| | Models | Description |
| 1. |
A cerebellar model of phase-locked tACS for essential tremor (Schreglmann et al., 2021)
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This model is a supplementary material for Schreglmann, Sebastian R., et al. "Non-invasive suppression of essential tremor via phase-locked disruption of its temporal coherence" Nature Communications (2021). The model demonstrates that phase-locked transcranial alternating current stimulation (tACS) is able to disrupt the tremor-related oscillations in the cerebellum, and its efficacy is highly dependent on the relative phase between the stimulation and tremor. |
| 2. |
A cortico-cerebello-thalamo-cortical loop model under essential tremor (Zhang & Santaniello 2019)
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We investigated the origins of oscillations under essential tremor (ET) by building a computational model of the cortico-cerebello-thalamo-cortical loop. It showed that an alteration of amplitudes and decay times of the GABAergic currents to the dentate nucleus can facilitate sustained oscillatory activity at tremor frequency throughout the network as well as a robust bursting activity in the thalamus, which is consistent with observations of thalamic tremor cells in ET patients. Tremor-related oscillations initiated in small neural populations and spread to a larger network as the
synaptic dysfunction increased, while thalamic high-frequency stimulation suppressed tremor-related activity in thalamus but increased the oscillation frequency in the olivocerebellar loop. |
| 3. |
Adaptive robotic control driven by a versatile spiking cerebellar network (Casellato et al. 2014)
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" ... We have coupled a realistic cerebellar spiking neural network (SNN) with a real robot and challenged it in multiple diverse sensorimotor tasks. ..." |
| 4. |
Basis for temporal filters in the cerebellar granular layer (Roessert et al. 2015)
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This contains the models, functions and resulting data as used in: Roessert C, Dean P, Porrill J. At the Edge of Chaos: How Cerebellar Granular Layer Network Dynamics Can Provide the Basis for Temporal Filters. It is based on code used for Yamazaki T, Tanaka S (2005) Neural modeling of an internal clock. Neural Comput 17:1032-58 |
| 5. |
Cancelling redundant input in ELL pyramidal cells (Bol et al. 2011)
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The paper investigates the property of the electrosensory lateral line lobe (ELL) of the brain of weakly electric fish to cancel predictable stimuli. Electroreceptors on the skin encode all signals in their firing activity, but superficial pyramidal (SP) cells in the ELL that receive this feedforward input do not respond to constant sinusoidal signals. This cancellation putatively occurs using a network of feedback delay lines and burst-induced synaptic plasticity between the delay lines and the SP cell that learns to cancel the redundant input. Biologically, the delay lines are parallel fibres from cerebellar-like granule cells in the eminentia granularis posterior.
A model of this network (e.g. electroreceptors, SP cells, delay lines and burst-induced plasticity) was constructed to test whether the current knowledge of how the network operates is sufficient to cancel redundant stimuli.
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| 6. |
Cerebellar cortex oscil. robustness from Golgi cell gap jncs (Simoes de Souza and De Schutter 2011)
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" ... Previous one-dimensional network modeling of the cerebellar granular layer has been successfully
linked with a range of cerebellar cortex oscillations observed in vivo. However, the recent discovery of gap
junctions between Golgi cells (GoCs), which may cause oscillations by themselves, has raised the question of how
gap-junction coupling affects GoC and granular-layer oscillations. To investigate this question, we developed a
novel two-dimensional computational model of the GoC-granule cell (GC) circuit with and without gap junctions
between GoCs. ..." |
| 7. |
Cerebellar gain and timing control model (Yamazaki & Tanaka 2007)(Yamazaki & Nagao 2012)
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This paper proposes a hypothetical computational mechanism for unified gain and timing control in the cerebellum. The hypothesis is justified by computer simulations of a large-scale spiking network model of the cerebellum. |
| 8. |
Cerebellar granular layer (Maex and De Schutter 1998)
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Circuit model of the granular layer representing a one-dimensional array of single-compartmental granule cells (grcs) and Golgi cells (Gocs). This paper examines the effects of feedback inhibition (grc -> Goc -> grc) versus feedforward inhibition (mossy fibre -> Goc -> grc) on synchronization and oscillatory behaviour. |
| 9. |
Cerebellar Model for the Optokinetic Response (Kim and Lim 2021)
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We consider a cerebellar spiking neural network for the optokinetic response (OKR). Individual granule (GR) cells exhibit diverse spiking patterns which are in-phase, anti-phase, or complex out-of-phase with respect to their population-averaged firing activity. Then, these diversely-recoded signals via parallel fibers (PFs) from GR cells are effectively depressed by the error-teaching signals via climbing fibers from the inferior olive which are also in-phase ones. Synaptic weights at in-phase PF-Purkinje cell (PC) synapses of active GR cells are strongly depressed via strong long-term depression (LTD), while those at anti-phase and complex out-of-phase PF-PC synapses are weakly depressed through weak LTD. This kind of ‘‘effective’’ depression at the PF-PC synapses causes a big modulation in firings of PCs, which then exert effective inhibitory coordination on the vestibular nucleus (VN) neuron (which evokes OKR). For the firing of the VN neuron, the learning gain degree, corresponding to the modulation gain ratio, increases with increasing the learning cycle, and it saturates. |
