LTP regulates burst initiation and frequency at mossy fiber-granule cell synapses of rat cerebellum: experimental observations and theoretical predictions

Brain-like hardware, do we need it?

The brain's ability to perform efficient and fault-tolerant data processing is strongly related to its peculiar interconnected adaptive architecture, based on redundant neural circuits interacting at different scales. By emulating the brain's processing and learning mechanisms, computing technologies strive to achieve higher levels of energy efficiency and computational performance. Although efforts to address neuromorphic solutions through hardware based on top-down CMOS-based technologies have obtained interesting results in terms of energetic efficiency improvement, the replication of brain's self-assembled and redundant architectures is not considered in the roadmaps of data processing electronics. The exploration of solutions based on self-assembled elemental blocks to mimic biological networks' complexity is explored in the general frame of unconventional computing and it has not reached yet a maturity stage enabling a benchmark with standard electronic approaches in terms of performances, compatibility and scalability. Here we discuss some aspects related to advantages and disadvantages in the emulation of the brain for neuromorphic hardware. We also discuss possible directions in terms of hybrid hardware solutions where self-assembled substrates coexist and integrate with conventional electronics in view of neuromorphic architectures.

Understanding Cerebellar Input Stage through Computational and Plasticity Rules

A central hypothesis concerning brain functioning is that plasticity regulates the signal transfer function by modifying the efficacy of synaptic transmission. In the cerebellum, the granular layer has been shown to control the gain of signals transmitted through the mossy fiber pathway. Until now, the impact of plasticity on incoming activity patterns has been analyzed by combining electrophysiological recordings in acute cerebellar slices and computational modeling, unraveling a broad spectrum of different forms of synaptic plasticity in the granular layer, often accompanied by forms of intrinsic excitability changes. Here, we attempt to provide a brief overview of the most prominent forms of plasticity at the excitatory synapses formed by mossy fibers onto primary neuronal components (granule cells, Golgi cells and unipolar brush cells) in the granular layer. Specifically, we highlight the current understanding of the mechanisms and their functional implications for synaptic and intrinsic plasticity, providing valuable insights into how inputs are processed and reconfigured at the cerebellar input stage.

Long-Term Synaptic Plasticity Tunes the Gain of Information Channels through the Cerebellum Granular Layer

A central hypothesis on brain functioning is that long-term potentiation (LTP) and depression (LTD) regulate the signals transfer function by modifying the efficacy of synaptic transmission. In the cerebellum, granule cells have been shown to control the gain of signals transmitted through the mossy fiber pathway by exploiting synaptic inhibition in the glomeruli. However, the way LTP and LTD control signal transformation at the single-cell level in the space, time and frequency domains remains unclear. Here, the impact of LTP and LTD on incoming activity patterns was analyzed by combining patch-clamp recordings in acute cerebellar slices and mathematical modeling. LTP reduced the delay, increased the gain and broadened the frequency bandwidth of mossy fiber burst transmission, while LTD caused opposite changes. These properties, by exploiting NMDA subthreshold integration, emerged from microscopic changes in spike generation in individual granule cells such that LTP anticipated the emission of spikes and increased their number and precision, while LTD sorted the opposite effects. Thus, akin with the expansion recoding process theoretically attributed to the cerebellum granular layer, LTP and LTD could implement selective filtering lines channeling information toward the molecular and Purkinje cell layers for further processing.

A cerebellum inspired spiking neural network as a multi-model for pattern classification and robotic trajectory prediction

Spiking neural networks were introduced to understand spatiotemporal information processing in neurons and have found their application in pattern encoding, data discrimination, and classification. Bioinspired network architectures are considered for event-driven tasks, and scientists have looked at different theories based on the architecture and functioning. Motor tasks, for example, have networks inspired by cerebellar architecture where the granular layer recodes sparse representations of the mossy fiber (MF) inputs and has more roles in motor learning. Using abstractions from cerebellar connections and learning rules of deep learning network (DLN), patterns were discriminated within datasets, and the same algorithm was used for trajectory optimization. In the current work, a cerebellum-inspired spiking neural network with dynamics of cerebellar neurons and learning mechanisms attributed to the granular layer, Purkinje cell (PC) layer, and cerebellar nuclei interconnected by excitatory and inhibitory synapses was implemented. The model’s pattern discrimination capability was tested for two tasks on standard machine learning (ML) datasets and on following a trajectory of a low-cost sensor-free robotic articulator. Tuned for supervised learning, the pattern classification capability of the cerebellum-inspired network algorithm has produced more generalized models than data-specific precision models on smaller training datasets. The model showed an accuracy of 72%, which was comparable to standard ML algorithms, such as MLP (78%), Dl4jMlpClassifier (64%), RBFNetwork (71.4%), and libSVM-linear (85.7%). The cerebellar model increased the network’s capability and decreased storage, augmenting faster computations. Additionally, the network model could also implicitly reconstruct the trajectory of a 6-degree of freedom (DOF) robotic arm with a low error rate by reconstructing the kinematic parameters. The variability between the actual and predicted trajectory points was noted to be ± 3 cm (while moving to a position in a cuboid space of 25 × 30 × 40 cm). Although a few known learning rules were implemented among known types of plasticity in the cerebellum, the network model showed a generalized processing capability for a range of signals, modulating the data through the interconnected neural populations. In addition to potential use on sensor-free or feed-forward based controllers for robotic arms and as a generalized pattern classification algorithm, this model adds implications to motor learning theory.

Model simulations unveil the structure-function-dynamics relationship of the cerebellar cortical microcircuit

The cerebellar network is renowned for its regular architecture that has inspired foundational computational theories. However, the relationship between circuit structure, function and dynamics remains elusive. To tackle the issue, we developed an advanced computational modeling framework that allows us to reconstruct and simulate the structure and function of the mouse cerebellar cortex using morphologically realistic multi-compartmental neuron models. The cerebellar connectome is generated through appropriate connection rules, unifying a collection of scattered experimental data into a coherent construct and providing a new model-based ground-truth about circuit organization. Naturalistic background and sensory-burst stimulation are used for functional validation against recordings in vivo, monitoring the impact of cellular mechanisms on signal propagation, inhibitory control, and long-term synaptic plasticity. Our simulations show how mossy fibers entrain the local neuronal microcircuit, boosting the formation of columns of activity travelling from the granular to the molecular layer providing a new resource for the investigation of local microcircuit computation and of the neural correlates of behavior.

Computational models of neurotransmission at cerebellar synapses unveil the impact on network computation

The neuroscientific field benefits from the conjoint evolution of experimental and computational techniques, allowing for the reconstruction and simulation of complex models of neurons and synapses. Chemical synapses are characterized by presynaptic vesicle cycling, neurotransmitter diffusion, and postsynaptic receptor activation, which eventually lead to postsynaptic currents and subsequent membrane potential changes. These mechanisms have been accurately modeled for different synapses and receptor types (AMPA, NMDA, and GABA) of the cerebellar cortical network, allowing simulation of their impact on computation. Of special relevance is short-term synaptic plasticity, which generates spatiotemporal filtering in local microcircuits and controls burst transmission and information flow through the network. Here, we present how data-driven computational models recapitulate the properties of neurotransmission at cerebellar synapses. The simulation of microcircuit models is starting to reveal how diverse synaptic mechanisms shape the spatiotemporal profiles of circuit activity and computation.

Facial Stimulation Induces Long-Term Potentiation of Mossy Fiber-Granule Cell Synaptic Transmission via GluN2A-Containing N-Methyl-D-Aspartate Receptor/Nitric Oxide Cascade in the Mouse Cerebellum

Long-term synaptic plasticity in the cerebellar cortex is a possible mechanism for motor learning. Previous studies have demonstrated the induction of mossy fiber-granule cell (MF-GrC) synaptic plasticity under in vitro and in vivo conditions, but the mechanisms underlying sensory stimulation-evoked long-term synaptic plasticity of MF-GrC in living animals are unclear. In this study, we investigated the mechanism of long-term potentiation (LTP) of MF-GrC synaptic transmission in the cerebellum induced by train of facial stimulation at 20 Hz in urethane-anesthetized mice using electrophysiological recording, immunohistochemistry techniques, and pharmacological methods. Blockade of GABA_A receptor activity and repetitive facial stimulation at 20 Hz (240 pulses) induced an LTP of MF-GrC synapses in the mouse cerebellar cortical folium Crus II, accompanied with a decrease in paired-pulse ratio (N2/N1). The facial stimulation-induced MF-GrC LTP was abolished by either an N-methyl-D-aspartate (NMDA) receptor blocker, i.e., D-APV, or a specific GluNR2A subunit-containing NMDA receptor antagonist, PEAQX, but was not prevented by selective GluNR2B or GluNR2C/D subunit-containing NMDA receptor blockers. Application of GNE-0723, a selective and brain-penetrant-positive allosteric modulator of GluN2A subunit-containing NMDA receptors, produced an LTP of N1, accompanied with a decrease in N2/N1 ratio, and occluded the 20-Hz facial stimulation-induced MF-GrC LTP. Inhibition of nitric oxide synthesis (NOS) prevented the facial stimulation-induced MF-GrC LTP, while activation of NOS produced an LTP of N1, with a decrease in N2/N1 ratio, and occluded the 20-Hz facial stimulation-induced MF-GrC LTP. In addition, GluN2A-containing NMDA receptor immunoreactivity was observed in the mouse cerebellar granular layer. These results indicate that facial stimulation at 20 Hz induced LTP of MF-GrC synaptic transmission via the GluN2A-containing NMDA receptor/nitric oxide cascade in mice. The results suggest that the sensory stimulation-evoked LTP of MF-GrC synaptic transmission in the granular layer may play a critical role in cerebellar adaptation to native mossy fiber excitatory inputs and motor learning behavior in living animals.

