Multiplexed coding by cerebellar Purkinje neurons

The cerebellum converts input data into a hyper low-resolution granule cell code with spatial dimensions: a hypothesis

We present a theory of the inner layer of the cerebellar cortex, the granular layer, where the main excitatory input to the cerebellum is received. We ask how input signals are converted into an internal code and what form that has. While there is a computational element, and the ideas are quantified with a computer simulation, the approach is primarily evidence-led and aimed at experimenters rather than the computational community. Network models are often simplified to provide a noiseless medium for sophisticated computations. We propose, with evidence, the reverse: physiology is highly adapted to provide a noiseless medium for straightforward computations. We find that input data are converted to a hyper low-resolution internal code. Information is coded in the joint activity of large cell groups and therefore has minimum spatial dimensions-the dimensions of a code group. The conversion exploits statistical effects of random sampling. Code group dimensions are an effect of topography, cell morphologies and granular layer architecture. The activity of a code group is the smallest unit of information but not the smallest unit of code-the same information is coded in any random sample of signals. Code in this form is unexpectedly wasteful-there is a huge sacrifice of resolution-but may be a solution to fundamental problems involved in the biological representation of information.

Spike Attention Coding for Spiking Neural Networks

Spiking neural networks (SNNs), an important family of neuroscience-oriented intelligent models, play an essential role in the neuromorphic computing community. Spike rate coding and temporal coding are the mainstream coding schemes in the current modeling of SNNs. However, rate coding usually suffers from limited representation resolution and long latency, while temporal coding usually suffers from under-utilization of spike activities. To this end, we propose spike attention coding (SAC) for SNNs. By introducing learnable attention coefficients for each time step, our coding scheme can naturally unify rate coding and temporal coding, and then flexibly learn optimal coefficients for better performance. Several normalization and regularization techniques are further incorporated to control the range and distribution of the learned attention coefficients. Extensive experiments on classification, generation, and regression tasks are conducted and demonstrate the superiority of the proposed coding scheme. This work provides a flexible coding scheme to enhance the representation power of SNNs and extends their application scope beyond the mainstream classification scenario.

Branch-specific clustered parallel fiber input controls dendritic computation in Purkinje cells

Most central neurons have intricately branched dendritic trees that integrate massive numbers of synaptic inputs. Intrinsic active mechanisms in dendrites can be heterogeneous and be modulated in a branch-specific way. However, it remains poorly understood how heterogeneous intrinsic properties contribute to processing of synaptic input. We propose the first computational model of the cerebellar Purkinje cell with dendritic heterogeneity, in which each branch is an individual unit and is characterized by its own set of ion channel conductance densities. When simultaneously activating a cluster of parallel fiber synapses, we measure the peak amplitude of a response and observe how changes in P-type calcium channel conductance density shift the dendritic responses from a linear one to a bimodal one including dendritic calcium spikes and vice-versa. These changes relate to the morphology of each branch. We show how dendritic calcium spikes propagate and how Kv4.3 channels block spreading depolarization to nearby branches.

Purkinje cells in Crus I and II encode the visual stimulus and the impending choice as monkeys learn a reinforcement based visuomotor association task

Visuomotor association involves linking an arbitrary visual cue to a well-learned movement. Transient inactivation of Crus I/II impairs primates' ability to learn new associations and delays motor responses without affecting the kinematics of the movement. The simple spikes of Purkinje cells in the Crus regions signal cognitive errors as monkeys learn to associate specific fractal stimuli with movements of the left or right hand. Here we show that as learning progresses, the simple spike activity of individual neurons becomes more selective for stimulus-response associations, with selectivity developing closer to the appearance of visual stimuli. Initially, most neurons respond to both associations, irrespective of the identity of the stimulus and the associated movement, but as learning advances, more neurons distinguish between specific stimulus-hand associations. Using a linear decoder, it was found that in early learning stages, the visual stimulus can be decoded only when the choice can also be decoded. As learning improves, the visual stimulus is decoded earlier than the choice. A simple model can replicate the observed simple spike signals and the monkeys' behavior in both the early and late learning stages.

Simple spike patterns and synaptic mechanisms encoding sensory and motor signals in Purkinje cells and the cerebellar nuclei

Whisker stimulation in awake mice evokes transient suppression of simple spike probability in crus I/II Purkinje cells. Here, we investigated how simple spike suppression arises synaptically, what it encodes, and how it affects cerebellar output. In vitro, monosynaptic parallel fiber (PF)-excitatory postsynaptic currents (EPSCs) facilitated strongly, whereas disynaptic inhibitory postsynaptic currents (IPSCs) remained stable, maximizing relative inhibitory strength at the onset of PF activity. Short-term plasticity thus favors the inhibition of Purkinje spikes before PFs facilitate. In vivo, whisker stimulation evoked a 2-6 ms synchronous spike suppression, just 6-8 ms (∼4 synaptic delays) after sensory onset, whereas active whisker movements elicited broadly timed spike rate increases that did not modulate sensory-evoked suppression. Firing in the cerebellar nuclei (CbN) inversely correlated with disinhibition from sensory-evoked simple spike suppressions but was decoupled from slow, non-synchronous movement-associated elevations of Purkinje firing rates. Synchrony thus allows the CbN to high-pass filter Purkinje inputs, facilitating sensory-evoked cerebellar outputs that can drive movements.

Cerebellar state estimation enables resilient coupling across behavioural domains

Cerebellar computations are necessary for fine behavioural control and may rely on internal models for estimation of behaviourally relevant states. Here, we propose that the central cerebellar function is to estimate how states interact with each other, and to use these estimates to coordinates extra-cerebellar neuronal dynamics underpinning a range of interconnected behaviours. To support this claim, we describe a cerebellar model for state estimation that includes state interactions, and link this model with the neuronal architecture and dynamics observed empirically. This is formalised using the free energy principle, which provides a dual perspective on a system in terms of both the dynamics of its physical-in this case neuronal-states, and the inferential process they entail. As a demonstration of this proposal, we simulate cerebellar-dependent synchronisation of whisking and respiration, which are known to be tightly coupled in rodents, as well as limb and tail coordination during locomotion. In summary, we propose that the ubiquitous involvement of the cerebellum in behaviour arises from its central role in precisely coupling behavioural domains.

