Voltage-gated Na⁺ channels (Na_V) are involved in determining active properties of neurons including voltage threshold for generating AP at the axon hillock and amplitude of AP spike [40,41,42]. In the cerebellar PCs, various subtypes of voltage-gated Na⁺ channels are expressed, for instance, Na_V1.1, Na_V1.2 and Na_V1.6 have been observed in rodent PCs [45,46,47,48,49]. Observation of [Na⁺]_i changes and electrophysiological recordings via outside-out patch clamp configuration have revealed that Na⁺ spikes are generated within the somatic area of PC and then passively spread into the dendrites [49]. Despite some subtypes of Na_V and changes in [Na⁺]_i in the PC dendrites were observed, backpropagation of AP into the dendrite from soma is absent, suggesting that the [Na⁺]_i influx and subtypes of Na⁺ channels expressed in dendrites are not sufficient to generate AP in PC dendrites. In addition, electrophysiological recordings of I_Na in the cerebellar PCs have revealed a fast inactivating and/or a persistent conductance of Na⁺ [47,50].

Among subtypes of Na_V, Na_V1.6 shows a distinct feature, which contributes to transient and resurgent components, but not to persistent components (Table 1). Na_V1.6 was remarkably observed in the dendritic area in the cerebellar PCs [51]. The resurgent I_Na facilitates reopen Na_V when the membrane potential is repolarized to approximately −40 mV following the long period of depolarization exceeds +30 mV enough to produce maximal inactivation of Na_V [52,53]. This distinctive current flow contributes to ensuring the fast-spiking activity of the cerebellar PCs via the rapid open-channel block and unblock mechanism because the PCs, in particular, spontaneously fire AP spikes at high frequency. Resurgent current, carried by Na_V1.6, has been found to be a mechanism by which the refractory period between AP firing is shortened by rapid recovery from inactivation of I_Na [54,55]. Transgenic mice which resurgent Na⁺ current is disrupted showed an abnormality in the spiking activity of PCs and manifestation of cerebellar ataxia and failure of motor coordination [54,56]. Recent studies have shown that Na_V channel auxiliary subunit FGF14′b′ isoform is involved in controlling the resurgent current and excitability of PCs [57]. In parallel with previous observations, ablation of this auxiliary subunit manifests the abnormality of the firing activity in PCs and motor behavior [57,58]. Interestingly, inactivation of Na_V1.6 affects not only the motor performance but also associative classical conditioning and spatial memory formation. Purkinje cell-specific deletion of Scn8a, encoding Na_V1.6, impaired the performance in the delayed eyeblink conditioning and the Morris water maze [59].

K⁺ channels are another major players in determining the excitability of the neurons. As molecular techniques have been advanced, various subtypes of K⁺ channels and their gating properties have been characterized [60]. Like Na⁺ channels, many K⁺ channels have shown quite distinct and divergent gating properties depending on the types of auxiliary proteins. K⁺ channels are classified into several types, including voltage-gated channels (K_V), Ca²⁺-activated K⁺ channels (K_Ca), inwardly rectifying channels (inward rectifier) and Na⁺-activated K⁺ channels. In this review, we focused on the roles of several K_V subfamilies (Table 2) and Ca²⁺-activated K⁺ channels (Table 2) in intrinsic firing properties of the cerebellar PCs.

