Pausing purkinje cells in the cerebellum of the awake cat

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.

Neuronal activity patterns in microcircuits of the cerebellar cortical C3 zone during reaching

The cerebellum is the largest sensorimotor structure in the brain. A fundamental organizational feature of its cortex is its division into a series of rostrocaudally elongated zones. These are defined by their inputs from specific parts of the inferior olive and Purkinje cell output to specific cerebellar and vestibular nuclei. However, little is known about how patterns of neuronal activity in zones, and their microcircuit subdivisions, microzones, are related to behaviour in awake animals. In the present study, we investigated the organization of microzones within the C3 zone and their activity during a skilled forelimb reaching task in cats. Neurons in different microzones of the C3 zone, functionally determined by receptive field characteristics, differed in their patterns of activity during movement. Groups of Purkinje cells belonging to different receptive field classes, and therefore belonging to different microzones, were found to collectively encode different aspects of the reach controlled by the C3 zone. Our results support the hypothesis that the cerebellar C3 zone is organized and operates within a microzonal frame of reference, with a specific relationship between the sensory input to each microzone and its motor output. KEY POINTS: A defining feature of cerebellar organization is its division into a series of zones and smaller subunits termed microzones. Much of how zones and microzones are organized has been determined in anaesthetized preparations, and little is known about their function in awake animals. We recorded from neurons in the forelimb part of the C3 zone 'in action' by recording from single cerebellar cortical neurons located in different microzones defined by their peripheral receptive field properties during a forelimb reach-retrieval task in cats. Neurons from individual microzones had characteristic patterns of activity during movement, indicating that function is organized in relation to microcomplexes.

Gating by Memory: a Theory of Learning in the Cerebellum

This paper presents a model of learning by the cerebellar circuit. In the traditional and dominant learning model, training teaches finely graded parallel fibre synaptic weights which modify transmission to Purkinje cells and to interneurons that inhibit Purkinje cells. Following training, input in a learned pattern drives a training-modified response. The function is that the naive response to input rates is displaced by a learned one, trained under external supervision. In the proposed model, there is no weight-controlled graduated balance of excitation and inhibition of Purkinje cells. Instead, the balance has two functional states-a switch-at synaptic, whole cell and microzone level. The paper is in two parts. The first is a detailed physiological argument for the synaptic learning function. The second uses the function in a computational simulation of pattern memory. Against expectation, this generates a predictable outcome from input chaos (real-world variables). Training always forces synaptic weights away from the middle and towards the limits of the range, causing them to polarise, so that transmission is either robust or blocked. All conditions teach the same outcome, such that all learned patterns receive the same, rather than a bespoke, effect on transmission. In this model, the function of learning is gating-that is, to select patterns that trigger output merely, and not to modify output. The outcome is memory-operated gate activation which operates a two-state balance of weight-controlled transmission. Group activity of parallel fibres also simultaneously contains a second code contained in collective rates, which varies independently of the pattern code. A two-state response to the pattern code allows faithful, and graduated, control of Purkinje cell firing by the rate code, at gated times.

Parvalbumin subtypes of cerebellar Purkinje cells contribute to differential intrinsic firing properties

Purkinje cells (PCs) are central to cerebellar information coding and appreciation for the diversity of their firing patterns and molecular profiles is growing. Heterogeneous subpopulations of PCs have been identified that display differences in intrinsic firing properties without clear mechanistic insight into what underlies the divergence in firing parameters. Although long used as a general PC marker, we report that the calcium binding protein parvalbumin labels a subpopulation of PCs, based on high and low expression, with a conserved distribution pattern across the animals examined. We trained a convolutional neural network to recognize the parvalbumin subtypes and create maps of whole cerebellar distribution and find that PCs within these areas have differences in spontaneous firing that can be modified by altering calcium buffer content. These subtypes also show differential responses to potassium and calcium channel blockade, suggesting a mechanistic role for variability in PC intrinsic firing through differences in ion channel composition. It is proposed that ion channels drive the diversity in PC intrinsic firing phenotype and parvalbumin calcium buffering provides capacity for the highest firing rates observed. These findings open new avenues for detailed classification of PC subtypes.

Radiofrequency electromagnetic field affects heart rate variability in rabbits

The aim of this study was to assess the effects of radiofrequency electromagnetic field (RF EMF) on heart rate variability (HRV) in rabbits with intensity slightly exceeding the limits for occupations. Totally 21 New Zealand white rabbits divided into two groups were used in this double-blind study. The first group of animals without general anesthesia was subjected to HRV examination under exposure to a device generated RF EMF source (frequency 1788 MHz, intensity 160 V/m, lasting 150 min.). The second group (premedications + alpha chloralose mg/kg) underwent the same protocol under the exposure to the real RF EMF signal from the base stations of mobile providers (frequency range 1805 - 1870 MHz - corresponding to the downlink signal of Slovak mobile providers, 160 V/m, 150 min., respectively). Individual 5 min records were used to analyze the HRV parameters: heart rate and root Mean Square of the Successive Differences (rMSSD) for time domain analysis and spectral powers in the low (LF-VFS) and high frequency (HF-VFS) bands for frequency domain analysis. Our study revealed the increased in HRV parameters (HF-HRV, rMSSD) associated with lower heart rate indicating increased cardiac vagal control under the exposure to RF EMF in experimental methods.

Functional Alteration of Cerebello-Cerebral Coupling in an Experimental Mouse Model of Parkinson's Disease

In Parkinson's disease, the degeneration of the midbrain dopaminergic neurons is consistently associated with modified metabolic activity in the cerebellum. Here we examined the functional reorganization taking place in the cerebello-cerebral circuit in a murine model of Parkinson's disease with 6-OHDA lesion of midbrain dopaminergic neurons. Cerebellar optogenetic stimulations evoked similar movements in control and lesioned mice, suggesting a normal coupling of cerebellum to the motor effectors after the lesion. In freely moving animals, the firing rate in the primary motor cortex was decreased after the lesion, while cerebellar nuclei neurons showed an increased firing rate. This increase may result from reduced inhibitory Purkinje cells inputs, since a population of slow and irregular Purkinje cells was observed in the cerebellar hemispheres of lesioned animals. Moreover, cerebellar stimulations generated smaller electrocortical responses in the motor cortex of lesioned animals suggesting a weaker cerebello-cerebral coupling. Overall these results indicate the presence of functional changes in the cerebello-cerebral circuit, but their ability to correct cortical dysfunction may be limited due to functional uncoupling between the cerebellum and cerebral cortex.

The Role of BTBD9 in the Cerebellum, Sleep-like Behaviors and the Restless Legs Syndrome

Recent genome-wide association studies (GWAS) have found cerebellum as a top hit for sleep regulation. Restless legs syndrome (RLS) is a sleep-related sensorimotor disorder characterized by uncomfortable sensations in the extremities, generally at night, which are often relieved by movements. Clinical studies have found that RLS patients have structural and functional abnormalities in the cerebellum. However, whether and how cerebellar pathology contributes to sleep regulation and RLS is not known. GWAS identified polymorphisms in BTBD9 conferring a higher risk of sleep disruption and RLS. Knockout of the BTBD9 homolog in mice (Btbd9) and fly results in motor restlessness and sleep disruption. We performed manganese-enhanced magnetic resonance imaging on the Btbd9 knockout mice and found decreased neural activities in the cerebellum, especially in lobules VIII, X, and the deep cerebellar nuclei. Electrophysiological recording of Purkinje cells (PCs) from Btbd9 knockout mice revealed an increased number of non-tonic PCs. Tonic PCs showed increased spontaneous activity and intrinsic excitability. To further investigate the cerebellar contribution to RLS and sleep-like behaviors, we generated PC-specific Btbd9 knockout mice (Btbd9 pKO) and performed behavioral studies. Btbd9 pKO mice showed significant motor restlessness during the rest phase but not in the active phase. Btbd9 pKO mice also had an increased probability of waking at rest. Unlike the Btbd9 knockout mice, there was no increased thermal sensation in the Btbd9 pKO. Our results indicate that the Btbd9 knockout influences the PC activity; dysfunction in the cerebellum may contribute to the motor restlessness found in the Btbd9 knockout mice.