Sensorimotor content of multi-unit activity recorded in the paramedian lobule of the cerebellum using carbon fiber microelectrode arrays

The cerebellum takes in a great deal of sensory information from the periphery and descending signals from the cerebral cortices. It has been debated whether the paramedian lobule (PML) in the rat and its paravermal regions that project to the interpositus nucleus (IPN) are primarily involved in motor execution or motor planning. Studies that have relied on single spike recordings in behaving animals have led to conflicting conclusions regarding this issue. In this study, we tried a different approach and investigated the correlation of field potentials and multi-unit signals recorded with multi-electrode arrays from the PML cortex along with the forelimb electromyography (EMG) signals in rats during behavior. Linear regression was performed to predict the EMG signal envelopes using the PML activity for various time shifts (±25, ±50, ±100, and ± 400 ms) between the two signals to determine a causal relation. The highest correlations (~0.5 on average) between the neural and EMG envelopes were observed for zero and small (±25 ms) time shifts and decreased with larger time shifts in both directions, suggesting that paravermal PML is involved both in processing of sensory signals and motor execution in the context of forelimb reaching behavior. EMG envelopes were predicted with higher success rates when neural signals from multiple phases of the behavior were utilized for regression. The forelimb extension phase was the most difficult to predict while the releasing of the bar phase prediction was the most successful. The high frequency (>300 Hz) components of the neural signal, reflecting multi-unit activity, had a higher contribution to the EMG prediction than did the lower frequency components, corresponding to local field potentials. The results of this study suggest that the paravermal PML in the rat cerebellum is primarily involved in the execution of forelimb movements rather than the planning aspect and that the PML is more active at the initiation and termination of the behavior, rather than the progression.

Implications of variable synaptic weights for rate and temporal coding of cerebellar outputs

Purkinje cell (PC) synapses onto cerebellar nuclei (CbN) neurons allow signals from the cerebellar cortex to influence the rest of the brain. PCs are inhibitory neurons that spontaneously fire at high rates, and many PC inputs are thought to converge onto each CbN neuron to suppress its firing. It has been proposed that PCs convey information using a rate code, a synchrony and timing code, or both. The influence of PCs on CbN neuron firing was primarily examined for the combined effects of many PC inputs with comparable strengths, and the influence of individual PC inputs has not been extensively studied. Here, we find that single PC to CbN synapses are highly variable in size, and using dynamic clamp and modeling we reveal that this has important implications for PC-CbN transmission. Individual PC inputs regulate both the rate and timing of CbN firing. Large PC inputs strongly influence CbN firing rates and transiently eliminate CbN firing for several milliseconds. Remarkably, the refractory period of PCs leads to a brief elevation of CbN firing prior to suppression. Thus, individual PC-CbN synapses are suited to concurrently convey rate codes and generate precisely timed responses in CbN neurons. Either synchronous firing or synchronous pauses of PCs promote CbN neuron firing on rapid time scales for nonuniform inputs, but less effectively than for uniform inputs. This is a secondary consequence of variable input sizes elevating the baseline firing rates of CbN neurons by increasing the variability of the inhibitory conductance. These findings may generalize to other brain regions with highly variable inhibitory synapse sizes.

Recent data on the cerebellum require new models and theories

The cerebellum has been a popular topic for theoretical studies because its structure was thought to be simple. Since David Marr and James Albus related its function to motor skill learning and proposed the Marr-Albus cerebellar learning model, this theory has guided and inspired cerebellar research. In this review, we summarize the theoretical progress that has been made within this framework of error-based supervised learning. We discuss the experimental progress that demonstrates more complicated molecular and cellular mechanisms in the cerebellum as well as new cell types and recurrent connections. We also cover its involvement in diverse non-motor functions and evidence of other forms of learning. Finally, we highlight the need to explain these new experimental findings into an integrated cerebellar model that can unify its diverse computational functions.

Implications of variable synaptic weights for rate and temporal coding of cerebellar outputs

Purkinje cell (PC) synapses onto cerebellar nuclei (CbN) neurons convey signals from the cerebellar cortex to the rest of the brain. PCs are inhibitory neurons that spontaneously fire at high rates, and many uniform sized PC inputs are thought to converge onto each CbN neuron to suppress or eliminate firing. Leading theories maintain that PCs encode information using either a rate code, or by synchrony and precise timing. Individual PCs are thought to have limited influence on CbN neuron firing. Here, we find that single PC to CbN synapses are highly variable in size, and using dynamic clamp and modelling we reveal that this has important implications for PC-CbN transmission. Individual PC inputs regulate both the rate and timing of CbN firing. Large PC inputs strongly influence CbN firing rates and transiently eliminate CbN firing for several milliseconds. Remarkably, the refractory period of PCs leads to a brief elevation of CbN firing prior to suppression. Thus, PC-CbN synapses are suited to concurrently convey rate codes, and generate precisely-timed responses in CbN neurons. Variable input sizes also elevate the baseline firing rates of CbN neurons by increasing the variability of the inhibitory conductance. Although this reduces the relative influence of PC synchrony on the firing rate of CbN neurons, synchrony can still have important consequences, because synchronizing even two large inputs can significantly increase CbN neuron firing. These findings may be generalized to other brain regions with highly variable sized synapses.

Multidimensional cerebellar computations for flexible kinematic control of movements

Both the environment and our body keep changing dynamically. Hence, ensuring movement precision requires adaptation to multiple demands occurring simultaneously. Here we show that the cerebellum performs the necessary multi-dimensional computations for the flexible control of different movement parameters depending on the prevailing context. This conclusion is based on the identification of a manifold-like activity in both mossy fibers (MFs, network input) and Purkinje cells (PCs, output), recorded from monkeys performing a saccade task. Unlike MFs, the PC manifolds developed selective representations of individual movement parameters. Error feedback-driven climbing fiber input modulated the PC manifolds to predict specific, error type-dependent changes in subsequent actions. Furthermore, a feed-forward network model that simulated MF-to-PC transformations revealed that amplification and restructuring of the lesser variability in the MF activity is a pivotal circuit mechanism. Therefore, the flexible control of movements by the cerebellum crucially depends on its capacity for multi-dimensional computations.

Bilateral increase in MEG planar gradients prior to saccade onset

Every time we move our eyes, the retinal locations of objects change. To distinguish the changes caused by eye movements from actual external motion of the objects, the visual system is thought to anticipate the consequences of eye movements (saccades). Single neuron recordings have indeed demonstrated changes in receptive fields before saccade onset. Although some EEG studies with human participants have also demonstrated a pre-saccadic increased potential over the hemisphere that will process a stimulus after a saccade, results have been mixed. Here, we used magnetoencephalography to investigate the timing and lateralization of visually evoked planar gradients before saccade onset. We modelled the gradients from trials with both a saccade and a stimulus as the linear combination of the gradients from two conditions with either only a saccade or only a stimulus. We reasoned that any residual gradients in the condition with both a saccade and a stimulus must be uniquely linked to visually-evoked neural activity before a saccade. We observed a widespread increase in residual planar gradients. Interestingly, this increase was bilateral, showing activity both contralateral and ipsilateral to the stimulus, i.e. over the hemisphere that would process the stimulus after saccade offset. This pattern of results is consistent with predictive pre-saccadic changes involving both the current and the future receptive fields involved in processing an attended object, well before the start of the eye movement. The active, sensorimotor coupling of vision and the oculomotor system may underlie the seamless subjective experience of stable and continuous perception.

