Spatiotemporal Firing Patterns in the Cerebellum

Most models of brain function assume that neurons communicate information by altering their firing fre-quency and that neuronal plasticity mechanisms are sen-sitive to the firing frequency of the inputs that a neuron receives1. More recently, however, it has become clear that the exact timing of spikes can convey more infor-mation than that which is mediated by the firing rate averaged over tens or hundreds of milliseconds2. In fact, evidence from experiments in both higher and lower brain regions indicates that the exact time point at which a spike occurs (the spike time) may have, in addition to rate coding, an important role in relaying and storing information3–5.

The role of rate coding in the cerebellum is well estab-lished6–14. Numerous experimental studies that focused on topics varying from adaptive eye movement control to dynamic limb control have provided a firm basis for models that can explain large parts of cerebellar func-tion using rate coding mechanisms6–14. However, various properties of the olivocerebellar system raise the possi-bility that spatiotemporal coding might support cerebel-lar processing in addition to rate coding15. For example, the olivocerebellar system is highly topographically organized in modules with reverberating loops, alternat-ing divergence and convergence ratios, and intracortical feedforward and feedback loops (BOX 1). Furthermore, one of the main functions of both the vestibulocerebel-lum and neocerebellum is to control the amplitude and timing of movements at a high resolution14–16. Indeed, recently, evidence has emerged that spatiotemporal pat-terns can occur in both the complex-spike activity and

simple-spike activity of Purkinje cells, which form the sole output of the cerebellar cortex. Complex spikes and simple spikes, which are named after the distinct shapes of their waveforms (FIG. 1), influence each other directly at the Purkinje cell level as well as indirectly at the network level, both upstream and downstream. In this Review, we describe how spatiotemporal patterns in complex-spike and simple-spike activities in Purkinje cells may be generated, and show that the olivocerebellar system is in principle optimally designed to create and employ these patterns. We show that the interaction between complex spikes and simple spikes may endow the cerebellum with unique abilities to relay the patterns to downstream tar-gets. Finally, we propose possible functions that may be served by these patterns at both the computational and behavioural levels.

Complex-spike patternsThe complex-spike activity of a Purkinje cell, which can reach a maximum frequency of ~12 Hz, results directly from its activation by a climbing fibre (BOX 1). In the adult stage, each Purkinje cell is innervated by a single climbing fibre with ~1,000 release sites. Activation of this fibre depolarizes the bulk of the Purkinje cell dendritic tree, and thus provides an exceptionally strong synaptic connection16,17. Therefore, both single action potentials and high-frequency bursts in the climbing fibre are reli-ably transmitted to the Purkinje cell18,19. The resulting action potential in the Purkinje cell — known as the complex spike — has various components (FIG. 1). The initial action potential originates from the most proximal

*Department of Neuroscience, Erasmus Medical Center, 3000 DR Rotterdam, The Netherlands.‡Netherlands Institute for Neuroscience, Royal Academy of Arts and Sciences (KNAW), 1105 BA Amsterdam, The Netherlands.§These authors contributed equally to this workCorrespondence to C.I.D.Z. e-mail: [email protected]:10.1038/nrn3011Published online 5 May 2011

Convergence ratioThe ratio of input cells versus output cells — for example, many Purkinje cells of the same microzone project to the same target neuron in the cerebellar nuclei, resulting in a high ratio.

VestibulocerebellumPart of the cerebellum (including the flocculus, nodulus and uvula) that controls compensatory eye and head movements.

Spatiotemporal firing patterns in the cerebellumChris I. De Zeeuw*‡§ Freek E. Hoebeek*§, Laurens W. J. Bosman*‡§, Martijn Schonewille*§, Laurens Witter‡§ and Sebastiaan K. Koekkoek*

Abstract | Neurons are generally considered to communicate information by increasing or decreasing their firing rate. However, in principle, they could in addition convey messages by using specific spatiotemporal patterns of spiking activities and silent intervals. Here, we review expanding lines of evidence that such spatiotemporal coding occurs in the cerebellum, and that the olivocerebellar system is optimally designed to generate and employ precise patterns of complex spikes and simple spikes during the acquisition and consolidation of motor skills. These spatiotemporal patterns may complement rate coding, thus enabling precise control of motor and cognitive processing at a high spatiotemporal resolution by fine-tuning sensorimotor integration and coordination.

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part of the axon of the Purkinje cell20,21. The subsequent plateau potential and superimposed Ca2+ spikelets have been traditionally considered to result from depolari-zations in the Purkinje cell soma and dendritic tree, respectively17,22,23, but more recent evidence indicates that the spikelets are generated axonally24. The duration of the pause that immediately follows the complex spike may be regulated by dendritic spiking24.

Coupling and synchrony. As all climbing fibres arise from the inferior olive, the properties of the olivary neurons determine the spatiotemporal characteristics of complex-spike patterns. Dendritic spines of neighbouring olivary neurons are electrotonically coupled by gap junctions composed of connexin 36 (CX36) within glomeruli25–30

(BOX 1). This enhances the coherence and synchrony of complex spikes of the Purkinje cells that they innervate31–34

(TABLE 1). Complex-spike coherence (which we define as co-occurrences during bins of 3 to 10 ms) can occur among Purkinje cells across larger parts of the cerebellar cortex31,35–37, whereas complex-spike synchrony (defined as occurring within 2-ms bins) is usually largely restricted to the parasagittal zones (up to ~500 μm) or microzones (up to ~100 μm)34,38 (FIG. 2a). A microzone is usually 3 to 19 dendritic arbors wide34,39,40. Complex-spike activi-ties of cells within a microzone are characterized by a common sensitivity to particular internal or external stimuli, and can show high levels of synchrony. The spa-tial boundaries of synchronously activated Purkinje cells within a microzone that occur during rest are largely maintained following sensorimotor activation (FIG. 2a), and decoding the functional information of complex-spike patterns following such activation is most reliable and precise when it includes the signals from all den-dritic arbors within a microzone34,39,40. Thus, although the temporal aspects of activities within an individual microzone can be dynamically controlled by afferents (FIG. 2a), modification of their spatial aspects probably requires more long-term processes such as a recomposi-tion of the olivary glomeruli, which contain electrically coupled dendritic spines that are extremely long and likely to be plastic36,41.

