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Fig. 21.1 Cerebellar granule cell properties. (a) Confocal microscope reconstruction of a GrC injected with neurobiotin. The image shows the dendrites with terminal digitization and the thin axon ascending through the granular layer into the molecular layer (Gall and D’Angelo, unpublished). (b) Synaptic transmission at GrC synapses. In this schematic drawing, a GrC receives activation from 4 MFs and 2 GoCs. In the glomerulus, spillover generates slow responses. Several GrC excitatory synaptic currents (EPSC; red) and inhibitory synaptic currents (IPSC; blue) generated in responses to minimal stimulation are shown superimposed (Redrawn from D’Angelo 2013). Note spontaneous activity

are propagated from initial segment backward to GrC dendrites and forward to AA synapses in about 0.1ms, thus gen-

generated by GoC discharge. The inset shows the invivo response of a GrC to air-puff stimulation of the whisker pad, revealing EPSC bursts with short-term depression (Reprinted from Rancz etal. 2007). (c) The GrC is silent at rest and generates repetitive spike discharge during current injection. It can generate bursts and is resonant at theta frequency (Modied from D’Angelo etal. 2001). (d) Ionic currents involved in GrC spike electrogenesis (Adapted from D’Angelo et al. 2001). I (Transient Na

current), ICa (Ca2+ current), IDR (Delayed Rectier K+ current), IBK

(Ca

current), INaR (Resurgent Na+ current), INaP (Persistent

-dependent K+ current), and I

(M-like K+ current)

M-like

NaT

21.2 Glomerular Organization ofGrCs

Synaptic Inputs

erating a close coincidence between excitation of GrCs and of PCs (Diwakar etal. 2011). During responses to MF prolonged discharges, GrCs show different ranges of adaptation or even acceleration of ring thanks to the expression of TRPM2 channels (Masoli etal. 2020).

GrC activity is determined by the interplay of excitatory and inhibitory inputs, which impinge onto a specialized structure called cerebellar glomerulus. Each glomerulus is made of a glial sheet enwrapping a MF terminal and as many as 50 GrC

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dendrites, as well as GoC axonal terminals and dendrites. In the glomerulus, in addition to fast synaptic transmission between axonal terminals and GrC dendrites, neurotransmitter diffusion in the glomerulus determines spillover effects and metabotropic activation on all the elements involved, setting up a complex regulatory mechanism (Mapelli etal.

2014).

MFs release glutamate and activate GrC AMPA and

NMDA receptors (AMPARs and NMDARs), regulating membrane depolarization and Ca2+ inux (D’Angelo et al.

1990; Silver etal. 1992). AMPARs contain GluR2, have fast

kinetics, and are Ca2+ impermeable. NMDARs contain NR2A and NR2C subunit conferring specic voltage dependence and kinetics (Rossi etal. 2002; Schwartz etal. 2012). GoC terminals release GABA activating GrC GABA-A receptors (Mapelli et al. 2009). Metabotropic receptors on granule cells (mGluR1 and GABA-B), on MF terminals (mGluR2 and GABA-B) and on GoC axon terminals (mGluR2 and GABA-B), regulate neurotransmitter release and GrC ionic channel gating (Mapelli etal. 2014).

21.3 Synaptic Transmission andPlasticity

The MF-GrC synapse is enriched with synaptic vesicles and can release quanta at high rate for sustained time periods. During bursts, the postsynaptic response [i.e., excitatory postsynaptic current (EPSC)] shows a marked short-term depression due both to vesicle depletion and AMPAR desensitization (Nieus etal. 2014). Glutamate spillover activates NMDARs and contributes to generate a slow AMPARdependent component (Rossi et al. 2002). The GoC-GrC synapse also shows a marked short-term depression during burst transmission (Mapelli etal. 2009). Both synapses show complex regulatory mechanisms based on metabotropic receptors (Mapelli etal. 2014).

