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Models of the Cortico-cerebellar System

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Neuroscience in the 21st Century
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Abstract

Without the cerebellum, organisms are challenged in the learning and execution of accurate and coordinated actions. It has a central position in the nervous system receiving and projecting to the spinal cord, midbrain, and cerebral cortex, implying convergence of sensory and motor streams. Its highly conserved neuroarchitecture would imply it is very good at what it does and that what it does is very general. Here we review theoretical, modeling, and computational work that has attempted to capture the dynamics and/or function of the cerebellum.

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References

  • Albus JS (1971) A theory of cerebellar function. Math Biosci 10(1/2):25–61. doi:10.1016/j.gaitpost.2012.10.015

    Article  Google Scholar 

  • Angelaki DE, Klier EM, Snyder LH (2009) A vestibular sensation: probabilistic approaches to spatial perception. Neuron 64(4):448–461. doi:10.1016/j.neuron.2009.11.010

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Ankri L, Husson Z, Pietrajtis K, Proville R, Léna C, Yarom Y et al (2015) A novel inhibitory nucleo-cortical circuit controls cerebellar Golgi cell activity. eLife 4. doi:10.7554/eLife.06262

    Google Scholar 

  • Antunes G, De Schutter E (2012) A stochastic signaling network mediates the probabilistic induction of cerebellar long-term depression. J Neurosci 32(27):9288–9300. doi:10.1523/JNEUROSCI.5976-11.2012

    Article  CAS  PubMed  Google Scholar 

  • Anwar H, Hong S, De Schutter E (2012) Controlling Ca2+-activated K+ channels with models of Ca2+ buffering in Purkinje cells. Cerebellum (London, UK) 11(3):681–693. doi:10.1007/s12311-010-0224-3

    Article  CAS  Google Scholar 

  • Anwar H, Hepburn I, Nedelescu H, Chen W, De Schutter E (2013) Stochastic calcium mechanisms cause dendritic calcium spike variability. J Neurosci 33(40):15848–15867. doi:10.1523/JNEUROSCI.1722-13.2013

    Article  CAS  PubMed  Google Scholar 

  • Apps R, Hawkes R (2009) Cerebellar cortical organization: a one-map hypothesis. Nat Rev Neurosci 10(9):670–681. doi:10.1038/nrn2698

    Article  CAS  PubMed  Google Scholar 

  • Armstrong BD, Harvey RJ (1966) Responses in the inferior olive to stimulation of the cerebellar and cerebral cortices in the cat. J Physiol 187(3):553–574

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Armstrong DM, Harvey RJ (1968) Responses to a spino-olivo-cerebellar pathway in the cat. J Physiol 194(1):147–168

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Barbour B (1993) Synaptic currents evoked in Purkinje cells by stimulating individual granule cells. Neuron 11(4):759–769

    Article  CAS  PubMed  Google Scholar 

  • Barbour B, Brunel N, Hakim V, Nadal J-P (2007) What can we learn from synaptic weight distributions? Trends Neurosci 30(12):622–629. doi:10.1016/j.tins.2007.09.005

    Article  CAS  PubMed  Google Scholar 

  • Bazzigaluppi P, Bazzigali (2013) The inferior olive: coupling, oscillations and bursting activity. Erasmus MC, Rotterdam

    Google Scholar 

  • Bazzigaluppi P, Ruigrok TJ, Saisan P, de Jeu MTG, De Zeeuw CI (2012) Properties of the nucleo-olivary pathway: an in vivo whole-cell patch clamp study. PLoS One 7(9):e46360. doi:10.1371/journal.pone.0046360.t003

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Billings G, Piasini E, Lorincz A, Nusser Z, Silver RA (2014) Network structure within the cerebellar input layer enables lossless sparse encoding. Neuron 83(4):960–974. doi:10.1016/j.neuron.2014.07.020

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Bloedel JR, Roberts WJ (1971) Action of climbing fibers in cerebellar cortex of the cat. J Neurophysiol 34(1):17–31

    CAS  PubMed  Google Scholar 

  • Blot A, Barbour B (2013) Analysis of the study of the cerebellar pinceau by Korn and Axelrad. Biorxiv preprint server http://doi.org/10.1101/001123

  • Blot A, Barbour B (2014) Ultra-rapid axon-axon ephaptic inhibition of cerebellar Purkinje cells by the pinceau. Nat Neurosci 17(2):289–295. doi:10.1038/nn.3624

