Bistability in Purkinje neurons: ups and downs in cerebellar research

Purkinje cell models: past, present and future

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

A machine-learning tool to identify bistable states from calcium imaging data

Mapping neuronal activation using calcium imaging in vivo during behavioural tasks has advanced our understanding of nervous system function. In almost all of these studies, calcium imaging is used to infer spike probabilities because action potentials activate voltage-gated calcium channels and increase intracellular calcium levels. However, neurons not only fire action potentials, but also convey information via intrinsic dynamics such as by generating bistable membrane potential states. Although a number of tools for spike inference have been developed and are currently being used, no tool exists for converting calcium imaging signals to maps of cellular state in bistable neurons. Purkinje neurons in the larval zebrafish cerebellum exhibit membrane potential bistability, firing either tonically or in bursts. Several studies have implicated the role of a population code in cerebellar function, with bistability adding an extra layer of complexity to this code. In the present study, we develop a tool, CaMLSort, which uses convolutional recurrent neural networks to classify calcium imaging traces as arising from either tonic or bursting cells. We validate this classifier using a number of different methods and find that it performs well on simulated event rasters as well as real biological data that it had not previously seen. Moreover, we find that CaMLsort generalizes to other bistable neurons, such as dopaminergic neurons in the ventral tegmental area of mice. Thus, this tool offers a new way of analysing calcium imaging data from bistable neurons to understand how they participate in network computation and natural behaviours. KEY POINTS: Calcium imaging, compriising the gold standard of inferring neuronal activity, does not report cellular state in neurons that are bistable, such as Purkinje neurons in the cerebellum of larval zebrafish. We model the relationship between Purkinje neuron electrical activity and its corresponding calcium signal to compile a dataset of state-labelled simulated calcium signals. We apply machine-learning methods to this dataset to develop a tool that can classify the state of a Purkinje neuron using only its calcium signal, which works well on real data even though it was trained only on simulated data. CaMLsort (Calcium imaging and Machine Learning based tool to sort intracellular state) also generalizes well to bistable neurons in a different brain region (ventral tegmental area) in a different model organism (mouse). This tool can facilitate our understanding of how these neurons carry out their functions in a circuit.

Dynamic model assuming mutually inhibitory biomarkers of frailty suggests bistability with contrasting mobility phenotypes

Bistability is a fundamental biological phenomenon associated with "switch-like" behavior reflecting the capacity of a system to exist in either of two stable states. It plays a role in gene regulation, cell fate switch, signal transduction and cell oscillation, with relevance for cognition, hearing, vision, sleep, gait and voiding. Here we consider a potential role for bistability in the existence of specific frailty states or phenotypes as part of disablement pathways. We use mathematical modeling with two frailty biomarkers (insulin growth factor-1, IGF-1 and interleukin-6, IL-6), which mutually inhibit each other. In our model, we demonstrate that small variations around critical IGF-1 or IL-6 blood levels lead to strikingly different mobility outcomes. We employ deterministic modeling of mobility outcomes, calculating the average trends in population health. Our model predicts the bistability of clinical outcomes: the deterministically-computed likelihood of an individual remaining mobile, becoming less mobile, or dying over time either increases to almost 100% or decreases to almost zero. Contrary to statistical models that attempt to estimate the likelihood of final outcomes based on probabilities and correlations, our model predicts functional outcomes over time based on specific hypothesized molecular mechanisms. Instead of estimating probabilities based on stochastic distributions and arbitrary priors, we deterministically simulate model outcomes over a wide range of physiological parameter values within experimentally derived boundaries. Our study is "a proof of principle" as it is based on a major assumption about mutual inhibition of pathways that is oversimplified. However, by making such an assumption, interesting effects can be described qualitatively. As our understanding of molecular mechanisms involved in aging deepens, we believe that such modeling will not only lead to more accurate predictions, but also help move the field from using mostly studies of associations to mechanistically guided approaches.