The MF-GrC relay is site of long-term synaptic plasticity,

which manifests as long-term potentiation (LTP) or longterm depression (LTD) depending on input bursts patterns: long high-frequency bursts generate LTP, and vice versa (Gall etal. 2005; D’Errico etal. 2009). This LTP and LTD depend on NMDARs and metabotropic glutamate receptors (mGluRs) receptors depending on the input patterns and require Ca2+ entry and NO (Gall etal. 2005). MF-GrC plasticity is expressed presynaptically through an increase in release probability and can ne tune the delay to st spike in GrCs by controlling quantal release and EPSC short-term plasticity (Nieus etal. 2014). LTP and LTD can also be generated through the precise coincidence of pre-and postsynaptic spikes (spike-timing-dependent plasticity, STDP (Sgritta etal. 2017). Following patterned input bursts, GrCs also show persistent changes in intrinsic excitability (Armano etal. 2000; see Chap. 38).

NO generated by granule cells plays a critical role not only for LTP and LTD but also for regulating neurovascular coupling and blood ow in the cerebellum (Mapelli et al.

2017; Gagliano etal. 2021).

21.4 Granular Layer Coding

andTransmission ofGrC Output totheMolecular Layer Through AA andPF

While theory predicts that sparse coding is critical for GCL functioning (Marr 1969), empirical evidence suggests that GrCs are activated in dense clusters (Diwakar etal. 2011; Gilmer and Person 2018). The structural organization of GrC dendrites and connections imposes constraints on GCL information coding (Billings etal. 2014; Gilmer and Person

2017; Lanore etal. 2021) under inhibitory GoC control gen-

erating a high-dimensional input–output space (Duguid etal.

2015; Powell etal. 2015; Casali etal. 2020). By exploiting

their ionic channels and synaptic properties, the GrCs efciently recode input spikes trains into bursts with precise timing and number of emitted spikes (Nieus et al. 2014). GrCs transmit their output spike patterns through the AA and PFs to PCs, GoCs and MLIs (Mapelli etal. 2013; Masoli and D’Angelo 2017). AA and PFs are normally myelinated and conduct spikes at around 0.1m/s. The PF–PC synapse has normally a low release probability and shows short-term facilitation, so that it responds better to spike doublets or triplets (van Beugen etal. 2013; Rizza etal. 2021). Moreover, following patterned activity, the PF terminals generate various forms of long-term synaptic plasticity, some of which are presynaptic and involve NMDARs and NO production. Neurotransmission at synapses with MLIs and GoCs also involve forms of short- and long-term plasticity but these are less known (D’Angelo 2014; Masoli etal. 2020, see Chaps.

43 and 45).

21.5 Functional Activation ofGrCs InVitro

andInVivo

Experiments invitro have revealed complex patterns of granule cell activation, which occurs in center surround and can generate combinatorial operations (D’Angelo 2013; Gandol et al. 2014). Recordings in vivo have conrmed that the properties observed in vitro actually regulate GrC activity during responses to sensorimotor inputs (Rancz etal. 2007; Lanore etal. 2021). Most GrCs are normally silent and then respond in short burst or long spike sequences depending on the input MF patterns. Computational modeling has allowed to investigate the implications of GrC properties for the granular layer and cerebellar function (Masoli etal. 2020, Masoli

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et al. 2017; Casali et al. 2019; De Schepper et al. 2021; Solinas et al. 2010; Casali et al. 2020). The picture that emerges is that of a fast relay neuron, which can regulate timing and intensity of spike transmission to PCs exploiting long-term synaptic plasticity and glomerular interactions.

Acknowledgements We thank Simona Tritto for technical assistance. This work was supported by European Union grants to ED [CEREBNET FP7-ITN238686, REALNET FP7-ICT270434, Human Brain Project (HBP-604102)].

