Statistical characteristics of climbing fiber spikes necessary for efficient cerebellar learning

 Mean firing rates (MFRs), with analogue values, have thus far been used as information carriers of neurons in most brain theories of learning. However, the neurons transmit the signal by spikes, which are discrete events. The climbing fibers (CFs), which are known to be essential for cerebellar motor learning, fire at the ultra-low firing rates (around 1 Hz), and it is not yet understood theoretically how high-frequency information can be conveyed and how learning of smooth and fast movements can be achieved. Here we address whether cerebellar learning can be achieved by CF spikes instead of conventional MFR in an eye movement task, such as the ocular following response (OFR), and an arm movement task. There are two major afferents into cerebellar Purkinje cells: parallel fiber (PF) and CF, and the synaptic weights between PFs and Purkinje cells have been shown to be modulated by the stimulation of both types of fiber. The modulation of the synaptic weights is regulated by the cerebellar synaptic plasticity. In this study we simulated cerebellar learning using CF signals as spikes instead of conventional MFR. To generate the spikes we used the following four spike generation models: (1) a Poisson model in which the spike interval probability follows a Poisson distribution, (2) a gamma model in which the spike interval probability follows the gamma distribution, (3) a max model in which a spike is generated when a synaptic input reaches maximum, and (4) a threshold model in which a spike is generated when the input crosses a certain small threshold. We found that, in an OFR task with a constant visual velocity, learning was successful with stochastic models, such as Poisson and gamma models, but not in the deterministic models, such as max and threshold models. In an OFR with a stepwise velocity change and an arm movement task, learning could be achieved only in the Poisson model. In addition, for efficient cerebellar learning, the distribution of CF spike-occurrence time after stimulus onset must capture at least the first, second and third moments of the temporal distribution of error signals. Received: 28 January 2000 / Accepted in revised form: 2 August 2000     

Roles of phospholipase Cbeta4 in synapse elimination and plasticity in developing and mature cerebellum

The beta isoforms of phospholipase C (PLCbetas) are thought to mediate signals from metabotropic glutamate receptor subtype 1 (mGluR1) that is crucial for the modulation of synaptic transmission and plasticity. Among four PLCbeta isoforms, PLCbeta4 is one of the two major isoforms expressed in cerebellar Purkinje cells. The authors have studied the roles of PLCbeta4 by analyzing PLCbeta4 knockout mice, which are viable, but exhibit locomotor ataxia. Their cerebellar histology, parallel fiber synapse formation, and basic electrophysiology appear normal. However, developmental elimination of multiple climbing fiber innervation is clearly impaired in the rostral portion of the cerebellar vermis, where PLCbeta4 mRNA is predominantly expressed in the wild-type mice. In the adult, long-term depression is deficient at parallel fiber to Purkinje cell synapses in the rostral cerebellum of the PLCbeta4 knockout mice. The impairment of climbing fiber synapse elimination and the loss of long-term depression are similar to those seen in mice defective in mGluR1, Galphaq, or protein kinase C. Thus, the authors' results strongly suggest that PLCbeta4 is part of a signaling pathway, including the mGluR1, Galphaq and protein kinase C, which is crucial for both climbing fiber synapse elimination in the developing cerebellum and long-term depression induction in the mature cerebellum.     

Effect of Climbing Fiber Deprivation on Release of Endogenous Aspartate, Glutamate, and Homocysteate in Slices of Rat Cerebellar Hemispheres and Vermis