Considering the Hodgkin-Huxley model, ionic flow carried by Na⁺ and K⁺ determines the active and passive properties of neurons. Of interest, K⁺ conductance controls the resting membrane potential, membrane resistance, neuronal excitability, duration of AP and delay time to fire AP spike. Electrophysiological observations and immunohistochemistry data have shown that various types of K⁺ channels are expressed in cerebellar PC soma and dendrites [61,62,63,64,65,66,67,68]. Gähwiler and Llano [61] observed that outward I_K is found to be elicited by membrane depolarization above −30 mV from excised somatic membrane. This suprathreshold-activated I_K shows sensitivity for general K⁺ current inhibitors, tetraethylammonium (TEA) and 4-aminopyrimidine (4-AP), indicating that the I_K is governed by K_v3 subfamily of K⁺ channel [66,69]. This class of K⁺ channels (especially K_V3.3 and 3.4) repolarizes the Na⁺ spike discharge to maintain repetitive AP firing in both soma and dendritic area [68,70,71,72]. Therefore, dysfunction of this subfamily results in the impairment of repetitive AP spike discharge with a high frequency and an abnormal behavior [73]. In addition, the pharmacological inhibition with 1~10 mM of 4-AP or 2~5 mM TEA affects the dendritic Ca²⁺ spike discharge, indicating that the dendritic K_V3 channels contribute to shaping membrane excitability of PC dendrites as well as soma [74]. In spite of lacking backpropagation of Na⁺ spikes into PC dendrites, membrane depolarization passively propagates into proximal and distal dendrites thereby generating regenerative Na⁺ spikes and plateau potential which promotes bursting Na⁺ spikes [48,75]. In addition, strong depolarization induced by CF activation leads to Ca²⁺ influx into the dendrite, resulting in the Na⁺ - Ca²⁺ complex spike responses. The mixed Na⁺ - Ca²⁺ spike discharge activates dendritic K_V3.1/3.3 channels, enabling PC spiking activity to be stably maintained with high frequency though preventing Na⁺ channel inactivation. When [Ca²⁺]_i is increased by CF activation, large conductance Ca²⁺-activated K⁺ (BK) channels are also activated. Interestingly, co-activation of K_V3 and BK channels promotes coupling between Na⁺ and Ca²⁺ spike discharge via reducing Na⁺ channel inactivation, resulting in burst output of the cerebellar PCs [68].

Differently from K_V3 family, some other types of K⁺ channels show distinct gating properties, for instance, K_V1 and 4 subtypes are activated at subthreshold voltage whereas K_V3 family shows high voltage-activating and fast deactivating voltage dependency [76]. Storm [77] categorized the subthreshold-activated K⁺ channels into 2 types depending on their sensitivity for 4-AP concentration and on the gating properties, A-type and D-type K_V channels, governed by K_V1.4, K_V4.X and K_V1.1, 1.2, 1.6, respectively. D-type K⁺ channels, sensitive to dendrotoxin (DTX) and low concentration of 4-AP, are well known for determining spike output timing, latency and threshold for AP firing onset and firing frequency [14,77,78,79,80,81]. In the cerebellar PCs, large depolarization can induce Na⁺ - Ca²⁺ coupling in dendritic area leading to slowly depolarized potential (SDP), facilitating Na⁺ burst spike generation. Pharmacological inhibition of the D-type currents shortens the SDP and reduces latency to Ca²⁺ spikes [65], suggesting that the D-type channels are involved in the regulation of dendritic excitability. Application of DTX in cerebellar slices also increases spontaneous rhythmic activity through the enhancement of rebound firing, indicating that D-type I_K plays a modulatory role in defining spiking pattern in PCs [82]. In addition, K_V1.2-containing K⁺ channels have been shown to inhibit the spontaneous and non-specific Ca²⁺ activity in the PC dendrites to encode motor timing signals. Furthermore, these ion channels contribute to the synaptic integration of PF inputs [83]. Taken together, low-threshold activated and non-inactivating D-type K⁺ channels take a part in the integration and generation of finely tuned signals in PCs, thereby signal tuning within physiological appropriate ranges.

Previous studies have shown that A-type and D-type K⁺ channels play similar physiological roles. For example, the A-type I_K contributes to spike acceleration and determines the firing patterns in the cerebellar PCs [84,85]. Strikingly, this subfamily of K⁺ channels is absent in PC somata or dissociated PC, suggesting an exclusive dendritic expression (and axon fiber). In PC dendrites, K_V3 family is also expressed and regulates dendritic active properties. Given the distinct gating properties of A-type K⁺ channels from K_V3 family, this subfamily of K⁺ channels is implicated in regulating the subthreshold variations of the membrane potential and processing the synaptic inputs [86,87].

