Distributed cerebellar plasticity implements adaptable gain control in a manipulation task: A closed-loop robotic simulation

Frontiers in Neural Circuits

Volumn 7, Issue OCT, 2013, Pages

  Garrido, Jesús A ^a   Luque, Niceto R ^b   D'Angelo, Egidio ^a,c   Ros, Eduardo ^b  

^a UNIVERSITY OF PAVIA   (Italy)

^b UNIVERSITY OF GRANADA   (Spain)

^c C MONDINO NATIONAL NEUROLOGICAL INSTITUTE   (Italy)

Author keywords

Cerebellar nuclei; Gain control; Learning consolidation; Long term synaptic plasticity; Modeling

Indexed keywords

ADAPTABLE GAIN CONTROL; ARTICLE; CEREBELLAR MOSSY FIBER; CEREBELLAR PARALLEL FIBER; CEREBELLUM; CEREBELLUM NUCLEUS; CORRELATION ANALYSIS; LEARNING; LONG TERM DEPRESSION; MATHEMATICAL ANALYSIS; MOTOR CONTROL; NERVE CELL; NERVE CELL NETWORK; NERVE CELL PLASTICITY; OBJECT MANIPULATION; OBSERVATION; PURKINJE CELL; ROBOTICS; SIGNAL PROCESSING; SIMULATION; SIMULATOR; SYNAPSE; TASK PERFORMANCE; TIME; BIOLOGICAL MODEL; GAIN CONTROL; HUMAN; LEARNING CONSOLIDATION; LONG-TERM SYNAPTIC PLASTICITY; MODEL; MOVEMENT (PHYSIOLOGY); PHYSIOLOGY;

CEREBELLAR NUCLEI; GAIN CONTROL; LEARNING CONSOLIDATION; LONG-TERM SYNAPTIC PLASTICITY; MODELING;

HUMANS; LEARNING; MODELS, NEUROLOGICAL; MOVEMENT; NEURONAL PLASTICITY; NEURONS; ROBOTICS; SYNAPSES;

EID: 84886835922     PISSN: 16625110     EISSN: None     Source Type: Journal    
DOI: 10.3389/fncir.2013.00159     Document Type: Article

References (122)

