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

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.

Complex Electroresponsive Dynamics in Olivocerebellar Neurons Represented With Extended-Generalized Leaky Integrate and Fire Models

The neurons of the olivocerebellar circuit exhibit complex electroresponsive dynamics, which are thought to play a fundamental role for network entraining, plasticity induction, signal processing, and noise filtering. In order to reproduce these properties in single-point neuron models, we have optimized the Extended-Generalized Leaky Integrate and Fire (E-GLIF) neuron through a multi-objective gradient-based algorithm targeting the desired input–output relationships. In this way, E-GLIF was tuned toward the unique input–output properties of Golgi cells, granule cells, Purkinje cells, molecular layer interneurons, deep cerebellar nuclei cells, and inferior olivary cells. E-GLIF proved able to simulate the complex cell-specific electroresponsive dynamics of the main olivocerebellar neurons including pacemaking, adaptation, bursting, post-inhibitory rebound excitation, subthreshold oscillations, resonance, and phase reset. The integration of these E-GLIF point-neuron models into olivocerebellar Spiking Neural Networks will allow to evaluate the impact of complex electroresponsive dynamics at the higher scales, up to motor behavior, in closed-loop simulations of sensorimotor tasks.

Transcranial Alternating Current Stimulation (tACS) Mechanisms and Protocols

Perception, cognition and consciousness can be modulated as a function of oscillating neural activity, while ongoing neuronal dynamics are influenced by synaptic activity and membrane potential. Consequently, transcranial alternating current stimulation (tACS) may be used for neurological intervention. The advantageous features of tACS include the biphasic and sinusoidal tACS currents, the ability to entrain large neuronal populations, and subtle control over somatic effects. Through neuromodulation of phasic, neural activity, tACS is a powerful tool to investigate the neural correlates of cognition. The rapid development in this area requires clarity about best practices. Here we briefly introduce tACS and review the most compelling findings in the literature to provide a starting point for using tACS. We suggest that tACS protocols be based on functional brain mechanisms and appropriate control experiments, including active sham and condition blinding.

Inverse Stochastic Resonance in Cerebellar Purkinje Cells

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

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

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.

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

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

Bidirectional modulation of deep cerebellar nuclear cells revealed by optogenetic manipulation of inhibitory inputs from Purkinje cells

In the mammalian cerebellum, deep cerebellar nuclear (DCN) cells convey all information from cortical Purkinje cells (PCs) to premotor nuclei and other brain regions. However, how DCN cells integrate inhibitory input from PCs with excitatory inputs from other sources has been difficult to assess, in part due to the large spatial separation between cortical PCs and their target cells in the nuclei. To circumvent this problem we have used a Cre-mediated genetic approach to generate mice in which channelrhodopsin-2 (ChR2), fused with a fluorescent reporter, is selectively expressed by GABAergic neurons, including PCs. In recordings from brain slice preparations from this model, mammalian PCs can be robustly depolarized and discharged by brief photostimulation. In recordings of postsynaptic DCN cells, photostimulation of PC axons induces a strong inhibition that resembles these cells' responses to focal electrical stimulation, but without a requirement for the glutamate receptor blockers typically applied in such experiments. In this optogenetic model, laser pulses as brief as 1 ms can reliably induce an inhibition that shuts down the spontaneous spiking of a DCN cell for ∼50 ms. If bursts of such brief light pulses are delivered, a fixed pattern of bistable bursting emerges. If these pulses are delivered continuously to a spontaneously bistable cell, the immediate response to such photostimulation is inhibitory in the cell's depolarized state and excitatory when the membrane has repolarized; a less regular burst pattern then persists after stimulation has been terminated. These results indicate that the spiking activity of DCN cells can be bidirectionally modulated by the optically activated synaptic inhibition of cortical PCs.

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.

Reduced spike frequency adaptation in Purkinje cells of the vestibulocerebellum

Firing regularity has long been an issue of firing dynamics in the vestibular circuitry. Spike frequency adaption (SFA) is ubiquitous in neuronal activity and can modulate neural coding, which may disrupt the regularity or accuracy of firing. We previously observed different characteristics of intrinsic excitability in Purkinje cells (PCs) of lobule X (vestibulocerebellum) compared to lobules III-V (spinocerebellum). However, systematic comparison of the extent of SFA in PCs of different lobules has not yet been made. In this study we examined the degree of SFA and compared the firing regularity by measuring interspike interval (ISI). During the course of low-frequency spike trains, PCs in lobules III-V showed gradual lengthening of ISI due to SFA. In contrast, ISI showed little change during the propagation of spikes in lobule X PCs. In high-frequency firing, PCs in lobules III-V exhibited gradual SFA, whereas lobule X neurons showed dramatic increase in ISI during the first four spikes and then stayed unchanged. The coefficient of variation of ISI of lobule X PCs was significantly lower in lobules III-V PCs during low-frequency firing. The comparison of duration of action potential showed no significant difference between lobules III-V and lobule X PCs during SFA even in low-frequency firing. The lack of SFA in lobule X PCs, as a part of vestibulocerebellum, might be involved in a consistent and regular coordination of vestibular function by the cerebellar cortex in response to low vestibular stimulation. However, the difference of SFA between lobules may be explained by other mechanisms than those which have been reported to be responsible for the SFA formation.

