Determinants of synaptic integration and heterogeneity in rebound firing explored with data-driven models of deep cerebellar nucleus cells

Significant inroads have been made to understand cerebellar cortical processing but neural coding at the output stage of the cerebellum in the deep cerebellar nuclei (DCN) remains poorly understood. The DCN are unlikely to just present a relay nucleus because Purkinje cell inhibition has to be turned into an excitatory output signal, and DCN neurons exhibit complex intrinsic properties. In particular, DCN neurons exhibit a range of rebound spiking properties following hyperpolarizing current injection, raising the question how this could contribute to signal processing in behaving animals. Computer modeling presents an ideal tool to investigate how intrinsic voltage-gated conductances in DCN neurons could generate the heterogeneous firing behavior observed, and what input conditions could result in rebound responses. To enable such an investigation we built a compartmental DCN neuron model with a full dendritic morphology and appropriate active conductances. We generated a good match of our simulations with DCN current clamp data we recorded in acute slices, including the heterogeneity in the rebound responses. We then examined how inhibitory and excitatory synaptic input interacted with these intrinsic conductances to control DCN firing. We found that the output spiking of the model reflected the ongoing balance of excitatory and inhibitory input rates and that changing the level of inhibition performed an additive operation. Rebound firing following strong Purkinje cell input bursts was also possible, but only if the chloride reversal potential was more negative than −70 mV to allow de-inactivation of rebound currents. Fast rebound bursts due to T-type calcium current and slow rebounds due to persistent sodium current could be differentially regulated by synaptic input, and the pattern of these rebounds was further influenced by HCN current. Our findings suggest that active properties of DCN neurons could play a crucial role for signal processing in the cerebellum.     

Deep cerebellar neurons mirror the spinal cord’s gain to implement an inverse controller

Smooth and coordinated motion requires precisely timed muscle activation patterns, which due to biophysical limitations, must be predictive and executed in a feed-forward manner. In a previous study, we tested Kawato’s original proposition, that the cerebellum implements an inverse controller, by mapping a multizonal microcomplex’s (MZMC) biophysics to a joint’s inverse transfer function and showing that inferior olivary neuron may use their intrinsic oscillations to mirror a joint’s oscillatory dynamics. Here, to continue to validate our mapping, we propose that climbing fiber input into the deep cerebellar nucleus (DCN) triggers rebounds, primed by Purkinje cell inhibition, implementing gain on IO’s signal to mirror the spinal cord reflex’s gain thereby achieving inverse control. We used biophysical modeling to show that Purkinje cell inhibition and climbing fiber excitation interact in a multiplicative fashion to set DCN’s rebound strength; where the former primes the cell for rebound by deinactivating its T-type Ca2⁺ channels and the latter triggers the channels by rapidly depolarizing the cell. We combined this result with our control theory mapping to predict how experimentally injecting current into DCN will affect overall motor output performance, and found that injecting current will proportionally scale the output and unmask the joint’s natural response as observed by motor output ringing at the joint’s natural frequency. Experimental verification of this prediction will lend support to a MZMC as a joint’s inverse controller and the role we assigned underlying biophysical principles that enable it.     

Presynaptic inhibition caused by retrograde signal from metabotropic glutamate to cannabinoid receptors

We report a type of synaptic modulation that involves retrograde signaling from postsynaptic metabotropic glutamate receptors (mGluRs) to presynaptic cannabinoid receptors. Activation of mGluR subtype 1 (mGluR1) expressed in cerebellar Purkinje cells (PCs) reduced neurotransmitter release from excitatory climbing fibers. This required activation of G proteins but not Ca2+ elevation in postsynaptic PCs. This effect was occluded by a cannabinoid agonist and totally abolished by cannabinoid antagonists. Depolarization-induced Ca2+ transients in PCs also caused cannabinoid receptor-mediated presynaptic inhibition. Thus, endocannabinoid production in PCs can be initiated by two distinct stimuli. Activation of mGluR1 by repetitive stimulation of parallel fibers, the other excitatory input to PCs, caused transient cannabinoid receptor-mediated depression of climbing fiber input. Our data highlight a signaling mechanism whereby activation of postsynaptic mGluR retrogradely influences presynaptic functions via endocannabinoid system.     

剌激中缝背核压抑大鼠小脑浦肯野细胞对苔状...