Complex-spike synchrony can also occur between different zones and microzones34,35, which raises the question of how such synchrony may be controlled. Two mechanisms may contribute. First, different olivary neurons projecting to different zones and/or microzones can receive common excitatory afferents, which means that they could be activated simultaneously41. The observation that interzonal and intermicrozonal syn-chrony can be increased during motor activity and/or sensory stimulation supports this possibility33–35,37–39,42,43. Second, afferents that innervate olivary glomeruli may exert dynamic control over the coupling of ensembles of olivary neurons that extend beyond zones and micro-zones28,34,36. The GABAergic input to the olive from the cerebellar nuclei is optimally designed to control the formation of coupled ensembles, as their terminals are adjacent to the electrically coupled dendritic spines in glomeruli, forming a continuum across the olivary neuropil36,41 (BOX 1). It is possible that activation of these

Box 1 | Modular organization of the cerebellum

The olivocerebellar system is organized in modules118 (see the figure; two modules are shown, one in red and one in blue). In each module a particular subnucleus of the inferior olive (IO) provides climbing fibres (CFs) to a particular, sagittally oriented zone of Purkinje cells (PCs), which in turn inhibit neurons in particular vestibular and/or cerebellar nuclei (CNs) that project back to the same olivary subnucleus. Olivary neurons are coupled by gap junctions within glomeruli, where the inhibitory terminals from the CN interact with excitatory terminals derived from brainstem areas such as the mesodiencephalic junction (MDJ)41. In the cerebellar cortex, the dendrites and axons of the molecular layer interneurons (MLIs) and Golgi cells (Golgi) stay within the boundaries of the sagittal PC zones160,161. MLIs and Golgi cells are innervated directly by parallel fibres (PFs) and, via spillover, by CFs82. MLIs and Golgi cells inhibit PCs and granule cells (GCs), respectively160,161. The mossy-fibre (MF) axons of the local excitatory interneurons — the so-called unipolar brush cells (UBCs) — are relatively short and they forward signals to GCs162. Thus, most cells involved in feedforward and feedback inhibition, as well as those involved in feedforward excitation, operate within the same sagittal PC zone as the CFs that provide the dominant drive of that particular PC zone. By contrast, the GCs, which are innervated by extracerebellar MFs and the MFs derived from UBCs147,158,163, show ambiguous possibilities in that the ascending parts of their axons stay within zones, whereas their PFs span multiple sagittal zones58,117,164. Together, the intra- and interzonal connections create a highly organized, three-dimensional matrix in the cerebellar cortex, which enables the modular CF system to facilitate PCs in selecting their input from the MF–PF system and in composing specific spatiotemporal patterns of both complex-spike activity and simple-spike activity. The terminals from MFs, CFs and PFs, as well as those from the olivary projection neurons in the MDJ are all excitatory; all remaining terminals are inhibitory.

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terminals causes a leakage current, which reduces cou-pling between the spines36,44. As the afferents from the cerebellar nuclei also elicit tonic inhibition by means of asynchronous GABA release, they may simultaneously control the firing frequency of olivary neurons and the composition of their ensembles45. Indeed, manipulation of this input influences both the spatial and the temporal aspects of the complex-spike pattern across zones and even across hemispheres36,42,46 (FIG. 2a).

The effect of this GABAergic input may be comple-mented by that of excitatory inputs that innervate the same coupled spines within a glomerulus41. Blocking glutamate within the olivary neuropil causes an enhance-ment of both complex-spike rhythmicity and of the nor-mal banding pattern of complex-spike synchrony, with higher synchrony among sagittally aligned Purkinje cells47,48 (FIG. 2a). Considering the ultrastructural con-figuration of the GABAergic and glutamatergic inputs, interactions between these inputs in the olive may oper-ate in a timing-dependent fashion, in the sense that the timing of GABAergic and glutamatergic activities rela-tive to each other is crucial for their impact41; this would imply that the GABAergic input can only be effective during a relatively narrow time window with respect to the activity of the excitatory input. Indeed, it is tempt-ing to postulate that these inputs dynamically control correlated sets of different but stable microzones that require activation of different groups of motor domains at different moments during a movement (FIG. 2a). Thus, GABAergic and glutamatergic inputs to the olive may have crucial, and complementary, roles in determining the spatiotemporal patterns of complex-spike activity in the cerebellar cortex.

Oscillations and rhythmicity. Owing to their unique combination of conductances, which are probably dif-ferentially distributed over their somatic and dendritic cell membrane27,49, olivary neurons can produce oscilla-tions in the membrane potential during rest29,50 (FIG. 1). In vivo, such subthreshold oscillations occur at pre-ferred frequencies of around 2–4 Hz or 6–9 Hz50 (FIG. 2b), which are thought to be mediated by NMDA receptor activation51 and voltage-gated calcium currents, respec-tively49,52. When coupling between olivary neurons is ablated, the oscillations are sustained within individual olivary neurons28,29,33,53. However, reducing coupling affects the strength and preferred frequency of the oscil-lations27,29,42,45,51 as well as the phase of the oscillating membrane potentials of neighbouring olivary neurons53. Thus, the oscillatory properties of single olivary neurons endow the system with frequency dynamics, and the gap junctions serve to synchronize the activities of neuronal ensembles, both at the subthreshold level influencing the membrane potential and at the suprathreshold level regulating spiking behaviour (FIG. 2b).