Neural Signals in Red Nucleus during Reactive and Proactive Adjustments in Behavior

The ability to adjust behavior is an essential component of cognitive control. Much is known about frontal and striatal processes that support cognitive control, but few studies have investigated how motor signals change during reactive and proactive adjustments in motor output. To address this, we characterized neural signals in red nucleus (RN), a brain region linked to motor control, as male and female rats performed a novel variant of the stop-signal task. We found that activity in RN represented the direction of movement and was strongly correlated with movement speed. Additionally, we found that directional movement signals were amplified on STOP trials before completion of the response and that the strength of RN signals was modulated when rats exhibited cognitive control. These results provide the first evidence that neural signals in RN integrate cognitive control signals to reshape motor outcomes reactively within trials and proactivity across them.SIGNIFICANCE STATEMENT Healthy human behavior requires the suppression or inhibition of errant or maladaptive motor responses, often called cognitive control. While much is known about how frontal brain regions facilitate cognitive control, less is known about how motor regions respond to rapid and unexpected changes in action selection. To address this, we recorded from neurons in the red nucleus, a motor region thought to be important for initiating movement in rats performing a cognitive control task. We show that red nucleus tracks motor plans and that selectivity was modulated on trials that required shifting from one motor response to another. Collectively, these findings suggest that red nucleus contributes to modulating motor behavior during cognitive control.

Online Detection of Multiple Stimulus Changes Based on Single Neuron Interspike Intervals

Nervous systems need to detect stimulus changes based on their neuronal responses without using any additional information on the number, times, and types of stimulus changes. Here, two relatively simple, biologically realistic change point detection methods are compared with two common analysis methods. The four methods are applied to intra- and extracellularly recorded responses of a single cricket interneuron (AN2) to acoustic simulation. Solely based on these recorded responses, the methods should detect an unknown number of different types of sound intensity in- and decreases shortly after their occurrences. For this task, the methods rely on calculating an adjusting interspike interval (ISI). Both simple methods try to separate responses to intensity in- or decreases from activity during constant stimulation. The Pure-ISI method performs this task based on the distribution of the ISI, while the ISI-Ratio method uses the ratio of actual and previous ISI. These methods are compared to the frequently used Moving-Average method, which calculates mean and standard deviation of the instantaneous spike rate in a moving interval. Additionally, a classification method provides the upper limit of the change point detection performance that can be expected for the cricket interneuron responses. The classification learns the statistical properties of the actual and previous ISI during stimulus changes and constant stimulation from a training data set. The main results are: (1) The Moving-Average method requires a stable activity in a long interval to estimate the previous activity, which was not always given in our data set. (2) The Pure-ISI method can reliably detect stimulus intensity increases when the neuron bursts, but it fails to identify intensity decreases. (3) The ISI-Ratio method detects stimulus in- and decreases well, if the spike train is not too noisy. (4) The classification method shows good performance for the detection of stimulus in- and decreases. But due to the statistical learning, this method tends to confuse responses to constant stimulation with responses triggered by a stimulus change. Our results suggest that stimulus change detection does not require computationally costly mechanisms. Simple nervous systems like the cricket's could effectively apply ISI-Ratios to solve this fundamental task.

Discrimination of bursts and tonic activity in multifunctional sensorimotor neural network using the extended hill-valley method

Individual neurons can exhibit a wide range of activity, including spontaneous spiking, tonic spiking, bursting, or spike-frequency adaptation, and can also transition between these activity types. Manual identification of these activity patterns can be subjective and inconsistent. The extended hill-valley (EHV) analysis discriminates tonic spiking and bursts in a spike train by detecting fluctuations in a local, history-dependent analysis signal derived from the spike train. Consequently, the EHV method is not susceptible to changes in baseline firing rate and can identify different types of activity patterns. In addition, output from the EHV method can be used to identify more complex activity patterns such as phasotonic bursting, in which a burst is immediately followed by a period of tonic spiking.NEW & NOTEWORTHY Neurons exhibit diverse spiking patterns, but automated activity classification has focused mainly on detecting bursts. The novel extended hill-valley algorithm uses a smoothed, history-dependent signal to discriminate different types of activity, such as bursts and tonic spiking.

Complex Spike Wars: a New Hope

The climbing fiber-Purkinje cell circuit is one of the most powerful and highly conserved in the central nervous system. Climbing fibers exert a powerful excitatory action that results in a complex spike in Purkinje cells and normal functioning of the cerebellum depends on the integrity of climbing fiber-Purkinje cell synapse. Over the last 50 years, multiple hypotheses have been put forward on the role of the climbing fibers and complex spikes in cerebellar information processing and motor control. Central to these theories is the nature of the interaction between the low-frequency complex spike discharge and the high-frequency simple spike firing of Purkinje cells. This review examines the major hypotheses surrounding the action of the climbing fiber-Purkinje cell projection, discussing both supporting and conflicting findings. The review describes newer findings establishing that climbing fibers and complex spikes provide predictive signals about movement parameters and that climbing fiber input controls the encoding of behavioral information in the simple spike firing of Purkinje cells. Finally, we propose the dynamic encoding hypothesis for complex spike function that strives to integrate established and newer findings.

Cerebellar learning using perturbations

The cerebellum aids the learning of fast, coordinated movements. According to current consensus, erroneously active parallel fibre synapses are depressed by complex spikes signalling movement errors. However, this theory cannot solve the credit assignment problem of processing a global movement evaluation into multiple cell-specific error signals. We identify a possible implementation of an algorithm solving this problem, whereby spontaneous complex spikes perturb ongoing movements, create eligibility traces and signal error changes guiding plasticity. Error changes are extracted by adaptively cancelling the average error. This framework, stochastic gradient descent with estimated global errors (SGDEGE), predicts synaptic plasticity rules that apparently contradict the current consensus but were supported by plasticity experiments in slices from mice under conditions designed to be physiological, highlighting the sensitivity of plasticity studies to experimental conditions. We analyse the algorithm's convergence and capacity. Finally, we suggest SGDEGE may also operate in the basal ganglia.

Switching in Feedforward Control of Grip Force During Tool-Mediated Interaction With Elastic Force Fields

Switched systems are common in artificial control systems. Here, we suggest that the brain adopts a switched feedforward control of grip forces during manipulation of objects. We measured how participants modulated grip force when interacting with soft and rigid virtual objects when stiffness varied continuously between trials. We identified a sudden phase transition between two forms of feedforward control that differed in the timing of the synchronization between the anticipated load force and the applied grip force. The switch occurred several trials after a threshold stiffness level in the range 100–200 N/m. These results suggest that in the control of grip force, the brain acts as a switching control system. This opens new research questions as to the nature of the discrete state variables that drive the switching.