In anaesthetized and paralyzed rats, the effect of dorsal raphe (DR) conditioning stimulation on cerebellar Purkinje cell (PC) responses to mossy fiber and climbing fiber inputs were examined. The main results are as follows: (1) Stimulation of cerebral sensorimotor cortex elicits widespread activation of mossy and climbing fiber inputs to PCs in contralateral VI and VII lobules of the cerebellum and generates two kinds of evoked responses, i.e. the simple spike (SS) and the complex spike (CS) responses with respectively a latency 8-25 and 12-30 ms. (2) These PC responses could be markedly suppressed by stimulation of DR at intensities which by themselves were subthreshold for directly affecting PC's spontaneous SS and CS activities. (3) This DR-induced depressive effects on evoked PC's SS and CS excitations could be attenuated or blocked by systemic administration of 5-HT receptor blocker methysergide. These results demonstrate that serotonergic fiber input from DR can suppress the efficacy of mossy and climbing fiber synaptic action on PC, or decrease the responsiveness of PC itself to afferent synaptic action. The findings of this study also suggest that the raphe-cerebellar serotonergic fiber afferent system may be involved in some of the important neuronal processing in the cerebellum.     

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.     

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.     

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.     

Cerebellar Purkinje cells: membrane property changes on partial deafferentation

The responses of the cerebellar Purkinje cell to removal of its climbing fiber input has been studied electrophysiologically in slices of rat cerebella. Using single electrode current clamp methods, membrane potentials were recorded in various conditions from normal and 3-AP deafferented Purkinje cells (PC). The membrane of the deafferented PC showed a rectification for hyperpolarizing currents which varied in degree with length of time after removal of the climbing fiber input. While this rectification was the most pronounced change in membrane properties provoked by the deafferentation, other more subtle effects were observed in experiments with changes in extracellular ionic compositions. Since the rectification began at membrane potentials near -60 mV, it could prevent membrane hyperpolarization by inhibitory synaptic inputs and thus produce an apparent hypersensitivity to excitatory inputs.     

Ratio of inferior olivary cells to Purkinje cells in a marsupial (Trichosurus vulpecula)

An indirect estimate of the extent of branching of the olivary axons in the cerebellum in a marsupial (Trichosurus vulpecula) was carried out. The cells in the inferior olivary nuclear complex (IOC) of both sides were estimated (mean = 57,200), as were the cerebellar Purkinje cells (mean = 881,300). Assuming that all climbing fibers arise from IOC cells and that each Purkinje cell receives a climbing fiber input, each IOC cell sends climbing fiber terminals to 15 Purkinje cells.     

Visualization of IP(3) dynamics reveals a novel AMPA receptor-triggered IP(3) production pathway mediated by voltage-dependent Ca(2+) influx in Purkinje cells

IP(3) signaling in Purkinje cells is involved in the regulation of cell functions including LTD. We have used a GFP-tagged pleckstrin homology domain to visualize IP(3) dynamics in Purkinje cells. Surprisingly, IP(3) production was observed in response not only to mGluR activation, but also to AMPA receptor activation in Purkinje cells in culture. AMPA-induced IP(3) production was mediated by depolarization-induced Ca(2+) influx because it was mimicked by depolarization and was blocked by inhibition of the P-type Ca(2+) channel. Furthermore, trains of complex spikes, elicited by climbing fiber stimulation (1 Hz), induced IP(3) production in Purkinje cells in cerebellar slices. These results revealed a novel IP(3) signaling pathway in Purkinje cells that can be elicited by synaptic inputs from climbing fibers.     

Specific Relationship between Excitatory Inputs and Climbing Fiber Receptive Fields in Deep Cerebellar Nuclear Neurons

Many mossy fiber pathways to the neurons of the deep cerebellar nucleus (DCN) originate from the spinal motor circuitry. For cutaneously activated spinal neurons, the receptive field is a tag indicating the specific motor function the spinal neuron has. Similarly, the climbing fiber receptive field of the DCN neuron reflects the specific motor output function of the DCN neuron. To explore the relationship between the motor information the DCN neuron receives and the output it issues, we made patch clamp recordings of DCN cell responses to tactile skin stimulation in the forelimb region of the anterior interposed nucleus in vivo. The excitatory responses were organized according to a general principle, in which the DCN cell responses became stronger the closer the skin site was located to its climbing fiber receptive field. The findings represent a novel functional principle of cerebellar connectivity, with crucial importance for our understanding of the function of the cerebellum in movement coordination.     