Non-Linear Frequency Dependence of Neurovascular Coupling in the Cerebellar Cortex Implies Vasodilation-Vasoconstriction Competition

Neurovascular coupling (NVC) is the process associating local cerebral blood flow (CBF) to neuronal activity (NA). Although NVC provides the basis for the blood oxygen level dependent (BOLD) effect used in functional MRI (fMRI), the relationship between NVC and NA is still unclear. Since recent studies reported cerebellar non-linearities in BOLD signals during motor tasks execution, we investigated the NVC/NA relationship using a range of input frequencies in acute mouse cerebellar slices of vermis and hemisphere. The capillary diameter increased in response to mossy fiber activation in the 6-300 Hz range, with a marked inflection around 50 Hz (vermis) and 100 Hz (hemisphere). The corresponding NA was recorded using high-density multi-electrode arrays and correlated to capillary dynamics through a computational model dissecting the main components of granular layer activity. Here, NVC is known to involve a balance between the NMDAR-NO pathway driving vasodilation and the mGluRs-20HETE pathway driving vasoconstriction. Simulations showed that the NMDAR-mediated component of NA was sufficient to explain the time course of the capillary dilation but not its non-linear frequency dependence, suggesting that the mGluRs-20HETE pathway plays a role at intermediate frequencies. These parallel control pathways imply a vasodilation-vasoconstriction competition hypothesis that could adapt local hemodynamics at the microscale bearing implications for fMRI signals interpretation.

Discovering Microcircuit Secrets With Multi-Spot Imaging and Electrophysiological Recordings: The Example of Cerebellar Network Dynamics

The cerebellar cortex microcircuit is characterized by a highly ordered neuronal architecture having a relatively simple and stereotyped connectivity pattern. For a long time, this structural simplicity has incorrectly led to the idea that anatomical considerations would be sufficient to understand the dynamics of the underlying circuitry. However, recent experimental evidence indicates that cerebellar operations are much more complex than solely predicted by anatomy, due to the crucial role played by neuronal and synaptic properties. To be able to explore neuronal and microcircuit dynamics, advanced imaging, electrophysiological techniques and computational models have been combined, allowing us to investigate neuronal ensembles activity and to connect microscale to mesoscale phenomena. Here, we review what is known about cerebellar network organization, neural dynamics and synaptic plasticity and point out what is still missing and would require experimental assessments. We consider the available experimental techniques that allow a comprehensive assessment of circuit dynamics, including voltage and calcium imaging and extracellular electrophysiological recordings with multi-electrode arrays (MEAs). These techniques are proving essential to investigate the spatiotemporal pattern of activity and plasticity in the cerebellar network, providing new clues on how circuit dynamics contribute to motor control and higher cognitive functions.

Transcranial direct current stimulation of cerebellum alters spiking precision in cerebellar cortex: A modeling study of cellular responses

Transcranial direct current stimulation (tDCS) of the cerebellum has rapidly raised interest but the effects of tDCS on cerebellar neurons remain unclear. Assessing the cellular response to tDCS is challenging because of the uneven, highly stratified cytoarchitecture of the cerebellum, within which cellular morphologies, physiological properties, and function vary largely across several types of neurons. In this study, we combine MRI-based segmentation of the cerebellum and a finite element model of the tDCS-induced electric field (EF) inside the cerebellum to determine the field imposed on the cerebellar neurons throughout the region. We then pair the EF with multicompartment models of the Purkinje cell (PC), deep cerebellar neuron (DCN), and granule cell (GrC) and quantify the acute response of these neurons under various orientations, physiological conditions, and sequences of presynaptic stimuli. We show that cerebellar tDCS significantly modulates the postsynaptic spiking precision of the PC, which is expressed as a change in the spike count and timing in response to presynaptic stimuli. tDCS has modest effects, instead, on the PC tonic firing at rest and on the postsynaptic activity of DCN and GrC. In Purkinje cells, anodal tDCS shortens the repolarization phase following complex spikes (-14.7 ± 6.5% of baseline value, mean ± S.D.; max: -22.7%) and promotes burstiness with longer bursts compared to resting conditions. Cathodal tDCS, instead, promotes irregular spiking by enhancing somatic excitability and significantly prolongs the repolarization after complex spikes compared to baseline (+37.0 ± 28.9%, mean ± S.D.; max: +84.3%). tDCS-induced changes to the repolarization phase and firing pattern exceed 10% of the baseline values in Purkinje cells covering up to 20% of the cerebellar cortex, with the effects being distributed along the EF direction and concentrated in the area under the electrode over the cerebellum. Altogether, the acute effects of tDCS on cerebellum mainly focus on Purkinje cells and modulate the precision of the response to synaptic stimuli, thus having the largest impact when the cerebellar cortex is active. Since the spatiotemporal precision of the PC spiking is critical to learning and coordination, our results suggest cerebellar tDCS as a viable therapeutic option for disorders involving cerebellar hyperactivity such as ataxia.

Transcranial direct current stimulation (tDCS) of the cerebellum is gaining momentum as a neuromodulation tool for the treatment of neurological diseases like movement disorders. Nonetheless, the response of cells in the cerebellum to tDCS is unclear and hardly generalizes from our understanding of tDCS of the cerebral cortex. We use computational models to investigate the response of several types of cerebellar neurons to the electric field induced by tDCS and show that, differently from the cerebral cortex, tDCS has significant acute effects on the cerebellar cortex. These effects (i) primarily alter the way Purkinje cells encode synaptic stimuli from the molecular layer and (ii) can help hyperactive cells regain postsynaptic spiking precision. Since the spatiotemporal precision of the Purkinje cell spiking is critical to learning and coordination, the study shows how tDCS can operate at the cellular level to treat movement disorders like tremor and ataxia.

Modeling Neurotransmission: Computational Tools to Investigate Neurological Disorders

The investigation of synaptic functions remains one of the most fascinating challenges in the field of neuroscience and a large number of experimental methods have been tuned to dissect the mechanisms taking part in the neurotransmission process. Furthermore, the understanding of the insights of neurological disorders originating from alterations in neurotransmission often requires the development of (i) animal models of pathologies, (ii) invasive tools and (iii) targeted pharmacological approaches. In the last decades, additional tools to explore neurological diseases have been provided to the scientific community. A wide range of computational models in fact have been developed to explore the alterations of the mechanisms involved in neurotransmission following the emergence of neurological pathologies. Here, we review some of the advancements in the development of computational methods employed to investigate neuronal circuits with a particular focus on the application to the most diffuse neurological disorders.

An Intensified Acrolein Exposure Can Affect Memory and Cognition in Rat

Acrolein is a clear, colorless liquid and a highly reactive α, β-unsaturated aldehyde. Acrolein, a byproduct and initiator of oxidative stress, has a major role in the pathogenesis of disorders including pulmonary, cardiovascular, atherosclerosis, and neurodegenerative diseases. Environmental or dietary exposure and endogenous production are common sources of acrolein. Widespread exposure to acrolein is a major risk for human health; therefore, we decided to investigate the neurological effects of acrolein. In this study, we used male Sprague-Dawley rats and exposed them orally to acrolein (0.5, 1, 3, and 5 mg/kg/day) for 90 days and investigated the neurobehavioral and electrophysiological disturbances. We also assessed the correlation between neurotoxicity and CSF concentration of acrolein in the rats. The results showed that chronic oral administration of acrolein at 5 mg/kg/day impaired learning and memory in the neurobehavioral tests. In addition, acrolein decreased the release of excitatory neurotransmitters such as glutamate in electrophysiological studies. Our data demonstrated that chronic oral exposure of acrolein at a dose of 5 mg/kg leads to a direct correlation between neurotoxicity and its CSF concentration. In conclusion, exposure to acrolein as a major pollutant in the environment may cause cognitive problems and may have serious neurocognitive effects on humans.

