Unsupervised learning of granule cell sparse codes enhances cerebellar adaptive control

Understanding Cerebellar Input Stage through Computational and Plasticity Rules

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

Mesoscale simulations predict the role of synergistic cerebellar plasticity during classical eyeblink conditioning

According to the motor learning theory by Albus and Ito, synaptic depression at the parallel fibre to Purkinje cells synapse (pf-PC) is the main substrate responsible for learning sensorimotor contingencies under climbing fibre control. However, recent experimental evidence challenges this relatively monopolistic view of cerebellar learning. Bidirectional plasticity appears crucial for learning, in which different microzones can undergo opposite changes of synaptic strength (e.g. downbound microzones-more likely depression, upbound microzones-more likely potentiation), and multiple forms of plasticity have been identified, distributed over different cerebellar circuit synapses. Here, we have simulated classical eyeblink conditioning (CEBC) using an advanced spiking cerebellar model embedding downbound and upbound modules that are subject to multiple plasticity rules. Simulations indicate that synaptic plasticity regulates the cascade of precise spiking patterns spreading throughout the cerebellar cortex and cerebellar nuclei. CEBC was supported by plasticity at the pf-PC synapses as well as at the synapses of the molecular layer interneurons (MLIs), but only the combined switch-off of both sites of plasticity compromised learning significantly. By differentially engaging climbing fibre information and related forms of synaptic plasticity, both microzones contributed to generate a well-timed conditioned response, but it was the downbound module that played the major role in this process. The outcomes of our simulations closely align with the behavioural and electrophysiological phenotypes of mutant mice suffering from cell-specific mutations that affect processing of their PC and/or MLI synapses. Our data highlight that a synergy of bidirectional plasticity rules distributed across the cerebellum can facilitate finetuning of adaptive associative behaviours at a high spatiotemporal resolution.

Theoretical limits on the speed of learning inverse models explain the rate of adaptation in arm reaching tasks

An essential aspect of human motor learning is the formation of inverse models, which map desired actions to motor commands. Inverse models can be learned by adjusting parameters in neural circuits to minimize errors in the performance of motor tasks through gradient descent. However, the theory of gradient descent establishes limits on the learning speed. Specifically, the eigenvalues of the Hessian of the error surface around a minimum determine the maximum speed of learning in a task. Here, we use this theoretical framework to analyze the speed of learning in different inverse model learning architectures in a set of isometric arm-reaching tasks. We show theoretically that, in these tasks, the error surface and, thus the speed of learning, are determined by the shapes of the force manipulability ellipsoid of the arm and the distribution of targets in the task. In particular, rounder manipulability ellipsoids generate a rounder error surface, allowing for faster learning of the inverse model. Rounder target distributions have a similar effect. We tested these predictions experimentally in a quasi-isometric reaching task with a visuomotor transformation. The experimental results were consistent with our theoretical predictions. Furthermore, our analysis accounts for the speed of learning in previous experiments with incompatible and compatible virtual surgery tasks, and with visuomotor rotation tasks with different numbers of targets. By identifying aspects of a task that influence the speed of learning, our results provide theoretical principles for the design of motor tasks that allow for faster learning.

Adaptive Filter Model of Cerebellum for Biological Muscle Control With Spike Train Inputs

Prior applications of the cerebellar adaptive filter model have included a range of tasks within simulated and robotic systems. However, this has been limited to systems driven by continuous signals. Here, the adaptive filter model of the cerebellum is applied to the control of a system driven by spiking inputs by considering the problem of controlling muscle force. The performance of the standard adaptive filter algorithm is compared with the algorithm with a modified learning rule that minimizes inputs and a simple proportional-integral-derivative (PID) controller. Control performance is evaluated in terms of the number of spikes, the accuracy of spike input locations, and the accuracy of muscle force output. Results show that the cerebellar adaptive filter model can be applied without change to the control of systems driven by spiking inputs. The cerebellar algorithm results in good agreement between input spikes and force outputs and significantly improves on a PID controller. Input minimization can be used to reduce the number of spike inputs, but at the expense of a decrease in accuracy of spike input location and force output. This work extends the applications of the cerebellar algorithm and demonstrates the potential of the adaptive filter model to be used to improve functional electrical stimulation muscle control.

Task-dependent optimal representations for cerebellar learning

The cerebellar granule cell layer has inspired numerous theoretical models of neural representations that support learned behaviors, beginning with the work of Marr and Albus. In these models, granule cells form a sparse, combinatorial encoding of diverse sensorimotor inputs. Such sparse representations are optimal for learning to discriminate random stimuli. However, recent observations of dense, low-dimensional activity across granule cells have called into question the role of sparse coding in these neurons. Here, we generalize theories of cerebellar learning to determine the optimal granule cell representation for tasks beyond random stimulus discrimination, including continuous input-output transformations as required for smooth motor control. We show that for such tasks, the optimal granule cell representation is substantially denser than predicted by classical theories. Our results provide a general theory of learning in cerebellum-like systems and suggest that optimal cerebellar representations are task-dependent.

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.

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.

The quest for multiscale brain modeling

Addressing the multiscale organization of the brain, which is fundamental to the dynamic repertoire of the organ, remains challenging. In principle, it should be possible to model neurons and synapses in detail and then connect them into large neuronal assemblies to explain the relationship between microscopic phenomena, large-scale brain functions, and behavior. It is more difficult to infer neuronal functions from ensemble measurements such as those currently obtained with brain activity recordings. In this article we consider theories and strategies for combining bottom-up models, generated from principles of neuronal biophysics, with top-down models based on ensemble representations of network activity and on functional principles. These integrative approaches are hoped to provide effective multiscale simulations in virtual brains and neurorobots, and pave the way to future applications in medicine and information technologies.

