Computational Theory Underlying Acute Vestibulo-ocular Reflex Motor Learning with Cerebellar Long-Term Depression and Long-Term Potentiation

The vestibulo-ocular reflex (VOR) can be viewed as an adaptive control system that maintains compensatory eye movements during head motion. As the cerebellar flocculus is intimately involved in this adaptive motor control of the VOR, the VOR has been a popular model system for investigating cerebellar motor learning. Long-term depression (LTD) and long-term potentiation (LTP) at the parallel fiber–Purkinje cell synapses are considered to play major roles in cerebellar motor learning. A recent study using mutant mice demonstrated cerebellar motor learning with hampered LTD; the study concluded that the parallel fiber–Purkinje cell LTD is not essential. More recently, multiple forms of plasticity have been found in the cerebellum, and they are believed to contribute to cerebellar motor learning. However, it is still unclear how synaptic plasticity modifies the signal processing that underlies motor learning in the flocculus. A computational simulation suggested that the plasticity present in mossy fiber–granule cell synapses improves VOR-related sensory-motor information transferred into granule cells, whereas the plasticity in the molecular layer stores this information as a memory under guidance from climbing fiber teaching signals. Thus, motor learning and memory are thought to be induced mainly by LTD and LTP at parallel fiber–Purkinje cell synapses and by rebound potentiation at molecular interneuron–Purkinje cell synapses among the multiple forms of plasticity in the cerebellum. In this study, we focused on the LTD and LTP at parallel fiber–Purkinje cell synapses. Based on our simulation, we propose that acute VOR motor learning accomplishes by simultaneous enhancement of eye movement signals via LTP and suppression of vestibular signals via LTD to increase VOR gain (gain-up learning). To decrease VOR gain (gain-down learning), these two signals are modified in the opposite directions; namely, LTD suppresses eye movement signals, whereas LTP enhances vestibular signals.     

The cerebellum as an adaptive filter: a general model?

Many functional models of the cerebellar microcircuit are based on the adaptive-filter model first proposed by Fujita. The adaptive filter has powerful signal processing capacities that are suitable for both sensory and motor tasks, and uses a simple and intuitively plausible decorrelation learning rule that offers and account of the evolution of the inferior olive. Moreover, in those cases where the input-output transformations of cerebellar microzones have been sufficiently characterised, they appear to conform to those predicted by the adaptive-filter model. However, these cases are few in number, and comparing the model with the internal operations of the microcircuit itself has not proved straightforward. Whereas some microcircuit features appear compatible with adaptive-filter function, others such as simple granular-layer processing or Purkinje cell bistability, do not. How far these seeming incompatibilities indicate additional computational roles for the cerebellar microcircuit remains to be determined.     

Depressed by Learning—Heterogeneity of the Plasticity Rules at Parallel Fiber Synapses onto Purkinje Cells

Climbing fiber-driven long-term depression (LTD) of parallel fiber synapses onto cerebellar Purkinje cells has long been investigated as a putative mechanism of motor learning. We recently discovered that the rules governing the induction of LTD at these synapses vary across different regions of the cerebellum. Here, we discuss the design of LTD induction protocols in light of this heterogeneity in plasticity rules. The analytical advantages of the cerebellum provide an opportunity to develop a deeper understanding of how the specific plasticity rules at synapses support the implementation of learning.     

The Errors of Our Ways: Understanding Error Representations in Cerebellar-Dependent Motor Learning

The cerebellum is essential for error-driven motor learning and is strongly implicated in detecting and correcting for motor errors. Therefore, elucidating how motor errors are represented in the cerebellum is essential in understanding cerebellar function, in general, and its role in motor learning, in particular. This review examines how motor errors are encoded in the cerebellar cortex in the context of a forward internal model that generates predictions about the upcoming movement and drives learning and adaptation. In this framework, sensory prediction errors, defined as the discrepancy between the predicted consequences of motor commands and the sensory feedback, are crucial for both on-line movement control and motor learning. While many studies support the dominant view that motor errors are encoded in the complex spike discharge of Purkinje cells, others have failed to relate complex spike activity with errors. Given these limitations, we review recent findings in the monkey showing that complex spike modulation is not necessarily required for motor learning or for simple spike adaptation. Also, new results demonstrate that the simple spike discharge provides continuous error signals that both lead and lag the actual movements in time, suggesting errors are encoded as both an internal prediction of motor commands and the actual sensory feedback. These dual error representations have opposing effects on simple spike discharge, consistent with the signals needed to generate sensory prediction errors used to update a forward internal model.     

