Ca2+ requirements for cerebellar long-term synaptic depression: role for a postsynaptic leaky integrator

Purkinje cell models: past, present and future

The investigation of the dynamics of Purkinje cell (PC) activity is crucial to unravel the role of the cerebellum in motor control, learning and cognitive processes. Within the cerebellar cortex (CC), these neurons receive all the incoming sensory and motor information, transform it and generate the entire cerebellar output. The relatively homogenous and repetitive structure of the CC, common to all vertebrate species, suggests a single computation mechanism shared across all PCs. While PC models have been developed since the 70's, a comprehensive review of contemporary models is currently lacking. Here, we provide an overview of PC models, ranging from the ones focused on single cell intracellular PC dynamics, through complex models which include synaptic and extrasynaptic inputs. We review how PC models can reproduce physiological activity of the neuron, including firing patterns, current and multistable dynamics, plateau potentials, calcium signaling, intrinsic and synaptic plasticity and input/output computations. We consider models focusing both on somatic and on dendritic computations. Our review provides a critical performance analysis of PC models with respect to known physiological data. We expect our synthesis to be useful in guiding future development of computational models that capture real-life PC dynamics in the context of cerebellar computations.

A cerebellar granule cell-climbing fiber computation to learn to track long time intervals

In classical cerebellar learning, Purkinje cells (PkCs) associate climbing fiber (CF) error signals with predictive granule cells (GrCs) that were active just prior (∼150 ms). The cerebellum also contributes to behaviors characterized by longer timescales. To investigate how GrC-CF-PkC circuits might learn seconds-long predictions, we imaged simultaneous GrC-CF activity over days of forelimb operant conditioning for delayed water reward. As mice learned reward timing, numerous GrCs developed anticipatory activity ramping at different rates until reward delivery, followed by widespread time-locked CF spiking. Relearning longer delays further lengthened GrC activations. We computed CF-dependent GrC→PkC plasticity rules, demonstrating that reward-evoked CF spikes sufficed to grade many GrC synapses by anticipatory timing. We predicted and confirmed that PkCs could thereby continuously ramp across seconds-long intervals from movement to reward. Learning thus leads to new GrC temporal bases linking predictors to remote CF reward signals-a strategy well suited for learning to track the long intervals common in cognitive domains.

Contiguity in perception: origins in cellular associative computations

Our brains are good at detecting and learning associative structures; according to some linguistic theories, this capacity even constitutes a prerequisite for the development of syntax and compositionality in language and verbalized thought. I will argue that the search for associative motifs in input patterns is an evolutionary old brain function that enables contiguity in sensory perception and orientation in time and space. It has its origins in an elementary material property of cells that is particularly evident at chemical synapses: input-assigned calcium influx that activates calcium sensor proteins involved in memory storage. This machinery for the detection and learning of associative motifs generates knowledge about input relationships and integrates this knowledge into existing networks through updates in connectivity patterns.

Stochastic reaction-diffusion modeling of calcium dynamics in 3D dendritic spines of Purkinje cells

Calcium (Ca²⁺) is a second messenger assumed to control changes in synaptic strength in the form of both long-term depression and long-term potentiation at Purkinje cell dendritic spine synapses via inositol trisphosphate (IP₃)-induced Ca²⁺ release. These Ca²⁺ transients happen in response to stimuli from parallel fibers (PFs) from granule cells and climbing fibers (CFs) from the inferior olivary nucleus. These events occur at low numbers of free Ca²⁺, requiring stochastic single-particle methods when modeling them. We use the stochastic particle simulation program MCell to simulate Ca²⁺ transients within a three-dimensional Purkinje cell dendritic spine. The model spine includes the endoplasmic reticulum, several Ca²⁺ transporters, and endogenous buffer molecules. Our simulations successfully reproduce properties of Ca²⁺ transients in different dynamical situations. We test two different models of the IP₃ receptor (IP₃R). The model with nonlinear concentration response of binding of activating Ca²⁺ reproduces experimental results better than the model with linear response because of the filtering of noise. Our results also suggest that Ca²⁺-dependent inhibition of the IP₃R needs to be slow to reproduce experimental results. Simulations suggest the experimentally observed optimal timing window of CF stimuli arises from the relative timing of CF influx of Ca²⁺ and IP₃ production sensitizing IP₃R for Ca²⁺-induced Ca²⁺ release. We also model ataxia, a loss of fine motor control assumed to be the result of malfunctioning information transmission at the granule to Purkinje cell synapse, resulting in a decrease or loss of Ca²⁺ transients. Finally, we propose possible ways of recovering Ca²⁺ transients under ataxia.

Autonomous Purkinje cell activation instructs bidirectional motor learning through evoked dendritic calcium signaling

The signals in cerebellar Purkinje cells sufficient to instruct motor learning have not been systematically determined. Therefore, we applied optogenetics in mice to autonomously excite Purkinje cells and measured the effect of this activity on plasticity induction and adaptive behavior. Ex vivo, excitation of channelrhodopsin-2-expressing Purkinje cells elicits dendritic Ca²⁺ transients with high-intensity stimuli initiating dendritic spiking that additionally contributes to the Ca²⁺ response. Channelrhodopsin-2-evoked Ca²⁺ transients potentiate co-active parallel fiber synapses; depression occurs when Ca²⁺ responses were enhanced by dendritic spiking. In vivo, optogenetic Purkinje cell activation drives an adaptive decrease in vestibulo-ocular reflex gain when vestibular stimuli are paired with relatively small-magnitude Purkinje cell Ca²⁺ responses. In contrast, pairing with large-magnitude Ca²⁺ responses increases vestibulo-ocular reflex gain. Optogenetically induced plasticity and motor adaptation are dependent on endocannabinoid signaling, indicating engagement of this pathway downstream of Purkinje cell Ca²⁺ elevation. Our results establish a causal relationship among Purkinje cell Ca²⁺ signal size, opposite-polarity plasticity induction, and bidirectional motor learning.

Plastic reweighting of parallel fiber synaptic strength is a mechanism for the acquisition of cerebellum-dependent motor learning. Here, the authors found that optogenetic activation of PCs generates dendritic Ca2+ signals that induce plasticity in vitro and instruct learned changes to coincident eye movements in vivo.