Instead of dendritic Na⁺ channels, cerebellar PC dendrites express Ca²⁺ channels with high density. Therefore, strong depolarization causes synchronization of the passively conducted Na⁺ spike and Ca²⁺ spike in dendrites to shape the appropriate spiking activity of PCs. The influx of dendritic Ca²⁺ can activate an ionic flow carried by K⁺, Ca²⁺-activated K⁺ channels. These types of channels are classified into two; small conductance and large conductance Ca²⁺-activated K⁺ channel (SK and BK channel, respectively) (Table 3). Both SK and BK channels are also implicated in controlling the spiking activity in PCs [88]. When the dendritic membrane is depolarized by synaptic inputs, local [Ca²⁺]_i is elevated through P/Q type Ca²⁺ channels, leading to the activation of the SK channels [89]. The SK channels are expressed in PC somata as well as in dendrites. Interestingly, dendrosomatic electrical coupling is governed by SK2 channels in PC soma and dendrite [90]. In addition, somatic and dendritic SK channels show distinct roles in regulating PC activity. SK channels in soma set the maximal level of PC firing frequency, and on the other hand, dendritic SK channels determine the extent of dendritic regions contributing to the firing rates of PCs. The other types of Ca²⁺-activated K⁺ channel, BK channels are also involved in the spiking activity in PCs. As we described above, co-activity of K_V3 and BK channels modulates dendritic Na⁺ - Ca²⁺ coupling burst elicited by CF inputs through suppression of Na⁺ channel inactivation [68]. Both SK and BK channels are activated by Ca²⁺ entering through P/Q type Ca²⁺ channels and regulate PC firing patterns. However, these channels differently contribute to firing behavior in PCs. SK channels have an impact on the setting intrinsic firing frequency [90] whereas BK channels are involved in the regulation of AP waveform and presumably climbing fiber responses [68,91]. Recent studies have shown that CF-evoked pause of spontaneous firing and generation of burst firing in PCs require BK channels coupled to Ca²⁺ channels [92,93]. Because SK and BK channels in PCs play a critical role in the regulation of firing behavior, dysfunction of these channels has been implicated in cerebellar disease such as ataxia. Mutations in P/Q type Ca²⁺ channels resulted in the decrease in the precision of PC pacemaking activity and perfusion of 1-ethyl-2-benzimidazolinone (EBIO), K_Ca activator improves the regularity of spontaneous firing and motor performance [94]. In addition, dysregulation of SK and/or BK channels has been reported in various genetic ataxia animal models [94,95,96,97], suggesting that modulation of SK and BK channels may be therapeutic targets for cerebella disease and motor dysfunction.

Many theories have implicated that the potentiation or depression of the synaptic transmission at the PF-PC synapses and non-synaptic intrinsic plasticity are required for cerebellar-dependent learning and memory. Intriguingly, the intrinsic plasticity requires an activity-dependent modulation of ion channels (Fig. 2) [13,14,15,98,99,100]. The ion channels in the cerebellar PCs are regulated by various factors such as an activation of metabotropic receptor or synaptic plasticity-related intracellular signaling [13,15,100,101]. When the chronic changes in network activity occur, the neuronal activity is homeostatically regulated in order to maintain the stability of network activity [102,103,104,105]. Prolonged application of tetrodotoxin (TTX) to organotypic cultures of cerebellar slices exhibits downregulation of the intrinsic excitability [100]. This homeostatic intrinsic plasticity is derived from an augmentation of hyperpolarization-activated cyclic nucleotide-gated (HCN) channel current (I_h) in the cerebellar PCs. Interestingly, the activity-dependent upregulation of I_h in PCs requires an agonist-independent activity of metabotropic glutamate receptor 1 (mGluR1) and its G_S-coupled downstream of PKA signaling. Ablation of HCN channels in PCs exclusively disrupts the integration of inhibitory synaptic inputs and bi-stability of PC firing behavior [22]. Furthermore, HCN channels regulate a balance between excitation and inhibition through the integration of glutamatergic and GABAergic transmission and firing stability, thereby promoting memory formation at the late stages of cerebellar learning [106].

Recently, plasticity of the intrinsic excitability of the cerebellar PCs has been found to be accompanied by the synaptic plasticity [13,15,107]. In fact, PF-PC synaptic LTP derives the long-term potentiation of intrinsic excitability (LTP-IE). LTP-IE requires the downregulation of SK2 channels in dendritic area. The SK channel-dependent intrinsic plasticity may play a role in shaping the cerebellar PC output to adjust the impact of synaptic inputs within optimal ranges. The LTP-IE dampens the impact of PF inputs on the firing behavior of PCs, enabling effects of non-potentiated, weaker synaptic inputs on cellular output signal to minimize [13]. Interestingly, although local dendritic Ca²⁺ signaling is enhanced after formation of LTP-IE, prior induction of intrinsic plasticity prevents subsequent induction of synaptic LTP in PCs. Therefore, the role of intrinsic excitability in signal processing in the PCs is quite distinct from other types of neurons such as hippocampal pyramidal neurons or cortical neurons because enhanced Ca²⁺ signaling has been regarded as enlargements of synaptic inputs and increases in possibility of subsequent plasticity induction [108,109]. Considering that one important role of SK channels is setting the firing frequency in physiological limits, SK channel-mediated LTP-IE may ensure that excitatory drive stays within the physiological limits and prevent non-specific subsequent synaptic plasticity induction thereby stabilizing and maximizing the information processing after learning.