Calcium Imaging Reveals Coordinated Simple Spike Pauses in Populations of Cerebellar Purkinje Cells

The brain's control of movement is thought to involve coordinated activity between cerebellar Purkinje cells. The results reported here demonstrate that somatic Ca²⁺ imaging is a faithful reporter of Na⁺-dependent "simple spike" pauses and enables us to optically record changes in firing rates in populations of Purkinje cells in brain slices and in vivo. This simultaneous calcium imaging of populations of Purkinje cells reveals a striking spatial organization of pauses in Purkinje cell activity between neighboring cells. The source of this organization is shown to be the presynaptic gamma-Aminobutyric acid producing (GABAergic) network, and blocking ionotropic gamma-Aminobutyric acid receptor (GABA_ARs) abolishes the synchrony. These data suggest that presynaptic interneurons synchronize (in)activity between neighboring Purkinje cells, and thereby maximize their effect on downstream targets in the deep cerebellar nuclei.

Climbing Fibers Control Purkinje Cell Representations of Behavior

A crucial issue in understanding cerebellar function is the interaction between simple spike (SS) and complex spike (CS) discharge, the two fundamentally different activity modalities of Purkinje cells. Although several hypotheses have provided insights into the interaction, none fully explains or is completely consistent with the spectrum of experimental observations. Here, we show that during a pseudo-random manual tracking task in the monkey (Macaca mulatta), climbing fiber discharge dynamically controls the information present in the SS firing, triggering robust and rapid changes in the SS encoding of motor signals in 67% of Purkinje cells. The changes in encoding, tightly coupled to CS occurrences, consist of either increases or decreases in the SS sensitivity to kinematics or position errors and are not due to differences in SS firing rates or variability. Nor are the changes in sensitivity due to CS rhythmicity. In addition, the CS-coupled changes in encoding are not evoked by changes in kinematics or position errors. Instead, CS discharge most often leads alterations in behavior. Increases in SS encoding of a kinematic parameter are associated with larger changes in that parameter than are decreases in SS encoding. Increases in SS encoding of position error are followed by and scale with decreases in error. The results suggest a novel function of CSs, in which climbing fiber input dynamically controls the state of Purkinje cell SS encoding in advance of changes in behavior.SIGNIFICANCE STATEMENT Purkinje cells, the sole output of the cerebellar cortex, manifest two fundamentally different activity modalities, complex spike (CS) discharge and simple spike (SS) firing. Elucidating cerebellar function will require an understanding of the interactions, both short- and long-term, between CS and SS firing. This study shows that CSs dynamically control the information encoded in a Purkinje cell's SS activity by rapidly increasing or decreasing the SS sensitivity to kinematics and/or performance errors independent of firing rate. In many cases, the CS-coupled shift in SS encoding leads a change in behavior. These novel findings on the interaction between CS and SS firing provide for a new hypothesis in which climbing fiber input adjusts the encoding of SS information in advance of a change in behavior.

Power Spectral Density Analysis of Purkinje Cell Tonic and Burst Firing Patterns From a Rat Model of Ataxia and Riluzole Treated

Introduction:

Purkinje Cell (PC) output displays a complex firing pattern consisting of high frequency sodium spikes and low frequency calcium spikes, and disruption in this firing behavior may contribute to cerebellar ataxia. Riluzole, neuroprotective agent, has been demonstrated to have neuroprotective effects in cerebellar ataxia. Here, the spectral analysis of PCs firing in control, 3-acetylpyridine (3-AP), neurotoxin agent, treated alone and riluzole plus 3-AP treated were investigated to determine changes in the firing properties. Difference in the power spectra of tonic and burst firing was assessed. Furthermore, the role of calcium-activated potassium channels in the power spectra was evaluated.

Methods:

Analysis was performed using Matlab. Power spectral density (PSD) of PCs output were obtained. Peak frequencies were extracted from the spectrum and statistical comparisons were done. In addition, a multi-compartment computational model of a Purkinje cell was used. This computational stimulation allowed us to study the changes in the power spectral density of the PC output as a result of alteration in ion channels.

Results:

Spectral analysis showed that in the spectrum of tonic and burst firing pattern only high sodium frequency and low calcium frequency was seen, respectively. In addition, there was a significant difference between the frequency components of PCs firing obtained from normal, ataxia and riluzole treated rats. Results indicated that sodium firing frequency of normal, ataxic and treated PCs occurred in approximate frequency of 22.53±5.49, 6.46±0.23, and 31.34±4.07 Hz, respectively; and calcium frequency occurred in frequency of 4.22±2.02, 1.52±1.19, and 3.88±1.37 Hz, respectively. The simulation results demonstrated that blockade of calcium-activated potassium channels in the PC model changed the PSD of the PC model firing activity. This change was similar to PSD changes in ataxia condition.

Conclusion:

These alterations in the spectrum of PC output may be a basis for developing possible new treatment strategies to improve cerebellar ataxia.

Inverse Stochastic Resonance in Cerebellar Purkinje Cells

Purkinje neurons play an important role in cerebellar computation since their axons are the only projection from the cerebellar cortex to deeper cerebellar structures. They have complex internal dynamics, which allow them to fire spontaneously, display bistability, and also to be involved in network phenomena such as high frequency oscillations and travelling waves. Purkinje cells exhibit type II excitability, which can be revealed by a discontinuity in their f-I curves. We show that this excitability mechanism allows Purkinje cells to be efficiently inhibited by noise of a particular variance, a phenomenon known as inverse stochastic resonance (ISR). While ISR has been described in theoretical models of single neurons, here we provide the first experimental evidence for this effect. We find that an adaptive exponential integrate-and-fire model fitted to the basic Purkinje cell characteristics using a modified dynamic IV method displays ISR and bistability between the resting state and a repetitive activity limit cycle. ISR allows the Purkinje cell to operate in different functional regimes: the all-or-none toggle or the linear filter mode, depending on the variance of the synaptic input. We propose that synaptic noise allows Purkinje cells to quickly switch between these functional regimes. Using mutual information analysis, we demonstrate that ISR can lead to a locally optimal information transfer between the input and output spike train of the Purkinje cell. These results provide the first experimental evidence for ISR and suggest a functional role for ISR in cerebellar information processing.

How neurons generate output spikes in response to various combinations of inputs is a central issue in contemporary neuroscience. Due to their large dendritic tree and complex intrinsic properties, cerebellar Purkinje cells are an important model system to study this input-output transformation. Here we examine how noise can change the parameters of this transformation. In experiments we found that spike generation in Purkinje cells can be efficiently inhibited by noise of a particular amplitude. This effect is called inverse stochastic resonance (ISR) and has previously been described only in theoretical models of neurons. We explain the mechanism underlying ISR using a simple model matching the properties of experimentally characterized Purkinje cells. We found that ISR is present in Purkinje cells when the mean input current is near threshold for spike generation. ISR can be explained by the co-existence of resting and spiking solutions of the simple model. Changes of the input noise variance change the lifetime of these resting and spiking states, suggesting a mechanism for a tunable filter with long time constants implemented by a Purkinje cell population in the cerebellum. Finally, ISR leads to locally optimal information transfer from the input to the output of a Purkinje cell.