Granular layEr Simulator: Design and Multi-GPU Simulation of the Cerebellar Granular Layer

In modern computational modeling, neuroscientists need to reproduce long-lasting activity of large-scale networks, where neurons are described by highly complex mathematical models. These aspects strongly increase the computational load of the simulations, which can be efficiently performed by exploiting parallel systems to reduce the processing times. Graphics Processing Unit (GPU) devices meet this need providing on desktop High Performance Computing. In this work, authors describe a novel Granular layEr Simulator development implemented on a multi-GPU system capable of reconstructing the cerebellar granular layer in a 3D space and reproducing its neuronal activity. The reconstruction is characterized by a high level of novelty and realism considering axonal/dendritic field geometries, oriented in the 3D space, and following convergence/divergence rates provided in literature. Neurons are modeled using Hodgkin and Huxley representations. The network is validated by reproducing typical behaviors which are well-documented in the literature, such as the center-surround organization. The reconstruction of a network, whose volume is 600 × 150 × 1,200 μm³ with 432,000 granules, 972 Golgi cells, 32,399 glomeruli, and 4,051 mossy fibers, takes 235 s on an Intel i9 processor. The 10 s activity reproduction takes only 4.34 and 3.37 h exploiting a single and multi-GPU desktop system (with one or two NVIDIA RTX 2080 GPU, respectively). Moreover, the code takes only 3.52 and 2.44 h if run on one or two NVIDIA V100 GPU, respectively. The relevant speedups reached (up to ~38× in the single-GPU version, and ~55× in the multi-GPU) clearly demonstrate that the GPU technology is highly suitable for realistic large network simulations.

The effects of the general anesthetic sevoflurane on neurotransmission: an experimental and computational study

The brain functions can be reversibly modulated by the action of general anesthetics. Despite a wide number of pharmacological studies, an extensive analysis of the cellular determinants of anesthesia at the microcircuits level is still missing. Here, by combining patch-clamp recordings and mathematical modeling, we examined the impact of sevoflurane, a general anesthetic widely employed in the clinical practice, on neuronal communication. The cerebellar microcircuit was used as a benchmark to analyze the action mechanisms of sevoflurane while a biologically realistic mathematical model was employed to explore at fine grain the molecular targets of anesthetic analyzing its impact on neuronal activity. The sevoflurane altered neurotransmission by strongly increasing GABAergic inhibition while decreasing glutamatergic NMDA activity. These changes caused a notable reduction of spike discharge in cerebellar granule cells (GrCs) following repetitive activation by excitatory mossy fibers (mfs). Unexpectedly, sevoflurane altered GrCs intrinsic excitability promoting action potential generation. Computational modelling revealed that this effect was triggered by an acceleration of persistent sodium current kinetics and by an increase in voltage dependent potassium current conductance. The overall effect was a reduced variability of GrCs responses elicited by mfs supporting the idea that sevoflurane shapes neuronal communication without silencing neural circuits.

Stellate cell computational modeling predicts signal filtering in the molecular layer circuit of cerebellum

The functional properties of cerebellar stellate cells and the way they regulate molecular layer activity are still unclear. We have measured stellate cells electroresponsiveness and their activation by parallel fiber bursts. Stellate cells showed intrinsic pacemaking, along with characteristic responses to depolarization and hyperpolarization, and showed a marked short-term facilitation during repetitive parallel fiber transmission. Spikes were emitted after a lag and only at high frequency, making stellate cells to operate as delay-high-pass filters. A detailed computational model summarizing these physiological properties allowed to explore different functional configurations of the parallel fiber-stellate cell-Purkinje cell circuit. Simulations showed that, following parallel fiber stimulation, Purkinje cells almost linearly increased their response with input frequency, but such an increase was inhibited by stellate cells, which leveled the Purkinje cell gain curve to its 4 Hz value. When reciprocal inhibitory connections between stellate cells were activated, the control of stellate cells over Purkinje cell discharge was maintained only at very high frequencies. These simulations thus predict a new role for stellate cells, which could endow the molecular layer with low-pass and band-pass filtering properties regulating Purkinje cell gain and, along with this, also burst delay and the burst-pause responses pattern.

Cerebellar Golgi cell models predict dendritic processing and mechanisms of synaptic plasticity

The Golgi cells are the main inhibitory interneurons of the cerebellar granular layer. Although recent works have highlighted the complexity of their dendritic organization and synaptic inputs, the mechanisms through which these neurons integrate complex input patterns remained unknown. Here we have used 8 detailed morphological reconstructions to develop multicompartmental models of Golgi cells, in which Na, Ca, and K channels were distributed along dendrites, soma, axonal initial segment and axon. The models faithfully reproduced a rich pattern of electrophysiological and pharmacological properties and predicted the operating mechanisms of these neurons. Basal dendrites turned out to be more tightly electrically coupled to the axon initial segment than apical dendrites. During synaptic transmission, parallel fibers caused slow Ca-dependent depolarizations in apical dendrites that boosted the axon initial segment encoder and Na-spike backpropagation into basal dendrites, while inhibitory synapses effectively shunted backpropagating currents. This oriented dendritic processing set up a coincidence detector controlling voltage-dependent NMDA receptor unblock in basal dendrites, which, by regulating local calcium influx, may provide the basis for spike-timing dependent plasticity anticipated by theory.

Cellular-resolution mapping uncovers spatial adaptive filtering at the rat cerebellum input stage

Long-term synaptic plasticity is thought to provide the substrate for adaptive computation in brain circuits but very little is known about its spatiotemporal organization. Here, we combined multi-spot two-photon laser microscopy in rat cerebellar slices with realistic modeling to map the distribution of plasticity in multi-neuronal units of the cerebellar granular layer. The units, composed by ~300 neurons activated by ~50 mossy fiber glomeruli, showed long-term potentiation concentrated in the core and long-term depression in the periphery. This plasticity was effectively accounted for by an NMDA receptor and calcium-dependent induction rule and was regulated by the inhibitory Golgi cell loops. Long-term synaptic plasticity created effective spatial filters tuning the time-delay and gain of spike retransmission at the cerebellum input stage and provided a plausible basis for the spatiotemporal recoding of input spike patterns anticipated by the motor learning theory.

Casali, Tognolina et al. use two-photon laser microscopy to spatially map long-term synaptic plasticity in rat cerebellar granular cells following stimulation of mossy fibers. Their data allow them to apply realistic modeling to test hypotheses about the synaptic spiking dynamics and reveal the importance of synaptic inhibition to defining these microcircuits.

Optimization of Efficient Neuron Models With Realistic Firing Dynamics. The Case of the Cerebellar Granule Cell

Biologically relevant large-scale computational models currently represent one of the main methods in neuroscience for studying information processing primitives of brain areas. However, biologically realistic neuron models tend to be computationally heavy and thus prevent these models from being part of brain-area models including thousands or even millions of neurons. The cerebellar input layer represents a canonical example of large scale networks. In particular, the cerebellar granule cells, the most numerous cells in the whole mammalian brain, have been proposed as playing a pivotal role in the creation of somato-sensorial information representations. Enhanced burst frequency (spiking resonance) in the granule cells has been proposed as facilitating the input signal transmission at the theta-frequency band (4–12 Hz), but the functional role of this cell feature in the operation of the granular layer remains largely unclear. This study aims to develop a methodological pipeline for creating neuron models that maintain biological realism and computational efficiency whilst capturing essential aspects of single-neuron processing. Therefore, we selected a light computational neuron model template (the adaptive-exponential integrate-and-fire model), whose parameters were progressively refined using an automatic parameter tuning with evolutionary algorithms (EAs). The resulting point-neuron models are suitable for reproducing the main firing properties of a realistic granule cell from electrophysiological measurements, including the spiking resonance at the theta-frequency band, repetitive firing according to a specified intensity-frequency (I-F) curve and delayed firing under current-pulse stimulation. Interestingly, the proposed model also reproduced some other emergent properties (namely, silent at rest, rheobase and negligible adaptation under depolarizing currents) even though these properties were not set in the EA as a target in the fitness function (FF), proving that these features are compatible even in computationally simple models. The proposed methodology represents a valuable tool for adjusting AdEx models according to a FF defined in the spiking regime and based on biological data. These models are appropriate for future research of the functional implication of bursting resonance at the theta band in large-scale granular layer network models.

