Ca2+ regulation of a large conductance K+ channel in cultured rat cerebellar Purkinje neurons

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.

Controlling Ca2+-activated K+ channels with models of Ca2+ buffering in Purkinje cells

Intracellular Ca(2+) concentrations play a crucial role in the physiological interaction between Ca(2+) channels and Ca(2+)-activated K(+) channels. The commonly used model, a Ca(2+) pool with a short relaxation time, fails to simulate interactions occurring at multiple time scales. On the other hand, detailed computational models including various Ca(2+) buffers and pumps can result in large computational cost due to radial diffusion in large compartments, which may be undesirable when simulating morphologically detailed Purkinje cell models. We present a method using a compensating mechanism to replace radial diffusion and compared the dynamics of different Ca(2+) buffering models during generation of a dendritic Ca(2+) spike in a single compartment model of a PC dendritic segment with Ca(2+) channels of P- and T-type and Ca(2+)-activated K(+) channels of BK- and SK-type. The Ca(2+) dynamics models used are (1) a single Ca(2+) pool; (2) two Ca(2+) pools, respectively, for the fast and slow transients; (3) detailed Ca(2+) dynamics with buffers, pump, and diffusion; and (4) detailed Ca(2+) dynamics with buffers, pump, and diffusion compensation. Our results show that detailed Ca(2+) dynamics models have significantly better control over Ca(2+)-activated K(+) channels and lead to physiologically more realistic simulations of Ca(2+) spikes and bursting. Furthermore, the compensating mechanism largely eliminates the effect of removing diffusion from the model on Ca(2+) dynamics over multiple time scales.

L-type Ca2+ channels contribute to current-evoked spike firing and associated Ca2+ signals in cerebellar Purkinje neurons

The physiological properties of Purkinje neurons play a central role in their ability to regulate information transfer through the cerebellum. A number of ion channels contribute to Purkinje neuron physiology including an abundance of P-type Ca2+ channels, particularly in the dendritic region. Purkinje neurons also express L-type Ca2+ channels both during development and in the mature state. However, a role for L-type channels in Purkinje neuron physiology has yet to be fully defined. In the current study we used physiological recordings from cultured Purkinje neurons and the L-type Ca2+ channel agonist S-(-)-Bay K to assess a potential role for L-type Ca2+ channels in spike firing. Results show that Bay K alters current-evoked spike firing in young, immature Purkinje neurons without dendritic structure and in older, more mature Purkinje neurons with dendritic structure. Bay K also enhanced Ca2+ signals associated with the current-evoked spike firing. The effect of Bay K was more prominent in the young Purkinje neurons than in the older Purkinje neurons, suggesting that L-type Ca2+ channels may be more important in the Purkinje neuron physiology during the early stages of development rather than at mature stages. In the older Purkinje neurons, immunohistochemical studies using antibodies to L-type Ca2+ channels showed more intense immunolabeling in the somatic region than in the dendritic region. This result suggests that L-type Ca2+ channels may play a more important role in somatic physiology than dendritic physiology, whereas P-type channels may play a more important role in dendritic physiology.

Eye movements of the murine P/Q calcium channel mutant tottering, and the impact of aging

Mice carrying mutations of the gene encoding the ion pore of the P/Q calcium channel (Cacna1a) are an instance in which cerebellar dysfunction may be attributable to altered electrophysiology and thus provide an opportunity to study how neuronal intrinsic properties dictate signal processing in the ocular motor system. P/Q channel mutations can engender multiple effects at the single neuron, circuit, and behavioral levels; correlating physiological and behavioral abnormalities in multiple allelic strains will ultimately facilitate determining which alterations of physiology are responsible for specific behavioral aberrations. We used videooculography to quantify ocular motor behavior in tottering mutants aged 3 mo to 2 yr and compared their performance to data previously obtained in the allelic mutant rocker and C57BL/6 controls. Tottering mutants shared numerous abnormalities with rocker, including upward deviation of the eyes at rest, increased vestibuloocular reflex (VOR) phase lead at low stimulus frequencies, reduced VOR gain at high stimulus frequencies, reduced gain of the horizontal and vertical optokinetic reflex, reduced time constants of the neural integrator, and reduced plasticity of the VOR as assessed in a cross-axis training paradigm. Unlike rocker, young tottering mutants exhibited normal peak velocities of nystagmus fast phases, arguing against a role for neuromuscular transmission defects in the attenuation of compensatory eye movements. Tottering also differed by exhibiting directional asymmetries of the gains of optokinetic reflexes. The data suggest at least four pathophysiological mechanisms (two congenital and two acquired) are required to explain the ocular motor deficits in the two Cacna1a mutant strains.