Useful Caged Compounds for Cell Physiology

Light has been instrumental in the study of living cells since its use helped in their discovery in the late 17th century. Further, combining chemical technology with light microscopy was an essential part of the Nobel Prize for Physiology in 1906. Such landmark scientific findings involved passive observation of cells. However, over the past 50 years, a "second use" of light has emerged in cell physiology, namely one of rational control. The seminal method for this emerged in late 1970s with the invention of caged compounds. This was the point when "caged compounds" were defined as optical probes in which the active functionality of a physiological signaling molecule was blocked with a photochemical protecting group. Caged compounds are analogous to prodrugs; in both, the activity of the effector is latent. However, caged compounds, unlike prodrugs, use a trigger that confers the power of full temporal and spatial manipulation of the effects of release of its latent biological cargo. Light is distinct because it is bio-orthogonal, passes through living tissue (even into the cell interior), and initiates rapid release of the "caged" biomolecule. Further, because light can be directed to broad areas or focused to small points, caged compounds offer an array of timing scenarios for physiologists to dissect virtually any type of cellular process.The collaborative interaction between chemists and physiologists plays a fundamental role in the development of caged compounds. First, the physiologists must define the problem to be addressed; then, with the help of chemists, decide if a caged compound would be useful. For this, structure-activity relationships of the potential optical probe and receptor must be determined. If rational targets seem feasible, synthetic organic chemistry is used to make the caged compound. The crucial property of prephotolysis bio-inertness relies on physiological or biochemical assays. Second, detailed optical characterization of the caged compound requires the skill of photochemists because the rate and efficiency of uncaging are also crucial properties for a useful caged compound. Often, these studies reveal limitations in the caged compound which has been developed; thus, chemists and physiologists use their abilities for iterative development of even more powerful optical probes. A similar dynamic will be familiar to scientists in the pharmaceutical industry. Therefore, caged compound development provides an excellent training framework for (young) chemists both intellectually and professionally. In this Account, I draw on my long experience in the field of making useful caged compounds for cell physiology by showing how each probe I have developed has been defined by an important physiological problem. Fundamental to this process has been my initial training by the pioneers in aromatic photochemistry, Derek Bryce-Smith and Andrew Gilbert. I discuss making a range of "caged calcium" probes, ones which went on to be the most widely used of all caged compounds. Then, I describe the development of caged neurotransmitters for two-photon uncaging microscopy. Finally, I survey recent work on making new photochemical protecting groups for wavelength orthogonal, two-color, and ultraefficient two-photon uncaging.

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.

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.

Binding of Filamentous Actin to CaMKII as Potential Regulation Mechanism of Bidirectional Synaptic Plasticity by β CaMKII in Cerebellar Purkinje Cells

Calcium-calmodulin dependent protein kinase II (CaMKII) regulates many forms of synaptic plasticity, but little is known about its functional role during plasticity induction in the cerebellum. Experiments have indicated that the β isoform of CaMKII controls the bidirectional inversion of plasticity at parallel fibre (PF)-Purkinje cell (PC) synapses in cerebellar cortex. Because the cellular events that underlie these experimental findings are still poorly understood, we developed a simple computational model to investigate how β CaMKII regulates the direction of plasticity in cerebellar PCs. We present the first model of AMPA receptor phosphorylation that simulates the induction of long-term depression (LTD) and potentiation (LTP) at the PF-PC synapse. Our simulation results suggest that the balance of CaMKII-mediated phosphorylation and protein phosphatase 2B (PP2B)-mediated dephosphorylation of AMPA receptors can determine whether LTD or LTP occurs in cerebellar PCs. The model replicates experimental observations that indicate that β CaMKII controls the direction of plasticity at PF-PC synapses, and demonstrates that the binding of filamentous actin to CaMKII can enable the β isoform of the kinase to regulate bidirectional plasticity at these synapses.

Complex spike clusters and false-positive rejection in a cerebellar supervised learning rule

KEY POINTS

Spike doublets comprise ∼10% of in vivo complex spike events under spontaneous conditions and ∼20% (up to 50%) under evoked conditions. Under near-physiological slice conditions, single complex spikes do not induce parallel fibre long-term depression. Doublet stimulation is required to induce long-term depression with an optimal parallel-fibre to first-complex-spike timing interval of 150 ms.

ABSTRACT

The classic example of biological supervised learning occurs at cerebellar parallel fibre (PF) to Purkinje cell synapses, comprising the most abundant synapse in the mammalian brain. Long-term depression (LTD) at these synapses is driven by climbing fibres (CFs), which fire continuously about once per second and therefore generate potential false-positive events. We show that pairs of complex spikes are required to induce LTD. In vivo, sensory stimuli evoked complex-spike doublets with intervals ≤150 ms in up to 50% of events. Using realistic [Ca2+ ]o and [Mg2+ ]o concentrations in slices, we determined that complex-spike doublets delivered 100-150 ms after PF stimulus onset were required to trigger PF-LTD, which is consistent with the requirements for eyeblink conditioning. Inter-complex spike intervals of 50-150 ms provided optimal decoding. This stimulus pattern prolonged evoked spine calcium signals and promoted CaMKII activation. Doublet activity may provide a means for CF instructive signals to stand out from background firing.

Switching On Depression and Potentiation in the Cerebellum

Long-term depression (LTD) and long-term potentiation (LTP) in the cerebellum are important for motor learning. However, the signaling mechanisms controlling whether LTD or LTP is induced in response to synaptic stimulation remain obscure. Using a unified model of LTD and LTP at the cerebellar parallel fiber-Purkinje cell (PF-PC) synapse, we delineate the coordinated pre- and postsynaptic signaling that determines the direction of plasticity. We show that LTP is the default response to PF stimulation above a well-defined frequency threshold. However, if the calcium signal surpasses the threshold for CaMKII activation, then an ultrasensitive "on switch" activates an extracellular signal-regulated kinase (ERK)-based positive feedback loop that triggers LTD instead. This postsynaptic feedback loop is sustained by another, trans-synaptic, feedback loop that maintains nitric oxide production throughout LTD induction. When full depression is achieved, an automatic "off switch" inactivates the feedback loops, returning the network to its basal state and demarcating the end of the early phase of LTD.

Persistent cytosolic Ca2+ increase induced by angiotensin II at nanomolar concentrations in acutely dissociated subfornical organ (SFO) neurons of rats

It is known that angiotensin II (AII) is sensed by subfornical organ (SFO) to induce drinking behaviors and autonomic changes. AII at picomolar concentrations have been shown to induce Ca²⁺ oscillations and increase in the amplitude and frequency of spontaneous Ca²⁺ oscillations in SFO neurons. The present study was conducted to examine effects of nanomolar concentrations of AII using the Fura-2 Ca²⁺-imaging technique in acutely dissociated SFO neurons. AII at nanomolar concentrations induced an initial [Ca²⁺]_i peak followed by a persistent [Ca²⁺]_i increase lasting for longer than 1 hour. By contrast, [Ca²⁺]_i responses to 50 mM K⁺, maximally effective concentrations of glutamate, carbachol, and vasopressin, and AII given at picomolar concentrations returned to the basal level within 20 min. The AII-induced [Ca²⁺]_i increase was blocked by the AT1 antagonist losartan. However, losartan had no effect when added during the persistent phase. The persistent phase was suppressed by extracellular Ca2+ removal, significantly inhibited by blockers of L and P/Q type Ca²⁺ channels , but unaffected by inhibition of Ca²⁺ store Ca²⁺ ATPase. The persistent phase was reversibly suppressed by GABA and inhibited by CaMK and PKC inhibitors. These results suggest that the persistent [Ca²⁺]_i increase evoked by nanomolar concentrations of AII is initiated by AT1 receptor activation and maintained by Ca²⁺ entry mechanisms in part through L and P/Q type Ca²⁺ channels, and that CaMK and PKC are involved in this process. The persistent [Ca²⁺]_i increase induced by AII at high pathophysiological levels may have a significant role in altering SFO neuronal functions.