    Article  CAS  PubMed  Google Scholar 

  • Bower J (2010) Model-founded explorations of the roles of molecular layer inhibition in regulating Purkinje cell responses in cerebellar cortex: more trouble for the beam hypothesis. Front Neurosci 4:1–37

    Google Scholar 

  • Braitenberg V (1965) A note on the control of voluntary movements. In: Proceedings from cybernetics of neural processes, Napoli, pp 1–8

    Google Scholar 

  • Braitenberg V (1967) Is the cerebellar cortex a biological clock in the millisecond range? Prog Brain Res, 1–15

    Google Scholar 

  • Braitenberg V (1983) The cerebellum revisited. J Theoret Neurobiol 2:237–241

    Google Scholar 

  • Braitenberg V (1987) The cerebellum and the physics of movement: some speculations. In: Cerebellum and neuronal plasticity. Plenum Press, New York, pp 193–208

    Chapter  Google Scholar 

  • Braitenberg V, Atwood R (1958) Morphological observations on the cerebellar cortex. J Comp Neurol 109(1):1

    Article  CAS  PubMed  Google Scholar 

  • Braitenberg V, Heck D, Sultan F (1997) The detection and generation of sequences as a key to cerebellar function: experiments and theory. Behav Brain Sci 20(2):229–245; discussion 245–277

    Article  CAS  PubMed  Google Scholar 

  • Casellato C, Antonietti A, Garrido JA, Carrillo RR, Luque NR, Ros E et al (2014) Adaptive robotic control driven by a versatile spiking cerebellar network. PLoS One 9(11):e112265. doi:10.1371/journal.pone.0112265

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Chaumont J, Guyon N, Valera AM, Dugué GP, Popa D, Marcaggi P et al (2013) Clusters of cerebellar Purkinje cells control their afferent climbing fiber discharge. Proc Natl Acad Sci 110(40):16223–16228. doi:10.1073/pnas.1302310110

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Clark SL (1939) Responses following electrical stimulation of the cerebellar cortex in the normal cat. J Neurosci 2(1):19–35

    Google Scholar 

  • Clopath C, Nadal J-P, Brunel N (2012) Storage of correlated patterns in standard and bistable Purkinje cell models. PLoS Comput Biol 8(4):e1002448. doi:10.1371/journal.pcbi.1002448.g005

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Clopath C, Badura A, De Zeeuw CI, Brunel N (2014) A cerebellar learning model of vestibulo-ocular reflex adaptation in wild-type and mutant mice. J Neurosci 34(21):7203–7215. doi:10.1523/JNEUROSCI.2791-13.2014

    Article  CAS  PubMed  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. doi:10.1016/j.neuron.2004.10.031

    Article  CAS  PubMed  Google Scholar 

  • D’Angelo E, Nieus T, Maffei A, Armano S, Rossi P, Taglietti V et al (2001) Theta-frequency bursting and resonance in cerebellar granule cells: experimental evidence and modeling of a slow k+-dependent mechanism. J Neurosci 21(3):759–770

    PubMed  Google Scholar 

  • De Gruijl JR (2012) Timing and graded signals in the inferior olive. Erasmus MC, Rotterdam

    Google Scholar 

  • De Gruijl JR, Bazzigaluppi P, de Jeu MTG, De Zeeuw CI (2012) Climbing fiber burst size and olivary sub-threshold oscillations in a network setting. PLoS Comput Biol 8(12):e1002814. doi:10.1371/journal.pcbi.1002814

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • De Gruijl JR, Bosman LWJ, De Zeeuw CI, de Jeu MTG (2013) Inferior olive: all ins and outs. In: Handbook of the cerebellum and cerebellar disorders. Springer Netherlands, Dordrecht, pp 1013–1058. doi:10.1007/978-94-007-1333-8_43

    Chapter  Google Scholar 

  • De Schutter E, Bower JM (1994a) An active membrane model of the cerebellar Purkinje cell II. Simulation of synaptic responses. J Neurophysiol 71(1):401–419

    PubMed  Google Scholar 

  • De Schutter E, Bower JM (1994b) An active membrane model of the cerebellar Purkinje cell. I. Simulation of current clamps in slice. J Neurophysiol 71(1):375–400

    PubMed  Google Scholar 

  • De Schutter E, Bower JM (1994c) Simulated responses of cerebellar Purkinje cells are independent of the dendritic location of granule cell synaptic inputs. Proc Natl Acad Sci U S A 91(11):4736–4740

    Article  PubMed  PubMed Central  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 