Aspartate (Asp) and/or glutamate (Glu) have been proposed as putative excitatory transmitters released from synaptic terminals of the olivo-cerebellar climbing fiber afferents to the Purkinje cells. Investigations of the climbing fiber transmitter(s) separately for hemispheres and vermis were performed to examine whether the current controversy over the role of Asp as a neurotransmitter in the climbing fibers may be due to topographic differences. K(+)-induced Ca2(+)-dependent release of endogenous substances was investigated in slices of cerebellar hemisphere and vermis of control rats and those deprived of climbing fibers by 3-acetylpyridine (3-AP) treatment. A release of Asp and Glu, as well as a small but significant release of homocysteic acid (HCA) was confirmed in control rats. Climbing fiber deprivation by 3-AP treatment reduced the stimulated release of Asp by 48% in slices of cerebellar hemispheres, but not in vermis. Climbing fiber deprivation completely abolished the release of HCA in both hemispheres and vermis. The release of HCA, Asp, and Glu from slices of control and climbing fiber-deprived rats evoked by 50 mM K+ was greater than 90% Ca2(+)-dependent. These results support the hypothesis that Asp is a transmitter candidate of the climbing fibers projecting to the cerebellar hemispheres, but not to the vermis, and provide the first evidence that HCA can be linked to a specific pathway.     

A neural network model of the cerebellar cortex performing dynamic associations

The present paper proposes a model which applies formal neural network modeling techniques to construct a theoretical representation of the cerebellar cortex and its performances in motor control. A schema that makes explicit use of propagation delays of neural signals, is introduced to describe the ability to store temporal sequences of patterns in the Golgi-granule cell system. A perceptron association is then performed on these sequences of patterns by the Purkinje cell layer. The model conforms with important biological constraints, such as the known excitatory or inhibitory nature of the various synapses. Also, as suggested by experimental evidence, the synaptic plasticity underlying the learning ability of the model, is confined to the parallel fiber — Purkinje cell synapses, and takes place under the control of the climbing fibers. The result is a neural network model, constructed according to the anatomy of the cerebellar cortex, and capable of learning and retrieval of temporal sequences of patterns. It provides a framework to represent and interpret properties of learning and control of movements by the cerebellum, and to assess the capacity of formal neural network techniques for modeling of real neural systems.     

Long-term depression of the cerebellar climbing fiber--Purkinje neuron synapse

In classic Marr-Albus-Ito models of cerebellar function, coactivation of the climbing fiber (CF) synapse, which provides massive, invariant excitation of Purkinje neurons (coding the unconditioned stimulus), together with a graded parallel fiber synaptic array (coding the conditioned stimulus) leads to long-term depression (LTD) of parallel fiber-Purkinje neuron synapses, underlying production of a conditioned response. Here, we show that the supposedly invariant CF synapse can also express LTD. Brief 5 Hz stimulation of the CF resulted in a sustained depression of CF EPSCs that did not spread to neighboring parallel fiber synapses. Like parallel fiber LTD, CF LTD required postsynaptic Ca2+ elevation, activation of group 1 mGluRs, and activation of PKC. CF LTD is potentially relevant for models of cerebellar motor control and learning and the developmental conversion from multiple to single CF innervation of Purkinje neurons.     

Climbing Fiber Burst Size and Olivary Sub-threshold Oscillations in a Network Setting

The inferior olivary nucleus provides one of the two main inputs to the cerebellum: the so-called climbing fibers. Activation of climbing fibers is generally believed to be related to timing of motor commands and/or motor learning. Climbing fiber spikes lead to large all-or-none action potentials in cerebellar Purkinje cells, overriding any other ongoing activity and silencing these cells for a brief period of time afterwards. Empirical evidence shows that the climbing fiber can transmit a short burst of spikes as a result of an olivary cell somatic spike, potentially increasing the information being transferred to the cerebellum per climbing fiber activation. Previously reported results from in vitro studies suggested that the information encoded in the climbing fiber burst is related to the occurrence of the spike relative to the ongoing sub-threshold membrane potential oscillation of the olivary cell, i.e. that the phase of the oscillation is reflected in the size of the climbing fiber burst. We used a detailed three-compartmental model of an inferior olivary cell to further investigate the possible factors determining the size of the climbing fiber burst. Our findings suggest that the phase-dependency of the burst size is present but limited and that charge flow between soma and dendrite is a major determinant of the climbing fiber burst. From our findings it follows that phenomena such as cell ensemble synchrony can have a big effect on the climbing fiber burst size through dendrodendritic gap-junctional coupling between olivary cells.     

