Long-term depression at parallel fiber to Golgi cell synapses

The Cerebellar Cortex

The cerebellar cortex is an important system for relating neural circuits and learning. Its promise reflects the longstanding idea that it contains simple, repeated circuit modules with only a few cell types and a single plasticity mechanism that mediates learning according to classical Marr-Albus models. However, emerging data have revealed surprising diversity in neuron types, synaptic connections, and plasticity mechanisms, both locally and regionally within the cerebellar cortex. In light of these findings, it is not surprising that attempts to generate a holistic model of cerebellar learning across different behaviors have not been successful. While the cerebellum remains an ideal system for linking neuronal function with behavior, it is necessary to update the cerebellar circuit framework to achieve its great promise. In this review, we highlight recent advances in our understanding of cerebellar-cortical cell types, synaptic connections, signaling mechanisms, and forms of plasticity that enrich cerebellar processing.

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.

Synergistic excitability plasticity in cerebellar functioning

The cerebellum, a universal processor for sensory acquisition and internal models, and its association with synaptic and nonsynaptic plasticity have been envisioned as the biological correlates of learning, perception, and even thought. Indeed, the cerebellum is no longer considered merely as the locus of motor coordination and its learning. Here, we introduce the mechanisms underlying the induction of multiple types of plasticity in cerebellar circuit and give an overview focusing on the plasticity of nonsynaptic intrinsic excitability. The discovery of long-term potentiation of synaptic responsiveness in hippocampal neurons led investigations into changes of their intrinsic excitability. This activity-dependent potentiation of neuronal excitability is distinct from that of synaptic efficacy. Systematic examination of excitability plasticity has indicated that the modulation of various types of Ca²⁺ - and voltage-dependent K⁺ channels underlies the phenomenon, which is also triggered by immune activity. Intrinsic plasticity is expressed specifically on dendrites and modifies the integrative processing and filtering effect. In Purkinje cells, modulation of the discordance of synaptic current on soma and dendrite suggested a novel type of cellular learning mechanism. This property enables a plausible synergy between synaptic efficacy and intrinsic excitability, by amplifying electrical conductivity and influencing the polarity of bidirectional synaptic plasticity. Furthermore, the induction of intrinsic plasticity in the cerebellum correlates with motor performance and cognitive processes, through functional connections from the cerebellar nuclei to neocortex and associated regions: for example, thalamus and midbrain. Taken together, recent advances in neuroscience have begun to shed light on the complex functioning of nonsynaptic excitability and the synergy.

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

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

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.

Non-synaptic signaling from cerebellar climbing fibers modulates Golgi cell activity

Golgi cells are the principal inhibitory neurons at the input stage of the cerebellum, providing feedforward and feedback inhibition through mossy fiber and parallel fiber synapses. In vivo studies have shown that Golgi cell activity is regulated by climbing fiber stimulation, yet there is little functional or anatomical evidence for synapses between climbing fibers and Golgi cells. Here, we show that glutamate released from climbing fibers activates ionotropic and metabotropic receptors on Golgi cells through spillover-mediated transmission. The interplay of excitatory and inhibitory conductances provides flexible control over Golgi cell spiking, allowing either excitation or a biphasic sequence of excitation and inhibition following single climbing fiber stimulation. Together with prior studies of spillover transmission to molecular layer interneurons, these results reveal that climbing fibers exert control over inhibition at both the input and output layers of the cerebellar cortex.

Granular Layer Neurons Control Cerebellar Neurovascular Coupling Through an NMDA Receptor/NO-Dependent System

Neurovascular coupling (NVC) is the process whereby neuronal activity controls blood vessel diameter. In the cerebellum, the molecular layer is regarded as the main NVC determinant. However, the granular layer is a region with variable metabolic demand caused by large activity fluctuations that shows a prominent expression of NMDA receptors (NMDARs) and nitric oxide synthase (NOS) and is therefore much more suitable for effective NVC. Here, we show, in the granular layer of acute rat cerebellar slices, that capillary diameter changes rapidly after mossy fiber stimulation. Vasodilation required neuronal NMDARs and NOS stimulation and subsequent guanylyl cyclase activation that probably occurred in pericytes. Vasoconstriction required metabotropic glutamate receptors and CYP ω-hydroxylase, the enzyme regulating 20-hydroxyeicosatetraenoic acid production. Therefore, granular layer capillaries are controlled by the balance between vasodilating and vasoconstricting systems that could finely tune local blood flow depending on neuronal activity changes at the cerebellar input stage.