Cerebellum Involvement in Dystonia During Associative Motor Learning: Insights From a Data-Driven Spiking Network Model

Dystonia is a movement disorder characterized by sustained or intermittent muscle contractions causing abnormal, often repetitive movements, postures, or both. Although dystonia is traditionally associated with basal ganglia dysfunction, recent evidence has been pointing to a role of the cerebellum, a brain area involved in motor control and learning. Cerebellar abnormalities have been correlated with dystonia but their potential causative role remains elusive. Here, we simulated the cerebellar input-output relationship with high-resolution computational modeling. We used a data-driven cerebellar Spiking Neural Network and simulated a cerebellum-driven associative learning task, Eye-Blink Classical Conditioning (EBCC), which is characteristically altered in relation to cerebellar lesions in several pathologies. In control simulations, input stimuli entrained characteristic network dynamics and induced synaptic plasticity along task repetitions, causing a progressive spike suppression in Purkinje cells with consequent facilitation of deep cerebellar nuclei cells. These neuronal processes caused a progressive acquisition of eyelid Conditioned Responses (CRs). Then, we modified structural or functional local neural features in the network reproducing alterations reported in dystonic mice. Either reduced olivocerebellar input or aberrant Purkinje cell burst-firing resulted in abnormal learning curves imitating the dysfunctional EBCC motor responses (in terms of CR amount and timing) of dystonic mice. These behavioral deficits might be due to altered temporal processing of sensorimotor information and uncoordinated control of muscle contractions. Conversely, an imbalance of excitatory and inhibitory synaptic densities on Purkinje cells did not reflect into significant EBCC deficit. The present work suggests that only certain types of alterations, including reduced olivocerebellar input and aberrant PC burst-firing, are compatible with the EBCC changes observed in dystonia, indicating that some cerebellar lesions can have a causative role in the pathogenesis of symptoms.

The anterior paired lateral neuron normalizes odour-evoked activity in the Drosophila mushroom body calyx

To identify and memorize discrete but similar environmental inputs, the brain needs to distinguish between subtle differences of activity patterns in defined neuronal populations. The Kenyon cells (KCs) of the Drosophila adult mushroom body (MB) respond sparsely to complex olfactory input, a property that is thought to support stimuli discrimination in the MB. To understand how this property emerges, we investigated the role of the inhibitory anterior paired lateral (APL) neuron in the input circuit of the MB, the calyx. Within the calyx, presynaptic boutons of projection neurons (PNs) form large synaptic microglomeruli (MGs) with dendrites of postsynaptic KCs. Combining electron microscopy (EM) data analysis and in vivo calcium imaging, we show that APL, via inhibitory and reciprocal synapses targeting both PN boutons and KC dendrites, normalizes odour-evoked representations in MGs of the calyx. APL response scales with the PN input strength and is regionalized around PN input distribution. Our data indicate that the formation of a sparse code by the KCs requires APL-driven normalization of their MG postsynaptic responses. This work provides experimental insights on how inhibition shapes sensory information representation in a higher brain centre, thereby supporting stimuli discrimination and allowing for efficient associative memory formation.

GluA4 facilitates cerebellar expansion coding and enables associative memory formation

AMPA receptors (AMPARs) mediate excitatory neurotransmission in the central nervous system (CNS) and their subunit composition determines synaptic efficacy. Whereas AMPAR subunits GluA1–GluA3 have been linked to particular forms of synaptic plasticity and learning, the functional role of GluA4 remains elusive. Here, we demonstrate a crucial function of GluA4 for synaptic excitation and associative memory formation in the cerebellum. Notably, GluA4-knockout mice had ~80% reduced mossy fiber to granule cell synaptic transmission. The fidelity of granule cell spike output was markedly decreased despite attenuated tonic inhibition and increased NMDA receptor-mediated transmission. Computational network modeling incorporating these changes revealed that deletion of GluA4 impairs granule cell expansion coding, which is important for pattern separation and associative learning. On a behavioral level, while locomotor coordination was generally spared, GluA4-knockout mice failed to form associative memories during delay eyeblink conditioning. These results demonstrate an essential role for GluA4-containing AMPARs in cerebellar information processing and associative learning.

Drawing inspiration from biological dendrites to empower artificial neural networks

This article highlights specific features of biological neurons and their dendritic trees, whose adoption may help advance artificial neural networks used in various machine learning applications. Advancements could take the form of increased computational capabilities and/or reduced power consumption. Proposed features include dendritic anatomy, dendritic nonlinearities, and compartmentalized plasticity rules, all of which shape learning and information processing in biological networks. We discuss the computational benefits provided by these features in biological neurons and suggest ways to adopt them in artificial neurons in order to exploit the respective benefits in machine learning.

Electrophysiology of ionotropic GABA receptors

GABA_A receptors are ligand-gated chloride channels and ionotropic receptors of GABA, the main inhibitory neurotransmitter in vertebrates. In this review, we discuss the major and diverse roles GABA_A receptors play in the regulation of neuronal communication and the functioning of the brain. GABA_A receptors have complex electrophysiological properties that enable them to mediate different types of currents such as phasic and tonic inhibitory currents. Their activity is finely regulated by membrane voltage, phosphorylation and several ions. GABA_A receptors are pentameric and are assembled from a diverse set of subunits. They are subdivided into numerous subtypes, which differ widely in expression patterns, distribution and electrical activity. Substantial variations in macroscopic neural behavior can emerge from minor differences in structure and molecular activity between subtypes. Therefore, the diversity of GABA_A receptors widens the neuronal repertoire of responses to external signals and contributes to shaping the electrical activity of neurons and other cell types.