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.     

Cerebellar complex spikes multiplex complementary behavioral information

Purkinje cell (PC) discharge, the only output of cerebellar cortex, involves 2 types of action potentials, high-frequency simple spikes (SSs) and low-frequency complex spikes (CSs). While there is consensus that SSs convey information needed to optimize movement kinematics, the function of CSs, determined by the PC’s climbing fiber input, remains controversial. While initially thought to be specialized in reporting information on motor error for the subsequent amendment of behavior, CSs seem to contribute to other aspects of motor behavior as well. When faced with the bewildering diversity of findings and views unraveled by highly specific tasks, one may wonder if there is just one true function with all the other attributions wrong? Or is the diversity of findings a reflection of distinct pools of PCs, each processing specific streams of information conveyed by climbing fibers? With these questions in mind, we recorded CSs from the monkey oculomotor vermis deploying a repetitive saccade task that entailed sizable motor errors as well as small amplitude saccades, correcting them. We demonstrate that, in addition to carrying error-related information, CSs carry information on the metrics of both primary and small corrective saccades in a time-specific manner, with changes in CS firing probability coupled with changes in CS duration. Furthermore, we also found CS activity that seemed to predict the upcoming events. Hence PCs receive a multiplexed climbing fiber input that merges complementary streams of information on the behavior, separable by the recipient PC because they are staggered in time.

Purkinje cell (PC) discharge, the only output of cerebellar cortex, involves both high-frequency simple spikes and low-frequency complex spikes; the function of the latter, determined by a PC’s climbing fibre input, remains controversial. This study shows that PCs receive a multiplexed climbing fibre input that merges complementary streams of information relevant for behaviour.     

Electrophysiological analysis of the circuitry and of the corticonuclear relationships in the agranular cerebellum of irradiated rats.

The cerebellar circuitry and the corticonuclear relationships were studied in the cerebellum of adult rats rendered agranular through 7 successive exposures to X-ray radiations during infancy. Data were obtained through examination of electrical responses induced in Purkinje cells (PC) and in neurons of the lateral vestibular nucleus (LVN) by cerebellar and spinal stimulations. In irradiated rats, PC exhibited antidromic activation with a high axonal threshold and 70% of them also presented typical climbing fiber responses (CFRs). By contrast, they exceptionnally exhibited responses via the mossy fiber (MF)-granule cell pathway, but two other classes of responses were identified: i) short latency single spike responses attributed to a direct excitatory impingement of MF onto PC; ii) atypical CFRs formed of high frequency bursts of simple spikes which were seen in 76% of PC tested. Furthermore, 53% of these cells also presented typical CFRs, strongly suggesting these PC were innervated by more than one CF, thus confirming previous data on the same type of agranular cerebellum. In the LVN neurons of control and irradiated rats, spinal and cerebellar stimulations evoked clear cut IPSPs. On the basis of their shape, latency, and occurrence in animals with or without cerebellum and with or without lesion of the CF pathway, they were interpreted as mediated through direct or synaptic activation of PC or through an extracerebellar pathway. In irradiated rats, the quantitative study of these IPSPs gave further arguments in favor of a multiinnervation of PC by CF and of an important reafferentation of MF onto PC. However, the functional efficiency of this reafferentation appeared very low, as tested by activation of MF originating in the spinal cord. Finally, the intracellular recording of LVN neurons showed that a large majority of PC axons retained normal synaptic connections with nuclear cells in treated animals, indicating that corticonuclear relationships do not markedly depend upon granule cells and normal CF input.     

Potentiation of mossy fiber EPSCs in the cerebellar nuclei by NMDA receptor activation followed by postinhibitory rebound current

Behavioral and computational studies predict that synaptic plasticity of excitatory mossy fiber inputs to cerebellar nuclear neurons is required for associative learning, but standard tetanization protocols fail to potentiate nuclear cell EPSCs in mouse cerebellar slices. Nuclear neurons fire action potentials spontaneously unless strongly inhibited by Purkinje neurons, raising the possibility that plasticity-triggering signals in these cells differ from those at classical Hebbian synapses. Based on predictions of neuronal activity during delay eyelid conditioning, we developed quasi-physiological induction protocols consisting of high-frequency mossy fiber stimulation and postsynaptic hyperpolarization. Robust, NMDA receptor-dependent potentiation of nuclear cell EPSCs occurred with protocols including a 150-250 ms hyperpolarization in which mossy fiber stimulation preceded a postinhibitory rebound depolarization. Mossy fiber stimulation potentiated EPSCs even when postsynaptic spiking was prevented by voltage-clamp, as long as rebound current was evoked. These data suggest that Purkinje cell inhibition guides the strengthening of excitatory synapses in the cerebellar nuclei.     