Influence of data sampling methods on the representation of neural spiking activity in vivo

In vivo single-unit recordings distinguish the basal spiking properties of neurons in different experimental settings and disease states. Here, we examined over 300 spike trains recorded from Purkinje cells and cerebellar nuclei neurons to test whether data sampling approaches influence the extraction of rich descriptors of firing properties. Our analyses included neurons recorded in awake and anesthetized control mice, and disease models of ataxia, dystonia, and tremor. We find that recording duration circumscribes overall representations of firing rate and pattern. Notably, shorter recording durations skew estimates for global firing rate variability toward lower values. We also find that only some populations of neurons in the same mouse are more similar to each other than to neurons recorded in different mice. These data reveal that recording duration and approach are primary considerations when interpreting task-independent single neuron firing properties. If not accounted for, group differences may be concealed or exaggerated.

Computational models of neurotransmission at cerebellar synapses unveil the impact on network computation

The neuroscientific field benefits from the conjoint evolution of experimental and computational techniques, allowing for the reconstruction and simulation of complex models of neurons and synapses. Chemical synapses are characterized by presynaptic vesicle cycling, neurotransmitter diffusion, and postsynaptic receptor activation, which eventually lead to postsynaptic currents and subsequent membrane potential changes. These mechanisms have been accurately modeled for different synapses and receptor types (AMPA, NMDA, and GABA) of the cerebellar cortical network, allowing simulation of their impact on computation. Of special relevance is short-term synaptic plasticity, which generates spatiotemporal filtering in local microcircuits and controls burst transmission and information flow through the network. Here, we present how data-driven computational models recapitulate the properties of neurotransmission at cerebellar synapses. The simulation of microcircuit models is starting to reveal how diverse synaptic mechanisms shape the spatiotemporal profiles of circuit activity and computation.

A Neurorobotic Embodiment for Exploring the Dynamical Interactions of a Spiking Cerebellar Model and a Robot Arm During Vision-Based Manipulation Tasks

While the original goal for developing robots is replacing humans in dangerous and tedious tasks, the final target shall be completely mimicking the human cognitive and motor behavior. Hence, building detailed computational models for the human brain is one of the reasonable ways to attain this. The cerebellum is one of the key players in our neural system to guarantee dexterous manipulation and coordinated movements as concluded from lesions in that region. Studies suggest that it acts as a forward model providing anticipatory corrections for the sensory signals based on observed discrepancies from the reference values. While most studies consider providing the teaching signal as error in joint-space, few studies consider the error in task-space and even fewer consider the spiking nature of the cerebellum on the cellular-level. In this study, a detailed cellular-level forward cerebellar model is developed, including modeling of Golgi and Basket cells which are usually neglected in previous studies. To preserve the biological features of the cerebellum in the developed model, a hyperparameter optimization method tunes the network accordingly. The efficiency and biological plausibility of the proposed cerebellar-based controller is then demonstrated under different robotic manipulation tasks reproducing motor behavior observed in human reaching experiments.

Calcium Imaging and the Curse of Negativity

The imaging of neuronal activity using calcium indicators has become a staple of modern neuroscience. However, without ground truths, there is a real risk of missing a significant portion of the real responses. Here, we show that a common assumption, the non-negativity of the neuronal responses as detected by calcium indicators, biases all levels of the frequently used analytical methods for these data. From the extraction of meaningful fluorescence changes to spike inference and the analysis of inferred spikes, each step risks missing real responses because of the assumption of non-negativity. We first show that negative deviations from baseline can exist in calcium imaging of neuronal activity. Then, we use simulated data to test three popular algorithms for image analysis, CaImAn, suite2p, and CellSort, finding that suite2p may be the best suited to large datasets. We also tested the spike inference algorithms included in CaImAn, suite2p, and Cellsort, as well as the dedicated inference algorithms MLspike and CASCADE, and found each to have limitations in dealing with inhibited neurons. Among these spike inference algorithms, FOOPSI, from CaImAn, performed the best on inhibited neurons, but even this algorithm inferred spurious spikes upon the return of the fluorescence signal to baseline. As such, new approaches will be needed before spikes can be sensitively and accurately inferred from calcium data in inhibited neurons. We further suggest avoiding data analysis approaches that, by assuming non-negativity, ignore inhibited responses. Instead, we suggest a first exploratory step, using k-means or PCA for example, to detect whether meaningful negative deviations are present. Taking these steps will ensure that inhibition, as well as excitation, is detected in calcium imaging datasets.