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Mapelli L, Rossi P, Nieus T, D’Angelo E (2009) Tonic activation of

GABA(B) receptors reduces release probability at inhibitory connections in the cerebellar glomerulus. J Neurophysiol 101:3089–3099

Mapelli L, Solinas S, D’Angelo E (2014) Integration and regulation of

glomerular inhibition in the cerebellar granular layer circuit. Front

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(2007) High-delity transmission of sensory information by single

cerebellar mossy bre boutons. Nature 450:1245–1248 Rossi P, Sola E, Taglietti V, Borchardt T, Steigerwald F, Utvik JK,

Ottersen OP, Kohr G, D’Angelo E (2002) NMDA receptor 2

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22:9687–9697 Schwartz EJ, Rothman JS, Dugue GP, Diana M, Rousseau C, Silver

RA, Dieudonne S (2012) NMDA receptors with incomplete Mg2+

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situ. Nature 355:163–166 Solinas S, Nieus T, D’Angelo E (2010) A realistic large-scale model of

the cerebellum granular layer predicts circuit spatio-temporal l-

tering properties. Front Cell Neurosci 4:12. https://doi.org/10.3389/

fncel.2010.00012.eCollection

Further Reading

Armano S, Rossi P, Taglietti V, D’Angelo E (2000) Long-term potentia-

tion of intrinsic excitability at the mossy ber–granule cell synapse

of rat cerebellum. J Neurosci 20(14):5208–5216 Casali S, Marenzi E, Medini C, Casellato C, D’Angelo E (2019)

Reconstruction and simulation of a scaffold model of the cerebellar

network. Front Neuroinform 13:37 Casali S, Tognolina M, Gandol D, Mapelli J, D’Angelo E (2020)

Cellular-resolution mapping uncovers spatial adaptive ltering at

the rat cerebellum input stage. Commun Biol 3(1):635 De Schepper R, Robin AG, Masoli S, Rizza MF, Antonietti A, Casellato

C, D’Angelo E (2021) Scaffold modelling captures the structure–

function–dynamics relationship in brain microcircuits. bioRxiv

2021:454314 Diwakar S, Lombardo P, Solinas S, Naldi G, D’Angelo E (2011)

Local eld potential modeling predicts dense activation in cerebel-

lar granule cells clusters under LTP and LTD control. PLoS One

6(7):e21928 Dover K, Marra C, Solinas S, Popovic M, Subramaniyam S, Zecevic

D, D’Angelo E, Goldfarb M (2016) FHF-independent conduction

of action potentials along the leak-resistant cerebellar granule cell

axon. Nat Commun 7:12895 Duguid I, Branco T, Chadderton P, Arlt C, Powell K, Häusser

M (2015) Control of cerebellar granule cell output by sen-

sory-evoked Golgi cell inhibition. Proc Natl Acad Sci U S A

112(42):13099–13104 Gagliano G, Monteverdi A, Casali S, Laforenza U, Gandini Wheeler-

Kingshott CAM, D’Angelo E, Mapelli L (2021) Non-linear

frequency- dependence of neurovascular coupling in the cerebel-

lar cortex implies vasodilation–vasoconstriction competition. Cell

11(6):1047

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Galliano E, Gao Z, Schonewille M, Todorov B, Simons E, Pop AS,

D’Angelo E, Van Den Maagdenberg AMJM, Hoebeek FE, De Zeeuw CI (2013) Silencing the majority of cerebellar granule cells uncovers their essential role in motor learning and consolidation. Cell Rep 3(4):1239–1251

Gilmer JI, Person AL (2017) Morphological constraints on cerebellar

granule cell combinatorial diversity. J Neurosci 37(50):12153–12166

Gilmer JI, Person AL (2018) Theoretically sparse, empirically

dense: new views on cerebellar granule cells. Trends Neurosci 41(12):874–877

Lanore F, Alex Cayco-Gajic N, Gurnani H, Coyle D, Angus Silver R

(2021) Cerebellar granule cell axons support high-dimensional representations. Nat Neurosci 24(8):1142–1150