Although complex spikes may seem to be randomly distributed, several reports show that their firing pat-tern can be rhythmic at frequencies of around 2–4 Hz or 6–9 Hz15,32,33,37,42,50 (FIG. 2b). As the complex spikes are ‘all-or-none’ spikes, perfectly reflecting the activity in the climbing fibres and thereby that of the olivary neurons,

Figure 1 | Spike waveforms of the main cell types in olivocerebellar modules. a | A mouse inferior olive neuron in vivo has an oscillatory membrane potential (left panel, shown in orange) and shows occasional spiking. Inferior olive spikes are mediated by calcium channels (mostly T- and P/Q-type channels; right panel, shown in red), voltage-gated sodium channels (right panel, shown in green) and calcium-dependent potassium channels27,49 (right panel, shown in blue). The low-threshold T-type voltage-gated calcium channels can depolarize the soma and enable the spread of calcium into the dendrites following activation of the high-threshold P/Q-type channels. Upon the dendritic calcium influx, calcium-dependent potassium channels hyperpolarize the dendrite. This hyperpolarization spreads to the soma, deinactivates T- and P/Q-type channels and initiates hyperpolarization-activated depolarizing currents, which in turn open T-type channels to restart the oscillatory sequence26,27. b | Purkinje cell activity in an alert mouse shows simple spikes (left panel, negative events) and a complex spike (left panel, positive event). The complex spike is followed by a pause in simple-spike activity. Complex spikes are mediated by voltage-gated sodium channels (right panel, shown in green) and calcium channels (right panel, shown in red), whereas the subsequent afterhy-perpolarization is mediated by calcium-dependent potassium channels17,22,23,65,112 (right panel, shown in blue). Note the extended timescale for the afterhyperpolarization. The initial action potential originates from the most proximal part of the axon of the Purkinje cell20,21, whereas the subsequent plateau potential and superimposed Ca2+ spikelets result predominantly from depolarizations in the dendritic tree and perisomatic axonal region, respectively24. c | An electrical stimulus to the cerebellar cortex (left panel, shown by a grey bar) can elicit a burst of rebound action potentials in a mouse cerebellar-nucleus neuron126. The right panel shows the averaged action potential of cerebellar-nucleus neurons, indicating the roles of sodium channels (shown in green) and low- and high-voltage activated calcium channels137,185,199 (mostly T- and N-type calcium channels, respectively; shown in red). The slow-spike afterhyperpolarization is controlled by SK calcium-dependent K+ currents200 (shown in blue). The membrane potential of these neurons is continuously depolarized by calcium channel activation137.

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ZoneA sagittal region of Purkinje cells in the cerebellar cortex that is up to 500 μm wide and that receives climbing fibres from a particular olivary subnucleus.

this rhythmicity is consistent with the intrinsic properties of olivary neurons. Thus, the subthreshold oscillations in olivary neurons may influence the firing frequency of complex spikes and may also influence their absolute tim-ing33,54. In vivo whole-cell recordings of olivary neurons indeed have shown that both spontaneous activity and sensory evoked action potentials are more prominently present during the depolarizing phase of an oscillation33,50 (FIG. 2b). Externally triggered action potentials, in turn, can control subthreshold oscillations of olivary neurons by resetting their phase33,50 (FIG. 2b). Thus, these proper-ties raise the possibility that complex-spike patterns can ‘restart’ after a strong, unexpected sensory input, thereby triggering a new motor program55. For example, when a

perturbation of a general motor program (such as loco-motion) occurs, a new motor program may be activated rapidly through a new synchronized complex-spike pat-tern33. In addition, olivary neurons seem to be able to maintain phase differences with respect to each other while increasing the speed of motor programs56. This may enable them to mediate temporal spiking patterns at different rates and thereby control the execution of the same motor task at different speeds while preserving the appropriate consecutive order of its individual compo-nents. The two mechanisms — switching to a different motor program and speeding up the current motor program — could in principle be used individually or successively to correct motor activity.

Table 1 | Cerebellar mouse mutants on correlations between spike coding, plasticity and motor behaviour

Mutation(s) Simple spike (SS) Complex spike (CS) Plasticity Motor behaviour Refs

FF CV CV2 Pauses FF CV CF elim.

CS–SS rec. CS–CS syn.

PC LTD PC LTP PC IP

Perf. Learn. (1 day)

Learn. (>3 day)

Cons.

A6c-CACNA1Al/l n n ↓ CF n n n Rec. n LTD ↓ LTP ↓

n n Imp. Imp. 73||

CX36 KO* CF n n ↑ Syn. ↓ n Imp. Imp. 29, 33, 170

L7-PKCi KI n n n CF n SS ↑

n n Imp. Rec. n LTD ↓ n Imp. Imp. Imp. 92, 204–206

CAMK2A KO Imp. LTD ↓ LTP n

n Imp. 90

L7c-γ2l/l n ↓ ↓ CF ↑ n n Rec. n LTD n LTP n

Imp. n Imp. Imp. 72

PKCγ KO Imp. LTD n Imp. n Fac. 207

L7c-CNB1l/l (or L7-PP2B)

n ↓ ↓ CF n n n n Rec. n LTD n LTP ↓ IP ↓

Imp. Imp. Imp. 76

mGluR1 KO and L7-mGluR1 rescue

↓‡ Imp. LTD ↓ Ataxic Imp. 208–210

CACNA1A-P601L (tottering)

↓ ↑ ↑ CF ↓ n n n Rec. n Ataxic 75

calretinin KO ↑ ↑ CF ↓ n n Ataxic 84||

BK KO L7c-BKl/l

↓ ↑ CF ↑ ↓ Ataxic Ataxic

Imp. Imp. 211–213

DOX-treated RNB (granule cell off)

↓↓ nm nm nm n n Imp. Ataxic Imp. 69

CAMK2B KO ↓ ↑ ↑ CF ↓ ↓ ↑ LTD rev. LTP rev.

Ataxic 214¶

CACNA1A-S218L ↓ ↑ ↑ CF ↑ n n Ataxic 168#

GIRK2-G156S (weaver)

n ↑ ↑ Imp. Ataxic 215–16

Ptf1ac-Robo3l/l n § ↑ CF n n n n Rec rev. Ataxic 120

γ2, GABAA receptor, subunit γ2; BK, large-conductance calcium-activated potassium channel subunit b1 (also known as BKb); CACNA1A, voltage-dependent

P/Q-type calcium channel subunit a1A; CAMK2A, calcium/calmodulin-dependent protein kinase type II subunit alpha; CAMK2B, calcium/calmodulin-dependent protein kinase II subunit beta; CF, climbing fibre; CF elim., CF elimination; Cons., consolidation; CS, complex spike; CV, coefficient of variance (no unit); CV