  • de Solages C, Szapiro G, Brunel N, Hakim V, Isope P, Buisseret P et al (2008) High-frequency organization and synchrony of activity in the Purkinje cell layer of the cerebellum. Neuron 58(5):775–788. doi:10.1016/j.neuron.2008.05.008

    Article  PubMed  CAS  Google Scholar 

  • De Zeeuw CI, Koekkoek SK, Wylie DR, Simpson JI (1997) Association between dendritic lamellar bodies and complex spike synchrony in the olivocerebellar system. J Neurophysiol 77(4):1747–1758

    PubMed  Google Scholar 

  • De Zeeuw CI, van Hemmen L, Kistler WM (2000) Time window control: a model for cerebellar function based on synchronization, reverberation, and time slicing. Prog Brain Res 124:275–297

    Article  PubMed  Google Scholar 

  • Del Olmo MF, Cheeran B, Koch G, Rothwell JC (2007) Role of the cerebellum in externally paced rhythmic finger movements. J Neurophysiol 98(1):145–152. doi:10.1152/jn.01088.2006

    Article  PubMed  Google Scholar 

  • Dieudonne S (1998) Submillisecond kinetics and low efficacy of parallel fibre-Golgi cell synaptic currents in the rat cerebellum. J Physiol 510(Pt 3):845–866

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Diwakar S, Magistretti J, Goldfarb M, Naldi G, D’Angelo E (2009) Axonal Na+ channels ensure fast spike activation and back-propagation in cerebellar granule cells. J Neurophysiol 101(2):519–532. doi:10.1152/jn.90382.2008

    Article  CAS  PubMed  Google Scholar 

  • Donchin O, Rabe K, Diedrichsen J, Lally N, Schoch B, Gizewski ER, Timmann D (2012) Cerebellar regions involved in adaptation to force field and visuomotor perturbation. J Neurophysiol 107(1):134–147. doi:10.1152/jn.00007.2011

    Article  PubMed  Google Scholar 

  • Doya K (2002) Metalearning and neuromodulation. Neural Netw 15(4–6):495–506

    Article  PubMed  Google Scholar 

  • Dugué GP, Brunel N, Hakim V, Schwartz E, Chat M, Lévesque M et al (2009) Electrical coupling mediates tunable low-frequency oscillations and resonance in the cerebellar Golgi cell network. Neuron 61(1):126–139. doi:10.1016/j.neuron.2008.11.028

    Article  PubMed  CAS  Google Scholar 

  • Ebner TJ, Bloedel JR (1981) Temporal patterning in simple spike discharge of Purkinje cells and its relationship to climbing fiber activity. J Neurophysiol 45(5):933–947

    CAS  PubMed  Google Scholar 

  • Eccles JC, Llinas RR, Sasaki K (1966) Parallel fibre stimulation and the responses induced thereby in the Purkinje cells of the cerebellum. Exp Brain Res (Experimentelle Hirnforschung Expérimentation Cérébrale) 1(1):17–39. doi:10.1007/BF00235207

    CAS  Google Scholar 

  • Eccles JC, Ito M, Szentágothai J (1967) The cerebellum as a neuronal machine. Springer, Berlin

    Book  Google Scholar 

  • Eccles JC, Sabah NH, Schmidt RF, Táboríková H (1972) Cutaneous mechanoreceptors influencing impulse discharges in cerebellar cortex. II. In Purkynĕ cells by mossy fiber input. Experimental Brain Research Experimentelle Hirnforschung Expérimentation Cérébrale 15(3):261–277

    Article  CAS  PubMed  Google Scholar 

  • Edelman GM, Gally JA (2001) Degeneracy and complexity in biological systems. Proc Natl Acad Sci U S A 98(24):13763–13768. doi:10.1073/pnas.231499798

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Ekerot CF, Gustavsson P, Oscarsson O, Schouenborg J (1987) Climbing fibres projecting to cat cerebellar anterior lobe activated by cutaneous A and C fibres. J Physiol 386:529–538

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Fagg AH, Sitko N, Barto AG, Houk J (1997) A computational model of cerebellar learning for limb control. Mh. In: Neural Computation Meeting proceedings, NCM 1997

    Google Scholar 

  • Frens MA, Mathoera AL, van der Steen J (2001) Floccular complex spike response to transparent retinal slip. Neuron 30(3):795–801

    Article  CAS  PubMed  Google Scholar 

  • Gabbiani F, Midtgaard J, Knöpfel T (1994) Synaptic integration in a model of cerebellar granule cells. J Neurophysiol 72(2):999–1009