Dendritic control of spontaneous bursting in cerebellar Purkinje cells

We investigated the mechanisms that contribute to spontaneous regular bursting in adult Purkinje neurons in acutely prepared cerebellar slices. Bursts consisted of 3-20 spikes and showed a stereotypic waveform. Each burst developed with an increase in firing rate and was terminated by a more rapid increase in firing rate and a decrease in spike height. Whole-cell current-clamp recordings showed that each burst ended with a rapid depolarization followed by a hyperpolarization. Dual dendritic and somatic extracellular recordings revealed that each burst was terminated by a dendritic calcium spike. The contributions of T- and P/Q-type calcium current, large (BK) and small (SK) conductance calcium-activated potassium currents, and hyperpolarization-activated (I(H)) current to bursting were investigated with specific channel blockers. None of the currents, except for P/Q, were required to sustain spontaneous bursting or the stereotypic burst waveform. T-type calcium, BK, and SK channels contributed to interspike and interburst intervals. The effect of T-type calcium channel block was more pronounced after BK channel block and vice versa, indicating that these two currents interact to regulate burst firing. Block of I(H) current had no effect on bursting. Partial block of P/Q-type calcium channels concurrently eliminated dendritic calcium spikes and caused a switch from regular bursting to tonic firing or irregular bursting. Dendritic calcium spikes persisted in the presence of tetrodotoxin, indicating that their initiation did not require somatic sodium spikes. Our results demonstrate an important role for dendritic conductances in burst firing in intact Purkinje neurons.

Conditional protein phosphorylation regulates BK channel activity in rat cerebellar Purkinje neurons

Large conductance calcium- and voltage-activated potassium (BK) channels are widely expressed in the mammalian central nervous system. Although the activity of BK channels in endocrine and vascular cells is regulated by protein kinases and phosphatases associated with the channel complex, direct evidence for such modulation in neurons is largely lacking. Single-channel analysis from inside-out patches isolated from the soma of dissociated rat cerebellar Purkinje neurons demonstrated that the activity of BK channels is regulated by multiple endogenous protein kinases and protein phosphatases in the membrane patch. The majority of BK channels were non-inactivating and displayed a 'low' activity phenotype determined at +40 mV and 1 muM intracellular free calcium. These channels were activated by cAMP-dependent protein kinase (PKA) associated with the patch and the extent of PKA activation was limited by an opposing endogenous type 2A-like protein phosphatase (PP2A). Importantly, PKA activation was dependent upon the prior phosphorylation status of the BK channel complex dynamically controlled by protein kinase C (PKC) and protein phosphatase 1 (PP1). In contrast, Purkinje cells also displayed a low proportion of non-inactivating BK channels with a 'high' activity under the same recording conditions and these channels were inhibited by endogenous PKA. Our data suggest that: (1) multiple endogenous protein kinases and phosphatases functionally couple to the BK channel complex to allow conditional modulation of BK channel activity in neurons, and (2) native, phenotypically distinct, neuronal BK channels are differentially sensitive to PKA-dependent phosphorylation.

