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Models that contain the Region : Cerebellum

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    Models   Description
1.  A cerebellar model of phase-locked tACS for essential tremor (Schreglmann et al., 2021)
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 Computational Model of Bidirectional Plasticity Regulation by betaCaMKII (Pinto et al. 2019)
We present a computational model that suggests how calcium-calmodulin dependent protein kinase II can act as a molecular switch in synaptic plasticity induction at an important cerebellar synapse (between parallel fibres and Purkinje cells). Our simulation results provide a potential explanation for experimental data by van Woerden et al (Van Woerden G, Hoebeek F, Gao Z, Nagaraja R, Hoogenraad C, Kushner S, et al. [beta]CaMKII controls the direction of plasticity at parallel fiber-Purkinje cell synapses. Nat Neurosci. 2009;12(7):823-825). These experiments were performed in the lab led by Professor Chris De Zeeuw.
3.  A cortico-cerebello-thalamo-cortical loop model under essential tremor (Zhang & Santaniello 2019)
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.
4.  A detailed Purkinje cell model (Masoli et al 2015)
The Purkinje cell is one of the most complex type of neuron in the central nervous system and is well known for its massive dendritic tree. The initiation of the action potential was theorized to be due to the high calcium channels presence in the dendritic tree but, in the last years, this idea was revised. In fact, the Axon Initial Segment, the first section of the axon was seen to be critical for the spontaneous generation of action potentials. The model reproduces the behaviours linked to the presence of this fundamental sections and the interplay with the other parts of the neuron.
5.  A model of cerebellar LTD including RKIP inactivation of Raf and MEK (Hepburn et al 2017)
An updated stochastic model of cerebellar Long Term Depression (LTD) with improved realism. Dissociation of Raf kinase inhibitor protein (RKIP) from Mitogen-activated protein kinase kinase (MEK) and Raf kinase are added to an earlier published model. Calcium dynamics is updated as a constant-rate influx to more closely match experiment. AMPA receptor interactions are improved by adding phosphorylation and dephosphorylation of AMPA receptors when bound to glutamate receptor interacting protein (GRIP). The model is tuned to reproduce experimental calcium peak vs LTD amplitude curves accurately at 4 different calcium pulse durations.
6.  A simplified cerebellar Purkinje neuron (the PPR model) (Brown et al. 2011)
These models were implemented in NEURON by Sherry-Ann Brown in the laboratory of Leslie M. Loew. The files reproduce Figures 2c-f from Brown et al, 2011 "Virtual NEURON: a Strategy For Merged Biochemical and Electrophysiological Modeling".
7.  Adaptive robotic control driven by a versatile spiking cerebellar network (Casellato et al. 2014)
" ... We have coupled a realistic cerebellar spiking neural network (SNN) with a real robot and challenged it in multiple diverse sensorimotor tasks. ..."
8.  Alcohol action in a detailed Purkinje neuron model and an efficient simplified model (Forrest 2015)
" ... we employ a novel reduction algorithm to produce a 2 compartment model of the cerebellar Purkinje neuron from a previously published, 1089 compartment model. It runs more than 400 times faster and retains the electrical behavior of the full model. So, it is more suitable for inclusion in large network models, where computational power is a limiting issue. We show the utility of this reduced model by demonstrating that it can replicate the full model’s response to alcohol, which can in turn reproduce experimental recordings from Purkinje neurons following alcohol application. ..."
9.  Alcohol excites Cerebellar Golgi Cells by inhibiting the Na+/K+ ATPase (Botta et al.2010)
Patch-clamp in cerebellar slices and computer modeling show that ethanol excites Golgi cells by inhibiting the Na+/K+ ATPase. In particular, voltage-clamp recordings of Na+/K+ ATPase currents indicated that ethanol partially inhibits this pump and this effect could be mimicked by low concentrations of the Na+/K+ ATPase blocker ouabain. The partial inhibition of Na+/K+ ATPase in a computer model of the Golgi cell reproduced these experimental findings that established a novel mechanism of action of ethanol on neural excitability.
10.  Basis for temporal filters in the cerebellar granular layer (Roessert et al. 2015)
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
11.  Ca2+ requirements for Long-Term Depression in Purkinje Cells (Criseida Zamora et al 2018)
An updated stochastic model of cerebellar Long-Term Depression (LTD) to study the requirements of calcium to induce LTD. Calcium signal is generated as a train of calcium pulses and this can be modulated by its amplitude, frequency, width and number of pulses. CaMKII activation and its regulatory pathway are added to an earlier published model to study the sensitivity to calcium frequency. The model is useful to investigate systematically the dependence of LTD induction on calcium stimuli parameters.