A Mathematical Model of the Cerebellar-Olivary System I: Self-Regulating Equilibrium of Climbing Fiber Activity

We use a mathematical model to investigate how climbing fiber-dependent plasticity at granule cell to Purkinje cell (grPkj) synapses in the cerebellar cortex is influenced by the synaptic organization of the cerebellar-olivary system. Based on empirical studies, grPkj synapses are assumed to decrease in strength when active during a climbing fiber input (LTD) and increase in strength when active without a climbing fiber input (LTP). Results suggest that the inhibition of climbing fibers by cerebellar output combines with LTD/P to self-regulate spontaneous climbing fiber activity to an equilibrium level at which LTP and LTD balance and the expected net change in grPkj synaptic weights is zero. The synaptic weight vector is asymptotically confined to an equilibrium hyperplane defining the set of all possible combinations of synaptic weights consistent with climbing fiber equilibrium. Results also suggest restrictions on LTP/D at grPkj synapses required to produce synaptic weights that do not drift spontaneously.     

In vivo analysis of inhibitory synaptic inputs and rebounds in deep cerebellar nuclear neurons

Neuronal function depends on the properties of the synaptic inputs the neuron receive and on its intrinsic responsive properties. However, the conditions for synaptic integration and activation of intrinsic responses may to a large extent depend on the level of background synaptic input. In this respect, the deep cerebellar nuclear (DCN) neurons are of particular interest: they feature a massive background synaptic input and an intrinsic, postinhibitory rebound depolarization with profound effects on the synaptic integration. Using in vivo whole cell patch clamp recordings from DCN cells in the cat, we find that the background of Purkinje cell input provides a tonic inhibitory synaptic noise in the DCN cell. Under these conditions, individual Purkinje cells appear to have a near negligible influence on the DCN cell and clear-cut rebounds are difficult to induce. Peripheral input that drives the simple spike output of the afferent PCs to the DCN cell generates a relatively strong DCN cell inhibition, but do not induce rebounds. In contrast, synchronized climbing fiber activation, which leads to a synchronized input from a large number of Purkinje cells, can induce profound rebound responses. In light of what is known about climbing fiber activation under behaviour, the present findings suggest that DCN cell rebound responses may be an unusual event. Our results also suggest that cortical modulation of DCN cell output require a substantial co-modulation of a large proportion of the PCs that innervate the cell, which is a possible rationale for the existence of the cerebellar microcomplex.     

Delayed reverberation through time windows as a key to cerebellar function

We present a functional model of the cerebellum comprising cerebellar cortex, inferior olive, deep cerebellar nuclei, and brain stem nuclei. The discerning feature of the model being time coding, we consistently describe the system in terms of postsynaptic potentials, synchronous action potentials, and propagation delays. We show by means of detailed single-neuron modeling that (i) Golgi cells can fulfill a gating task in that they form short and well-defined time windows within which granule cells can reach firing threshold, thus organizing neuronal activity in discrete `time slices', and that (ii) rebound firing in cerebellar nuclei cells is a robust mechanism leading to a delayed reverberation of Purkinje cell activity through cerebellar-reticular projections back to the cerebellar cortex. Computer simulations of the whole cerebellar network consisting of several thousand neurons reveal that reverberation in conjunction with long-term plasticity at the parallel fiber-Purkinje cell synapses enables the system to learn, store, and recall spatio-temporal patterns of neuronal activity. Climbing fiber spikes act both as a synchronization and as a teacher signal, not as an error signal. They are due to intrinsic oscillatory properties of inferior olivary neurons and to delayed reverberation within the network. In addition to clear experimental predictions the present theory sheds new light on a number of experimental observation such as the synchronicity of climbing fiber spikes and provides a novel explanation of how the cerebellum solves timing tasks on a time scale of several hundreds of milliseconds. Received: 23 July 1999 / Accepted in revised form: 31 August 1999     

Ectopic release of synaptic vesicles

Exocytosis of synaptic vesicles is generally assumed to occur only at ultrastructurally defined presynaptic active zones. If release is restricted to these sites, receptors not located within the synaptic cleft must be activated by transmitter that diffuses out of the cleft or not be activated at all. Here we report that AMPA receptor-mediated quantal events resulting from climbing fiber release are observed in Bergmann glial cells in the cerebellar cortex. These quantal events are not coincident with quanta recorded in neighboring Purkinje cells which receive input from the same climbing fiber. As Bergmann glial membranes are excluded from the synaptic cleft, we propose that exocytosis can occur from climbing fiber release sites located directly across from Bergmann glial membranes. Such ectopic release may account for the majority of the Bergmann glial AMPA response evoked by climbing fiber stimulation.     