Ionic mechanisms of burst firing in dissociated Purkinje neurons

Cerebellar Purkinje neurons have intrinsic membrane properties that favor burst firing, seen not only during complex spikes elicited by climbing fiber input but also with direct electrical stimulation of cell bodies. We examined the ionic conductances that underlie all-or-none burst firing elicited in acutely dissociated mouse Purkinje neurons by short depolarizing current injections. Blocking voltage-dependent calcium entry by cadmium or replacement of external calcium by magnesium enhanced burst firing, but it was blocked by cobalt replacement of calcium, probably reflecting block of sodium channels. In voltage-clamp experiments, we used the burst waveform of each cell as a voltage command and used ionic substitutions and pharmacological manipulations to isolate tetrodotoxin (TTX)-sensitive sodium current, P-type and T-type calcium current, hyperpolarization-activated cation current (Ih), voltage-activated potassium current, large-conductance calcium-activated potassium current, and small-conductance calcium-activated potassium (SK) current. Measured near the middle of the first interspike interval, TTX-sensitive sodium current carried the largest inward current, and T-type calcium current was also substantial. Current through P-type channels was large immediately after a spike but decayed rapidly. These inward currents were opposed by substantial components of voltage-dependent and calcium-dependent potassium current. Termination of the burst is caused partly by decay of sodium current, together with a progressive buildup of SK current after the first interspike interval. Although burst firing depends on the net balance between multiple large currents flowing after a spike, it is surprisingly robust, probably reflecting complex interactions between the exact voltage waveform and voltage and calcium dependence of the various currents.

Properties and functional role of voltage-dependent potassium channels in dendrites of rat cerebellar Purkinje neurons

We characterized the properties and functional roles of voltage-dependent potassium channels in the dendrites of Purkinje neurons studied in rat cerebellar slices. Using outside-out patches formed <or=250 microm away from the soma, we found that depolarization-activated potassium channels were present at high density throughout the dendritic tree. Currents required relatively large depolarizations for activation (midpoint, approximately -10 mV), had rapid activation and deactivation kinetics, and inactivated partially (20-70% over 200 msec) with both fast (time constant, 15-20 msec) and slow (300-400 msec) components. Inactivating and noninactivating components were both blocked potently by external tetraethylammonium (half-block by 150 microm) and 4-aminopyridine (half-block by 110 microm). The voltage dependence, kinetics, and pharmacology suggest a predominant contribution by Kv3 family subunits, and immunocytochemical experiments showed staining for both Kv3.3 and Kv3.4 subunits in the dendritic tree. In the proximal dendrite, potassium channels were activated by passively spread sodium spikes recorded at the same position, and experiments using dual recordings showed that the channels serve to actively dampen back-propagation of somatic sodium spikes. In more distal dendrites, potassium currents were activated by voltage waveforms taken from climbing fiber responses, suggesting that they help shape these responses as well. The requirement for large depolarizations allows dendritic Kv3 channels to shape large depolarizing events while not disrupting spatial and temporal summation of smaller excitatory postsynaptic potentials.

Distinct contributions of small and large conductance Ca2+-activated K+ channels to rat Purkinje neuron function

The cerebellum is important for many aspects of behaviour, from posture maintenance and goal-oriented reaching movements to timing tasks and certain forms of learning. In every case, information flowing through the cerebellum passes through Purkinje neurons, which receive input from the two primary cerebellar afferents and generate continuous streams of action potentials that constitute the sole output from the cerebellar cortex to the deep nuclei. The tonic firing behaviour observed in Purkinje neurons in vivo is maintained in brain slices even when synaptic inputs are blocked, suggesting that Purkinje neuron activity relies to a significant extent on intrinsic conductances. Previous research has suggested that the interplay between Ca2+ currents and Ca2+-activated K+ channels (KCa channels) is important for Purkinje cell activity, but how many different KCa channel types are present and what each channel type contributes to cell behaviour remains unclear. In order to better understand the ionic mechanisms that control the behaviour of these neurons, we investigated the effects of different Ca2+ channel and KCa channel antagonists on Purkinje neurons in acute slices of rat cerebellum. Our data show that Ca2+ entering through P-type voltage-gated Ca2+ channels activates both small-conductance (SK) and large-conductance (BK) KCa channels. SK channels play a role in setting the intrinsic firing frequency, while BK channels regulate action potential shape and may contribute to the unique climbing fibre response.