2, same

for adjacent intervals (no unit); CX36; connexin 36; DOX, doxycycline; Fac., facilitated; FF, firing frequency (Hz); GIRK2, G protein-activated inward rectifier potassium channel 2; Imp., impaired; IP, intrinsic plasticity; KI, knock-in; KO, knockout; LTD, long-term depression; LTP, long-term potentiation; Mot., motor; n, normal; mGluR1, metabotropic glutamate receptor 1; nm, not measureable; PC, Purkinje cell; Perf., performance; PF, parallel fibre; PC, Purkinje cell; PKCγ, protein kinase C γ-type; Ptfla, pancreas specific transcription factor, 1a; Rec., reciprocity; rev., reversed; RNB, reversible transmission blocking; Robo3, roundabout homologue 3; SS, simple spike; Syn., synchrony. ↑, higher; ↓, lower; ↓↓ absent. *see also results with Parvalbumin-Cre x Cx36lox/lox and pharmacological block of CX36 in the IO33; ‡data recorded in vitro, see REF. 217; ||F.E. Hoebeek, unpublished observations; ¶M. Schonewille and F.E. Hoebeek, unpublished observations; #Z. Gao & F. E. Hoebeek, unpublished observations; §SS and CS data recorded during visual stimulation-induced modulation.

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MicrozoneA sagittal region of Purkinje cells within a cerebellar zone that is approximately 50 to 100 μm wide, that can be activated by a particular functional stimulus and that receives climbing fibres from a cluster of coupled olivary neurons.

Leakage currentElectrical current that is induced by synaptic afferents (for example, at olivary spines) that affects the efficiency of gap junction coupling between these spines.

Figure 2 | Complex-spike synchrony and rhythmicity. a | Complex-spike synchrony in zones (top panels, shown by the dashed lines) and microzones (bottom panels) is influenced by the level of gap junction coupling (second column), excitation (third column) and inhibition (fourth column) in the olive. The panels show schematic interpretations of data from REFS 32–34,39,43,47. Each circle in the top panels represents a Purkinje cell, and the cells are spaced 250 μm apart: the larger the diameter of a circle, the stronger the complex-spike synchrony of that Purkinje cell with respect to the ‘master cell’ (M). Complex-spike synchrony occurs in parasagittal zones of normal, resting animals (first column), but is abolished when olivary coupling is blocked (second column)32. Manipulation of the excitatory input to the olive does not greatly alter the spatial pattern of complex-spike synchrony47 but enhances the strength of complex-spike synchrony within the parasagittal zone (third column). Blocking inhibitory input to the olive increases the area in which complex-spike synchrony can be found (fourth column)33,43. The bottom panels show how each zone of Purkinje cells can be subdivided into microzones based on the uniform, synchronized complex-spike response to a particular sensory stimulus. A microzone is about 3–19 Purkinje cells wide, the dendrites of which are represented by a coloured line (Purkinje cells with the same colour show complex-spike responses to the same stimulus). Disrupting olivary coupling abolishes almost all complex-spike synchrony34, resulting in a loss of the microzonal banding pattern (second column). Remarkably, the microzone pattern is relatively little affected by stimulating the associated sensory input39 (third column). The effects of blocking GABA type A (GABA

A) receptors in the olive

on microzones are currently not known, but we suggest that this would yield wider microzones, analogous to those in the zonal studies (fourth column). b | Olivary oscillations influence the rhythmicity of complex spikes33. The frequencies of subthreshold oscillations (STOs, x axis) and spikes (y axis) in wild-type olivary neurons (top left panel) occur mostly in the range from 1–3 Hz and 6–9 Hz. In mice that lack olivary coupling owing to genetic knockout of connexin 36 (Cx36); top right panel), the correlation between the preferred frequency of the oscillations and that of the spiking activities is less strong. The phase of the subthreshold activity is reset in wild-type mice after a spontaneous or triggered (see the stimulus artefact at time = 1 s) action potential (middle left panel), whereas this resetting is less clear and less stable in Cx36–/– mice (middle right panel). In wild-type mice, peripheral stimuli (shown by a grey bar) evoke mostly single complex spikes in Purkinje cells (bottom left panel), whereas in Cx36–/– mice they often produce doublets (bottom right panel). These recordings show that olivary oscillations influence the timing of complex spikes in Purkinje cells, and that a lack of olivary coupling results in altered interactions between subthreshold oscillations and spiking activities33. Vmem, membrane potential. Part b is reproduced, with permission, from REF. 33 © (2008) Cell Press.

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JitterA measure for noise in spiking activities.

PatchA group of Purkinje cells characterized by a common response to a particular mossy fibre input, and that covers a small irregular area rather than a parallel beam or sagittal zone.

Optokinetic reflexCompensatory eye movements following visual whole-field stimulation.

Crus 2Part of the cerebellar hemisphere immediately rostral to the paramedian lobule.

Paramedian lobulePart of the cerebellar hemisphere immediately caudal to Crus 2.

CV2 valueCoefficient of variation for adjacent interspike intervals.

Olivary oscillations have also been suggested to contribute to adaptive motor behaviour by regulating long-term plasticity of neuronal activity in the cerebellar cortex19,33. In vitro studies have shown that the phase of olivary oscillations determines the number of spikelets per high-frequency burst travelling through the climbing fibre, and this may affect the complex-spike waveform and modulate synaptic plasticity at the parallel fibre–Purkinje cell synapse19. Alternatively (but compatible with the potential downstream impact on plasticity), in vivo whole-cell recordings of olivary neurons suggest that the amplitude of the oscillations correlates best with the number of climbing-fibre spikelets (M. De Jeu, P. Bazzigaluppi and C.I.D.Z., unpublished observations). Taken together, these findings may explain why indi-vidual Purkinje cells show different levels of jitter in their complex-spike responses to sensory stimulation, why it may be more fruitful to look for functional correlations in the coding of ensembles of Purkinje cells than in the coding of single cells and why olivary oscillations may be relevant for learning processes19,33–35,37,39.