Multiplexed coding by cerebellar Purkinje neurons

Purkinje cells (PC), the sole output neurons of the cerebellar cortex, encode sensorimotor information, but how they do it remains a matter of debate. Here we show that PCs use a multiplexed spike code. Synchrony/spike time and firing rate encode different information in behaving monkeys during saccadic eye motion tasks. Using the local field potential (LFP) as a probe of local network activity, we found that infrequent pause spikes, which initiated or terminated intermittent pauses in simple spike trains, provide a temporally reliable signal for eye motion onset, with strong phase-coupling to the β/γ band LFP. Concurrently, regularly firing, non-pause spikes were weakly correlated with the LFP, but were crucial to linear encoding of eye movement kinematics by firing rate. Therefore, PC spike trains can simultaneously convey information necessary to achieve precision in both timing and continuous control of motion.

DOI:http://dx.doi.org/10.7554/eLife.13810.001

The cerebellum is a part of the brain that uses information from the senses to coordinate movement. Cells called Purkinje neurons in the cerebellum produce the final ‘output’ of its cortex. Therefore, Purkinje neurons have to communicate precise information about different aspects of the movement, such as its speed and timing. This information is likely to be represented by patterns of electrical activity within Purkinje neurons, but these patterns are still not fully understood.

Hong et al. recorded and analyzed electrical ‘spikes’, the output activity of Purkinje neurons, while monkeys made rapid eye movements. The recordings showed that occasional pauses in the otherwise regularly firing spikes of Purkinje neurons signaled the start of the eye movements. The pauses were accompanied by a sharp change in the local field potential, another electrical signal that comes from many neurons in the neighborhood. In the same cells, the rate of regularly firing spikes increased and decreased with the direction and speed of eye movements, following a simple relationship and independently of the local field potential.

Purkinje neurons therefore appear to use both the timing and the rate of their spiking activity to represent movement. This resolves conflicting reports in the literature claiming that either rates of spiking or their timing code essential information about movements: both are important. This way of representing information by combining more than one source is known as multiplexed coding.

Next, experiments recording electrical activity from many cells in the cerebellum at the same time are needed to find out how multiple Purkinje neurons can pause their spiking activity at the same time. Future experiments should also uncover how pauses in spiking and firing rates change with learning.

DOI:http://dx.doi.org/10.7554/eLife.13810.002

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

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

Long Pauses in Cerebellar Interneurons in Anesthetized Animals

Are long pauses in the firing of cerebellar interneurons (CINs) related to Purkinje cell (PC) pauses? If PC pauses affect the larger network, then we should find a close relationship between CIN pauses and those in PCs. We recorded activity of 241 cerebellar cortical neurons (206 CINs and 35 PCs) in three anesthetized cats. One fifth of the CINs and more than half of the PCs were identified as pausing. Pauses in CINs and PCs showed some differences: CIN mean pause length was shorter, and, after pauses, only CINs had sustained reduction in their firing rate (FR). Almost all pausing CINs fell into same cluster when we used different methods of clustering CINs by their spontaneous activity. The mean spontaneous firing rate of that cluster was approximately 53 Hz. We also examined cross-correlations in simultaneously recorded neurons. Of 39 cell pairs examined, 14 (35 %) had cross-correlations significantly different from those expected by chance. Almost half of the pairs with two CINs showed statistically significant negative correlations. In contrast, PC/CIN pairs did not often show significant effects in the cross-correlation (12/15 pairs). However, for both CIN/CIN and PC/CIN pairs, pauses in one unit tended to correspond to a reduction in the firing rate of the adjacent unit. In our view, our results support the possibility that previously reported PC bistability is part of a larger network response and not merely a biophysical property of PCs. Any functional role for PC bistability should probably be sought in the context of the broader network.

Determinants of rebound burst responses in rat cerebellar nuclear neurons to physiological stimuli

KEY POINTS

Cerebellar Purkinje cells project GABAergic inhibitory input to neurons of the deep cerebellar nuclei (DCN) that generate a rebound increase in firing, but the specific patterns of input that might elicit a rebound response have not been established. We used recordings of Purkinje cell firing obtained during perioral whisker stimulation in vivo to create a physiological stimulus template to activate Purkinje cell afferents in vitro. DCN cell bursts were evoked by the stimulus pattern but not in relation to the perioral whisker stimulus, complex spikes or regular patterns within the Purkinje cell record. Reverse correlation revealed that bursts were triggered by an elevation-pause pattern of Purkinje cell firing, with pause duration a key factor in burst generation. Our data identify for the first time a physiological pattern of Purkinje cell input that can be encoded by the generation of rebound bursts in DCN cells.

ABSTRACT

The end result of signal processing in cerebellar cortex is encoded in the output of Purkinje cells that project inhibitory input to deep cerebellar nuclear (DCN) neurons. DCN cells can respond to a period of inhibition in vitro with a rebound burst of firing, yet the optimal physiological pattern of Purkinje cell input that might evoke a rebound burst is unknown. The current study used spike trains recorded from rat Purkinje cells in response to perioral stimuli in vivo to create a physiological pattern to stimulate Purkinje cell axons in vitro. The perioral stimulus-evoked Purkinje cell firing pattern proved to be virtually ineffective in evoking a rebound burst despite the ability to reliably evoke rebounds using a traditional brief 100 Hz stimulus. Similarly, neither complex spike firing nor Purkinje cell patterns identified by CV2 analysis were reliably associated with rebound bursts. Reverse correlation revealed that the optimal Purkinje cell input to evoke a rebound burst was a sequential increase in mean firing rate of at least 30 Hz above baseline over 250 ms followed by a reduction of 40-60 Hz below baseline for up to 500 ms. The most important factor was the duration of a pause in Purkinje cell firing that allowed DCN cells to recover from a state of net inhibitory influence. These data indicate that physiological patterns of Purkinje cell firing can elicit rebound bursts in DCN cells in vitro, with pauses in Purkinje cell firing rate acting as a key stimulus for DCN cell rebound responses.

AMPA receptor mediated synaptic excitation drives state-dependent bursting in Purkinje neurons of zebrafish larvae

Purkinje neurons are central to cerebellar function and show membrane bistability when recorded in vitro or in vivo under anesthesia. The existence of bistability in vivo in awake animals is disputed. Here, by recording intracellularly from Purkinje neurons in unanesthetized larval zebrafish (Danio rerio), we unequivocally demonstrate bistability in these neurons. Tonic firing was seen in depolarized regimes and bursting at hyperpolarized membrane potentials. In addition, Purkinje neurons could switch from one state to another spontaneously or with current injection. While GABAAR or NMDAR were not required for bursting, activation of AMPARs by climbing fibers (CFs) was sufficient to trigger bursts. Further, by recording Purkinje neuron membrane potential intracellularly, and motor neuron spikes extracellularly, we show that initiation of motor neuron spiking is correlated with increased incidence of CF EPSPs and membrane depolarization. Developmentally, bistability was observed soon after Purkinje neuron specification and persists at least until late larval stages.

