The principal signal generated by glutamate released by PFs is a brief depolarization due to an excitatory post-synaptic current (EPSC) though postsynaptic glutamate receptors of the α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) type, formed by subunits GluA1–4 (Tempia et al., 1996). The influx of Ca²⁺ through these receptors is negligible, as it has been measured to constitute about 0.6% of the total inward current. This means that, under physiological conditions, PC AMPA receptors are strongly selective for monovalent cations, such as sodium and potassium ions. The exclusion of Ca²⁺ ions from the selectivity filter is due to the presence of an arginine residue (R) in a critical position called Q/R site. The mechanism that allows PC AMPA receptors to have an R residue is peculiar, because all four genes of AMPA receptor subunits, GluA1, 2, 3 and 4, code for a glutamine (Q) residue (Hollmann et al., 1991; Hume et al., 1991). However, the GluA2 subunit undergoes an mRNA editing process, which converts a Q-coding triplet into and R-coding one (Sommer et al., 1991). In cerebellar PCs the efficiency of the editing process is almost 100%, as can be inferred by the negligible Ca²⁺ permeability of AMPA receptors. In addition to a complete editing of the GluA2 mRNA, a strong expression of this subunit is also necessary, so that virtually all AMPA receptors, which are tetramers, contain at least one R in the selectivity filter, which is sufficient to exclude Ca²⁺. This is the case in PCs.

It is interesting to note that the majority of PF-PC synapses have been shown to be silent but this has a series of advantages (Ekerot and Jörntell, 2001; Isope and Barbour, 2002). First, simulation studies using a perceptron neural network model have shown that the presence of 50% silent PF-PC synapses optimizes the information storage in terms of reliability and capacity (Brunel et al., 2004). Second, even if most PF-PC synapses are silent, the remaining synapses show a high release probability with only a few failures (Isope and Barbour, 2002). Third, PFs have a fast vesicle replenishment rate (Valera et al., 2012), which allows the active granule cells to transmit signals to PC with high efficiency and reliability (Isope and Barbour, 2002; Valera et al., 2012). These functional features endow the PF-PC synapse to sustain very high firing frequencies, up to 1 kHz, which are generated in bursts of activity during physiological stimulation in vivo (Eccles et al., 1966; Chadderton et al., 2004; van Beugen et al., 2013). In such a way PF-PC synapses can guarantee a high fidelity transmission even at high frequencies (Isope and Barbour, 2002; Valera et al., 2012), but also assure a linear transfer function for frequencies up to 300 Hz (van Beugen et al., 2013).

In addition to AMPA receptors located in front of the presynaptic active zone from which glutamate is released, PC dendritic spines innervated by PFs also express mGlu₁ G-protein coupled receptors, localized perisynaptically (Nusser et al., 1994). As a consequence of their location, more distant from the release site, and because of the high efficiency of glutamate reuptake mechanisms (Takahashi et al., 1995), isolated action potentials are not effective for the activation of mGlu₁ receptors, but a brief train of PF action potentials is required, so that glutamate concentration can build up in the synaptic cleft and diffuse to the perisynaptic zone. The activation of mGlu₁ receptors generates a localized increase of Ca²⁺ in a portion of the dendritic tree (Finch and Augustine, 1998; Takechi et al., 1998; Tempia et al., 2001), accompanied by an excitatory post-synaptic potential (Batchelor and Garthwaite, 1993; Batchelor et al., 1994).

The mechanism responsible for the mGlu₁-dependent intradendritic Ca²⁺ signal is the canonical transduction pathway. The resulting Ca²⁺ signal is independent of the membrane potential because it is generated by the release of Ca²⁺ from the endoplasmic reticulum (Finch and Augustine, 1998; Takechi et al., 1998; Tempia et al., 2001). The mGlu₁ receptor activates a G_q protein, which activates phospholipase C (PLC), starting the production of diacylglycerol (DAG) and inositol 1,4, 5-trisphosphate (IP₃). IP₃ opens Ca²⁺ release channels (IP₃ receptors: IP₃Rs) in the endoplasmic reticulum. The coincident activation of PF leading to Ca²⁺ release, and CF, causing Ca²⁺ entry through voltage-gated channels, is considered a critical signal to trigger synaptic plasticity (Tempia and Konnerth, 1994).