Signal processing in cerebellar Purkinje cells

Mechanisms and functional implications of signal processing in cerebellar Purkinje cells have been the subject of recent extensive investigations. Complex patterns of their planar dendritic arbor are analysed with computer-aided reconstructions and also topological analyses. Local computation may occur in Purkinje cell dendrites, but its extent is not clear at present. Synaptic transmission and electrical and ionic activity of Purkinje cell membrane have been revealed in detail, and related biochemical processes are being uncovered. A special type of synaptic plasticity is present in Purkinje cell dendrites; long-term depression (LTD) occurs in parallel fiber-Purkinje cell transmission when the parallel fibers are activated with a climbing fiber innervating that Purkinje cell. Evidence indicates that synaptic plasticity in Purkinje cells is due to sustained desensitization of Purkinje dendritic receptors to glutamate, which is a putative neurotransmitter of parallel fibers, and that conjunctive activation of a climbing fiber and parallel fibers leads to desensitization through enhanced intradendritic calcium concentration. A microzone of the cerebellar cortex is connected to an extracerebellar neural system through the inhibitory projection of Purkinje cells to a cerebellar or vestibular nuclear cell group. Climbing fiber afferents convey signals representing control errors in the performance of a neural system, and evoke complex spikes in Purkinje cells of the microzone connected to the neural system. Complex spikes would modify the performance of the microzone by producing LTD in parallel fiber-Purkinje cell synapses, and consequently would improve the overall performance of the neural system. The primary function of the cerebellum thus appears to be endowing adaptability to numerous neural control systems in the brain and spinal cord through error-triggered reorganization of the cerebellar cortical circuitry.     

Muscarinic Receptor Modulation of the Cerebellar Interpositus Nucleus In Vitro

How the cerebellum carries out its functions is not clear, even for its established roles in motor control. In particular, little is known about how the cerebellar nuclei (CN) integrate their synaptic and neuromodulatory inputs to generate cerebellar output. CN neurons receive inhibitory inputs from Purkinje cells, excitatory inputs from mossy fibre and climbing fibre collaterals, as well as a variety of neuromodulatory inputs, including cholinergic inputs. In this study we tested how activation of acetylcholine receptors modulated firing rate, intrinsic properties and synaptic transmission in the CN. Using in vitro whole-cell patch clamp recordings from neurons in the interpositus nucleus, the acetylcholine receptor agonist carbachol was shown to induce a short-term increase in firing rate, increase holding current and decrease input resistance of interpositus CN neurons. Carbachol also induced long-term depression of evoked inhibitory postsynaptic currents and a short-term depression of evoked excitatory postsynaptic currents. All effects were shown to be dependent upon muscarinic acetylcholine receptor activation. Overall, the present study has identified muscarinic receptor activation as a modulator of CN activity.

     

Storing covariance with nonlinearly interacting neurons

Summary A time-dependent, nonlinear model of neuronal interaction which was probabilistically analyzed in a previous article is shown here to be a natural generalization of the Hartline-Ratliff model of the Limulus retina. Although the primary physical variables in the model are the membrane potentials of neurons, the equations which govern the means and covariances of the membrane potentials are coupled through the average firing rates; as a consequence, the average firing rates control the selective storage and retrieval of covariance information. Motor learning in the cerebellar cortex is treated as a problem of covariance storage, and a prediction is made for the underlying synaptic plasticity: the change in synaptic strength between a parallel fiber and a Purkinje cell should be proportional to the covariance between discharges in the parallel fiber and the climbing fiber. Unlike previous proposals for synaptic plasticity, this prediction requires both facilitation and depression to occur (under different conditions) at the same synapse.     