Simple-spike patternsTypically, the simple-spike frequency of a Purkinje cell can reach a maximum of ~250 Hz. The patterns of sim-ple-spike activity are determined by the intrinsic activ-ity of Purkinje cells, input from parallel fibres and input from molecular layer interneurons. Parallel fibres excite Purkinje cells as well as molecular layer interneurons and Golgi cells (BOX 1). Molecular layer interneurons, in turn, inhibit Purkinje cells, providing feedforward inhibition. Golgi cells influence simple-spike patterns indirectly by inhibiting granule cells; as the Golgi cells themselves receive an excitatory input from mossy fibres and parallel fibres, the inhibition of granule cells can occur through both a feedforward and a feedback loop57. This inhibition is optimally designed to generate time windows of granule cell activity, and this activity may be further regulated by plasticity at the mossy fibre–granule cell synapse57. The simple-spike patterns of Purkinje cells are thus determined by a complex interplay of various types of cells and processes in the cerebellar cortex.

Parallel fibre configuration and activation. As parallel fibres run transversely to the climbing fibre zones, dif-ferent Purkinje cells along a parallel fibre beam can in principle be activated consecutively by a spreading wave of excitation, the speed of which is probably propor-tional to the conduction velocity of the parallel fibre58. Such transverse excitatory ‘travelling waves’ (not to be confused with travelling waves mediated by inhibitory Purkinje cell collaterals in the developing cerebellum59) can indeed be induced by direct electrical stimulation of a parallel fibre beam60. However, they are relatively sparse and weak under physiological conditions61,62. Similarly to complex-spike activity, simple-spike activity in different Purkinje cells can be coherent and synchronous31,62. In general, simple-spike coherence is likely to occur within a ‘patch’ of Purkinje cells that is fed by the numerous varicosities of the ascending parts of a set of granule cell axons60,63. This possibility is supported by the fact that

somatosensory stimulation of specific parts of the body induces simple-spike modulations in patches64. The for-mation of these patches might be enhanced by inhibitory input from stellate cells, which may be predominantly excited by the more distal parts of parallel fibres63. However, simple-spike synchrony can also occur between Purkinje cells that are distributed over longer distances, often in particular planes. In the vestibulocerebellum for example, simple-spike synchrony can be correlated to complex-spike synchrony during the optokinetic reflex and, accordingly, mainly occurs in the sagittal plane31 (FIG. 3a). By contrast, synchronous simple-spike activity in Crus 2 and the paramedian lobule — which can be time-locked to whisker stimulation or reaching movements, respectively — is largely restricted to Purkinje cells ori-ented along the parallel fibre beam37,62. The patchy and longitudinal organizations of simple-spike synchrony are not mutually exclusive and can occur at the same time. This could explain why simple-spike synchrony can occur along the parallel fibre beams and sagittal zones but is most prominent within small patches30,57.

Intrinsic activity, and synaptic excitation and inhibi-tion. Purkinje cells are intrinsically active; they fire action potentials in the absence of synaptic input and in dissociated preparations65,66. This intrinsic pacemak-ing activity, which originates mainly from resurgent sodium conductances and potassium conductances65,67, is highly regular and fast (30–150 Hz) (FIG. 1). However, acute, inducible and reversible cancellation of the gran-ule cell or molecular layer interneuron output in vivo decreases and increases simple-spike firing, respec-tively68,69 (TABLE 1). This indicates that the inhibitory input to Purkinje cells can overrule the intrinsic pace-making activity in the absence of excitation, and that excitatory input outweighs it in the absence of inhibition. But these excitatory and inhibitory inputs do more than controlling average firing frequency. Following paral-lel fibre stimulation in vitro, a transient, short-latency increase in Purkinje cell firing is immediately followed by feedforward inhibition induced by activation of molecular layer interneurons, rendering a new tempo-ral pattern of simple-spike activity70,71 (FIG. 3b). In vivo, chronic reduction of excitatory input from granule cells or of inhibitory input from molecular layer interneurons increases the regularity of simple-spike firing without affecting simple-spike firing frequency72,73 (see CV and CV2 values in TABLE 1). Conversely, chronic enhancement of the inhibitory control of excitatory inputs to Purkinje cells (in mice with a mutation in the gene encoding the P/Q-type voltage-gated Ca2+-channel74) increases the irregularity of simple-spike activity, with only a mild con-comitant increase in firing frequency75 (BOX 2; TABLE 1). Thus, given enough time, the cellular properties of Purkinje cells can compensate for factors that affect their firing frequency, but Purkinje cells do require excitatory and inhibitory inputs to create temporal pat-terns of simple spikes72,73,76. In other words, the intrinsic activity of Purkinje cells seems to drive simple-spike frequency, whereas the inhibitory and excitatory inputs are essential for precision of simple-spike timing.

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DownstateThe state of a cell in which the membrane potential is low and hardly any spikes are fired.

Inter-simple-spike intervals. The temporal pattern of simple spikes can be described in terms of regularity of the interspike intervals (or ‘pauses’)70,71 (FIG. 3c). Pauses with a duration longer than several hundred milliseconds — which have been attributed to the downstate of bistable

Purkinje cells77 — occur frequently in anaesthetized ani-mals but substantially less often in awake animals, and are therefore unlikely to play a prominent part in functional behaviour78. It is possible that such long pauses may be functional during sleep, to avoid an unnecessary or