The excitatory post-synaptic potential evoked by the activation of mGlu₁ receptors (Batchelor and Garthwaite, 1993; Batchelor et al., 1994) is due to an inward current (PF-mGlu₁-EPSC; Tempia et al., 1998). The PF-mGlu₁-EPSC has an amplitude and a duration, which encode the frequency and the number of PF action potentials (Tempia et al., 1998). The latency of the PF-mGlu₁-EPSC is in the subsecond range, relatively short for a G protein-mediated process, with the smallest value of 0.14 s (Tempia et al., 1998). The transduction pathway leading to the PF-mGlu₁-EPSC is an unconventional one. PCs selectively express G proteins of the G_q subclass (Tanaka et al., 2000), and more precisely G_q and G_alpha11 (Tanaka et al., 2000). Among these two proteins, only G_q is required for the generation of PF-mGlu₁-EPSC (Hartmann et al., 2004); but its downstream pathway leading to the activation of PLC, IP₃ or protein kinase C (PKC) is not involved (Tempia et al., 1998; Canepari et al., 2001). The ionic mechanism of the PF-mGlu₁-EPSC is associated with a relevant sodium influx, which has been studied by optical methods (Knöpfel et al., 2000). As a result of several pioneering studies, hyperpolarization-activated cation channels (Canepari et al., 2001), purinergic receptors (Canepari et al., 2001), Na⁺/Ca²⁺-exchangers (Hirono et al., 1998) and voltage-gated Ca²⁺ channels (Tempia et al., 2001) have been excluded as molecular candidates responsible for the generation of the mGlu₁-induced inward current in PCs. A few years later, it was shown that the mGlu₁-induced current is in part mediated by a member of the class of canonical transient receptor potential (TRPC) channels (Kim et al., 2003), subsequently identified as TRPC3 (Hartmann et al., 2008). Recently, it has been proposed that activation of delta-2 glutamate (GluD2) receptors can also contribute to the PF-mGlu₁-EPSC (Ady et al., 2014). GluD2 is an ion channel selectively permeable to the monovalent cations, unlike the TRPC3 channel, which has a non-selective permeability to Na⁺ and Ca²⁺, GluD2 is not gated by glutamate, so that for a long time it had been considered an orphan receptor, belonging to the glutamate receptors family merely on the basis of sequence similarity with the other members of this group. Since the mechanism of GluD2 gating upon glutamate binding to mGlu₁ receptors is not known, further studies are necessary to confirm this finding.

Although the PF-mGlu₁-EPSC does not require release of Ca²⁺ from internal stores of the endoplasmic reticulum (Tempia et al., 2001), it is strongly modulated by extracellular (Tempia et al., 1998, 2001; Tabata et al., 2002) and by intradendritic Ca²⁺ (Batchelor and Garthwaite, 1997; Tempia et al., 1997). Because of its sensitivity to intracellular Ca²⁺, PF-mGlu₁-EPSC acts as coincidence detector. In fact, a train of PF action potentials, combined with an elevation of intradendritic Ca²⁺, causes a marked potentiation of the PF-mGlu₁-EPSC (Batchelor and Garthwaite, 1997; Tempia et al., 1997; Dzubay and Otis, 2002). It should be pointed out that PCs possess several mechanisms for the control of intradendritic Ca²⁺. The first route of Ca²⁺ entry into PC dendrites is constituted by voltage-dependent Ca²⁺ channels. Thus, all mechanisms that depolarize PC dendrites enough to reach the threshold for Ca²⁺ channel gating can generate intradendritic Ca²⁺ signals. In fact, a strong activation of PFs can evoke a localized dendritic Ca²⁺ elevation (Eilers et al., 1995; Rancz and Häusser, 2006). However, the largest Ca²⁺ signals of PC dendrites are caused by the massive depolarization due to the activation of the CF-PC synapse, but in this case, the signal is spread throughout the dendritic tree (Konnerth et al., 1992; Miyakawa et al., 1992). Moreover, the coincidence of PF and CF activity has an additive effect leading to even larger elevations of intradendritic Ca²⁺ localized to the dendritic spines receiving both signals (Wang et al., 2000).