Mapelli L, Gagliano G, Soda T, Laforenza U, Moccia F, D’Angelo

EU (2017) Granular layer neurons control cerebellar neurovascular coupling through an NMDA receptor/NO-dependent system. J

Neurosci 37(5):1340–1351 Marr D (1969) A theory of cerebellar cortex. J Physiol 202(2):437–470 Masoli S, D’Angelo E (2017) Synaptic activation of a detailed pur-

kinje cell model predicts voltage-dependent control of burst-pause

responses in active dendrites. Front Cell Neurosci 11:1–18 Masoli S, Rizza MF, Sgritta M, Van Geit W, Schürmann F, D’Angelo

E (2017) Single neuron optimization as a basis for accurate bio-

physical modeling: the case of cerebellar granule cells. Front Cell Neurosci 11:71

Masoli S, Ottaviani A, D’Angelo E (2020a) Cerebellar Golgi cell mod-

els predict dendritic processing and mechanisms of synaptic plasticity. PLoS Comput Biol 16(12):e1007937

Masoli S, Tognolina M, Laforenza U, Moccia F, D’Angelo E (2020b)

Parameter tuning differentiates granule cell subtypes enriching transmission properties at the cerebellum input stage. Commun Biol 3(1):1–12

Powell K, Mathy A, Duguid I, Häusser M (2015) Synaptic representa-

tion of locomotion in single cerebellar granule cells. Elife 4:e07290

Rizza MF, Locatelli F, Masoli S, Sánchez-Ponce D, Muñoz A, Prestori

F, D’Angelo E (2021) Stellate cell computational modeling predicts signal ltering in the molecular layer circuit of cerebellum. Sci Rep 11(1):3873

Sgritta M, Locatelli F, Soda T, Prestori F, D’Angelo EU (2017) Hebbian

spike-timing dependent plasticity at the cerebellar input stage. J Neurosci 37(11):2809–2823

van Beugen BJ, Gao Z, Boele HJ, Hoebeek F, De Zeeuw CI (2013)

High frequency burst ring of granule cells ensures transmission at the parallel ber to Purkinje cell synapse at the cost of temporal coding. Front Neural Circuits 7:95

Purkinje Cells

https://t.me/medicina_free

ThéoRossi andPhilippeIsope

Abstract

Purkinje cells (PCs), the sole output neuron of the cere-

bellar cortex, are inhibitory projection neurons targeting

the cerebellar and vestibular nuclei. They compute excit-

atory information from granule cells (GCs) and climbing

bers (CFs), and inhibitory information from molecular

interneurons (MLIs). PCs display two distinct types of the

action potential, the simple spike (SS), which is a regular

action potential elicited spontaneously and modulated by

GCs, and the complex spike (CS), which is generated by

the climbing ber input. PC dysfunctions lead to the

motor as well as non-motor cerebellar disorders.

Keywords

Purkinje cells · Zebrin · Dendritic integration · Simple

spike · Complex spike · Spontaneous activity

22.1 PC Identity

22.1.1 Morphology

PCs were discovered in 1837 by a Czech anatomist, Jan Evangelista Purkynĕ and described by Ramón y Cajal in 1899 using Golgi’s staining method. PCs have a very large planar and multibranched dendritic tree oriented in the parasagittal plane and they are aligned in a single layer. The dendritic arbor stems from a primary dendrite that emerges from a large pear-shaped cell body with a single axon (Fig.22.1ai). A very high density of elongated spines (660,000/mm2 in rats) arranged in helix covers the most distal dendrites, the spiny branchlets (Fig.22.1aii, iii; Harvey and Napper 1991).