Diverse role of NMDA receptors for dendritic integration of neural dynamics

Neurons, represented as a tree structure of morphology, have various distinguished branches of dendrites. Different types of synaptic receptors distributed over dendrites are responsible for receiving inputs from other neurons. NMDA receptors (NMDARs) are expressed as excitatory units, and play a key physiological role in synaptic function. Although NMDARs are widely expressed in most types of neurons, they play a different role in the cerebellar Purkinje cells (PCs). Utilizing a computational PC model with detailed dendritic morphology, we explored the role of NMDARs at different parts of dendritic branches and regions. We found somatic responses can switch from silent, to simple spikes and complex spikes, depending on specific dendritic branches. Detailed examination of the dendrites regarding their diameters and distance to soma revealed diverse response patterns, yet explain two firing modes, simple and complex spike. Taken together, these results suggest that NMDARs play an important role in controlling excitability sensitivity while taking into account the factor of dendritic properties. Given the complexity of neural morphology varying in cell types, our work suggests that the functional role of NMDARs is not stereotyped but highly interwoven with local properties of neuronal structure.

Coexisting neuronal coding strategies in the barrel cortex

During tactile sensation by rodents, whisker movements across surfaces generate complex whisker motions, including discrete, transient stick-slip events, which carry information about surface properties. The characteristics of these events and how the brain encodes this tactile information remain enigmatic. We found that cortical neurons show a mixture of synchronized and nontemporally correlated spikes in their tactile responses. Synchronous spikes convey the magnitude of stick-slip events by numerous aspects of temporal coding. These spikes show preferential selectivity for kinetic and kinematic whisker motion. By contrast, asynchronous spikes in each neuron convey the magnitude of stick-slip events by their discharge rates, response probability, and interspike intervals. We further show that the differentiation between these two types of activity is highly dependent on the magnitude of stick-slip events and stimulus and response history. These results suggest that cortical neurons transmit multiple components of tactile information through numerous coding strategies.

The Cerebellar Cortex

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

Feedback inhibition underlies new computational functions of cerebellar interneurons

The function of a feedback inhibitory circuit between cerebellar Purkinje cells and molecular layer interneurons (MLIs) was defined by combining optogenetics, neuronal activity recordings both in cerebellar slices and in vivo, and computational modeling. Purkinje cells inhibit a subset of MLIs in the inner third of the molecular layer. This inhibition is non-reciprocal, short-range (less than 200 μm) and is based on convergence of one to two Purkinje cells onto MLIs. During learning-related eyelid movements in vivo, the activity of a subset of MLIs progressively increases as Purkinje cell activity decreases, with Purkinje cells usually leading the MLIs. Computer simulations indicate that these relationships are best explained by the feedback circuit from Purkinje cells to MLIs and that this feedback circuit plays a central role in making cerebellar learning efficient.

The Shape of Data: a Theory of the Representation of Information in the Cerebellar Cortex

This paper presents a model of rate coding in the cerebellar cortex. The pathway of input to output of the cerebellum forms an anatomically repeating, functionally modular network, whose basic wiring is preserved across vertebrate taxa. Each network is bisected centrally by a functionally defined cell group, a microzone, which forms part of the cerebellar circuit. Input to a network may be from tens of thousands of concurrently active mossy fibres. The model claims to quantify the conversion of input rates into the code received by a microzone. Recoding on entry converts input rates into an internal code which is homogenised in the functional equivalent of an imaginary plane, occupied by the centrally positioned microzone. Homogenised means the code exists in any random sample of parallel fibre signals over a minimum number. The nature of the code and the regimented architecture of the cerebellar cortex mean that the threshold can be represented by space so that the threshold can be met by the physical dimensions of the Purkinje cell dendritic arbour and planar interneuron networks. As a result, the whole population of a microzone receives the same code. This is part of a mechanism which orchestrates functionally indivisible behaviour of the cerebellar circuit and is necessary for coordinated control of the output cells of the circuit. In this model, fine control of Purkinje cells is by input rates to the system and not by learning so that it is in conflict with the for-years-dominant supervised learning model.

Impact of Purkinje Cell Simple Spike Synchrony on Signal Transmission from Flocculus

Purkinje cells (PCs) in the cerebellar flocculus carry rate-coded information that ultimately drives eye movement. Floccular PCs lying nearby each other exhibit partial synchrony of their simple spikes (SS). Elsewhere in the cerebellum, PC SS synchrony has been demonstrated to influence activity of the PCs' synaptic targets, and some suggest it constitutes another vector for information transfer. We investigated in the cerebellar flocculus the extent to which the rate code and PC synchrony interact. One motivation for the study was to explain the cerebellar deficits in ataxic mice like tottering; we speculated that PC synchrony has a positive effect on rate code transmission that is lost in the mutants. Working in transgenic mice whose PCs express channelrhodopsin, we exploited a property of optogenetics to control PC synchrony: pulsed photostimulation engenders stimulus-locked spiking, whereas continuous photostimulation engenders spiking whose timing is unconstrained. We photoactivated flocculus PCs using pulsed stimuli with sinusoidally varying timing vs. continuous stimuli with sinusoidally varying intensity. Recordings of PC pairs confirmed that pulsed stimuli engendered greater PC synchrony. We quantified the efficiency of transmission of the evoked PC firing rate modulation from the amplitudes of firing rate modulation and eye movement. Rate code transmission was slightly poorer in the conditions that generated greater PC synchrony, arguing against our motivating speculation regarding the origin of ataxia in tottering. Floccular optogenetic stimulation prominently augmented a 250-300 Hz local field potential oscillation, and we demonstrate relationships between the oscillation power and the evoked PC synchrony.

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.

4E-BP2-dependent translation in cerebellar Purkinje cells controls spatial memory but not autism-like behaviors

Recent studies have demonstrated that selective activation of mammalian target of rapamycin complex 1 (mTORC1) in the cerebellum by deletion of the mTORC1 upstream repressors TSC1 or phosphatase and tensin homolog (PTEN) in Purkinje cells (PCs) causes autism-like features and cognitive deficits. However, the molecular mechanisms by which overactivated mTORC1 in the cerebellum engenders these behaviors remain unknown. The eukaryotic translation initiation factor 4E-binding protein 2 (4E-BP2) is a central translational repressor downstream of mTORC1. Here, we show that mice with selective ablation of 4E-BP2 in PCs display a reduced number of PCs, increased regularity of PC action potential firing, and deficits in motor learning. Surprisingly, although spatial memory is impaired in these mice, they exhibit normal social interaction and show no deficits in repetitive behavior. Our data suggest that, downstream of mTORC1/4E-BP2, there are distinct cerebellar mechanisms independently controlling social behavior and memory formation.