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.     

The role of calcium in synaptic plasticity and motor learning in the cerebellar cortex

The cerebellum is important for motor coordination, as well as motor learning and memories. Learning is believed to occur in the cerebellar cortex, in the form of synaptic plasticity. Central to motor learning theory are Purkinje cells (PCs), which are the sole output neurons of the cerebellar cortex. Motor memories are postulated to be stored in the form of long-term depression (LTD) at parallel fiber synapses with PCs, once thought to be the only plastic synapse in the cerebellar cortex. However, in the past few decades many studies have demonstrated that several other synapses in the cerebellar cortex are indeed plastic, and that LTD or long-term potentiation at these various synapses could affect the overall output signal of PCs from the cerebellar cortex. Almost all of these forms of synaptic plasticity are dependent on calcium to some extent. In the current review we discuss various types of synaptic plasticity in the cerebellar cortex and the role of calcium in these forms of plasticity.     

Input minimization: a model of cerebellar learning without climbing fiber error signals.

The cerebellum is critical for motor learning. Current cerebellar learning models follow the Marr/Albus paradigm, in which climbing fibers provide error signals that shape plastic synapses between parallel fibers and Purkinje cells. However, climbing fibers have slow and largely random discharge, and seem unlikely to provide error signals with resolution sufficient to guide cerebellar learning. Parallel fibers carry error signals and could direct the plasticity of their own synapses, but the error signals are carried along with other signals. This report presents the new input minimization (InMin) model, in which Purkinje cells reduce error by minimizing their overall parallel fiber input. The slowly, randomly firing climbing fiber provides only synchronization pulses. InMin offers an alternative that can unify cerebellar findings.     

Cerebellar contributions to reach adaptation and learning sensory consequences of action

When we use a novel tool, the motor commands may not produce the expected outcome. In healthy individuals, with practice the brain learns to alter the motor commands. This change depends critically on the cerebellum as damage to this structure impairs adaptation. However, it is unclear precisely what the cerebellum contributes to the process of adaptation in human motor learning. Is the cerebellum crucial for learning to associate motor commands with novel sensory consequences, called forward model, or is the cerebellum important for learning to associate sensory goals with novel motor commands, called inverse model? Here, we compared performance of cerebellar patients and healthy controls in a reaching task with a gradual perturbation schedule. This schedule allowed both groups to adapt their motor commands. Following training, we measured two kinds of behavior: in one case, people were presented with reach targets near the direction in which they had trained. The resulting generalization patterns of patients and controls were similar, suggesting comparable inverse models. In the second case, participants reached without a target and reported the location of their hand. In controls, the pattern of change in reported hand location was consistent with simulation results of a forward model that had learned to associate motor commands with new sensory consequences. In patients, this change was significantly smaller. Therefore, in our sample of patients, we observed that while adaptation of motor commands can take place despite cerebellar damage, cerebellar integrity appears critical for learning to predict visual sensory consequences of motor commands.     

The cerebellum in action: a simulation and robotics study

The control or prediction of the precise timing of events are central aspects of the many tasks assigned to the cerebellum. Despite much detailed knowledge of its physiology and anatomy, it remains unclear how the cerebellar circuitry can achieve such an adaptive timing function. We present a computational model pursuing this question for one extensively studied type of cerebellar-mediated learning: the classical conditioning of discrete motor responses. This model combines multiple current assumptions on the function of the cerebellar circuitry and was used to investigate whether plasticity in the cerebellar cortex alone can mediate adaptive conditioned response timing. In particular, we studied the effect of changes in the strength of the synapses formed between parallel fibres and Purkinje cells under the control of a negative feedback loop formed between inferior olive, cerebellar cortex and cerebellar deep nuclei. The learning performance of the model was evaluated at the circuit level in simulated conditioning experiments as well as at the behavioural level using a mobile robot. We demonstrate that the model supports adaptively timed responses under real-world conditions. Thus, in contrast to many other models that have focused on cerebellar-mediated conditioning, we investigated whether and how the suggested underlying mechanisms could give rise to behavioural phenomena.     