Parameter tuning differentiates granule cell subtypes enriching transmission properties at the cerebellum input stage

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.

Inhibitory Plasticity: From Molecules to Computation and Beyond

Synaptic plasticity is the cellular and molecular counterpart of learning and memory and, since its first discovery, the analysis of the mechanisms underlying long-term changes of synaptic strength has been almost exclusively focused on excitatory connections. Conversely, inhibition was considered as a fixed controller of circuit excitability. Only recently, inhibitory networks were shown to be finely regulated by a wide number of mechanisms residing in their synaptic connections. Here, we review recent findings on the forms of inhibitory plasticity (IP) that have been discovered and characterized in different brain areas. In particular, we focus our attention on the molecular pathways involved in the induction and expression mechanisms leading to changes in synaptic efficacy, and we discuss, from the computational perspective, how IP can contribute to the emergence of functional properties of brain circuits.

Implementation of an Advanced Frequency-Based Hebbian Spike Timing Dependent Plasticity

The brain is provided with an enormous computing capability and exploits neural plasticity to store and elaborate complex information. One of the multiple mechanisms that neural circuits express is the Spike-timing-dependent plasticity (STDP), a form of long-term synaptic plasticity exploiting the time relationship between pre- and post-synaptic action potentials (i.e., neuron spikes). It has been found that in certain cases, for instance at the input stage of the cerebellum, between mossy fibers and granular neurons, the plasticity is not only driven by the timing of the spikes, but also by the oscillation frequency of the inputs. This complex behaviour has been implemented in this work, where we developed a novel form of advanced synaptic plasticity model to be used in a well-established neural network simulator (NEST). The subsequent tests proved the proper functioning of the plasticity and its range of applicability, demonstrating the possibility to adopt it in noisy and variable conditions, similar to the biological settings.

Diverse Neuron Properties and Complex Network Dynamics in the Cerebellar Cortical Inhibitory Circuit

Neuronal inhibition can be defined as a spatiotemporal restriction or suppression of local microcircuit activity. The importance of inhibition relies in its fundamental role in shaping signal processing in single neurons and neuronal circuits. In this context, the activity of inhibitory interneurons proved the key to endow networks with complex computational and dynamic properties. In the last 50 years, the prevailing view on the functional role of cerebellar cortical inhibitory circuits was that excitatory and inhibitory inputs sum spatially and temporally in order to determine the motor output through Purkinje cells (PCs). Consequently, cerebellar inhibition has traditionally been conceived in terms of restricting or blocking excitation. This assumption has been challenged, in particular in the cerebellar cortex where all neurons except granule cells (and unipolar brush cells in specific lobules) are inhibitory and fire spontaneously at high rates. Recently, a combination of electrophysiological recordings in vitro and in vivo, imaging, optogenetics and computational modeling, has revealed that inhibitory interneurons play a much more complex role in regulating cerebellar microcircuit functions: inhibition shapes neuronal response dynamics in the whole circuit and eventually regulate the PC output. This review elaborates current knowledge on cerebellar inhibitory interneurons [Golgi cells, Lugaro cells (LCs), basket cells (BCs) and stellate cells (SCs)], starting from their ontogenesis and moving up to their morphological, physiological and plastic properties, and integrates this knowledge with that on the more renown granule cells and PCs. We will focus on the circuit loops in which these interneurons are involved and on the way they generate feed-forward, feedback and lateral inhibition along with complex spatio-temporal response dynamics. In this perspective, inhibitory interneurons emerge as the real controllers of cerebellar functioning.

Reconstruction and Simulation of a Scaffold Model of the Cerebellar Network

Reconstructing neuronal microcircuits through computational models is fundamental to simulate local neuronal dynamics. Here a scaffold model of the cerebellum has been developed in order to flexibly place neurons in space, connect them synaptically, and endow neurons and synapses with biologically-grounded mechanisms. The scaffold model can keep neuronal morphology separated from network connectivity, which can in turn be obtained from convergence/divergence ratios and axonal/dendritic field 3D geometries. We first tested the scaffold on the cerebellar microcircuit, which presents a challenging 3D organization, at the same time providing appropriate datasets to validate emerging network behaviors. The scaffold was designed to integrate the cerebellar cortex with deep cerebellar nuclei (DCN), including different neuronal types: Golgi cells, granule cells, Purkinje cells, stellate cells, basket cells, and DCN principal cells. Mossy fiber inputs were conveyed through the glomeruli. An anisotropic volume (0.077 mm³) of mouse cerebellum was reconstructed, in which point-neuron models were tuned toward the specific discharge properties of neurons and were connected by exponentially decaying excitatory and inhibitory synapses. Simulations using both pyNEST and pyNEURON showed the emergence of organized spatio-temporal patterns of neuronal activity similar to those revealed experimentally in response to background noise and burst stimulation of mossy fiber bundles. Different configurations of granular and molecular layer connectivity consistently modified neuronal activation patterns, revealing the importance of structural constraints for cerebellar network functioning. The scaffold provided thus an effective workflow accounting for the complex architecture of the cerebellar network. In principle, the scaffold can incorporate cellular mechanisms at multiple levels of detail and be tuned to test different structural and functional hypotheses. A future implementation using detailed 3D multi-compartment neuron models and dynamic synapses will be needed to investigate the impact of single neuron properties on network computation.

Consensus paper: Decoding the Contributions of the Cerebellum as a Time Machine. From Neurons to Clinical Applications

Time perception is an essential element of conscious and subconscious experience, coordinating our perception and interaction with the surrounding environment. In recent years, major technological advances in the field of neuroscience have helped foster new insights into the processing of temporal information, including extending our knowledge of the role of the cerebellum as one of the key nodes in the brain for this function. This consensus paper provides a state-of-the-art picture from the experts in the field of the cerebellar research on a variety of crucial issues related to temporal processing, drawing on recent anatomical, neurophysiological, behavioral, and clinical research.The cerebellar granular layer appears especially well-suited for timing operations required to confer millisecond precision for cerebellar computations. This may be most evident in the manner the cerebellum controls the duration of the timing of agonist-antagonist EMG bursts associated with fast goal-directed voluntary movements. In concert with adaptive processes, interactions within the cerebellar cortex are sufficient to support sub-second timing. However, supra-second timing seems to require cortical and basal ganglia networks, perhaps operating in concert with cerebellum. Additionally, sensory information such as an unexpected stimulus can be forwarded to the cerebellum via the climbing fiber system, providing a temporally constrained mechanism to adjust ongoing behavior and modify future processing. Patients with cerebellar disorders exhibit impairments on a range of tasks that require precise timing, and recent evidence suggest that timing problems observed in other neurological conditions such as Parkinson's disease, essential tremor, and dystonia may reflect disrupted interactions between the basal ganglia and cerebellum.The complex concepts emerging from this consensus paper should provide a foundation for further discussion, helping identify basic research questions required to understand how the brain represents and utilizes time, as well as delineating ways in which this knowledge can help improve the lives of those with neurological conditions that disrupt this most elemental sense. The panel of experts agrees that timing control in the brain is a complex concept in whom cerebellar circuitry is deeply involved. The concept of a timing machine has now expanded to clinical disorders.

Spike burst-pause dynamics of Purkinje cells regulate sensorimotor adaptation

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. A detailed Purkinje cell model reproduces the three spike-firing patterns that are shown to regulate the cerebellar output. Our results suggest that pauses following Purkinje complex spikes (bursts) encode transient disinhibition of target medial vestibular nuclei, critically gating the vestibular signals conveyed by mossy fibres. This gating mechanism accounts for early and coarse VOR acquisition, prior to the late reflex consolidation. In addition, properly timed and sized Purkinje cell bursts allow the ratio between long-term depression and potentiation (LTD/LTP) to be finely shaped at mossy fibre-medial vestibular nuclei synapses, which optimises VOR consolidation. Tonic Purkinje cell firing maintains the consolidated VOR through time. Importantly, pauses are crucial to facilitate VOR phase-reversal learning, by reshaping previously learnt synaptic weight distributions. Altogether, these results predict that Purkinje spike burst-pause dynamics are instrumental to VOR learning and reversal adaptation.