12.  Calcium dynamics depend on dendritic diameters (Anwar et al. 2014)
"... in dendrites there is a strong contribution of morphology because the peak calcium levels are strongly determined by the surface to volume ratio (SVR) of each branch, which is inversely related to branch diameter. In this study we explore the predicted variance of dendritic calcium concentrations due to local changes in dendrite diameter and how this is affected by the modeling approach used. We investigate this in a model of dendritic calcium spiking in different reconstructions of cerebellar Purkinje cells and in morphological analysis of neocortical and hippocampal pyramidal neurons. ..."
13.  Cancelling redundant input in ELL pyramidal cells (Bol et al. 2011)
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.
14.  Cerebellar cortex oscil. robustness from Golgi cell gap jncs (Simoes de Souza and De Schutter 2011)
" ... 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. ..."
15.  Cerebellar gain and timing control model (Yamazaki & Tanaka 2007)(Yamazaki & Nagao 2012)
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.
16.  Cerebellar Golgi cell (Solinas et al. 2007a, 2007b)
"... Our results suggest that a complex complement of ionic mechanisms is needed to fine-tune separate aspects of the neuronal response dynamics. Simulations also suggest that the Golgi cell may exploit these mechanisms to obtain a fine regulation of timing of incoming mossy fiber responses and granular layer circuit oscillation and bursting."
17.  Cerebellar Golgi cells, dendritic processing, and synaptic plasticity (Masoli et al 2020)
The Golgi cells are the main inhibitory interneurons of the cerebellar granular layer. To study the mechanisms through which these neurons integrate complex input patterns, a new set of models were developed using the latest experimental information and a genetic algorithm approach to fit the maximum ionic channel conductances. The models faithfully reproduced a rich pattern of electrophysiological and pharmacological properties and predicted the operating mechanisms of these neurons.
18.  Cerebellar granular layer (Maex and De Schutter 1998)
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.
19.  Cerebellar granule cell (Masoli et al 2020)
"The cerebellar granule cells (GrCs) are classically described as a homogeneous neuronal population discharging regularly without adaptation. We show that GrCs in fact generate diverse response patterns to current injection and synaptic activation, ranging from adaptation to acceleration of firing. Adaptation was predicted by parameter optimization in detailed computational models based on available knowledge on GrC ionic channels. The models also predicted that acceleration required additional mechanisms. We found that yet unrecognized TRPM4 currents specifically accounted for firing acceleration and that adapting GrCs outperformed accelerating GrCs in transmitting high-frequency mossy fiber (MF) bursts over a background discharge. This implied that GrC subtypes identified by their electroresponsiveness corresponded to specific neurotransmitter release probability values. Simulations showed that fine-tuning of pre- and post-synaptic parameters generated effective MF-GrC transmission channels, which could enrich the processing of input spike patterns and enhance spatio-temporal recoding at the cerebellar input stage."
20.  Cerebellar Model for the Optokinetic Response (Kim and Lim 2021)
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.
21.  Cerebellar nuclear neuron (Sudhakar et al., 2015)
"... In this modeling study, we investigate different forms of Purkinje neuron simple spike pause synchrony and its influence on candidate coding strategies in the cerebellar nuclei. That is, we investigate how different alignments of synchronous pauses in synthetic Purkinje neuron spike trains affect either time-locking or rate-changes in the downstream nuclei. We find that Purkinje neuron synchrony is mainly represented by changes in the firing rate of cerebellar nuclei neurons. ..."
22.  Cerebellar Nucleus Neuron (Steuber, Schultheiss, Silver, De Schutter & Jaeger, 2010)
This is the GENESIS 2.3 implementation of a multi-compartmental deep cerebellar nucleus (DCN) neuron model with a full dendritic morphology and appropriate active conductances. We generated a good match of our simulations with DCN current clamp data we recorded in acute slices, including the heterogeneity in the rebound responses. We then examined how inhibitory and excitatory synaptic input interacted with these intrinsic conductances to control DCN firing. We found that the output spiking of the model reflected the ongoing balance of excitatory and inhibitory input rates and that changing the level of inhibition performed an additive operation. Rebound firing following strong Purkinje cell input bursts was also possible, but only if the chloride reversal potential was more negative than -70 mV to allow de-inactivation of rebound currents. Fast rebound bursts due to T-type calcium current and slow rebounds due to persistent sodium current could be differentially regulated by synaptic input, and the pattern of these rebounds was further influenced by HCN current. Our findings suggest that active properties of DCN neurons could play a crucial role for signal processing in the cerebellum.