LTD at the PF-PC synapse is the best characterized form of synaptic plasticity in the cerebellum since it is believed to underlie several forms of motor learning, including the adaptation of the vestibulo-ocular reflex (VOR), associative eyeblink conditioning, and limb load adjustment (Ito, 1982, 1989; Krupa and Thompson, 1997). Indeed, an important feature of cerebellar LTD is the property of associativity: the long-lasting depression of PF responses results from the coincident activation of CF and PF inputs to a PC. LTD was originally described in vivo by Ito et al. (1982) in decerebrated rabbits. In this study, they demonstrated that stimulation of the vestibular nerve, which conveys mossy fibers to the flocculus, conjunctively with the stimulation of the inferior olive, the sole source of CFs, induced a long-lasting depression of the PC responses to vestibular nerve stimulation. Afterward, studies of in vitro preparations (i.e., cerebellar slices and cultures) have provided further insight into the cellular and molecular mechanisms of LTD (Ito, 2002). These studies indicate that PF-LTD requires the Ca²⁺ influx through P/Q voltage-gated channels, triggered by the CF-evoked depolarization, together with the release of glutamate by PFs, which acts upon both mGlu₁ metabotropic receptors and AMPA receptors (Figure 1A). As reported above, stimulation of the mGlu₁ receptor promotes, via G-protein (G_q/11), DAG production and Ca²⁺ release from the endoplasmic reticulum (Aiba et al., 1994; Conquet et al., 1994; Matsumoto et al., 1996; Ichise et al., 2000; Hirono et al., 2001; Miyata et al., 2001; Hartmann et al., 2004; Kano et al., 2008). The PF-induced release of Ca²⁺ together with the Ca²⁺ entry evoked by CF stimulation determines a significant increase of Ca²⁺ concentration particularly at the level of spines and shafts of PC dendrites (Miyakawa et al., 1992; Eilers et al., 1995). DAG and Ca²⁺ act synergistically to activate PKC, which in turn activates a series of kinases, including Raf, MEK and ERK1/ERK2 (Tanaka and Augustine, 2008). Among the different PKC isoforms expressed in PCs, PKCα is critically required for LTD induction (Leitges et al., 2004). Indeed, cerebellar LTD is absent in PCs derived from PKCα null mice and is rescued by transfection with an expression plasmid encoding PKCα but not other PKC isoforms (Leitges et al., 2004). Activated PKC induces the phosphorylation of AMPA receptors at serin-880 of the GluA2 terminus, which results in the elimination of the receptor from the dendritic spines via clathrin-mediated endocytosis (Wang and Linden, 2000). The reduction in the number of postsynaptic AMPA receptors represents the key change for LTD expression since it is responsible for the reduced responsiveness to glutamate and therefore for the decreased transmission at the PF-PC synapse. It is now clear that the endocytic removal of postsynaptic AMPA receptors is a complex phenomenon regulated by the interaction of GluA2 not only with PKC but also with glutamate receptor-interacting proteins (GRIP1 and GRIP2/ABP) and the PDZ domain-containing protein PICK1 (protein interacting with C kinase 1). In particular, it has been demonstrated that GluA2 binds GRIP1 and GRIP2 in the dephospho-Ser-880 state; however, when GluA2 Ser-880 is phosphorylated by PKC, the affinity of GRIP1/2 for GluA2 is disrupted and this allows the binding of the receptor to PICK1 (Hirai, 2001). PICK1 is indeed considered a key regulator of AMPA receptor traffic since it is directly involved in the removal of AMPA receptors from the synaptic plasma membrane (Hanley, 2008). Recently, it has been found that the targeting of PKCα to the synapses is also regulated by a diacylglycerol kinase ζ (DGKζ), that can interact with PKCα and as well as with postsynaptic density protein 95 (PSD-95; Lee et al., 2015). DGKζ has the ability to metabolize DAG thus reducing the PKCα activity to the basal level. Following LTD induction, the activated PKCα phosphorylates and releases DGKζ so that PKCα can interact with PICK1 to enhance AMPA receptors internalization. By recruiting Raf kinase, PKC can also induce the sequential activation of MEK, ERK1/2 and phospholipase A₂, resulting in the production of arachidonic acid and subsequent activation of PKC. The MAPK-PKC positive feedback loop is likely responsible for the sustained PKC activation and the maintenance of LTD (Yamamoto et al., 2012).

In addition to LTD, PF-PC synapses can undergo both pre- and postsynaptically expressed types of LTP (Figures 1B,C). The presynaptically expressed LTP is induced by brief PF stimulations at the frequency of 4–8 Hz. The leading event is the increase of Ca²⁺ influx within PF terminals that activates a Ca²⁺/calmodulin-dependent adenylyl cyclase, resulting in enhanced presynaptic cAMP levels and protein kinase A (PKA) activation (Salin et al., 1996; Chen and Regehr, 1997; Storm et al., 1998; Jacoby et al., 2001). PKA then phosphorylates the vesicle-release related proteins, RIM1α and Rab3, thus increasing glutamate release from PFs (Kaeser et al., 2008). Although most of the presynaptic Ca²⁺ enters PFs through N-type and P/Q-type Ca²⁺ channels, PF-LTP can still occur when both of these channel types are blocked and the global Ca²⁺ levels are largely reduced by 50% (Myoga and Regehr, 2011). On the other hand, blocking R-type Ca²⁺ channels disrupts PF-LTP, despite these channels play a minor role in basal transmission and contribute modestly to overall Ca²⁺ entry. Presynaptic LTP appears to be finely regulated by endocannabinoids (eCB), which are released by PCs following PF stimulation (Maejima et al., 2001, 2005; Brown et al., 2003). Activation of CB₁ receptors on PF terminals inhibits AC and PKA activity, thus preventing LTP induction. Interestingly, the coactivation of CF can enhance eCB retrograde inhibition of PF transmission thus promoting PF-LTD while suppressing PF-LTP (van Beugen et al., 2006).

