Advertisement

Journal of Computational Neuroscience

, Volume 17, Issue 2, pp 149–164 | Cite as

A Biophysical Model of Synaptic Delay Learning and Temporal Pattern Recognition in a Cerebellar Purkinje Cell

  • Volker Steuber
  • David Willshaw
Article

Abstract

It has been suggested that information in the brain is encoded in temporal spike patterns which are decoded by a combination of time delays and coincidence detection. Here, we show how a multi-compartmental model of a cerebellar Purkinje cell can learn to recognise temporal parallel fibre activity patterns by adapting latencies of calcium responses after activation of metabotropic glutamate receptors (mGluRs). In each compartment of our model, the mGluR signalling cascade is represented by a set of differential equations that reflect the underlying biochemistry. Phosphorylation of the mGluRs changes the concentration of receptors which are available for activation by glutamate and thereby adjusts the time delay between mGluR stimulation and voltage response. The adaptation of a synaptic delay as opposed to a weight represents a novel non-Hebbian learning mechanism that can also implement the adaptive timing of the classically conditioned eye-blink response.

cerebellum calcium mGluR temporal coding 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Armstrong DM, Rawson JA (1979) Activity patterns of cerebellar cortical neurones and climbing fibre afferents in the awake cat. J. Physiol 289: 425–448.PubMedGoogle Scholar
  2. Batchelor AM, Garthwaite J (1993)Novel synaptic potentials in cerebellar Purkinje cells: Probable mediation by metabotropic glutamate receptors. Neuropharmacology 32: 11–20.CrossRefPubMedGoogle Scholar
  3. Batchelor AM, Garthwaite J (1997) Frequency detection and temporally dispersed synaptic signal association through a metabotropic glutamate receptor pathway. Nature 385: 74–77.CrossRefPubMedGoogle Scholar
  4. Batchelor AM, Madge DJ, Garthwaite J (1994) Synaptic activation of metabotropic glutamate receptors in the parallel fibre-Purkinje cell pathway in rat cerebellar slices. Neuroscience 63: 911–915.CrossRefPubMedGoogle Scholar
  5. Berridge MJ, Cobbold PH, Cuthbertson KSR (1988) Spatial and temporal aspects of cell signalling. Phil. Trans. R. Soc. Lond. B 320: 325–343.Google Scholar
  6. Bezprozvanny I, Watras J, Ehrlich BE (1991) Bell-shaped calciumdependent curves of Ins(l,4,5)-P3 gated and calcium gated channels from endoplasmic reticulum of cerebellum. Nature 351: 751–754.CrossRefPubMedGoogle Scholar
  7. Bhalla US, Iyengar R (1999) Emergent properties of networks of biological signaling pathways. Science 283: 381–387.CrossRefPubMedGoogle Scholar
  8. Bialek W, Rieke F, de Ruyter van Steveninck R, Warland D (1991) Reading a neural code. Science 252: 1854–1857.PubMedGoogle Scholar
  9. Blackwell KT, Vogl TP, Alkon DL (1998) Pattern matching in a model of dendritic spines. Network 9: 107–121.PubMedGoogle Scholar
  10. Bloedel JR, Roberts WJ(1971) Action of climbing fibres in cerebellar cortex of the cat. J. Neurophysiol. 34: 17–31.PubMedGoogle Scholar
  11. Brakeman PR, Lanahan AA, O'Brien R, Roche K, Barnes CA, Huganir RL, Worely FP (1997) Homer: A protein that selectively binds metabotropic glutamate receptors. Nature 386: 284–288.CrossRefPubMedGoogle Scholar
  12. BrayD(1995) Protein molecules as computational elements in living cells. Nature 376: 307–312.Google Scholar
  13. Bredt DS, Hwang PM, Snyder SH (1990) Localization of nitric oxide synthase indicating a neural role for nitric oxide. Nature 347:768–770.CrossRefPubMedGoogle Scholar