1. Aizenman, C. D., Manis, P. B., and Linden, D. J. (1998). Polarity of long-term synaptic gain change is related to postsynaptic spike firing at a cerebellar inhibitory synapse. Neuron 21, 827-835. doi: 10.1016/S0896-6273(00)80598-X
2. Albus, J. S. (1971). A theory of cerebellar function. Math. Biosci. 10, 25-61. doi: 10.1016/0025-5564(71)90051-4
3. Albu-Schäffer, A., Eiberger, O., Fuchs, M., Grebenstein, M., Haddadin, S., Ott, C., et al. (2011). Anthropomorphic soft robotics-from torque control to variable intrinsic compliance. Rob. Res. 70, 185-207. doi: 10.1007/978-3-642-19457-3_12
4. Albu-Schäffer, A., Haddadin, S., Ott, C., Stemmer, A., Wimböck, T., and Hirzinger, G. (2007). The DLR lightweight robot: design and control concepts for robots in human environments. Ind. Rob. Int. J. 34, 376-385. doi: 10.1108/01439910710774386
5. Anastasio, T. J. (2001). Input minimization: a model of cerebellar learning without climbing fiber error signals. Neuroreport 12, 3825. doi: 10.1097/00001756-200112040-00045
6. Armano, S., Rossi, P., Taglietti, V., and D'Angelo, E. (2000). Long-term potentiation of intrinsic excitability at the mossy fiber-granule cell synapse of rat cerebellum. J. Neurosci. 20, 5208.
7. Bagnall, M. W., and du Lac, S. (2006). A new locus for synaptic plasticity in cerebellar circuits. Neuron 51, 5-7. doi: 10.1016/j.neuron.2006.06.014
8. Bazzigaluppi, P., De Gruijl, J. R., van der Giessen, R. S., Khosrovani, S., De Zeeuw, C. I., and de Jeu, M. T. (2012). Olivary subthreshold oscillations and burst activity revisited. Front. Neural Circuits 6:91. doi: 10.3389/fncir.2012.00091
9. Bellebaum, C., Koch, B., Schwarz, M., and Daum, I. (2008). Focal basal ganglia lesions are associated with impairments in reward-based reversal learning. Brain 131, 829-841. doi: 10.1093/brain/awn011
10. Berkley, K., and Hand, P. (1978). Projections to the inferior olive of the cat II. Comparisons of input from the gracile, cuneate and the spinal trigeminal nuclel. J. Comp. Neurol. 180, 253-264. doi: 10.1002/cne.901800205
11. Bliss, T. V., and Collingridge, G. L. (1993). A synaptic model of memory: long-term potentiation in the hippocampus. Nature 361, 31-39. doi: 10.1038/361031a0
12. Bona, B., and Curatella, A. (2005). "Identification of industrial robot parameters for advanced model-based controllers design, " in Robotics and Automation, 2005. ICRA 2005. Proceedings of the 2005 IEEE International Conference on (IEEE), (Barcelona), 1681-1686.
13. Bostan, A. C., Dum, R. P., and Strick, P. L. (2013). Cerebellar networks with the cerebral cortex and basal ganglia. Trends Cogn. Sci. 17, 241-254. doi: 10.1016/j.tics.2013.03.003
14. Boyden, E. S., Katoh, A., and Raymond, J. L. (2004). Cerebellum-dependent learning: the role of multiple plasticity mechanisms. Neuroscience 27, 581-609. doi: 10.1146/annurev.neuro.27.070203.144238
15. Brashers-Krug, T., Shadmehr, R., and Bizzi, E. (1996). Consolidation in human motor memory. Nature 382, 252-255. doi: 10.1038/382252a0
16. Cheron, G., Dufief, M. P., Gerrits, N. M., Draye, J. P., and Godaux, E. (1997). Behavioural analysis of Purkinje cell output from the horizontal zone of the cat flocculus. Prog. Brain Res. 114, 347-356. doi: 10.1016/S0079-6123(08)63374-9
17. Coesmans, M., Weber, J. T., De Zeeuw, C. I., and Hansel, C. (2004). Bidirectional parallel fiber plasticity in the cerebellum under climbing fiber control. Neuron 44, 691-700. doi: 10.1016/j.neuron.2004.10.031
