A realistic large-scale model of the cerebellum granular layer predicts circuit spatio-temporal filtering properties

Artificial cerebellum on FPGA: realistic real-time cerebellar spiking neural network model capable of real-world adaptive motor control

The cerebellum plays a central role in motor control and learning. Its neuronal network architecture, firing characteristics of component neurons, and learning rules at their synapses have been well understood in terms of anatomy and physiology. A realistic artificial cerebellum with mimetic network architecture and synaptic plasticity mechanisms may allow us to analyze cerebellar information processing in the real world by applying it to adaptive control of actual machines. Several artificial cerebellums have previously been constructed, but they require high-performance hardware to run in real-time for real-world machine control. Presently, we implemented an artificial cerebellum with the size of 104 spiking neuron models on a field-programmable gate array (FPGA) which is compact, lightweight, portable, and low-power-consumption. In the implementation three novel techniques are employed: (1) 16-bit fixed-point operation and randomized rounding, (2) fully connected spike information transmission, and (3) alternative memory that uses pseudo-random number generators. We demonstrate that the FPGA artificial cerebellum runs in real-time, and its component neuron models behave as those in the corresponding artificial cerebellum configured on a personal computer in Python. We applied the FPGA artificial cerebellum to the adaptive control of a machine in the real world and demonstrated that the artificial cerebellum is capable of adaptively reducing control error after sudden load changes. This is the first implementation and demonstration of a spiking artificial cerebellum on an FPGA applicable to real-world adaptive control. The FPGA artificial cerebellum may provide neuroscientific insights into cerebellar information processing in adaptive motor control and may be applied to various neuro-devices to augment and extend human motor control capabilities.

An emergent temporal basis set robustly supports cerebellar time-series learning

The cerebellum is considered a "learning machine" essential for time interval estimation underlying motor coordination and other behaviors. Theoretical work has proposed that the cerebellum's input recipient structure, the granule cell layer (GCL), performs pattern separation of inputs that facilitates learning in Purkinje cells (P-cells). However, the relationship between input reformatting and learning has remained debated, with roles emphasized for pattern separation features from sparsification to decorrelation. We took a novel approach by training a minimalist model of the cerebellar cortex to learn complex time-series data from time-varying inputs, typical during movements. The model robustly produced temporal basis sets from these inputs, and the resultant GCL output supported better learning of temporally complex target functions than mossy fibers alone. Learning was optimized at intermediate threshold levels, supporting relatively dense granule cell activity, yet the key statistical features in GCL population activity that drove learning differed from those seen previously for classification tasks. These findings advance testable hypotheses for mechanisms of temporal basis set formation and predict that moderately dense population activity optimizes learning.NEW & NOTEWORTHY During movement, mossy fiber inputs to the cerebellum relay time-varying information with strong intrinsic relationships to ongoing movement. Are such mossy fibers signals sufficient to support Purkinje signals and learning? In a model, we show how the GCL greatly improves Purkinje learning of complex, temporally dynamic signals relative to mossy fibers alone. Learning-optimized GCL population activity was moderately dense, which retained intrinsic input variance while also performing pattern separation.

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.

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.

Towards the Simulation of a Realistic Large-Scale Spiking Network on a Desktop Multi-GPU System

The reproduction of the brain ’sactivity and its functionality is the main goal of modern neuroscience. To this aim, several models have been proposed to describe the activity of single neurons at different levels of detail. Then, single neurons are linked together to build a network, in order to reproduce complex behaviors. In the literature, different network-building rules and models have been described, targeting realistic distributions and connections of the neurons. In particular, the Granular layEr Simulator (GES) performs the granular layer network reconstruction considering biologically realistic rules to connect the neurons. Moreover, it simulates the network considering the Hodgkin–Huxley model. The work proposed in this paper adopts the network reconstruction model of GES and proposes a simulation module based on Leaky Integrate and Fire (LIF) model. This simulator targets the reproduction of the activity of large scale networks, exploiting the GPU technology to reduce the processing times. Experimental results show that a multi-GPU system reduces the simulation of a network with more than 1.8 million neurons from approximately 54 to 13 h.

CerebelluMorphic: Large-Scale Neuromorphic Model and Architecture for Supervised Motor Learning

The cerebellum plays a vital role in motor learning and control with supervised learning capability, while neuromorphic engineering devises diverse approaches to high-performance computation inspired by biological neural systems. This article presents a large-scale cerebellar network model for supervised learning, as well as a cerebellum-inspired neuromorphic architecture to map the cerebellar anatomical structure into the large-scale model. Our multinucleus model and its underpinning architecture contain approximately 3.5 million neurons, upscaling state-of-the-art neuromorphic designs by over 34 times. Besides, the proposed model and architecture incorporate 3411k granule cells, introducing a 284 times increase compared to a previous study including only 12k cells. This large scaling induces more biologically plausible cerebellar divergence/convergence ratios, which results in better mimicking biology. In order to verify the functionality of our proposed model and demonstrate its strong biomimicry, a reconfigurable neuromorphic system is used, on which our developed architecture is realized to replicate cerebellar dynamics during the optokinetic response. In addition, our neuromorphic architecture is used to analyze the dynamical synchronization within the Purkinje cells, revealing the effects of firing rates of mossy fibers on the resonance dynamics of Purkinje cells. Our experiments show that real-time operation can be realized, with a system throughput of up to 4.70 times larger than previous works with high synaptic event rate. These results suggest that the proposed work provides both a theoretical basis and a neuromorphic engineering perspective for brain-inspired computing and the further exploration of cerebellar learning.