  14. Carafoli E (1987) Intracellular calcium homeostasis. Ann. Rev. Biochem. 56: 395–433.CrossRefPubMedGoogle Scholar
  15. Clark RE, Manns JR, Squire LR(2001)Trace and delay eyeblink conditioning: Contrasting phenomena of declarative and nondeclarative memory. Psychol. Sci. 12: 304–308.CrossRefPubMedGoogle Scholar
  16. Daniel H, Levenes C, Crepel F (1998) Cellular mechanisms of cerebellar LTD. Trends Neurosci. 21: 401–407.CrossRefPubMedGoogle Scholar
  17. De Schutter E (1995) Cerebellar long-term depression might normalize excitation of Purkinje cells:Ahypothesis. Trends Neurosci. 18: 291–295.CrossRefPubMedGoogle Scholar
  18. De Schutter E (1997) A new functional role for cerebellar long term depression. Prog. Brain Res. 114: 531–544.Google Scholar
  19. De Schutter E, Bower JM (1994) An active membrane model of the cerebellar Purkinje cell. II. Simulation of synaptic responses. J. Neurophysiol 71: 401–419.PubMedGoogle Scholar
  20. Eccles JC, Sabah NH, Schmidt RF, Taborikova H (1972a) Cutaneous mechanoreceptors influencing impulse discharges in cerebellar cortex. 2. In Purkyne cells by mossy fiber input. Exp. Brain Res. 15: 261–277.Google Scholar
  21. Eccles JC, Sabah NH, Schmidt RF, Taborikova H (1972b) Cutaneous mechanoreceptors influencing impulse discharges in cerebellar cortex. 3. In Purkyne cells by climbing fiber input. Exp. Brain Res. 15: 484–497.PubMedGoogle Scholar
  22. Eurich CW, Cowan JD, Milton JG (1997) Hebbian delay adaptation in a network of integrate-and-fire neurons. In:W Gerstner, A Germond, M Hasler, JD Nicoud, eds. Proceedings of the 7th International Conference on Artifical Neural Networks ICANN 97, Springer Verlag, Berlin, pp. 157–162.Google Scholar
  23. Eurich CW, Ernst U, Pawelzik K (1998) Continous dynamics of neuronal delay adaptation. In: L Niklasson, M Bodén, T Ziemke, eds. Proceedings of the 8th International Conference on Artifical Neural Networks ICANN 98, Springer Verlag, Berlin, pp. 355–360.Google Scholar
  24. Fagni L, Bossu JL, Bockaert J (1991) Activation of a Largeconductance Ca2+-DependentK+ Channel by Stimulation of Glutamate Phosphoinositide-coupled Receptors in Cultured Cerebellar Granule Cells. Eur. J. Neurosci. 3: 778–789.PubMedGoogle Scholar
  25. Fagni L, Chavis P, Ango F, Bockaert J (2000) Complex interactions between mGluRs, intracellular Ca2+ stores and ion channels in neurons. Trends Neurosci. 23: 80–88.CrossRefPubMedGoogle Scholar
  26. 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.PubMedGoogle Scholar
  27. Finch EA, Augustine GJ (1998) Local calcium signalling by inositol-1,4,5-trisphosphate in Purkinje cell dendrites. Nature 396: 753–756.CrossRefPubMedGoogle Scholar
  28. Fiorillo CD, Williams JT (1998) Glutamate mediates an inhibitory postsynaptic potential in dopamine neurons. Nature 394: 19–21.CrossRefPubMedGoogle Scholar
  29. Gerstner W, Kempter R, van Hemmen J, Wagner H(1996)Aneuronal learning rule for sub-millisecond temporal coding. Nature 383: 76–78.CrossRefPubMedGoogle Scholar
  30. Hamori J, Szentagothai J (1966) Identification under the electron microscope of climbing fibers and their synaptic contacts. Exp. Brain Res. 1: 65–81.PubMedGoogle Scholar
  31. Hansel C, Linden DJ, D'Angelo E (2001) Beyond parallel fiber LTD: The diversity of synaptic and non-synaptic plasticity in the cerebellum. Nat. Neurosci. 4: 467–475.PubMedGoogle Scholar
  32. Harata N, Katayama J, Takeshita Y, Murai Y, Akaike N (1996) Two components of metabotropic glutamate responses in acutely dissociated CA3 pyramidal neurons of the rat. Brain Res. 711: 223–233.CrossRefPubMedGoogle Scholar
