticity in a cerebellum-like structure depends on temporal order. Nature 1997; 387: 278–281.PubMedCrossRefGoogle Scholar
  64. 64.
    Wang SS, Denk W, Hausser M. Coincidence detection in single dendritic spines mediated by calcium release. Nat Neurosci 2000; 3: 1266–1273.PubMedCrossRefGoogle Scholar
  65. 65.
    Gerstner W, van Hemmen JL. Associative memory in a network of ‘spiking’ neurons. Network 1992; 3: 139–164.CrossRefGoogle Scholar
  66. 66.
    Gerstner W. Time structure of the activity in neural network models. Phys Rev E 1995; 51: 738–758.CrossRefGoogle Scholar
  67. 67.
    Kistler WM, Gerstner W, van Hemmen JL. Reduction of the Hodgkin-Huxley equations to a single-variable threshold model. Neural Comput 1997; 9: 1015–1045.CrossRefGoogle Scholar
  68. 68.
    Schwarz C, Welsh JP. Dynamic modulation of mossy fiber system throughput by inferior olive synchrony: a multielectrode study of cerebellar cortex activated by motor cortex. J Neurophysiol 2001; 86: 2489–2504.PubMedGoogle Scholar
  69. 69.
    Ruigrok TJH, Voogd J. Cerebellar in uence on olivary excitability in the cat. Eur J Neurosci 1995; 7: 679–693.PubMedCrossRefGoogle Scholar
  70. 70.
    Armstrong DM, Cogdell B, Harvey RJ. Effects of afferent volleys from the limbs on the discharge patterns of interpositus neurones in cats anaesthetized with α-chloralose. J Physiol (Lond) 1975; 248: 489–517.Google Scholar
  71. 71.
    Armstrong DM, Cogdell B, Harvey RJ. Discharge patterns of Purkinje cells in cats anaesthetized with α-chloralose. J Physiol (Lond) 1979; 291: 351–366.Google Scholar
  72. 72.
    Yamamoto T, Fukuda M, Llinás R. Bilaterally synchronous complex spike Purkinje cell activity in the mammalian cerebellum. Europ J Neurosci 2001; 13: 327–339.CrossRefGoogle Scholar
  73. 73.
    Hartmann MJ, Bower JM. Oscillatory activity in the cerebellar hemispheres of unrestrained rats. J Neurophysiol 1998; 80: 1598–1604.PubMedGoogle Scholar
  74. 74.
    Pellerin JP, Lamarre Y. Local field potential oscillations in primate cerebellar cortex during voluntary movements. J Neurophysiol 1997; 78: 3502–3507.PubMedGoogle Scholar
  75. 75.
    Keating JG, Thach WT. Nonclock behavior of inferior olive neurons: interspike interval of Purkinje cell complex spike discharge in the awake behaving monkey is random. J Neurophysiol 1995; 73: 1329–1340.PubMedGoogle Scholar
  76. 76.
    Keating JG, Thach WT. No clock signal in the discharge of neurons in the deep cerebellar nuclei. J Neurophysiol 1997; 77: 2232–2234.PubMedGoogle Scholar
  77. 77.
    Welsh JP, Lang EJ, Sugihara I, Llinás R. Dynamic organization of motor control within the olivocerebellar system. Nature 1995; 374: 453–457.PubMedCrossRefGoogle Scholar
  78. 78.
    Lang EJ, Sugihara I, Welsh JP, Llinás R. Patterns of spontaneous Purkinje cell complex spike activity in the awake rat. J Neurosci 1999; 19: 2728–2739.PubMedGoogle Scholar
  79. 79.
    Perret SP, Ruiz BP, Mauk MD. Cerebellar cortex lesions disrupt learning-dependent timing of conditioned eyelid response. J Neurosci 1993; 13: 1708–1718.Google Scholar
  80. 80.
    Yeo CH, Hesslow G. Cerebellum and conditioned reflexes. Trends Cognit Sci 1998; 2: 322–330.CrossRefGoogle Scholar

Copyright information

© Taylor & Francis 2003

Authors and Affiliations

  1. 1.Department of NeuroscienceErasmus MC, RotterdamRotterdamThe Netherlands

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