Postsynaptic Stability and Variability Described by a Stochastic Model of Endosomal Trafficking

Neurons undergo dynamic processes of constitutive AMPA-type glutamate receptor (AMPAR) trafficking, such as the insertion and internalization of AMPARs by exocytosis and endocytosis, while stably maintaining synaptic efficacy. Studies using advanced imaging techniques have suggested that the frequency of these constitutive trafficking processes, as well as the number of AMPARs that are involved in a particular event highly fluctuate. In addition, mechanisms that trigger some forms of synaptic plasticity have been shown to include not only these processes but also additional fluctuating processes, such as the sorting of AMPARs to late endosomes (LEs). Thus, the regulation of postsynaptic AMPARs by the endosomal trafficking system appears to have superficially conflicting properties between the stability or organized control of plasticity and highly fluctuating or stochastic processes. However, it is not clear how the endosomal trafficking system reconciles and utilizes such conflicting properties. Although deterministic models have been effective to describe the stable maintenance of synaptic AMPAR numbers by constitutive recycling, as well as the involvement of endosomal trafficking in synaptic plasticity, they do not take stochasticity into account. In this study, we introduced the stochasticity into the model of each crucial machinery of the endosomal trafficking system. The specific questions we solved by our improved model are whether stability is accomplished even with a combination of fluctuating processes, and how overall variability occurs while controlling long-term synaptic depression (LTD). Our new stochastic model indeed demonstrated the stable regulation of postsynaptic AMPAR numbers at the basal state and during LTD maintenance, despite fast fluctuations in AMPAR numbers as well as high variability in the time course and amounts of LTD. In addition, our analysis suggested that the high variability arising from this stochasticity is beneficial for reproducing the relatively constant timing of LE sorting for LTD. We therefore propose that the coexistence of stability and stochasticity in the endosomal trafficking system is suitable for stable synaptic transmission and the reliable induction of synaptic plasticity, with variable properties that have been observed experimentally.

Ca2+ Requirements for Long-Term Depression Are Frequency Sensitive in Purkinje Cells

Cerebellar long-term depression (LTD) is a form of synaptic plasticity dependent on postsynaptic Ca²⁺ changes. One fundamental question is how LTD is selectively induced by specific numbers of Ca²⁺ pulses and which are the frequency and duration of this train of pulses required for LTD induction. The molecular mechanism which leads the integration of postsynaptic Ca²⁺ pulses in the LTD signaling network has not been elucidated either. Recent publications have shown that Ca²⁺/calmodulin-dependent protein kinase II (CaMKII) is required for LTD induction. Additionally, protein kinase C (PKC), CaMKII, and MAPK play an important role to transduce the frequency of Ca²⁺ pulses into their enzymatic activity levels; however, it is still unknown which enzymes are involved in decoding Ca²⁺ pulses in LTD. We have extended a stochastic model of LTD by adding the molecular network regulating CaMKII activity and its activation. We solved this model with stochastic engine for pathway simulation to include the effect of biochemical noise in LTD. We systematically investigated the dependence of LTD induction on stimulus frequencies, and we found that LTD is selectively induced by a specific number of Ca²⁺ spikes at different frequencies. We observed that CaMKII is essential to induce LTD, and LTD is only weakly induced when its Thr286 phosphorylation site has been deleted. We found that CaMKII decodes the frequency of Ca²⁺ spikes into different amounts of kinase activity during LTD induction. In addition, PKC and ERK enzyme activity is highly sensitive to the frequency and the number of Ca²⁺ pulses and this sensitivity has an important effect on LTD activation. This research predicts the postsynaptic Ca²⁺ requirements to induce LTD using a typical synaptic activation sequence and explains how LTD is selectively induced by specific number of Ca²⁺ pulses at different frequencies.

Inhibition gates supralinear Ca2+ signaling in Purkinje cell dendrites during practiced movements

Motor learning involves neural circuit modifications in the cerebellar cortex, likely through re-weighting of parallel fiber inputs onto Purkinje cells (PCs). Climbing fibers instruct these synaptic modifications when they excite PCs in conjunction with parallel fiber activity, a pairing that enhances climbing fiber-evoked Ca²⁺ signaling in PC dendrites. In vivo, climbing fibers spike continuously, including during movements when parallel fibers are simultaneously conveying sensorimotor information to PCs. Whether parallel fiber activity enhances climbing fiber Ca²⁺ signaling during motor behaviors is unknown. In mice, we found that inhibitory molecular layer interneurons (MLIs), activated by parallel fibers during practiced movements, suppressed parallel fiber enhancement of climbing fiber Ca²⁺ signaling in PCs. Similar results were obtained in acute slices for brief parallel fiber stimuli. Interestingly, more prolonged parallel fiber excitation revealed latent supralinear Ca²⁺ signaling. Therefore, the balance of parallel fiber and MLI input onto PCs regulates concomitant climbing fiber Ca²⁺ signaling.

Graded Control of Climbing-Fiber-Mediated Plasticity and Learning by Inhibition in the Cerebellum

Purkinje cell dendrites convert excitatory climbing fiber input into signals that instruct plasticity and motor learning. Modulation of instructive signaling may increase the range in which learning is encoded, yet the mechanisms that allow for this are poorly understood. We found that optogenetic activation of molecular layer interneurons (MLIs) that inhibit Purkinje cells suppressed climbing-fiber-evoked dendritic Ca²⁺ spiking. Inhibitory suppression of Ca²⁺ spiking depended on the level of MLI activation and influenced the induction of associative synaptic plasticity, converting climbing-fiber-mediated potentiation of parallel fiber-evoked responses into depression. In awake mice, optogenetic activation of floccular climbing fibers in association with head rotation produced an adaptive increase in the vestibulo-ocular reflex (VOR). However, when climbing fibers were co-activated with MLIs, adaptation occurred in the opposite direction, decreasing the VOR. Thus, MLIs can direct a continuous spectrum of plasticity and learning through their influence on Purkinje cell dendritic Ca²⁺ signaling.

Diffusion of Ca2+ from Small Boutons en Passant into the Axon Shapes AP-Evoked Ca2+ Transients

Not only the amplitude but also the time course of a presynaptic Ca²⁺ transient determine multiple aspects of synaptic transmission. In small bouton-type synapses, the mechanisms underlying the Ca²⁺ decay kinetics have not been fully investigated. Here, factors that shape an action-potential-evoked Ca²⁺ transient were quantitatively studied in synaptic boutons of neocortical layer 5 pyramidal neurons. Ca²⁺ transients were measured with different concentrations of fluorescent Ca²⁺ indicators and analyzed based on a single-compartment model. We found a small endogenous Ca²⁺-binding ratio (7 ± 2) and a high activity of Ca²⁺ transporters (0.64 ± 0.03 ms^-1), both of which enable rapid clearance of Ca²⁺ from the boutons. However, contrary to predictions of the single-compartment model, the decay time course of the measured Ca²⁺ transients was biexponential and became prolonged during repetitive stimulation. Measurements of [Ca²⁺]_i along the adjoining axon, together with an experimentally constrained model, showed that the initial fast decay of the Ca²⁺ transients predominantly arose from the diffusion of Ca²⁺ from the boutons into the axon. Therefore, for small boutons en passant, factors like terminal volume, axon diameter, and the concentration of mobile Ca²⁺-binding molecules are critical determinants of Ca²⁺ dynamics and thus Ca²⁺-dependent processes, including short-term synaptic plasticity.