Releasing Dentate Nucleus Cells from Purkinje Cell Inhibition Generates Output from the Cerebrocerebellum

The cerebellum generates its vast amount of output to the cerebral cortex through the dentate nucleus (DN) that is essential for precise limb movements in primates. Nuclear cells in DN generate burst activity prior to limb movement, and inactivation of DN results in cerebellar ataxia. The question is how DN cells become active under intensive inhibitory drive from Purkinje cells (PCs). There are two excitatory inputs to DN, mossy fiber and climbing fiber collaterals, but neither of them appears to have sufficient strength for generation of burst activity in DN. Therefore, we can assume two possible mechanisms: post-inhibitory rebound excitation and disinhibition. If rebound excitation works, phasic excitation of PCs and a concomitant inhibition of DN cells should precede the excitation of DN cells. On the other hand, if disinhibition plays a primary role, phasic suppression of PCs and activation of DN cells should be observed at the same timing. To examine these two hypotheses, we compared the activity patterns of PCs in the cerebrocerebellum and DN cells during step-tracking wrist movements in three Japanese monkeys. As a result, we found that the majority of wrist-movement-related PCs were suppressed prior to movement onset and the majority of wrist-movement-related DN cells showed concurrent burst activity without prior suppression. In a minority of PCs and DN cells, movement-related increases and decreases in activity, respectively, developed later. These activity patterns suggest that the initial burst activity in DN cells is generated by reduced inhibition from PCs, i.e., by disinhibition. Our results indicate that suppression of PCs, which has been considered secondary to facilitation, plays the primary role in generating outputs from DN. Our findings provide a new perspective on the mechanisms used by PCs to influence limb motor control and on the plastic changes that underlie motor learning in the cerebrocerebellum.     

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.     

Multiple innervation of Purkinje cells by climbing fibers in the cerebellum of the adult staggerer mutant mouse

Intracellular recordings from Purkinje cells (PC) in the cerebellum of adult staggerer mutant mice revealed that the orthodromic response of PCs to juxtafastigial (JF) stimulation closely resembled a climbing fiber response (CFR). However, for most of the PCs studied, these responses were graded in a stepwise manner when the stimulus strength was increased. The underlying excitatory synaptic potentials (EPSPs) had the typical shape of EPSPs mediated through climbing fibers (CFs), but their size fluctuated in discrete steps, the highest one reaching the firing level. In the same PCs, the size of the spontaneous EPSPs fluctuated in a similar fashion and the frequency of each step was in the range of CF-mediated EPSPs. These results strongly suggest that in staggerer mice several CFs synapse with each PC instead of a single CF as in normal adults. Furthermore, the activation through some of these CFs does not reach the firing level of the corresponding PC.     

A long-term depression of AMPA currents in cultured cerebellar Purkinje neurons.

Cerebellar long-term depression (LTD) is a model of synaptic plasticity in which conjunctive stimulation of parallel fiber and climbing fiber inputs to a Purkinje neuron induces a persistent depression of the parallel fiber-Purkinje neuron synapse. We report that an analogous phenomenon may be elicited in the cultured mouse Purkinje neuron when iontophoretic glutamate application and depolarization of the Purkinje neurons are substituted for parallel fiber and climbing fiber stimulation, respectively. The induction of LTD in these cerebellar cultures requires activation of both ionotropic (AMPA) and metabotropic quisqualate receptors, together with depolarization in the presence of external Ca2+. This postsynaptic alteration is manifest as a depression of glutamate or AMPA currents, but not aspartate or NMDA currents. These results strengthen the contention that the expression of cerebellar LTD is at least in part postsynaptic and provide evidence that activation of both ionotropic and metabotropic quisqualate receptors are necessary for LTD induction.