18. D'Angelo, E. (2011). Neural circuits of the cerebellum: Hypothesis for function. J. Integr. Neurosci. 10, 317-352. doi: 10.1142/S0219635211002762
19. D'Angelo, E., and Casali, S. (2012). Seeking a unified framework for cerebellar function and dysfunction: from circuit operations to cognition. Front. Neural Circuits 6:116. doi: 10.3389/fncir.2012.00116
20. D'Angelo, E., and De Zeeuw, C. I. (2009). Timing and plasticity in the cerebellum: focus on the granular layer. Trends Neurosci. 32, 30-40. doi: 10.1016/j.tins.2008.09.007
21. D'Angelo, E., Koekkoek, S. K. E., Lombardo, P., Solinas, S., Ros, E., Garrido, J., et al. (2009). Timing in the cerebellum: oscillations and resonance in the granular layer. Neuroscience 162, 805-815. doi: 10.1016/j.neuroscience.2009.01.048
22. D'Angelo, E., Rossi, P., Armano, S., and Taglietti, V. (1999). Evidence for NMDA and mGlu receptor-dependent long-term potentiation of mossy fiber-granule cell transmission in rat cerebellum. J. Neurophysiol. 81, 277.
23. D'Angelo, E., Solinas, S., Mapelli, J., Gandolfi, D., Mapelli, L., and Prestori, F. (2013). The cerebellar Golgi cell and spatiotemporal organization of granular layer activity. Front. Neural Circuits 7:93. doi: 10.3389/fncir.2013.00093
24. D'Errico, A., Prestori, F., and D'Angelo, E. (2009). Differential induction of bidirectional long-term changes in neurotransmitter release by frequency-coded patterns at the cerebellar input. J. Physiol. 587, 5843-5857. doi: 10.1113/jphysiol.2009.177162
25. De Gruijl, J. R., Bazzigaluppi, P., de Jeu, M. T., and De Zeeuw, C. I. (2012). Climbing fiber burst size and olivary sub-threshold oscillations in a network setting. PLoS Comput. Biol. 8:e1002814. doi: 10.1371/journal.pcbi.1002814
26. De Zeeuw, C. I., and Yeo, C. H. (2005). Time and tide in cerebellar memory formation. Curr. Opin. Neurobiol. 15, 667-674. doi: 10.1016/j.conb.2005.10.008
27. Dean, P., Porrill, J., Ekerot, C. F., and Jörntell, H. (2009). The cerebellar microcircuit as an adaptive filter: experimental and computational evidence. Nat. Rev. Neurosci. 11, 30-43. doi: 10.1038/nrn2756
28. Diedrichsen, J., Hashambhoy, Y., Rane, T., and Shadmehr, R. (2005). Neural correlates of reach errors. J. Neurosci. 25, 9919-9931. doi: 10.1523/JNEUROSCI.1874-05.2005
29. Ebner, T., and Pasalar, S. (2008). Cerebellum predicts the future motor state. Cerebellum 7, 583-588. doi: 10.1007/s12311-008-0059-3
30. Escudero, M., Cheron, G., and Godaux, E. (1996). Discharge properties of brain stem neurons projecting to the flocculus in the alert cat. II. Prepositus hypoglossal nucleus. J. Neurophysiol. 76, 1775-1785.
31. Fujita, M. (1982). Adaptive filter model of the cerebellum. Biol. Cybern. 45, 195-206. doi: 10.1007/BF00336192
32. Gall, D., Prestori, F., Sola, E., D'Errico, A., Roussel, C., Forti, L., et al. (2005). Intracellular calcium regulation by burst discharge determines bidirectional long-term synaptic plasticity at the cerebellum input stage. J. Neurosci. 25, 4813. doi: 10.1523/JNEUROSCI.0410-05.2005
33. Galliano, E., Gao, Z., Schonewille, M., Todorov, B., Simons, E., Pop, A. S., et al. (2013). Silencing the majority of cerebellar granule cells uncovers their essential role in motor learning and consolidation. Cell Rep. 3, 1239-1251. doi: 10.1016/j.celrep.2013.03.023
34. Gao, Z., van Beugen, B. J., and De Zeeuw, C. I. (2012). Distributed synergistic plasticity and cerebellar learning. Nat. Rev. Neurosci. 13, 619-635. doi: 10.1038/nrn3312