Cerebellar regulation mechanisms learned from studies on GluRδ2

The amino acid sequence suggests that glutamate receptor σ2 (GluRσ2) belongs to an ionotropic GluR (iGluR) subunit family. However, neither the direct binding to glutamate nor the incorporation into any native iGluRs has been demonstrated. One prominent feature of GluRσ2 is its predominant expression at parallel fiber-Purkinje cell synapses in the cerebellum. Knockdown or knockout of GluRσ2 impairs synaptic plasticity, stabilization, elimination, motor control, and learning. Therefore, GluRσ2 plays a crucial role in the cerebellar function. Several ataxic spontaneous mutant mice have defects in the GluRσ2 gene. Numerous proteins interacting with GluRσ2 have been identified. Recent in vivo studies on GluRσ2 knockout mice shed light on the mechanism by which GluRσ2 deficiency causes ataxia and unveiled some secondary influence of the GluRσ2 deficiency on the function of the central nervous system. Studies on GluRσ2 might provide unique clues regarding not only the molecular mechanism of synaptic regulations but also the functioning mechanism of the entire cerebellar system     

A computational model of four regions of the cerebellum based on feedback-error learning

We propose a computationally coherent model of cerebellar motor learning based on the feedback-error-learning scheme. We assume that climbing fiber responses represent motor-command errors generated by some of the premotor networks such as the feedback controllers at the spinal-, brain stem- and cerebral levels. Thus, in our model, climbing fiber responses are considered to convey motor errors in the motor-command coordinates rather than in the sensory coordinates. Based on the long-term depression in Purkinje cells each corticonuclear microcomplex in different regions of the cerebellum learns to execute predictive and coordinative control of different types of movements. Ultimately, it acquires an inverse model of a specific controlled object and complements crude control by the premotor networks. This general model is developed in detail as a specific neural circuit model for the lateral hemisphere. A new experiment is suggested to elucidate the coordinate frame in which climbing fiber responses are represented.     

Computation of inverse dynamics for the control of movements

 Accuracy of movements requires that the central nervous system computes approximate inverse functions of the mechanical functions of limb articulations. In vertebrates, this is known to be achieved within the cerebellar pathways, and also in the cerebral cortex of primates. A cybernetic circuit achieving this computation allows accurate simulation of fast movements of the eye or forearm. It is consistent with anatomy, and with the classical view of the cerebellum as permanently supervised by the inferior olive. The inferior olive detects over- or under-shoots of movements, and the resulting climbing fiber activity corrects ongoing movements, regulates the function of cerebellar cortex and nuclei, and sets the gains of the sensorimotor reactions. Received: 25 September 1995/Accepted in revised form: 9 May 1996     

Cerebellar long-term depression: a mechanism for learning and memory

It is commonly thought that a persistent change in the efficacy of the synaptic transmission is the basic mechanism underlying learning and memory. The cerebellum, key structure of the motor function, exhibits a synaptic plasticity named cerebellar long-term depression or LTD. This phenomenon appears in the Purkinje cell when the two main excitatory inputs (one consists of the parallel fibers which relay information on the task to accomplish and the other one includes the climbing fiber which conveys error signals) are activated in combination, resulting in a persistent decrease of the efficacy of the parallel fiber-Purkinje cell synapse. Studies made in the last 20 years show that activation of ionotropic and metabotropic glutamate receptors triggers complex signal transduction processes, leading to the phosphorylation and the internalization of AMPA receptors, a subtype of glutamatergic receptors. The aim of this paper is firstly to present mechanisms involved in LTD induction and maintenance. The second part introduces briefly experimental data that show that LTD is indeed strongly associated with motor learning. Recent studies on the involvement of the cerebellum in cognitive tasks also suggest that LTD may play some role other than that in the sole motor learning.     

