The cerebellum input stage has been known to perform combinatorial operations on input signals. In this paper, two types of mathematical models were used to reproduce the role of feed-forward inhibition and computation in the granular layer microcircuitry to investigate spike train processing. A simple spiking model and a biophysically-detailed model of the network were used to study signal recoding in the granular layer and to test observations like center-surround organization and time-window hypothesis in addition to effects of induced plasticity. Simulations suggest that simple neuron models may be used to abstract timing phenomenon in large networks, however detailed models were needed to reconstruct population coding via evoked local field potentials (LFP) and for simulating changes in synaptic plasticity. Our results also indicated that spatio-temporal code of the granular network is mainly controlled by the feed-forward inhibition from the Golgi cell synapses. Spike amplitude and total number of spikes were modulated by LTP and LTD. Reconstructing granular layer evoked-LFP suggests that granular layer propagates the nonlinearities of individual neurons. Simulations indicate that granular layer network operates a robust population code for a wide range of intervals, controlled by the Golgi cell inhibition and is regulated by the post-synaptic excitability. 1. Introduction Decoding neural activity is the key to understand spatiotemporal patterns that the brain receives as sensory information regarding the world. Time-scale of operation is closely correlated to the activity of the neural circuit and decoding such activity reveals principles regarding the function. One of the main circuits in the cerebellum is the large input layer circuit formed of granule and Golgi cells. Spatiotemporal information is one of the unique functional characteristics observed in the cerebellar input layer network [1, 2]. Cerebellar granular layer forms the input stage of the cerebellum in which information coming from the peripheral and central systems converge through the mossy fibers. The granular layer has by far the smallest (~5？μm) and the most numerous neurons (~1011) in humans. Understanding how the granular layer process information appears critical to understand the cerebellar function, since signals coming into upper cortical layers are provided by the granular layer. The granule cells form the largest neuronal population in the mammalian brain and regulate information transfer along the major afferent systems to the cerebellum. The granule layer receives
References
[1]
S. Solinas, T. Nieus, and E. D. Angelo, “A realistic large-scale model of the cerebellum granular layer predicts circuit spatio-temporal filtering properties,” Frontiers in Cellular Neuroscience, vol. 4, article 12, 2010.
[2]
E. D'Angelo and C. I. De Zeeuw, “Timing and plasticity in the cerebellum: focus on the granular layer,” Trends in Neurosciences, vol. 32, no. 1, pp. 30–40, 2009.
[3]
J. S. Albus, “A theory of cerebellar function,” Mathematical Biosciences, vol. 10, no. 1-2, pp. 25–61, 1971.
[4]
D. Marr, “A theory of cerebellar cortex,” Journal of Physiology, vol. 202, no. 2, pp. 437–470, 1969.
[5]
F. Prestori, P. Rossi, B. Bearzatto et al., “Altered neuron excitability and synaptic plasticity in the cerebellar granular layer of juvenile prion protein knock-out mice with impaired motor control,” Journal of Neuroscience, vol. 28, no. 28, pp. 7091–7103, 2008.
[6]
S. P. Perrett, B. P. Ruiz, and M. D. Mauk, “Cerebellar cortex lesions disrupt learning-dependent timing of conditioned eyelid responses,” Journal of Neuroscience, vol. 13, no. 4, pp. 1708–1718, 1993.
[7]
M. Goldfarb, J. Schoorlemmer, A. Williams et al., “Fibroblast growth factor homologous factors control neuronal excitability through modulation of voltage-gated sodium channels,” Neuron, vol. 55, no. 3, pp. 449–463, 2007.
[8]
J. Mapelli, D. Gandolfi, and E. D'Angelo, “Combinatorial responses controlled by synaptic inhibition in the cerebellum granular layer,” Journal of Neurophysiology, vol. 103, no. 1, pp. 250–261, 2010.
[9]
E. D'Angelo, T. Nieus, A. Maffei et al., “Theta-frequency bursting and resonance in cerebellar granule cells: experimental evidence and modeling of a slow K+-dependent mechanism,” Journal of Neuroscience, vol. 21, no. 3, pp. 759–770, 2001.
[10]
P. Dean, J. Porrill, C. F. Ekerot, and H. J？rntell, “The cerebellar microcircuit as an adaptive filter: experimental and computational evidence,” Nature Reviews Neuroscience, vol. 11, no. 1, pp. 30–43, 2010.