35. Garrido, J. A., Ros, E., and D'Angelo, E. (2013). Spike timing regulation on the millisecond scale by distributed synaptic plasticity at the cerebellum input stage: a simulation study. Front. Comput. Neurosci. 7:64. doi: 10.3389/fncom.2013.00064
36. Haith, A., and Vijayakumar, S. (2007). "Robustness of VOR and OKR adaptation under kinematics and dynamics transformations, " in Development and Learning, 2007. ICDL 2007. IEEE 6th International Conference on, (London), 37-42.
37. Hansel, C., Linden, D. J., and Angelo, E. D. (2001). Beyond parallel fiber LTD: the diversity of synaptic and non-synaptic plasticity in the cerebellum. Nat. Neurosci. 4, 467-476.
38. Hoellinger, T., Petieau, M., Duvinage, M., Castermans, T., Seetharaman, K., Cebolla, A. M., et al. (2013). Biological oscillations for learning walking coordination: dynamic recurrent neural network functionally models physiological central pattern generator. Front. Comput. Neurosci. 7:70. doi: 10.3389/fncom.2013.00070
39. Hoffmann, H., Petkos, G., Bitzer, S., and Vijayakumar, S. (2007). "Sensor-assisted adaptive motor control under continuously varying context. Icinco 2007, " in Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics, Vol Icso, (Angers), 262-269.
40. Houk, J. C., Buckingham, J. T., and Barto, A. G. (1996). Models of the cerebellum and motor learning. Behav. Brain Sci. 19, 368-383. doi: 10.1017/S0140525X00081474
41. Huang, C. C., Sugino, K., Shima, Y., Guo, C., Bai, S., Mensh, B. D., et al. (2013). Convergence of pontine and proprioceptive streams onto multimodal cerebellar granule cells. Elife 2, e00400. doi: 10.7554/eLife.00400
42. Hwang, E. J., and Shadmehr, R. (2005). Internal models of limb dynamics and the encoding of limb state. J. Neural Eng. 2, S266. doi: 10.1088/1741-2560/2/3/S09
43. Imamizu, H., Miyauchi, S., Tamada, T., Sasaki, Y., Takino, R., Pütz, B., et al. (2000). Human cerebellar activity reflecting an acquired internal model of a new tool. Nature 403, 192-195. doi: 10.1038/35003194
44. Ito, M. (2001). Cerebellar long-term depression: characterization, signal transduction, and functional roles. Physiol. Rev. 81, 1143-1195.
45. Ito, M. (2013). Error detection and representation in the olivo-cerebellar system. Front. Neural Circuits 7:1. doi: 10.3389/fncir.2013.00001
46. Ito, M., and Kano, M. (1982). Long-lasting depression of parallel fiber-Purkinje cell transmission induced by conjunctive stimulation of parallel fibers and climbing fibers in the cerebellar cortex. Neurosci. Lett. 33, 253-258. doi: 10.1016/0304-3940(82)90380-9
47. Izawa, J., Pekny, S. E., Marko, M. K., Haswell, C. C., Shadmehr, R., and Mostofsky, S. H. (2012). Motor learning relies on integrated sensory inputs in ADHD, but over-selectively on proprioception in autism spectrum conditions. Autism Res. 5, 124-136. doi: 10.1002/aur.1222
48. Jordan, M. I., and Rumelhart, D. E. (1992). Forward models: supervised learning with a distal teacher. Cogn. Sci. 16, 307-354. doi: 10.1207/s15516709cog1603_1
49. Kawato, M. (1999). Internal models for motor control and trajectory planning. Curr. Opin. Neurobiol. 9, 718-727. doi: 10.1016/S0959-4388(99)00028-8
50. Kawato, M., Furukawa, K., and Suzuki, R. (1987). A hierarchical neural-network model for control and learning of voluntary movement. Biol. Cybern. 57, 169-185. doi: 10.1007/BF00364149
51. Khalil, W., and Dombre, E. (2004). Modeling, Identification and Control of Robots. Oxford: Butterworth-Heinemann.