  33. Hartell NA (1994) cGMP acts within cerebellar Purkinje cells to produce long term depression via mechanisms involving PKC and PKG. Neuroreport 5: 833–836.PubMedGoogle Scholar
  34. Hodgkin AL, Nunn BJ (1987) The effect of ions on sodium-calcium exchange in salamander rods. J. Physiol. 391: 371–398.PubMedGoogle Scholar
  35. Hoehler FK, Leonard DW(1976) Double responding in classical nictitating membrane conditioning with single-CS dual-ISI training. Pavlov J. Biol. Sci. 11: 180–190.PubMedGoogle Scholar
  36. Hopfield JJ (1995) Pattern recognition computation using action potential timing for stimulus representation. Nature 376: 33–36.CrossRefPubMedGoogle Scholar
  37. Huang K-P, Huang FL, Mahoney CW, Chen K-H (1991) Protein kinase C subtypes and their respective roles. Prog. Brain Res. 89: 143–155.PubMedGoogle Scholar
  38. Huning H, Glunder H, Palm G (1998) Synaptic delay learning in pulse-coupled neurons. Neural Comp. 10: 555–565.CrossRefGoogle Scholar
  39. Ito M (1996) The new hypothesis does not detract from the MAIT theory. Trends Neurosci. 19: 11.CrossRefPubMedGoogle Scholar
  40. Ito M, Karachot L (1992) Protein kinases and phosphatase inhibitors mediating long-term desensitization of glutamate receptors in cerebellar Purkinje cells. Neuroscience Res. 14: 27–38.Google Scholar
  41. Ito M, Sakurai M, Tongroach P (1982) Climbing fibre induced depression of both mossy fibre responsiveness and glutamate sensitivity of cerebellar Purkinje cells. J. Physiol. 324: 133–134.Google Scholar
  42. James GO, Hardiman MJ, Yeo CH (1987) Hippocampal lesions and trace conditioning in the rabbit. Behav. Brain Res. 23: 109–116.CrossRefPubMedGoogle Scholar
  43. 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.CrossRefPubMedGoogle Scholar
  44. Kehoe EJ, Graham-Clarke P, Schreurs BG (1989) Temporal patterns of the rabbit's nictitating membrane response to compound and component stimuli under mixed CS-US intervals. Behav. Neurosci. 103: 283–295.CrossRefPubMedGoogle Scholar
  45. Khodakhah K, Ogden D (1993) Functional heterogeneity of calcium release by inositol trisphosphate in single Purkinje neurones, cultured cerebellar astrocytes, and peripheral tissues. Proc. Natl. Acad. Sci. USA 90: 4976–4980.PubMedGoogle Scholar
  46. Khodakhah K, Ogden D (1995) Fast activation and inactivation of inositol trisphosphate-evoked Ca2+ release in rat cerebellar Purkinje neurones. J. Physiol. 487: 343–358.PubMedGoogle Scholar
  47. Kishimoto Y, Kawahara S, Mori H, Mishina M, Kirino Y (2001) Long-trace interval eyeblink conditioning is impaired in mutant mice lacking the NMDA receptor subunit epsilon 1. Eur. J. Neurosci. 13: 1221–1227.CrossRefPubMedGoogle Scholar
  48. Laurent G (1996) Dynamical representation of odors by oscillating and evolving neural assemblies. Trends Neurosci. 19: 489–496.CrossRefPubMedGoogle Scholar
  49. Lev-Ram V, Jiang T, Wood J, Lawrence DS, Tsien RY (1997) Synergies and coincidence requirements between NO, cGMP, and Ca2+ in the induction of cerebellar long-term depression. Neuron 18: 1025–1038.CrossRefPubMedGoogle Scholar
  50. Linden DJ, Connor JA (1993) Cellular mechanisms of long-term depression in the cerebellum. Curr. Opin. Neurobiol. 3: 401–406.CrossRefPubMedGoogle Scholar
  51. Lytton J, Westlin M, Burk SE, Shull GE, MacLennan DH (1992) Functional comparisons between isoforms of the sarcoplasmic or endoplasmic reticulum family of calcium pumps. J. Biol. Chem. 267: 14483–14489.PubMedGoogle Scholar
  52. Marais RM, Nguyen O, Woodgett JR, Parker PJ (1990) Studies of the primary sequence requirements for PKC-α,-β1 and-?peptide substrates. FEBS letters 277: 151–155.CrossRefPubMedGoogle Scholar