[11]
J. F. Medina and M. D. Mauk, “Computer simulation of cerebellar information processing,” Nature Neuroscience, vol. 3, pp. 1205–1211, 2000.
[12]
R. Maex and E. De Schutter, “Synchronization of Golgi and granule cell firing in a detailed network model of the cerebellar granule cell layer,” Journal of Neurophysiology, vol. 80, no. 5, pp. 2521–2537, 1998.
[13]
H. Parasuram, B. Nair, G. Naldi, E. D'Angelo, and S. Diwakar, “A modeling based study on the origin and nature of evoked post-synaptic local field potentials in granular layer,” Journal of Physiology Paris, vol. 105, no. 1–3, pp. 71–82, 2011.
[14]
R. Naud, N. Marcille, C. Clopath, and W. Gerstner, “Firing patterns in the adaptive exponential integrate-and-fire model,” Biological Cybernetics, vol. 99, no. 4-5, pp. 335–347, 2008.
[15]
S. Solinas, L. Forti, E. Cesana, J. Mapelli, E. De Schutter, and E. D' Angelo, “Fast-reset of pacemaking and theta-frequency resonance patterns in cerebellar Golgi cells: simulations of their impact in vivo,” Frontiers in Cellular Neuroscience, vol. 1, article 4, 2007.
[16]
S. Solinas, L. Forti, E. Cesana, J. Mapelli, E. De Schutter, and E. D' Angelo, “Computational reconstruction of pacemaking and intrinsic electroresponsiveness in cerebellar Golgi cells,” Frontiers in Cellular Neuroscience, vol. 1, article 2, 2007.
[17]
D. A. McCormick, Z. Wang, and J. Huguenard, “Neurotransmitter control of neocortical neuronal activity and excitability,” Cerebral Cortex, vol. 3, no. 5, pp. 387–398, 1993.
[18]
J. Mapelli and E. D'Angelo, “The spatial organization of long-term synaptic plasticity at the input stage of cerebellum,” Journal of Neuroscience, vol. 27, no. 6, pp. 1285–1296, 2007.
[19]
S. Diwakar, J. Magistretti, M. Goldfarb, G. Naldi, and E. D'Angelo, “Axonal Na+ channels ensure fast spike activation and back-propagation in cerebellar granule cells,” Journal of Neurophysiology, vol. 101, no. 2, pp. 519–532, 2009.
[20]
N. Abdulmanaph, H. Parasuram, B. Nair, and S. Diwakar, “Modeling granular layer local field potential using single neuron and network based approaches to predict LTP/LTD in extracellular recordings,” in Proceedings of Neurocomp, Lyon, France, 2010.
[21]
T. Nieus, E. Sola, J. Mapelli, E. Saftenku, P. Rossi, and E. D'Angelo, “LTP regulates burst initiation and frequency at mossy fiber-granule cell synapses of rat cerebellum: experimental observations and theoretical predictions,” Journal of Neurophysiology, vol. 95, no. 2, pp. 686–699, 2006.
[22]
L. Chen and L. Y. M. Huang, “Protein kinase C reduces Mg2+ block of NMDA-receptor channels as a mechanism of modulation,” Nature, vol. 356, no. 6369, pp. 521–523, 1992.
[23]
C. J. McBain and R. Dingledine, “Dual-component miniature excitatory synaptic currents in rat hippocampal CA3 pyramidal neurons,” Journal of Neurophysiology, vol. 68, no. 1, pp. 16–27, 1992.
[24]
N. Ropert, R. Miles, and H. Korn, “Characteristics of miniature inhibitory postsynaptic currents in CA1 pyramidal neurones of rat hippocampus,” Journal of Physiology, vol. 428, pp. 707–722, 1990.
[25]
T. S. Otis, Y. De Koninck, and I. Mody, “Characterization of synaptically elicited responses using patch-clamp recordings in rat hippocampal slices,” Journal of Physiology, vol. 463, pp. 391–407, 1993.
[26]
S. Diwakar, P. Lombardo, S. Solinas, G. Naldi, and E. D'Angelo, “Local field potential modeling predicts dense activation in cerebellar granule cells clusters under LTP and LTD control,” PLoS ONE, vol. 6, no. 7, Article ID e21928, 2011.
[27]
E. D'Angelo, G. De Filippi, P. Rossi, and V. Taglietti, “Synaptic excitation of individual rat cerebellar granule cells in situ: evidence for the role of NMDA receptors,” Journal of Physiology, vol. 484, no. 2, pp. 397–413, 1995.