52. Kistler, W. M., and Leo van Hemmen, J. (1999). Delayed reverberation through time windows as a key to cerebellar function. Biol. Cybern. 81, 373-380. doi: 10.1007/s004220050569
53. Kitazawa, S., Kimura, T., and Yin, P. B. (1998). Cerebellar complex spikes encode both destinations and errors in arm movements. Nature 392, 494-497. doi: 10.1038/33141
54. Krichmar, J., Ascoli, G., Hunter, L., and Olds, J. (1997). A model of cerebellar saccadic motor learning using qualitative reasoning. Biol. Artif. Comput. Neurosci. Tech. 1240, 133-145. doi: 10.1007/BFb0032471
55. Lepora, N. F., Porrill, J., Yeo, C. H., and Dean, P. (2010). Sensory prediction or motor control. Application of marr-albus type models of cerebellar function to classical conditioning. Front. Comput. Neurosci. 4:140. doi: 10.3389/fncom.2010.00140
56. Lisberger, S. G., and Fuchs, A. F. (1978). Role of primate flocculus during rapid behavioral modification of vestibuloocular reflex. I. Purkinje cell activity during visually guided horizontal smooth-pursuit eye movements and passive head rotation. J. Neurophysiol. 41, 733-763.
57. Luque, N. R., Garrido, J. A., Carrillo, R. R., Coenen, O. J., and Ros, E. (2011a). Cerebellar input configuration toward object model abstraction in manipulation tasks. IEEE Trans. Neural Netw. 22, 1321-1328. doi: 10.1109/TNN.2011.2156809
58. Luque, N. R., Garrido, J. A., Carrillo, R. R., Coenen, O. J., and Ros, E. (2011b). Cerebellarlike corrective model inference engine for manipulation tasks. IEEE Trans. Syst. Man Cybern. B Cybern. 41, 1-14. doi: 10.1109/TSMCB.2011.2138693
59. Luque, N. R., Garrido, J. A., Carrillo, R. R., Tolu, S., and Ros, E. (2011c). Adaptive cerebellar spiking model embedded in the control loop: context switching and robustness against noise. Int. J. Neural Syst. 21, 385-401. doi: 10.1142/S0129065711002900
60. Maffei, A., Prestori, F., Rossi, P., Taglietti, V., and D'Angelo, E. (2002). Presynaptic current changes at the mossy fiber-granule cell synapse of cerebellum during LTP. J. Neurophysiol. 88, 627.
61. Manto, M., Bower, J. M., Conforto, A. B., Delgado-García, J. M., da Guarda, S. N., Gerwig, M., et al. (2012). Consensus paper: roles of the cerebellum in motor control-the diversity of ideas on cerebellar involvement in movement. Cerebellum 11, 457-487. doi: 10.1007/s12311-011-0331-9
62. Mapelli, J., and D'Angelo, E. (2007). The spatial organization of long-term synaptic plasticity at the input stage of cerebellum. J. Neurosci. 27, 1285. doi: 10.1523/JNEUROSCI.4873-06.2007
63. Mapelli, J., Gandolfi, D., and D'Angelo, E. (2010). Combinatorial responses controlled by synaptic inhibition in the cerebellum granular layer. J. Neurophysiol. 103, 250. doi: 10.1152/jn.00642.2009
64. Márquez-Ruiz, J., and Cheron, G. (2012). Sensory stimulation-dependent plasticity in the cerebellar cortex of alert mice. PLoS ONE 7:e36184. doi: 10.1371/journal.pone.0036184
65. Marr, D. (1969). A theory of cerebellar cortex. J. Physiol. 202, 437-470.
66. Masuda, N., and Amari, S. (2008). A computational study of synaptic mechanisms of partial memory transfer in cerebellar vestibulo-ocular-reflex learning. J. Comput. Neurosci. 24, 137-156. doi: 10.1007/s10827-007-0045-7
67. Medina, J. F., Garcia, K. S., Nores, W. L., Taylor, N. M., and Mauk, M. D. (2000). Timing mechanisms in the cerebellum: testing predictions of a large-scale computer simulation. J. Neurosci. 20, 5516-5525.