    CAS  PubMed  Google Scholar 

  • Gao Z, Todorov B, Barrett CF, van Dorp S, Ferrari MD, van den Maagdenberg AMJM et al (2012a) Cerebellar ataxia by enhanced CaV2.1 currents is alleviated by Ca2+-dependent K+-channel activators in Cacna1aS218L mutant mice. J Neurosci 32(44):15533–15546. doi:10.1523/JNEUROSCI.2454-12.2012

    Article  CAS  PubMed  Google Scholar 

  • Gao Z, van Beugen BJ, De Zeeuw CI (2012b) Distributed synergistic plasticity and cerebellar learning. Nat Neurosci 13:619–635. doi:10.1038/nrn3312

    Article  CAS  Google Scholar 

  • Glickstein M, Sultan F, Voogd J (2011) Functional localization in the cerebellum. Cortex 47(1):59–80. doi:10.1016/j.cortex.2009.09.001

    Article  PubMed  Google Scholar 

  • Han VZ, Grant K, Bell CC (2000) Reversible associative depression and nonassociative potentiation at a parallel fiber synapse. Neuron 27(3):611–622

    Article  CAS  PubMed  Google Scholar 

  • 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(5):467–475. doi:10.1038/87419

    CAS  PubMed  Google Scholar 

  • Hawkes R, Sillitoe RV, Chung SH, Fritschy JM, Hoy M (2008) Golgi cell dendrites are restricted by Purkinje cell stripe boundaries in the adult mouse cerebellar cortex. J Neurosci 28(11):2820–2826. doi:10.1523/JNEUROSCI.4145-07.2008

    Article  PubMed  CAS  Google Scholar 

  • Heck D, Sultan F (2002) Cerebellar structure and function: making sense of parallel fibers. Hum Mov Sci 21(3):411–421

    Article  PubMed  Google Scholar 

  • Herzfeld DJ, Kojima Y, Soetedjo R, Shadmehr R (2015) Encoding of action by the Purkinje cells of the cerebellum. Nature 526(7573):439–442. doi:10.1038/nature15693

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Hoogland TM, De Gruijl JR, Witter L, Canto CB, De Zeeuw CI (2015) Role of synchronous activation of cerebellar Purkinje cell ensembles in multi-joint movement control. Curr Biol 25(9):1–10. doi:10.1016/j.cub.2015.03.009

    Article  CAS  Google Scholar 

  • Houck BD, Person AL (2014) Cerebellar loops: a review of the nucleocortical pathway. Cerebellum 13(3):378–385. doi:10.1007/s12311-013-0543-2

    Article  PubMed  PubMed Central  Google Scholar 

  • Houk J, Fagg A (2014) A computational model for cerebellar learning for limb control. 1–16

    Google Scholar 

  • Hull C, Regehr WG (2012) Identification of an inhibitory circuit that regulates cerebellar Golgi cell activity. Neuron 73(1):149–158. doi:10.1016/j.neuron.2011.10.030

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  • Ito M, Kano M (1982) Long-lasting depression of parallel fiber-purkinje cell transmission induced by conjunctive stimulationo of parallel fibers and climbing fibers in the cerebellar cortex. Neurosci Lett 33:253–258

    Article  CAS  PubMed  Google Scholar 

  • Jacobson GA, Lev I, Yarom Y, Cohen D (2009) Invariant phase structure of olivo-cerebellar oscillations and its putative role in temporal pattern generation. Proc Natl Acad Sci 106(9):3579–3584. doi:10.1073/pnas.0806661106

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Jaeger D (2003) No parallel fiber volleys in the cerebellar cortex: evidence from cross-correlation analysis between Purkinje cells in a computer model and in recordings from anesthetized rats. J Comput Neurosci 14(3):311–327

    Article  PubMed  Google Scholar 

  • Jirenhed DA, Hesslow G, Bengtsson F (2007) Acquisition, extinction, and reacquisition of a cerebellar cortical memory trace. J Neurosci 27(10):2493–2502. doi:10.1523/JNEUROSCI.4202-06.2007

    Article  CAS  PubMed  Google Scholar 

  • Jörntell H, Bengtsson F, Schonewille M, De Zeeuw CI (2010) Cerebellar molecular layer interneurons – computational properties and roles in learning. Trends Neurosci 33(11):524–532. doi:10.1016/j.tins.2010.08.004