Nicotine Facilitates Facial Stimulation-Evoked Mossy Fiber-Granule Cell Long-Term Potentiation in vivo in Mice

Nicotine is a psychoactive component of tobacco that plays critical roles in the regulation of neuronal circuit function and neuroplasticity and contributes to the improvement of working memory performance and motor learning function via nicotinic acetylcholine receptors (nAChRs). Under in vivo conditions, nicotine enhances facial stimulation-evoked mossy fiber-granule cell (MF-GrC) synaptic transmission, which suggests that nicotine regulates MF-GrC synaptic plasticity in the mouse cerebellar cortex. In this study, we investigated the effects of nicotine on facial stimulation-induced long-term potentiation (LTP) of MF-GrC synaptic transmission in urethane-anesthetized mice. Our results showed that facial stimulation at 20 Hz induced an MF-GrC LTP in the mouse cerebellar granular layer that was significantly enhanced by the application of nicotine (1 μM). Blockade of α4β2 nAChRs, but not α7 nAChRs, during delivery of 20 Hz facial stimulation prevented the nicotine-induced facilitation of MF-GrC LTP. Notably, the facial stimulation-induced MF-GrC LTP was abolished by an N-methyl-D-aspartate (NMDA) receptor antagonist, but it was restored by additional application of nicotine during delivery of 20 Hz facial stimulation. Furthermore, antagonism of α4β2 nAChRs, but not α7 nAChRs, during delivery of 20 Hz facial stimulation prevented nicotine-induced MF-GrC LTP. Moreover, inhibition of nitric oxide synthase (NOS) abolished the facial stimulation-induced MF-GrC LTP, as well as the effect of nicotine on it. Our results indicated that 20 Hz facial stimulation induced MF-GrC LTP via an NMDA receptor/nitric oxide (NO) cascade, but MF-GrC LTP was enhanced by nicotine through the α4β2 AChR/NO signaling pathway. These results suggest that nicotine-induced facilitation of MF-GrC LTP may play a critical role in the improvement of working memory performance and motor learning function.

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.

Regulating synchronous oscillations of cerebellar granule cells by different types of inhibition

Synchronous oscillations in neural populations are considered being controlled by inhibitory neurons. In the granular layer of the cerebellum, two major types of cells are excitatory granular cells (GCs) and inhibitory Golgi cells (GoCs). GC spatiotemporal dynamics, as the output of the granular layer, is highly regulated by GoCs. However, there are various types of inhibition implemented by GoCs. With inputs from mossy fibers, GCs and GoCs are reciprocally connected to exhibit different network motifs of synaptic connections. From the view of GCs, feedforward inhibition is expressed as the direct input from GoCs excited by mossy fibers, whereas feedback inhibition is from GoCs via GCs themselves. In addition, there are abundant gap junctions between GoCs showing another form of inhibition. It remains unclear how these diverse copies of inhibition regulate neural population oscillation changes. Leveraging a computational model of the granular layer network, we addressed this question to examine the emergence and modulation of network oscillation using different types of inhibition. We show that at the network level, feedback inhibition is crucial to generate neural oscillation. When short-term plasticity was equipped on GoC-GC synapses, oscillations were largely diminished. Robust oscillations can only appear with additional gap junctions. Moreover, there was a substantial level of cross-frequency coupling in oscillation dynamics. Such a coupling was adjusted and strengthened by GoCs through feedback inhibition. Taken together, our results suggest that the cooperation of distinct types of GoC inhibition plays an essential role in regulating synchronous oscillations of the GC population. With GCs as the sole output of the granular network, their oscillation dynamics could potentially enhance the computational capability of downstream neurons.

Projection-dependent heterogeneity of cerebellar granule cell calcium responses

Cerebellar granule cells (GCs) relay mossy fiber (MF) inputs to Purkinje cell dendrites via their axons, the parallel fibers (PFs), which are individually located at a given sublayer of the molecular layer (ML). Although a certain degree of heterogeneity among GCs has been recently reported, variability of GC responses to MF inputs has never been associated with their most notable structural variability, location of their projecting PFs in the ML. Here, we utilize an adeno-associated virus (AAV)-mediated labeling technique that enables us to categorize GCs according to the location of their PFs, and compare the Ca²⁺ responses to MF stimulations between three groups of GCs, consisting of either GCs having PFs at the deep (D-GCs), middle (M-GCs), or superficial (S-GCs) sublayer. Our structural analysis revealed that there was no correlation between position of GC soma in the GC layer and location of its PF in the ML, confirming that our AAV-mediated labeling was important to test the projection-dependent variability of the Ca²⁺ responses in GCs. We then found that the Ca²⁺ responses of D-GCs differed from those of M-GCs. Pharmacological experiments implied that the different Ca²⁺ responses were mainly attributable to varied distributions of GABA_A receptors (GABA_ARs) at the synaptic and extrasynaptic regions of GC dendrites. In addition to GABA_AR distributions, amounts of extrasynaptic NMDA receptors appear to be also varied, because Ca²⁺ responses were different between D-GCs and M-GCs when glutamate spillover was enhanced. Whereas the Ca²⁺ responses of S-GCs were mostly equivalent to those of D-GCs and M-GCs, the blockade of GABA uptake resulted in larger Ca²⁺ responses in S-GCs compared with D-GCs and M-GCs, implying existence of mechanisms leading to more excitability in S-GCs with increased GABA release. Thus, this study reveals MF stimulation-mediated non-uniform Ca²⁺ responses in the cerebellar GCs associated with the location of their PFs in the ML, and raises a possibility that combination of inherent functional variability of GCs and their specific axonal projection contributes to the information processing through the GCs.