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.

Acute β-tetrabromoethylcyclohexane (β-TBECH) treatment inhibits the electrical activity of rat Purkinje neurons

Brominated flame-retardants are environmentally pervasive and persistent synthetic chemicals, some of which have been demonstrated to disrupt neuroendocrine signaling and electrical activity of neurons. 1,2-dibromo-4-(1,2-dibromoethyl)-cyclohexane (TBECH) lacks the toxicity of other classes of BFRs, however its safety is still questioned, as little is known of its neurological effects. Therefore, we sought to determine if TBECH could acutely alter the electrical activity of Purkinje neurons maintained in vitro. Briefly, cerebella from gestational day 20 rats were dissociated and maintained for up to three weeks in culture. Action potentials of Purkinje neurons were detected by cell-attached patch clamp before, during, and after application of β-TBECH. β-TBECH decreased action potential activity in a dose-dependent manner with an apparent EC₅₀ of 396 nM. β-TBECH did not significantly alter the coefficient of variation, a measure of the regularity of firing, suggesting that the mechanism of β-TBECH's effects on firing frequency may be independent of Purkinje neuron intracellular calcium handling. Because levels of β-TBECH in exposed individuals may not approach the EC₅₀, these data suggest that any abnormal neurodevelopment or behavior linked with β-TBECH exposure may result from endocrinological effects as opposed to direct disruption of electrical activity.

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.

A cerebellar adaptation to uncertain inputs

Noise and variability are inherent and unavoidable features of neural processing. Despite this physiological challenge, brain systems function well, suggesting the existence of adaptations that cope with noise. We report a novel adaptation that the cerebellum implements to maintain correct responses in the face of ambiguous inputs. We found that under these conditions, the cerebellum used a probabilistic binary choice: Although the probability of behavioral response gradually increased or decreased depending on the degree of similarity between current and trained inputs, the size of response remained constant. That way the cerebellum kept responses adaptive to trained input corrupted by noise while minimizing false responses to novel stimuli. Recordings and analysis of Purkinje cells activity showed that the binary choice is made in the cerebellar cortex. Results from large-scale simulation suggest that internal feedback from cerebellar nucleus back to cerebellar cortex plays a critical role in implementation of binary choice.

Purkinje Cell Signaling Deficits in Animal Models of Ataxia

Purkinje cell (PC) dysfunction or degeneration is the most frequent finding in animal models with ataxic symptoms. Mutations affecting intrinsic membrane properties can lead to ataxia by altering the firing rate of PCs or their firing pattern. However, the relationship between specific firing alterations and motor symptoms is not yet clear, and in some cases PC dysfunction precedes the onset of ataxic signs. Moreover, a great variety of ionic and synaptic mechanisms can affect PC signaling, resulting in different features of motor dysfunction. Mutations affecting Na⁺ channels (Na_V1.1, Na_V1.6, Na_Vβ4, Fgf14 or Rer1) reduce the firing rate of PCs, mainly via an impairment of the Na⁺ resurgent current. Mutations that reduce Kv3 currents limit the firing rate frequency range. Mutations of Kv1 channels act mainly on inhibitory interneurons, generating excessive GABAergic signaling onto PCs, resulting in episodic ataxia. Kv4.3 mutations are responsible for a complex syndrome with several neurologic dysfunctions including ataxia. Mutations of either Cav or BK channels have similar consequences, consisting in a disruption of the firing pattern of PCs, with loss of precision, leading to ataxia. Another category of pathogenic mechanisms of ataxia regards alterations of synaptic signals arriving at the PC. At the parallel fiber (PF)-PC synapse, mutations of glutamate delta-2 (GluD2) or its ligand Crbl1 are responsible for the loss of synaptic contacts, abolishment of long-term depression (LTD) and motor deficits. At the same synapse, a correct function of metabotropic glutamate receptor 1 (mGlu1) receptors is necessary to avoid ataxia. Failure of climbing fiber (CF) maturation and establishment of PC mono-innervation occurs in a great number of mutant mice, including mGlu1 and its transduction pathway, GluD2, semaphorins and their receptors. All these models have in common the alteration of PC output signals, due to a variety of mechanisms affecting incoming synaptic signals or the way they are processed by the repertoire of ionic channels responsible for intrinsic membrane properties. Although the PC is a final common pathway of ataxia, the link between specific firing alterations and neurologic symptoms has not yet been systematically studied and the alterations of the cerebellar contribution to motor signals are still unknown.