Report on a workshop concerning the cerebellum and motor learning,held in St Louis October 2004

A one-day meeting on the cerebellum and motor learning was held in St Louis (October 2004), to address issues arising from a previous larger meeting (Tuebingen, June 2004). The learning tasks considered were VOR adaptation, saccadic adaptation and eyeblink conditioning. A theoretical development was reported that indicated how the cerebellum could use sensory error signals for adaptive control, by decorrelating them from an efferent copy of motor commands. The main topics for discussion were the nature of the error signals actually used by the cerebellum, and the evidence for multiple sites of synaptic plasticity. Reports of studies on VOR adaptation confirmed the presence of error signals in addition to retinal slip, in particular the eye-movement related simple-spike firing of floccular PCs. This firing appears to drive synaptic plasticity in the vestibular nuclei. From a theoretical perspective, a second site of plasticity in the brainstem has two advantages: it improves the high-frequency performance of the VOR given a delayed slip signal, and it allows VOR adaptation when smooth pursuit effectively removes the retinal slip signal. In contrast, some of the physiological data reported on saccadic adaptation seemed incompatible with current theoretical ideas about error signals. However, since other reported data were broadly consistent with those ideas, an important area of experimental disagreement was identified. Furthermore, behavioural studies indicated the presence of multiple sites of plasticity, consistent with earlier lesion studies that suggested one such site within cerebellar cortex and another outside it. Data from eyeblink conditioning suggested that the predictability of the error signal was important. Related ideas have previously emerged from studies of skeletal movement, but their theoretical implications for the cerebellar algorithm have yet to be fully explored. Finally, the long-standing controversy concerning sites of plasticity in eyeblink conditioning illustrated the technical difficulties involved in tracking down such sites.     

The fragile X-cerebellum connection

Fragile X syndrome (FXS) is an inherited form of mental retardation that results from the loss of function of the fragile X mental retardation protein (FMRP). A recent report demonstrated alterations in the structure and plasticity of synapses on cerebellar Purkinje cells in Fmr1 knockout mice, which are a model of FXS. These synaptic alterations are associated with deficits in the cerebellar learning both in the mice and humans with FXS. This work forges an important link between the FMR1 gene, altered synaptic plasticity in the cerebellum and mental retardation.     

Classical conditioning of motor responses: What is the learning mechanism?

According to a widely held assumption, the main mechanism underlying motor learning in the cerebellum, such as eyeblink conditioning, is long-term depression (LTD) of parallel fibre to Purkinje cell synapses. Here we review some recent physiological evidence from Purkinje cell recordings during conditioning with implications for models of conditioning. We argue that these data pose four major challenges to the LTD hypothesis of conditioning. (i) LTD cannot account for the pause in Purkinje cell firing that is believed to drive the conditioned blink. (ii) The temporal conditions conducive to LTD do not match those for eyeblink conditioning. (iii) LTD cannot readily account for the adaptive timing of the conditioned response. (iv) The data suggest that parallel fibre to Purkinje cell synapses are not depressed after learning a Purkinje cell CR. Models based on metabotropic glutamate receptors are also discussed and found to be incompatible with the recording data.     

Distinct subsynaptic localization of type 1 metabotropic glutamate receptors at glutamatergic and GABAergic synapses in the rodent cerebellar cortex

Type 1 metabotropic glutamate (mGlu1) receptors play a pivotal role in different forms of synaptic plasticity in the cerebellar cortex, e.g. long‐term depression at glutamatergic synapses and rebound potentiation at GABAergic synapses. These various forms of plasticity might depend on the subsynaptic arrangement of the receptor in Purkinje cells that can be regulated by protein–protein interactions. This study investigated, by means of the freeze‐fracture replica immunogold labelling method, the subcellular localization of mGlu1 receptors in the rodent cerebellum and whether Homer proteins regulate their subsynaptic distribution. We observed a widespread extrasynaptic localization of mGlu1 receptors and confirmed their peri‐synaptic enrichment at glutamatergic synapses. Conversely, we detected mGlu1 receptors within the main body of GABAergic synapses onto Purkinje cell dendrites. Although Homer proteins are known to interact with the mGlu1 receptor C‐terminus, we could not detect Homer3, the most abundant Homer protein in the cerebellar cortex, at GABAergic synapses by pre‐embedding and post‐embedding immunoelectron microscopy. We then hypothesized a critical role for Homer proteins in the peri‐junctional localization of mGlu1 receptors at glutamatergic synapses. To disrupt Homer‐associated protein complexes, mice were tail‐vein injected with the membrane‐permeable dominant‐negative TAT‐Homer1a. Freeze‐fracture replica immunogold labelling analysis showed no significant alteration in the mGlu1 receptor distribution pattern at parallel fibre–Purkinje cell synapses, suggesting that other scaffolding proteins are involved in the peri‐synaptic confinement. The identification of interactors that regulate the subsynaptic localization of the mGlu1 receptor at neurochemically distinct synapses may offer new insight into its trafficking and intracellular signalling.     