[28]
E. D'Angelo, G. De Filippi, P. Rossi, and V. Taglietti, “Ionic mechanism of electroresponsiveness in cerebellar granule cells implicates the action of a persistent sodium current,” Journal of Neurophysiology, vol. 80, no. 2, pp. 493–503, 1998.
[29]
W. Rall, “Branching dendritic trees and motoneuron membrane resistivity,” Experimental Neurology, vol. 1, no. 5, pp. 491–527, 1959.
[30]
P. Rossi, E. Sola, V. Taglietti et al., “NMDA receptor 2 (NR2) C-terminal control of NR open probability regulates synaptic transmission and plasticity at a cerebellar synapse,” Journal of Neuroscience, vol. 22, no. 22, pp. 9687–9697, 2002.
[31]
L. Mapelli, P. Rossi, T. Nieus, and E. D'Angelo, “Tonic activation of receptors reduces release probability at inhibitory connections in the cerebellar glomerulus,” Journal of Neurophysiology, vol. 101, no. 6, pp. 3089–3099, 2009.
[32]
M. L. Hines and N. T. Carnevale, “The NEURON simulation environment,” Neural Computation, vol. 9, no. 6, pp. 1179–1209, 1997.
[33]
L. Roggeri, B. Rivieccio, P. Rossi, and E. D'Angelo, “Tactile stimulation evokes long-term synaptic plasticity in the granular layer of cerebellum,” Journal of Neuroscience, vol. 28, no. 25, pp. 6354–6359, 2008.
[34]
E. Sola, F. Prestori, P. Rossi, V. Taglietti, and E. D'Angelo, “Increased neurotransmitter release during long-term potentiation at mossy fibre-granule cell synapses in rat cerebellum,” Journal of Physiology, vol. 557, no. 3, pp. 843–861, 2004.
[35]
S. Armano, P. Rossi, V. Taglietti, and E. D'Angelo, “Long-term potentiation of intrinsic excitability at the mossy fibergranule cell synapse of rat cerebellum,” Journal of Neuroscience, vol. 20, no. 14, pp. 5208–5216, 2000.
[36]
P. James, N. Abdulmanaph, B. Nair, and S. Diwakar, “Exploring input-output characteristics of the cerebellar granule neuron: role of synaptic inhibition, spike timing and plasticity,” in Proceeding of Neurocomp, Lyon, France, 2010.
[37]
R. A. Silver, S. G. Cull-Candy, and T. Takahashi, “Non-NMDA glutamate receptor occupancy and open probability at a rat cerebellar synapse with single and multiple release sites,” Journal of Physiology, vol. 494, no. 1, pp. 231–250, 1996.
[38]
P. Rossi, L. Mapelli, L. Roggeri et al., “Inhibition of constitutive inward rectifier currents in cerebellar granule cells by pharmacological and synaptic activation of receptors,” European Journal of Neuroscience, vol. 24, no. 2, pp. 419–432, 2006.
[39]
J. C. Eccles, M. Ito, and J. Szentagothai, The Cerebellum as a Neuronal Machine, Springer, Berlin, Germany, 1967.
[40]
C. Palay and S. L. Palay, Cerebellar Cortex: Cytology and Organization, Springer, Berlin, Germany, 1974.
[41]
E. D'Angelo, “The critical role of Golgi cells in regulating spatio-temporal integration and plasticity at the cerebellum input stage,” Frontiers in Neuroscience, vol. 2, pp. 35–46, 2008.
[42]
S. Subramaniyam, C. Medini, B. Nair, and S. Diwakar, “Modeling spatio-temporal processing in cerebellar granular layer and effects of controlled inhbition on plasticity,” in Proceedings of Neurocomp, Lyon, France, 2010.
[43]
A. D'Errico, F. Prestori, and E. D'Angelo, “Differential induction of bidirectional long-term changes in neurotransmitter release by frequency-coded patterns at the cerebellar input,” Journal of Physiology, vol. 587, no. 24, pp. 5843–5857, 2009.
[44]
H. J？rntell and C. F. Ekerot, “Properties of somatosensory synaptic integration in cerebellar granule cells in vivo,” Journal of Neuroscience, vol. 26, no. 45, pp. 11786–11797, 2006.