Calcium Channel-Dependent Induction of Long-Term Synaptic Plasticity at Excitatory Golgi Cell Synapses of Cerebellum

Golgi cells, together with granule cells and mossy fibers, form a neuronal microcircuit regulating information transfer at the cerebellum input stage. Despite theoretical predictions, little was known about long-term synaptic plasticity at Golgi cell synapses. Here, we have used whole-cell patch-clamp recordings and calcium imaging to investigate long-term synaptic plasticity at excitatory synapses impinging on Golgi cells. In acute mouse cerebellar slices, mossy fiber theta-burst stimulation (TBS) could induce either long-term potentiation (LTP) or long-term depression (LTD) at mossy fiber-Golgi cell and granule cell-Golgi cell synapses. This synaptic plasticity showed a peculiar voltage dependence, with LTD or LTP being favored when TBS induction occurred at depolarized or hyperpolarized potentials, respectively. LTP required, in addition to NMDA channels, activation of T-type Ca²⁺ channels, while LTD required uniquely activation of L-type Ca²⁺ channels. Notably, the voltage dependence of plasticity at the mossy fiber-Golgi cell synapses was inverted with respect to pure NMDA receptor-dependent plasticity at the neighboring mossy fiber-granule cell synapse, implying that the mossy fiber presynaptic terminal can activate different induction mechanisms depending on the target cell. In aggregate, this result shows that Golgi cells show cell-specific forms of long-term plasticity at their excitatory synapses, that could play a crucial role in sculpting the response patterns of the cerebellar granular layer.SIGNIFICANCE STATEMENT This article shows for the first time a novel form of Ca²⁺ channel-dependent synaptic plasticity at the excitatory synapses impinging on cerebellar Golgi cells. This plasticity is bidirectional and inverted with respect to NMDA receptor-dependent paradigms, with long-term depression (LTD) and long-term potentiation (LTP) being favored at depolarized and hyperpolarized potentials, respectively. Furthermore, LTP and LTD induction requires differential involvement of T-type and L-type voltage-gated Ca²⁺ channels rather than the NMDA receptors alone. These results, along with recent computational predictions, support the idea that Golgi cell plasticity could play a crucial role in controlling information flow through the granular layer along with cerebellar learning and memory.

The Cerebellum on Cocaine

The traditional cerebellum’s role has been linked to the high computational demands for sensorimotor control. However, several findings have pointed to its involvement in executive and emotional functions in the last decades. First in 2009 and then, in 2016, we raised why we should consider the cerebellum when thinking about drug addiction. A decade later, mounting evidence strongly suggests the cerebellar involvement in this disorder. Nevertheless, direct evidence is still partial and related mainly to drug-induced reward memory, but recent results about cerebellar functions may provide new insights into its role in addiction. The present review does not intend to be a compelling revision on available findings, as we did in the two previous reviews. This minireview focuses on specific findings of the cerebellum’s role in drug-related reward memories and the way ahead for future research. The results discussed here provide grounds for involving the cerebellar cortex’s apical region in regulating behavior driven by drug-cue associations. They also suggest that the cerebellar cortex dysfunction may facilitate drug-induced learning by increasing glutamatergic output from the deep cerebellar nucleus (DCN) to the ventral tegmental area (VTA) and neural activity in its projecting areas.

50 Years Since the Marr, Ito, and Albus Models of the Cerebellum

Fifty years have passed since David Marr, Masao Ito, and James Albus proposed seminal models of cerebellar functions. These models share the essential concept that parallel-fiber-Purkinje-cell synapses undergo plastic changes, guided by climbing-fiber activities during sensorimotor learning. However, they differ in several important respects, including holistic versus complementary roles of the cerebellum, pattern recognition versus control as computational objectives, potentiation versus depression of synaptic plasticity, teaching signals versus error signals transmitted by climbing-fibers, sparse expansion coding by granule cells, and cerebellar internal models. In this review, we evaluate different features of the three models based on recent computational and experimental studies. While acknowledging that the three models have greatly advanced our understanding of cerebellar control mechanisms in eye movements and classical conditioning, we propose a new direction for computational frameworks of the cerebellum, that is, hierarchical reinforcement learning with multiple internal models.

Re-evaluating Circuit Mechanisms Underlying Pattern Separation

When animals interact with complex environments, their neural circuits must separate overlapping patterns of activity that represent sensory and motor information. Pattern separation is thought to be a key function of several brain regions, including the cerebellar cortex, insect mushroom body, and dentate gyrus. However, recent findings have questioned long-held ideas on how these circuits perform this fundamental computation. Here, we re-evaluate the functional and structural mechanisms underlying pattern separation. We argue that the dimensionality of the space available for population codes representing sensory and motor information provides a common framework for understanding pattern separation. We then discuss how these three circuits use different strategies to separate activity patterns and facilitate associative learning in the presence of trial-to-trial variability.

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.

Sparse synaptic connectivity is required for decorrelation and pattern separation in feedforward networks

Pattern separation is a fundamental function of the brain. The divergent feedforward networks thought to underlie this computation are widespread, yet exhibit remarkably similar sparse synaptic connectivity. Marr-Albus theory postulates that such networks separate overlapping activity patterns by mapping them onto larger numbers of sparsely active neurons. But spatial correlations in synaptic input and those introduced by network connectivity are likely to compromise performance. To investigate the structural and functional determinants of pattern separation we built models of the cerebellar input layer with spatially correlated input patterns, and systematically varied their synaptic connectivity. Performance was quantified by the learning speed of a classifier trained on either the input or output patterns. Our results show that sparse synaptic connectivity is essential for separating spatially correlated input patterns over a wide range of network activity, and that expansion and correlations, rather than sparse activity, are the major determinants of pattern separation.