Inferring phenomenological models of first passage processes

Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often infeasible. Instead, here we propose a systematic framework for building phenomenological models of such networks from experimental data, focusing on accurately approximating the time it takes to complete the process, the First Passage (FP) time. Our phenomenological models are mixtures of Gamma distributions, which have a natural biophysical interpretation. The complexity of the models is adapted automatically to account for the amount of available data and its temporal resolution. The framework can be used for predicting behavior of FP systems under varying external conditions. To demonstrate the utility of the approach, we build models for the distribution of inter-spike intervals of a morphologically complex neuron, a Purkinje cell, from experimental and simulated data. We demonstrate that the developed models can not only fit the data, but also make nontrivial predictions. We demonstrate that our coarse-grained models provide constraints on more mechanistically accurate models of the involved phenomena.

Modulation of the dynamics of cerebellar Purkinje cells through the interaction of excitatory and inhibitory feedforward pathways

The dynamics of cerebellar neuronal networks is controlled by the underlying building blocks of neurons and synapses between them. For which, the computation of Purkinje cells (PCs), the only output cells of the cerebellar cortex, is implemented through various types of neural pathways interactively routing excitation and inhibition converged to PCs. Such tuning of excitation and inhibition, coming from the gating of specific pathways as well as short-term plasticity (STP) of the synapses, plays a dominant role in controlling the PC dynamics in terms of firing rate and spike timing. PCs receive cascade feedforward inputs from two major neural pathways: the first one is the feedforward excitatory pathway from granule cells (GCs) to PCs; the second one is the feedforward inhibition pathway from GCs, via molecular layer interneurons (MLIs), to PCs. The GC-PC pathway, together with short-term dynamics of excitatory synapses, has been a focus over past decades, whereas recent experimental evidence shows that MLIs also greatly contribute to controlling PC activity. Therefore, it is expected that the diversity of excitation gated by STP of GC-PC synapses, modulated by strong inhibition from MLI-PC synapses, can promote the computation performed by PCs. However, it remains unclear how these two neural pathways are interacted to modulate PC dynamics. Here using a computational model of PC network installed with these two neural pathways, we addressed this question to investigate the change of PC firing dynamics at the level of single cell and network. We show that the nonlinear characteristics of excitatory STP dynamics can significantly modulate PC spiking dynamics mediated by inhibition. The changes in PC firing rate, firing phase, and temporal spike pattern, are strongly modulated by these two factors in different ways. MLIs mainly contribute to variable delays in the postsynaptic action potentials of PCs while modulated by excitation STP. Notably, the diversity of synchronization and pause response in the PC network is governed not only by the balance of excitation and inhibition, but also by the synaptic STP, depending on input burst patterns. Especially, the pause response shown in the PC network can only emerge with the interaction of both pathways. Together with other recent findings, our results show that the interaction of feedforward pathways of excitation and inhibition, incorporated with synaptic short-term dynamics, can dramatically regulate the PC activities that consequently change the network dynamics of the cerebellar circuit.

It is well known that the dynamics of neuronal networks are controlled by various types of neural pathways that are interactively routing excitation and inhibition converged to postsynaptic neurons. In addition, gating of a specific neural pathway is enhanced by short-term plasticity of the synapses between neurons. However, it remains unclear how a combination of these factors, the strengths of excitation and inhibition, and their short-term dynamics respectively, contributes to the dynamics of single cells and neuronal networks. Using a network model of cerebellar Purkinje cells embedded with the feedforward excitatory pathway from granule cells and feedforward inhibition pathway of molecular layer interneurons. We show that the dynamics of firing rate, firing phase, and temporal spike pattern are notably yet differently modulated by these two pathways. At the single cell level, excitatory short-term plasticity nonlinearly modulates the input-output relationship of firing activity. At the network level, the diversity of synchronization and pause response is governed not only by the balance of excitation and inhibition, but also by synaptic short-term dynamics. Only when both neural pathways are incorporated, there is a strong pause response shown in the network. Our results, together with recent in vivo experimental observations in the cerebellum, show that the interaction of feedforward pathways of excitation and inhibition, together with synaptic short-term dynamics, can dramatically change the network dynamics of Purkinje cells.

The Cellular Electrophysiological Properties Underlying Multiplexed Coding in Purkinje Cells

Neuronal firing patterns are crucial to underpin circuit level behaviors. In cerebellar Purkinje cells (PCs), both spike rates and pauses are used for behavioral coding, but the cellular mechanisms causing code transitions remain unknown. We use a well-validated PC model to explore the coding strategy that individual PCs use to process parallel fiber (PF) inputs. We find increasing input intensity shifts PCs from linear rate-coders to burst-pause timing-coders by triggering localized dendritic spikes. We validate dendritic spike properties with experimental data, elucidate spiking mechanisms, and predict spiking thresholds with and without inhibition. Both linear and burst-pause computations use individual branches as computational units, which challenges the traditional view of PCs as linear point neurons. Dendritic spike thresholds can be regulated by voltage state, compartmentalized channel modulation, between-branch interaction and synaptic inhibition to expand the dynamic range of linear computation or burst-pause computation. In addition, co-activated PF inputs between branches can modify somatic maximum spike rates and pause durations to make them carry analog signals. Our results provide new insights into the strategies used by individual neurons to expand their capacity of information processing.

SIGNIFICANCE STATEMENT Understanding how neurons process information is a fundamental question in neuroscience. Purkinje cells (PCs) were traditionally regarded as linear point neurons. We used computational modeling to unveil their electrophysiological properties underlying the multiplexed coding strategy that is observed during behaviors. We demonstrate that increasing input intensity triggers localized dendritic spikes, shifting PCs from linear rate-coders to burst-pause timing-coders. Both coding strategies work at the level of individual dendritic branches. Our work suggests that PCs have the ability to implement branch-specific multiplexed coding at the cellular level, thereby increasing the capacity of cerebellar coding and learning.