Enhanced synaptic inhibition disrupts the efferent code of cerebellar Purkinje neurons in leaner Cav2.1 Ca 2+ channel mutant mice

Cerebellar Purkinje cells (PCs) encode afferent information in the rate and temporal structure of their spike trains. Both spontaneous firing in these neurons and its modulation by synaptic inputs depend on Ca(2+) current carried by Ca(v)2.1 (P/Q) type channels. Previous studies have described how loss-of-function Ca(v)2.1 mutations affect intrinsic excitability and excitatory transmission in PCs. This study examines the effects of the leaner mutation on fast GABAergic transmission and its modulation of spontaneous firing in PCs. The leaner mutation enhances spontaneous synaptic inhibition of PCs, leading to transitory reductions in PC firing rate and increased spike rate variability. Enhanced inhibition is paralleled by an increase in the frequency and amplitude of spontaneous inhibitory postsynaptic currents (sIPSCs) measured under voltage clamp. These differences are abolished by tetrodotoxin, implicating effects of the mutation on spike-induced GABA release. Elevated sIPSC frequency in leaner PCs is not accompanied by increased mean firing rate in molecular layer interneurons, but IPSCs evoked in PCs by direct stimulation of these neurons exhibit larger amplitude, slower decay rate, and a higher burst probability compared to wild-type PCs. Ca(2+) release from internal stores appears to be required for enhanced inhibition since differences in sIPSC frequency and amplitude in leaner and wild-type PCs are abolished by thapsigargin, an ER Ca(2+) pump inhibitor. These findings represent the first account of the functional consequences of a loss-of-function P/Q channel mutation on PC firing properties through altered GABAergic transmission. Gain in synaptic inhibition shown here would compromise the fidelity of information coding in these neurons and may contribute to impaired cerebellar function resulting from loss-of function mutations in the Ca(V)2.1 channel gene.

Bistability in Purkinje neurons: ups and downs in cerebellar research

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

Dendritic calcium signaling in cerebellar Purkinje cell

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

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

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

Signals and circuits in the purkinje neuron

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

The cerebellar network: from structure to function and dynamics

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

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

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

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

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

High-Pass Filtering and Dynamic Gain Regulation Enhance Vertical Bursts Transmission along the Mossy Fiber Pathway of Cerebellum

Signal elaboration in the cerebellum mossy fiber input pathway presents controversial aspects, especially concerning gain regulation and the spot-like (rather than beam-like) appearance of granular to molecular layer transmission. By using voltage-sensitive dye imaging in rat cerebellar slices (Mapelli et al., 2010), we found that mossy fiber bursts optimally excited the granular layer above ∼50 Hz and the overlaying molecular layer above ∼100 Hz, thus generating a cascade of high-pass filters. NMDA receptors enhanced transmission in the granular, while GABA-A receptors depressed transmission in both the granular and molecular layer. Burst transmission gain was controlled through a dynamic frequency-dependent involvement of these receptors. Moreover, while high-frequency transmission was enhanced along vertical lines connecting the granular to molecular layer, no high-frequency enhancement was observed along the parallel fiber axis in the molecular layer. This was probably due to the stronger effect of Purkinje cell GABA-A receptor-mediated inhibition occurring along the parallel fibers than along the granule cell axon ascending branch. The consequent amplification of burst responses along vertical transmission lines could explain the spot-like activation of Purkinje cells observed following punctuate stimulation in vivo.

A Signal Processing Analysis of Purkinje Cells in vitro

Cerebellar Purkinje cells in vitro fire recurrent sequences of Sodium and Calcium spikes. Here, we analyze the Purkinje cell using harmonic analysis, and our experiments reveal that its output signal is comprised of three distinct frequency bands, which are combined using Amplitude and Frequency Modulation (AM/FM). We find that the three characteristic frequencies – Sodium, Calcium and Switching – occur in various combinations in all waveforms observed using whole-cell current clamp recordings. We found that the Calcium frequency can display a frequency doubling of its frequency mode, and the Switching frequency can act as a possible generator of pauses that are typically seen in Purkinje output recordings. Using a reversibly photo-switchable kainate receptor agonist, we demonstrate the external modulation of the Calcium and Switching frequencies. These experiments and Fourier analysis suggest that the Purkinje cell can be understood as a harmonic signal oscillator, enabling a higher level of interpretation of Purkinje signaling based on modern signal processing techniques.