Input decorrelation, expansion recoding and sparse activity have been proposed to separate overlapping activity patterns in feedforward networks. Here the authors use reduced and detailed spiking models to elucidate how synaptic connectivity affects the contribution of these mechanisms to pattern separation in cerebellar cortex.

Dysfunctions of the basal ganglia-cerebellar-thalamo-cortical system produce motor tics in Tourette syndrome

Motor tics are a cardinal feature of Tourette syndrome and are traditionally associated with an excess of striatal dopamine in the basal ganglia. Recent evidence increasingly supports a more articulated view where cerebellum and cortex, working closely in concert with basal ganglia, are also involved in tic production. Building on such evidence, this article proposes a computational model of the basal ganglia-cerebellar-thalamo-cortical system to study how motor tics are generated in Tourette syndrome. In particular, the model: (i) reproduces the main results of recent experiments about the involvement of the basal ganglia-cerebellar-thalamo-cortical system in tic generation; (ii) suggests an explanation of the system-level mechanisms underlying motor tic production: in this respect, the model predicts that the interplay between dopaminergic signal and cortical activity contributes to triggering the tic event and that the recently discovered basal ganglia-cerebellar anatomical pathway may support the involvement of the cerebellum in tic production; (iii) furnishes predictions on the amount of tics generated when striatal dopamine increases and when the cortex is externally stimulated. These predictions could be important in identifying new brain target areas for future therapies. Finally, the model represents the first computational attempt to study the role of the recently discovered basal ganglia-cerebellar anatomical links. Studying this non-cortex-mediated basal ganglia-cerebellar interaction could radically change our perspective about how these areas interact with each other and with the cortex. Overall, the model also shows the utility of casting Tourette syndrome within a system-level perspective rather than viewing it as related to the dysfunction of a single brain area.

Tourette syndrome is a neuropsychiatric disorder characterized by vocal and motor tics. Tics represent a cardinal symptom traditionally associated with a dysfunction of the basal ganglia leading to an excess of the dopamine neurotransmitter. This view gives a restricted clinical picture and limits therapeutic approaches because it ignores the influence of altered interactions between the basal ganglia and other brain areas. In this respect, recent evidence supports a more articulated framework where cerebellum and cortex are also involved in tic production. Building on these data, we propose a computational model of the basal ganglia-cerebellar-thalamo-cortical network to investigate the specific mechanisms underlying motor tic production. The model reproduces the results of recent experiments and suggests an explanation of the system-level processes underlying tic production. Moreover, it furnishes predictions related to the amount of tics generated when there are dysfunctions in the basal ganglia-cerebellar-thalamo-cortical circuits. These predictions could be important in identifying new brain target areas for future therapies based on a system-level view of Tourette syndrome.

Optimal Degrees of Synaptic Connectivity

Synaptic connectivity varies widely across neuronal types. Cerebellar granule cells receive five orders of magnitude fewer inputs than the Purkinje cells they innervate, and cerebellum-like circuits, including the insect mushroom body, also exhibit large divergences in connectivity. In contrast, the number of inputs per neuron in cerebral cortex is more uniform and large. We investigate how the dimension of a representation formed by a population of neurons depends on how many inputs each neuron receives and what this implies for learning associations. Our theory predicts that the dimensions of the cerebellar granule-cell and Drosophila Kenyon-cell representations are maximized at degrees of synaptic connectivity that match those observed anatomically, showing that sparse connectivity is sometimes superior to dense connectivity. When input synapses are subject to supervised plasticity, however, dense wiring becomes advantageous, suggesting that the type of plasticity exhibited by a set of synapses is a major determinant of connection density.

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.

Questioning the role of sparse coding in the brain

Coding principles are central to understanding the organization of brain circuitry. Sparse coding offers several advantages, but a near-consensus has developed that it only has beneficial properties, and these are partially unique to sparse coding. We find that these advantages come at the cost of several trade-offs, with the lower capacity for generalization being especially problematic, and the value of sparse coding as a measure and its experimental support are both questionable. Furthermore, silent synapses and inhibitory interneurons can permit learning speed and memory capacity that was previously ascribed to sparse coding only. Combining these properties without exaggerated sparse coding improves the capacity for generalization and facilitates learning of models of a complex and high-dimensional reality.

Integrated plasticity at inhibitory and excitatory synapses in the cerebellar circuit

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

The cerebellum and psychiatric disorders

The cerebellum has been considered for a long time to play a role solely in motor coordination. However, studies over the past two decades have shown that the cerebellum also plays a key role in many motor, cognitive, and emotional processes. In addition, studies have also shown that the cerebellum is implicated in many psychiatric disorders including attention deficit hyperactivity disorder, autism spectrum disorders, schizophrenia, bipolar disorder, major depressive disorder, and anxiety disorders. In this review, we discuss existing studies reporting cerebellar dysfunction in various psychiatric disorders. We will also discuss future directions for studies linking the cerebellum to psychiatric disorders.

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).