23.  Cerebellar stellate cells: changes in threshold, latency and frequency of firing (Mitry et al 2020)
"Cerebellar stellate cells are inhibitory molecular interneurons that regulate the firing properties of Purkinje cells, the sole output of cerebellar cortex. Recent evidence suggests that these cells exhibit temporal increase in excitability during whole-cell patch-clamp configuration in a phenomenon termed runup. They also exhibit a non-monotonic first-spike latency profile as a function of the holding potential in response to a fixed step-current. In this study, we use modeling approaches to unravel the dynamics of runup and categorize the firing behavior of cerebellar stellate cells as either type I or type II oscillators. We then extend this analysis to investigate how the non-monotonic latency profile manifests itself during runup. We employ a previously developed, but revised, Hodgkin–Huxley type model to show that stellate cells are indeed type I oscillators possessing a saddle node on an invariant cycle (SNIC) bifurcation. The SNIC in the model acts as a “threshold” for tonic firing and produces a slow region in the phase space called the ghost of the SNIC. The model reveals that (i) the SNIC gets left-shifted during runup with respect to I app = I test in the current-step protocol, and (ii) both the distance from the stable limit cycle along with the slow region produce the non-monotonic latency profile as a function of holding potential. Using the model, we elucidate how latency can be made arbitrarily large for a specific range of holding potentials close to the SNIC during pre-runup (post-runup). We also demonstrate that the model can produce transient single spikes in response to step- currents entirely below I SNIC , and that a pair of dynamic inhibitory and excitatory post- synaptic inputs can robustly evoke action potentials, provided that the magnitude of the inhibition is either low or high but not intermediate. Our results show that the topology of the SNIC is the key to explaining such behaviors."
24.  Cerebellum granule cell FHF (Dover et al. 2016)
"Neurons in vertebrate central nervous systems initiate and conduct sodium action potentials in distinct subcellular compartments that differ architecturally and electrically. Here, we report several unanticipated passive and active properties of the cerebellar granule cell's unmyelinated axon. Whereas spike initiation at the axon initial segment relies on sodium channel (Nav)-associated fibroblast growth factor homologous factor (FHF) proteins to delay Nav inactivation, distal axonal Navs show little FHF association or FHF requirement for high-frequency transmission, velocity and waveforms of conducting action potentials. ...'
25.  Cerebellum Purkinje cell: dendritic ion channels activated by climbing fibre (Ait Ouares et al 2019)
"In cerebellar Purkinje neuron (PN) dendrites, the transient depolarisation associated with a climbing fibre (CF) EPSP activates voltage-gated Ca2+ channels (VGCCs), voltage-gated K+ channels (VGKCs) and Ca2+ activated SK and BK K+ channels. The resulting membrane potential (Vm) and Ca2+ transients play a fundamental role in dendritic integration and synaptic plasticity of parallel fibre inputs. Here we report a detailed investigation of the kinetics of dendritic Ca2+ and K+ channels activated by CF-EPSPs, based on optical measurements of Vm and Ca2+ transients and on a single-compartment NEURON model reproducing experimental data. ... "
26.  Complex dynamics: reproducing Golgi cell electroresponsiveness (Geminiani et al 2018, 2019ab)
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). ..."
27.  Computational model of cerebellar tDCS (Zhang et al., 2021)
This archive contains models used in (Zhang et al. 2021) and simulates Purkinje cell, granule cell, and deep cerebellar neuron activities under cerebellar tDCS (transcranial direct current stimulation).
28.  Distributed cerebellar plasticity implements adaptable gain control (Garrido et al., 2013)
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.