Cerebellar Purkinje cells regulate accurate eye movement coordination. However, it remains unclear how cerebellar-dependent oculomotor adaptation depends on the interplay between Purkinje cell characteristic response patterns: tonic, high frequency bursting, and post-complex spike pauses. We explore the role of Purkinje spike burst-pause dynamics in VOR adaptation. A biophysical model of Purkinje cell is at the core of a spiking network model, which captures the cerebellar microcircuit properties and incorporates spike-based synaptic plasticity mechanisms at different cerebellar sites. We show that Purkinje spike burst-pause dynamics are critical for (1) gating the vestibular-motor response association during VOR acquisition; (2) mediating the LTD/LTP balance for VOR consolidation; (3) reshaping synaptic efficacy distributions for VOR phase-reversal adaptation; (4) explaining the reversal VOR gain discontinuities during sleeping.

Hyperexcitability and Hyperplasticity Disrupt Cerebellar Signal Transfer in the IB2 KO Mouse Model of Autism

Autism spectrum disorders (ASDs) are pervasive neurodevelopmental conditions that often involve mutations affecting synaptic mechanisms. Recently, the involvement of cerebellum in ASDs has been suggested, but the underlying functional alterations remained obscure. We investigated single-neuron and microcircuit properties in IB2 (Islet Brain-2) KO mice of either sex. The IB2 gene (chr22q13.3 terminal region) deletion occurs in virtually all cases of Phelan-McDermid syndrome, causing autistic symptoms and a severe delay in motor skill acquisition. IB2 KO granule cells showed a larger NMDA receptor-mediated current and enhanced intrinsic excitability, raising the excitatory/inhibitory balance. Furthermore, the spatial organization of granular layer responses to mossy fibers shifted from a "Mexican hat" to a "stovepipe hat" profile, with stronger excitation in the core and weaker inhibition in the surround. Finally, the size and extension of long-term synaptic plasticity were remarkably increased. These results show for the first time that hyperexcitability and hyperplasticity disrupt signal transfer in the granular layer of IB2 KO mice, supporting cerebellar involvement in the pathogenesis of ASD.SIGNIFICANCE STATEMENT This article shows for the first time a complex set of alterations in the cerebellum granular layer of a mouse model [IB2 (Islet Brain-2) KO] of autism spectrum disorders. The IB2 KO in mice mimics the deletion of the corresponding gene in the Phelan-McDermid syndrome in humans. The changes reported here are centered on NMDA receptor hyperactivity, hyperplasticity, and hyperexcitability. These, in turn, increase the excitatory/inhibitory balance and alter the shape of center/surround structures that emerge in the granular layer in response to mossy fiber activity. These results support recent theories suggesting the involvement of cerebellum in autism spectrum disorders.

Altered Cerebellar Short-Term Plasticity but No Change in Postsynaptic AMPA-Type Glutamate Receptors in a Mouse Model of Juvenile Batten Disease

Juvenile Batten disease is the most common progressive neurodegenerative disorder of childhood. It is associated with mutations in the CLN3 gene, causing loss of function of CLN3 protein and degeneration of cerebellar and retinal neurons. It has been proposed that changes in granule cell AMPA-type glutamate receptors (AMPARs) contribute to the cerebellar dysfunction. In this study, we compared AMPAR properties and synaptic transmission in cerebellar granule cells from wild-type and Cln3 knock-out mice. In Cln3Δex1-6 cells, the amplitude of AMPA-evoked whole-cell currents was unchanged. Similarly, we found no change in the amplitude, kinetics, or rectification of synaptic currents evoked by individual quanta, or in their underlying single-channel conductance. We found no change in cerebellar expression of GluA2 or GluA4 protein. By contrast, we observed a reduced number of quantal events following mossy-fiber stimulation in Sr2+, altered short-term plasticity in conditions of reduced extracellular Ca2+, and reduced mossy fiber vesicle number. Thus, while our results suggest early presynaptic changes in the Cln3Δex1-6 mouse model of juvenile Batten disease, they reveal no evidence for altered postsynaptic AMPARs.

Physiology of the cerebellum

The cerebellum is a central brain structure deeply integrated into major loops with the cerebral cortex, brainstem, and spinal cord. The cerebellum shows a complex regional organization consisting of modules with sagittal orientation. The cerebellum takes part in motor control and its lesions cause a movement incoordination syndrome called ataxia. Recent observations also imply involvement of the cerebellum in cognition and executive control, with an impact on pathologies like dyslexia and autism. The cerebellum operates as a forward controller learning to predict the precise timing of correlated events. The physiologic mechanisms of cerebellar functioning are still the object of intense research. The signals entering the cerebellum through the mossy fibers are processed in the granular layer and transmitted to Purkinje cells, while a collateral pathway activates the deep cerebellar nuclei (DCN). Purkinje cells in turn inhibit DCN, so that the cerebellar cortex operates as a side loop controlling the DCN. Learning is now known to occur through synaptic plasticity at multiple synapses in the granular layer, molecular layer, and DCN, extending the original concept of the Motor Learning Theory that predicted a single form of plasticity at the synapse between parallel fibers and Purkinje cells under the supervision of climbing fibers deriving from the inferior olive. Coordination derives from the precise regulation of timing and gain in the different cerebellar modules. The investigation of cerebellar dynamics using advanced physiologic recordings and computational models is now providing new clues on how the cerebellar network performs its internal computations.

Fuzzy neuronal model of motor control inspired by cerebellar pathways to online and gradually learn inverse biomechanical functions in the presence of delay

Contrary to forward biomechanical functions, which are deterministic, inverse biomechanical functions are generally not. Calculating an inverse biomechanical function is an ill-posed problem, which has no unique solution for a manipulator with several degrees of freedom. Studies of the command and control of biological movements suggest that the cerebellum takes part in the computation of approximate inverse functions, and this ability can control fast movements by predicting the consequence of current motor command. Limb movements toward a goal are defined as fast if they last less than the total duration of the processing and transmission delays in the motor and sensory pathways. Because of these delays, fast movements cannot be continuously controlled in a closed loop by use of sensory signals. Thus, fast movements must be controlled by some open loop controller, of which cerebellar pathways constitute an important part. This article presents a system-level fuzzy neuronal motor control circuit, inspired by the cerebellar pathways. The cerebellar cortex (CC) is assumed to embed internal models of the biomechanical functions of the limb segments. Such neural models are able to predict the consequences of motor commands and issue predictive signals encoding movement variables, which are sent to the controller via internal feedback loops. Differences between desired and expected values of variables of movements are calculated in the deep cerebellar nuclei (DCN). After motor learning, the whole circuit can approximate the inverse function of the biomechanical function of a limb and acts as a controller. In this research, internal models of direct biomechanical functions are learned and embedded in the connectivity of the cerebellar pathways. Two fuzzy neural networks represent the two parts of the cerebellum, and an online gradual learning drives the acquisition of the internal models in CC and the controlling rules in DCN. As during real learning, exercise and repetition increase skill and speed. The learning procedure is started by a simple and slow movement, controlled in the presence of delays by a simple closed loop controller comparable to the spinal reflexes. The speed of the movements is then increased gradually, and output error signals are used to compute teaching signals and drive learning. Repetition of movements at each speed level allows to properly set the two neural networks, and progressively learn the movement. Finally, conditions of stability of the proposed model as an inverter are identified. Next, the control of a single segment arm, moved by two muscles, is simulated. After proper setting by motor learning, the circuit is able to reject perturbations.

Understanding Cerebellum Granular Layer Network Computations through Mathematical Reconstructions of Evoked Local Field Potentials

Background

The cerebellar granular layer input stage of cerebellum receives information from tactile and sensory regions of the body. The somatosensory activity in the cerebellar granular layer corresponds to sensory and tactile input has been observed by recording Local Field Potential (LFP) from the Crus-IIa regions of cerebellum in brain slices and in anesthetized animals.

Purpose

In this paper, a detailed biophysical model of Wistar rat cerebellum granular layer network model and LFP modelling schemas were used to simulate circuit's evoked response.

Methods

Point Source Approximation and Line Source Approximation were used to reconstruct the network LFP. The LFP mechanism in in vitro was validated in network model and generated the in vivo LFP using the same mechanism.

Results

The network simulations distinctly displayed the Trigeminal and Cortical (TC) wave components generated by 2 independent bursts implicating the generation of TC waves by 2 independent granule neuron populations. Induced plasticity was simulated to estimate granule neuron activation related population responses. As a prediction, cerebellar dysfunction (ataxia) was also studied using the model. Dysfunction at individual neurons in the network was affected by the population response.

Conclusion

Our present study utilizes available knowledge on known mechanisms in a single cell and associates network function to population responses.