T. Rossi · P. Isope (*) Institut des Neurosciences Cellulaires et Integratives CNRS, Université de Strasbourg, Strasbourg, France e-mail: t.rossi@inci-cnrs.unistra.fr;

philippe.isope@inci-cnrs.unistra.fr

Each spine receives a single input from the GC axon, the parallel ber (PF), as an en passant bouton. PCs receive converging inputs from about 175,000 glutamatergic PF synapses (Fig. 22.1aiii, v). Since the total number of PCs is 338,000 in rats (220,000 in mice, 7,100,000 in monkeys, 15,000,000 in humans), the rat cerebellum may contain around 62 billion PF–PC synapses (Harvey and Napper

1991), which are a major site of information storage in the

cerebellum (Ito 2006). Proximal and secondary dendritic branches are essentially smooth and carry clusters of stubby spines (200–300 thorny spines) all contacted by a single glutamatergic CF originating in the inferior olive (Fig.22.1aiv). During development, PF and CF excitatory inputs compete for their respective territory on the dendritic tree with specic interacting pre and postsynaptic proteins enabling PF– PC or CF–PC synapses formation (e.g., cerebellin—GluD2 receptor, neurexin—neuroligin; Uemura etal. 2010; Yuzaki

2017). While in early life several CFs contact a single PC,

this multi-innervation regresses during the 2–3 rst postnatal weeks yielding a single CF on the PC dendrites. Any alteration in this developmental step leads to severe motor coordination impairments (Kano and Hashimoto 2012). The smooth dendritic parts and the soma are also contacted by axons of the local inhibitory molecular layer interneurons (MLIs), the stellate, and the basket cells (Fig.22.1av; Palay and Chan-Palay 1974).

22.1.2 Diversity

While all PCs are GABAergic inhibitory neurons and express calbindin (a calcium binding protein), a combination of neurochemical markers, the zebrins, involved in developmental and other physiological mechanisms dene an array of nonuniform cerebellar modules (Apps and Hawkes 2009; Apps etal. 2018). Zebrin markers are expressed in subsets of PCs dening parasagittal bands. These bands coincide with boundaries of CF inputs originating in specic subnuclei of

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 D. L. Gruol et al. (eds.), Essentials of Cerebellum and Cerebellar Disorders, https://doi.org/10.1007/978-3-031-15070-8_22

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iii

PFs

GC exc.

CF exc.

MLI inh.

Intracellular recordings Extracellular recordings

10 ms

10 mV

25 ms

GrCs

MLIs

10 µV

10 ms

Normal Purkinje cell discharge Pathological

Fig. 22.1 The Purkinje cell. (ai), rat PC lled with biocytin and revealed using avidin–streptavidin complex. Scale bar: 10μm. (ii), PC dendrites magnication from (ai). Scale bar: 5μm. (iii), a PF bouton (red) contacting a PC spine (green) lled with biocytin and revealed using different colors. Scale bar: 1μm. Pictures from (ai–iii) courtesy of Boris Barbour. (iv) A CF (green) contacting PC dendrites (blue). Picture from (González-Calvo etal. 2021) (v), diagram of the monosynaptic PF-PC and the disynaptic PF-MLI-PC pathways. MLIs molecular layer interneurons (stellate and basket cells), PC Purkinje cell, GCs granule cells, PFs parallel ber, GC exc. GC excitation, CF exc CF

Purkinje cell discharge

excitation, MLI inh. MLI inhibition. (b) Left panel, simple spikes (black) and a complex spike (blue) recorded in a PC using whole-cell patch clamp in acute cerebellar slices. Note the fast repolarization and spontaneous after-depolarization of SSs, and the after hyperpolarization (AHP) at the end of the CS. Right panel, simple SSs and a CS recorded in juxtacellular mode in an anesthetized animal. (c) Left panel, diagram illustrating regular spiking behavior of SSs (black ticks), the low frequency of CS (blue ticks) and the pause in SSs observed after a CS. Right panel, illustration of an erratic PC discharge underlying cerebellar dysfunctions