  53. Masu M, Tanabe Y, Tsuchida K, Shigemoto R, Nakanishi S (1991) Sequence and expression of a metabotropic glutamate receptor. Nature 349: 760–765.CrossRefPubMedGoogle Scholar
  54. McCormick DA, Thompson RF (1984) Cerebellum: Essential involvement in the classically conditioned eyelid response. Science 223: 296–299.PubMedGoogle Scholar
  55. McEchron MD, Weible AP, Disterhoft JF (2001) Aging and learningspecific changes in single-neuron activity in CA1 hippocampus during rabbit trace eyeblink conditioning. J. Neurophysiol. 86: 1839–1857.PubMedGoogle Scholar
  56. Medina JF, Garcia KS, Nores WL, Taylor NM, Mauk MD (2000) Timing mechanisms in the cerebellum: Testing predictions of a large-scale computer simulation. J. Neurosci. 20: 5516–5525.PubMedGoogle Scholar
  57. Meissner G, Darling E, Eveleth J (1986) Kinetics of rapid Ca2+ release by sarcoplasmic reticulum. Effects of Ca2+, Mg2+ and adenine nucleotides. Biochemistry 25: 236–244.PubMedGoogle Scholar
  58. Mignery GA, Johnston PA, Sudhof TC (1992) Mechanism of Ca2+ inhibition of inositol 1,4,5-trisphosphate (InsP3) binding to the cerebellar InsP3 receptor. J. Biol. Chem. 267: 7450–7455.PubMedGoogle Scholar
  59. Moyer JRJ, Deyo RA, Disterhoft JF (1990) Hippocampectomy disrupts trace eye-blink conditioning in rabbits. Behav. Neurosc. 104: 243–252.CrossRefGoogle Scholar
  60. Murphy JT, Sabah NH (1970) Spontaneous firing of cerebellar Purkinje cells in decerebrate and barbiturate anesthesized cats. Brain Res. 17: 515–519.CrossRefPubMedGoogle Scholar
  61. Napp-Zinn H, Jansen M, Eckmiller R (1996) Recognition and tracking of impulse patterns with delay adaptation in biology-inspired pulse processing neural net (BPN) hardware. Biol. Cybernetics 74: 449–453.Google Scholar
  62. Natschlager T, Ruf B (1998) Spatial and temporal pattern analysis via spiking neurons. Network 9: 319–332.PubMedGoogle Scholar
  63. Netzeband JG, Parsons KL, Sweeney DD, Gruol DL (1997) Metabotropic glutamate receptor agonists alter neuronal excitability and Ca2+ levels via the phospholipase C transduction pathway in cultured Purkinje neurons. J. Neurophysiol. 78: 63–75.PubMedGoogle Scholar
  64. Nishizuka Y, Shearman MS, Oda T, Berry N, Tanaka C(1991) Protein kinase C family and nervous function. Prog. Brain Res. 89: 125–141.PubMedGoogle Scholar
  65. Ohyama T, Mauk MD (2001) Latent acquisition of timed responses in cerebellar cortex. J. Neurosci. 21: 682–690.PubMedGoogle Scholar
  66. Rainnie DG, Holmes KH, Shinnick-Gallagher P (1994) Activation of postsynaptic metabotropic glutamate receptors by trans-ACPD hyperpolarizes neurons of the basolateral amygdala. J. Neurosci. 14: 7208–7220.PubMedGoogle Scholar
  67. Rieke F, Warland D, de Ruyter van Steveninck R, Bialek W (1997) Spikes: Exploring the Neural Code. MIT Press, Cambridge, MA.Google Scholar
  68. Ross RT, Scavio MJJ (1983) Perseveration of associative strength in rabbit nictitating membrane conditioning following ISI shifts. Anim. Learn. Behav. 11: 435–438.Google Scholar
  69. Schreurs BG, Alkon DL (1993) Rabbit cerebellar slice analysis of long-term depression and its role in classical conditioning. Brain Res. 631: 235–240.CrossRefPubMedGoogle Scholar
  70. Schweighofer N, Ferriol G (2000) Diffusion of nitric oxide can facilitate cerebellar learning: A simulation study. Proc. Natl. Acad. Sci. USA 97: 10661–10665.CrossRefPubMedGoogle Scholar
  71. Sejnowski TJ (1995) Time for a newneural code? Nature 376: 21–22.CrossRefPubMedGoogle Scholar