    Article  PubMed  CAS  Google Scholar 

  • Kalmbach BE, Voicu H, Ohyama T, Mauk MD (2011) A subtraction mechanism of temporal coding in cerebellar cortex. J Neurosci 31(6):2025–2034. doi:10.1523/JNEUROSCI.4212-10.2011

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Kazantsev VB, Nekorkin VI, Makarenko VI, Llinas RR (2003) Olivo-cerebellar cluster-based universal control system. Proc Natl Acad Sci U S A 100(22):13064–13068. doi:10.1073/pnas.1635110100

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Kazantsev VB, Nekorkin VI, Makarenko VI, Llinas RR (2004) Self-referential phase reset based on inferior olive oscillator dynamics. Proc Natl Acad Sci U S A 101(52):18183–18188. doi:10.1073/pnas.0407900101

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Khaliq ZM, Raman IM (2006) Relative contributions of axonal and somatic Na channels to action potential initiation in cerebellar Purkinje neurons. J Neurosci 26(7):1935–1944. doi:10.1523/JNEUROSCI.4664-05.2006

    Article  CAS  PubMed  Google Scholar 

  • Khaliq ZM, Gouwens NW, Raman IM (2003) The contribution of resurgent sodium current to high-frequency firing in Purkinje neurons: an experimental and modeling study. J Neurosci 23(12):4899–4912

    CAS  PubMed  Google Scholar 

  • Kistler WM, van Hemmen L (1999) Delayed reverberation through time windows as a key to cerebellar function. Biol Cybern 81(5–6):373–380

    Article  CAS  PubMed  Google Scholar 

  • Lang EJ, Llinas RR, Sugihara I (2006) Isochrony in the olivocerebellar system underlies complex spike synchrony. J Physiol 573(Pt 1):277–9– author reply 281–2. doi:10.1113/jphysiol.2006.571101

    Google Scholar 

  • Latorre R, Aguirre C, Rabinowitch M, Varona P (2013) Transient dynamics and rhythm coordination of inferior olive spatio-temporal patterns. Front Neural Circuits 1–18. doi:10.3389/fncir.2013.00138/abstract

    Google Scholar 

  • Lefler Y, Torben-Nielsen B, Yarom Y (2013) Oscillatory activity, phase differences, and phase resetting in the inferior olivary nucleus. Front Syst Neurosci 1–9. doi:10.3389/fnsys.2013.00022/abstract

    Google Scholar 

  • Llinas RR, Yarom Y (1981) Properties and distribution of ionic conductances generating electroresponsiveness of mammalian inferior olivary neurones in vitro. J Physiol 315:569–584

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Llinas RR, BAKER R, Sotelo C (1974) Electrotonic coupling between neurons in cat inferior olive. J Neurophysiol 37(3):560–571

    CAS  PubMed  Google Scholar 

  • Llinas RR, Walton K, Hillman DE, Sotelo C (1975) Inferior olive: its role in motor learing. Science (New York, NY) 190(4220):1230–1231. doi:10.1126/science.128123

    Article  CAS  Google Scholar 

  • Maex R, De Schutter E (1998) Synchronization of golgi and granule cell firing in a detailed network model of the cerebellar granule cell layer. J Neurophysiol 80(5):2521–2537

    CAS  PubMed  Google Scholar 

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

    CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Marshall SP, Lang EJ (2004) Inferior olive oscillations gate transmission of motor cortical activity to the cerebellum. J Neurosci 24(50):11356–11367. doi:10.1523/JNEUROSCI.3907-04.2004

    Article  CAS  PubMed  Google Scholar 

  • Mathy A, Ho SSN, Davie JT, Duguid IC, Clark BA, Häusser 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  CAS  PubMed  PubMed Central  Google Scholar 

  • Mauk MD, Steinmetz JE, Thompson RF (1986) Classical conditioning using stimulation of the inferior olive as the unconditioned stimulus. Proc Natl Acad Sci U S A 83(14):5349–5353

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. Bull Math Biophys

    Google Scholar 

  • Medina JF (2010) A recipe for bidirectional motor learning: using inhibition to cook plasticity in the vestibular nuclei. Neuron 68(4):607–609. doi:10.1016/j.neuron.2010.11.011

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Medina JF, Lisberger SG (2008) Links from complex spikes to local plasticity and motor learning in the cerebellum of awake-behaving monkeys. Nat Neurosci 11(10):1185–1192. doi:10.1038/nn.2197

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Mitchell SJ, Silver RA (2000) Glutamate spillover suppresses inhibition by activating presynaptic mGluRs. Nature 404(6777):498–502. doi:10.1038/35006649