The making of a complex spike: ionic composition and plasticity

Climbing fiber (CF) activation evokes a large all-or-nothing electrical response in Purkinje cells (PCs), the complex spike. It has been suggested that the role of CFs (and thus complex spikes) is that of a "teacher" in simple learning paradigms such as associative eyeblink conditioning. An alternative hypothesis describes the olivocerebellar system as part of a timing device and denies a role of the CF input in learning. To date, neither of these hypotheses nor others can definitively be verified or discounted. Similarly, the complex spike evades a clear understanding when it comes to the cellular events underlying complex spike generation. What is known, however, is that complex spikes are associated with large dendritic calcium signals that are required for the induction of long-term depression (LTD) at the parallel fiber (PF)-PC synapse. PF-LTD is a form of long-term synaptic plasticity that has been suggested to underlie certain forms of cerebellar motor learning. In contrast to the PF input, the CF input has been considered invariant. Our recent discovery of LTD at the CF input shows that complex spikes are less static than previously assumed. In addition to depression of CF-evoked excitatory postsynaptic currents, long-lasting, selective reduction of slow complex spike components could be observed after brief CF tetanization. To understand the functional implications of CF-LTD, it is crucial to know the types of currents constituting the specific complex spike components. Here we review the "anatomy" of the complex spike as well as our observations of activity-dependent complex spike waveform modifications. In addition, we discuss which properties CF-LTD might add to the circuitry of the cerebellar cortex.

Characterization of large conductance Ca2+-activated K+ channels in cerebellar Purkinje neurons

We investigated the role of large conductance, calcium-activated potassium channels (BK channels) in regulation of the excitability of cerebellar Purkinje neurons. Block of BK channels by iberiotoxin reduced the afterhyperpolarization of spontaneous action potentials in Purkinje neurons in acutely prepared cerebellar slices. To establish the conditions required for activation of BK channels in Purkinje neurons, the dependence of BK channel open probability on calcium concentration and membrane voltage were investigated in excised patches from soma of acutely prepared Purkinje cells. Single channel currents were studied under conditions designed to select for potassium currents and in which voltage-activated currents were largely inactivated. Micromolar calcium concentrations activated channels with a mean single channel conductance of 266 pS. BK channels were activated by both calcium and membrane depolarization, and showed no sign of inactivation. At a given calcium concentration, depolarization over a 60-mV range increased the mean open probability (P(O)) from < 0.1 to > 0.8. Increasing the calcium concentration shifted the voltage required for half maximal activation to more hyperpolarized potentials. The apparent affinity of the channels for calcium increased with depolarization. At -60 mV the apparent affinity was approximately 35 micro m decreasing to approximately 3 micro M at +40 mV. These results suggest that BK channels are unlikely to be activated at resting membrane potentials and calcium concentrations. We tested the hypothesis that Purkinje cell BK channels may be activated by calcium entry during individual action potentials. Significant BK channel activation could be detected when brief action potential-like depolarizations were applied to patches under conditions in which the sole source of calcium was flux across the plasma membrane via the endogenous voltage-gated calcium channels. It is proposed that BK channels regulate the excitability of Purkinje cells by contributing to afterhyperpolarizations and perhaps by shaping individual action potentials.

A-type potassium currents active at subthreshold potentials in mouse cerebellar Purkinje cells