Sensorimotor transformation via sparse coding

Sensorimotor transformation is indispensable to the accurate motion of the human body in daily life. For instance, when we grasp an object, the distance from our hands to an object needs to be calculated by integrating multisensory inputs, and our motor system needs to appropriately activate the arm and hand muscles to minimize the distance. The sensorimotor transformation is implemented in our neural systems, and recent advances in measurement techniques have revealed an important property of neural systems: a small percentage of neurons exhibits extensive activity while a large percentage shows little activity, i.e., sparse coding. However, we do not yet know the functional role of sparse coding in sensorimotor transformation. In this paper, I show that sparse coding enables complete and robust learning in sensorimotor transformation. In general, if a neural network is trained to maximize the performance on training data, the network shows poor performance on test data. Nevertheless, sparse coding renders compatible the performance of the network on both training and test data. Furthermore, sparse coding can reproduce reported neural activities. Thus, I conclude that sparse coding is necessary and a biologically plausible factor in sensorimotor transformation.

Functional connectivity changes during a working memory task in rat via NMF analysis

Working memory (WM) is necessary in higher cognition. The brain as a complex network is formed by interconnections among neurons. Connectivity results in neural dynamics to support cognition. The first aim is to investigate connectivity dynamics in medial prefrontal cortex (mPFC) networks during WM. As brain neural activity is sparse, the second aim is to find the intrinsic connectivity property in a feature space. Using multi-channel electrode recording techniques, spikes were simultaneously obtained from mPFC of rats that performed a Y-maze WM task. Continuous time series converted from spikes were embedded in a low-dimensional space by non-negative matrix factorization (NMF). mPFC network in original space was constructed by measuring connections among neurons. And the same network in NMF space was constructed by computing connectivity values between the extracted NMF components. Causal density (Cd) and global efficiency (E) were estimated to present the network property. The results showed that Cd and E significantly peaked in the interval right before the maze choice point in correct trials. However, the increase did not emerge in error trials. Additionally, Cd and E in two spaces displayed similar trends in correct trials. The difference was that the measures in NMF space were significantly greater than those in original space. Our findings indicated that the anticipatory changes in mPFC networks may have an effect on future WM behavioral choices. Moreover, the NMF analysis achieves a better characterization for a brain network.

Fast convergence of learning requires plasticity between inferior olive and deep cerebellar nuclei in a manipulation task: a closed-loop robotic simulation

The cerebellum is known to play a critical role in learning relevant patterns of activity for adaptive motor control, but the underlying network mechanisms are only partly understood. The classical long-term synaptic plasticity between parallel fibers (PFs) and Purkinje cells (PCs), which is driven by the inferior olive (IO), can only account for limited aspects of learning. Recently, the role of additional forms of plasticity in the granular layer, molecular layer and deep cerebellar nuclei (DCN) has been considered. In particular, learning at DCN synapses allows for generalization, but convergence to a stable state requires hundreds of repetitions. In this paper we have explored the putative role of the IO-DCN connection by endowing it with adaptable weights and exploring its implications in a closed-loop robotic manipulation task. Our results show that IO-DCN plasticity accelerates convergence of learning by up to two orders of magnitude without conflicting with the generalization properties conferred by DCN plasticity. Thus, this model suggests that multiple distributed learning mechanisms provide a key for explaining the complex properties of procedural learning and open up new experimental questions for synaptic plasticity in the cerebellar network.

Network structure within the cerebellar input layer enables lossless sparse encoding

The synaptic connectivity within neuronal networks is thought to determine the information processing they perform, yet network structure-function relationships remain poorly understood. By combining quantitative anatomy of the cerebellar input layer and information theoretic analysis of network models, we investigated how synaptic connectivity affects information transmission and processing. Simplified binary models revealed that the synaptic connectivity within feedforward networks determines the trade-off between information transmission and sparse encoding. Networks with few synaptic connections per neuron and network-activity-dependent threshold were optimal for lossless sparse encoding over the widest range of input activities. Biologically detailed spiking network models with experimentally constrained synaptic conductances and inhibition confirmed our analytical predictions. Our results establish that the synaptic connectivity within the cerebellar input layer enables efficient lossless sparse encoding. Moreover, they provide a functional explanation for why granule cells have approximately four dendrites, a feature that has been evolutionarily conserved since the appearance of fish.

Integration and regulation of glomerular inhibition in the cerebellar granular layer circuit

Inhibitory synapses can be organized in different ways and be regulated by a multitude of mechanisms. One of the best known examples is provided by the inhibitory synapses formed by Golgi cells onto granule cells in the cerebellar glomeruli. These synapses are GABAergic and inhibit granule cells through two main mechanisms, phasic and tonic. The former is based on vesicular neurotransmitter release, the latter on the establishment of tonic γ-aminobutyric acid (GABA) levels determined by spillover and regulation of GABA uptake. The mechanisms of post-synaptic integration have been clarified to a considerable extent and have been shown to differentially involve α1 and α6 subunit-containing GABA-A receptors. Here, after reviewing the basic mechanisms of GABAergic transmission in the cerebellar glomeruli, we examine how inhibition controls signal transfer at the mossy fiber-granule cell relay. First of all, we consider how vesicular release impacts on signal timing and how tonic GABA levels control neurotransmission gain. Then, we analyze the integration of these inhibitory mechanisms within the granular layer network. Interestingly, it turns out that glomerular inhibition is just one element in a large integrated signaling system controlled at various levels by metabotropic receptors. GABA-B receptor activation by ambient GABA regulates glutamate release from mossy fibers through a pre-synaptic cross-talk mechanisms, GABA release through pre-synaptic auto-receptors, and granule cell input resistance through post-synaptic receptor activation and inhibition of a K inward-rectifier current. Metabotropic glutamate receptors (mGluRs) control GABA release from Golgi cell terminals and Golgi cell input resistance and autorhythmic firing. This complex set of mechanisms implements both homeostatic and winner-take-all processes, providing the basis for fine-tuning inhibitory neurotransmission and for optimizing signal transfer through the cerebellar cortex.