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.

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.

Simulation of a Human-Scale Cerebellar Network Model on the K Computer

Computer simulation of the human brain at an individual neuron resolution is an ultimate goal of computational neuroscience. The Japanese flagship supercomputer, K, provides unprecedented computational capability toward this goal. The cerebellum contains 80% of the neurons in the whole brain. Therefore, computer simulation of the human-scale cerebellum will be a challenge for modern supercomputers. In this study, we built a human-scale spiking network model of the cerebellum, composed of 68 billion spiking neurons, on the K computer. As a benchmark, we performed a computer simulation of a cerebellum-dependent eye movement task known as the optokinetic response. We succeeded in reproducing plausible neuronal activity patterns that are observed experimentally in animals. The model was built on dedicated neural network simulation software called MONET (Millefeuille-like Organization NEural neTwork), which calculates layered sheet types of neural networks with parallelization by tile partitioning. To examine the scalability of the MONET simulator, we repeatedly performed simulations while changing the number of compute nodes from 1,024 to 82,944 and measured the computational time. We observed a good weak-scaling property for our cerebellar network model. Using all 82,944 nodes, we succeeded in simulating a human-scale cerebellum for the first time, although the simulation was 578 times slower than the wall clock time. These results suggest that the K computer is already capable of creating a simulation of a human-scale cerebellar model with the aid of the MONET simulator.

Acetylcholine Modulates Cerebellar Granule Cell Spiking by Regulating the Balance of Synaptic Excitation and Inhibition

Sensorimotor integration in the cerebellum is essential for refining motor output, and the first stage of this processing occurs in the granule cell layer. Recent evidence suggests that granule cell layer synaptic integration can be contextually modified, although the circuit mechanisms that could mediate such modulation remain largely unknown. Here we investigate the role of ACh in regulating granule cell layer synaptic integration in male rats and mice of both sexes. We find that Golgi cells, interneurons that provide the sole source of inhibition to the granule cell layer, express both nicotinic and muscarinic cholinergic receptors. While acute ACh application can modestly depolarize some Golgi cells, the net effect of longer, optogenetically induced ACh release is to strongly hyperpolarize Golgi cells. Golgi cell hyperpolarization by ACh leads to a significant reduction in both tonic and evoked granule cell synaptic inhibition. ACh also reduces glutamate release from mossy fibers by acting on presynaptic muscarinic receptors. Surprisingly, despite these consistent effects on Golgi cells and mossy fibers, ACh can either increase or decrease the spike probability of granule cells as measured by noninvasive cell-attached recordings. By constructing an integrate-and-fire model of granule cell layer population activity, we find that the direction of spike rate modulation can be accounted for predominately by the initial balance of excitation and inhibition onto individual granule cells. Together, these experiments demonstrate that ACh can modulate population-level granule cell responses by altering the ratios of excitation and inhibition at the first stage of cerebellar processing.SIGNIFICANCE STATEMENT The cerebellum plays a key role in motor control and motor learning. While it is known that behavioral context can modify motor learning, the circuit basis of such modulation has remained unclear. Here we find that a key neuromodulator, ACh, can alter the balance of excitation and inhibition at the first stage of cerebellar processing. These results suggest that ACh could play a key role in altering cerebellar learning by modifying how sensorimotor input is represented at the input layer of the cerebellum.

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.

VOR Adaptation on a Humanoid iCub Robot Using a Spiking Cerebellar Model

We embed a spiking cerebellar model within an adaptive real-time (RT) control loop that is able to operate a real robotic body (iCub) when performing different vestibulo-ocular reflex (VOR) tasks. The spiking neural network computation, including event- and time-driven neural dynamics, neural activity, and spike-timing dependent plasticity (STDP) mechanisms, leads to a nondeterministic computation time caused by the neural activity volleys encountered during cerebellar simulation. This nondeterministic computation time motivates the integration of an RT supervisor module that is able to ensure a well-orchestrated neural computation time and robot operation. Actually, our neurorobotic experimental setup (VOR) benefits from the biological sensory motor delay between the cerebellum and the body to buffer the computational overloads as well as providing flexibility in adjusting the neural computation time and RT operation. The RT supervisor module provides for incremental countermeasures that dynamically slow down or speed up the cerebellar simulation by either halting the simulation or disabling certain neural computation features (i.e., STDP mechanisms, spike propagation, and neural updates) to cope with the RT constraints imposed by the real robot operation. This neurorobotic experimental setup is applied to different horizontal and vertical VOR adaptive tasks that are widely used by the neuroscientific community to address cerebellar functioning. We aim to elucidate the manner in which the combination of the cerebellar neural substrate and the distributed plasticity shapes the cerebellar neural activity to mediate motor adaptation. This paper underlies the need for a two-stage learning process to facilitate VOR acquisition.

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.