29.  Effect of voltage sensitive fluorescent proteins on neuronal excitability (Akemann et al. 2009)
"Fluorescent protein voltage sensors are recombinant proteins that are designed as genetically encoded cellular probes of membrane potential using mechanisms of voltage-dependent modulation of fluorescence. Several such proteins, including VSFP2.3 and VSFP3.1, were recently reported with reliable function in mammalian cells. ... Expression of these proteins in cell membranes is accompanied by additional dynamic membrane capacitance, ... We used recordings of sensing currents and fluorescence responses of VSFP2.3 and of VSFP3.1 to derive kinetic models of the voltage-dependent signaling of these proteins. Using computational neuron simulations, we quantitatively investigated the perturbing effects of sensing capacitance on the input/output relationship in two central neuron models, a cerebellar Purkinje and a layer 5 pyramidal neuron. ... ". The Purkinje cell model is included in ModelDB.
30.  Fast convergence of cerebellar learning (Luque et al. 2015)
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.
31.  Information transmission in cerebellar granule cell models (Rossert et al. 2014)
" ... In this modeling study we analyse how electrophysiological granule cell properties and spike sampling influence information coded by firing rate modulation, assuming no signal-related, i.e., uncorrelated inhibitory feedback (open-loop mode). A detailed one-compartment granule cell model was excited in simulation by either direct current or mossy-fiber synaptic inputs. Vestibular signals were represented as tonic inputs to the flocculus modulated at frequencies up to 20 Hz (approximate upper frequency limit of vestibular-ocular reflex, VOR). Model outputs were assessed using estimates of both the transfer function, and the fidelity of input-signal reconstruction measured as variance-accounted-for. The detailed granule cell model with realistic mossy-fiber synaptic inputs could transmit infoarmation faithfully and linearly in the frequency range of the vestibular-ocular reflex. ... "
32.  Inverse stochastic resonance of cerebellar Purkinje cell (Buchin et al. 2016)
This code shows the simulations of the adaptive exponential integrate-and-fire model ( at different stimulus conditions. The parameters of the model were tuned to the Purkinje cell of cerebellum to reproduce the inhibiion of these cells by noisy current injections. Similar experimental protocols were also applied to the detailed biophysical model of Purkinje cells, de Shutter & Bower (1994) model. The repository also includes the XPPaut version of the model with the corresponding bifurcation analysis.
33.  Logarithmic distributions prove that intrinsic learning is Hebbian (Scheler 2017)
"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."
34.  Model of cerebellar parallel fiber-Purkinje cell LTD and LTP (Gallimore et al 2018)
Model of cerebellar parallel fiber-Purkinje cell LTD and LTP implemented in Matlab Simbiology
35.  Model of the cerebellar granular network (Sudhakar et al 2017)
"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. ..."
36.  Molecular layer interneurons in cerebellum encode valence in associative learning (Ma et al 2020)
We used two-photon microscopy to study the role of ensembles of cerebellar molecular layer interneurons (MLIs) in a go-no go task where mice obtain a sugar water reward. In order to begin understanding the circuit basis of our findings in changes in lick behavior with chemogenetics in the go-no go associative learning olfactory discrimination task we generated a simple computational model of MLI interaction with PCs.
37.  Multicompartmental cerebellar granule cell model (Diwakar et al. 2009)
A detailed multicompartmental model was used to study neuronal electroresponsiveness of cerebellar granule cells in rats. Here we show that, in cerebellar granule cells, Na+ channels are enriched in the axon, especially in the hillock, but almost absent from soma and dendrites. Numerical simulations indicated that granule cells have a compact electrotonic structure allowing EPSPs to diffuse with little attenuation from dendrites to axon. The spike arose almost simultaneously along the whole axonal ascending branch and invaded the hillock, whose activation promoted spike back-propagation with marginal delay (<200 micros) and attenuation (<20 mV) into the somato-dendritic compartment. For details check the cited article.
38.  Multiplexed coding in Purkinje neuron dendrites (Zang and De Schutter 2021)
Neuronal firing patterns are crucial to underpin circuit level behaviors. In cerebellar Purkinje cells (PCs), both spike rates and pauses are used for behavioral coding, but the cellular mechanisms causing code transitions remain unknown. We use a well-validated PC model to explore the coding strategy that individual PCs use to process parallel fiber (PF) inputs. We find increasing input intensity shifts PCs from linear rate-coders to burst-pause timing-coders by triggering localized dendritic spikes. We validate dendritic spike properties with experimental data, elucidate spiking mechanisms, and predict spiking thresholds with and without inhibition. Both linear and burst-pause computations use individual branches as computational units, which challenges the traditional view of PCs as linear point neurons. Dendritic spike thresholds can be regulated by voltage state, compartmentalized channel modulation, between-branch interaction and synaptic inhibition to expand the dynamic range of linear computation or burst-pause computation. In addition, co-activated PF inputs between branches can modify somatic maximum spike rates and pause durations to make them carry analogue signals. Our results provide new insights into the strategies used by individual neurons to expand their capacity of information processing.