Optogenetic Visualization of Presynaptic Tonic Inhibition of Cerebellar Parallel Fibers

Tonic inhibition was imaged in cerebellar granule cells of transgenic mice expressing the optogenetic chloride indicator, Clomeleon. Blockade of GABAA receptors substantially reduced chloride concentration in granule cells due to block of tonic inhibition. This indicates that tonic inhibition is a significant contributor to the resting chloride concentration of these cells. Tonic inhibition was observed not only in granule cell bodies, but also in their axons, the parallel fibers (PFs). This presynaptic tonic inhibition could be observed in slices both at room and physiological temperatures, as well as in vivo, and has many of the same properties as tonic inhibition measured in granule cell bodies. GABA application revealed that PFs possess at least two types of GABAA receptor: one high-affinity receptor that is activated by ambient GABA and causes a chloride influx that mediates tonic inhibition, and a second with a low affinity for GABA that causes a chloride efflux that excites PFs. Presynaptic tonic inhibition regulates glutamate release from PFs because GABAA receptor blockade enhanced both the frequency of spontaneous EPSCs and the amplitude of evoked EPSCs at the PF-Purkinje cell synapse. We conclude that tonic inhibition of PFs could play an important role in regulating information flow though cerebellar synaptic circuits. Such cross talk between phasic and tonic signaling could be a general mechanism for fine tuning of synaptic circuits.

SIGNIFICANCE STATEMENT

This paper demonstrates that an unconventional form of signaling, known as tonic inhibition, is found in presynaptic terminals and affects conventional synaptic communication. Our results establish the basic characteristics and mechanisms of presynaptic tonic inhibition and show that it occurs in vivo as well as in isolated brain tissue.

A Model of Induction of Cerebellar Long-Term Depression Including RKIP Inactivation of Raf and MEK

We report an updated stochastic model of cerebellar Long Term Depression (LTD) with improved realism. Firstly, we verify experimentally that dissociation of Raf kinase inhibitor protein (RKIP) from Mitogen-activated protein kinase kinase (MEK) is required for cerebellar LTD and add this interaction to an earlier published model, along with the known requirement of dissociation of RKIP from Raf kinase. We update Ca²⁺ dynamics as a constant-rate influx, which captures experimental input profiles accurately. We improve α-amino-3-hydroxy-5-methyl-4 isoxazolepropionic acid (AMPA) receptor interactions by adding phosphorylation and dephosphorylation of AMPA receptors when bound to glutamate receptor interacting protein (GRIP). The updated model is tuned to reproduce experimental Ca²⁺ peak vs. LTD amplitude curves at four different Ca²⁺ pulse durations as closely as possible. We find that the updated model is generally more robust with these changes, yet we still observe some sensitivity of LTD induction to copy number of the key signaling molecule Protein kinase C (PKC). We predict natural variability in this number by stochastic diffusion may influence the probabilistic LTD response to Ca²⁺ input in Purkinje cell spines and propose this as an extra source of stochasticity that may be important also in other signaling systems.

Calcium threshold shift enables frequency-independent control of plasticity by an instructive signal

At glutamatergic synapses, both long-term potentiation (LTP) and long-term depression (LTD) can be induced at the same synaptic activation frequency. Instructive signals determine whether LTP or LTD is induced, by modulating local calcium transients. Synapses maintain the ability to potentiate or depress over a wide frequency range, but it remains unknown how calcium-controlled plasticity operates when frequency variations alone cause differences in calcium amplitudes. We addressed this problem at cerebellar parallel fiber-Purkinje cell synapses, which can undergo LTD or LTP in response to 1-Hz and 100-Hz stimulation. We observed that high-frequency activation elicits larger spine calcium transients than low-frequency stimulation under all stimulus conditions, but, regardless of activation frequency, climbing fiber (CF) coactivation provides an instructive signal that further enhances calcium transients and promotes LTD. At both frequencies, buffering calcium prevents LTD induction and LTP results instead, identifying the enhanced calcium signal amplitude as the critical parameter contributed by the instructive CF signal. These observations show that it is not absolute calcium amplitudes that determine whether LTD or LTP is evoked but, instead, the LTD threshold slides, thus preserving the requirement for relatively larger calcium transients for LTD than for LTP induction at any given stimulus frequency. Cerebellar LTD depends on the activation of calcium/calmodulin-dependent kinase II (CaMKII). Using genetically modified (TT305/6VA and T305D) mice, we identified α-CaMKII inhibition upon autophosphorylation at Thr305/306 as a molecular event underlying the threshold shift. This mechanism enables frequency-independent plasticity control by the instructive CF signal based on relative, not absolute, calcium thresholds.

Stochastic Induction of Long-Term Potentiation and Long-Term Depression

Long-term depression (LTD) and long-term potentiation (LTP) of granule-Purkinje cell synapses are persistent synaptic alterations induced by high and low rises of the intracellular calcium ion concentration ([Ca²⁺]), respectively. The occurrence of LTD involves the activation of a positive feedback loop formed by protein kinase C, phospholipase A₂, and the extracellular signal-regulated protein kinase pathway, and its expression comprises the reduction of the population of synaptic AMPA receptors. Recently, a stochastic computational model of these signalling processes demonstrated that, in single synapses, LTD is probabilistic and bistable. Here, we expanded this model to simulate LTP, which requires protein phosphatases and the increase in the population of synaptic AMPA receptors. Our results indicated that, in single synapses, while LTD is bistable, LTP is gradual. Ca²⁺ induced both processes stochastically. The magnitudes of the Ca²⁺ signals and the states of the signalling network regulated the likelihood of LTP and LTD and defined dynamic macroscopic Ca²⁺ thresholds for the synaptic modifications in populations of synapses according to an inverse Bienenstock, Cooper and Munro (BCM) rule or a sigmoidal function. In conclusion, our model presents a unifying mechanism that explains the macroscopic properties of LTP and LTD from their dynamics in single synapses.

Purkinje cell intrinsic excitability increases after synaptic long term depression

Coding in cerebellar Purkinje cells not only depends on synaptic plasticity but also on their intrinsic membrane excitability. We performed whole cell patch-clamp recordings of Purkinje cells in sagittal cerebellar slices in mice. We found that inducing long-term depression (LTD) in the parallel fiber to Purkinje cell synapses results in an increase in the gain of the firing rate response. This increase in excitability is accompanied by an increase in the input resistance and a decrease in the amplitude of the hyperpolarization-activated cyclic nucleotide-gated (HCN) channel-mediated voltage sag. Application of a HCN channel blocker prevents the increase in input resistance and excitability without blocking the expression of synaptic LTD. We conclude that the induction of parallel fiber-Purkinje cell LTD is accompanied by an increase in excitability of Purkinje cells through downregulation of the HCN-mediated h current. We suggest that HCN downregulation is linked to the biochemical pathway that sustains synaptic LTD. Given the diversity of information carried by the parallel fiber system, we suggest that changes in intrinsic excitability enhance the coding capacity of the Purkinje cell to specific input sources.