Population coding in the cerebellum: a machine learning perspective

The cere resembles a feedforward, three-layer network of neurons in which the "hidden layer" consists of Purkinje cells (P-cells) and the output layer consists of deep cerebellar nucleus (DCN) neurons. In this analogy, the output of each DCN neuron is a prediction that is compared with the actual observation, resulting in an error signal that originates in the inferior olive. Efficient learning requires that the error signal reach the DCN neurons, as well as the P-cells that project onto them. However, this basic rule of learning is violated in the cerebellum: the olivary projections to the DCN are weak, particularly in adulthood. Instead, an extraordinarily strong signal is sent from the olive to the P-cells, producing complex spikes. Curiously, P-cells are grouped into small populations that converge onto single DCN neurons. Why are the P-cells organized in this way, and what is the membership criterion of each population? Here, I apply elementary mathematics from machine learning and consider the fact that P-cells that form a population exhibit a special property: they can synchronize their complex spikes, which in turn suppress activity of DCN neuron they project to. Thus complex spikes cannot only act as a teaching signal for a P-cell, but through complex spike synchrony, a P-cell population may act as a surrogate teacher for the DCN neuron that produced the erroneous output. It appears that grouping of P-cells into small populations that share a preference for error satisfies a critical requirement of efficient learning: providing error information to the output layer neuron (DCN) that was responsible for the error, as well as the hidden layer neurons (P-cells) that contributed to it. This population coding may account for several remarkable features of behavior during learning, including multiple timescales, protection from erasure, and spontaneous recovery of memory.

Firing rate-dependent phase responses of Purkinje cells support transient oscillations

Both spike rate and timing can transmit information in the brain. Phase response curves (PRCs) quantify how a neuron transforms input to output by spike timing. PRCs exhibit strong firing-rate adaptation, but its mechanism and relevance for network output are poorly understood. Using our Purkinje cell (PC) model, we demonstrate that the rate adaptation is caused by rate-dependent subthreshold membrane potentials efficiently regulating the activation of Na+ channels. Then, we use a realistic PC network model to examine how rate-dependent responses synchronize spikes in the scenario of reciprocal inhibition-caused high-frequency oscillations. The changes in PRC cause oscillations and spike correlations only at high firing rates. The causal role of the PRC is confirmed using a simpler coupled oscillator network model. This mechanism enables transient oscillations between fast-spiking neurons that thereby form PC assemblies. Our work demonstrates that rate adaptation of PRCs can spatio-temporally organize the PC input to cerebellar nuclei.

A Slow Short-Term Depression at Purkinje to Deep Cerebellar Nuclear Neuron Synapses Supports Gain-Control and Linear Encoding over Second-Long Time Windows

Modifications in the sensitivity of neural elements allow the brain to adapt its functions to varying demands. Frequency-dependent short-term synaptic depression (STD) provides a dynamic gain-control mechanism enabling adaptation to different background conditions alongside enhanced sensitivity to input-driven changes in activity. In contrast, synapses displaying frequency-invariant transmission can faithfully transfer ongoing presynaptic rates enabling linear processing, deemed critical for many functions. However, rigid frequency-invariant transmission may lead to runaway dynamics and low sensitivity to changes in rate. Here, I investigated the Purkinje cell to deep cerebellar nuclei neuron synapses (PC_DCNs), which display frequency invariance, and yet, PCs maintain background activity at disparate rates, even at rest. Using protracted PC_DCN activation (120 s) to mimic background activity in cerebellar slices from mature mice of both sexes, I identified a previously unrecognized, frequency-dependent, slow STD (S-STD), adapting IPSC amplitudes in tens of seconds to minutes. However, after changes in activation rates, over a behavior-relevant second-long time window, S-STD enabled scaled linear encoding of PC rates in synaptic charge transfer and DCN spiking activity. Combined electrophysiology, optogenetics, and statistical analysis suggested that S-STD mechanism is input-specific, involving decreased ready-to-release quanta, and distinct from faster short-term plasticity (f-STP). Accordingly, an S-STD component with a scaling effect (i.e., activity-dependent release sites inactivation), extending a model explaining PC_DCN release on shorter timescales using balanced f-STP, reproduced the experimental results. Thus, these results elucidates a novel slow gain-control mechanism able to support linear transfer of behavior-driven/learned PC rates concurrently with background activity adaptation, and furthermore, provides an alternative pathway to refine PC output.SIGNIFICANCE STATEMENT The brain can adapt to varying demands by dynamically changing the gain of its synapses; however, some tasks require ongoing linear transfer of presynaptic rates, seemingly incompatible with nonlinear gain adaptation. Here, I report a novel slow gain-control mechanism enabling scaled linear encoding of presynaptic rates over behavior-relevant time windows, and adaptation to background activity at the Purkinje to deep cerebellar nuclear neurons synapses (PC_DCNs). A previously unrecognized PC_DCNs slow and frequency-dependent short-term synaptic depression (S-STD) mediates this process. Experimental evidence and simulations suggested that scaled linear encoding emerges from the combination of S-STD slow dynamics and frequency-invariant transmission at faster timescales. These results demonstrate a mechanism reconciling rate code with background activity adaptation and suitable for flexibly tuning PCs output via background activity modulation.

Gradients in the mammalian cerebellar cortex enable Fourier-like transformation and improve storing capacity

Cerebellar granule cells (GCs) make up the majority of all neurons in the vertebrate brain, but heterogeneities among GCs and potential functional consequences are poorly understood. Here, we identified unexpected gradients in the biophysical properties of GCs in mice. GCs closer to the white matter (inner-zone GCs) had higher firing thresholds and could sustain firing with larger current inputs than GCs closer to the Purkinje cell layer (outer-zone GCs). Dynamic Clamp experiments showed that inner- and outer-zone GCs preferentially respond to high- and low-frequency mossy fiber inputs, respectively, enabling dispersion of the mossy fiber input into its frequency components as performed by a Fourier transformation. Furthermore, inner-zone GCs have faster axonal conduction velocity and elicit faster synaptic potentials in Purkinje cells. Neuronal network modeling revealed that these gradients improve spike-timing precision of Purkinje cells and decrease the number of GCs required to learn spike-sequences. Thus, our study uncovers biophysical gradients in the cerebellar cortex enabling a Fourier-like transformation of mossy fiber inputs.

Development and validation of a high-speed video system for measuring saccadic eye movement

Laboratory-based retroreflective and magnetic scleral search-coil technologies are the current standards for collecting saccadometric data, but such equipment is costly and cumbersome. We have validated a novel, portable, high-speed video camera-based system (Exilim EX-FH20, Casio, Tokyo, Japan) for measuring saccade reaction time (RT) and error rate in a well-lit environment. This system would enable measurements of pro- and antisaccades in athletes, which is important because antisaccade metrics provide a valid tool for concussion diagnosis and determining an athlete's safe return to play. A total of 529 trials collected from 15 participants were used to compare saccade RT and error rate measurements of the high-speed camera system to a retroreflective video-based eye tracker (Eye-Trac 6: Applied Sciences Laboratories, Bedford, MA). Bland-Altman analysis revealed that the RT measurements made by the high-speed video system were 11 ms slower than those made by the retroreflective system. Error rate measurements were identical between the two systems. An excellent degree of reliability was found between the system measurements and in the ratings of independent researchers examining the video data. A strong association (r = .97) between the RTs determined via the retroreflective and high-speed camera systems was observed across all trials. Our high-speed camera system is portable and easily set up, does not require extensive equipment calibration, and can be used in a well-lit environment. Accordingly, the camera-based capture of saccadometric data may provide a valuable tool for neurological assessment following a concussive event and for the continued monitoring of recovery.