    Article  CAS  PubMed  Google Scholar 

  • Najac M, Raman IM (2015) Integration of Purkinje cell inhibition by cerebellar nucleo-olivary neurons. J Neurosci 35(2):544–549. doi:10.1523/JNEUROSCI.3583-14.2015

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Neymotin SA, Lee H, Park E, Fenton AA, Lytton WW (2011) Emergence of physiological oscillation frequencies in a computer model of neocortex. Front Comput Neurosci 5:19. doi:10.3389/fncom.2011.00019

    Article  PubMed  PubMed Central  Google Scholar 

  • Ohyama T, Nores WL, Murphy M, Mauk MD (2003) What the cerebellum computes. Trends Neurosci 26(4):222–227

    Article  CAS  PubMed  Google Scholar 

  • Optican LM, Robinson DA (1980) Cerebellar-dependent adaptive control of primate saccadic system. J Neurophysiol 44(6):1058–1076

    CAS  PubMed  Google Scholar 

  • Ostojic S, Szapiro G, Schwartz E, Barbour B, Brunel N, Hakim V (2015) Neuronal morphology generates high-frequency firing resonance. J Neurosci 35(18):7056–7068. doi:10.1523/JNEUROSCI.3924-14.2015

    Article  CAS  PubMed  Google Scholar 

  • Pellionisz A, Llinas RR (1977) A computer model of cerebellar Purkinje cells. Neuroscience 2(1):37–48

    Article  CAS  PubMed  Google Scholar 

  • Pellionisz A, Llinas RR, Perkel DH (1977) A computer model of the cerebellar cortex of the frog. Neuroscience 2(1):19–35

    Article  CAS  PubMed  Google Scholar 

  • Person AL, Raman IM (2012) Purkinje neuron synchrony elicits time-locked spiking in the cerebellar nuclei. Nature 481(7382):502–505. doi:10.1038/nature10732

    Article  CAS  Google Scholar 

  • Phoka E, Cuntz H, Roth A, Häusser M (2010) A new approach for determining phase response curves reveals that Purkinje cells can act as perfect integrators. PLoS Comput Biol 6(4):e1000768. doi:10.1371/journal.pcbi.1000768

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Porrill J, Dean P (2007) Cerebellar motor learning: when is cortical plasticity not enough? PLoS Comput Biol 3(10):e197. doi:10.1371/journal.pcbi.0030197

    Article  PubMed Central  CAS  Google Scholar 

  • Prsa M, Dash S, Catz N, Dicke PW, Thier P (2009) Characteristics of responses of Golgi cells and mossy fibers to eye saccades and saccadic adaptation recorded from the posterior vermis of the cerebellum. J Neurosci 29(1):250–262. doi:10.1523/JNEUROSCI.4791-08.2009

    Article  CAS  PubMed  Google Scholar 

  • Rasmussen A, Jirenhed DA, Zucca R, Johansson F, Svensson P, Hesslow G (2013) Number of spikes in climbing fibers determines the direction of cerebellar learning. J Neurosci 33(33):13436–13440. doi:10.1523/JNEUROSCI.1527-13.2013

    Article  CAS  PubMed  Google Scholar 

  • Rosenblatt F (1957) The perceptron – a perceiving and recognizing automaton. Report 85-460-1. Cornell Aeronautical Laboratory

    Google Scholar 

  • Rosenblatt F (1958) The Perceptron–a perceiving and recognizing automaton. Cornell Aeronautical Laboratory, Report 85-460-1

    Google Scholar 

  • Ruigrok TJ, Voogd J (1995) Cerebellar influence on olivary excitability in the cat. Eur J Neurosci 7(4):679–693

    Article  CAS  PubMed  Google Scholar 

  • Sauerbrei BA, Lubenov EV, Siapas AG (2015) Structured variability in Purkinje cell activity during locomotion. Neuron 87(4):840–852. doi:10.1016/j.neuron.2015.08.003

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Schmahmann J, Caplan D (2006) Cognition, emotion and the cerebellum. Brain 129(Pt 2):290–292. doi:10.1093/brain/awh729

    PubMed  Google Scholar 

  • Schonewille M, Hoebeek FE, Belmeguenai A, Koekkoek SK, Houtman SH, Boele HJ et al (2010) Purkinje cell-specific knockout of the protein phosphatase PP2B impairs potentiation and cerebellar motor learning. Neuron 67(4):618–628. doi:10.1016/j.neuron.2010.07.009