Spinocerebellar ataxia type 6 protein aggregates cause deficits in motor learning and cerebellar plasticity

Spinocerebellar ataxia type 6 (SCA6) is linked to poly-glutamine (polyQ) within the C terminus (CT) of the pore-forming subunits of P/Q-type Ca(2+) channels (Cav2.1) and is characterized by CT protein aggregates found in cerebellar Purkinje cells (PCs). One hypothesis regarding SCA6 disease is that a CT fragment of the Cav2.1 channel, which is detected specifically in cytosolic and nuclear fractions in SCA6 patients, is associated with the SCA6 pathogenesis. To test this hypothesis, we expressed P/Q-type channel protein fragments from two different human CT splice variants, as predicted from SCA6 patients, in PCs of mice using viral and transgenic approaches. These splice variants represent a short (CT-short without polyQs) and a long (CT-long with 27 polyQs) CT fragment. Our results show that the different splice variants of the CTs differentially distribute within PCs, i.e., the short CTs reveal predominantly nuclear inclusions, whereas the long CTs prominently reveal both nuclear and cytoplasmic aggregates. Postnatal expression of CTs in PCs in mice reveals that only CT-long causes SCA6-like symptoms, i.e., deficits in eyeblink conditioning (EBC), ataxia, and PC degeneration. The physiological phenotypes associated specifically with the long CT fragment can be explained by an impairment of LTD and LTP at the parallel fiber-to-PC synapse and alteration in spontaneous PC activity. Thus, our results suggest that the polyQ carrying the CT fragment of the P/Q-type channel is sufficient to cause SCA6 pathogenesis in mice and identifies EBC as a new diagnostic strategy to evaluate Ca(2+) channel-mediated human diseases.

Redefining the cerebellar cortex as an assembly of non-uniform Purkinje cell microcircuits

The adult mammalian cerebellar cortex is generally assumed to have a uniform cytoarchitecture. Differences in cerebellar function are thought to arise primarily through distinct patterns of input and output connectivity rather than as a result of variations in cortical microcircuitry. However, evidence from anatomical, physiological and genetic studies is increasingly challenging this orthodoxy, and there are now various lines of evidence indicating that the cerebellar cortex is not uniform. Here, we develop the hypothesis that regional differences in properties of cerebellar cortical microcircuits lead to important differences in information processing.

Differential Purkinje cell simple spike activity and pausing behavior related to cerebellar modules

The massive computational capacity of the cerebellar cortex is conveyed by Purkinje cells onto cerebellar and vestibular nuclei neurons through their GABAergic, inhibitory output. This implies that pauses in Purkinje cell simple spike activity are potentially instrumental in cerebellar information processing, but their occurrence and extent are still heavily debated. The cerebellar cortex, although often treated as such, is not homogeneous. Cerebellar modules with distinct anatomical connectivity and gene expression have been described, and Purkinje cells in these modules also differ in firing rate of simple and complex spikes. In this study we systematically correlate, in awake mice, the pausing in simple spike activity of Purkinje cells recorded throughout the entire cerebellum, with their location in terms of lobule, transverse zone, and zebrin-identified cerebellar module. A subset of Purkinje cells displayed long (>500-ms) pauses, but we found that their occurrence correlated with tissue damage and lower temperature. In contrast to long pauses, short pauses (<500 ms) and the shape of the interspike interval (ISI) distributions can differ between Purkinje cells of different lobules and cerebellar modules. In fact, the ISI distributions can differ both between and within populations of Purkinje cells with the same zebrin identity, and these differences are at least in part caused by differential synaptic inputs. Our results suggest that long pauses are rare but that there are differences related to shorter intersimple spike intervals between and within specific subsets of Purkinje cells, indicating a potential further segregation in the activity of cerebellar Purkinje cells.

Action potential processing in a detailed Purkinje cell model reveals a critical role for axonal compartmentalization

The Purkinje cell (PC) is among the most complex neurons in the brain and plays a critical role for cerebellar functioning. PCs operate as fast pacemakers modulated by synaptic inputs but can switch from simple spikes to complex bursts and, in some conditions, show bistability. In contrast to original works emphasizing dendritic Ca-dependent mechanisms, recent experiments have supported a primary role for axonal Na-dependent processing, which could effectively regulate spike generation and transmission to deep cerebellar nuclei (DCN). In order to account for the numerous ionic mechanisms involved (at present including Nav1.6, Cav2.1, Cav3.1, Cav3.2, Cav3.3, Kv1.1, Kv1.5, Kv3.3, Kv3.4, Kv4.3, KCa1.1, KCa2.2, KCa3.1, Kir2.x, HCN1), we have elaborated a multicompartmental model incorporating available knowledge on localization and gating of PC ionic channels. The axon, including initial segment (AIS) and Ranvier nodes (RNs), proved critical to obtain appropriate pacemaking and firing frequency modulation. Simple spikes initiated in the AIS and protracted discharges were stabilized in the soma through Na-dependent mechanisms, while somato-dendritic Ca channels contributed to sustain pacemaking and to generate complex bursting at high discharge regimes. Bistability occurred only following Na and Ca channel down-regulation. In addition, specific properties in RNs K currents were required to limit spike transmission frequency along the axon. The model showed how organized electroresponsive functions could emerge from the molecular complexity of PCs and showed that the axon is fundamental to complement ionic channel compartmentalization enabling action potential processing and transmission of specific spike patterns to DCN.

Intracellular calcium dynamics permit a Purkinje neuron model to perform toggle and gain computations upon its inputs

Without synaptic input, Purkinje neurons can spontaneously fire in a repeating trimodal pattern that consists of tonic spiking, bursting and quiescence. Climbing fiber input (CF) switches Purkinje neurons out of the trimodal firing pattern and toggles them between a tonic firing and a quiescent state, while setting the gain of their response to Parallel Fiber (PF) input. The basis to this transition is unclear. We investigate it using a biophysical Purkinje cell model under conditions of CF and PF input. The model can replicate these toggle and gain functions, dependent upon a novel account of intracellular calcium dynamics that we hypothesize to be applicable in real Purkinje cells.

Stimulus discrimination in cerebellar Purkinje neurons

Cerebellar Purkinje neurons fire spontaneously in the absence of synaptic input. Overlaid on this intrinsic activity, excitatory input from parallel fibres can add simple spikes to the output train, whereas inhibitory input from interneurons can introduce pauses. These and other influences lead to an irregular spike train output in Purkinje neurons in vitro and in vivo, supplying a variable inhibitory drive to deep cerebellar nuclear neurons. From a computational perspective, this variability raises some questions, as individual spikes induced by excitatory inputs are indistinguishable from intrinsic firing activity. Although bursts of high-frequency excitatory input could be discriminated unambiguously from background activity, granule neurons are known to fire in vivo over a wide range of frequencies. This would mean that much of the sensory information relayed through the cerebellar cortex would be lost within the random variation in background activity. We speculated that alternative mechanisms for signal discrimination may exist, and sought to identify characteristic motifs within the sequence of spikes that followed stimulation events. We found that under certain conditions, parallel fibre stimulation could reliably add a “couplet” of spikes with an unusually short interspike interval to the output train. Therefore, despite representing a small fraction of the total number of spikes, these signals can be reliably discriminated from background firing on a moment-to-moment basis, and could result in a differential downstream response.

Emergence of a 600-Hz buzz UP state Purkinje cell firing in alert mice

Purkinje cell (PC) firing represents the sole output from the cerebellar cortex onto the deep cerebellar and vestibular nuclei. Here, we explored the different modes of PC firing in alert mice by extracellular recording. We confirm the existence of a tonic and/or bursting and quiescent modes corresponding to UP and DOWN state, respectively. We demonstrate the existence of a novel 600-Hz buzz UP state of firing characterized by simple spikes (SS) of very small amplitude. Climbing fiber (CF) input is able to switch the 600-Hz buzz to the DOWN state, as for the classical UP-to-DOWN state transition. Conversely, the CF input can initiate a typical SS pattern terminating into 600-Hz buzz. The 600-Hz buzz was transiently suppressed by whisker pad stimulation demonstrating that it remained responsive to peripheral input. It must not be mistaken for a DOWN state or the sign of PC inhibition. Complex spike (CS) frequency was increased during the 600-Hz buzz, indicating that this PC output actively contributes to the cerebello-olivary loop by triggering a disinhibition of the inferior olive. During the 600-Hz buzz, the first depolarizing component of the CS was reduced and the second depolarizing component was suppressed. Consistent with our experimental observations, using a 559-compartment single-PC model - in which PC UP state (of about -43mV) was obtained by the combined action of large tonic AMPA conductances and counterbalancing GABAergic inhibition - removal of this inhibition produced the 600-Hz buzz; the simulated buzz frequency decreased following an artificial CS.