Spatiotemporal network coding of physiological mossy fiber inputs by the cerebellar granular layer

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. Patterned mossy fiber activity induces rhythmic Golgi cell activity that is synchronized by shared parallel fiber input and by gap junctions. This leads to long distance synchrony of Golgi cells along the transverse axis, powerfully regulating granule cell firing by imposing inhibition during a specific time window. The essential network mechanisms, including tunable Golgi cell oscillations, on-beam inhibition and NMDA receptors causing first winner keeps winning of granule cells, illustrate how fundamental properties of the granule layer operate in tandem to produce (1) well timed and spatially bound output, (2) a wide dynamic range of granule cell firing and (3) transient and coherent gating oscillations. These results substantially enrich our understanding of granule cell layer processing, which seems to promote spatial group selection of granule cell activity as a function of timing of mossy fiber input.

The cerebellum is an organ of peculiar geometrical properties, and has been attributed the function of applying spatiotemporal transforms to sensorimotor data since Eccles. In this work we have analyzed the spatiotemporal response properties of the first part of the cerebellar circuit, the granule layer. On the basis of a biophysically plausible and large-scale model of the cerebellum, constrained by a wealth of anatomical data, we study the network dynamics and firing properties of individual cell populations in response to 'realistic' input patterns. We make specific predictions about the spatiotemporal features of granule layer processing regarding the effects of the gap junction coupled network of Golgi cells on a spatially restricted input, in an effect we denominate first-takes-all. Furthermore, we calculate that the granule cell layer has a wide dynamic range, indicating that this is a system that can transmit large variations of input intensities.

Synaptic Activation of a Detailed Purkinje Cell Model Predicts Voltage-Dependent Control of Burst-Pause Responses in Active Dendrites

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. Interestingly, the burst and pause of BPRs depended on the stimulated dendritic zone reflecting the different input conductance and local engagement of voltage-dependent channels. Multiple local inputs combined their actions generating complex spatio-temporal patterns of dendritic activity and BPRs. Thus, local control of intrinsic dendritic mechanisms by synaptic inputs emerges as a fundamental PC property in activity regimens characterized by bursting inputs from granular and molecular layer neurons.

Recurrently connected and localized neuronal communities initiate coordinated spontaneous activity in neuronal networks

Developing neuronal systems intrinsically generate coordinated spontaneous activity that propagates by involving a large number of synchronously firing neurons. In vivo, waves of spikes transiently characterize the activity of developing brain circuits and are fundamental for activity-dependent circuit formation. In vitro, coordinated spontaneous spiking activity, or network bursts (NBs), interleaved within periods of asynchronous spikes emerge during the development of 2D and 3D neuronal cultures. Several studies have investigated this type of activity and its dynamics, but how a neuronal system generates these coordinated events remains unclear. Here, we investigate at a cellular level the generation of network bursts in spontaneously active neuronal cultures by exploiting high-resolution multielectrode array recordings and computational network modelling. Our analysis reveals that NBs are generated in specialized regions of the network (functional neuronal communities) that feature neuronal links with high cross-correlation peak values, sub-millisecond lags and that share very similar structural connectivity motifs providing recurrent interactions. We show that the particular properties of these local structures enable locally amplifying spontaneous asynchronous spikes and that this mechanism can lead to the initiation of NBs. Through the analysis of simulated and experimental data, we also show that AMPA currents drive the coordinated activity, while NMDA and GABA currents are only involved in shaping the dynamics of NBs. Overall, our results suggest that the presence of functional neuronal communities with recurrent local connections allows a neuronal system to generate spontaneous coordinated spiking activity events. As suggested by the rules used for implementing our computational model, such functional communities might naturally emerge during network development by following simple constraints on distance-based connectivity.

Coordinated spontaneous spiking activity is fundamental for the normal formation of brain circuits during development. However, how ensembles of neurons generate these events remains unclear. To address this question, in the present study, we investigated the network properties that might be required to a neuronal system for the generation of these spontaneous waves of spikes. We performed our study on spontaneously active neuronal cell cultures using high-resolution electrical recordings and a computational network model developed to reproduce our experimental data both quantitatively and qualitatively. Through the analysis of both experimental and simulated data, we found that network bursts are initiated in regions of the network, or “functional communities”, characterized by particular local connectivity properties. We also found that these regions can amplify the background asynchronous spiking activity preceding a network burst and, in this way, can give rise to coordinated spiking events.

As a whole, our results suggest the presence of functional communities of neurons in a developing neuronal system that might naturally emerge by following simple constraints on distance-based connectivity. These regions are most likely required for the generation of the spontaneous coordinated activity that can drive activity-dependent circuit formation.

Long-Term Potentiation at the Mossy Fiber-Granule Cell Relay Invokes Postsynaptic Second-Messenger Regulation of Kv4 Channels

Mossy fiber afferents to cerebellar granule cells form the primary synaptic relay into cerebellum, providing an ideal site to process signal inputs differentially. Mossy fiber input is known to exhibit a long-term potentiation (LTP) of synaptic efficacy through a combination of presynaptic and postsynaptic mechanisms. However, the specific postsynaptic mechanisms contributing to LTP of mossy fiber input is unknown. The current study tested the hypothesis that LTP induces a change in intrinsic membrane excitability of rat cerebellar granule cells through modification of Kv4 A-type potassium channels. We found that theta-burst stimulation of mossy fiber input in lobule 9 granule cells lowered the current threshold to spike and increases the gain of spike firing by 2- to 3-fold. The change in postsynaptic excitability was traced to hyperpolarizing shifts in both the half-inactivation and half-activation potentials of Kv4 that occurred upon coactivating NMDAR and group I metabotropic glutamatergic receptors. The effects of theta-burst stimulation on Kv4 channel control of the gain of spike firing depended on a signaling cascade leading to extracellular signal-related kinase activation. Under physiological conditions, LTP of synaptically evoked spike output was expressed preferentially for short bursts characteristic of sensory input, helping to shape signal processing at the mossy fiber-granule cell relay.

SIGNIFICANCE STATEMENT

Cerebellar granule cells receive mossy fiber inputs that convey information on different sensory modalities and feedback from descending cortical projections. Recent work suggests that signal processing across multiple cerebellar lobules is controlled differentially by postsynaptic ionic mechanisms at the level of granule cells. We found that long-term potentiation (LTP) of mossy fiber input invoked a large increase in granule cell excitability by modifying the biophysical properties of Kv4 channels through a specific signaling cascade. LTP of granule cell output became evident in response to bursts of mossy fiber input, revealing that Kv4 control of intrinsic excitability is modified to respond most effectively to patterns of afferent input that are characteristic of physiological sensory patterns.

Single Neuron Optimization as a Basis for Accurate Biophysical Modeling: The Case of Cerebellar Granule Cells

In realistic neuronal modeling, once the ionic channel complement has been defined, the maximum ionic conductance (G_i-max) values need to be tuned in order to match the firing pattern revealed by electrophysiological recordings. Recently, selection/mutation genetic algorithms have been proposed to efficiently and automatically tune these parameters. Nonetheless, since similar firing patterns can be achieved through different combinations of G_i-max values, it is not clear how well these algorithms approximate the corresponding properties of real cells. Here we have evaluated the issue by exploiting a unique opportunity offered by the cerebellar granule cell (GrC), which is electrotonically compact and has therefore allowed the direct experimental measurement of ionic currents. Previous models were constructed using empirical tuning of G_i-max values to match the original data set. Here, by using repetitive discharge patterns as a template, the optimization procedure yielded models that closely approximated the experimental G_i-max values. These models, in addition to repetitive firing, captured additional features, including inward rectification, near-threshold oscillations, and resonance, which were not used as features. Thus, parameter optimization using genetic algorithms provided an efficient modeling strategy for reconstructing the biophysical properties of neurons and for the subsequent reconstruction of large-scale neuronal network models.