SIGNIFICANCE STATEMENT

The neuronal circuitry and the biochemical pathways that control local blood flow supply in the cerebellum are unclear. This is surprising given the emerging role played by this brain structure, not only in motor behavior, but also in cognitive functions. Although previous studies focused on the molecular layer, here, we shift attention onto the mossy fiber granule cell (GrC) relay. We demonstrate that GrC activity causes a robust vasodilation in nearby capillaries via the NMDA receptors-neuronal nitric oxide synthase signaling pathway. At the same time, metabotropic glutamate receptors mediate 20-hydroxyeicosatetraenoic acid-dependent vasoconstriction. These results reveal a complex signaling network that hints for the first time at the granular layer as a major determinant of cerebellar blood-oxygen-level-dependent signals.

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.

In vivo differences in inputs and spiking between neurons in lobules VI/VII of neocerebellum and lobule X of archaeocerebellum

The cerebellum plays an important role in the coordination and refinement of movements and cognitive processes. Recently, it has been shown that the main output neuron of the cerebellar cortex, i.e., the Purkinje cell, can show a different firing behavior dependent on its intrinsic electrophysiological properties. Yet, to what extent a different nature of mossy fiber inputs can influence the firing behavior of cerebellar cortical neurons remains to be elucidated. Here, we compared the firing rate and regularity of mossy fibers and neurons in two different regions of cerebellar cortex. One region intimately connected with the cerebral cortex, i.e., lobules VI/VII of the neocerebellum, and another one strongly connected with the vestibular apparatus, i.e., lobule X of the archaeocerebellum. Given their connections, we hypothesized that activity in neurons in lobules VI/VII and lobule X may be expected to be more phasic and tonic, respectively. Using whole-cell and cell-attached recordings in vivo in anesthetized mice, we show that the mossy fiber inputs to these functionally distinct areas of the cerebellum differ in that the irregularity and bursty character of their firing is significantly greater in lobules VI/VII than in lobule X. Importantly, this difference in mossy fiber regularity is propagated through the granule cells at the input stage to the Purkinje cells and molecular layer interneurons, ultimately resulting in different regularity of simple spikes. These data show that the firing behavior of cerebellar cortical neurons does not only reflect particular intrinsic properties but also an interesting interplay with the innate activity at the input stage.

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.

On the firing rate dependency of the phase response curve of rat Purkinje neurons in vitro

Synchronous spiking during cerebellar tasks has been observed across Purkinje cells: however, little is known about the intrinsic cellular mechanisms responsible for its initiation, cessation and stability. The Phase Response Curve (PRC), a simple input-output characterization of single cells, can provide insights into individual and collective properties of neurons and networks, by quantifying the impact of an infinitesimal depolarizing current pulse on the time of occurrence of subsequent action potentials, while a neuron is firing tonically. Recently, the PRC theory applied to cerebellar Purkinje cells revealed that these behave as phase-independent integrators at low firing rates, and switch to a phase-dependent mode at high rates. Given the implications for computation and information processing in the cerebellum and the possible role of synchrony in the communication with its post-synaptic targets, we further explored the firing rate dependency of the PRC in Purkinje cells. We isolated key factors for the experimental estimation of the PRC and developed a closed-loop approach to reliably compute the PRC across diverse firing rates in the same cell. Our results show unambiguously that the PRC of individual Purkinje cells is firing rate dependent and that it smoothly transitions from phase independent integrator to a phase dependent mode. Using computational models we show that neither channel noise nor a realistic cell morphology are responsible for the rate dependent shift in the phase response curve.

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.

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.