  72. Shibuki K, Okada D(1991) Endogenous nitric oxide release required for long-term synaptic depression in the cerebellum. Nature 349: 326–328.CrossRefPubMedGoogle Scholar
  73. Solomon PR, Vander Schaaf ER, Thompson RF, Weisz DJ (1986) Hippocampus and trace conditioning of the rabbit's classically conditioned eye-blink response. Behav. Neurosci. 100: 729–744.CrossRefPubMedGoogle Scholar
  74. Steinmetz JE (1990) Classical nictitating membrane conditioning in rabbits with varying interstimulus intervals and direct activation of cerebellar mossy fibres as the CS. Behav. Brain Res. 38: 97–108.CrossRefPubMedGoogle Scholar
  75. Stemmer PM, Klee CB (1994) Dual calcium ion regulation of calcineurin by calmodulin and calcineurin B. Biochemistry 33: 6859–6866.PubMedGoogle Scholar
  76. Steuber V, Willshaw DJ (1997) How a single Purkinje cell could learn the adaptive timing of the classically conditioned eye-blink response. In: W Gerstner, A Germond, M Hasler, JD Nicoud, eds. Proceedings of the 7th International Conference on Artifical Neural Networks ICANN 97, Springer Verlag, Berlin, pp. 115–120.Google Scholar
  77. Steuber V, Willshaw DJ (1999) Adaptive leaky integrator models of cerebellar Purkinje cells can learn the clustering of temporal patterns. Neurocomputing 26: 271–276.CrossRefGoogle Scholar
  78. Takatsuki K, Kawahara S, Takehara K, Kishimoto Y, Kirino Y(2001) Effects of the noncompetitiveNMDAreceptor antagonist MK-801 on classical eyeblink conditioning in mice. Neuropharmacology 41: 618–628.CrossRefPubMedGoogle Scholar
  79. Tempia F, Miniaci MC, Anchisi D, Strata P (1998) Postsynaptic currents mediated by metabotropic glutamate receptors in cerebellar Purkinje cells. J. Neurophysiol. 80: 520–528.PubMedGoogle Scholar
  80. Thompson RF, Kim JJ (1996) Memory systems in the brain and localization of a memory. Proc. Natl. Acad. Sci. USA 93: 13438–13444.CrossRefPubMedGoogle Scholar
  81. Thompson RF, Krupa DJ (1994) Organization of memory traces in the mammalian brain. Ann. Rev. Neurosci. 17: 519–549.CrossRefPubMedGoogle Scholar
  82. Thorpe S, Fize F, Marlot C (1996) Speed of processing in the human visual system. Nature 381: 520–522.CrossRefPubMedGoogle Scholar
  83. Tu JC, Xiao B, Yuan JP, Lanahan AA, Leoffert K, Li M, Linden DJ, Worley PF (1998) Homer binds a novel proline-rich motif and links group 1 metabotropic glutamate receptors with IP3 receptors. Neuron 21: 717–726.CrossRefPubMedGoogle Scholar
  84. Vincent SR, Kimura H(1992) Histochemical mapping of nitric oxide synthase in the rat brain. Neuroscience 46: 755–784.CrossRefPubMedGoogle Scholar
  85. Wang SS, Denk W, Hausser M(2000) Coincidence detection in single dendritic spines mediated by calcium release. Nat. Neurosci. 3: 1266–1273.CrossRefPubMedGoogle Scholar
  86. Wehr M, Laurent G (1996) Odour encoding by temporal sequences of firing in oscillating neural assemblies. Nature 384: 162–166.CrossRefPubMedGoogle Scholar
  87. Woodruff-Pak DS, Lavond DG, Thompson RF (1985) Trace conditioning: Abolished by cerebellar nuclear lesions but not lateral cerebellar cortex aspirations. Brain Res. 348: 249–260.CrossRefPubMedGoogle Scholar
  88. Yeo CH, Hesslow G (1998) Cerebellum and conditioned reflexes. Trends Cognitive Sci. 2: 322–330.CrossRefGoogle Scholar
  89. Yeo CH, Lobo DH, Baum A (1997) Acquisition of a new-latency conditioned nictitating membrane response-Major, but not complete, dependence on the ipsilateral cerebellum. Learn. Mem. 3: 557–577.PubMedGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Volker Steuber
    • 1
  • David Willshaw
    • 1
  1. 1.Institute for Adaptive and Neural ComputationUniversity of EdinburghEdinburghUK

Personalised recommendations