Adaptive filters and internal models: Multilevel description of cerebellar function

Cerebellar function is increasingly discussed in terms of engineering schemes for motor control and signal processing that involve internal models. To address the relation between the cerebellum and internal models, we adopt the chip metaphor that has been used to represent the combination of a homogeneous cerebellar cortical microcircuit with individual microzones having unique external connections. This metaphor indicates that identifying the function of a particular cerebellar chip requires knowledge of both the general microcircuit algorithm and the chip’s individual connections.Here we use a popular candidate algorithm as embodied in the adaptive filter, which learns to decorrelate its inputs from a reference (‘teaching’, ‘error’) signal. This algorithm is computationally powerful enough to be used in a very wide variety of engineering applications. However, the crucial issue is whether the external connectivity required by such applications can be implemented biologically.We argue that some applications appear to be in principle biologically implausible: these include the Smith predictor and Kalman filter (for state estimation), and the feedback–error–learning scheme for adaptive inverse control. However, even for plausible schemes, such as forward models for noise cancellation and novelty-detection, and the recurrent architecture for adaptive inverse control, there is unlikely to be a simple mapping between microzone function and internal model structure.This initial analysis suggests that cerebellar involvement in particular behaviours is therefore unlikely to have a neat classification into categories such as ‘forward model’. It is more likely that cerebellar microzones learn a task-specific adaptive-filter operation which combines a number of signal-processing roles.     

Mechanisms of locomotor control in the cerebellum

Animals as well as humans adapt their locomotor patterns to suit different situations. To perform smooth and stable locomotion, they coordinate not only parts of a limb but also different limbs. The cerebellum is important for sensorimotor control and plays a crucial role in intra- and inter-limb coordination. Cerebellar gait ataxia is characterized by postural deficiencies and decomposition of movements. During locomotion, the vermis and the intermediate region of the cerebellum receive information through the spinocerebellar pathways about the ongoing activities in the spinal stepping generator and the somatosensory receptors. The information is conveyed by mossy fiber afferents to Purkinje neurons via granule cells and their axons, i.e., parallel fibers. Purkinje neurons transform the mossy fiber input signals to output signals that in turn modulate activities in the brainstem descending tract neurons of the brainstem that are involved in locomotion. Further, Purkinje neurons receive enhanced climbing fiber signals during perturbed locomotion. These climbing fiber signals may induce synaptic plasticity at the parallel fiber-Purkinje neuron synapses. Long-term depression (LTD) occurs in parallel fiber-Purkinje neuron synapses and is regarded as the cellular basis for the learning mechanism of the cerebellar neuronal circuit. The activation of parallel fibers releases glutamate and nitric oxide, and the released glutamate activates the glutamate receptors in the Purkinje neurons. mGluR1, a subtype of the metabotropic glutamate receptors, is highly expressed in Purkinje neurons. In addition, delta 2 glutamate receptor is expressed in only Purkinje neurons throughout the brain. Genetically targeted mice for these glutamate receptors and/or pharmacological blocking studies have been promoted to determine the functional linkage between the molecules at the cellular level and the adaptability of locomotion at the behavioral level. This article highlights some recent advances in the understanding of the role played by the cerebellum in the adaptive control of locomotion.     

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.     

Glutamate-Receptor-Like Molecule GluRδ2 Involved in Synapse Formation at Parallel Fiber-Purkinje Neuron Synapses

Glutamate-receptor-like molecule δ2 (GluRδ2, GluD2) has been classified as an ionotropic glutamate receptor subunit. It is selectively expressed on the postsynaptic membrane at parallel fiber-Purkinje neuron synapses in the cerebellum. Mutant mice deficient in GluRδ2 show impaired synaptic plasticity, the decrease in the number of parallel fiber-Purkinje neuron synapses, multiple innervation of climbing fibers on a Purkinje neuron, and defects in motor control and learning. Thus, GluRδ2 plays crucial roles in the cerebellar function. Recent studies on GluRδ2 have shown that it has synaptogenic activity. GluRδ2 expressed in a non-neuronal cell induces presynaptic differentiation of granule neurons in a co-culture preparation. This synaptogenic activity depends on an extracellular N-terminal leucine/isoleucine/valine binding protein-like domain of GluRδ2. GluRδ2 plays critical roles in formation, maturation, and/or maintenance of granule neuron–Purkinje neuron synapses.     