Large Ca²⁺-dependent facilitation of Ca(V)2.1 channels revealed by Ca²⁺ photo-uncaging

KEY POINTS

CaV 2.1 channels constitute a dominant Ca(2+) entry pathway into brain neurons, triggering downstream Ca(2+) -dependent processes such as neurotransmitter release. CaV 2.1 is itself modulated by Ca(2+) , resulting in activity-dependent enhancement of channel opening termed Ca(2+) -dependent facilitation (CDF). Real-time Ca(2+) imaging and Ca(2+) uncaging here reveal that CDF turns out to be strikingly faster, more Ca(2+) sensitive, and larger than anticipated on previous grounds. Robust resolution of the quantitative profile of CDF enables deduction of a realistic biophysical model for this process. These results suggest that CaV 2.1 CDF would figure most prominently in short-term synaptic plasticity and cerebellar Purkinje cell rhythmicity.

ABSTRACT

CaV 2.1 (P-type) voltage-gated Ca(2+) channels constitute a major source of neuronal Ca(2+) current, strongly influencing rhythmicity and triggering neurotransmitter release throughout the central nervous system. Fitting with such stature among Ca(2+) entry pathways, CaV 2.1 is itself feedback regulated by intracellular Ca(2+) , acting through calmodulin to facilitate channel opening. The precise neurophysiological role of this calcium-dependent facilitation (CDF) remains uncertain, however, in large measure because the very magnitude, Ca(2+) dependence and kinetics of CDF have resisted quantification by conventional means. Here, we utilize the photo-uncaging of Ca(2+) with CaV 2.1 channels fluxing Li(+) currents, so that voltage-dependent activation of channel gating is no longer conflated with Ca(2+) entry, and CDF is then driven solely by light-induced increases in Ca(2+) . By using this strategy, we now find that CDF can be unexpectedly large, enhancing currents by as much as twofold at physiological voltages. CDF is steeply Ca(2+) dependent, with a Hill coefficient of approximately two, a half-maximal effect reached by nearly 500 nm Ca(2+) , and Ca(2+) on/off kinetics in the order of milliseconds to tens of milliseconds. These properties were established for both native P-type currents in cerebellar Purkinje neurons, as well as their recombinant channel counterparts under heterologous expression. Such features suggest that CDF of CaV 2.1 channels may substantially enhance the regularity of rhythmic firing in cerebellar Purkinje neurons, where regularity is believed crucial for motor coordination. In addition, this degree of extensive CDF would be poised to exert large order-of-magnitude effects on short-term synaptic plasticity via rapid modulation of presynaptic Ca(2+) entry.

A Computational Model for the AMPA Receptor Phosphorylation Master Switch Regulating Cerebellar Long-Term Depression

The expression of long-term depression (LTD) in cerebellar Purkinje cells results from the internalisation of α-amino-3-hydroxy-5-methylisoxazole-4-propionic acid receptors (AMPARs) from the postsynaptic membrane. This process is regulated by a complex signalling pathway involving sustained protein kinase C (PKC) activation, inhibition of serine/threonine phosphatase, and an active protein tyrosine phosphatase, PTPMEG. In addition, two AMPAR-interacting proteins-glutamate receptor-interacting protein (GRIP) and protein interacting with C kinase 1 (PICK1)-regulate the availability of AMPARs for trafficking between the postsynaptic membrane and the endosome. Here we present a new computational model of these overlapping signalling pathways. The model reveals how PTPMEG cooperates with PKC to drive LTD expression by facilitating the effect of PKC on the dissociation of AMPARs from GRIP and thus their availability for trafficking. Model simulations show that LTD expression is increased by serine/threonine phosphatase inhibition, and negatively regulated by Src-family tyrosine kinase activity, which restricts the dissociation of AMPARs from GRIP under basal conditions. We use the model to expose the dynamic balance between AMPAR internalisation and reinsertion, and the phosphorylation switch responsible for the perturbation of this balance and for the rapid plasticity initiation and regulation. Our model advances the understanding of PF-PC LTD regulation and induction, and provides a validated extensible platform for more detailed studies of this fundamental synaptic process.

Luminopsins integrate opto- and chemogenetics by using physical and biological light sources for opsin activation

Luminopsins are fusion proteins of luciferase and opsin that allow interrogation of neuronal circuits at different temporal and spatial resolutions by choosing either extrinsic physical or intrinsic biological light for its activation. Building on previous development of fusions of wild-type Gaussia luciferase with channelrhodopsin, here we expanded the utility of luminopsins by fusing bright Gaussia luciferase variants with either channelrhodopsin to excite neurons (luminescent opsin, LMO) or a proton pump to inhibit neurons (inhibitory LMO, iLMO). These improved LMOs could reliably activate or silence neurons in vitro and in vivo. Expression of the improved LMO in hippocampal circuits not only enabled mapping of synaptic activation of CA1 neurons with fine spatiotemporal resolution but also could drive rhythmic circuit excitation over a large spatiotemporal scale. Furthermore, virus-mediated expression of either LMO or iLMO in the substantia nigra in vivo produced not only the expected bidirectional control of single unit activity but also opposing effects on circling behavior in response to systemic injection of a luciferase substrate. Thus, although preserving the ability to be activated by external light sources, LMOs expand the use of optogenetics by making the same opsins accessible to noninvasive, chemogenetic control, thereby allowing the same probe to manipulate neuronal activity over a range of spatial and temporal scales.

Intracellular Ca(2+) thresholds for induction of excitatory long-term depression and inhibitory long-term potentiation in a cerebellar Purkinje neuron

Synaptic plasticity in the cerebellar cortex contributes to motor learning. In particular, long-term depression at excitatory parallel fiber - Purkinje neuron synapses has been intensively studied as a primary cellular mechanism for motor learning. Recent studies showed that synaptic plasticity other than long-term depression such as long-term potentiation at inhibitory interneuron - Purkinje neuron synapses called rebound potentiation is also involved in motor learning. It was suggested that long-term depression and rebound potentiation might synergistically support motor learning. Here, we have examined induction conditions of long-term depression and rebound potentiation in cultured rat Purkinje neurons, and found that both of them were induced simultaneously by certain patterns of depolarization of a Purkinje neuron. Further, we found that long-term depression was induced by shorter depolarizing pulses causing a smaller intracellular Ca(2+) increase than rebound potentiation. These results support an idea that long-term depression and rebound potentiation synergistically contribute to motor learning, and suggest that long-term depression may play a primary role in wider variety of motor learning paradigms than rebound potentiation.

The 5-HT7 receptor triggers cerebellar long-term synaptic depression via PKC-MAPK

The 5-HT7 receptor (5-HT7R) mediates important physiological effects of serotonin, such as memory and emotion, and is emerging as a therapeutic target for the treatment of cognitive disorders and depression. Although previous studies have revealed an expression of 5-HT7R in cerebellum, particularly at Purkinje cells, its functional role and signaling mechanisms have never been described. Using patch-clamp recordings in cerebellar slices of adult mice, we investigated the effects of a selective 5-HT7R agonist, LP-211, on the main plastic site of the cerebellar cortex, the parallel fiber-Purkinje cell synapse. Here we show that 5-HT7R activation induces long-term depression of parallel fiber-Purkinje cell synapse via a postsynaptic mechanism that involves the PKC-MAPK signaling pathway. Moreover, a 5-HT7R antagonist abolished the expression of PF-LTD, produced by pairing parallel fiber stimulation with Purkinje cell depolarization; whereas, application of a 5-HT7R agonist impaired LTP induced by 1 Hz parallel fiber stimulation. Our results indicate for the first time that 5-HT7R exerts a fine regulation of cerebellar bidirectional synaptic plasticity that might be involved in cognitive processes and neuropsychiatric disorders involving the cerebellum.