Figure 3 | Spatial and temporal patterns in simple-spike firing. a | Simple-spike synchrony seems to be most prominent in small patches (<100 μm in diameter, shown by light red circles), in which the synchronous cell pairs are not oriented in any particular direction142. However, it also occurs between neurons across longer distances in a particular direction (shown by red arrows). In the flocculus, it follows the spatial pattern of complex-spike synchrony (shown by dashed grey arrows), along the parasagittal plane31. In Crus 2, such ‘long distance’ simple-spike synchrony is relatively rare, but if it occurs it is preferentially oriented along the transverse axis, perpendicular to the orientation of complex-spike synchrony37,62. In the paramedian lobule, simple-spike synchrony is more prominent than in Crus 2, but is also mainly oriented transversely62. b | Direct stimulation of parallel fibres (shown by the lightning symbol) can induce a burst of simple spikes, which in control animals is followed by a pause in simple-spike firing owing to feedforward inhibition (top panel). This pause does not occur in the absence of feedforward inhibition72 (middle panel), whereas it lasts longer in mice with enhanced inhibitory control of excitatory transmission owing to a mutation in the gene encoding voltage-gated Ca2+ channels74,75 (bottom panel). Notably, with decreasing Purkinje cell (PC) inhibition, simple-spike firing becomes more regular72,75 (middle panel). c | Simple-spike patterns tend to occur in short, regular patterns, with a constant interspike interval (shown by coloured spikes). Most patterns have a length of two or three identical inter-spike intervals, but longer patterns also occur. In addition, irregular spikes occur (shown by black spikes). The onset of a regular pattern is often synchronous between Purkinje cells located close together (<500-μm apart; shown by yellow bars), but not between Purkinje cells further apart. However, subsequent simple spikes are generally not synchronized between Purkinje cells79. Note that these schemes reflect the relatively simple patterns described so far79 but that theoretically more complicated patterns may occur. d | Simple-spike firing patterns can be influenced by complex spikes. An overlay of eight fragments of an extracellular recording of a Purkinje cell in an awake, adult mouse aligned on the onset of the complex spike (time = 0 ms) shows three phases following a complex spike37 (top and middle panels). First, an absolute pause in simple-spike firing directly follows the complex spikes (the climbing-fibre (CF) pause); second, this pause is often — but not always — followed by a period of increased simple-spike firing (simple-spike facilitation); and last, there is a phase known as simple-spike suppression, during which simple-spike firing is decreased but not fully abolished87. The lower panel is a histogram of simple-spike times of the same Purkinje cell relative to the firing of complex spikes (time = 0ms), using 5-ms bins. The dashed line shows the average number of simple spikes per bin during the 200 ms before the complex spike. Simple-spike suppression can also occur in association with complex spikes of other Purkinje cells within the same sagittal zone37,88. Parts a, b and c, based on data from REFS 31,37,62,71,72,74,75,79,142. Part d, data from REF. 87.

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UpstateThe state of a cell in which the membrane potential is normal or high, and spikes are fired.

disturbing read-out of spatiotemporal simple-spike pat-terns in the cerebellar nuclei when no movement con-trol is required. Interspike intervals of short durations (<100 ms) — which are associated with the upstate of Purkinje cells — occur in both anaesthetized and awake states78,79. In awake mice most regular simple-spike pat-terns last on average ~50 ms and contain two to three intervals, but they can also last hundreds of milliseconds and contain tens of intervals79. Thus, simple-spike firing of Purkinje cells, which in vivo is considered to be quite irregular, in fact consists of many short, regular periods.

The occurrence of these short patterns is reflected in the CV2 value (coefficient of variation for adjacent interspike intervals), which is low when the level of reg-ularity is high (TABLE 1). Regular simple-spike patterns — defined by a low variability of successive interspike intervals — comprise over half of the Purkinje cell spikes. Interestingly, regular patterns often coincide in neigh-bouring Purkinje cells without precise synchronization of individual spikes, and in the awake state these coincid-ing patterns seem to be better preserved in the sagittal than in the transverse plane61,79. Thus, as suggested above

Box 2 | Deficits in firing patterns can lead to cerebellar ataxia

Tottering (tg) mutant mice, which suffer from a loss of function in the α1a subunit of the P/Q-type voltage-gated Ca2+ channel encoded by Cacna1a, show severe ataxia165. In these tg mutants (see the figure, shown in red), the floccular Purkinje cells show average simple-spike firing frequencies (negative potentials that are comparable to those of wild-type littermates (wt; see the figure, shown in blue) during both spontaneous activity (part a) and optokinetic stimulation (part b). However, the pattern of their simple spikes shows more irregularities75 (see the raster plots in part c). Note that the amplitude of the compensatory eye movements in tg mice is affected but not reduced to zero (part d), which points to a role for both rate coding and temporal coding. The irregular Purkinje cell pacemaking activity is induced by lack of SK-channel activation113, which — together with a disrupted parallel-fibre input166 and increased GABAergic input from interneurons74,75,167 — causes irregular simple-spike patterns75. Interestingly, gain-of-function mutations of the same channel can also deregulate simple-spike patterns and induce ataxia168. For example, the Purkinje cells in S218L mutants (S218L, shown in green) show irregular simple-spike patterns during spontaneous activity (part e), and show bursts and pauses following parallel-fibre stimulation (part f, shown by arrows), whereas in wt mice the activity is more regular under these circumstances. Likewise, S218L mutants show impaired locomotor performance and learning on an accelerating rotarod (part g; see REFS 75,168,169). The similarities in the behavioural phenotypes of these two mouse models, which suffer from loss-of-function and gain-of-function mutations of the same gene (Cacna1a), reveals a narrow window for optimal Ca2+ homeostasis in controlling simple-spike firing: both an increased and a decreased Ca2+ influx can induce abnormal temporal simple-spike patterns as well as ataxia (see also TABLE 1). Sp, spikes. Parts a–c are reproduced, with permission, from REF. 75 © (2005) Cell Press. Part d is reproduced, with permission, from REF. 57 © (2009) Cell Press. Part g is modified, with permission, from REF. 169 © (2010) Wiley.

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Rebound potentiationPotentiation at the molecular layer interneuron–Purkinje cell synapse, which is facilitated by co-activition of the molecular layer interneuron and the climbing fibre innervating the same Purkinje cell.

for complex-spike activity, it may be easier to find the function of temporal coding in simple-spike patterns of a population of Purkinje cells than of individual cells.

Regular simple-spike patterns occur more often in ani-mals undergoing tactile stimulation or learning compared with non-stimulated animals, and this increase is larger than one would expect based on only the evoked increase in firing rate79. Moreover, the duration of regular patterns following stimulation is in line with that of the tempo-ral domain of cerebellar motor control — that is, tens to several hundreds of milliseconds33,80. Together, these findings indicate that the apparent irregularity in simple-spike trains in vivo is most probably caused by mixing of different regular simple-spike patterns over time, and that the use of spatiotemporal patterns of simple-spike coding in ensembles of Purkinje cells may provide func-tional features for cerebellar control that complement those of average firing-rate coding.