Neural Evidence of the Cerebellum as a State Predictor

We here provide neural evidence that the cerebellar circuit can predict future inputs from present outputs, a hallmark of an internal forward model. Recent computational studies hypothesize that the cerebellum performs state prediction known as a forward model. To test the forward-model hypothesis, we analyzed activities of 94 mossy fibers (inputs to the cerebellar cortex), 83 Purkinje cells (output from the cerebellar cortex to dentate nucleus), and 73 dentate nucleus cells (cerebellar output) in the cerebro-cerebellum, all recorded from a monkey performing step-tracking movements of the right wrist. We found that the firing rates of one population could be reconstructed as a weighted linear sum of those of preceding populations. We then went on to investigate if the current outputs of the cerebellum (dentate cells) could predict the future inputs of the cerebellum (mossy fibers). The firing rates of mossy fibers at time t + t₁ could be well reconstructed from as a weighted sum of firing rates of dentate cells at time t, thereby proving that the dentate activities contained predictive information about the future inputs. The average goodness-of-fit (R²) decreased moderately from 0.89 to 0.86 when t₁ was increased from 20 to 100 ms, hence indicating that the prediction is able to compensate the latency of sensory feedback. The linear equations derived from the firing rates resembled those of a predictor known as Kalman filter composed of prediction and filtering steps. In summary, our analysis of cerebellar activities supports the forward-model hypothesis of the cerebellum.

Differential Coding Strategies in Glutamatergic and GABAergic Neurons in the Medial Cerebellar Nucleus

The cerebellum drives motor coordination and sequencing of actions at the millisecond timescale through adaptive control of cerebellar nuclear output. Cerebellar nuclei integrate high-frequency information from both the cerebellar cortex and the two main excitatory inputs of the cerebellum: the mossy fibers and the climbing fiber collaterals. However, how nuclear cells process rate and timing of inputs carried by these inputs is still debated. Here, we investigate the influence of the cerebellar cortical output, the Purkinje cells, on identified cerebellar nuclei neurons in vivo in male mice. Using transgenic mice expressing Channelrhodopsin2 specifically in Purkinje cells and tetrode recordings in the medial nucleus, we identified two main groups of neurons based on the waveform of their action potentials. These two groups of neurons coincide with glutamatergic and GABAergic neurons identified by optotagging after Chrimson expression in VGLUT2-cre and GAD-cre mice, respectively. The glutamatergic-like neurons fire at high rate and respond to both rate and timing of Purkinje cell population inputs, whereas GABAergic-like neurons only respond to the mean population firing rate of Purkinje cells at high frequencies. Moreover, synchronous activation of Purkinje cells can entrain the glutamatergic-like, but not the GABAergic-like, cells over a wide range of frequencies. Our results suggest that the downstream effect of synchronous and rhythmic Purkinje cell discharges depends on the type of cerebellar nuclei neurons targeted.SIGNIFICANCE STATEMENT Motor coordination and skilled movements are driven by the permanent discharge of neurons from the cerebellar nuclei that communicate cerebellar computation to other brain areas. Here, we set out to study how specific subtypes of cerebellar nuclear neurons of the medial nucleus are controlled by Purkinje cells, the sole output of the cerebellar cortex. We could isolate different subtypes of nuclear cell that differentially encode Purkinje cell inhibition. Purkinje cell stimulation entrains glutamatergic projection cells at their firing frequency, whereas GABAergic neurons are only inhibited. These differential coding strategies may favor temporal precision of cerebellar excitatory outputs associated with specific features of movement control while setting the global level of cerebellar activity through inhibition via rate coding mechanisms.

Climbing Fibers Provide Graded Error Signals in Cerebellar Learning

The cerebellum plays a critical role in coordinating and learning complex movements. Although its importance has been well recognized, the mechanisms of learning remain hotly debated. According to the classical cerebellar learning theory, depression of parallel fiber synapses instructed by error signals from climbing fibers, drives cerebellar learning. The uniqueness of long-term depression (LTD) in cerebellar learning has been challenged by evidence showing multi-site synaptic plasticity. In Purkinje cells, long-term potentiation (LTP) of parallel fiber synapses is now well established and it can be achieved with or without climbing fiber signals, making the role of climbing fiber input more puzzling. The central question is how individual Purkinje cells extract global errors based on climbing fiber input. Previous data seemed to demonstrate that climbing fibers are inefficient instructors, because they were thought to carry “binary” error signals to individual Purkinje cells, which significantly constrains the efficiency of cerebellar learning in several regards. In recent years, new evidence has challenged the traditional view of “binary” climbing fiber responses, suggesting that climbing fibers can provide graded information to efficiently instruct individual Purkinje cells to learn. Here we review recent experimental and theoretical progress regarding modulated climbing fiber responses in Purkinje cells. Analog error signals are generated by the interaction of varying climbing fibers inputs with simultaneous other synaptic input and with firing states of targeted Purkinje cells. Accordingly, the calcium signals which trigger synaptic plasticity can be graded in both amplitude and spatial range to affect the learning rate and even learning direction. We briefly discuss how these new findings complement the learning theory and help to further our understanding of how the cerebellum works.

Computational Principles of Supervised Learning in the Cerebellum

Supervised learning plays a key role in the operation of many biological and artificial neural networks. Analysis of the computations underlying supervised learning is facilitated by the relatively simple and uniform architecture of the cerebellum, a brain area that supports numerous motor, sensory, and cognitive functions. We highlight recent discoveries indicating that the cerebellum implements supervised learning using the following organizational principles: ( a) extensive preprocessing of input representations (i.e., feature engineering), ( b) massively recurrent circuit architecture, ( c) linear input-output computations, ( d) sophisticated instructive signals that can be regulated and are predictive, ( e) adaptive mechanisms of plasticity with multiple timescales, and ( f) task-specific hardware specializations. The principles emerging from studies of the cerebellum have striking parallels with those in other brain areas and in artificial neural networks, as well as some notable differences, which can inform future research on supervised learning and inspire next-generation machine-based algorithms.