Propofol effects on cerebellar long-term depression

Propofol is an intravenously administered anesthetic that induces γ-aminobutyric acid-mediated inhibition in the central nervous system. It has been implicated in prolonged movement disorders. Since the cerebellum is important for motor coordination and learning, we investigated the potential effects of propofol on cerebellar circuitry. Using the whole-cell patch-clamp technique in Wister rat cerebellar slices, we demonstrated that propofol administration impaired long-term depression from the parallel fiber (PF) to Purkinje cell (PC) synapses (PF-LTD). Also, propofol reduced metabotropic glutamate receptor 1 (mGluR1)-mediated and group I mGluR agonist-induced slow currents in PCs. These results suggest that the propofol-induced PF-LTD impairment may be related to an alteration in mGluR1 signaling, which is essential to motor learning.

Around LTD hypothesis in motor learning

Long-term depression (LTD) at parallel fiber-Purkinje neuron synapses has been regarded as a primary cellular mechanism for motor learning. However, this hypothesis has been challenged. Demonstration of normal motor learning under LTD-suppressed conditions suggested that motor learning can occur without LTD. Synaptic plasticity mechanisms other than LTD have been found at various synapses in the cerebellum. Animals may achieve motor learning using several types of synaptic plasticity in the cerebellum including LTD.

Protein tyrosine phosphatase receptor type R is required for Purkinje cell responsiveness in cerebellar long-term depression

Background

Regulation of synaptic connectivity, including long-term depression (LTD), allows proper tuning of cellular signalling processes within brain circuitry. In the cerebellum, a key centre for motor coordination, a positive feedback loop that includes mitogen-activated protein kinases (MAPKs) is required for proper temporal control of LTD at cerebellar Purkinje cell synapses. Here we report that the tyrosine-specific MAPK-phosphatase PTPRR plays a role in coordinating the activity of this regulatory loop.

Results

LTD in the cerebellum of Ptprr^−/− mice is strongly impeded, in vitro and in vivo. Comparison of basal phospho-MAPK levels between wild-type and PTPRR deficient cerebellar slices revealed increased levels in mutants. This high basal phospho-MAPK level attenuated further increases in phospho-MAPK during chemical induction of LTD, essentially disrupting the positive feedback loop and preventing α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptor (AMPAR) phosphorylation and endocytosis.

Conclusions

Our findings indicate an important role for PTPRR in maintaining low basal MAPK activity in Purkinje cells. This creates an optimal ‘window’ to boost MAPK activity following signals that induce LTD, which can then propagate through feed-forward signals to cause AMPAR internalization and LTD.

Coding of stimulus strength via analog calcium signals in Purkinje cell dendrites of awake mice

The climbing fiber input to Purkinje cells acts as a teaching signal by triggering a massive influx of dendritic calcium that marks the occurrence of instructive stimuli during cerebellar learning. Here, we challenge the view that these calcium spikes are all-or-none and only signal whether the instructive stimulus has occurred, without providing parametric information about its features. We imaged ensembles of Purkinje cell dendrites in awake mice and measured their calcium responses to periocular airpuffs that serve as instructive stimuli during cerebellar-dependent eyeblink conditioning. Information about airpuff duration and pressure was encoded probabilistically across repeated trials, and in two additional signals in single trials: the synchrony of calcium spikes in the Purkinje cell population, and the amplitude of the calcium spikes, which was modulated by a non-climbing fiber pathway. These results indicate that calcium-based teaching signals in Purkinje cells contain analog information that encodes the strength of instructive stimuli trial-by-trial.

DOI:http://dx.doi.org/10.7554/eLife.03663.001

A region of the brain known as the cerebellum plays a key role in learning how to anticipate an event. For example, if you know that a puff of air is going to be directed at your eye, it's a good idea to close it in advance. However, how much you need to close it depends on how strong that puff of air is. A very strong puff might require closing the eye completely to protect it. In contrast, it is probably better to only partially close the eye if you know a lighter puff of air is coming, so that you can still see.

Extensive research has focused on how neurons in and around the cerebellum work together to achieve this goal. When an event—such as a puff of air—occurs, signals are sent to large neurons in the cerebellum, called Purkinje cells, by ‘climbing fibers’. However, climbing fibers were thought to be able to respond in only two ways: either they fire in a single burst to signal that an event has occurred, or they don't fire. It was therefore unclear how the finer details of the event (for example, the strength of the puff of air) are transmitted to the cerebellum.

Najafi et al. imaged the level of calcium in the cerebellum of mice, as this indicates how active the neurons are. When a puff of air was directed at the eyes of the mice, Najafi et al. saw that the size of the response of the Purkinje cells corresponded with how big the puff of air was. Najafi et al. show that the size of this response, which is based mostly on input from the climbing fibers, is also influenced by input from an additional unknown source.

These findings show that Purkinje cells of the cerebellum receive detailed information about the nature of an event, such as a puff of air. What remains to be seen is whether the cerebellum uses this information to learn the correct response, that is how hard to blink to avoid the expected puff.

DOI:http://dx.doi.org/10.7554/eLife.03663.002

Nitrophenyl-based caged neurotransmitters

Nitroaromatic photochemical protecting groups were developed for organic synthesis in 1966. Since the early 1990s, this type of chromophore has been used by neuroscientists to liberate a wide variety of amino acid neurotransmitters such as ACh, glutamate, GABA, and glycine, among others. Since 2001, several laboratories have used two-photon excitation of nitroaromatic cages for highly localized uncaging of glutamate in acute brain slices.

Sensory-driven enhancement of calcium signals in individual Purkinje cell dendrites of awake mice

Climbing fibers (CFs) are thought to contribute to cerebellar plasticity and learning by triggering a large influx of dendritic calcium in the postsynaptic Purkinje cell (PC) to signal the occurrence of an unexpected sensory event. However, CFs fire about once per second whether or not an event occurs, raising the question of how sensory-driven signals might be distinguished from a background of ongoing spontaneous activity. Here, we report that in PC dendrites of awake mice, CF-triggered calcium signals are enhanced when the trigger is a sensory event. In addition, we show that a large fraction of the total enhancement in each PC dendrite can be accounted for by an additional boost of calcium provided by sensory activation of a non-CF input. We suggest that sensory stimulation may modulate dendritic voltage and calcium concentration in PCs to increase the strength of plasticity signals during cerebellar learning.