Complex spike–simple spike interactionsThe patterns of complex spikes and simple spikes can influence one another. Simple-spike activity can, as dis-cussed above, modify climbing-fibre activity patterns through GABAergic feedback from the cerebellar nuclei to the inferior olive41,42, and climbing-fibre activity in turn can influence the generation of simple-spike activity in the cerebellar cortex. These influences can be divided into acute effects, heterosynaptic plasticity effects and global effects. Acute effects occur directly after the occurrence of a complex spike, and include the phenomena called — in consecutive order — climbing-fibre pause, simple-spike facilitation and simple-spike suppression (FIG. 3d). Heterosynaptic plasticity effects of climbing-fibre activity include plasticity at the parallel fibre–Purkinje cell synapse, at the molecular layer interneuron–Purkinje cell synapse and, through spillover81,82, at the parallel fibre–molecular layer interneuron synapse. Global effects involve short-term and long-term inhibitory effects of climbing fibres that profoundly affect the basic firing frequency of simple spikes during rest and during modulation.

Climbing-fibre pause. The climbing-fibre pause, which occurs in all Purkinje cells, is a short period of approxi-mately ten or more milliseconds that occurs immediately after the initiation of the complex-spike waveform, and during which a Purkinje cell does not elicit any simple spikes16,83 (FIG. 3d). Despite the fixed sequence of current activations (FIG. 1b), the length of the climbing-fibre pause varies considerably from trial to trial, and it varies even among Purkinje cells within the same microzone16,37,84–87

(TABLE 1). This variability is consistent with dendritic regulation of spiking24 and it suggests a contribution of a dynamic network-level effect, such as inhibition from molecular layer interneurons onto the dendrites. Indeed, climbing fibres modulate the activity of molecular layer interneurons81,82, and blocking the output of molecular layer interneurons shortens the climbing-fibre pause72.

Simple-spike facilitation. Immediately after the climbing- fibre pause an increase in simple-spike activity that lasts 20–40 ms16,37,83 is often observed (FIG. 3d). This increase is

transient37,86. It is possible that glutamate spillover from climbing-fibre terminals activates glutamate receptors on Purkinje cells and molecular layer interneurons for relatively long periods, and thereby influences the fre-quency and regularity of simple-spike firing after the climbing-fibre pause82. This possibility is supported by the observation that simple-spike facilitation in some cases depends on the strength of inhibition from the molecular layer interneurons and/or the duration of the climbing-fibre pause46.

Simple-spike suppression. After the simple-spike facili-tation — that is, about 40 ms after the initiation of the complex spike — many Purkinje cells show a phase of simple-spike suppression that lasts several tens of milli-seconds37,46. Simple-spike suppression comprises a ~30% reduction in simple-spike firing37,87 (FIG. 3d). Interestingly, it can occur following complex-spike activity of other Purkinje cells as well as following that of the same Purkinje cell37,88. This implies that a climbing fibre affects more Purkinje cells than the one with which it forms direct synaptic contacts. As simple-spike suppression is most prominent in the sagittal plane37,87, it is possible that it is supported by the sagittally oriented axons of the molecular layer interneurons and/or by the similarly oriented climbing-fibre ramifications of neurons that are coupled in the inferior olive. Occasionally, the simple-spike suppression ‘fuses’ with the complex-spike pause, resulting in a long period of reduced simple-spike firing that is expressed as a long climbing-fibre pause37,87.

Plasticity at Purkinje cells. Combined climbing-fibre and parallel-fibre activity can induce postsynaptic long-term depression (LTD) at the parallel fibre–Purkinje cell synapse9,89–91 (FIG. 4a). LTD may elicit, counter-intuitively, a shortened after-hyperpolarization, and thereby shorter pauses in simple-spike activity92 (TABLE 1). These effects may be further facilitated by retrograde, presynaptic, short-term depression (STD) at the same synapse; this process, which is mediated by endocannabinoids and lasts for several seconds, is also enhanced by climbing-fibre activity93,94. Interestingly, induction of depression at the parallel fibre–Purkinje cell synapse may depend on the temporal structure of the presynaptic action potential trains in the parallel fibres, owing to high-pass filter qualities implemented by NMDA autoreceptors95. Considering the presynaptic locus of this mechanism, the same phenomenon might also occur during poten-tiation at the parallel fibre–molecular layer interneuron synapse (described below), which is also dependent on concomitant climbing-fibre activation81,82. Potentiation at the parallel fibre–molecular layer interneuron syn-apse can thus act synergistically with both LTD at the parallel fibre–Purkinje cell and rebound potentiation at the molecular layer interneuron–Purkinje cell synapse96. Sensorimotor training patterns that evoke parallel-fibre activity in the absence of climbing-fibre activity induce long-term potentiation (LTP) at the parallel fibre–Purkinje cell synapse76,97,98 and modify the intrinsic excitability and intrinsic plasticity of Purkinje cells76,99. In addition, parallel fibre bursts can induce immediate,

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↑

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Figure 4 | Synaptic plasticity affects simple-spike firing. a | Mossy fibres (MFs) terminate on granule cells (GCs), which then innervate Purkinje cells (PCs) (1) and molecular layer interneurons (MLIs) (2) through parallel fibres (PFs). MLIs provide inhibitory input to PCs (3). Hence, depending on the strength of the synapses involved, a GC can provide a PC with a predominantly excitatory input (PC I), with both excitatory and (indirectly) inhibitory input (PC II), or only (indirectly) inhibitory input (PC III). These excitatory and inhibitory synapses can show homosynaptic plasticity (indicated by the + or – symbols inside terminals) but also undergo heterosynaptic plasticity upon interaction with climbing-fibre (CF) input. CF activity has a predominantly depressing effect on the PF–PC synapse (shown by the – symbol outside terminals), whereas it potentiates the PF–MLI and MLI–PC synapses (shown by the + symbol outside terminals). During sensorimotor coordination, such as during active whisker exploration, MFs and CFs can be activated37. b | The strengths of PF–PC synapses (1) and those of the disynaptic feedforward inhibition (2 + 3) are subject to plastic changes following specific activity patterns in the PFs and CFs. The numbers 1, 2 and 3 refer to the sites indicated in panel a. In general, stronger excitatory postsynaptic potentials (EPSPs) at PF–PC synapses evoke an increased simple-spike frequency and increased CV