Sensory-evoked synaptic integration in cerebellar and cerebral cortical neurons

Neurons integrate synaptic inputs across time and space, a process that determines the transformation of input signals into action potential output. This article explores how synaptic integration contributes to the richness of sensory signalling in the cerebellar and cerebral cortices. Whether a neuron receives a few or a few thousand discrete inputs, most evoked synaptic activity generates only subthreshold membrane potential fluctuations. Sensory tuning of synaptic inputs is typically broad, but short-term dynamics and the interplay between excitation and inhibition restrict action potential firing to narrow windows of opportunity. We highlight the challenges and limitations of the use of somatic recordings in the study of synaptic integration and the importance of active dendritic mechanisms in sensory processing.

The organization of plasticity in the cerebellar cortex: from synapses to control

The cerebellum is thought to play a critical role in procedural learning, but the relationship between this function and the underlying cellular and synaptic mechanisms remains largely speculative. At present, at least nine forms of long-term synaptic and nonsynaptic plasticity (some of which are bidirectional) have been reported in the cerebellar cortex and deep cerebellar nuclei. These include long-term potentiation (LTP) and long-term depression at the mossy fiber-granule cell synapse, at the synapses formed by parallel fibers, climbing fibers, and molecular layer interneurons on Purkinje cells, and at the synapses formed by mossy fibers and Purkinje cells on deep cerebellar nuclear cells, as well as LTP of intrinsic excitability in granule cells, Purkinje cells, and deep cerebellar nuclear cells. It is suggested that the complex properties of cerebellar learning would emerge from the distribution of plasticity in the network and from its dynamic remodeling during the different phases of learning. Intrinsic and extrinsic factors may hold the key to explain how the different forms of plasticity cooperate to select specific transmission channels and to regulate the signal-to-noise ratio through the cerebellar cortex. These factors include regulation of neuronal excitation by local inhibitory networks, engagement of specific molecular mechanisms by spike bursts and theta-frequency oscillations, and gating by external neuromodulators. Therefore, a new and more complex view of cerebellar plasticity is emerging with respect to that predicted by the original "Motor Learning Theory," opening issues that will require experimental and computational testing.

Questioning the cerebellar doctrine

The basic principles of cerebellar function were originally described by Flourens, Cajal, and Marr/Albus/Ito, and they constitute the pillars of what can be considered to be the classic cerebellar doctrine. In their concepts, the main cerebellar function is to control motor behavior, Purkinje cells are the only cortical neuron receiving and integrating inputs from climbing fiber and mossy-parallel fiber pathways, and plastic modification at the parallel fiber synapses onto Purkinje cells constitutes the substrate of motor learning. Yet, because of recent technical advances and new angles of investigation, all pillars of the cerebellar doctrine now face regular re-examination. In this review, after summarizing the classic concepts and recent disputes, we attempt to synthesize an integrated view and propose a revisited version of the cerebellar doctrine.

Distributed cerebellar plasticity implements adaptable gain control in a manipulation task: a closed-loop robotic simulation

Adaptable gain regulation is at the core of the forward controller operation performed by the cerebro-cerebellar loops and it allows the intensity of motor acts to be finely tuned in a predictive manner. In order to learn and store information about body-object dynamics and to generate an internal model of movement, the cerebellum is thought to employ long-term synaptic plasticity. LTD at the PF-PC synapse has classically been assumed to subserve this function (Marr, 1969). However, this plasticity alone cannot account for the broad dynamic ranges and time scales of cerebellar adaptation. We therefore tested the role of plasticity distributed over multiple synaptic sites (Hansel et al., 2001; Gao et al., 2012) by generating an analog cerebellar model embedded into a control loop connected to a robotic simulator. The robot used a three-joint arm and performed repetitive fast manipulations with different masses along an 8-shape trajectory. In accordance with biological evidence, the cerebellum model was endowed with both LTD and LTP at the PF-PC, MF-DCN and PC-DCN synapses. This resulted in a network scheme whose effectiveness was extended considerably compared to one including just PF-PC synaptic plasticity. Indeed, the system including distributed plasticity reliably self-adapted to manipulate different masses and to learn the arm-object dynamics over a time course that included fast learning and consolidation, along the lines of what has been observed in behavioral tests. In particular, PF-PC plasticity operated as a time correlator between the actual input state and the system error, while MF-DCN and PC-DCN plasticity played a key role in generating the gain controller. This model suggests that distributed synaptic plasticity allows generation of the complex learning properties of the cerebellum. The incorporation of further plasticity mechanisms and of spiking signal processing will allow this concept to be extended in a more realistic computational scenario.

Gating of long-term potentiation by nicotinic acetylcholine receptors at the cerebellum input stage

The brain needs mechanisms able to correlate plastic changes with local circuit activity and internal functional states. At the cerebellum input stage, uncontrolled induction of long-term potentiation or depression (LTP or LTD) between mossy fibres and granule cells can saturate synaptic capacity and impair cerebellar functioning, which suggests that neuromodulators are required to gate plasticity processes. Cholinergic systems innervating the cerebellum are thought to enhance procedural learning and memory. Here we show that a specific subtype of acetylcholine receptors, the α7-nAChRs, are distributed both in cerebellar mossy fibre terminals and granule cell dendrites and contribute substantially to synaptic regulation. Selective α7-nAChR activation enhances the postsynaptic calcium increase, allowing weak mossy fibre bursts, which would otherwise cause LTD, to generate robust LTP. The local microperfusion of α7-nAChR agonists could also lead to in vivo switching of LTD to LTP following sensory stimulation of the whisker pad. In the cerebellar flocculus, α7-nAChR pharmacological activation impaired vestibulo-ocular-reflex adaptation, probably because LTP was saturated, preventing the fine adjustment of synaptic weights. These results show that gating mechanisms mediated by specific subtypes of nicotinic receptors are required to control the LTD/LTP balance at the mossy fibre-granule cell relay in order to regulate cerebellar plasticity and behavioural adaptation.