A Metric for Evaluating Neural Input Representation in Supervised Learning Networks

Supervised learning has long been attributed to several feed-forward neural circuits within the brain, with particular attention being paid to the cerebellar granular layer. The focus of this study is to evaluate the input activity representation of these feed-forward neural networks. The activity of cerebellar granule cells is conveyed by parallel fibers and translated into Purkinje cell activity, which constitutes the sole output of the cerebellar cortex. The learning process at this parallel-fiber-to-Purkinje-cell connection makes each Purkinje cell sensitive to a set of specific cerebellar states, which are roughly determined by the granule-cell activity during a certain time window. A Purkinje cell becomes sensitive to each neural input state and, consequently, the network operates as a function able to generate a desired output for each provided input by means of supervised learning. However, not all sets of Purkinje cell responses can be assigned to any set of input states due to the network's own limitations (inherent to the network neurobiological substrate), that is, not all input-output mapping can be learned. A key limiting factor is the representation of the input states through granule-cell activity. The quality of this representation (e.g., in terms of heterogeneity) will determine the capacity of the network to learn a varied set of outputs. Assessing the quality of this representation is interesting when developing and studying models of these networks to identify those neuron or network characteristics that enhance this representation. In this study we present an algorithm for evaluating quantitatively the level of compatibility/interference amongst a set of given cerebellar states according to their representation (granule-cell activation patterns) without the need for actually conducting simulations and network training. The algorithm input consists of a real-number matrix that codifies the activity level of every considered granule-cell in each state. The capability of this representation to generate a varied set of outputs is evaluated geometrically, thus resulting in a real number that assesses the goodness of the representation.

Pathway-Specific Drive of Cerebellar Golgi Cells Reveals Integrative Rules of Cortical Inhibition

Cerebellar granule cells (GrCs) constitute over half of all neurons in the vertebrate brain and are proposed to decorrelate convergent mossy fiber (MF) inputs in service of learning. Interneurons within the GrC layer, Golgi cells (GoCs), are the primary inhibitors of this vast population and therefore play a major role in influencing the computations performed within the layer. Despite this central function for GoCs, few studies have directly examined how GoCs integrate inputs from specific afferents, which vary in density to regulate GrC population activity. We used a variety of methods in mice of either sex to study feedforward inhibition recruited by identified MFs, focusing on features that would influence integration by GrCs. Comprehensive 3D reconstruction and quantification of GoC axonal boutons revealed tightly clustered boutons that focus feedforward inhibition in the neighborhood of GoC somata. Acute whole-cell patch-clamp recordings from GrCs in brain slices showed that, despite high GoC bouton density, fast phasic inhibition was very sparse relative to slow spillover mediated inhibition. Dynamic-clamp simulating inhibition combined with optogenetic MF activation at moderate rates supported a predominant role of slow spillover mediated inhibition in reducing GrC activity. Whole-cell recordings from GoCs revealed a role for the density of active MFs in preferentially driving them. Thus, our data provide empirical confirmation of predicted rules by which MFs activate GoCs to regulate GrC activity levels.SIGNIFICANCE STATEMENT A unifying framework in neural circuit analysis is identifying circuit motifs that subserve common computations. Wide-field inhibitory interneurons globally inhibit neighbors and have been studied extensively in the insect olfactory system and proposed to serve pattern separation functions. Cerebellar Golgi cells (GoCs), a type of mammalian wide-field inhibitory interneuron observed in the granule cell layer, are well suited to perform normalization or pattern separation functions, but the relationship between spatial characteristics of input patterns to GoC-mediated inhibition has received limited attention. This study provides unprecedented quantitative structural details of GoCs and identifies a role for population input activity levels in recruiting inhibition using in vitro electrophysiology and optogenetics.

Temporal constrained objects for modelling neuronal dynamics

BACKGROUND

Several new programming languages and technologies have emerged in the past few decades in order to ease the task of modelling complex systems. Modelling the dynamics of complex systems requires various levels of abstractions and reductive measures in representing the underlying behaviour. This also often requires making a trade-off between how realistic a model should be in order to address the scientific questions of interest and the computational tractability of the model.

METHODS

In this paper, we propose a novel programming paradigm, called temporal constrained objects, which facilitates a principled approach to modelling complex dynamical systems. Temporal constrained objects are an extension of constrained objects with a focus on the analysis and prediction of the dynamic behaviour of a system. The structural aspects of a neuronal system are represented using objects, as in object-oriented languages, while the dynamic behaviour of neurons and synapses are modelled using declarative temporal constraints. Computation in this paradigm is a process of constraint satisfaction within a time-based simulation.

RESULTS

We identified the feasibility and practicality in automatically mapping different kinds of neuron and synapse models to the constraints of temporal constrained objects. Simple neuronal networks were modelled by composing circuit components, implicitly satisfying the internal constraints of each component and interface constraints of the composition. Simulations show that temporal constrained objects provide significant conciseness in the formulation of these models. The underlying computational engine employed here automatically finds the solutions to the problems stated, reducing the code for modelling and simulation control. All examples reported in this paper have been programmed and successfully tested using the prototype language called TCOB. The code along with the programming environment are available at http://github.com/compneuro/TCOB_Neuron.

DISCUSSION

Temporal constrained objects provide powerful capabilities for modelling the structural and dynamic aspects of neural systems. Capabilities of the constraint programming paradigm, such as declarative specification, the ability to express partial information and non-directionality, and capabilities of the object-oriented paradigm especially aggregation and inheritance, make this paradigm the right candidate for complex systems and computational modelling studies. With the advent of multi-core parallel computer architectures and techniques or parallel constraint-solving, the paradigm of temporal constrained objects lends itself to highly efficient execution which is necessary for modelling and simulation of large brain circuits.

Fentanyl Induces Cerebellar Internal Granular Cell Layer Apoptosis in Healthy Newborn Pigs

Background

Opioids like fentanyl are regularly used in neonates for analgesia and sedation. So far, they have been reported to be safe and eligible to use. The cerebellum has become a focus of neurodevelopmental research within the last years, as it is known to play an important role in long-lasting motor, cognitive, and other behavioral changes. The cerebellar cortex is of major importance in the coordinative role of the cerebellum and highly vulnerable to injury and impaired growth.