[45]
S. G. Brickley, S. G. Cull-Candy, and M. Farrant, “Development of a tonic form of synaptic inhibition in rat cerebellar granule cells resulting from persistent activation of receptors,” Journal of Physiology, vol. 497, no. 3, pp. 753–759, 1996.
[46]
J. Magistretti, L. Castelli, L. Forti, and E. D'Angelo, “Kinetic and functional analysis of transient, persistent and resurgent sodium currents in rat cerebellar granule cells in situ: an electrophysiological and modelling study,” Journal of Physiology, vol. 573, no. 1, pp. 83–106, 2006.
[47]
P. Chadderton, T. W. Margie, and M. H？usser, “Integration of quanta in cerebellar granule cells during sensory processing,” Nature, vol. 428, no. 6985, pp. 856–860, 2004.
[48]
E. A. Rancz, T. Ishikawa, I. Duguid, P. Chadderton, S. Mahon, and M. H？usser, “High-fidelity transmission of sensory information by single cerebellar mossy fibre boutons,” Nature, vol. 450, no. 7173, pp. 1245–1248, 2007.
[49]
N. H. Barmack and V. Yakhnitsa, “Functions of interneurons in mouse cerebellum,” Journal of Neuroscience, vol. 28, no. 5, pp. 1140–1152, 2008.
[50]
W. Truccolo, J. A. Donoghue, L. R. Hochberg et al., “Single-neuron dynamics in human focal epilepsy,” Nature Neuroscience, vol. 14, no. 5, pp. 635–641, 2011.
[51]
A. Maffei, F. Prestori, P. Rossi, V. Taglietti, and E. D'Angelo, “Presynaptic current changes at the mossy fiber-granule cell synapse of cerebellum during LTP,” Journal of Neurophysiology, vol. 88, no. 2, pp. 627–638, 2002.
[52]
M. Kase, D. C. Miller, and H. Noda, “Discharges of Purkinje cells and mossy fibres in the cerebellar vermis of the monkey during saccadic eye movements and fixation,” Journal of Physiology, vol. 300, pp. 539–555, 1980.
[53]
A. Volny-Luraghi, R. Maex, B. Vos, and E. De Schutter, “Peripheral stimuli excite coronal beams of Golgi cells in rat cerebellar cortex,” Neuroscience, vol. 113, no. 2, pp. 363–373, 2002.
[54]
T. Yamazaki and S. Tanaka, “A spiking network model for passage-of-time representation in the cerebellum,” European Journal of Neuroscience, vol. 26, no. 8, pp. 2279–2292, 2007.
[55]
G. Buzsáki, “Large-scale recording of neuronal ensembles,” Nature Neuroscience, vol. 7, no. 5, pp. 446–451, 2004.
[56]
M. A. L. Nicolelis and S. Ribeiro, “Multielectrode recordings: the next steps,” Current Opinion in Neurobiology, vol. 12, no. 5, pp. 602–606, 2002.
[57]
K. Ohki, S. Chung, Y. H. Ch'ng, P. Kara, and R. C. Reid, “Functional imaging with cellular resolution reveals precise microarchitecture in visual cortex,” Nature, vol. 433, no. 7026, pp. 597–603, 2005.
[58]
C. Stosiek, O. Garaschuk, K. Holthoff, and A. Konnerth, “In vivo two-photon calcium imaging of neuronal networks,” Proceedings of the National Academy of Sciences of the United States of America, vol. 100, no. 12, pp. 7319–7324, 2003.
[59]
C. E. Andreescu, F. Prestori, F. Brandalise et al., “NR2A subunit of the N-methyl d-aspartate receptors are required for potentiation at the mossy fiber to granule cell synapse and vestibulo-cerebellar motor learning,” Neuroscience, vol. 176, pp. 274–283, 2011.
[60]
R. L. Jenison, “Decoding first-spike latency: a likelihood approach,” Neurocomputing, vol. 38–40, pp. 239–248, 2001.
[61]
M. Fujita, “Adaptive filter model of the cerebellum,” Biological Cybernetics, vol. 45, no. 3, pp. 195–206, 1982.
[62]
M. Uusisaari and E. de Schutter, “The mysterious microcircuitry of the cerebellar nuclei,” Journal of Physiology, vol. 589, no. 14, pp. 3441–3457, 2011.
[63]
L. Bao, A. M. Rapin, E. C. Holmstrand, and D. H. Cox, “Elimination of the channel's high-affinity Ca2+ sensitivity,” Journal of General Physiology, vol. 120, no. 2, pp. 173–189, 2002.