39.  Network model of movement disorders (Yousif et al 2020)
This is a Wilson-Cowan model of the basal ganglia thalamocortical cerebellar network that demonstrates healthy gamma band oscillations, Parkinsonian oscillations in the beta band and oscillations in the tremor frequency range arising from the dynamics of the network.
40.  Network model of the granular layer of the cerebellar cortex (Maex, De Schutter 1998)
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.
41.  Neural modeling of an internal clock (Yamazaki and Tanaka 2008)
"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. ..."
42.  Parallel STEPS: Large scale stochastic spatial reaction-diffusion simulat. (Chen & De Schutter 2017)
" ... In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies..."
43.  Purkinje cell: Synaptic activation predicts voltage control of burst-pause (Masoli & D'Angelo 2017)
"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. ..."
44.  Purkinje neuron network (Zang et al. 2020)
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.
45.  Rapid desynchronization of an electrically coupled Golgi cell network (Vervaeke et al. 2010)
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.
46.  Robust transmission in the inhibitory Purkinje Cell to Cerebellar Nuclei pathway (Abbasi et al 2017)
47.  Sparse connectivity is required for decorrelation, pattern separation (Cayco-Gajic et al 2017)
" ... 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. ..."
48.  Spike burst-pause dynamics of Purkinje cells regulate sensorimotor adaptation (Luque et al 2019)
"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. ..."
49.  Stochastic calcium mechanisms cause dendritic calcium spike variability (Anwar et al. 2013)
" ... In single Purkinje cells, spontaneous and synaptically evoked dendritic calcium bursts come in a variety of shapes with a variable number of spikes. The mechanisms causing this variability have never been investigated thoroughly. In this study, a detailed computational model employing novel simulation routines is applied to identify the roles that stochastic ion channels, spatial arrangements of ion channels and stochastic intracellular calcium have towards producing calcium burst variability. … Our findings suggest that stochastic intracellular calcium mechanisms play a crucial role in dendritic calcium spike generation and are, therefore, an essential consideration in studies of neuronal excitability and plasticity."
50.  Tonic activation of extrasynaptic NMDA-R promotes bistability (Gall & Dupont 2020)
Our theoretical model provides a simple description of neuronal electrical activity that takes into account the tonic activity of extrasynaptic NMDA receptors and a cytosolic calcium compartment. We show that calcium influx mediated by the tonic activity of NMDA-R can be coupled directly to the activation of calcium-activated potassium channels, resulting in an overall inhibitory effect on neuronal excitability. Furthermore, the presence of tonic NMDA-R activity promotes bistability in electrical activity by dramatically increasing the stimulus interval where both a stable steady state and repetitive firing can coexist. These results could provide an intrinsic mechanism for the constitution of memory traces in neuronal circuits.
51.  Using Strahler's analysis to reduce realistic models (Marasco et al, 2013)
Building on our previous work (Marasco et al., (2012)), we present a general reduction method based on Strahler's analysis of neuron morphologies. We show that, without any fitting or tuning procedures, it is possible to map any morphologically and biophysically accurate neuron model into an equivalent reduced version. Using this method for Purkinje cells, we demonstrate how run times can be reduced up to 200-fold, while accurately taking into account the effects of arbitrarily located and activated synaptic inputs.
52.  Vestibulo-Ocular Reflex model in Matlab (Clopath at al. 2014)
" ... 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. "
53.  Voltage- and Branch-specific Climbing Fiber Responses in Purkinje Cells (Zang et al 2018)
"Climbing fibers (CFs) provide instructive signals driving cerebellar learning, but mechanisms causing the variable CF responses in Purkinje cells (PCs) are not fully understood. Using a new experimentally validated PC model, we unveil the ionic mechanisms underlying CF-evoked distinct spike waveforms on different parts of the PC. We demonstrate that voltage can gate both the amplitude and the spatial range of CF-evoked Ca2+ influx by the availability of K+ currents. ... The voltage- and branch-specific CF responses can increase dendritic computational capacity and enable PCs to actively integrate CF signals."

Re-display model names without descriptions