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the inferior olive and conveying similar integrated sensorimotor information (Ruigrok 2011). Furthermore, zebrin markers are associated with specic physiological properties. For example, a subset of PCs (called zebrin II positive) expresses aldolase C (a glycolytic enzyme), EAAT4 (a glutamate transporter), and PLCβ3 (a phospholipase involved in intracellular transduction pathways), while another subset of PCs (zebrin II negative) expresses PLCβ4, a very low level of EAAT4 and no aldolase C.Therefore, PCs belonging to different bands can develop specic computations (Cerminara etal. 2015). Notably, long-term depression (LTD) at the PF– PC synapses is facilitated in zebrin II negative bands as the level of expression of EAAT4 is low (Wadiche and Jahr

2005; De Zeeuw 2021). Also, the mean PC ring rate is

higher in zebrin II negative bands (Zhou etal. 2014).

22.2 PC Activity

22.2.1 Two Types ofAction Potentials

PCs emit two types of action potentials, a classical fast spike, the simple spike (SS), and a longer fat spike, the complex spike (CS), elicited by a CF input as an all-or-none event at low frequency (1–2Hz; Fig.22.1b; Eccles etal. 1967). While SSs are exclusively generated at the axonal initial segment (AIS; Palmer etal. 2010), CSs are the result of a strong dendritic depolarization leading to an initial sodium spike elicited at the AIS followed by smaller sodium spikelets (Davie etal. 2008). The number of spikelets and the shape of the CS is PC-specic, but can be regulated by activity-dependent processing (Weber et al. 2003; Yang and Lisberger 2014). The depolarization induced by the CS also activates high (Cav2.1, called P/Q type) and low-threshold (Cav3.1, called T-type) voltage-dependent calcium channels in the dendritic shaft and spines (Otsu etal. 2014), leading to an after hyperpolarization of the cell (Schmolesky etal. 2002). Calcium entry propagates as a calcium spike and controls long-term synaptic plasticity at the PF–PC synapses (Wang etal. 2000).

The two types of action potentials (SS and CS) interact in PCs. For example, an increase (or a decrease) in CS frequency induces a decrease (or an increase) in SS frequency (De Zeeuw etal. 2011). In addition, a CS is always followed by a pause in SS activity (Fig.22.1c). This latter effect has been associated to a strong activation of calcium activated potassium channels as well as the activation of local inhibitory interneurons by CFs (Szapiro and Barbour 2007). PC axons are myelinated and propagate SSs and CSs reliably to the cerebellar nuclei, transmitting both rate and temporal code to specic subsets of nuclear neurons (Khaliq and Raman 2005).

22.2.2 Spontaneous SS Activity

PCs are spontaneously ring neurons that elicit SSs between 10 and 100Hz during all their life without the need of excitatory inputs (Fig.22.1b, c; Latham and Paul 1971; Gruol and Franklin 1987; Häusser and Clark 1997; Raman and Bean

1997). This pacemaker activity is regulated by several types

of voltage-gated ionic channels. A cationic non-specic ion channel activated by membrane hyperpolarization (Ih current) can depolarize PCs below −70mV enabling voltagedependent sodium channels to open and trigger a SS (Fig. 22.1b). The PC–SS is mediated by several sodium channels including the Nav1.6 channel that reopens after inactivation yielding a resurgent depolarizing current (Raman and Bean 1997). The combined activation of Ih and resurgent currents enables PC tonic ring (Raman and Bean

1997; Williams etal. 2002; Swensen and Bean 2003). Tonic

ring is also controlled by the interplay between fast highthreshold potassium channels (Kv3.3; Akemann and Knöpfel

2006) and voltage-dependent calcium channels (Cav2.1 and

Cav3.1; Swensen and Bean 2003). The former repolarizes quickly the cell after a SS (Fig.22.1b), while the latter triggers the opening of calcium-dependent potassium channels (KCa 1, 2, or 3, called BK, SK, and IK channels, respectively; Womack etal. 2009). The resulting hyperpolarization activates Ih current, which triggers another cycle of depolarization. Many of these conductances underlying spiking behavior are active at “rest” suggesting that PCs do not have proper resting membrane potential. Furthermore, in rodents, these conductances lead to a bistable state with silent (a down state) or tonically active (an up state) PCs. Strong depolarization such as a CS or inhibition can bidirectionally toggle PCs from one to the other (Williams et al. 2002; Loewenstein etal. 2005; but see Schonewille etal. 2006; Hong etal. 2016).