68. Medina, J. F., and Lisberger, S. G. (2009). Encoding and decoding of learned smooth-pursuit eye movements in the floccular complex of the monkey cerebellum. J. Neurophysiol. 102, 2039-2054. doi: 10.1152/jn.00075.2009
69. Medina, J. F., and Mauk, M. D. (1999). Simulations of cerebellar motor learning: computational analysis of plasticity at the mossy fiber to deep nucleus synapse. J. Neurosci. 19, 7140-7151.
70. Medina, J. F., and Mauk, M. D. (2000). Computer simulation of cerebellar information processing. Nat. Neurosci. 3, 1205-1211. doi: 10.1038/81486
71. Middleton, F. A., and Strick, P. L. (2000). Basal ganglia and cerebellar loops: motor and cognitive circuits. Brain Res. Brain Res. Rev. 31, 236-250. doi: 10.1016/S0165-0173(99)00040-5
72. Molinari, H. H., Schultze, K. E., and Strominger, N. L. (1996). Gracile, cuneate, and spinal trigeminal projections to inferior olive in rat and monkey. J. Comp. Neurol. 375, 467-480. doi: 10.1002/(SICI)1096-9861(19961118)375:3<467::AID-CNE9>3.0.CO;2-0
73. Morishita, W., and Sastry, B. R. (1996). Postsynaptic mechanisms underlying long-term depression of GABAergic transmission in neurons of the deep cerebellar nuclei. J. Neurophysiol. 76, 59-68.
74. Nakano, E., Imamizu, H., Osu, R., Uno, Y., Gomi, H., Yoshioka, T., et al. (1999). Quantitative examinations of internal representations for arm trajectory planning: minimum commanded torque change model. J. Neurophysiol. 81, 2140-2155.
75. Nieus, T., Sola, E., Mapelli, J., Saftenku, E., Rossi, P., and D'Angelo, E. (2006). LTP regulates burst initiation and frequency at mossy fiber-granule cell synapses of rat cerebellum: experimental observations and theoretical predictions. J. Neurophysiol. 95, 686. doi: 10.1152/jn.00696.2005
76. Ohyama, T., Nores, W. L., Medina, J. F., Riusech, F. A., and Mauk, M. D. (2006). Learning-induced plasticity in deep cerebellar nucleus. J. Neurosci. 26, 12656-12663. doi: 10.1523/JNEUROSCI.4023-06.2006
77. Ouardouz, M., and Sastry, B. R. (2000). Mechanisms underlying LTP of inhibitory synaptic transmission in the deep cerebellar nuclei. J. Neurophysiol. 84, 1414-1421.
78. Porrill, J., and Dean, P. (2007). Cerebellar motor learning: when is cortical plasticity not enough. PLoS Comput. Biol. 3:e197. doi: 10.1371/journal.pcbi.0030197
79. Porrill, J., Dean, P., and Stone, J. V. (2004). Recurrent cerebellar architecture solves the motor-error problem. Proc. R. Soc. Lond. B 271, 789-796. doi: 10.1098/rspb.2003.2658
80. Pugh, J. R., and Raman, I. M. (2006). Potentiation of mossy fiber EPSCs in the cerebellar nuclei by NMDA receptor activation followed by postinhibitory rebound current. Neuron 51, 113-123. doi: 10.1016/j.neuron.2006.05.021
81. Racine, R., Wilson, D., Gingell, R., and Sunderland, D. (1986). Long-term potentiation in the interpositus and vestibular nuclei in the rat. Exp. Brain Res. 63, 158-162. doi: 10.1007/BF00235658
82. Roggeri, L., Rivieccio, B., Rossi, P., and D'Angelo, E. (2008). Tactile stimulation evokes long-term synaptic plasticity in the granular layer of cerebellum. J. Neurosci. 28, 6354-6359. doi: 10.1523/JNEUROSCI.5709-07.2008
83. Roitman, A. V., Pasalar, S., and Ebner, T. J. (2009). Single trial coupling of Purkinje cell activity to speed and error signals during circular manual tracking. Exp. Brain. Res. 192, 241-251. doi: 10.1007/s00221-008-1580-9
84. Rossi, P., Sola, E., Taglietti, V., Borchardt, T., Steigerwald, F., Utvik, K., et al. (2002). Cerebellar synaptic excitation and plasticity require proper NMDA receptor positioning and density in granule cells. J. Neurosci. 22, 9687-9697.