Translational approach to behavioral learning: lessons from cerebellar plasticity

The role of cerebellar plasticity has been increasingly recognized in learning. The privileged relationship between the cerebellum and the inferior olive offers an ideal circuit for attempting to integrate the numerous evidences of neuronal plasticity into a translational perspective. The high learning capacity of the Purkinje cells specifically controlled by the climbing fiber represents a major element within the feed-forward and feedback loops of the cerebellar cortex. Reciprocally connected with the basal ganglia and multimodal cerebral domains, this cerebellar network may realize fundamental functions in a wide range of behaviors. This review will outline the current understanding of three main experimental paradigms largely used for revealing cerebellar functions in behavioral learning: (1) the vestibuloocular reflex and smooth pursuit control, (2) the eyeblink conditioning, and (3) the sensory envelope plasticity. For each of these experimental conditions, we have critically revisited the chain of causalities linking together neural circuits, neural signals, and plasticity mechanisms, giving preference to behaving or alert animal physiology. Namely, recent experimental approaches mixing neural units and local field potentials recordings have demonstrated a spike timing dependent plasticity by which the cerebellum remains at a strategic crossroad for deciphering fundamental and translational mechanisms from cellular to network levels.

The minimum transition hypothesis for intermittent hierarchical motor control

In intermittent control, instead of continuously calculating the control signal, the controller occasionally changes this signal at certain sparse points in time. The control law may include feedback, adaptation, optimization, or any other control strategies. When, where, and how does the brain employ intermittency as it controls movement? These are open questions in motor neuroscience. Evidence for intermittency in human motor control has been repeatedly observed in the neural control of movement literature. Moreover, some researchers have provided theoretical models to address intermittency. Even so, the vast majority of current models, and I would dare to say the dogma in most of the current motor neuroscience literature involves continuous control. In this paper, I focus on an area in which intermittent control has not yet been thoroughly considered, the structure of muscle synergies. A synergy in the muscle space is a group of muscles activated together by a single neural command. Under the assumption that the motor control is intermittent, I present the minimum transition hypothesis (MTH) and its predictions with regards to the structure of muscle synergies. The MTH asserts that the purpose of synergies is to minimize the effort of the higher level in the hierarchy by minimizing the number of transitions in an intermittent control signal. The implications of the MTH are not only for the structure of the muscle synergies but also to the intermittent and hierarchical nature of the motor system, with various predictions as to the process of skill learning, and important implications to the design of brain machine interfaces and human robot interaction.

Bistability in Purkinje neurons: ups and downs in cerebellar research

The output of cerebellar Purkinje cells has been characterized extensively and theories regarding the role of simple spike (SS) and complex spike (CS) patterns have evolved through many different studies. A bistable pattern of SS output can be observed in vitro; however, differing views exist regarding the occurrence of bistable SS output in vivo. Bistability in Purkinje cell output is characterized by abrupt transitions between tonic firing and quiescence, usually evoked by synaptic inputs to the neuron. This is in contrast to the trimodal pattern of activity which has been found in vitro and in vivo when climbing fiber input to Purkinje cells is removed. The mechanisms underlying bistable membrane properties in Purkinje cells have been determined through in vitro studies and computational analysis. In vitro studies have further established that Purkinje cells possess the ability to toggle between firing states, but in vivo studies in both awake and anesthetized animals have found conflicting results as to the presence of toggling in the intact circuit. Here, we provide an overview of the current state of research on bistability, examining the mechanisms underlying bistability and current findings from in vivo studies. We also suggest possible reasons for discrepancies between in vivo studies and propose future studies which would aid in clarifying the role of bistability in the cerebellar circuit.

Dendritic calcium signaling in cerebellar Purkinje cell

The Purkinje cells in the cerebellum are unique neurons that generate local and global Ca(2+) signals in response to two types of excitatory inputs, parallel fiber and climbing fiber, respectively. The spatiotemporal distribution and interaction of these synaptic inputs produce complex patterns of Ca(2+) dynamics in the Purkinje cell dendrites. The Ca(2+) signals originate from Ca(2+) influx through voltage-gated Ca(2+) channels and Ca(2+) release from intracellular stores that are mediated by the metabotropic glutamate receptor signaling pathway. These Ca(2+) signals are essential for the induction of various forms of synaptic plasticity and for controlling the input-output relationship of Purkinje cells. In this article we review Ca(2+) signaling in Purkinje cell dendrites.

Behavior-related pauses in simple-spike activity of mouse Purkinje cells are linked to spike rate modulation

Purkinje cells (PCs) in the mammalian cerebellum express high-frequency spontaneous activity with average spike rates between 30 and 200 Hz. Cerebellar nuclear (CN) neurons receive converging input from many PCs, resulting in a continuous barrage of inhibitory inputs. It has been hypothesized that pauses in PC activity trigger increases in CN spiking activity. A prediction derived from this hypothesis is that pauses in PC simple-spike activity represent relevant behavioral or sensory events. Here, we asked whether pauses in the simple-spike activity of PCs related to either fluid licking or respiration, play a special role in representing information about behavior. Both behaviors are widely represented in cerebellar PC simple-spike activity. We recorded PC activity in the vermis and lobus simplex of head-fixed mice while monitoring licking and respiratory behavior. Using cross-correlation and Granger causality analysis, we examined whether short interspike intervals (ISIs) had a different temporal relationship to behavior than long ISIs or pauses. Behavior-related simple-spike pauses occurred during low-rate simple-spike activity in both licking- and breathing-related PCs. Granger causality analysis revealed causal relationships between simple-spike pauses and behavior. However, the same results were obtained from an analysis of surrogate spike trains with gamma ISI distributions constructed to match rate modulations of behavior-related Purkinje cells. Our results therefore suggest that the occurrence of pauses in simple-spike activity does not represent additional information about behavioral or sensory events that goes beyond the simple-spike rate modulations.

Detection of bursts and pauses in spike trains

Midbrain dopaminergic neurons in vivo exhibit a wide range of firing patterns. They normally fire constantly at a low rate, and speed up, firing a phasic burst when reward exceeds prediction, or pause when an expected reward does not occur. Therefore, the detection of bursts and pauses from spike train data is a critical problem when studying the role of phasic dopamine (DA) in reward related learning, and other DA dependent behaviors. However, few statistical methods have been developed that can identify bursts and pauses simultaneously. We propose a new statistical method, the Robust Gaussian Surprise (RGS) method, which performs an exhaustive search of bursts and pauses in spike trains simultaneously. We found that the RGS method is adaptable to various patterns of spike trains recorded in vivo, and is not influenced by baseline firing rate, making it applicable to all in vivo spike trains where baseline firing rates vary over time. We compare the performance of the RGS method to other methods of detecting bursts, such as the Poisson Surprise (PS), Rank Surprise (RS), and Template methods. Analysis of data using the RGS method reveals potential mechanisms underlying how bursts and pauses are controlled in DA neurons.