Activity-dependent axonal and synaptic plasticity in the cerebellum

The cerebellum is a brain region endowed with a high degree of plasticity also in adulthood. After damage or alteration in the patterns of activity, it is able to undergo remarkable changes in its architecture and to form new connections based upon a process of synaptic reorganization. This review addresses cellular and molecular mechanisms that regulate the competition between two inputs belonging to different neuronal populations in innervating two contiguous but separate domains of the same target cell. The two inputs are the parallel fibers, the axon of the cerebellar granule cells, and the olivocerebellar neurons, that terminate as climbing fibers in the cerebellar cortex. The target is the Purkinje cell characterized by two dendritic domains that are different in size and number of spines, upon which the two afferent inputs impinge. Both inputs express several genes related to plasticity throughout the life span conferring the ability to remodel their synapses. In addition, we provided evidence that climbing fibers and Purkinje cells show remarkable reciprocal trophic interactions that are required for the maintenance of the correct synaptic connectivity. Through their activity, climbing fibers sustain the competition with parallel fibers by displacing this input to the distal territory of the Purkinje cell dendrite. In addition, they operate on the Purkinje cells through AMPA receptor suppressing spines in the territory surrounding their synapses. In this way, climbing fibers are able to optimize spine distribution and functional connectivity.     

Transynaptic modulation by insulin-like growth factor I of dendritic spines in Purkinje cells

Purkinje cells synthesize insulin-like growth factor I and express insulin-like growth factor I receptors during their entire life. An additional source of insulin-like growth factor I for these cells is provided by climbing fiber afferents originating in the inferior olive nucleus. Recently we found that insulin-like growth factor I from the inferior olive is necessary for motor learning processes probably involving Purkinje cell synaptic plasticity. We now studied whether inferior olive insulin-like growth factor I influences the synaptic structure of Purkinje cells, because changes in synaptic morphology are related to neuronal plasticity events. We injected an insulin-like growth factor I antisense in the inferior olive of adult rats, a procedure which we previously found to elicit a significant and reversible decrease of insulin-like growth factor I levels in the contralateral cerebellum. Ultrastructural analysis of the cerebellar cortex of these animals showed a significant reduction in the size of dendritic spines on Purkinje cells of antisense-treated rats compared to controls. The decrease in spine size was linked to a diminished numerical density of dendritic spines on Purkinje cells, without affecting the numerical density of synapses in the molecular layer of the cerebellum. This reduction was not due to a change in the thickness of the molecular layer. Climbing or parallel fiber terminals were also unaffected.Taken together with previous findings, these results support a role for insulin-like growth factor I produced in the inferior olive in the maintenance of Purkinje cell synaptic plasticity.     

Long-Term Depression in Rat Cerebellum Requires both NO Synthase and NO-sensitive Guanylyl Cyclase

Long-term depression (LTD) of synaptic transmission between parallel fibres and Purkinje cells is a well-known example of synaptic plasticity taking place in the cerebellum. Nitric oxide (NO) has been implicated in synaptic plasticity in other brain areas, but its function in cerebellar LTD is controversial. Even when an involvement is suggested, the NO signal transduction pathway is unclear. One candidate is the cyclic GMP-synthesizing enzyme, soluble guanylyl cyclase, whose activity in the brain and elsewhere is powerfully stimulated by NO. By recording intracellularly from Purkinje cells in cerebellar slices, we demonstrate that blockade of NO synthase completely inhibits LTD induced by pairing parallel fibre stimulation with postsynaptic Ca²⁺ spike firing. LTD was also blocked by intracellular application of 1H-[1, 2, 4]oxadiazolo[4, 3-a]quinoxalin-1-one, a recently identified potent and selective inhibitor of soluble guanylyl cyclase. These findings indicate that soluble guanylyl cyclase is required for cerebellar LTD and suggest that this enzyme, located within Purkinje cells, transduces the NO signal in this form of synaptic plasticity.