85. Rothganger, F. H., and Anastasio, T. J. (2009). Using input minimization to train a cerebellar model to simulate regulation of smooth pursuit. Biol. Cybern. 101, 339-359. doi: 10.1007/s00422-009-0340-7
86. Saint-Cyr, J. (1983). The projection from the motor cortex to the inferior olive in the cat: an experimental study using axonal transport techniques. Neuroscience 10, 667-684. doi: 10.1016/0306-4522(83)90209-9
87. Sawtell, N. B. (2010). Multimodal integration in granule cells as a basis for associative plasticity and sensory prediction in a cerebellum-like circuit. Neuron 66, 573-584. doi: 10.1016/j.neuron.2010.04.018
88. Schweighofer, N., Arbib, M. A., and Dominey, P. F. (1996a). A model of the cerebellum in adaptive control of saccadic gain. I. The model and its biological substrate. Biol. Cybern. 75, 19-28. doi: 10.1007/BF00238736
89. Schweighofer, N., Arbib, M. A., and Dominey, P. F. (1996b). A model of the cerebellum in adaptive control of saccadic gain. II. Simulation results. Biol. Cybern. 75, 29-36. doi: 10.1007/BF00238737
90. Schweighofer, N., Arbib, M. A., and Kawato, M. (1998a). Role of the cerebellum in reaching movements in humans. I. Distributed inverse dynamics control. Eur. J. Neurosci. 10, 86-94. doi: 10.1046/j.1460-9568.1998.00006.x
91. Schweighofer, N., Spoelstra, J., Arbib, M. A., and Kawato, M. (1998b). Role of the cerebellum in reaching movements in humans. II. A neural model of the intermediate cerebellum. Eur. J. Neurosci. 10, 95-105. doi: 10.1046/j.1460-9568.1998.00007.x
92. Schweighofer, N., Doya, K., and Lay, F. (2001). Unsupervised learning of granule cell sparse codes enhances cerebellar adaptive control. Neuroscience 103, 35-50. doi: 10.1016/S0306-4522(00)00548-0
93. Shadmehr, R., and Brashers-Krug, T. (1997). Functional stages in the formation of human long-term motor memory. J. Neurosci. 17, 409-419.
94. Shadmehr, R., and Holcomb, H. H. (1997). Neural correlates of motor memory consolidation. Science 277, 821-825. doi: 10.1126/science.277.5327.821
95. Shadmehr, R., and Krakauer, J. W. (2008). A computational neuroanatomy for motor control. Exp. Brain Res. 185, 359-381. doi: 10.1007/s00221-008-1280-5
96. Shadmehr, R., and Mussa-Ivaldi, S. (2012). Biological Learning and Control: How the Brain Builds Representations, Predicts Events, and Makes Decisions. Cambridge, MA: Mit Press.
97. Siciliano, B., and Khatib, O. (2008). Springer Handbook of Robotics; Part G. Human-Centered and Life-like Robotics. New York, NY: Springer-Verlag New York Inc. doi: 10.1007/978-3-540-30301-5
98. Sola, E., Prestori, F., Rossi, P., Taglietti, V., and D'Angelo, E. (2004). Increased neurotransmitter release during long-term potentiation at mossy fibre-granule cell synapses in rat cerebellum. J. Physiol. 557, 843. doi: 10.1113/jphysiol.2003.060285
99. Solinas, S., Nieus, T., and 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
100. Spencer, R. M. C., Ivry, R. B., and Zelaznik, H. N. (2005). Role of the cerebellum in movements: control of timing or movement transitions. Exp. Brain Res. 161, 383-396. doi: 10.1007/s00221-004-2088-6
101. Spitzer, M. (2000). "Hidden layers, " in The Mind Within the Net: Models of Learning, Thinking and Acting, ed M. Spitzer (Cambridge, MA: The MIT press), 115-136.
102. Spoelstra, J., Schweighofer, N., and Arbib, M. A. (2000). Cerebellar learning of accurate predictive control for fast-reaching movements. Biol. Cybern. 82, 321-333. doi: 10.1007/s004220050586