Physiological properties of afferents and synaptic reorganization in the rat cerebellum degranulated by postnatal x-irradiation

Elimination of most granule, basket, and stellate interneurons in the rat cerebellum was achieved by repeated doses of low level x-irradiation applied during the first two weeks of postnatal life. Electrical stimulation of the brain stem and peripheral limbs was employed to investigate the properties of afferent cerebellar pathways and the nature of the reorganized neuronal synaptic circuitry in the degranulated cerebellum of the adult. Direct contacts of mossy fibers on Purkinje cells were indicated by short latency, single spike responses: 1.9 msec from the lateral reticular nucleus of brain stem and 5.4 msec from ipsilateral forlimb. These were shorter than in normal rats by 0.9 and 2.1 msec, respectively. The topography of projections from peripheral stimulation was approximately normal. Mossy fiber responses followed stimulation at up to 20/sec, whereas climbing fiber pathways fatigued at 10/sec. The latency of climbing fiber input to peripheral limb stimulation in x-irradiated cerebellum was 23 ± 8 (SD) msec. In x-irradiated rats, the climbing fiber pathways evoked highly variable extracellular burst responses and intracellular EPSPs of different, discrete sizes. These variable responses suggest that multiple climbing fibers contact single Purkinje cells. We conclude that each type of afferent retains identifying characteristics of transmission. However, rules for synaptic specification appear to break down so that: (1) abnormal classes of neurons develop synaptic connections, i.e., mossy fibers to Purkinje cells; (2) incorrect numbers of neurons share postsynaptic targets, i.e., more than one climbing fiber to a Purkinje cell; and (3) inhibitory synaptic actions may be carried out in the absence of the major inhibitory interneurons, i.e., Purkinje cell collaterals may be effective in lieu of basket and stellate cells.     

Analysis of the dynamic behavior of neuron populations in the turtle cerebellum: II. Lumped circuit model

A lumped circuit model was constructed which consisted of two input channels, climbing fiber and mossy fiber afferents, which described the magnitudes of synaptic transmission and which accounted for synaptic and transmission delays. The parameters and coefficients of the transfer function were chosen such that they corresponded to physiological observable quantities. The corresponding time function approximated the data points. The results indicated that the dynamic behavior of the cerebellar circuit was satisfactorily accounted for by a parallel excitatory and inhibitory system with a combined climbing fiber and mossy-parallel fiber input exciting the Purkinje cells. The initial negative was predominantly a climbing fiber response of the Purkinje cell supporting the inference which was derived from purely electrophysiological data.     

Physiological properties of afferents and synaptic reorganization in the rat cerebellum degranulated by postnatal X-irradiation.

Elimination of most granule, basket, and stellate interneurons in the rat cerebellum was achieved by repeated doses of low level x-irradiation applied during the first two weeks of postnatal life. Electrical stimulation of the brain stem and peripheral limbs was employed to investigate the properties of afferent cerebellar pathways and the nature of the reorganized neuronal synaptic circuitry in the degranulated cerebellum of the adult. Direct contacts of mossy fibers on Purkinje cells were indicated by short latency, single spike responses: 1.9 msec from the lateral reticular nucleus of brain stem and 5.4 msec from ipsilpateral forelimb. These were shorter than in normal rats by 0.9 and 2.1 msec, respectively. The topography of projections from peripheral stimulation was approximately normal. Mossy fiber responses followed stimulation at up to 20/sec, whereas climbing fiber pathways fatigued at 10/sec. The latency of climbing fiber input to peripheral limb stimulation in x-irradiated cerebellum was 23 +/- 8 (SD) msec. In x-irradiated rats, the climbing fiber pathways evoked highly variable extracellular burst responses and intracellular EPSPs of different, discrete sizes. These variable responses suggest that multiple climbing fibers contact single Purkinje cells. We conclude that each type of afferent retains identifying characteristics of transmission. However, rules for synaptic specification appear to break down so that: (1) abnormal classes of neurons develop synaptic connections, i.e., mossy fibers to Purkinje cells; (2) incorrect numbers of neurons share postsynaptic targets, i.e., more than one climbing fiber to a Purkinje cell; and (3) inhibitory synaptic actions may be carried out in the absence of the major inhibitory interneurons, i.e., Purkinje cell collaterals may be effective in lieu of basket and stellate cells.