Spike timing regulation on the millisecond scale by distributed synaptic plasticity at the cerebellum input stage: a simulation study

The way long-term synaptic plasticity regulates neuronal spike patterns is not completely understood. This issue is especially relevant for the cerebellum, which is endowed with several forms of long-term synaptic plasticity and has been predicted to operate as a timing and a learning machine. Here we have used a computational model to simulate the impact of multiple distributed synaptic weights in the cerebellar granular-layer network. In response to mossy fiber (MF) bursts, synaptic weights at multiple connections played a crucial role to regulate spike number and positioning in granule cells. The weight at MF to granule cell synapses regulated the delay of the first spike and the weight at MF and parallel fiber to Golgi cell synapses regulated the duration of the time-window during which the first-spike could be emitted. Moreover, the weights of synapses controlling Golgi cell activation regulated the intensity of granule cell inhibition and therefore the number of spikes that could be emitted. First-spike timing was regulated with millisecond precision and the number of spikes ranged from zero to three. Interestingly, different combinations of synaptic weights optimized either first-spike timing precision or spike number, efficiently controlling transmission and filtering properties. These results predict that distributed synaptic plasticity regulates the emission of quasi-digital spike patterns on the millisecond time-scale and allows the cerebellar granular layer to flexibly control burst transmission along the MF pathway.

ADAPTIVE AND PREDICTIVE CONTROL OF A SIMULATED ROBOT ARM

In this work, a basic cerebellar neural layer and a machine learning engine are embedded in a recurrent loop which avoids dealing with the motor error or distal error problem. The presented approach learns the motor control based on available sensor error estimates (position, velocity, and acceleration) without explicitly knowing the motor errors. The paper focuses on how to decompose the input into different components in order to facilitate the learning process using an automatic incremental learning model (locally weighted projection regression (LWPR) algorithm). LWPR incrementally learns the forward model of the robot arm and provides the cerebellar module with optimal pre-processed signals. We present a recurrent adaptive control architecture in which an adaptive feedback (AF) controller guarantees a precise, compliant, and stable control during the manipulation of objects. Therefore, this approach efficiently integrates a bio-inspired module (cerebellar circuitry) with a machine learning component (LWPR). The cerebellar-LWPR synergy makes the robot adaptable to changing conditions. We evaluate how this scheme scales for robot-arms of a high number of degrees of freedom (DOFs) using a simulated model of a robot arm of the new generation of light weight robots (LWRs).

Adaptive coupling of inferior olive neurons in cerebellar learning

In the cerebellar learning hypothesis, inferior olive neurons are presumed to transmit high fidelity error signals, despite their low firing rates. The idea of chaotic resonance has been proposed to realize efficient error transmission by desynchronized spiking activities induced by moderate electrical coupling between inferior olive neurons. A recent study suggests that the coupling strength between inferior olive neurons can be adaptive and may decrease during the learning process. We show that such a decrease in coupling strength can be beneficial for motor learning, since efficient coupling strength depends upon the magnitude of the error signals. We introduce a scheme of adaptive coupling that enhances the learning of a neural controller for fast arm movements. Our numerical study supports the view that the controlling strategy of the coupling strength provides an additional degree of freedom to optimize the actual learning in the cerebellum.

Bio-inspired adaptive feedback error learning architecture for motor control

This study proposes an adaptive control architecture based on an accurate regression method called Locally Weighted Projection Regression (LWPR) and on a bio-inspired module, such as a cerebellar-like engine. This hybrid architecture takes full advantage of the machine learning module (LWPR kernel) to abstract an optimized representation of the sensorimotor space while the cerebellar component integrates this to generate corrective terms in the framework of a control task. Furthermore, we illustrate how the use of a simple adaptive error feedback term allows to use the proposed architecture even in the absence of an accurate analytic reference model. The presented approach achieves an accurate control with low gain corrective terms (for compliant control schemes). We evaluate the contribution of the different components of the proposed scheme comparing the obtained performance with alternative approaches. Then, we show that the presented architecture can be used for accurate manipulation of different objects when their physical properties are not directly known by the controller. We evaluate how the scheme scales for simulated plants of high Degrees of Freedom (7-DOFs).

Neural circuits of the cerebellum: hypothesis for function

The rapid growth of cerebellar research is going to clarify several aspects of cellular and circuit physiology. However, the concepts about cerebellar mechanisms of function are still largely related to clinical observations and to models elaborated before the last discoveries appeared. In this paper, the major issues are revisited, suggesting that previous concepts can now be refined and modified. The cerebellum is fundamentally involved in timing and in controlling the ordered and precise execution of motor sequences. The fast reaction of the cerebellum to the inputs is sustained by specific cellular mechanisms ensuring precision on the millisecond scale. These include burst-burst reconversion in the granular layer and instantaneous frequency modulation on the 100-Hz band in Purkinje and deep cerebellar nuclei cells. Precisely timed signals can be used for perceptron operations in Purkinje cells and to establish appropriate correlations with climbing fiber signals inducing learning at parallel fiber synapses. In the granular layer, plasticity turns out to be instrumental to timing, providing a conceptual solution to the discrepancy between cerebellar learning and timing. The granular layer sub-circuit can be tuned by long-term synaptic plasticity and synaptic inhibition to delay the incoming signals over a 100-ms range. For longer sequences, large circuit sections can be entrained into coherent activity in 100-ms cycles. These dynamic aspects, which have not been accounted for by original theories, could in fact represent the essence of cerebellar functioning. It is suggested that the cerebellum can, in this way, operate the realignment of temporally incongruent signals, allowing their binding and pattern recognition in Purkinje cells. The demonstration of these principles, their behavioral relevance and their relationship with internal model theories represent a challenge for future cerebellar research.