Objective

This study was performed to evaluate the apoptotic effect of intravenous fentanyl infusion on the cerebellum in healthy newborn pigs.

Methods

Thirteen healthy pigs (<median 12 h old) were randomized into (1) 24 h of intravenous fentanyl at normothermia (NTFe, n = 6) or (2) non-ventilated controls at normothermia (NTCTR, n = 7). Cerebellar sections were morphologically assessed after staining with hematoxylin–eosin. In addition, paired sections were immuno-stained for cell death [Cleaved caspase-3 and terminal deoxynucleotidyl transferase-mediated deoxyuridine-triphosphate nick-end labeling (TUNEL)], and positive cells were counted in defined areas of the internal granular cell layer. In total, cells in three cerebellar gyri were counted.

Results

We found that there was an increase in cells with apoptotic morphology in the internal granular cell layer in the NTFe group. For quantification, we found a significant increase in cell death in group (1) [median (range) number of caspase-3-positive cell group (1) 8 (1–22) vs. group (2) 1 (1–6) and TUNEL-positive cells (1) 6 (1–10) vs. (2) 1 (0–4)]. In both groups, there was no difference in the number of Purkinje cells. Both groups had comparable and stable physiological parameters throughout the 24 h period.

Conclusion

Twenty-four hours of continuous intravenous fentanyl infusion increased apoptosis in the internal granular cell layer in the cerebellum of healthy newborn pigs.

Morphological Constraints on Cerebellar Granule Cell Combinatorial Diversity

Combinatorial expansion by the cerebellar granule cell layer (GCL) is fundamental to theories of cerebellar contributions to motor control and learning. Granule cells (GrCs) sample approximately four mossy fiber inputs and are thought to form a combinatorial code useful for pattern separation and learning. We constructed a spatially realistic model of the cerebellar GCL and examined how GCL architecture contributes to GrC combinatorial diversity. We found that GrC combinatorial diversity saturates quickly as mossy fiber input diversity increases, and that this saturation is in part a consequence of short dendrites, which limit access to diverse inputs and favor dense sampling of local inputs. This local sampling also produced GrCs that were combinatorially redundant, even when input diversity was extremely high. In addition, we found that mossy fiber clustering, which is a common anatomical pattern, also led to increased redundancy of GrC input combinations. We related this redundancy to hypothesized roles of temporal expansion of GrC information encoding in service of learned timing, and we show that GCL architecture produces GrC populations that support both temporal and combinatorial expansion. Finally, we used novel anatomical measurements from mice of either sex to inform modeling of sparse and filopodia-bearing mossy fibers, finding that these circuit features uniquely contribute to enhancing GrC diversification and redundancy. Our results complement information theoretic studies of granule layer structure and provide insight into the contributions of granule layer anatomical features to afferent mixing.SIGNIFICANCE STATEMENT Cerebellar granule cells are among the simplest neurons, with tiny somata and, on average, just four dendrites. These characteristics, along with their dense organization, inspired influential theoretical work on the granule cell layer as a combinatorial expander, where each granule cell represents a unique combination of inputs. Despite the centrality of these theories to cerebellar physiology, the degree of expansion supported by anatomically realistic patterns of inputs is unknown. Using modeling and anatomy, we show that realistic input patterns constrain combinatorial diversity by producing redundant combinations, which nevertheless could support temporal diversification of like combinations, suitable for learned timing. Our study suggests a neural substrate for producing high levels of both combinatorial and temporal diversity in the granule cell layer.

Model-Driven Analysis of Eyeblink Classical Conditioning Reveals the Underlying Structure of Cerebellar Plasticity and Neuronal Activity