In addition to the intrinsic plasticity followed by induction of LTP, the activity-dependent downregulation of PF-PC synaptic function accompanies the intrinsic plasticity. Yang and Santamaria [107] described that the potentiation of excitability in PCs is found following an induction of PF-PC LTD through downregulation of HCN channel conductance. Many observations have shown that the associative eyeblink conditioning training exerts modification of synaptic strength (PF-PC LTD) as well as intrinsic properties of the cerebellar PCs (potentiation of excitability) [110,111]. Those described that the activity-dependent plasticity of intrinsic excitability may be homeostatically regulated which is similar to hippocampal intrinsic plasticity [18,19]. Alternatively, Shim et al. [15] demonstrated that the intrinsic excitability is found to be decreased following induction of synaptic LTD. This result is parallel with the previous observation in which population spiking activity is attenuated by synaptic LTD induction [112]. Those contradictory results may be derived from different experimental conditions: Yang and Santamaria [107] delivered PF stimuli with somatic depolarization instead of CF activation whereas Shim et al. [15] synaptically induced synaptic plasticity by delivering simultaneous and conjunctive stimulation of PF and CF within specific time-window. Behavioral training could induce neural plasticity through divergent pathways. Thus, the intrinsic plasticity following synaptic depression may be presumably modulated in various aspects including potentiation or depression of firing rates, responsiveness of synaptic inputs or patterns of spiking activity to achieve maximizing the information storage in the cerebellar circuits.

Several observations have shown that associative eyeblink conditioning accompanies the experience- and use-dependent plasticity in the cerebellar cortex [113,114,115,116,117]. The experience-dependent plasticity of dendritic membrane excitability can be maintained 1 month after conditioning. Recently, it was shown that the delayed eyeblink conditioning increases intrinsic excitability and changes in AP waveforms, presumably derived from SK channel downregulation [118]. There are several evidence supporting that the memory trace in PCs is not just an increase or a decrease in firing rates. In fact, PC activity reflects adaptively timed activity pattern with intrinsic cellular mechanisms rather than a temporal pattern of excitatory or inhibitory synaptic inputs [113,114,115]. Taken together, experience-dependent modulation of PC intrinsic excitability is another form of memory engram for the cerebellardependent motor learning.

Since Ito hypothesized that synaptic LTD between PF-PC synapses is the principal elements for the cerebellar-dependent motor learning [24], much of investigation has been extensively focused on the cellular mechanism of the modification of synaptic function to account memory storage in the cerebellum and motor control. Unlikely to synaptic plasticity or LTP-IE, the underlying mechanism for LTD-IE has less been elucidated. Previous reports described that the intrinsic plasticity and synaptic plasticity indeed share intracellular signaling including protein phosphatase and/or protein kinases (Fig. 2). Several signaling molecules are required to induce PF-PC LTD such as protein kinase C (PKC) and CaMKII. In the hippocampus, HCN channel activity is mediated by PKC signaling during mGluR-dependent plasticity induction, which results in intrinsic plasticity. However, mGluR-PKC signaling suppresses I_h, insisting that the LTD-IE in the cerebellar PCs may not be reflected by this signaling cascade. CaMKII is also known for a crucial element of synaptic and intrinsic plasticity. In the VN neurons, the activity-dependent plasticity of excitability requires bidirectional modulation of BK channels mediated by the balance between PKC and CaMKII activity [119,120,121,122]. The cerebellar PF-PC synaptic LTD recruits CaMKII signaling which increases open probability of BK channels, thus this type of K_Ca may be one possible candidate for the activity-dependent intrinsic plasticity in the cerebellar PCs. Since the cellular and molecular basis for LTD-IE of the cerebellar PCs remain unclear, the detailed mechanisms for the intrinsic plasticity should be further investigated.