The postsynaptically expressed LTP is evoked by PF stimulation at low frequency (typically 1 Hz) that triggers the GluA2-containing AMPA receptors insertion in the spine membrane. The GluA2 subunit insertion at synaptic sites involves N-ethylmaleimide-sensitive factor (NSF), an essential component of SNARE-mediated fusion machinery, which binds GluA2 and reduces the receptor internalization by PICK1 (Anggono and Huganir, 2012). In contrast, during LTD, the elevated postsynaptic [Ca²⁺] inhibits NSF–GluA2 interaction, thus promoting GluA2–PICK1 binding and synaptic removal of GluA2-containing AMPA receptors. Unlike LTD, the induction of postsynaptic LTP depends on lower Ca²⁺ transients and requires the activation of protein phosphatases PP1, PP2A and PP2B (Belmeguenai and Hansel, 2005). These phosphatases enhance GluA2 binding to GRIP, which in turn stabilizes the AMPA receptors to the membrane. Indeed, mutant mice, in which the PP2B (or calcineurin) was deleted only in cerebellar PCs, show deficit in postsynaptic PF-PC LTP and motor learning, whereas LTD induction was unaffected (Schonewille et al., 2010).

The observation of concomitant impaired LTP and motor learning, with no alteration of LTD, challenged the common view that cerebellar LTD alone underlies motor learning. Indeed, cerebellar motor learning during eyeblink conditioning and adaptation of the VOR appears to be completely normal in mutants in which LTD induction was impaired by inactivation of AMPA receptor internalization (Schonewille et al., 2011). This suggests that learning may result from the interaction of several forms of synaptic plasticity and not just from classical LTD alone. Indeed, it is now clear that different forms of plasticity take place in the granular layer, in the molecular layer and DCN involving both excitatory and inhibitory synaptic transmission (Gao et al., 2012; D’Angelo et al., 2016). These forms of synaptic plasticity are believed to operate in conjunction with long-lasting modifications in neuronal excitability during memory formation in the cerebellum (Schreurs et al., 1998; Belmeguenai et al., 2010; Grasselli et al., 2016). Indeed, Purkinje cell recordings from cerebellar slices of rabbits that had acquired delay eyelid conditioning revealed an increased PC membrane excitability that lasted for 30 days after training.

But what is then the role of CFs? The principal hypothesis is that the complex spike discharge of PCs encodes motor error signals and serves as a teaching signal that drives motor adaptation. This means that LTD should be driven by error-related signals carried by CFs whereas LTP should occur when such error signals are absent, without CF supervision (Sakurai, 1987). A corollary of this hypothesis is that the CFs may regulate PC activity under certain conditions, such as when attention is enhanced or errors in motor execution become large, as suggested Kimpo et al. (2014). In their study, monkeys sat in a rotating chair (to provide vestibular stimuli), and were trained to track a visual object with their eyes. They found that when the visual stimulus was moved in the opposite direction from the vestibular stimulus so that a bigger reflexive eye movement was required to stabilize the image (VOR-increase training), the activation of the CFs in response to the error led to a change in the response of the PCs. However, when the visual stimulus moved together with the head and a smaller reflexive eye movement was needed (VOR-decrease training), the error signals carried by CFs did not alter the PC firing rate. Interestingly, the optogenetic activation of CFs, mimicking the visual error signals provided by retinal slip, was able to induce VOR-increase but not VOR-decrease learning. These results indicate that the CF activity and the plasticity of the PC responses are not so correlated during VOR-decrease training, as they are during VOR-increase learning. Thus, although both motor learning paradigms elicited error signals in the CFs, PCs could regulate the CF-triggered plasticity.

Moreover, there is growing evidence that long-term plastic changes can occur in the cerebellar cortical network in the absence of the intervention of CFs. For example, Ramakrishnan et al. (2016) have recently demonstrated that theta burst tactile stimulation (a burst of 80 air puffs delivered at 4 Hz) mimicking natural stimulation patterns can induce a long-lasting potentiation of PC discharge and long-lasting decrease of molecular layer interneurons firing in the absence of complex spike changes. Interestingly, there are also indications that memory of fear is accompanied by LTP at PF-PC synapses, which is consistent with the view that Hebbian learning occurs in the cerebellar cortex during fear conditioning (Sacchetti et al., 2004; Zhu et al., 2007). This fear conditioning-induced potentiation is postsynaptically expressed and displays some properties of LTP elicited in vitro by repetitive stimulation of PFs.