Synaptic mechanisms of sensorimotor learning in the cerebellum

The cerebellum plays an essential role in motor learning. The ability to identify specific sensory and motor signals carried by neurons with known connectivity makes the cerebellum an attractive system for investigating how synaptic plasticity relates to learning. Early studies focused primarily on a single form of plasticity, long-term depression at parallel fiber-Purkinje cell synapses. Recent work has highlighted both the diversity of synaptic plasticity that exists within the cerebellum and the fact that individual plasticity mechanisms can have unexpected consequences when they act within neural circuits.

Local field potential modeling predicts dense activation in cerebellar granule cells clusters under LTP and LTD control

Local field-potentials (LFPs) are generated by neuronal ensembles and contain information about the activity of single neurons. Here, the LFPs of the cerebellar granular layer and their changes during long-term synaptic plasticity (LTP and LTD) were recorded in response to punctate facial stimulation in the rat in vivo. The LFP comprised a trigeminal (T) and a cortical (C) wave. T and C, which derived from independent granule cell clusters, co-varied during LTP and LTD. To extract information about the underlying cellular activities, the LFP was reconstructed using a repetitive convolution (ReConv) of the extracellular potential generated by a detailed multicompartmental model of the granule cell. The mossy fiber input patterns were determined using a Blind Source Separation (BSS) algorithm. The major component of the LFP was generated by the granule cell spike Na⁺ current, which caused a powerful sink in the axon initial segment with the source located in the soma and dendrites. Reproducing the LFP changes observed during LTP and LTD required modifications in both release probability and intrinsic excitability at the mossy fiber-granule cells relay. Synaptic plasticity and Golgi cell feed-forward inhibition proved critical for controlling the percentage of active granule cells, which was 11% in standard conditions but ranged from 3% during LTD to 21% during LTP and raised over 50% when inhibition was reduced. The emerging picture is that of independent (but neighboring) trigeminal and cortical channels, in which synaptic plasticity and feed-forward inhibition effectively regulate the number of discharging granule cells and emitted spikes generating “dense” activity clusters in the cerebellar granular layer.

How synaptic release probability shapes neuronal transmission: information-theoretic analysis in a cerebellar granule cell

A nerve cell receives multiple inputs from upstream neurons by way of its synapses. Neuron processing functions are thus influenced by changes in the biophysical properties of the synapse, such as long-term potentiation (LTP) or depression (LTD). This observation has opened new perspectives on the biophysical basis of learning and memory, but its quantitative impact on the information transmission of a neuron remains partially elucidated. One major obstacle is the high dimensionality of the neuronal input-output space, which makes it unfeasible to perform a thorough computational analysis of a neuron with multiple synaptic inputs. In this work, information theory was employed to characterize the information transmission of a cerebellar granule cell over a region of its excitatory input space following synaptic changes. Granule cells have a small dendritic tree (on average, they receive only four mossy fiber afferents), which greatly bounds the input combinatorial space, reducing the complexity of information-theoretic calculations. Numerical simulations and LTP experiments quantified how changes in neurotransmitter release probability (p) modulated information transmission of a cerebellar granule cell. Numerical simulations showed that p shaped the neurotransmission landscape in unexpected ways. As p increased, the optimality of the information transmission of most stimuli did not increase strictly monotonically; instead it reached a plateau at intermediate p levels. Furthermore, our results showed that the spatiotemporal characteristics of the inputs determine the effect of p on neurotransmission, thus permitting the selection of distinctive preferred stimuli for different p values. These selective mechanisms may have important consequences on the encoding of cerebellar mossy fiber inputs and the plasticity and computation at the next circuit stage, including the parallel fiber-Purkinje cell synapses.

The cerebellar network: from structure to function and dynamics

Since the discoveries of Camillo Golgi and Ramón y Cajal, the precise cellular organization of the cerebellum has inspired major computational theories, which have then influenced the scientific thought not only on the cerebellar function but also on the brain as a whole. However, six major issues revealing a discrepancy between morphologically inspired hypothesis and function have emerged. (1) The cerebellar granular layer does not simply operate a simple combinatorial decorrelation of the inputs but performs more complex non-linear spatio-temporal transformations and is endowed with synaptic plasticity. (2) Transmission along the ascending axon and parallel fibers does not lead to beam formation but rather to vertical columns of activation. (3) The olivo-cerebellar loop could perform complex timing operations rather than error detection and teaching. (4) Purkinje cell firing dynamics are much more complex than for a linear integrator and include pacemaking, burst-pause discharges, and bistable states in response to mossy and climbing fiber synaptic inputs. (5) Long-term synaptic plasticity is far more complex than traditional parallel fiber LTD and involves also other cerebellar synapses. (6) Oscillation and resonance could set up coherent cycles of activity designing a functional geometry that goes far beyond pre-wired anatomical circuits. These observations clearly show that structure is not sufficient to explain function and that a precise knowledge on dynamics is critical to understand how the cerebellar circuit operates.