Regulation and functional roles of rebound potentiation at cerebellar stellate cell-Purkinje cell synapses

Purkinje cells receive both excitatory and inhibitory synaptic inputs and send sole output from the cerebellar cortex. Long-term depression (LTD), a type of synaptic plasticity, at excitatory parallel fiber-Purkinje cell synapses has been studied extensively as a primary cellular mechanism of motor learning. On the other hand, at inhibitory synapses on a Purkinje cell, postsynaptic depolarization induces long-lasting potentiation of GABAergic synaptic transmission. This synaptic plasticity is called rebound potentiation (RP), and its molecular regulatory mechanisms have been studied. The increase in intracellular Ca(2+) concentration caused by depolarization induces RP through enhancement of GABAA receptor (GABAAR) responsiveness. RP induction depends on binding of GABAAR with GABAAR associated protein (GABARAP) which is regulated by Ca(2+)/calmodulin-dependent kinase II (CaMKII). Whether RP is induced or not is determined by the balance between phosphorylation and de-phosphorylation activities regulated by intracellular Ca(2+) and by metabotropic GABA and glutamate receptors. Recent studies have revealed that the subunit composition of CaMKII has significant impact on RP induction. A Purkinje cell expresses both α- and β-CaMKII, and the latter has much higher affinity for Ca(2+)/calmodulin than the former. It was shown that when the relative amount of α- to β-CaMKII is large, RP induction is suppressed. The functional significance of RP has also been studied using transgenic mice in which a peptide inhibiting association of GABARAP and GABAAR is expressed selectively in Purkinje cells. The transgenic mice show abrogation of RP and subnormal adaptation of vestibulo-ocular reflex (VOR), a type of motor learning. Thus, RP is involved in a certain type of motor learning.

Non-invasive activation of optogenetic actuators

The manipulation of genetically targeted neurons with light (optogenetics) continues to provide unprecedented avenues into studying the function of the mammalian brain. However, potential translation into the clinical arena faces a number of significant hurdles, foremost among them the need for insertion of optical fibers into the brain to deliver light to opsins expressed on neuronal membranes. In order to overcome these hardware-related problems, we have developed an alternative strategy for delivering light to opsins which does not involve fiber implants. Rather, the light is produced by a protein, luciferase, which oxidizes intravenously applied substrate, thereby emitting bioluminescence. In proof-of-principle studies employing a fusion protein of a light-generating luciferase to a light-sensing opsin (luminopsin), we showed that light emitted by Gaussia luciferase is indeed able to activate channelrhodopsin, allowing modulation of neuronal activity when expressed in cultured neurons. Here we assessed applicability of the concept in vivo in mice expressing luminopsins from viral vectors and from genetically engineered transgenes. The experiments demonstrate that intravenously applied substrate reaches neurons in the brain, causing the luciferase to produce bioluminescence which can be imaged in vivo, and that activation of channelrhodopsin by bioluminescence is sufficient to affect behavior. Further developments of such technology based on combining optogenetics with bioluminescence - i.e. combining light-sensing molecules with biologically produced light through luciferases - should bring optogenetics closer to clinical applications.

Computational modeling of diffusion in the cerebellum

Diffusion is a major transport mechanism in living organisms. In the cerebellum, diffusion is responsible for the propagation of molecular signaling involved in synaptic plasticity and metabolism, both intracellularly and extracellularly. In this chapter, we present an overview of the cerebellar structure and function. We then discuss the types of diffusion processes present in the cerebellum and their biological importance. We particularly emphasize the differences between extracellular and intracellular diffusion and the presence of tortuosity and anomalous diffusion in different parts of the cerebellar cortex. We provide a mathematical introduction to diffusion and a conceptual overview of various computational modeling techniques. We discuss their scope and their limit of application. Although our focus is the cerebellum, we have aimed at presenting the biological and mathematical foundations as general as possible to be applicable to any other area in biology in which diffusion is of importance.

A model-based prediction of the calcium responses in the striatal synaptic spines depending on the timing of cortical and dopaminergic inputs and post-synaptic spikes

The dopamine-dependent plasticity of the cortico-striatal synapses is considered as the cellular mechanism crucial for reinforcement learning. The dopaminergic inputs and the calcium responses affect the synaptic plasticity by way of the signaling cascades within the synaptic spines. The calcium concentration within synaptic spines, however, is dependent on multiple factors including the calcium influx through ionotropic glutamate receptors, the intracellular calcium release by activation of metabotropic glutamate receptors, and the opening of calcium channels by EPSPs and back-propagating action potentials. Furthermore, dopamine is known to modulate the efficacies of NMDA receptors, some of the calcium channels, and sodium and potassium channels that affect the back propagation of action potentials. Here we construct an electric compartment model of the striatal medium spiny neuron with a realistic morphology and predict the calcium responses in the synaptic spines with variable timings of the glutamatergic and dopaminergic inputs and the postsynaptic action potentials. The model was validated by reproducing the responses to current inputs and could predict the electric and calcium responses to glutamatergic inputs and back-propagating action potential in the proximal and distal synaptic spines during up- and down-states. We investigated the calcium responses by systematically varying the timings of the glutamatergic and dopaminergic inputs relative to the action potential and found that the calcium response and the subsequent synaptic potentiation is maximal when the dopamine input precedes glutamate input and action potential. The prediction is not consistent with the hypothesis that the dopamine input provides the reward prediction error for reinforcement learning. The finding suggests that there is an unknown learning mechanisms at the network level or an unknown cellular mechanism for calcium dynamics and signaling cascades.

Beyond "all-or-nothing" climbing fibers: graded representation of teaching signals in Purkinje cells

Arguments about the function of the climbing fiber (CF) input to the cerebellar cortex have fueled a rabid debate that started over 40 years ago, and continues to polarize the field to this day. The origin of the controversy can be traced back to 1969, the year David Marr published part of his dissertation work in a paper entitled “A theory of cerebellar cortex.” In Marr’s theory, CFs play a key role during the process of motor learning, providing an instructive signal that serves as a “teacher” for the post-synaptic Purkinje cells. Although this influential idea has found its way into the mainstream, a number of objections have been raised. For example, several investigators have pointed out that the seemingly “all-or-nothing” activation of the CF input provides little information and is too ambiguous to serve as an effective instructive signal. Here, we take a fresh look at these arguments in light of new evidence about the peculiar physiology of CFs. Based on recent findings we propose that at the level of an individual Purkinje cell, a graded instructive signal can be effectively encoded via pre- or post-synaptic modulation of its one and only CF input.

A common framework of signal processing in the induction of cerebellar LTD and cortical STDP

Cerebellar long-term depression (LTD) and cortical spike-timing-dependent synaptic plasticity (STDP) are two well-known and well-characterized types of synaptic plasticity. Induction of both types of synaptic plasticity depends on the spike timing, pairing frequency, and pairing numbers of two different sources of spiking. This implies that the induction of synaptic plasticity may share common frameworks in terms of signal processing regardless of the different signaling pathways involved in the two types of synaptic plasticity. Here we propose that both types share common frameworks of signal processing for spike-timing, pairing-frequency, and pairing-numbers detection. We developed system models of both types of synaptic plasticity and analyzed signal processing in the induction of synaptic plasticity. We found that both systems have upstream subsystems for spike-timing detection and downstream subsystems for pairing-frequency and pairing-numbers detection. The upstream systems used multiplication of signals from the feedback filters and nonlinear functions for spike-timing detection. The downstream subsystems used temporal filters with longer time constants for pairing-frequency detection and nonlinear switch-like functions for pairing-numbers detection, indicating that the downstream subsystems serve as a leaky integrate-and-fire system. Thus, our findings suggest that a common conceptual framework for the induction of synaptic plasticity exists despite the differences in molecular species and pathways.