Voltage-dependent and calcium-independent K+ currents were whole-cell recorded from cerebellar Purkinje cells in slices. Tetraethylammonium (TEA, 4 mM) application isolated an A-type K+ current (I(K(A))) with a peak amplitude, at +20 mV, of about one third of the total voltage-dependent and calcium-independent K+ current. The I(K(A)) activated at about -60 mV, had a V(0.5) of activation of -24.9 mV and a V(0.5) of inactivation of -69.2 mV. The deactivation time constant at -70 mV was 3.4 +/- 0.4 ms, while the activation time constant at +20 mV was 0.9 +/- 0.2 ms. The inactivation kinetics was weakly voltage dependent, with two time constants; those at +20 mV were 19.3 +/- 3.1 and 97.6 +/- 9.8 ms. The recovery from inactivation had two time constants of 60.8 ms (78.4 %) and 962.3 ms (21.6 %). The I(K(A)) was blocked by 4-aminopyridine with an IC50 of 67.6 microM. Agitoxin-2 (2 nM) blocked 17.4 +/- 2.1 % of the I(K(A)). Flecainide completely blocked the I(K(A)) with a biphasic effect with IC50 values of 4.4 and 183.2 microM. In current-clamp recordings the duration of evoked action potentials was affected neither by agitoxin-2 (2 nM) nor by flecainide (3 microM), but action potentials that were already broadened by TEA were further prolonged by 4-aminopyridine (100 microM). The amplitude of the hyperpolarisation at the end of depolarising steps was reduced by all these blockers.

Control of the propagation of dendritic low-threshold Ca(2+) spikes in Purkinje cells from rat cerebellar slice cultures

To investigate the ionic mechanisms controlling the dendrosomatic propagation of low-threshold Ca(2+) spikes (LTS) in Purkinje cells (PCs), somatically evoked discharges of action potentials (APs) were recorded under current-clamp conditions. The whole-cell configuration of the patch-clamp method was used in PCs from rat cerebellar slice cultures. Full blockade of the P/Q-type Ca(2+) current revealed slow but transient depolarizations associated with bursts of fast Na(+) APs. These can occur as a single isolated event at the onset of current injection, or repetitively (i.e. a slow complex burst). The initial transient depolarization was identified as an LTS Blockade of P/Q-type Ca(2+) channels increased the likelihood of recording Ca(2+) spikes at the soma by promoting dendrosomatic propagation. Slow rhythmic depolarizations shared several properties with the LTS (kinetics, activation/inactivation, calcium dependency and dendritic origin), suggesting that they correspond to repetitively activated dendritic LTS, which reach the soma when P/Q channels are blocked. Somatic LTS and slow complex burst activity were also induced by K(+) channel blockers such as TEA (2.5 x 10(-4) M) charybdotoxin (CTX, 10(-5) M), rIberiotoxin (10(-7) M), and 4-aminopyridine (4-AP, 10(-3) M), but not by apamin (10(-4) M). In the presence of 4-AP, slow complex burst activity occurred even at hyperpolarized potentials (-80 mV). In conclusion, we suggest that the propagation of dendritic LTS is controlled directly by 4-AP-sensitive K(+) channels, and indirectly modulated by activation of calcium-activated K(+) (BK) channels via P/Q-mediated Ca(2+) entry. The slow complex burst resembles strikingly the complex spike elicited by climbing fibre stimulation, and we therefore propose, as a hypothesis, that dendrosomatic propagation of the LTS could underlie the complex spike.

Homeostatic compensation maintains Ca2+ signaling functions in Purkinje neurons in the leaner mutant mouse

Several human neurological disorders have been associated with mutations in the gene coding for the alpha1 subunit of the P/Q type voltage-gated calcium channel (alpha1A/Ca(v)2.1). Mutations in this gene also occur in a number of neurologically affected mouse strains, including leaner (tg(la)/tg(la)). Because the P-type calcium current is very prominent in cerebellar Purkinje neurons, these cells from mice with alpha1 subunit mutations make excellent models for the investigation of the functional consequences of native mutations in a voltage-gated calcium channel of mammalian central nervous system. In this review, we describe the impact of altered channel function on cellular calcium homeostasis and signaling. Remarkably, calcium buffering functions of the endoplasmic reticulum and calcium-binding proteins appear to be regulated in order to compensate for altered calcium influx through the mutant channels. Although this compensation may serve to maintain calcium signaling functions, such as calcium-induced calcium release, it remains uncertain whether such compensation alleviates or contributes to the behavioral phenotype.