Hebbian Spike-Timing Dependent Plasticity at the Cerebellar Input Stage

Spike-timing-dependent plasticity (STDP) is a form of long-term synaptic plasticity exploiting the time relationship between postsynaptic action potentials (APs) and EPSPs. Surprisingly enough, very little was known about STDP in the cerebellum, although it is thought to play a critical role for learning appropriate timing of actions. We speculated that low-frequency oscillations observed in the granular layer may provide a reference for repetitive EPSP/AP phase coupling. Here we show that EPSP-spike pairing at 6 Hz can optimally induce STDP at the mossy fiber-granule cell synapse in rats. Spike timing-dependent long-term potentiation and depression (st-LTP and st-LTD) were confined to a ±25 ms time-window. Because EPSPs led APs in st-LTP while APs led EPSPs in st-LTD, STDP was Hebbian in nature. STDP occurred at 6-10 Hz but vanished >50 Hz or <1 Hz (where only LTP or LTD occurred). STDP disappeared with randomized EPSP/AP pairing or high intracellular Ca²⁺ buffering, and its sign was inverted by GABA-A receptor activation. Both st-LTP and st-LTD required NMDA receptors, but st-LTP also required reinforcing signals mediated by mGluRs and intracellular calcium stores. Importantly, st-LTP and st-LTD were significantly larger than LTP and LTD obtained by modulating the frequency and duration of mossy fiber bursts, probably because STDP expression involved postsynaptic in addition to presynaptic mechanisms. These results thus show that a Hebbian form of STDP occurs at the cerebellum input stage, providing the substrate for phase-dependent binding of mossy fiber spikes to repetitive theta-frequency cycles of granule cell activity.SIGNIFICANCE STATEMENT Long-term synaptic plasticity is a fundamental property of the brain, causing persistent modifications of neuronal communication thought to provide the cellular basis of learning and memory. The cerebellum is critical for learning the appropriate timing of sensorimotor behaviors, but whether and how appropriate spike patterns could drive long-term synaptic plasticity remained unknown. Here, we show that this can actually occur through a form of spike-timing-dependent plasticity (STDP) at the cerebellar inputs stage. Pairing presynaptic and postsynaptic spikes at 6-10 Hz reliably induced STDP at the mossy fiber-granule cell synapse, with potentiation and depression symmetrically distributed within a ±25 ms time window. Thus, STDP can bind plasticity to the mossy fiber burst phase with high temporal precision.

Distributed Circuit Plasticity: New Clues for the Cerebellar Mechanisms of Learning

The cerebellum is involved in learning and memory of sensory motor skills. However, the way this process takes place in local microcircuits is still unclear. The initial proposal, casted into the Motor Learning Theory, suggested that learning had to occur at the parallel fiber-Purkinje cell synapse under supervision of climbing fibers. However, the uniqueness of this mechanism has been questioned, and multiple forms of long-term plasticity have been revealed at various locations in the cerebellar circuit, including synapses and neurons in the granular layer, molecular layer and deep-cerebellar nuclei. At present, more than 15 forms of plasticity have been reported. There has been a long debate on which plasticity is more relevant to specific aspects of learning, but this question turned out to be hard to answer using physiological analysis alone. Recent experiments and models making use of closed-loop robotic simulations are revealing a radically new view: one single form of plasticity is insufficient, while altogether, the different forms of plasticity can explain the multiplicity of properties characterizing cerebellar learning. These include multi-rate acquisition and extinction, reversibility, self-scalability, and generalization. Moreover, when the circuit embeds multiple forms of plasticity, it can easily cope with multiple behaviors endowing therefore the cerebellum with the properties needed to operate as an effective generalized forward controller.

Heterosynaptic GABAergic plasticity bidirectionally driven by the activity of pre- and postsynaptic NMDA receptors

Dynamic changes of the strength of inhibitory synapses play a crucial role in processing neural information and in balancing network activity. Here, we report that the efficacy of GABAergic connections between Golgi cells and granule cells in the cerebellum is persistently altered by the activity of glutamatergic synapses. This form of plasticity is heterosynaptic and is expressed as an increase (long-term potentiation, LTPGABA) or a decrease (long-term depression, LTDGABA) of neurotransmitter release. LTPGABA is induced by postsynaptic NMDA receptor activation, leading to calcium increase and retrograde diffusion of nitric oxide, whereas LTDGABA depends on presynaptic NMDA receptor opening. The sign of plasticity is determined by the activation state of target granule and Golgi cells during the induction processes. By controlling the timing of spikes emitted by granule cells, this form of bidirectional plasticity provides a dynamic control of the granular layer encoding capacity.

Modeling the Cerebellar Microcircuit: New Strategies for a Long-Standing Issue

The cerebellar microcircuit has been the work bench for theoretical and computational modeling since the beginning of neuroscientific research. The regular neural architecture of the cerebellum inspired different solutions to the long-standing issue of how its circuitry could control motor learning and coordination. Originally, the cerebellar network was modeled using a statistical-topological approach that was later extended by considering the geometrical organization of local microcircuits. However, with the advancement in anatomical and physiological investigations, new discoveries have revealed an unexpected richness of connections, neuronal dynamics and plasticity, calling for a change in modeling strategies, so as to include the multitude of elementary aspects of the network into an integrated and easily updatable computational framework. Recently, biophysically accurate “realistic” models using a bottom-up strategy accounted for both detailed connectivity and neuronal non-linear membrane dynamics. In this perspective review, we will consider the state of the art and discuss how these initial efforts could be further improved. Moreover, we will consider how embodied neurorobotic models including spiking cerebellar networks could help explaining the role and interplay of distributed forms of plasticity. We envisage that realistic modeling, combined with closed-loop simulations, will help to capture the essence of cerebellar computations and could eventually be applied to neurological diseases and neurorobotic control systems.

Computational Modeling of Single Neuron Extracellular Electric Potentials and Network Local Field Potentials using LFPsim

Local Field Potentials (LFPs) are population signals generated by complex spatiotemporal interaction of current sources and dipoles. Mathematical computations of LFPs allow the study of circuit functions and dysfunctions via simulations. This paper introduces LFPsim, a NEURON-based tool for computing population LFP activity and single neuron extracellular potentials. LFPsim was developed to be used on existing cable compartmental neuron and network models. Point source, line source, and RC based filter approximations can be used to compute extracellular activity. As a demonstration of efficient implementation, we showcase LFPs from mathematical models of electrotonically compact cerebellum granule neurons and morphologically complex neurons of the neocortical column. LFPsim reproduced neocortical LFP at 8, 32, and 56 Hz via current injection, in vitro post-synaptic N_2a, N_2b waves and in vivo T-C waves in cerebellum granular layer. LFPsim also includes a simulation of multi-electrode array of LFPs in network populations to aid computational inference between biophysical activity in neural networks and corresponding multi-unit activity resulting in extracellular and evoked LFP signals.

Distributed Cerebellar Motor Learning: A Spike-Timing-Dependent Plasticity Model

Deep cerebellar nuclei neurons receive both inhibitory (GABAergic) synaptic currents from Purkinje cells (within the cerebellar cortex) and excitatory (glutamatergic) synaptic currents from mossy fibers. Those two deep cerebellar nucleus inputs are thought to be also adaptive, embedding interesting properties in the framework of accurate movements. We show that distributed spike-timing-dependent plasticity mechanisms (STDP) located at different cerebellar sites (parallel fibers to Purkinje cells, mossy fibers to deep cerebellar nucleus cells, and Purkinje cells to deep cerebellar nucleus cells) in close-loop simulations provide an explanation for the complex learning properties of the cerebellum in motor learning. Concretely, we propose a new mechanistic cerebellar spiking model. In this new model, deep cerebellar nuclei embed a dual functionality: deep cerebellar nuclei acting as a gain adaptation mechanism and as a facilitator for the slow memory consolidation at mossy fibers to deep cerebellar nucleus synapses. Equipping the cerebellum with excitatory (e-STDP) and inhibitory (i-STDP) mechanisms at deep cerebellar nuclei afferents allows the accommodation of synaptic memories that were formed at parallel fibers to Purkinje cells synapses and then transferred to mossy fibers to deep cerebellar nucleus synapses. These adaptive mechanisms also contribute to modulate the deep-cerebellar-nucleus-output firing rate (output gain modulation toward optimizing its working range).

Long-Term Spatiotemporal Reconfiguration of Neuronal Activity Revealed by Voltage-Sensitive Dye Imaging in the Cerebellar Granular Layer

Understanding the spatiotemporal organization of long-term synaptic plasticity in neuronal networks demands techniques capable of monitoring changes in synaptic responsiveness over extended multineuronal structures. Among these techniques, voltage-sensitive dye imaging (VSD imaging) is of particular interest due to its good spatial resolution. However, improvements of the technique are needed in order to overcome limits imposed by its low signal-to-noise ratio. Here, we show that VSD imaging can detect long-term potentiation (LTP) and long-term depression (LTD) in acute cerebellar slices. Combined VSD imaging and patch-clamp recordings revealed that the most excited regions were predominantly associated with granule cells (GrCs) generating EPSP-spike complexes, while poorly responding regions were associated with GrCs generating EPSPs only. The correspondence with cellular changes occurring during LTP and LTD was highlighted by a vector representation obtained by combining amplitude with time-to-peak of VSD signals. This showed that LTP occurred in the most excited regions lying in the core of activated areas and increased the number of EPSP-spike complexes, while LTD occurred in the less excited regions lying in the surround. VSD imaging appears to be an efficient tool for investigating how synaptic plasticity contributes to the reorganization of multineuronal activity in neuronal circuits.

