State-dependence of climbing fiber-driven calcium transients in Purkinje cells

Bistability in Hodgkin-Huxley-type equations

We study how initial conditions of the Hodgkin-Huxley model affect the dynamics of simulated neurons. We systematically vary the amplitudes of depolarization currents in order to bring neuron dynamics to stable equilibrium. Our results demonstrate that simulated neurons can have spontaneous spiking or a silent state, depending on the initial conditions. We propose the methodology to study the circumstances under which Purkinje cells transit between hyperpolarized quiescent state (down state) and a depolarized spiking state (up state). We show that results derived using the Hodgkin-Huxley methodology should be carefully analyzed before suggesting a direct relevance to neuroprosthetic implants.

Cerebellar involvement in an evidence-accumulation decision-making task

To make successful evidence-based decisions, the brain must rapidly and accurately transform sensory inputs into specific goal-directed behaviors. Most experimental work on this subject has focused on forebrain mechanisms. Using a novel evidence-accumulation task for mice, we performed recording and perturbation studies of crus I of the lateral posterior cerebellum, which communicates bidirectionally with numerous forebrain regions. Cerebellar inactivation led to a reduction in the fraction of correct trials. Using two-photon fluorescence imaging of calcium, we found that Purkinje cell somatic activity contained choice/evidence-related information. Decision errors were represented by dendritic calcium spikes, which in other contexts are known to drive cerebellar plasticity. We propose that cerebellar circuitry may contribute to computations that support accurate performance in this perceptual decision-making task.

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.

Signals and circuits in the purkinje neuron

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

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

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

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.

Lipid signaling in cytosolic phospholipase A2alpha-cyclooxygenase-2 cascade mediates cerebellar long-term depression and motor learning

In this study, we show the crucial roles of lipid signaling in long-term depression (LTD), that is, synaptic plasticity prevailing in cerebellar Purkinje cells. In mouse brain slices, we found that cPLA(2)alpha knockout blocked LTD induction, which was rescued by replenishing arachidonic acid (AA) or prostaglandin (PG) D(2) or E(2). Moreover, cyclooxygenase (COX)-2 inhibitors block LTD, which is rescued by supplementing PGD(2)/E(2). The blockade or rescue occurs when these reagents are applied within a time window of 5-15 min following the onset of LTD-inducing stimulation. Furthermore, PGD(2)/E(2) facilitates the chemical induction of LTD by a PKC activator but is unable to rescue the LTD blocked by a PKC inhibitor. We conclude that PGD(2)/E(2) mediates LTD jointly with PKC, and suggest possible pathways for their interaction. Finally, we demonstrate in awake mice that cPLA(2)alpha deficiency or COX-2 inhibition attenuates short-term adaptation of optokinetic eye movements, supporting the view that LTD underlies motor learning.

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

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

Climbing fiber signaling and cerebellar gain control

The physiology of climbing fiber signals in cerebellar Purkinje cells has been studied since the early days of electrophysiology. Both the climbing fiber-evoked complex spike and the role of climbing fiber activity in the induction of long-term depression (LTD) at parallel fiber-Purkinje cell synapses have become hallmark features of cerebellar physiology. However, the key role of climbing fiber signaling in cerebellar motor learning has been challenged by recent reports of forms of synaptic and non-synaptic plasticity in the cerebellar cortex that do not involve climbing fiber activity, but might well play a role in cerebellar learning. Moreover, cerebellar LTD does not seem to strictly require climbing fiber activity. These observations make it necessary to re-evaluate the role of climbing fiber signaling in cerebellar function. Here, we argue that climbing fiber signaling is about adjusting relative probabilities for the induction of LTD and long-term potentiation (LTP) at parallel fiber synapses. Complex spike-associated, dendritic calcium transients control postsynaptic LTD and LTP induction. High calcium transients, provided by complex spike activity, do not only favor postsynaptic LTD induction, but simultaneously trigger retrograde cannabinoid signaling, which blocks the induction of presynaptic LTP. Plasticity of the climbing fiber input itself provides additional means to fine-tune complex spike associated calcium signaling and thus to adjust the gain of heterosynaptic climbing fiber control. In addition to dendritic calcium transients, climbing fiber activity leads to the release of the neuropeptide corticotropin-releasing factor (CRF), which facilitates LTD induction at both parallel fiber and climbing fiber synapses.