22.2.3 PC Integration ofGC Inputs: Passive andActive Mechanisms

GC inputs control the frequency of PC discharge via direct PF–PC synapses located on dendritic spines (Eccles et al.

1967). PFs release glutamate that binds to non-calcium

permeant AMPA receptors (heteromeric GluA1–4; Perkel etal. 1990; Lambolez etal. 1992) and to mGluR1 receptors following burst of PF stimulation (Batchelor and Garthwaite

1993). Excitatory postsynaptic potentials are integrated and

heavily ltered along the PC dendritic tree before reaching the soma (Roth and Häusser 2001). A single PF input is unlikely to inuence PC discharge as it induces only a small depolarization at the soma (<100μV) and most of the PF–PC

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synapses are silent (Isope and Barbour 2002). However, temporal summation or coincident activation of a few PF inputs drive PC ring rate (Walter and Khodakhah 2006; GrangerayVilmint etal. 2018). Moreover, active conductances located in PC dendrites and spines inuence dendritic integration: low-threshold voltage-dependent potassium channels (Kv1 and Kv4 family; Engbers etal. 2012) alter electrotonic propagation of postsynaptic potentials, and voltage-dependent calcium channels trigger intracellular regulatory pathways. While a burst of PF inputs activates Cav3.1 channels and mGluR1 receptors (Takechi et al. 1998; Hildebrand et al.

2009), the combination of PF and CF inputs elicits a supra-

linear calcium rise via the activation of Cav2.1 channels (Wang et al. 2000). Calcium rise in PC dendrites directly inuence PC somatic spiking behavior via the activation of calcium-dependent potassium channels (BK, SK, and IK channels) as their activation can delay the occurrence of SSs (Edgerton and Reinhart 2003; Womack etal. 2009; Engbers et al. 2012). Moreover, the intracellular calcium rise triggered by synaptic inputs underlies long-term plasticity at the PF–PC synapses (Ito 2001; Jörntell and Hansel 2006); in particular, repetitive PF stimulation leads to long-term potentiation, while the conjunctive activation of PF and CF induces long-term depression (Hansel et al. 2006; Piochon et al.

2016). Finally, the activity-dependent regulation of voltage-

dependent conductances (e.g., Ih or SK channels) durably alters PC intrinsic excitability and have been associated to homeostatic plasticity and learning processes (Belmeguenai etal. 2010; Titley etal. 2020).

22.2.4 PC are Inhibited by MLIs

PFs make glutamatergic contacts not only to PC dendritic spines, but also to the GABAergic MLIs, the stellate and basket cells, which provide a feedforward inhibition to PCs. Hence, GCs control the balance between synaptic excitation and inhibition impinging on PCs (Mittmann et al. 2005; Jelitai et al. 2016; Grangeray-Vilmint et al. 2018). Furthermore, the interplay between postsynaptic long-term and presynaptic short-term plasticity at the GC-MLI, GC-PC, and MLI-PC connections can generate a wide range ring frequency in PCs, from a complete stop to very high frequencies (up to 200 Hz). Therefore, the GC-MLI-PC pathway determine the dynamic range of PC discharge. Basket cells inhibit PC dendrites both through chemical synapses and ephaptic coupling mediated by an axo-axonic connection (called the pinceau) around PC AIS (Blot and Barbour 2014). As an action potential travels in the pinceau, extracellular ionic concentrations are modied inhibiting instantaneously PC ring via ephaptic coupling.