Intrinsic plasticity plays a complementary role in integrating synaptic inputs and generating cellular output signal [15,18,19,105,123,124]. Synaptic-driven potentiation or depression of excitability show the same polarity with the corresponding direction of synaptic plasticity [13,15], indicating that the modifications in synaptic strength are synergistically reflected into the final net output of PCs following plasticity. When the synaptic weight is strengthened, the PC output signal is more potentiated, not compensated by intrinsic properties. In addition, cerebellar PC intrinsic plasticity occurs in the branch-dependent manner [98], indicating that synaptic inputs from specific-branches are potentiated by increased membrane excitability limited in conditioned dendritic branches. Otherwise, the plastic changes in synaptic transmission might be contaminated by global changes of excitability and less reflected into the neuronal firing output signal.

What is the physiological consequence of the bidirectional modulation of intrinsic excitability following plasticity induction or behavioral training? Vestibulo-ocular reflex (VOR) and optokinetic response (OKR) is a representative behavioral paradigm of cerebellar-dependent motor learning. The VOR gain, the ratio of vestibular stimuli to adaptive eye-movement, can be increased or decreased depending on the learning paradigm. Boyden and Raymond [37] reported that the VOR gain-up and -down learning are selectively engaged by the aspects of synaptic plasticity. There was a supporting evidence of this view in which injection of mGluR1 antagonist into the cerebellar flocculus, the core area for VOR learning in the cerebellum, suppresses gain-up learning whereas gain-down learning is not affected by either agonist and antagonist of mGluR1 [38]. In addition, an ultrastructural observation shows a reduction of surface AMPA receptor following the adaptive eye-movement learning, suggesting that the cerebellar LTD would occur during the motor learning [125]. Most recently, it was revealed that the adaptive eye-movement training is associated with modifications of synaptic transmission at the PF-PC synapses [6], indicating the prominent roles of bidirectional synaptic plasticity at PF-PC synapses in the motor learning.

In contrast to Ito's cerebellar LTD theory, many studies have shown that the PF-PC LTD may not be a sufficient cellular mechanism underlying motor learnings in spite of abundant studies describing the critical roles of PF-PC LTD in VOR learning [28,36,126,127,128,129]. Miles and Lisberger [130,131] proposed an alternative mechanism for motor learning, which suggests principal roles of VN neurons in the motor memory storage. There is, however, accumulating evidence showing that motor memory storage requires neuronal plasticity at multiple sites including neurons in the cerebellar cortex and VN [12,27]. Recently, a computational model for motor memory storage provided insights into the mechanism by which motor memory traces are seemingly transferred from cortical neurons (PC) to sub-cortical region (VN) [33,132]. Cumulative experimental data has shown that encoding the adaptive motor memory in the cerebellar cortex occurs within a few hours and the critical time window for memory transfer is approximately 2.5~4 hours after training [133,134]. Interestingly, Ito [129] recently suggested that an early adaption is dependent on the cerebellar cortical activity and the late phase of adaptation is accompanied by plasticity in the VN neurons. In parallel, the changes in the population spiking activity in VN neurons are manifested a day after training whereas there is no significant alteration of VN activity within an hour after training [135]. Until recently, this prediction for memory consolidation mechanism has not been investigated in a cellular and circuit level. Recent papers suggested that the intrinsic plasticity of the PCs might be the mechanism of the memory transfer from cerebellar cortex to sub-cortical areas [15,88]. Collectively, computational implications and experimental observations have both agreed to Ito's recent suggestion in which PF-PC synaptic plasticity may take part in the memory acquisition and plasticity in MF-VN synapses may be involved in long-term memory storage beyond two long-lasting conflicts for VOR memory: Marr-Albus-Ito's cerebellar LTD hypothesis vs. Miles and Lisberger' MF-VN synaptic plasticity theory.

Belmeguenai et al. [13] and Shim et al. [15] insisted that the intrinsic plasticity is modulated by synaptic activity pattern-dependent manner and this bidirectionality may function as an amplifier of the synaptic modification, enabling to transduce the finely tuned signal into the relay neurons such as neurons in DCN or VN. Given that the neural plasticity in the neurons in the cerebellar cortex and VN shows bidirectionality, the intrinsic plasticity would be also selectively engaged by certain forms of learning paradigm and the synergies with synaptic modulation may complete the scenario for the memory storage in the motor circuitry including cerebellum and VN.