Synaptic representation of locomotion in single cerebellar granule cells

The cerebellum plays a crucial role in the regulation of locomotion, but how movement is represented at the synaptic level is not known. Here, we use in vivo patch-clamp recordings to show that locomotion can be directly read out from mossy fiber synaptic input and spike output in single granule cells. The increase in granule cell spiking during locomotion is enhanced by glutamate spillover currents recruited during movement. Surprisingly, the entire step sequence can be predicted from input EPSCs and output spikes of a single granule cell, suggesting that a robust gait code is present already at the cerebellar input layer and transmitted via the granule cell pathway to downstream Purkinje cells. Thus, synaptic input delivers remarkably rich information to single neurons during locomotion.

Integrated plasticity at inhibitory and excitatory synapses in the cerebellar circuit

The way long-term potentiation (LTP) and depression (LTD) are integrated within the different synapses of brain neuronal circuits is poorly understood. In order to progress beyond the identification of specific molecular mechanisms, a system in which multiple forms of plasticity can be correlated with large-scale neural processing is required. In this paper we take as an example the cerebellar network, in which extensive investigations have revealed LTP and LTD at several excitatory and inhibitory synapses. Cerebellar LTP and LTD occur in all three main cerebellar subcircuits (granular layer, molecular layer, deep cerebellar nuclei) and correspondingly regulate the function of their three main neurons: granule cells (GrCs), Purkinje cells (PCs) and deep cerebellar nuclear (DCN) cells. All these neurons, in addition to be excited, are reached by feed-forward and feed-back inhibitory connections, in which LTP and LTD may either operate synergistically or homeostatically in order to control information flow through the circuit. Although the investigation of individual synaptic plasticities in vitro is essential to prove their existence and mechanisms, it is insufficient to generate a coherent view of their impact on network functioning in vivo. Recent computational models and cell-specific genetic mutations in mice are shedding light on how plasticity at multiple excitatory and inhibitory synapses might regulate neuronal activities in the cerebellar circuit and contribute to learning and memory and behavioral control.

The effect of desflurane on neuronal communication at a central synapse

Although general anesthetics are thought to modify critical neuronal functions, their impact on neuronal communication has been poorly examined. We have investigated the effect induced by desflurane, a clinically used general anesthetic, on information transfer at the synapse between mossy fibers and granule cells of cerebellum, where this analysis can be carried out extensively. Mutual information values were assessed by measuring the variability of postsynaptic output in relationship to the variability of a given set of presynaptic inputs. Desflurane synchronized granule cell firing and reduced mutual information in response to physiologically relevant mossy fibers patterns. The decrease in spike variability was due to an increased postsynaptic membrane excitability, which made granule cells more prone to elicit action potentials, and to a strengthened synaptic inhibition, which markedly hampered membrane depolarization. These concomitant actions on granule cells firing indicate that desflurane re-shapes the transfer of information between neurons by providing a less informative neurotransmission rather than completely silencing neuronal activity.

Action potential processing in a detailed Purkinje cell model reveals a critical role for axonal compartmentalization

The Purkinje cell (PC) is among the most complex neurons in the brain and plays a critical role for cerebellar functioning. PCs operate as fast pacemakers modulated by synaptic inputs but can switch from simple spikes to complex bursts and, in some conditions, show bistability. In contrast to original works emphasizing dendritic Ca-dependent mechanisms, recent experiments have supported a primary role for axonal Na-dependent processing, which could effectively regulate spike generation and transmission to deep cerebellar nuclei (DCN). In order to account for the numerous ionic mechanisms involved (at present including Nav1.6, Cav2.1, Cav3.1, Cav3.2, Cav3.3, Kv1.1, Kv1.5, Kv3.3, Kv3.4, Kv4.3, KCa1.1, KCa2.2, KCa3.1, Kir2.x, HCN1), we have elaborated a multicompartmental model incorporating available knowledge on localization and gating of PC ionic channels. The axon, including initial segment (AIS) and Ranvier nodes (RNs), proved critical to obtain appropriate pacemaking and firing frequency modulation. Simple spikes initiated in the AIS and protracted discharges were stabilized in the soma through Na-dependent mechanisms, while somato-dendritic Ca channels contributed to sustain pacemaking and to generate complex bursting at high discharge regimes. Bistability occurred only following Na and Ca channel down-regulation. In addition, specific properties in RNs K currents were required to limit spike transmission frequency along the axon. The model showed how organized electroresponsive functions could emerge from the molecular complexity of PCs and showed that the axon is fundamental to complement ionic channel compartmentalization enabling action potential processing and transmission of specific spike patterns to DCN.

Model cerebellar granule cells can faithfully transmit modulated firing rate signals

A crucial assumption of many high-level system models of the cerebellum is that information in the granular layer is encoded in a linear manner. However, granule cells are known for their non-linear and resonant synaptic and intrinsic properties that could potentially impede linear signal transmission. 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 information faithfully and linearly in the frequency range of the vestibular-ocular reflex. This was achieved most simply if the model neurons had a firing rate at least twice the highest required frequency of modulation, but lower rates were also adequate provided a population of neurons was utilized, especially in combination with push-pull coding. The exact number of neurons required for faithful transmission depended on the precise values of firing rate and noise. The model neurons were also able to combine excitatory and inhibitory signals linearly, and could be replaced by a simpler (modified) integrate-and-fire neuron in the case of high tonic firing rates. These findings suggest that granule cells can in principle code modulated firing-rate inputs in a linear manner, and are thus consistent with the high-level adaptive-filter model of the cerebellar microcircuit.

Regulation of output spike patterns by phasic inhibition in cerebellar granule cells

The complex interplay of multiple molecular mechanisms taking part to synaptic integration is hard to disentangle experimentally. Therefore, we developed a biologically realistic computational model based on the rich set of data characterizing the cerebellar glomerulus microcircuit. A specific issue was to determine the relative role of phasic and tonic inhibition in dynamically regulating granule cell firing, which has not been clarified yet. The model comprised the excitatory mossy fiber—granule cell and the inhibitory Golgi cell—granule cell synapses and accounted for vesicular release processes, neurotransmitter diffusion and activation of different receptor subtypes. Phasic inhibition was based on stochastic GABA release and spillover causing activation of two major classes of postsynaptic receptors, α1 and α6, while tonic inhibition was based on steady regulation of a Cl⁻ leakage. The glomerular microcircuit model was validated against experimental responses to mossy fiber bursts while metabotropic receptors were blocked. Simulations showed that phasic inhibition controlled the number of spikes during burst transmission but predicted that it specifically controlled time-related parameters (firing initiation and conclusion and first spike precision) when the relative phase of excitation and inhibition was changed. In all conditions, the overall impact of α6 was larger than that of α1 subunit-containing receptors. However, α1 receptors controlled granule cell responses in a narrow ±10 ms band while α6 receptors showed broader ±50 ms tuning. Tonic inhibition biased these effects without changing their nature substantially. These simulations imply that phasic inhibitory mechanisms can dynamically regulate output spike patterns, as well as calcium influx and NMDA currents, at the mossy fiber—granule cell relay of cerebellum without the intervention of tonic inhibition.

Computational modeling predicts the ionic mechanism of late-onset responses in unipolar brush cells

Unipolar Brush Cells (UBCs) have been suggested to play a critical role in cerebellar functioning, yet the corresponding cellular mechanisms remain poorly understood. UBCs have recently been reported to generate, in addition to early-onset glutamate receptor-dependent synaptic responses, a late-onset response (LOR) composed of a slow depolarizing ramp followed by a spike burst (Locatelli et al., 2013). The LOR activates as a consequence of synaptic activity and involves an intracellular cascade modulating H- and TRP-current gating. In order to assess the LOR mechanisms, we have developed a UBC multi-compartmental model (including soma, dendrite, initial segment, and axon) incorporating biologically realistic representations of ionic currents and a cytoplasmic coupling mechanism regulating TRP and H channel gating. The model finely reproduced UBC responses to current injection, including a burst triggered by a low-threshold spike (LTS) sustained by CaLVA currents, a persistent discharge sustained by CaHVA currents, and a rebound burst following hyperpolarization sustained by H- and CaLVA-currents. Moreover, the model predicted that H- and TRP-current regulation was necessary and sufficient to generate the LOR and its dependence on the intensity and duration of mossy fiber activity. Therefore, the model showed that, using a basic set of ionic channels, UBCs generate a rich repertoire of bursts, which could effectively implement tunable delay-lines in the local microcircuit.