The cerebellum plays a critical role in sensorimotor control. However, how the specific circuits and plastic mechanisms of the cerebellum are engaged in closed-loop processing is still unclear. We developed an artificial sensorimotor control system embedding a detailed spiking cerebellar microcircuit with three bidirectional plasticity sites. This proved able to reproduce a cerebellar-driven associative paradigm, the eyeblink classical conditioning (EBCC), in which a precise time relationship between an unconditioned stimulus (US) and a conditioned stimulus (CS) is established. We challenged the spiking model to fit an experimental data set from human subjects. Two subsequent sessions of EBCC acquisition and extinction were recorded and transcranial magnetic stimulation (TMS) was applied on the cerebellum to alter circuit function and plasticity. Evolutionary algorithms were used to find the near-optimal model parameters to reproduce the behaviors of subjects in the different sessions of the protocol. The main finding is that the optimized cerebellar model was able to learn to anticipate (predict) conditioned responses with accurate timing and success rate, demonstrating fast acquisition, memory stabilization, rapid extinction, and faster reacquisition as in EBCC in humans. The firing of Purkinje cells (PCs) and deep cerebellar nuclei (DCN) changed during learning under the control of synaptic plasticity, which evolved at different rates, with a faster acquisition in the cerebellar cortex than in DCN synapses. Eventually, a reduced PC activity released DCN discharge just after the CS, precisely anticipating the US and causing the eyeblink. Moreover, a specific alteration in cortical plasticity explained the EBCC changes induced by cerebellar TMS in humans. In this paper, for the first time, it is shown how closed-loop simulations, using detailed cerebellar microcircuit models, can be successfully used to fit real experimental data sets. Thus, the changes of the model parameters in the different sessions of the protocol unveil how implicit microcircuit mechanisms can generate normal and altered associative behaviors.The cerebellum plays a critical role in sensorimotor control. However, how the specific circuits and plastic mechanisms of the cerebellum are engaged in closed-loop processing is still unclear. We developed an artificial sensorimotor control system embedding a detailed spiking cerebellar microcircuit with three bidirectional plasticity sites. This proved able to reproduce a cerebellar-driven associative paradigm, the eyeblink classical conditioning (EBCC), in which a precise time relationship between an unconditioned stimulus (US) and a conditioned stimulus (CS) is established. We challenged the spiking model to fit an experimental data set from human subjects. Two subsequent sessions of EBCC acquisition and extinction were recorded and transcranial magnetic stimulation (TMS) was applied on the cerebellum to alter circuit function and plasticity. Evolutionary algorithms were used to find the near-optimal model parameters to reproduce the behaviors of subjects in the different sessions of the protocol. The main finding is that the optimized cerebellar model was able to learn to anticipate (predict) conditioned responses with accurate timing and success rate, demonstrating fast acquisition, memory stabilization, rapid extinction, and faster reacquisition as in EBCC in humans. The firing of Purkinje cells (PCs) and deep cerebellar nuclei (DCN) changed during learning under the control of synaptic plasticity, which evolved at different rates, with a faster acquisition in the cerebellar cortex than in DCN synapses. Eventually, a reduced PC activity released DCN discharge just after the CS, precisely anticipating the US and causing the eyeblink. Moreover, a specific alteration in cortical plasticity explained the EBCC changes induced by cerebellar TMS in humans. In this paper, for the first time, it is shown how closed-loop simulations, using detailed cerebellar microcircuit models, can be successfully used to fit real experimental data sets. Thus, the changes of the model parameters in the different sessions of the protocol unveil how implicit microcircuit mechanisms can generate normal and altered associative behaviors.

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.

Exploring the significance of morphological diversity for cerebellar granule cell excitability

The relatively simple and compact morphology of cerebellar granule cells (CGCs) has led to the view that heterogeneity in CGC shape has negligible impact upon the integration of mossy fibre (MF) information. Following electrophysiological recording, 3D models were constructed from high-resolution imaging data to identify morphological features that could influence the coding of MF input patterns by adult CGCs. Quantification of MF and CGC morphology provided evidence that CGCs could be connected to the multiple rosettes that arise from a single MF input. Predictions from our computational models propose that MF inputs could be more densely encoded within the CGC layer than previous models suggest. Moreover, those MF signals arriving onto the dendrite closest to the axon will generate greater CGC excitation. However, the impact of this morphological variability on MF input selectivity will be attenuated by high levels of CGC inhibition providing further flexibility to the MF → CGC pathway. These features could be particularly important when considering the integration of multimodal MF sensory input by individual CGCs.

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.

Increased whole cerebellar serotonin in aged C57BL/6 mice

Mobility and locomotor impairments have high prevalence, morbidity, and significant mortality in older adult populations. Cerebellar functional changes have been implicated in the pathogenesis of these age-related mobility and gait deficits unrelated to stroke, Parkinson's disease, or degenerative joint disease. We thus examined total cerebellar glutamate, glutamine, GABA, glycine, dopamine, norepinephrine, tryptophan, serotonin, alanine, threonine, and asparagine content from male 2-3-month (young, n = 6) and 21-24-month-old (aged, n = 6) C₅₇BL/6 mice. Neurotransmitter and amino acid concentrations were determined by high-performance liquid chromatography followed with mass spectroscopy. We found a significant increase in cerebellar serotonin in aged versus young mice, but otherwise no significant phenotypic differences in measured neurotransmitter concentrations. Applying current thought about cerebellar aging and cerebellar serotonergic systems, we consider how this age-related increase in cerebellar serotonin may contribute to gait ataxia.

Evaluation of Teaching Signals for Motor Control in the Cerebellum during Real-World Robot Application

Motor learning in the cerebellum is believed to entail plastic changes at synapses between parallel fibers and Purkinje cells, induced by the teaching signal conveyed in the climbing fiber (CF) input. Despite the abundant research on the cerebellum, the nature of this signal is still a matter of debate. Two types of movement error information have been proposed to be plausible teaching signals: sensory error (SE) and motor command error (ME); however, their plausibility has not been tested in the real world. Here, we conducted a comparison of different types of CF teaching signals in real-world engineering applications by using a realistic neuronal network model of the cerebellum. We employed a direct current motor (simple task) and a two-wheeled balancing robot (difficult task). We demonstrate that SE, ME or a linear combination of the two is sufficient to yield comparable performance in a simple task. When the task is more difficult, although SE slightly outperformed ME, these types of error information are all able to adequately control the robot. We categorize granular cells according to their inputs and the error signal revealing that different granule cells are preferably engaged for SE, ME or their combination. Thus, unlike previous theoretical and simulation studies that support either SE or ME, it is demonstrated for the first time in a real-world engineering application that both SE and ME are adequate as the CF teaching signal in a realistic computational cerebellar model, even when the control task is as difficult as stabilizing a two-wheeled balancing robot.

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.

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.