22.3 PC Roles andCerebellar Disorders

22.3.1 Physiological Role oftheSpontaneous Activity ofPCs

PCs are the sole output neuron of the cerebellar cortex; hence, the rate and temporal code generated by the population of PCs constitute the major outcome of cerebellar computation. Understanding how this message is transmitted to the cerebellar nuclei and the rest of the brain is essential to unravel the role of the cerebellum in the brain. PCs discharge can inhibit and entrain cerebellar nuclei (Person and Raman

2012; Özcan etal. 2020). Many experiments have demon-

strated that PC discharge is modied before, during, and after a movement suggesting that the cerebellum is involved in movement preparation, execution, and correction (Thach etal. 1992; Ito 2006; Shadmehr etal. 2010; Chen etal. 2016). Indeed, a wealth of studies suggest that the cerebellum can predict the sensory consequences of a motor command originating in the cerebral cortex and transmitted by the mossy ber pathway to the cerebellar cortex. The prediction is made using internal models of the body that are encoded in the cerebellum, notably at the PF-PC synapses (Wolpert et al.

1998; Ebner and Pasalar 2008; Sokolov etal. 2017). If the

prediction in incorrect, an error message is elicited and relayed by the CF to PCs in order to alter synaptic weights at the PF–PC synapses and modify the output of the cerebellum to correct the following movement (Yang and Lisberger

2014; Raymond and Medina 2018). Although the classical

view of the cerebellum limits its roles to the sensorimotor adaptation, many studies have now demonstrated that the different regions of the cerebellar cortex are associated to nonmotor behaviors, such as language, working memory, or emotional control (Sokolov etal. 2017; Diedrichsen et al.

2019; Schmahmann etal. 2019).

22.3.2 Cerebellar Disorders

Motor and non-motor roles of the cerebellum require PC discharge integrity. PCs re SS at a regular and steady rate most of the time, while relevant information is transmitted by frequency modulation, burst, or pauses in SSs. Many studies have shown that any alteration in PC discharge leads to motor disorders (Hoxha etal. 2018; Cook etal. 2021). For example, the selective genetic deletion of Nav1.6 sodium channels or an auxiliary subunit (β4-Nav1.6) in PCs suppresses the resurgent sodium current, reduces PCs intrinsic ring rate (Levin etal. 2006; Ransdell etal. 2017), and leads to severe motor coordination and balance decits. Similarly, in Kv3.3 knockout mice, PC ring rate is decreased and

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motor coordination is impaired. Rescuing Kv3.3 channels specically in PCs restore ring rate and motor skills (Joho etal. 2006; Hurlock et al. 2008). In humans, many of the neurodegenerative diseases involving cerebellar decits such as spinocerebellar ataxias (SCAs) are associated to specic PC loss or dysfunction (Meera etal. 2016; Binda etal. 2020). Reduced activity of BK and Kv3 channels in a PC-specic mouse model of SCA2 impairs pacemaker activity in PCs, and alters gait regularity and motor coordination (Dell’Orco etal. 2017). In a mouse model of episodic ataxia 2 (EA2), a mutation in Cav2.1 channels reduces the activation of SK channels, altering time precision of PC discharge. Interestingly, pharmacological activation of SK channels can restore PC ring rate and improve motor skills and movement disorders (Walter etal. 2006). Finally, neurodevelopmental diseases, such as autism spectrum disorders or schizophrenia can also be associated with PC dysfunctions (Wang etal. 2014). Indeed, imaging or postmortem studies of autistic patients have shown cerebellar abnormalities. Notably, specic deletion of Tsc1 gene (for Tuberous Sclerosis Complex disorder, a major monogenic causes of autism in humans) in mice PCs, whose protein negatively regulates mammalian target of rapamycin (mTOR) signaling pathway in dendrites, induces PC loss, impairs PC excitability, and leads to severe autistic-like behaviors (Tsai etal.

2012).

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