Dynamical Mechanism of Hyperpolarization-Activated Non-specific Cation Current Induced Resonance and Spike-Timing Precision in a Neuronal Model

Hyperpolarization-activated cyclic nucleotide-gated cation current (I_h) plays important roles in the achievement of many physiological/pathological functions in the nervous system by modulating the electrophysiological activities, such as the rebound (spike) to hyperpolarization stimulations, subthreshold membrane resonance to sinusoidal currents, and spike-timing precision to stochastic factors. In the present paper, with increasing g_h (conductance of I_h), the rebound (spike) and subthreshold resonance appear and become stronger, and the variability of the interspike intervals (ISIs) becomes lower, i.e., the enhancement of spike-timing precision, which are simulated in a conductance-based theoretical model and well explained by the nonlinear concept of bifurcation. With increasing g_h, the stable node to stable focus, to coexistence behavior, and to firing via the codimension-1 bifurcations (Hopf bifurcation, saddle-node bifurcation, saddle-node bifurcations on an invariant circle, and saddle homoclinic orbit) and codimension-2 bifurcations such as Bogdanov-Takens (BT) point related to the transition between saddle-node and Hopf bifurcations, are acquired with 1- and 2-parameter bifurcation analysis. The decrease of variability of ISIs with increasing g_h is induced by the fast decrease of the standard deviation of ISIs, which is related to the increase of the capacity of resisting noisy disturbance due to the firing becomes far away from the bifurcation point. The enhancement of the rebound (spike) with increasing g_h builds up a relationship to the decrease of the capacity of resisting disturbance like the hyperpolarization stimulus as the resting state approaches the bifurcation point. The “typical”-resonance and non-resonance appear in the parameter region of the stable focus and node far away from the bifurcation points, respectively. The complex or “strange” dynamics, such as the “weak”-resonance for the stable node near the transition point between the stable node and focus and the non-resonance for the stable focus close to the codimension-1 and −2 bifurcation points, are discussed.

Impact of Reduced Cerebellar EAAT Expression on Purkinje Cell Firing Pattern of NPC1-deficient Mice

Niemann-Pick disease Type C1 (NPC1) is a rare hereditary neurodegenerative disease. NPC1-patients suffer, amongst others, from ataxia, based on a loss of cerebellar Purkinje cells (PCs). Impaired expression/function of excitatory amino acid transporters (EAATs) are suspected of contributing to PC-degeneration in hereditary spinocerebellar ataxias (SCAs). Thus, we studied EAAT-expression and its impact to PC-activity in NPC1^−/–mice. Western blot revealed reduced EAAT1, EAAT2, EAAT4, and βIII-spectrin levels in NPC1^−/–mice. EAATs play a crucial role in synaptic transmission, thus we were interested in the impact of the reduced EAAT-expression on the function of PCs. Patch-clamp recordings of PCs showed no differences in the firing patterns of NPC1^+/+and NPC1^−/–mice using a low internal chloride concentration. Because EAAT4 also comprises a chloride permeable ion pore, we perturbed the chloride homeostasis using a high internal chloride concentration. We observed differences in the firing patterns of NPC1^+/+and NPC1^−/–mice, suggesting an impact of the altered EAAT4-expression. Additionally, the EAAT-antagonist DL-TBOA acts differently in NPC1^+/+and NPC1^−/–mice. Our data support the line of evidence that an altered EAAT-expression/function is involved in neurodegeneration of PCs observed in SCAs. Thus, we suggest that similar pathogenic mechanisms contribute the loss of PCs in NPC1.