| 10. |
Complex dynamics: reproducing Golgi cell electroresponsiveness (Geminiani et al 2018, 2019ab)
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Excerpts from three papers abstracts: "Brain neurons exhibit complex electroresponsive properties – including intrinsic subthreshold oscillations and pacemaking, resonance and phase-reset – which are thought to play a critical role in controlling neural network dynamics. Although these properties emerge from detailed representations of molecular-level mechanisms in “realistic” models, they cannot usually be generated by simplified neuronal models (although these may show spike-frequency adaptation and bursting). We report here that this whole set of properties can be generated by the extended generalized leaky integrate-and-fire (E-GLIF) neuron model. ..." "... In order to reproduce these properties in single-point neuron models, we have optimized the Extended-Generalized Leaky Integrate and Fire (E-GLIF) neuron through a multi-objective gradient-based algorithm targeting the desired input–output relationships. ..." " ... In order to investigate how single neuron dynamics and geometrical modular connectivity affect cerebellar processing, we have built an olivocerebellar Spiking Neural Network (SNN) based on a novel simplification algorithm for single point models (Extended Generalized Leaky Integrate and Fire, EGLIF) capturing essential non-linear neuronal dynamics (e.g., pacemaking, bursting, adaptation, oscillation and resonance). ..." |
| 11. |
Distributed cerebellar plasticity implements adaptable gain control (Garrido et al., 2013)
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We tested the role of plasticity distributed over multiple synaptic sites (Hansel et al., 2001; Gao et al., 2012) by generating an analog cerebellar model embedded into a control loop connected to a robotic simulator. The robot used a three-joint arm and performed repetitive fast manipulations with different masses along an 8-shape trajectory. In accordance with biological evidence, the cerebellum model was endowed with both LTD and LTP at the PF-PC, MF-DCN and PC-DCN synapses. This resulted in a network scheme whose effectiveness was extended considerably compared to one including just PF-PC synaptic plasticity. Indeed, the system including distributed plasticity reliably self-adapted to manipulate different masses and to learn the arm-object dynamics over a time course that included fast learning and consolidation, along the lines of what has been observed in behavioral tests. In particular, PF-PC plasticity operated as a time correlator between the actual input state and the system error, while MF-DCN and PC-DCN plasticity played a key role in generating the gain controller. This model suggests that distributed synaptic plasticity allows generation of the complex learning properties of the cerebellum. |
| 12. |
Fast convergence of cerebellar learning (Luque et al. 2015)
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The cerebellum is known to play a critical role in learning relevant patterns of activity for adaptive motor control, but the underlying network mechanisms are only partly understood. The classical long-term synaptic plasticity between parallel fibers (PFs) and Purkinje cells (PCs), which is driven by the inferior olive (IO), can only account for limited aspects of learning. Recently, the role of additional forms of plasticity in the granular layer, molecular layer and deep cerebellar nuclei (DCN) has been considered. In particular, learning at DCN synapses allows for generalization, but convergence to a stable state requires hundreds of repetitions. In this paper we have explored the putative role of the IO-DCN connection by endowing it with adaptable weights and exploring its implications in a closed-loop robotic manipulation task. Our results show that IO-DCN plasticity accelerates convergence of learning by up to two orders of magnitude without conflicting with the generalization properties conferred by DCN plasticity. Thus, this model suggests that multiple distributed learning mechanisms provide a key for explaining the complex properties of procedural learning and open up new experimental questions for synaptic plasticity in the cerebellar network. |
| 13. |
Logarithmic distributions prove that intrinsic learning is Hebbian (Scheler 2017)
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"In this paper, we present data for the lognormal distributions of spike rates,
synaptic weights and intrinsic excitability (gain) for neurons in various brain
areas, such as auditory or visual cortex, hippocampus, cerebellum, striatum,
midbrain nuclei. We find a remarkable consistency of heavy-tailed, specifically
lognormal, distributions for rates, weights and gains in all brain areas
examined. The difference between strongly recurrent and feed-forward
connectivity (cortex vs. striatum and cerebellum), neurotransmitter (GABA
(striatum) or glutamate (cortex)) or the level of activation (low in cortex, high in
Purkinje cells and midbrain nuclei) turns out to be irrelevant for this feature.