The cerebellum receives a dense innervation by serotonergic fibers, which represent the third largest population of afferent fibers extending into this brain region, after mossy and CFs. The serotonin inputs to the cerebellum originate mainly in the medullary and pontine reticular formation and distribute to both cerebellar cortex and nuclei (Chan-Palay, 1975; Bishop and Ho, 1985). Anatomical and pharmacological studies indicate that the cerebellar cortex expresses multiple subtypes of 5-hydroxytriptamine receptors (5-HTRs). In particular, there is clear evidence that PCs express the 5-HT₁, 5-HT₂, 5-HT₅ and 5-HT₇ subtypes whereas 5-HT₃Rs and 5-HT₆Rs are localized on granule cells (Pazos and Palacios, 1985; Geurts et al., 2002; Li et al., 2004). Expression of 5-HT_5AR has also been found on Golgi cells and molecular layer interneurons (Geurts et al., 2002; Oostland et al., 2014). Given the widespread distribution of serotonergic innervation and the richness of signals evoked by different 5-HTR subtypes, it is not surprising that 5-HT has the potential to modulate both excitatory and inhibitory synaptic signals throughout the cerebellar network. Indeed, it has been shown that activation of 5-HT₁Rs determines a general suppression of cerebellar cortex activity by reducing the release of the excitatory transmitter glutamate from PFs to PCs (Maura et al., 1986) and by increasing inhibitory synaptic transmission onto PCs (Mitoma et al., 1994; Mitoma and Konishi, 1999).

By using patch-clamp recordings in cerebellar slices of adult mice, Lippiello et al. (2016) have recently demonstrated that 5-HT₇Rs are critically implicated in synaptic plasticity of the PF-PC synapse, thus providing a novel cellular and molecular basis for the action of 5-HT at cerebellar level. In particular, they found that 5-HT₇R activation by a selective agonist causes LTD of the PF-PC synapse via a postsynaptic mechanism that involves the PKC-MAPK signaling pathway (Figure 2A). As previously described, MAPK activation may trigger a positive feedback, via phospholipase A₂, which is responsible for a sustained activation of PKC and consequent internalization of AMPA receptors. In addition, they showed that treatment with a 5-HT₇R antagonist reduced the expression of postsynaptic PF-LTD, produced by pairing PF stimulation with PC depolarization; on the other hand, application of a 5-HT₇R agonist impaired postsynaptic LTP induced by 1 Hz stimulation of PFs. These results suggest that 5-HT₇R exerts a fine regulation of bidirectional synaptic plasticity by favoring the emergence of LTD vs. LTP at PF-PC synapses. This type of synaptic control may enable the serotonergic pathways to prevent the simultaneous occurrence of conflicting forms of plasticity at PF-PC, such as potentiation of synaptic transmission under conditions that promote postsynaptic LTD.

The involvement of serotonin 5-HT in motor learning has been observed in several cerebellar-dependent paradigms. For example, depletion of brain 5-HT has been shown to impair the horizontal VOR adaptation in rabbits (Miyashita and Watanabe, 1984). In addition, application of a 5-HT receptor (5-HTR) antagonist, ritanserin, to the cerebellar vermis before training, impaired the formation of long-term memory of conditioned freezing and extinction of the defensive component of the acoustic startle reaction (Storozheva and Proshin, 2011). Furthermore, chronic treatment with buspirone, a 5-HT1AR partial agonist, improves the motor coordination deficits in Lurcher mouse, a model of cerebellar neurodegeneration (Le Marec et al., 2001). Serotonergic modulation of the cerebellum has been also a subject of clinical interest since the discovery that long-term administration of L-5-hydroxytryptophan, a precursor of 5-HT, improves the dysfunctions associated with cerebellar disorders in patients with inherited or acquired ataxia (Trouillas et al., 1988, 1995). Furthermore, there is evidence that neurodevelopmental disorders such as autism and schizophrenia are associated with a change in 5-HTR expression in the cerebellum (Slater et al., 1998; Eastwood et al., 2001).

