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Deep cerebellar neurons mirror the spinal cord’s gain to implement an inverse controller

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Abstract

Smooth and coordinated motion requires precisely timed muscle activation patterns, which due to biophysical limitations, must be predictive and executed in a feed-forward manner. In a previous study, we tested Kawato’s original proposition, that the cerebellum implements an inverse controller, by mapping a multizonal microcomplex’s (MZMC) biophysics to a joint’s inverse transfer function and showing that inferior olivary neuron may use their intrinsic oscillations to mirror a joint’s oscillatory dynamics. Here, to continue to validate our mapping, we propose that climbing fiber input into the deep cerebellar nucleus (DCN) triggers rebounds, primed by Purkinje cell inhibition, implementing gain on IO’s signal to mirror the spinal cord reflex’s gain thereby achieving inverse control. We used biophysical modeling to show that Purkinje cell inhibition and climbing fiber excitation interact in a multiplicative fashion to set DCN’s rebound strength; where the former primes the cell for rebound by deinactivating its T-type Ca2+ channels and the latter triggers the channels by rapidly depolarizing the cell. We combined this result with our control theory mapping to predict how experimentally injecting current into DCN will affect overall motor output performance, and found that injecting current will proportionally scale the output and unmask the joint’s natural response as observed by motor output ringing at the joint’s natural frequency. Experimental verification of this prediction will lend support to a MZMC as a joint’s inverse controller and the role we assigned underlying biophysical principles that enable it.

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References

  • Aizenman CD, Linden DJ (1999) Regulation of the rebound depolarization and spontaneous firing patterns of deep nuclear neurons in slices of rat cerebellum. J Neurophysiol 82(4): 1697–1709

    PubMed  CAS  Google Scholar 

  • Aksenov DP, Serdyukova NA, Bloedel JR, Bracha V (2005) Glutamate neurotransmission in the cerebellar interposed nuclei: involvement in classically conditioned eyeblinks and neuronal activity. J Neurophysiol 93(1): 44–52. doi:10.1152/jn.00586.2004

    Article  PubMed  CAS  Google Scholar 

  • Albus J (1971) Theory of cerebellar function. Math Biosci 10(1/2): 25–61

    Article  Google Scholar 

  • Allum JH, Mauritz KH (1984) Compensation for intrinsic muscle stiffness by short-latency reflexes in human triceps surae muscles. J Neurophysiol 52(5): 797–818

    PubMed  CAS  Google Scholar 

  • Alvarez R, Boahen K (2011) Inferior olive mirrors joint dynamics to implement an inverse controller. Biol Cybernet (under review)

  • Alvina K, Walter JT, Kohn A, Ellis-Davies G, Khodakhah K (2008) Questioning the role of rebound firing in the cerebellum. Nat Neurosci 11(11): 1256–1258. doi:10.1038/nn.2195

    Article  PubMed  CAS  Google Scholar 

  • Apps R, Garwicz M (2005) Anatomical and physiological foundations of cerebellar information processing. Nat Rev Neurosci 6(4): 297–311. doi:10.1038/nrn1646

    Article  PubMed  CAS  Google Scholar 

  • Baumel Y, Jacobson GA, Cohen D (2009) Implications of functional anatomy on information processing in the deep cerebellar nuclei. Front Cell Neurosci 3: 14. doi:10.3389/neuro.03.014.2009

    Article  PubMed  Google Scholar 

  • Bennett DJ (1994) Stretch reflex responses in the human elbow joint during a voluntary movement. J Physiol 474(2): 339–351

    PubMed  CAS  Google Scholar 

  • Berthier NE, Moore JW (1986) Cerebellar Purkinje cell activity related to the classically conditioned nictitating membrane response. Exp Brain Res 63(2): 341–350

    Article  PubMed  CAS  Google Scholar 

  • Berthier NE, Singh SP, Barto AG, Houk JC (1993) Distributed representation of limb motor programs in arrays of adjustable pattern generators. J Cognit Neurosc 5(1): 56–78. doi:10.1162/jocn.1993.5.1.56

    Article  Google Scholar 

  • Chan-Palay V (1973) On the identification of the afferent axon terminals in the nucleus lateralis of the cerebellum. An electron microscope study. Z Anat Entwicklungsgesch 142(2): 149–186

    Article  PubMed  CAS  Google Scholar 

  • Chorev E, Manor Y, Yarom Y (2006) Density is destiny–on [corrected] the relation between quantity of T-type Ca2+ channels and neuronal electrical behavior. CNS Neurol Disord Drug Targets 5(6): 655–662

    Article  PubMed  CAS  Google Scholar 

  • Chun SW, Choi JH, Kim MS, Park BR (2003) Characterization of spontaneous synaptic transmission in rat medial vestibular nucleus. Neuroreport 14(11): 1485–1488. doi:10.1097/01.wnr.0000079893.11980.a4

    Article  PubMed  Google Scholar 

  • De Schutter E, Steuber V (2009) Patterns and pauses in Purkinje cell simple spike trains: experiments, modeling and theory. Neuroscience 162(3): 816–826. doi:10.1016/j.neuroscience.2009.02.040