Storage of correlated patterns in standard and bistable Purkinje cell models

The cerebellum has long been considered to undergo supervised learning, with climbing fibers acting as a 'teaching' or 'error' signal. Purkinje cells (PCs), the sole output of the cerebellar cortex, have been considered as analogs of perceptrons storing input/output associations. In support of this hypothesis, a recent study found that the distribution of synaptic weights of a perceptron at maximal capacity is in striking agreement with experimental data in adult rats. However, the calculation was performed using random uncorrelated inputs and outputs. This is a clearly unrealistic assumption since sensory inputs and motor outputs carry a substantial degree of temporal correlations. In this paper, we consider a binary output neuron with a large number of inputs, which is required to store associations between temporally correlated sequences of binary inputs and outputs, modelled as Markov chains. Storage capacity is found to increase with both input and output correlations, and diverges in the limit where both go to unity. We also investigate the capacity of a bistable output unit, since PCs have been shown to be bistable in some experimental conditions. Bistability is shown to enhance storage capacity whenever the output correlation is stronger than the input correlation. Distribution of synaptic weights at maximal capacity is shown to be independent on correlations, and is also unaffected by the presence of bistability.

Tunable oscillations in the Purkinje neuron

In this paper, we experimentally study the dynamics of slow oscillations in Purkinje neurons in vitro, and derive a strong association with a forced parametric oscillator model. We observed the precise rhythmicity of these oscillations in Purkinje neurons, as well as a dynamic tunability of this oscillation using a photoswitchable compound. We found that this slow oscillation can be induced in every Purkinje neuron measured, having periods ranging between 10 and 25 s. Starting from a Hodgkin-Huxley model, we demonstrate that this oscillation can be externally modulated, and that the neurons will return to their intrinsic firing frequency after the forced oscillation is concluded. These findings signify an additional timing functional role of tunable oscillations within the cerebellum, as well as a dynamic control of a time scale in the brain in the range of seconds.

Dendritic calcium signaling triggered by spontaneous and sensory-evoked climbing fiber input to cerebellar Purkinje cells in vivo

Cerebellar Purkinje cells have one of the most elaborate dendritic trees in the mammalian CNS, receiving excitatory synaptic input from a single climbing fiber (CF) and from ∼200,000 parallel fibers. The dendritic Ca(2+) signals triggered by activation of these inputs are crucial for the induction of synaptic plasticity at both of these synaptic connections. We have investigated Ca(2+) signaling in Purkinje cell dendrites in vivo by combining targeted somatic or dendritic patch-clamp recording with simultaneous two-photon microscopy. Both spontaneous and sensory-evoked CF inputs triggered widespread Ca(2+) signals throughout the dendritic tree that were detectable even in individual spines of the most distal spiny branchlets receiving parallel fiber input. The amplitude of these Ca(2+) signals depended on dendritic location and could be modulated by membrane potential, reflecting modulation of dendritic spikes triggered by the CF input. Furthermore, the variability of CF-triggered Ca(2+) signals was regulated by GABAergic synaptic input. These results indicate that dendritic Ca(2+) signals triggered by sensory-evoked CF input can act as associative signals for synaptic plasticity in Purkinje cells in vivo and may differentially modulate plasticity at parallel fiber synapses depending on the location of synapses, firing state of the Purkinje cell, and ongoing GABAergic synaptic input.

Signals and circuits in the purkinje neuron

Purkinje neurons (PN) in the cerebellum have over 100,000 inputs organized in an orthogonal geometry, and a single output channel. As the sole output of the cerebellar cortex layer, their complex firing pattern has been associated with motor control and learning. As such they have been extensively modeled and measured using tools ranging from electrophysiology and neuroanatomy, to dynamic systems and artificial intelligence methods. However, there is an alternative approach to analyze and describe the neuronal output of these cells using concepts from electrical engineering, particularly signal processing and digital/analog circuits. By viewing the PN as an unknown circuit to be reverse-engineered, we can use the tools that provide the foundations of today’s integrated circuits and communication systems to analyze the Purkinje system at the circuit level. We use Fourier transforms to analyze and isolate the inherent frequency modes in the PN and define three unique frequency ranges associated with the cells’ output. Comparing the PN to a signal generator that can be externally modulated adds an entire level of complexity to the functional role of these neurons both in terms of data analysis and information processing, relying on Fourier analysis methods in place of statistical ones. We also re-describe some of the recent literature in the field, using the nomenclature of signal processing. Furthermore, by comparing the experimental data of the past decade with basic electronic circuitry, we can resolve the outstanding controversy in the field, by recognizing that the PN can act as a multivibrator circuit.

Dendritic signals command firing dynamics in a mathematical model of cerebellar Purkinje cells

Dendrites of cerebellar Purkinje cells (PCs) respond to brief excitations from parallel fibers with lasting plateau depolarizations. It is unknown whether these plateaus are local events that boost the synaptic signals or they propagate to the soma and directly take part in setting the cell firing dynamics. To address this issue, we analyzed a likely mechanism underlying plateaus in three representations of a reconstructed PC with increasing complexity. Analysis in an infinite cable suggests that Ca plateaus triggered by direct excitatory inputs from parallel fibers and their mirror signals, valleys (putatively triggered by the local feed forward inhibitory network), cannot propagate. However, simulations of the model in electrotonic equivalent cables prove that Ca plateaus (resp. valleys) are conducted over the entire cell with velocities typical of passive events once they are triggered by threshold synaptic inputs that turn the membrane current inward (resp. outward) over the whole cell surface. Bifurcation analysis of the model in equivalent cables, and simulations in a fully reconstructed PC both indicate that dendritic Ca plateaus and valleys, respectively, command epochs of firing and silencing of PCs.

The cerebellar network: from structure to function and dynamics

Since the discoveries of Camillo Golgi and Ramón y Cajal, the precise cellular organization of the cerebellum has inspired major computational theories, which have then influenced the scientific thought not only on the cerebellar function but also on the brain as a whole. However, six major issues revealing a discrepancy between morphologically inspired hypothesis and function have emerged. (1) The cerebellar granular layer does not simply operate a simple combinatorial decorrelation of the inputs but performs more complex non-linear spatio-temporal transformations and is endowed with synaptic plasticity. (2) Transmission along the ascending axon and parallel fibers does not lead to beam formation but rather to vertical columns of activation. (3) The olivo-cerebellar loop could perform complex timing operations rather than error detection and teaching. (4) Purkinje cell firing dynamics are much more complex than for a linear integrator and include pacemaking, burst-pause discharges, and bistable states in response to mossy and climbing fiber synaptic inputs. (5) Long-term synaptic plasticity is far more complex than traditional parallel fiber LTD and involves also other cerebellar synapses. (6) Oscillation and resonance could set up coherent cycles of activity designing a functional geometry that goes far beyond pre-wired anatomical circuits. These observations clearly show that structure is not sufficient to explain function and that a precise knowledge on dynamics is critical to understand how the cerebellar circuit operates.