103. Swain, R. A., Kerr, A. L., and Thompson, R. F. (2011). The cerebellum: a neural system for the study of reinforcement learning. Front. Behav. Neurosci. 5:8. doi: 10.3389/fnbeh.2011.00008
104. Thach, W. (1996). On the specific role of the cerebellum in motor learning and cognition: clues from PET activation and lesion studies in man. Behav. Brain Sci. 19, 411-433. doi: 10.1017/S0140525X00081504
105. Todorov, E. (2004). Optimality principles in sensorimotor control (review). Nat. Neurosci. 7, 907-915. doi: 10.1038/nn1309
106. Tolu, S., Vanegas, M., Garrido, J. A., Luque, N. R., and Ros, E. (2013). Adaptive and predictive control of a simulated robot arm. Int. J. Neural Syst. 23, 1-15. doi: 10.1142/S012906571350010X
107. Tseng, Y. W., Diedrichsen, J., Krakauer, J. W., Shadmehr, R., and Bastian, A. J. (2007). Sensory prediction errors drive cerebellum-dependent adaptation of reaching. J. Neurophysiol. 98, 54-62. doi: 10.1152/jn.00266.2007
108. Uno, Y., Kawato, M., and Suzuki, R. (1989). Formation and control of optimal trajectory in human multijoint arm movement. Minimum torque-change model. Biol. Cybern. 61, 89-101. doi: 10.1007/BF00204593
109. van der Smagt, P. (2000). Benchmarking cerebellar control. Rob. Auton. Syst. 32, 237-251. doi: 10.1016/S0921-8890(00)00090-7
110. Van Kan, P. L., Houk, J. C., and Gibson, A. R. (1993). Output organization of intermediate cerebellum of the monkey. J. Neurophysiol. 69, 57.
111. Wallman, J., and Fuchs, A. F. (1998). Saccadic gain modification: visual error drives motor adaptation. J. Neurophysiol. 80, 2405-2416.
112. Wang, J., Dam, G., Yildirim, S., Rand, W., Wilensky, U., and Houk, J. C. (2008). Reciprocity between the cerebellum and the cerebral cortex: nonlinear dynamics in microscopic modules fop generating voluntary motor commands. Complexity 14, 29-45. doi: 10.1002/cplx.20241
113. Weiss, E. J., and Flanders, M. (2011). Somatosensory comparison during haptic tracing. Cereb. Cortex 21, 425-434. doi: 10.1093/cercor/bhq110
114. Wolpert, D. M., and Ghahramani, Z. (2000). Computational principles of movement neuroscience. Nat. Neurosci. 3, 1212-1217. doi: 10.1038/81497
115. Wolpert, D. M., Miall, R. C., and Kawato, M. (1998). Internal models in the cerebellum. Trends Cogn. Sci. 2, 338-347. doi: 10.1016/S1364-6613(98)01221-2
116. 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, 1042-1049. doi: 10.1038/nn.2348
117. Xu-Wilson, M., Chen-Harris, H., Zee, D. S., and Shadmehr, R. (2009). Cerebellar contributions to adaptive control of saccades in humans. J. Neurosci. 29, 12930-12939. doi: 10.1523/JNEUROSCI.3115-09.2009
118. Yamazaki, T., and Nagao, S. (2012). A computational mechanism for unified gain and timing control in the cerebellum. PLoS ONE 7:e33319. doi: 10.1371/journal.pone.0033319
119. Yamazaki, T., and Tanaka, S. (2005). Neural modeling of an internal clock. Neural Comput. 17, 1032-1058. doi: 10.1162/0899766053491850
120. Yamazaki, T., and Tanaka, S. (2007). The cerebellum as a liquid state machine. Neural Netw. 20, 290-297. doi: 10.1016/j.neunet.2007.04.004
121. Yamazaki, T., and Tanaka, S. (2009). Computational models of timing mechanisms in the cerebellar granular layer. Cerebellum 8, 423-432. doi: 10.1007/s12311-009-0115-7
122. Zhang, W., and Linden, D. J. (2006). Long-term depression at the mossy fiber-deep cerebellar nucleus synapse. J. Neurosci. 26, 6935-6944. doi: 10.1523/JNEUROSCI.0784-06.2006