Gating of long-term depression by Ca2+/calmodulin-dependent protein kinase II through enhanced cGMP signalling in cerebellar Purkinje cells

Long-term depression (LTD) at parallel fibre synapses on a cerebellar Purkinje cell has been regarded as a cellular basis for motor learning. Although Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) has been implicated in the LTD induction as an important Ca(2+)-sensing molecule, the underlying signalling mechanism remains unclear. Here, we attempted to explore the potential signalling pathway underlying the CaMKII involvement in LTD using a systems biology approach, combined with validation by electrophysiological and FRET imaging experiments on a rat cultured Purkinje cell. Model simulation predicted the following cascade as a candidate mechanism for the CaMKII contribution to LTD: CaMKII negatively regulates phosphodiesterase 1 (PDE1), subsequently facilitates the cGMP/protein kinase G (PKG) signalling pathway and down-regulates protein phosphatase 2A (PP-2A), thus supporting the LTD-inducing positive feedback loop consisting of mutual activation of protein kinase C (PKC) and mitogen-activated protein kinase (MAPK). This model suggestion was corroborated by whole-cell patch clamp recording experiments. In addition, FRET measurement of intracellular cGMP concentration revealed that CaMKII activation causes sustained increase of cGMP, supporting the signalling mechanism of LTD induction by CaMKII. Furthermore, we found that activation of the cGMP/PKG pathway by nitric oxide (NO) can support LTD induction without activation of CaMKII. Thus, this study clarified interaction between NO and Ca(2+)/CaMKII, two important factors required for LTD.

Raf kinase inhibitory protein is required for cerebellar long-term synaptic depression by mediating PKC-dependent MAPK activation

It was demonstrated previously that a positive feedback loop, including protein kinase C (PKC) and mitogen-activated protein kinase (MAPK), is required for the gradual expression of cerebellar long-term depression (LTD). PKC and MAPK are mutually activated in this loop. MAPK-dependent PKC activation is likely to be mediated by phospholipase A2. On the other hand, it is not clear how PKC activates MAPK. Therefore, the entire picture of this loop was not fully understood. We here test the hypothesis that this loop is completed by the PKC substrate, Raf kinase inhibitory protein (RKIP). To test this hypothesis, we used a mutant form of RKIP that is not phosphorylated by PKC and thus constitutively inhibits Raf-1 and MEK, upstream kinases of MAPK. When this RKIP mutant was introduced into Purkinje cells of mouse cerebellar slices through patch-clamp electrodes, LTD was blocked, while wild-type (WT) RKIP had no effect on LTD. Physiological epistasis experiments demonstrated that RKIP works downstream of PKC and upstream of MAPK during LTD induction. Furthermore, biochemical analyses demonstrated that endogenous RKIP dissociates from Raf-1 and MEK during LTD induction in a PKC-dependent manner, suggesting that RKIP binding-dependent inhibition of Raf-1 and MEK is removed upon LTD induction. We therefore conclude that PKC-dependent regulation of RKIP leads to MAPK activation, with RKIP completing the positive feedback loop that is required for LTD.

Calcium as a trigger for cerebellar long-term synaptic depression

Cerebellar long-term depression (LTD) is a form of long-term synaptic plasticity that is triggered by calcium(Ca2+) signals in the postsynaptic Purkinje cell. This Ca2+comes both from IP3-mediated release from intracellular Ca2+ stores, as well as from Ca2+ influx through voltage-gated Ca2+ channels. The Ca2+ signal that triggers LTD occurs locally within dendritic spines and is due to supralinear summation of signals coming from these two Ca2+ sources. The properties of this postsynaptic Ca2+signal can explain several features of LTD, such as its associativity, synapse specificity, and dependence on thetiming of synaptic activity, and can account for the slow kinetics of LTD expression. Thus, from a Ca2+ signaling perspective, LTD is one of the best understood forms of synaptic plasticity.

Diffusion and extrusion shape standing calcium gradients during ongoing parallel fiber activity in dendrites of Purkinje neurons

Synaptically induced calcium transients in dendrites of Purkinje neurons (PNs) play a key role in the induction of plasticity in the cerebellar cortex (Ito, Physiol Rev 81:1143-1195, 2001). Long-term depression at parallel fiber-PN synapses can be induced by stimulation paradigms that are associated with long-lasting (>1 min) calcium signals. These signals remain strictly localized (Eilers et al., Learn Mem 3:159-168, 1997), an observation that was rather unexpected, given the high concentration of the mobile endogenous calcium-binding proteins parvalbumin and calbindin in PNs (Fierro and Llano, J Physiol (Lond) 496:617-625, 1996; Kosaka et al., Exp Brain Res 93:483-491, 1993). By combining two-photon calcium imaging experiments in acute slices with numerical computer simulations, we found that significant calcium diffusion out of active branches indeed takes places. It is outweighed, however, by rapid and powerful calcium extrusion along the dendritic shaft. The close interplay of diffusion and extrusion defines the spread of calcium between active and inactive dendritic branches, forming a steep gradient in calcium with drop ranges of ~13 μm (interquartile range, 10-18 μm).

The importance of stochastic signaling processes in the induction of long-term synaptic plasticity

A stochastic model of the signaling network responsible for the induction of long-term depression (LTD) at the parallel fiber to Purkinje cell synapse is described. The model includes a PKC-ERK-cPLA2 positive feedback loop and mechanisms of AMPA receptor trafficking. It was tuned to replicate calcium uncaging experiments that cause LTD. The ultrasensitive activation of ERK makes the signaling network activity bistable, causing either LTD or not. Therefore, in single synapses only two discrete stable states (LTD and non-LTD) can be expressed. The stochastic properties of the signaling network causes threshold dithering and probabilistic expression of LTD, which allows at the macroscopic level for many different and stable mean magnitudes of depression. When the volume of a single spine is simulated no thresholds for the calcium input signal are present. Such thresholds appear only when the volume of simulation is increased by a factor 100 or more and the model output is then bistable. Similarly, deterministic solutions of the same model show only bistable behavior. LTD induction requires activation of the PKC-ERK-cPLA2 positive feedback loop but this activity is not constant: the activities of ERK and of cPLA2 fluctuate strongly. This is much less the case for PKC which is more constantly activated and thereby promotes a stable output of the pathway.

Transient receptor potential canonical channels regulate the induction of cerebellar long-term depression

In the cerebellum, synaptic strength at the synapses between parallel fibers and Purkinje cells is best known to be modulated via metabotropic glutamate receptor 1 (mGluR1)-dependent cerebellar long-term depression (LTD). An increase in intracellular calcium levels plays an important role in inducing mGluR1-dependent cerebellar LTD. Downstream of mGluR1, there are two major sources of calcium: transient receptor potential canonical (TRPC) channels and inositol trisphosphate receptors (IP(3)R). IP(3)R triggers a calcium release from the intracellular calcium store. Here, we show that TRPC channels mediate mGluR1-evoked slow currents to regulate cerebellar LTD in Sprague Dawley rats. We found that the inhibition of TRPC channels blocks the induction of cerebellar LTD. Moreover, we show that processes known to underlie cerebellar LTD induction, such as increases in intracellular calcium concentration, the activation of protein kinase C, and the internalization of GluR2, are also hindered by blocking TRPC. These results suggest that the mGluR1-evoked activation of TRPC channels is required for the induction of cerebellar LTD.