Granule cell ascending axon excitatory synapses onto Golgi cells implement a potent feedback circuit in the cerebellar granular layer

The function of inhibitory interneurons within brain microcircuits depends critically on the nature and properties of their excitatory synaptic drive. Golgi cells (GoCs) of the cerebellum inhibit cerebellar granule cells (GrCs) and are driven both by feedforward mossy fiber (mf) and feedback GrC excitation. Here, we have characterized GrC inputs to GoCs in rats and mice. We show that, during sustained mf discharge, synapses from local GrCs contribute equivalent charge to GoCs as mf synapses, arguing for the importance of the feedback inhibition. Previous studies predicted that GrC-GoC synapses occur predominantly between parallel fibers (pfs) and apical GoC dendrites in the molecular layer (ML). By combining EM and Ca(2+) imaging, we now demonstrate the presence of functional synaptic contacts between ascending axons (aa) of GrCs and basolateral dendrites of GoCs in the granular layer (GL). Immunohistochemical quantification estimates these contacts to be ∼400 per GoC. Using Ca(2+) imaging to identify synaptic inputs, we show that EPSCs from aa and mf contacts in basolateral dendrites display similarly fast kinetics, whereas pf inputs in the ML exhibit markedly slower kinetics as they undergo strong filtering by apical dendrites. We estimate that approximately half of the local GrC contacts generate fast EPSCs, indicating their basolateral location in the GL. We conclude that GrCs, through their aa contacts onto proximal GoC dendrites, define a powerful feedback inhibitory circuit in the GL.

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.

High frequency burst firing of granule cells ensures transmission at the parallel fiber to purkinje cell synapse at the cost of temporal coding

Cerebellar granule cells (GrCs) convey information from mossy fibers (MFs) to Purkinje cells (PCs) via their parallel fibers (PFs). MF to GrC signaling allows transmission of frequencies up to 1 kHz and GrCs themselves can also fire bursts of action potentials with instantaneous frequencies up to 1 kHz. So far, in the scientific literature no evidence has been shown that these high-frequency bursts also exist in awake, behaving animals. More so, it remains to be shown whether such high-frequency bursts can transmit temporally coded information from MFs to PCs and/or whether these patterns of activity contribute to the spatiotemporal filtering properties of the GrC layer. Here, we show that, upon sensory stimulation in both un-anesthetized rabbits and mice, GrCs can show bursts that consist of tens of spikes at instantaneous frequencies over 800 Hz. In vitro recordings from individual GrC-PC pairs following high-frequency stimulation revealed an overall low initial release probability of ~0.17. Nevertheless, high-frequency burst activity induced a short-lived facilitation to ensure signaling within the first few spikes, which was rapidly followed by a reduction in transmitter release. The facilitation rate among individual GrC-PC pairs was heterogeneously distributed and could be classified as either “reluctant” or “responsive” according to their release characteristics. Despite the variety of efficacy at individual connections, grouped activity in GrCs resulted in a linear relationship between PC response and PF burst duration at frequencies up to 300 Hz allowing rate coding to persist at the network level. Together, these findings support the hypothesis that the cerebellar granular layer acts as a spatiotemporal filter between MF input and PC output (D’Angelo and De Zeeuw, 2009).

The cerebellar Golgi cell and spatiotemporal organization of granular layer activity

The cerebellar granular layer has been suggested to perform a complex spatiotemporal reconfiguration of incoming mossy fiber signals. Central to this role is the inhibitory action exerted by Golgi cells over granule cells: Golgi cells inhibit granule cells through both feedforward and feedback inhibitory loops and generate a broad lateral inhibition that extends beyond the afferent synaptic field. This characteristic connectivity has recently been investigated in great detail and been correlated with specific functional properties of these neurons. These include theta-frequency pacemaking, network entrainment into coherent oscillations and phase resetting. Important advances have also been made in terms of determining the membrane and synaptic properties of the neuron, and clarifying the mechanisms of activation by input bursts. Moreover, voltage sensitive dye imaging and multi-electrode array (MEA) recordings, combined with mathematical simulations based on realistic computational models, have improved our understanding of the impact of Golgi cell activity on granular layer circuit computations. These investigations have highlighted the critical role of Golgi cells in: generating dense clusters of granule cell activity organized in center-surround structures, implementing combinatorial operations on multiple mossy fiber inputs, regulating transmission gain, and cut-off frequency, controlling spike timing and burst transmission, and determining the sign, intensity and duration of long-term synaptic plasticity at the mossy fiber-granule cell relay. This review considers recent advances in the field, highlighting the functional implications of Golgi cells for granular layer network computation and indicating new challenges for cerebellar research.