Model-founded explorations of the roles of molecular layer inhibition in regulating purkinje cell responses in cerebellar cortex: more trouble for the beam hypothesis

For most of the last 50 years, the functional interpretation for inhibition in cerebellar cortical circuitry has been dominated by the relatively simple notion that excitatory and inhibitory dendritic inputs sum, and if that sum crosses threshold at the soma the Purkinje cell generates an action potential. Thus, inhibition has traditionally been relegated to a role of sculpting, restricting, or blocking excitation. At the level of networks, this relatively simply notion is manifest in mechanisms like "surround inhibition" which is purported to "shape" or "tune" excitatory neuronal responses. In the cerebellum, where all cell types except one (the granule cell) are inhibitory, these assumptions regarding the role of inhibition continue to dominate. Based on our recent series of modeling and experimental studies, we now suspect that inhibition may play a much more complex, subtle, and central role in the physiological and functional organization of cerebellar cortex. This paper outlines how model-based studies are changing our thinking about the role of feed-forward molecular layer inhibition in the cerebellar cortex. The results not only have important implications for continuing efforts to understand what the cerebellum computes, but might also reveal important features of the evolution of this large and quintessentially vertebrate brain structure.

Interneurons of the cerebellar cortex toggle Purkinje cells between up and down states

We demonstrate that single interneurons can toggle the output neurons of the cerebellar cortex (the Purkinje cells) between their two states. The firing of Purkinje cells has previously been shown to alternate between an "up" state in which the cell fires spontaneous action potentials and a silent "down" state. We show here that small hyperpolarizing currents in Purkinje cells can bidirectionally toggle Purkinje cells between down and up states and that blockade of the hyperpolarization-activated cation channels (H channels) with the specific antagonist ZD7288 (10 microM) blocks the transitions from down to up states. Likewise, hyperpolarizing inhibitory postsnyaptic potentials (IPSPs) produced by small bursts of action potentials (10 action potentials at 50 Hz) in molecular-layer interneurons induce these bidirectional transitions in Purkinje cells. Furthermore, single interneurons in paired interneuron --> Purkinje cell recordings, produce bidirectional switches between the two states of Purkinje cells. The ability of molecular-layer interneurons to toggle Purkinje cells occurs when Purkinje cells are recorded under whole-cell patch-clamp conditions as well as when action potentials are recorded in an extracellular loose cell-attached configuration. The mode switch demonstrated here indicates that a single presynaptic interneuron can have opposite effects on the output of a given Purkinje cell, which introduces a unique type of synaptic interaction that may play an important role in cerebellar signaling.

Implications of functional anatomy on information processing in the deep cerebellar nuclei

The cerebellum has been implicated as a major player in producing temporal acuity. Theories of cerebellar timing typically emphasize the role of the cerebellar cortex while overlooking the role of the deep cerebellar nuclei (DCN) that provide the sole output of the cerebellum. Here we review anatomical and electrophysiological studies to shed light on the DCN's ability to support temporal pattern generation in the cerebellum. Specifically, we examine data on the structure of the DCN, the biophysical properties of DCN neurons and properties of the afferent systems to evaluate their contribution to DCN firing patterns. In addition, we manipulate one of the afferent structures, the inferior olive (IO), using systemic harmaline injection to test for a network effect on activity of single DCN neurons in freely moving animals. Harmaline induces a rhythmic firing pattern of short bursts on a quiescent background at about 8 Hz. Other neurons become quiescent for long periods (seconds to minutes). The observed patterns indicate that the major effect harmaline exerts on the DCN is carried indirectly by the inhibitory Purkinje cells (PCs) activated by the IO, rather than by direct olivary excitation. Moreover, we suggest that the DCN response profile is determined primarily by the number of concurrently active PCs, their firing rate and the level of synchrony occurring in their transitions between continuous firing and quiescence. We argue that DCN neurons faithfully transfer temporal patterns resulting from strong correlations in PCs state transitions, while largely ignoring the timing of simple spikes from individual PCs. Future research should aim at quantifying the contribution of PC state transitions to DCN activity, and the interplay between the different afferent systems that drive DCN activity.

Regularity, variability and bi-stability in the activity of cerebellar purkinje cells

Recent studies have demonstrated that the membrane potential of Purkinje cells is bi-stable and that this phenomenon underlies bi-modal simple spike firing. Membrane potential alternates between a depolarized state, that is associated with spontaneous simple spike firing (up state), and a quiescent hyperpolarized state (down state). A controversy has emerged regarding the relevance of bi-stability to the awake animal, yet recordings made from behaving cat Purkinje cells have demonstrated that at least 50% of the cells exhibit bi-modal firing. The robustness of the phenomenon in vitro or in anaesthetized systems on the one hand, and the controversy regarding its expression in behaving animals on the other hand suggest that state transitions are under neuronal control. Indeed, we have recently demonstrated that synaptic inputs can induce transitions between the states and suggested that the role of granule cell input is to control the states of Purkinje cells rather than increase or decrease firing rate gradually. We have also shown that the state of a Purkinje cell does not only affect its firing but also the waveform of climbing fiber-driven complex spikes and the associated calcium influx. These findings call for a reconsideration of the role of Purkinje cells in cerebellar function. In this manuscript we review the recent findings on Purkinje cell bi-stability and add some analyses of its effect on the regularity and variability of Purkinje cell activity.

Neocortical networks entrain neuronal circuits in cerebellar cortex

Activity in neocortex is often characterized by synchronized oscillations of neurons and networks, resulting in the generation of a local field potential (LFP) and electroencephalogram. Do the neuronal networks of the cerebellum also generate synchronized oscillations and are they under the influence of those in the neocortex? Here we show that, in the absence of any overt external stimulus, the cerebellar cortex generates a slow oscillation that is correlated with that of the neocortex. Disruption of the neocortical slow oscillation abolishes the cerebellar slow oscillation, whereas blocking cerebellar activity has no overt effect on the neocortex. We provide evidence that the cerebellar slow oscillation results in part from the activation of granule, Golgi, and Purkinje neurons. In particular, we show that granule and Golgi cells discharge trains of single spikes, and Purkinje cells generate complex spikes, during the "up" state of the slow oscillation. Purkinje cell simple spiking is weakly related to the cerebellar and neocortical slow oscillation in a minority of cells. Our results indicate that the cerebellum generates rhythmic network activity that can be recorded as an LFP in the anesthetized animal, which is driven by synchronized oscillations of the neocortex. Furthermore, we show that correlations between neocortical and cerebellar LFPs persist in the awake animal, indicating that neocortical circuits modulate cerebellar neurons in a similar manner in natural behavioral states. Thus, the projection neurons of the neocortex collectively exert a driving and modulatory influence on cerebellar network activity.

Patterns and pauses in Purkinje cell simple spike trains: experiments, modeling and theory

We review our recent experimental and modeling results on how cerebellar Purkinje cells encode information in their simple spike trains and present a theory of the function of pauses and regular spiking patterns. The regular spiking patterns were discovered in extracellular recordings of simple spikes in awake and anesthetized rodents, where it was shown that more than half of the spontaneous activity consists of short epochs of regular spiking. These periods of regular spiking are interrupted by pauses, which can be tightly synchronized among nearby Purkinje cells, while the spikes in the regular patterns are not. Interestingly, pauses are affected by long-term depression of the parallel fiber synapses. Both in modeling and slice experiments it was demonstrated that long-term depression causes a decrease in the duration of pauses, leading to an increase of the spike output of the neuron. Based on these results we propose that pauses in the simple spike train form a temporal code which can lead to a rebound burst in the target deep cerebellar nucleus neurons. Conversely, the regular spike patterns may be a rate code, which presets the amplitude of future rebound bursts.