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Schonewille M, Gao Z, Boele H-J, Vinueza Veloz MF, Amerika WE, Šimek AAM et al (2011) Reevaluating the role of LTD in cerebellar motor learning. Neuron 70(1):43–50. doi:10.1016/j.neuron.2011.02.044

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Schweighofer N, Doya K, Kawato M (1999) Electrophysiological properties of inferior olive neurons: a compartmental model. J Neurophysiol 82(2):804–817

    CAS  PubMed  Google Scholar 

  • Schweighofer N, Doya K, Fukai H, Chiron JV, Furukawa T, Kawato M (2004) Chaos may enhance information transmission in the inferior olive. Proc Natl Acad Sci U S A 101(13):4655–4660. doi:10.1073/pnas.0305966101

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Shin SL, De Schutter E (2006) Dynamic synchronization of Purkinje cell simple spikes. J Neurophysiol 96(6):3485–3491. doi:10.1152/jn.00570.2006

    Article  PubMed  Google Scholar 

  • Shin SL, Hoebeek FE, Schonewille M, De Zeeuw CI, Aertsen A, De Schutter E (2007) Regular patterns in cerebellar Purkinje cell simple spike trains. PLoS One 2(5):e485

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  • Shinoda Y, Sugihara I, Wu HS, Sugiuchi Y (2000) The entire trajectory of single climbing and mossy fibers in the cerebellar nuclei and cortex. Prog Brain Res 124:173–186. doi:10.1016/S0079-6123(00)24015-6. Elsevier

    Article  CAS  PubMed  Google Scholar 

  • Soetedjo R, Kojima Y, Fuchs AF (2008) Complex spike activity in the oculomotor vermis of the cerebellum: a vectorial error signal for saccade motor learning? J Neurophysiol 100(4):1949–1966. doi:10.1152/jn.90526.2008

    Article  PubMed  PubMed Central  Google Scholar 

  • Solinas S, Forti L, Cesana E, Mapelli J, De Schutter E, D’Angelo E (2007) Computational reconstruction of pacemaking and intrinsic electroresponsiveness in cerebellar Golgi cells. Front Cell Neurosci 1:2. doi:10.3389/neuro.03.002.2007

    Article  PubMed  PubMed Central  Google Scholar 

  • Solinas S, Nieus T, D’Angelo E (2010) A realistic large-scale model of the cerebellum granular layer predicts circuit spatio-temporal filtering properties. Front Cell Neurosci 4:12. doi:10.3389/fncel.2010.00012

    PubMed  PubMed Central  Google Scholar 

  • Spencer RMC, Ivry RB (2009) Sequence learning is preserved in individuals with cerebellar degeneration when the movements are directly cued. J Cogn Neurosci 21(7):1302–1310. doi:10.1162/jocn.2009.21102

    Article  PubMed  PubMed Central  Google Scholar 

  • Steuber V, Mittmann W, Hoebeek FE, Silver RA, De Zeeuw CI, Häusser M, de Schutter E (2007) Cerebellar LTD and pattern recognition by Purkinje cells. Neuron 54(1):121–136. doi:10.1016/j.neuron.2007.03.015

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Steuber V, Schultheiss NW, Silver RA, Schutter E, Jaeger D (2010) Determinants of synaptic integration and heterogeneity in rebound firing explored with data-driven models of deep cerebellar nucleus cells. J Comput Neurosci 30(3):633–658. doi:10.1007/s10827-010-0282-z

    Article  PubMed  PubMed Central  Google Scholar 

  • Sugihara I, Wu HS, Shinoda Y (2001) The entire trajectories of single olivocerebellar axons in the cerebellar cortex and their contribution to cerebellar compartmentalization. J Neurosci 21(19):7715–7723

    CAS  PubMed  Google Scholar 

  • Ten Brinke MM, Boele H-J, Spanke JK, Potters JW, Kornysheva K, Wulff P et al (2015) Evolving models of Pavlovian conditioning: cerebellar cortical dynamics in awake behaving mice. CellReports 13(9):1977–1988

    Google Scholar 

  • Thier P, Dicke PW, Haas R, Barash S (2000) Encoding of movement time by populations of cerebellar Purkinje cells. Nature 405(6782):72–76. doi:10.1038/35011062

    Article  CAS  PubMed  Google Scholar 

  • Torben-Nielsen B, Segev I, Yarom Y (2012) The generation of phase differences in a network model of the inferior olive subthreshold oscillations. PLoS Comput Biol 1–10. doi:10.1371/journal.pcbi.1002580