    Article  PubMed  CAS  Google Scholar 

  • Fortier PA, Kalaska JF, Smith AM (1989) Cerebellar neuronal activity related to whole-arm reaching movements in the monkey. J Neurophysiol 62(1): 198–211

    PubMed  CAS  Google Scholar 

  • Fu QG, Flament D, Coltz JD, Ebner TJ (1997) Relationship of cerebellar Purkinje cell simple spike discharge to movement kinematics in the monkey. J Neurophysiol 78(1): 478–491

    PubMed  CAS  Google Scholar 

  • Fujita M (1982) Adaptive filter model of the cerebellum. Biol Cybern 45(3): 195–206

    Article  PubMed  CAS  Google Scholar 

  • Gauck V, Jaeger D (2000) The control of rate and timing of spikes in the deep cerebellar nuclei by inhibition. J Neurosci 20(8): 3006– 3016

    PubMed  CAS  Google Scholar 

  • Ghez C, Fahn S (1985) The cerebellum. In: Kandel E, Schwarts J, Jessel T (eds) Principles of neural science, 2nd edn. Elsevier, New York

    Google Scholar 

  • Hille B (2001) Ion channels of excitable membranes, 3rd edn. Sinauer, Sunderland

    Google Scholar 

  • Jahnsen H (1986) Electrophysiological characteristics of neurones in the guinea-pig deep cerebellar nuclei in vitro. J Physiol 372: 129–147

    PubMed  CAS  Google Scholar 

  • Kawato M, Gomi H (1992) A computational model of four regions of the cerebellum based on feedback-error learning. Biol Cybern 68(2): 95–103

    Article  PubMed  CAS  Google Scholar 

  • Kistler WM, De Zeeuw CI (2003) Time windows and reverberating loops: a reverse-engineering approach to cerebellar function. Cerebellum 2(1): 44–54. doi:10.1080/14734220309426

    Article  PubMed  Google Scholar 

  • Kistler WM, Hemmen JL, De Zeeuw CI (2000) Time window control: a model for cerebellar function based on synchronization, reverberation, and time slicing. Prog Brain Res 124: 275–297. doi:10.1016/S0079-6123(00)24023-5

    Article  PubMed  CAS  Google Scholar 

  • Llinas R, Muhlethaler M (1988) Electrophysiology of guinea-pig cerebellar nuclear cells in the in vitro brain stem-cerebellar preparation. J Physiol 404: 241–258

    PubMed  CAS  Google Scholar 

  • Llinas R, Walton K, Lang E (2004) Cerebellum. In: Sheperd G (eds) The synaptic Organization of the Brain. Oxford University Press, New York

    Google Scholar 

  • Mainen ZF, Sejnowski TJ (1996) Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382(6589): 363–366. doi:10.1038/382363a0

    Article  PubMed  CAS  Google Scholar 

  • Manor Y, Rinzel J, Segev I, Yarom Y (1997) Low-amplitude oscillations in the inferior olive: a model based on electrical coupling of neurons with heterogeneous channel densities. J Neurophysiol 77(5): 2736–2752

    PubMed  CAS  Google Scholar 

  • Marr D (1969) A theory of cerebellar cortex. J Physiol 202(2): 437–470

    PubMed  CAS  Google Scholar 

  • Mathy A, Ho SS, Davie JT, Duguid IC, Clark BA, Hausser M (2009) Encoding of oscillations by axonal bursts in inferior olive neurons. Neuron 62(3): 388–399. doi:10.1016/j.neuron.2009.03.023

    Article  PubMed  CAS  Google Scholar 

  • Monsivais P, Clark BA, Roth A, Hausser M (2005) Determinants of action potential propagation in cerebellar Purkinje cell axons. J Neurosci 25(2): 464–472. doi:10.1523/JNEUROSCI.3871-04.2005

    Article  PubMed  CAS  Google Scholar 

  • Raman IM, Gustafson AE, Padgett D (2000) Ionic currents and spontaneous firing in neurons isolated from the cerebellar nuclei. J Neurosci 20(24): 9004–9016

    PubMed  CAS  Google Scholar 

  • Rowland NC, Jaeger D (2008) Responses to tactile stimulation in deep cerebellar nucleus neurons result from recurrent activation in multiple pathways. J Neurophysiol 99(2): 704–717. doi:10.1152/jn.01100.2007

    Article  PubMed  Google Scholar 

  • Wetmore DZ, Mukamel EA, Schnitzer MJ (2008) Lock-and-Key mechanisms of cerebellar memory recall based on rebound currents. J Neurophysiol 100(4): 2328–2347. doi:10.1152/jn.00344.2007

    Article  PubMed  Google Scholar 

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Correspondence to Rodrigo Alvarez-Icaza.

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Alvarez-Icaza, R., Boahen, K. Deep cerebellar neurons mirror the spinal cord’s gain to implement an inverse controller. Biol Cybern 105, 29–40 (2011). https://doi.org/10.1007/s00422-011-0448-4

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