The noradrenergic innervation of the cerebellum originates from the locus coeruleus and distributes to all parts of the cerebellar cortex and DCN (Olson and Fuxe, 1971; Abbott and Sotelo, 2000). Studies using lesions and pharmacological approaches combined with behavioral analysis have provided a direct evidence that the noradrenergic locus coeruleus system is implicated in a wide variety of brain processes, including attention, arousal, decision making and memory (Aston-Jones et al., 1999; Clayton et al., 2004). The demonstration that the cerebellar cortex receives a widespread projection from the locus coeruleus has led researchers to hypothesize that the noradrenergic system may also be involved in the modulation of cerebellar functions and motor learning. To test this hypothesis, van Neerven et al. (1990) examined the effect of the noradrenergic system on the adaptive changes of the VOR in rabbits. They found that the injection of a β-adrenergic agonist, isoproterenol, into the flocculus enhanced the adaptive potentiation of VOR particularly in darkness; whereas the application of a β-antagonist, sotalol, significantly reduced the adaptation of the VOR in the light and darkness. Further studies in rabbit and rat have demonstrated that blockade of β-adrenergic receptors (β-ARs) through systemic administration of propranolol impaired the acquisition of the eyeblink conditioning (Gould, 1998; Cartford et al., 2002). Abnormal levels of noradrenaline (norepinephrine: NE) have been noted in the cerebella of patients with olivocerebellar atrophy, Parkinson’s and Alzheimer’s diseases (Kish et al., 1984a,b; Shimohama et al., 1986).

In situ hybridization studies indicate that the cerebellar cortex expresses mRNA encoding all subtypes of α₁-AR (α_1A, α_1B, α_1D) and α₂-AR (α_2A, α_2B, α_2C; Schambra et al., 2005). These results are confirmed by immunostainings analyses showing a strong expression of α_1A-AR as well as α_2A- and α_2B-AR in both molecular layer interneurons and PCs (Papay et al., 2004, 2006; Hirono et al., 2008). High-level expression of β₂-AR has been also observed in PC bodies and molecular layer (Lippiello et al., 2015).

According to electrophysiological studies, iontophoretically applied NE or activation of the locus coeruleus induces depression of spontaneous discharges in PCs (Hoffer et al., 1971; Siggins et al., 1971). Such effect is associated with the potentiation of inhibitory GABAergic transmission at basket cell-PC synapses, mediated by presynaptic β₂-ARs (Mitoma and Konishi, 1999; Saitow and Konishi, 2000). Interestingly, NE exerts also an inhibitory effect on the CF-PC synapse, acting presynaptically (on α₂-ARs) to decrease glutamate release from CFs (Carey and Regehr, 2009). Concerning the noradrenergic effect on the PF-PC synapse, early reports have shown an inhibitory action of NA, mediated by α₂-ARs, on the field potential evoked by PF stimulation (Mitoma and Konishi, 1999). Recent evidence indicates that noradrenaline functions as an endogenous ligand for both α₁- and α₂-ARs to produce synaptic depression between PFs and PCs, through a postsynaptic mechanism. (Figure 2B; Lippiello et al., 2015). This result is consistent with the immunochemical localization of both α₁- and α₂-ARs at the Purkinje cell dendrites (Papay et al., 2004, 2006; Hirono et al., 2008). The inhibitory effect α₁-ARs on PF-PC synaptic transmission is likely related to the sequential activation of G_q/11 and PLC which may induce DAG production and release of Ca²⁺ from intracellular stores. This may result in the activation of PKC and eventually phosphorylation of GluA2 and internalization of AMPA receptors (Herold et al., 2005). α₂-ARs are known to inhibit adenylyl cyclase, via G_i-proteins, leading to a decrease in cAMP concentration and PKA activity. A decrease in PKA activity determines the dephosphorylation of GluA1, which is considered a signal for internalization and synaptic depression (Yi et al., 2013). On the other hand, stimulation of the β-AR by isoproterenol determines a significant increase of PF-EPSCs (Lippiello et al., 2015). This short-term potentiation is postsynaptically expressed, requires PKA, and is mimicked by the β₂-AR agonist clenbuterol. Interestingly, activation of β-ARs facilitates PF-PC synaptic plasticity by enhancing the ability of low-threshold stimuli to induce postsynaptic LTP. The mechanism by which β-ARs facilitate synaptic transmission may involve the cAMP-PKA signaling pathway. Indeed it has been demonstrated that PKA can phosphorylate GluA1 on S845 thus promoting AMPA receptor insertion into synapses (Joiner et al., 2010). Such bidirectional regulation of PF-PC synaptic transmission by NE with facilitation via β₂-ARs and inhibition via α₁-and α₂-ARs may allow the noradrenergic inputs to finely regulate the signals arriving at PCs at particular arousal states or during learning.