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.

Oscillations, Timing, Plasticity, and Learning in the Cerebellum

The highly stereotyped, crystal-like architecture of the cerebellum has long served as a basis for hypotheses with regard to the function(s) that it subserves. Historically, most clinical observations and experimental work have focused on the involvement of the cerebellum in motor control, with particular emphasis on coordination and learning. Two main models have been suggested to account for cerebellar functioning. According to Llinás's theory, the cerebellum acts as a control machine that uses the rhythmic activity of the inferior olive to synchronize Purkinje cell populations for fine-tuning of coordination. In contrast, the Ito-Marr-Albus theory views the cerebellum as a motor learning machine that heuristically refines synaptic weights of the Purkinje cell based on error signals coming from the inferior olive. Here, we review the role of timing of neuronal events, oscillatory behavior, and synaptic and non-synaptic influences in functional plasticity that can be recorded in awake animals in various physiological and pathological models in a perspective that also includes non-motor aspects of cerebellar function. We discuss organizational levels from genes through intracellular signaling, synaptic network to system and behavior, as well as processes from signal production and processing to memory, delegation, and actual learning. We suggest an integrative concept for control and learning based on articulated oscillation templates.

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.

Corticotropin-releasing factor increases Purkinje neuron excitability by modulating sodium, potassium, and Ih currents

Corticotropin-releasing factor (CRF) is a neuromodulator closely associated with stress responses. It is synthesized and released in the central nervous system by various neurons, including neurons of the inferior olive. The targets of inferior olivary neurons, the cerebellar Purkinje neurons (PNs), are endowed with CRF receptors. CRF increases the excitability of PNs in vivo, but the biophysical mechanism is not clear. Here we examine the effect of CRF on the firing properties of PNs using acute rat cerebellar slices. CRF increased the PN firing rate, regardless of whether they were firing tonically or switching between firing and quiescent periods. Current- and voltage-clamp experiments showed that the increase in firing rate was associated with a voltage shift of the activation curve of the persistent sodium current and hyperpolarizing-activated current, as well as activation of voltage-dependent potassium current. The multiple effects on various ionic currents, which are in agreement with the possibility that activation of CRF receptors triggers several intracellular pathways, are manifested as an increase excitability of PN.

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.

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.

An integrator circuit in cerebellar cortex

The brain builds dynamic models of the body and the outside world to predict the consequences of actions and stimuli. A well-known example is the oculomotor integrator, which anticipates the position-dependent elasticity forces acting on the eye ball by mathematically integrating over time oculomotor velocity commands. Many models of neural integration have been proposed, based on feedback excitation, lateral inhibition or intrinsic neuronal nonlinearities. We report here that a computational model of the cerebellar cortex, a structure thought to implement dynamic models, reveals a hitherto unrecognized integrator circuit. In this model, comprising Purkinje cells, molecular layer interneurons and parallel fibres, Purkinje cells were able to generate responses lasting more than 10 s, to which both neuronal and network mechanisms contributed. Activation of the somatic fast sodium current by subthreshold voltage fluctuations was able to maintain pulse-evoked graded persistent activity, whereas lateral inhibition among Purkinje cells via recurrent axon collaterals further prolonged the responses to step and sine wave stimulation. The responses of Purkinje cells decayed with a time-constant whose value depended on their baseline spike rate, with integration vanishing at low (< 1 per s) and high rates (> 30 per s). The model predicts that the apparently fast circuit of the cerebellar cortex may control the timing of slow processes without having to rely on sensory feedback. Thus, the cerebellar cortex may contain an adaptive temporal integrator, with the sensitivity of integration to the baseline spike rate offering a potential mechanism of plasticity of the response time-constant.