Logarithmic scale distribution of weights and gains appears to be a general,
functional property in all cases analyzed. We then created a generic neural
model to investigate adaptive learning rules that create and maintain lognormal
distributions. We conclusively demonstrate that not only weights, but also
intrinsic gains, need to have strong Hebbian learning in order to produce and
maintain the experimentally attested distributions. This provides a solution to
the long-standing question about the type of plasticity exhibited by intrinsic
excitability." |
| 14. |
Model of the cerebellar granular network (Sudhakar et al 2017)
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"The granular layer, which mainly consists of granule and Golgi cells, is the first stage of the cerebellar cortex and processes spatiotemporal information transmitted by mossy fiber inputs with a wide variety of firing patterns. To study its dynamics at multiple time scales in response to inputs approximating real spatiotemporal patterns, we constructed a large-scale 3D network model of the granular layer. ..." |
| 15. |
Network model of the granular layer of the cerebellar cortex (Maex, De Schutter 1998)
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We computed the steady-state activity of a large-scale model of the granular layer of the rat cerebellum. Within a few tens of milliseconds after the start of random mossy fiber input, the populations of Golgi and granule cells became entrained in a single synchronous oscillation, the basic frequency of which ranged from 10 to 40 Hz depending on the average rate of firing in the mossy fiber population. ... The synchronous, rhythmic firing pattern was robust over a broad range of biologically realistic parameter values and to parameter randomization. Three conditions, however, made the oscillations more transient and could desynchronize the entire network in the end: a very low mossy fiber activity, a very dominant excitation of Golgi cells through mossy fiber synapses (rather than through parallel fiber synapses), and a tonic activation of granule cell GABAA receptors (with an almost complete absence of synaptically induced inhibitory postsynaptic currents). The model predicts that, under conditions of strong mossy fiber input to the cerebellum, Golgi cells do not only control the strength of parallel fiber activity but also the timing of the individual spikes. Provided that their parallel fiber synapses constitute an important source of excitation, Golgi cells fire rhythmically and synchronized with granule cells over large distances along the parallel fiber axis. See paper for more and details. |
| 16. |
Neural modeling of an internal clock (Yamazaki and Tanaka 2008)
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"We studied a simple random recurrent inhibitory network. Despite its simplicity, the dynamics was so rich that activity patterns of neurons
evolved with time without recurrence due to random recurrent connections
among neurons. The sequence of activity patterns was generated
by the trigger of an external signal, and the generation was stable against
noise.... Therefore, a
time passage from the trigger of an external signal could be represented by
the sequence of activity patterns, suggesting that this model could work
as an internal clock. ..." |
| 17. |
Purkinje cell: Synaptic activation predicts voltage control of burst-pause (Masoli & D'Angelo 2017)
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"The dendritic processing in cerebellar Purkinje cells (PCs), which integrate synaptic inputs coming from hundreds of thousands granule cells and molecular layer interneurons, is still unclear. Here we have tested a leading hypothesis maintaining that the significant PC output code is represented by burst-pause responses (BPRs), by simulating PC responses in a biophysically detailed model that allowed to systematically explore a broad range of input patterns. BPRs were generated by input bursts and were more prominent in Zebrin positive than Zebrin negative (Z+ and Z-) PCs. Different combinations of parallel fiber and molecular layer interneuron synapses explained type I, II and III responses observed in vivo. BPRs were generated intrinsically by Ca-dependent K channel activation in the somato-dendritic compartment and the pause was reinforced by molecular layer interneuron inhibition. BPRs faithfully reported the duration and intensity of synaptic inputs, such that synaptic conductance tuned the number of spikes and release probability tuned their regularity in the millisecond range. ..." |