The presence of cholinergic innervation in the cerebellum has been demonstrated by earlier immunocytochemical studies using antibodies against choline acetyltransferase (ChAT). Such analysis combined to retrograde tracing has revealed a significant amount of ChAT-positive mossy fibers in the flocculo-nodular lobe, originating mainly from the vestibular nuclei, and a moderate number of ChAT-immunoreactive fibers in the DCN (Barmack et al., 1992; Jaarsma et al., 1997). Autoradiographic and immunohistochemical analysis have later provided evidence that the cerebellum expresses both muscarinic and nicotinic cholinergic receptors. Muscarinic receptors are mainly M₂-type and are localized throughout the whole cerebellar cortex, particularly in the molecular layer of nodulus and ventral uvula, and in the cerebellar nuclei. On the other hand, the cerebellum expresses several subtypes of nicotinic acetylcholine receptors (nAChRs), with a predominance of the homomeric α₇-nAChRs and the heteromeric nAChRs composed of α₃ or α₄ subunits in pairwise combination with either β₂ or β₃ subunits (Turner and Kellar, 2005). A specific nAChR expression has been observed in interneurons, granule cells and mossy fibers. These results are consistent with electrophysiological studies showing an increase of GABA release from Golgi cells and basket/stellate interneurons following activation of nAChRs (Rossi et al., 2003). Furthermore, it has been demonstrated that nicotine increases mossy fiber-granule cell synaptic transmission by acting on α₇-nAChRs located at pre- and postsynaptic sites. On the other hand, Rinaldo and Hansel (2013) have recently demonstrated that muscarinic acetylcholine receptors (mAChRs) activation by a selective agonist induces a transient depression of PF-AMPA-EPSCs via a presynaptic effect mediated by M₃ receptors. Interestingly, mAChR activation has also a suppressive effect on presynaptic LTP induction at PF–PC synapses via retrograde eCB signaling. According to their results, the eCB synthesis and release occurs at the postsynaptic site and is triggered by G_q-coupled M₁/M₃ receptors expressed on PCs (Figure 2C). The effect of eCB is likely mediated by cannabinoid 1 receptors (CB₁Rs), located in presynaptic terminals and consists in a reduced release of neurotransmitter through a G_i/o-coupled pathway. Therefore, by activating multiple cholinergic receptor subtypes on different cellular targets, acetylcholine has the potential to modulate the cerebellar information processing within the cerebellar cortex.

Evidence for a role of cholinergic signaling in cerebellar motor learning has come from behavioral studies showing that the injections of muscarinic agonists into the vestibulocerebellum influenced the gains of optokinetic and vestibuloocular reflexes in the rabbit and the VOR gain in the decerebrate cat (Andre et al., 1992; Tan et al., 1993; van der Steen and Tan, 1997). The effect of nicotine has also been studied in human subjects scanned by functional magnetic resonance while performing an auditory-paced finger tapping task (Wylie et al., 2013). The task consisted in pressing a button with their right hand in response to an auditory cue at a constant rate of 1, 2 or 4 Hz. When compared to placebo treatment, subjects that received nicotine treatment showed an increased tapping rate, as a consequence of increased coordination, associated with an increased activity in the vermal area of the anterior cerebellum during the task.

nAChRs are also involved in developmental plasticity in the chick cerebellum and neurodevelopmental disorders such as autism (Kaneko et al., 1998). Indeed, developmental synaptogenic events are often accompanied by an increase in PC α₇ nAChR immunoreactivity. On the other hand, an abnormal expression of nAChR α₄ and α₇ has been observed in the cerebellar cortex of autistic subjects compared to normal individuals (Lee et al., 2002).

The PF-PC synapse is involved in several disorders with altered cerebellar function. Regarding neurologic diseases, most studies have been focused on spino-cerebellar ataxias (SCAs), hereditary forms of cerebellar disorder with an autosomic dominant transmission pattern and with a variable involvement of extra-cerebellar structures. At present, the mutations responsible for more than 40 distinct types of SCAs have been described (Durr, 2010), but the cause of a large fraction of SCAs (20–60%, depending on the geographical origin) is still unknown (Durr, 2010). The SCAs 1–3, 6–7, 17 and dentatorubral-pallidoluysian atrophy (DRPLA) are due to the expansion of CAG triplets coding for polyglutamine. SCA10, SCA12 and SCA31 are due to the expansion of non-coding regions of genes. The remaining SCAs are due to conventional mutations. The mechanisms of the SCAs affecting the PF-PC synapse are summarized in Figure 3.

Regarding psychiatric disorders, the cerebellum has been strongly implied in Autism Spectrum Disorders (ASD). In fact, cerebellar malformation and PC loss are frequent findings in the analysis of autoptic material from ASD patients (Bauman and Kemper, 2005; Amaral et al., 2008). In addition, the cerebellar injury is associated with a higher incidence of ASD (Limperopoulos et al., 2007). A central role of PCs in ASD has been confirmed by recent studies in animal models. Some of these studies have even showed that a genetic modification specifically restricted to PCs is sufficient to cause symptoms related to ASD. The main findings, regarding the PF-PC synapse, of studies of PC-selective mutants are summarized in Figure 4.