Distributed synergistic plasticity and cerebellar learning

Studies on synaptic plasticity in the context of learning have been dominated by the view that a single, particular type of plasticity forms the underlying mechanism for a particular type of learning. However, emerging evidence shows that many forms of synaptic and intrinsic plasticity at different sites are induced conjunctively during procedural memory formation in the cerebellum. Here, we review the main forms of long-term plasticity in the cerebellar cortex that underlie motor learning. We propose that the different forms of plasticity in the granular layer and the molecular layer operate synergistically in a temporally and spatially distributed manner, so as to ultimately create optimal output for behaviour.

Efficient estimation of phase-response curves via compressive sensing

The phase-response curve (PRC), relating the phase shift of an oscillator to external perturbation, is an important tool to study neurons and their population behavior. It can be experimentally estimated by measuring the phase changes caused by probe stimuli. These stimuli, usually short pulses or continuous noise, have a much wider frequency spectrum than that of neuronal dynamics. This makes the experimental data high dimensional while the number of data samples tends to be small. Current PRC estimation methods have not been optimized for efficiently discovering the relevant degrees of freedom from such data. We propose a systematic and efficient approach based on a recently developed signal processing theory called compressive sensing (CS). CS is a framework for recovering sparsely constructed signals from undersampled data and is suitable for extracting information about the PRC from finite but high-dimensional experimental measurements. We illustrate how the CS algorithm can be translated into an estimation scheme and demonstrate that our CS method can produce good estimates of the PRCs with simulated and experimental data, especially when the data size is so small that simple approaches such as naive averaging fail. The tradeoffs between degrees of freedom vs. goodness-of-fit were systematically analyzed, which help us to understand better what part of the data has the most predictive power. Our results illustrate that finite sizes of neuroscientific data in general compounded by large dimensionality can hamper studies of the neural code and suggest that CS is a good tool for overcoming this challenge.

Functional circuitry of a unique cerebellar specialization: the valvula cerebelli of a mormyrid fish

The valvula cerebelli of the mormyrid electric fish is a useful site for the study of cerebellar function. The valvula forms a part of the electrosensory-electromotor system of this fish, a system that offers many possibilities for the study of sensory-motor integration. The valvula also has a number of histological features not present in mammals which facilitate investigation of cerebellar circuitry and its plasticity. This initial study characterizes the basic physiology and pharmacology of cells in the valvula using an in vitro slice preparation. Intrinsic properties and synaptic responses of Purkinje cells and other cell types were examined. We found that Purkinje cells fire a small narrow Na(+) spike and a large broad Ca(2+) spike, generated in the axon initial segment and dendritic-soma region, respectively. Purkinje cells respond to parallel fiber inputs with graded excitatory postsynaptic potentials (EPSPs) and to climbing fiber inputs with all-or-none EPSPs. Efferent cells, Golgi cells, and deep stellate cells all fire a single type of large narrow spike and respond only to parallel fiber inputs. Both parallel fiber and climbing fiber responses in Purkinje cells appear to be entirely mediated by AMPA-type glutamate receptors, whereas parallel fiber responses in efferent cells and stellate cells include AMPA and NMDA components. In addition, a strong synaptic inhibition was uncovered in both Purkinje cells and efferent cells in response to the focal stimulation of parallel fibers. Dual cell recordings indicate that deep stellate cells contribute at least partially to this inhibition. We conclude that despite its unique histology, the local functional circuitry of the mormyrid valvula cerebelli is largely similar to that of the mammalian cerebellum. Thus, what is learned concerning the functioning of the mormyrid valvula cerebelli may be expected to be informative about cerebellar function in general.