| 18. |
Purkinje neuron network (Zang et al. 2020)
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Both spike rate and timing can transmit information in the brain. Phase response curves (PRCs) quantify how a neuron transforms input to output by spike timing. PRCs exhibit strong firing-rate adaptation, but its mechanism and relevance for network output are poorly understood. Using our Purkinje cell (PC) model we demonstrate that the rate adaptation is caused by rate-dependent subthreshold membrane potentials efficiently regulating the activation of Na+ channels. Then we use a realistic PC network model to examine how rate-dependent responses synchronize spikes in the scenario of reciprocal inhibition-caused high-frequency oscillations. The changes in PRC cause oscillations and spike correlations only at high firing rates. The causal role of the PRC is confirmed using a simpler coupled oscillator network model. This mechanism enables transient oscillations between fast-spiking neurons that thereby form PC assemblies. Our work demonstrates that rate adaptation of PRCs can spatio-temporally organize the PC input to cerebellar nuclei. |
| 19. |
Rapid desynchronization of an electrically coupled Golgi cell network (Vervaeke et al. 2010)
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Electrical synapses between interneurons contribute to synchronized firing and network oscillations in the brain. However, little is known about how such networks respond to excitatory synaptic input. In addition to detailed electrophysiological recordings and histological investigations of electrically coupled Golgi cells in the cerebellum, a detailed network model of these cells was created. The cell models are based on reconstructed Golgi cell morphologies and the active conductances are taken from an earlier abstract Golgi cell model (Solinas et al 2007, accession no. 112685). Our results show that gap junction coupling can sometimes be inhibitory and either promote network synchronization or trigger rapid network desynchronization depending on the synaptic input. The model is available as a neuroConstruct project and can executable scripts can be generated for the NEURON simulator. |
| 20. |
Sparse connectivity is required for decorrelation, pattern separation (Cayco-Gajic et al 2017)
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" ... To investigate the structural and functional determinants of pattern separation we built models of the cerebellar input layer with spatially correlated input patterns, and systematically varied their synaptic connectivity. ..." |
| 21. |
Spike burst-pause dynamics of Purkinje cells regulate sensorimotor adaptation (Luque et al 2019)
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"Cerebellar Purkinje cells mediate accurate eye movement
coordination. However, it remains unclear how oculomotor
adaptation depends on the interplay between the characteristic
Purkinje cell response patterns, namely tonic, bursting, and
spike pauses. Here, a spiking cerebellar model assesses the role
of Purkinje cell firing patterns in vestibular ocular
reflex (VOR) adaptation. The model captures the cerebellar
microcircuit properties and it incorporates spike-based synaptic
plasticity at multiple cerebellar sites. ..." |
| 22. |
Vestibulo-Ocular Reflex model in Matlab (Clopath at al. 2014)
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" ...
We then
introduce a minimal model that consists of learning at the parallel
fibers to Purkinje cells with the help of the climbing
fibers. Although the minimal model reproduces the behavior of the
wild-type animals and is analytically tractable, it fails at
reproducing the behavior of mutant mice and the electrophysiology
data. Therefore, we build a detailed model involving plasticity at the
parallel fibers to Purkinje cells' synapse guided by climbing fibers,
feedforward inhibition of Purkinje cells, and plasticity at the mossy
fiber to vestibular nuclei neuron synapse. The detailed model
reproduces both the behavioral and electrophysiological data of both
the wild-type and mutant mice and allows for experimentally testable
predictions.
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