The role of PCs in ASDs was first examined in a model of tuberous sclerosis, a complex disease associated with a high incidence of autism (Jeste et al., 2008). Tuberous sclerosis Complex 1 (TSC1), which is one of the main genes mutated in tuberous sclerosis, was selectively knocked out in cerebellar PCs (Tsai et al., 2012). Both homozygous and heterozygous mice showed social interaction deficits and repetitive behavior, reproducing salient features of patients with ASD. Moreover, while homozygous mice also displayed ataxia, heterozygotes presented autistic trait but normal motor performance. Although heterozygous Tsc1 mutant mice had no PC loss, the PC dendritic tree had an aberrant increase in the density of spines. It is interesting to note that in this model of ASD the efficacy of both PF-PC and CF-PC synapses was intact, but PCs showed a reduced rate of action potential firing. Thus, in this animal model, the alteration of dendritic spines was not accompanied by changes in the synaptic input impinging onto PCs, suggesting that the impairment in the output signals to the DCN is due to a deficiency in the intrinsic membrane properties regulating the generation of action potentials. This deficit and the associated behavioral symptoms could be ascribed to the loss of inhibition of mammalian target of rapamycin (mTOR) by Tsc1. In fact, an inhibitor of mTOR (rapamycin) was able to revert the autistic symptoms and the pathological alterations.

A second study examined the role of phosphatase and tensin homolog missing on chromosome 10 (PTEN), a gene involved in 5–10% cases of autism (Li et al., 1997; McBride et al., 2010). PTEN negatively regulates PI3K-AKT signaling, which controls in parallel mTOR and GSK3 pathways (Song et al., 2012). A selective deletion of Pten in PCs was sufficient to cause autistic-like behaviors (Cupolillo et al., 2016). These Pten mutant mice displayed PC soma enlargement, thicker dendrites with swellings and axonal torpedoes. While at 4 months the PC number was the same in Pten mutant and wild-type controls, at 6 months of age the mutant PCs showed a 50% reduction in number. Behavioral and electrophysiological analyses were performed at 3–4 months of age, when PC death was not yet evident and motor performance was still normal. Pten mutant mice displayed deficits in social interaction and repetitive behavior, suggestive of autistic symptoms. PC action potential firing was significantly reduced, similarly to Tsc1 mutants. However, the efficacy of the PF-PC synapse was strongly increased to double level relative to controls, through a postsynaptic mechanism. Interestingly, the CF-PC synapse was reduced via a presynaptic mechanism, as a consequence of the altered PF input or as a tentative compensation aimed at normalizing the balance of excitatory inputs to Pten mutant PCs.

A third study (Peter et al., 2006) focused on the postsynaptic scaffolding protein SHANK2, which is strongly linked to ASD. In accordance with ASD symptoms, mice with a PC-specific deletion of Shank2 showed impaired sociability, and behavioral inflexibility in the form of increased perseverance in a T-maze test. In contrast to the other two PC-selective ASD models, PC-Shank2 knockout mice had a normal PC firing frequency, but in vivo recordings disclosed an aberrant irregularity of PC discharge. The synaptic function was not investigated in PC-Shank2 knockout animals, but only in mice with a global Shank2 deletion, which showed normal PF-PC synaptic transmission but an increased frequency of postsynaptic inhibitory currents and impaired LTP of the PF-PC synapse associated with a deficit in intrinsic PC plasticity.

These three studies have in common the finding of an alteration of PC action potential firing. In Tsc1 and Pten PC-selective knockout mice the frequency was reduced, while the lack of Shank2 caused an increased irregularity of firing. These results, taken together, suggest that a preserved PC firing might be necessary to avoid ASD-related symptoms. Other features were present in some, but not in all models, like the alteration of the dendritic morphology, consisting of an increased number of spines or dendritic thickness in Tsc1 and Pten mice, which in Shank2 mice were normal. The role of the PF-PC synapse in ASD remains undefined, although the stronger efficacy in Pten mutants can definitely affect the afferent input signals to PCs and therefore the signal processing. Some of these alterations are likely responsible for autistic symptoms, but in order to know the relative importance of intrinsic properties relative to synaptic efficacy, it would be necessary to understand more about the mechanisms downstream of PCs. For example, optogenetic manipulations of PC firing parameters like frequency or regularity might confirm or reject the hypothesis that such signals play a central role in the pathogenesis of autism. Other relevant open questions include the consequences of an altered output from the cerebellar cortex to the DCN. Finally, we suggest that answers about this topic might arise from studies of the circuits, originating from the cerebellum, involved in the deficits of social communication, repetitive behavior and behavioral inflexibility, which are cardinal symptoms of ASD, reproduced in animal models (Lai et al., 2014).