    Google Scholar 

  • Uusisaari M, De Schutter E (2011) The mysterious microcircuitry of the cerebellar nuclei. J Physiol 589(14):3441–3457. doi:10.1113/jphysiol.2010.201582

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Uusisaari MY, Knöpfel T (2012) Diversity of neuronal elements and circuitry in the cerebellar nuclei. Cerebellum (London, England) 11(2):420–421. doi:10.1007/s12311-011-0350-6

    Article  Google Scholar 

  • van der Giessen RS (2007) Role of electrotonic coupling in the olivocerebelar system. Erasmus MC, Rotterdam

    Google Scholar 

  • Velarde MG, Nekorkin VI, Kazantsev VB, Makarenko VI, Llinas RR (2002) Modeling inferior olive neuron dynamics. Neural Netw 15(1):5–10

    Article  PubMed  Google Scholar 

  • Vervaeke K, Nusser Z, Silver RA (2010) Rapid desynchronization of an electrically coupled interneuron network with sparse excitatory synaptic input. Neuron 67(3):435–451. doi:10.1016/j.neuron.2010.06.028

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Vervaeke K, Lorincz A, Nusser Z, Silver RA (2012) Gap junctions compensate for sublinear dendritic integration in an inhibitory network. Science (New York, NY) 335(6076):1624–1628. doi:10.1126/science.1215101

    Article  CAS  Google Scholar 

  • Voogd J, Pardoe J, Ruigrok TJ, Apps R (2003) The distribution of climbing and mossy fiber collateral branches from the copula pyramidis and the paramedian lobule: congruence of climbing fiber cortical zones and the pattern of zebrin banding within the rat cerebellum. J Neurosci 23(11):4645–4656

    CAS  PubMed  Google Scholar 

  • Voogd J, De Zeeuw CI, Schraa-Tam CKL, Geest JN (2010) Visuomotor cerebellum in human and nonhuman primates. Cerebellum (London, England) 11(2):392–410. doi:10.1007/s12311-010-0204-7

    Article  Google Scholar 

  • Vos BP, Volny-Luraghi A, De Schutter E (1999) Cerebellar Golgi cells in the rat: receptive fields and timing of responses to facial stimulation. Eur J Neurosci 11(8):2621–2634

    Article  CAS  PubMed  Google Scholar 

  • Warnaar P, Couto J, Negrello M, Junker M, Smilgin A, Ignashchenkova A et al (2015) Duration of Purkinje cell complex spikes increases with their firing frequency. Front Cell Neurosci 9:1–30. doi:10.3389/fncel.2015.00122

    Article  Google Scholar 

  • Welsh JP, Lang EJ, Suglhara I, Llinas RR (1995) Dynamic organization of motor control within the olivocerebellar system. Nature 374(6521):453–457. doi:10.1038/374453a0

    Article  CAS  PubMed  Google Scholar 

  • Witter L, Canto CB, Hoogland TM, De Gruijl JR, De Zeeuw CI (2013) Strength and timing of motor responses mediated by rebound firing in the cerebellar nuclei after Purkinje cell activation. Front Neural Circuits 7:133. doi:10.3389/fncir.2013.00133

    Article  PubMed  PubMed Central  Google Scholar 

  • Wolpert DM, Kawato M (1998) Multiple paired forward and inverse models for motor control. Neural Netw 11(7–8):1317–1329

    Article  CAS  PubMed  Google Scholar 

  • Wulff P, Schonewille M, Renzi M, Viltono L, Sassoè-Pognetto M, Badura A et al (2009) Synaptic inhibition of Purkinje cells mediates consolidation of vestibulo-cerebellar motor learning. Nat Neurosci 12(8):1042–1049. doi:10.1038/nn.2348

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Yamazaki T, Tanaka S (2007) The cerebellum as a liquid state machine. Neural Netw 20(3):290–297. doi:10.1016/j.neunet.2007.04.004

    Article  PubMed  Google Scholar 

  • Zhou H, Lin Z, Voges K, Ju C, Gao Z, Bosman LW et al (2014) Cerebellar modules operate at different frequencies. eLife 3:e02536. doi:10.7554/eLife.02536

    PubMed  PubMed Central  Google Scholar 

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Negrello, M., De Schutter, E. (2016). Models of the Cortico-cerebellar System. In: Pfaff, D., Volkow, N. (eds) Neuroscience in the 21st Century. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-3474-4_171

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