Biphasic modulation of parallel fibre synaptic transmission by co-activation of presynaptic GABAA and GABAB receptors in mice

KEY POINTS

Many excitatory synapses co-express presynaptic GABAA and GABAB receptors, despite their opposing actions on synaptic transmission. It is still unclear how co-activation of these receptors modulates synapse function. We measured presynaptic GABA receptor function at parallel fibre synapses onto stellate cells in the cerebellum using whole-cell patch-clamp recording and photolytic uncaging of RuBi-GABA. Activation of presynaptic GABA receptors results in a transient (∼100 ms) enhancement of synaptic transmission (mediated by GABAA receptors) followed by a long lasting (>500 ms) inhibition of transmission (mediated by GABAB receptors). When activated just prior to high-frequency trains of stimulation, presynaptic GABAA and GABAB receptors work together to reduce short-term facilitation/enhance depression, altering the filtering properties of synaptic transmission. Inhibition of synaptic transmission by GABAB receptors is more sensitive to GABA than enhancement by GABAA receptors, suggesting GABAB receptors may be activated by ambient GABA or release from greater distances.

ABSTRACT

GABAA and GABAB receptors are co-expressed at many presynaptic terminals in the central nervous system. Previous studies have shown that GABAA receptors typically enhance vesicle release while GABAB receptors inhibit release. However, it is not clear how the competing actions of these receptors modulate synaptic transmission when co-activated, as is likely in vivo. We investigated this question at parallel fibre synapses in the cerebellum, which co-express presynaptic GABAA and GABAB receptors. In acute slices from C57BL/6 mice, we find that co-activation of presynaptic GABA receptors by photolytic uncaging of RuBi-GABA has a biphasic effect on EPSC amplitudes recorded from stellate cells. Synchronous and asynchronous EPSCs evoked within ∼100 ms of GABA uncaging were increased, while EPSCs evoked ∼300-600 ms after GABA uncaging were reduced compared to interleaved control sweeps. We confirmed these effects are presynaptic by measuring the paired-pulse ratio, variance of EPSC amplitudes, and response probability. During trains of high-frequency stimulation GABAA and GABAB receptors work together (rather than oppose one another) to reduce short-term facilitation when GABA is uncaged just prior to the onset of stimulation. We also find that GABAB receptor-mediated inhibition can be elicited by lower GABA concentrations than GABAA receptor-mediated enhancement of EPSCs, suggesting GABAB receptors may be selectively activated by ambient GABA or release from more distance synapses. These data suggest that GABA, acting through both presynaptic GABAA and GABAB receptors, modulate the amplitude and short-term plasticity of excitatory synapses, a result not possible from activation of either receptor type alone.

A Hybrid Model for the Computationally-Efficient Simulation of the Cerebellar Granular Layer

The aim of the present paper is to efficiently describe the membrane potential dynamics of neural populations formed by species having a high density difference in specific brain areas. We propose a hybrid model whose main ingredients are a conductance-based model (ODE system) and its continuous counterpart (PDE system) obtained through a limit process in which the number of neurons confined in a bounded region of the brain tissue is sent to infinity. Specifically, in the discrete model, each cell is described by a set of time-dependent variables, whereas in the continuum model, cells are grouped into populations that are described by a set of continuous variables. Communications between populations, which translate into interactions among the discrete and the continuous models, are the essence of the hybrid model we present here. The cerebellum and cerebellum-like structures show in their granular layer a large difference in the relative density of neuronal species making them a natural testing ground for our hybrid model. By reconstructing the ensemble activity of the cerebellar granular layer network and by comparing our results to a more realistic computational network, we demonstrate that our description of the network activity, even though it is not biophysically detailed, is still capable of reproducing salient features of neural network dynamics. Our modeling approach yields a significant computational cost reduction by increasing the simulation speed at least 270 times. The hybrid model reproduces interesting dynamics such as local microcircuit synchronization, traveling waves, center-surround, and time-windowing.

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).

At the Edge of Chaos: How Cerebellar Granular Layer Network Dynamics Can Provide the Basis for Temporal Filters

Models of the cerebellar microcircuit often assume that input signals from the mossy-fibers are expanded and recoded to provide a foundation from which the Purkinje cells can synthesize output filters to implement specific input-signal transformations. Details of this process are however unclear. While previous work has shown that recurrent granule cell inhibition could in principle generate a wide variety of random outputs suitable for coding signal onsets, the more general application for temporally varying signals has yet to be demonstrated. Here we show for the first time that using a mechanism very similar to reservoir computing enables random neuronal networks in the granule cell layer to provide the necessary signal separation and extension from which Purkinje cells could construct basis filters of various time-constants. The main requirement for this is that the network operates in a state of criticality close to the edge of random chaotic behavior. We further show that the lack of recurrent excitation in the granular layer as commonly required in traditional reservoir networks can be circumvented by considering other inherent granular layer features such as inverted input signals or mGluR2 inhibition of Golgi cells. Other properties that facilitate filter construction are direct mossy fiber excitation of Golgi cells, variability of synaptic weights or input signals and output-feedback via the nucleocortical pathway. Our findings are well supported by previous experimental and theoretical work and will help to bridge the gap between system-level models and detailed models of the granular layer network.