Coding Capacity of Purkinje Cells With Different Schemes of Morphological Reduction

The brain as a neuronal system has very complex structures with a large diversity of neuronal types. The most basic complexity is seen from the structure of neuronal morphology, which usually has a complex tree-like structure with dendritic spines distributed in branches. To simulate a large-scale network with spiking neurons, the simple point neuron, such as the integrate-and-fire neuron, is often used. However, recent experimental evidence suggests that the computational ability of a single neuron is largely enhanced by its morphological structure, in particular, by various types of dendritic dynamics. As the morphology reduction of detailed biophysical models is a classic question in systems neuroscience, much effort has been taken to simulate a neuron with a few compartments to include the interaction between the soma and dendritic spines. Yet, novel reduction methods are still needed to deal with the complex dendritic tree. Here, using 10 individual Purkinje cells of the cerebellum from three species of guinea-pig, mouse and rat, we consider four types of reduction methods and study their effects on the coding capacity of Purkinje cells in terms of firing rate, timing coding, spiking pattern, and modulated firing under different stimulation protocols. We found that there is a variation of reduction performance depending on individual cells and species, however, all reduction methods can preserve, to some degree, firing activity of the full model of Purkinje cell. Therefore, when stimulating large-scale network of neurons, one has to choose a proper type of reduced neuronal model depending on the questions addressed. Among these reduction schemes, Branch method, that preserves the geometrical volume of neurons, can achieve the best balance among different performance measures of accuracy, simplification, and computational efficiency, and reproduce various phenomena shown in the full morphology model of Purkinje cells. Altogether, these results suggest that the Branch reduction scheme seems to provide a general guideline for reducing complex morphology into a few compartments without the loss of basic characteristics of the firing properties of neurons.

Differentially synchronized spiking enables multiplexed neural coding

Multiplexing refers to the simultaneous encoding of two or more signals. Neurons have been shown to multiplex, but different stimuli require different multiplexing strategies. Whereas the frequency and amplitude of periodic stimuli can be encoded by the timing and rate of the same spikes, natural scenes, which comprise areas over which intensity varies gradually and sparse edges where intensity changes abruptly, require a different multiplexing strategy. Recording in vivo from neurons in primary somatosensory cortex during tactile stimulation, we found that stimulus onset and offset (edges) evoked highly synchronized spiking, whereas other spikes in the same neurons occurred asynchronously. Stimulus intensity modulated the rate of asynchronous spiking, but did not affect the timing of synchronous spikes. From this, we hypothesized that spikes driven by high- and low-contrast stimulus features can be distinguished on the basis of their synchronization, and that differentially synchronized spiking can thus be used to form multiplexed representations. Applying a Bayesian decoding method, we verified that information about high- and low-contrast features can be recovered from an ensemble of model neurons receiving common input. Equally good decoding was achieved by distinguishing synchronous from asynchronous spikes and applying reverse correlation methods separately to each spike type. This result, which we verified with patch clamp recordings in vitro, demonstrates that neurons receiving common input can use the rate of asynchronous spiking to encode the intensity of low-contrast features while using the timing of synchronous spikes to encode the occurrence of high-contrast features. We refer to this strategy as synchrony-division multiplexing.

Cerebellar Purkinje cells control eye movements with a rapid rate code that is invariant to spike irregularity

The rate and temporal pattern of neural spiking each have the potential to influence computation. In the cerebellum, it has been hypothesized that the irregularity of interspike intervals in Purkinje cells affects their ability to transmit information to downstream neurons. Accordingly, during oculomotor behavior in mice and rhesus monkeys, mean irregularity of Purkinje cell spiking varied with mean eye velocity. However, moment-to-moment variations revealed a tight correlation between eye velocity and spike rate, with no additional information conveyed by spike irregularity. Moreover, when spike rate and irregularity were independently controlled using optogenetic stimulation, the eye movements elicited were well-described by a linear population rate code with 3-5 ms temporal precision. Biophysical and random-walk models identified biologically realistic parameter ranges that determine whether spike irregularity influences responses downstream. The results demonstrate cerebellar control of movements through a remarkably rapid rate code, with no evidence for an additional contribution of spike irregularity.

Contributions of the Cerebellum for Predictive and Instructional Control of Movement

The cerebellum with its layered structure and stereotyped and conserved connectivity has long puzzled neurobiologists. While it is well established that the cerebellum functions in regulating balance, motor coordination and motor learning, how it achieves these end results has not been very clear. Recent technical advances have made it possible to tease apart the contributions of cerebellar cell types to movement in behaving animals. We review these studies focusing on the three major cerebellar cell types, namely: granule cells, Purkinje neurons and the cells of the deep cerebellar nuclei. Further, we also review our current understanding of cortico-cerebellar and basal ganglia-cerebellar interactions that play vital roles in motor planning and motor learning.

Detection of Activation Sequences in Spiking-Bursting Neurons by means of the Recognition of Intraburst Neural Signatures

Bursting activity is present in many cells of different nervous systems playing important roles in neural information processing. Multiple assemblies of bursting neurons act cooperatively to produce coordinated spatio-temporal patterns of sequential activity. A major goal in neuroscience is unveiling the mechanisms underlying neural information processing based on this sequential dynamics. Experimental findings have revealed the presence of precise cell-type-specific intraburst firing patterns in the activity of some bursting neurons. This characteristic neural signature coexists with the information encoded in other aspects of the spiking-bursting signals, and its functional meaning is still unknown. We investigate the ability of a neuron conductance-based model to detect specific presynaptic activation sequences taking advantage of intraburst fingerprints identifying the source of the signals building up a sequential pattern of activity. Our simulations point out that a reader neuron could use this information to contextualize incoming signals and accordingly compute a characteristic response by relying on precise phase relationships among the activity of different emitters. This would provide individual neurons enhanced capabilities to control and negotiate sequential dynamics. In this regard, we discuss the possible implications of the proposed contextualization mechanism for neural information processing.

Purkinje Cell Representations of Behavior: Diary of a Busy Neuron

Fundamental for understanding cerebellar function is determining the representations in Purkinje cell activity, the sole output of the cerebellar cortex. Up to the present, the most accurate descriptions of the information encoded by Purkinje cells were obtained in the context of motor behavior and reveal a high degree of heterogeneity of kinematic and performance error signals encoded. The most productive framework for organizing Purkinje cell firing representations is provided by the forward internal model hypothesis. Direct tests of this hypothesis show that individual Purkinje cells encode two different forward models simultaneously, one for effector kinematics and one for task performance. Newer results demonstrate that the timing of simple spike encoding of motor parameters spans an extend interval of up to ±2 seconds. Furthermore, complex spike discharge is not limited to signaling errors, can be predictive, and dynamically controls the information in the simple spike firing to meet the demands of upcoming behavior. These rich, diverse, and changing representations highlight the integrative aspects of cerebellar function and offer the opportunity to generalize the cerebellar computational framework over both motor and non-motor domains.