A Spiking Neural Simulator Integrating Event-Driven and Time-Driven Computation Schemes Using Parallel CPU-GPU Co-Processing: A Case Study

Time-driven simulation methods in traditional CPU architectures perform well and precisely when simulating small-scale spiking neural networks. Nevertheless, they still have drawbacks when simulating large-scale systems. Conversely, event-driven simulation methods in CPUs and time-driven simulation methods in graphic processing units (GPUs) can outperform CPU time-driven methods under certain conditions. With this performance improvement in mind, we have developed an event-and-time-driven spiking neural network simulator suitable for a hybrid CPU-GPU platform. Our neural simulator is able to efficiently simulate bio-inspired spiking neural networks consisting of different neural models, which can be distributed heterogeneously in both small layers and large layers or subsystems. For the sake of efficiency, the low-activity parts of the neural network can be simulated in CPU using event-driven methods while the high-activity subsystems can be simulated in either CPU (a few neurons) or GPU (thousands or millions of neurons) using time-driven methods. In this brief, we have undertaken a comparative study of these different simulation methods. For benchmarking the different simulation methods and platforms, we have used a cerebellar-inspired neural-network model consisting of a very dense granular layer and a Purkinje layer with a smaller number of cells (according to biological ratios). Thus, this cerebellar-like network includes a dense diverging neural layer (increasing the dimensionality of its internal representation and sparse coding) and a converging neural layer (integration) similar to many other biologically inspired and also artificial neural networks.

A realistic bi-hemispheric model of the cerebellum uncovers the purpose of the abundant granule cells during motor control

The cerebellar granule cells (GCs) have been proposed to perform lossless, adaptive spatio-temporal coding of incoming sensory/motor information required by downstream cerebellar circuits to support motor learning, motor coordination, and cognition. Here we use a physio-anatomically inspired bi-hemispheric cerebellar neuronal network (biCNN) to selectively enable/disable the output of GCs and evaluate the behavioral and neural consequences during three different control scenarios. The control scenarios are a simple direct current motor (1 degree of freedom: DOF), an unstable two-wheel balancing robot (2 DOFs), and a simulation model of a quadcopter (6 DOFs). Results showed that adequate control was maintained with a relatively small number of GCs (< 200) in all the control scenarios. However, the minimum number of GCs required to successfully govern each control plant increased with their complexity (i.e., DOFs). It was also shown that increasing the number of GCs resulted in higher robustness against changes in the initialization parameters of the biCNN model (i.e., synaptic connections and synaptic weights). Therefore, we suggest that the abundant GCs in the cerebellar cortex provide the computational power during the large repertoire of motor activities and motor plants the cerebellum is involved with, and bring robustness against changes in the cerebellar microcircuit (e.g., neuronal connections).

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.

A bi-hemispheric neuronal network model of the cerebellum with spontaneous climbing fiber firing produces asymmetrical motor learning during robot control

To acquire and maintain precise movement controls over a lifespan, changes in the physical and physiological characteristics of muscles must be compensated for adaptively. The cerebellum plays a crucial role in such adaptation. Changes in muscle characteristics are not always symmetrical. For example, it is unlikely that muscles that bend and straighten a joint will change to the same degree. Thus, different (i.e., asymmetrical) adaptation is required for bending and straightening motions. To date, little is known about the role of the cerebellum in asymmetrical adaptation. Here, we investigate the cerebellar mechanisms required for asymmetrical adaptation using a bi-hemispheric cerebellar neuronal network model (biCNN). The bi-hemispheric structure is inspired by the observation that lesioning one hemisphere reduces motor performance asymmetrically. The biCNN model was constructed to run in real-time and used to control an unstable two-wheeled balancing robot. The load of the robot and its environment were modified to create asymmetrical perturbations. Plasticity at parallel fiber-Purkinje cell synapses in the biCNN model was driven by error signal in the climbing fiber (cf) input. This cf input was configured to increase and decrease its firing rate from its spontaneous firing rate (approximately 1 Hz) with sensory errors in the preferred and non-preferred direction of each hemisphere, as demonstrated in the monkey cerebellum. Our results showed that asymmetrical conditions were successfully handled by the biCNN model, in contrast to a single hemisphere model or a classical non-adaptive proportional and derivative controller. Further, the spontaneous activity of the cf, while relatively small, was critical for balancing the contribution of each cerebellar hemisphere to the overall motor command sent to the robot. Eliminating the spontaneous activity compromised the asymmetrical learning capabilities of the biCNN model. Thus, we conclude that a bi-hemispheric structure and adequate spontaneous activity of cf inputs are critical for cerebellar asymmetrical motor learning.

Adaptive robotic control driven by a versatile spiking cerebellar network

The cerebellum is involved in a large number of different neural processes, especially in associative learning and in fine motor control. To develop a comprehensive theory of sensorimotor learning and control, it is crucial to determine the neural basis of coding and plasticity embedded into the cerebellar neural circuit and how they are translated into behavioral outcomes in learning paradigms. Learning has to be inferred from the interaction of an embodied system with its real environment, and the same cerebellar principles derived from cell physiology have to be able to drive a variety of tasks of different nature, calling for complex timing and movement patterns. We have coupled a realistic cerebellar spiking neural network (SNN) with a real robot and challenged it in multiple diverse sensorimotor tasks. Encoding and decoding strategies based on neuronal firing rates were applied. Adaptive motor control protocols with acquisition and extinction phases have been designed and tested, including an associative Pavlovian task (Eye blinking classical conditioning), a vestibulo-ocular task and a perturbed arm reaching task operating in closed-loop. The SNN processed in real-time mossy fiber inputs as arbitrary contextual signals, irrespective of whether they conveyed a tone, a vestibular stimulus or the position of a limb. A bidirectional long-term plasticity rule implemented at parallel fibers-Purkinje cell synapses modulated the output activity in the deep cerebellar nuclei. In all tasks, the neurorobot learned to adjust timing and gain of the motor responses by tuning its output discharge. It succeeded in reproducing how human biological systems acquire, extinguish and express knowledge of a noisy and changing world. By varying stimuli and perturbations patterns, real-time control robustness and generalizability were validated. The implicit spiking dynamics of the cerebellar model fulfill timing, prediction and learning functions.