Modulation of sensory prediction error in Purkinje cells during visual feedback manipulations

It is hypothesized that the cerebellum implements a forward internal model that transforms motor commands into predictions about upcoming movements. The predictions are compared with sensory feedback to generate sensory prediction errors critical to controlling movements. The simple spike firing of cerebellar Purkinje cells both lead and lag movement consistent with representations of motor predictions and sensory feedback. This study tests whether this leading and lagging modulation provides the prediction and sensory feedback necessary to compute sensory prediction errors. Two manipulations of the visual feedback are used in rhesus monkeys performing pseudo-random tracking. Consistent with a forward model, delaying the visual feedback demonstrates that the leading simple spike modulation with position error is time-locked to the hand movement. Reducing the feedback shows that the lagged modulation is directly driven by visual inputs. Therefore, Purkinje cell discharge carries both the motor predictions and sensory feedback required of a forward internal model.

Ion channel dysfunction in cerebellar ataxia

Cerebellar ataxias constitute a heterogeneous group of disorders that result in impaired speech, uncoordinated limb movements, and impaired balance, often ultimately resulting in wheelchair confinement. Motor dysfunction in ataxia can be attributed to dysfunction and degeneration of neurons in the cerebellum and its associated pathways. Recent work has suggested the importance of cerebellar neuronal dysfunction resulting from mutations in specific ion-channels that regulate membrane excitability in the pathogenesis of cerebellar ataxia in humans. Importantly, even in ataxias not directly due to ion-channel mutations, transcriptional changes resulting in ion-channel dysfunction are tied to motor dysfunction and degeneration in models of disease. In this review, we describe the role that ion-channel dysfunction plays in a variety of cerebellar ataxias, and postulate that a potential therapeutic strategy that targets specific ion-channels exists for cerebellar ataxia.

Cerebellar compartments for the processing of kinematic and kinetic information related to hindlimb stepping

We previously showed that proprioceptive sensory input from the hindlimbs to the anterior cerebellar cortex of the cat may not be simply organized with respect to a body map, but it may also be distributed to multiple discrete functional areas extending beyond classical body map boundaries. With passive hindlimb stepping movements, cerebellar activity was shown to relate to whole limb kinematics as does the activity of dorsal spinocerebellar tract (DSCT) neurons. For DSCT activity, whole limb kinematics provides a solid functional framework within which information about limb forces, such as those generated during active stepping, may also be embedded. In this study, we investigated this idea for the spinocerebellar cortex activity by examining the activity of cerebellar cortical neurons during both passive bipedal hindlimb stepping and active stepping on a treadmill. Our results showed a functional compartmentalization of cerebellar responses to hindlimb stepping movements depending on the two types of stepping and strong relationships between neural activities and limb axis kinematics during both. In fact, responses to passive and active stepping were generally different, but in both cases their waveforms were related strongly to the limb axis kinematics. That is, the different stepping conditions modified the kinematics representation without producing different components in the response waveforms. In sum, cerebellar activity was consistent with a global kinematics framework serving as a basis upon which detailed information about limb mechanics and/or about individual limb segments might be imposed.

Serial processing of kinematic signals by cerebellar circuitry during voluntary whisking

Purkinje cells (PCs) in Crus 1 represent whisker movement via linear changes in firing rate, but the circuit mechanisms underlying this coding scheme are unknown. Here we examine the role of upstream inputs to PCs-excitatory granule cells (GCs) and inhibitory molecular layer interneurons-in processing of whisking signals. Patch clamp recordings in GCs reveal that movement is accompanied by changes in mossy fibre input rate that drive membrane potential depolarisation and high-frequency bursting activity at preferred whisker angles. Although individual GCs are narrowly tuned, GC populations provide linear excitatory drive across a wide range of movement. Molecular layer interneurons exhibit bidirectional firing rate changes during whisking, similar to PCs. Together, GC populations provide downstream PCs with linear representations of volitional movement, while inhibitory networks invert these signals. The exquisite sensitivity of neurons at each processing stage enables faithful propagation of kinematic representations through the cerebellum.Cerebellar Purkinje cells (PCs) linearly encode whisker position but the precise circuit mechanisms that generate these signals are not well understood. Here the authors use patch clamp recordings to show that selective tuning of granule cell inputs and bidirectional tuning of interneuron inputs are required to generate the kinematic representations in PCs.

Selective Optogenetic Control of Purkinje Cells in Monkey Cerebellum

Purkinje cells of the primate cerebellum play critical but poorly understood roles in the execution of coordinated, accurate movements. Elucidating these roles has been hampered by a lack of techniques for manipulating spiking activity in these cells selectively-a problem common to most cell types in non-transgenic animals. To overcome this obstacle, we constructed AAV vectors carrying the channelrhodopsin-2 (ChR2) gene under the control of a 1 kb L7/Pcp2 promoter. We injected these vectors into the cerebellar cortex of rhesus macaques and tested vector efficacy in three ways. Immunohistochemical analyses confirmed selective ChR2 expression in Purkinje cells. Neurophysiological recordings confirmed robust optogenetic activation. Optical stimulation of the oculomotor vermis caused saccade dysmetria. Our results demonstrate the utility of AAV-L7-ChR2 for revealing the contributions of Purkinje cells to circuit function and behavior, and they attest to the feasibility of promoter-based, targeted, genetic manipulations in primates.

Responses of Purkinje cells in the oculomotor vermis of monkeys during smooth pursuit eye movements and saccades: comparison with floccular complex

We recorded the responses of Purkinje cells in the oculomotor vermis during smooth pursuit and saccadic eye movements. Our goal was to characterize the responses in the vermis using approaches that would allow direct comparisons with responses of Purkinje cells in another cerebellar area for pursuit, the floccular complex. Simple-spike firing of vermis Purkinje cells is direction selective during both pursuit and saccades, but the preferred directions are sufficiently independent so that downstream circuits could decode signals to drive pursuit and saccades separately. Complex spikes also were direction selective during pursuit, and almost all Purkinje cells showed a peak in the probability of complex spikes during the initiation of pursuit in at least one direction. Unlike the floccular complex, the preferred directions for simple spikes and complex spikes were not opposite. The kinematics of smooth eye movement described the simple-spike responses of vermis Purkinje cells well. Sensitivities were similar to those in the floccular complex for eye position and considerably lower for eye velocity and acceleration. The kinematic relations were quite different for saccades vs. pursuit, supporting the idea that the contributions from the vermis to each kind of movement could contribute independently in downstream areas. Finally, neither the complex-spike nor the simple-spike responses of vermis Purkinje cells were appropriate to support direction learning in pursuit. Complex spikes were not triggered reliably by an instructive change in target direction; simple-spike responses showed very small amounts of learning. We conclude that the vermis plays a different role in pursuit eye movements compared with the floccular complex.NEW & NOTEWORTHY The midline oculomotor cerebellum plays a different role in smooth pursuit eye movements compared with the lateral, floccular complex and appears to be much less involved in direction learning in pursuit. The output from the oculomotor vermis during pursuit lies along a null-axis for saccades and vice versa. Thus the vermis can play independent roles in the two kinds of eye movement.