2 value (that is, low regularity), whereas stronger inhibitory postsynaptic potentials (IPSPs) at MLI–PC synapses reduce

simple-spike frequency and increase the CV2 value. Thus, both types of plasticity combined can — depending on the level

of potentiation or depression — reconfigure the firing pattern in any composition desired, that is, high frequency with high or low regularity, or low frequency with high or low regularity. c | Simple-spike patterns during responses to a natural, somatosensory stimulus. Single whisker stimulation (WS, bottom row) can evoke a burst of, on average, three spikes in GCs (middle row)201. Depending on the particular whisker that is stimulated, three types of simple-spike responses can be observed in a single PC (top row; these responses correspond to the three types of activations of Purkinje cells in panel a): increased firing (type I), increased firing followed by a period of decreased firing (type II) and only decreased firing (type III))37. This suggests that the three types of functional connectivity depicted in panel a occur in the cerebellum, and that different simple-spike patterns may reflect the particular MFs that are involved. d | Long-term plasticity of the PF–PC synapse may alter the temporal structure of simple-spike trains. The duration of the pause (shown in yellow) in simple-spike firing following PF stimulation (PF stim.) in vitro can be modified by long-term plasticity92 (top row). During associative learning — which requires CF input to relay the unconditioned stimulus (US) — the number of simple spikes that occur during a conditioned stimulus (CS) — which is conveyed by the MF input — may decrease or increase during learning or extinction, respectively108 (bottom row). All figure parts are schematic drawings that represent mechanisms proposed in this article.

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HarmalineA tremorgenic drug that induces oscillations in neurons of the inferior olive.

paired-pulse facilitation100 or short-term potentiation (STP) of metabotropic glutamate receptor 1 (mGluR1)-evoked slow excitatory postsynaptic currents (EPSCs) (known as mGluR1-STP), which is enhanced by prior activation of climbing fibres with a delay of up to 90 s101,102. Thus, together, these forms of depression and potentia-tion can be expected to introduce patterning in simple-spike activity resulting in altered CV2 values76 (FIG. 4b).

Plasticity at molecular layer interneurons. At the paral-lel fibre–molecular layer interneuron synapse, optimal training patterns of conjunctive climbing-fibre activ-ity and parallel-fibre activity induce postsynaptic LTP, which probably requires nitric oxide production103,104. Together with the rebound potentiation mentioned above, this potentiation enhances the feedforward inhi-bition that curtails simple-spike activity following acti-vation of the mossy fibre–parallel fibre input70,72 (FIG. 4b;

TABLE 1). Interestingly, the impact of climbing-fibre activ-ity on potentiation at the parallel fibre–molecular layer interneuron synapse and at the molecular layer interneu-ron–Purkinje cell synapse seems to be consistent with its potential impact on LTD and STD at the parallel fibre–Purkinje cell synapse, reinforcing their overall unifying influence on simple-spike patterning85,103. One could even imagine that these forms of potentiation dominate the ultimate plastic inhibitory effects in Purkinje cells, making parallel fibre depression redundant91. If one applies parallel fibre stimulation without climbing-fibre input, the parallel fibre–basket cell synapse undergoes short-term depression (STD)105. Similar to STD at the parallel fibre–Purkinje cell synapse, the occurrence of STD and LTP at the parallel fibre–molecular layer interneuron synapse, and rebound potentiation at the molecular layer interneuron–Purkinje cell synapse, is compatible with the finding that the presence of a complex spike during a learning trial can be linked to a substantial depression of simple-spike responses on the subsequent trial, at a time when behavioural learn-ing is expressed106 (see also REFS. 107,108). The balance between direct excitation and disynaptic inhibition via molecular layer interneurons may determine whether a specific firing pattern of the granule cells will cause a net increase or decrease in the Purkinje cell firing rate and concomitantly control the level of pattern formation in simple-spike firing66,70,72. This balance itself may depend on the context70 and may be shifted towards a larger effect of inhibition — and thus result in altered simple-spike firing — during associative learning108 (FIG. 4b–d).

Global short-term inhibition. Overexciting olivary cells with acute, systemic injections of harmaline severely reduces the simple-spike firing frequency109, whereas permanent or reversible lesions of the inferior olive ablate complex-spike activity and concomitantly boost the simple-spike firing rate110. This suggests that climbing- fibre activity must inhibit simple-spike activity under physiological conditions. The mechanisms that under-lie this global inhibitory effect must diverge from those that mediate the climbing-fibre pause and the simple-spike suppression, because quantitatively, the global

inhibitory effect surpasses the acute inhibitory effects by far. Climbing-fibre activity probably directly affects the intrinsic pacemaking activity of Purkinje cells, because climbing-fibre ablation affects the simple-spike firing rate even when the parallel fibre inputs to Purkinje cells are blocked111. Indeed, in vitro studies have revealed that the ability of the climbing-fibre input to restore tonic discharge of Purkinje cells in vivo must be at least partly due to a block of the mechanisms that give rise to an intrinsic, slow trimodal oscillation pattern consisting of a Na+-spike tonic phase, a Ca2+–Na+ burst-firing phase, and a hyperpolarized quiescent phase mediated by Ca2+-dependent K+ currents23 (BOX 2; FIG. 1b). Together, these effects of climbing-fibre discharges reduce and stabilize simple-spike firing, and contribute to the timing precision of these discharges65,112–114.

Reciprocity between complex spikes and simple spikes. The global short-term inhibitory effect described above can be readily measured during spontaneous activity, but a similar inhibitory effect also comes into play dur-ing modulation of Purkinje cell activity in response to a natural stimulus. In most Purkinje cells, the frequencies of the simple-spike activity and complex-spike activ-ity are modulated reciprocally: an increase in complex spikes is associated with a decrease in simple spikes and vice versa16,37,107. As substantial parts of the mossy-fibre and parallel-fibre inputs show activity that is in phase with activity of climbing-fibre inputs115–117, these findings raise the question of how this reciprocity comes about. The preferred simple-spike modulation seems to depend heavily on the zonally organized climbing-fibre input118. Indeed, selectively rewiring the climbing-fibre system from a contralateral projection to a predominantly ipsilat-eral projection, as has been done in Ptf1a::Cre;Robo3lox/lox mice119 (mice in which roundabout homologue 3 (Robo3) is specifically deleted in cells that express pancreas spe-cific transcription factor 1a (Ptfla)) (TABLE 1), shifts the phase of both complex-spike activity and simple-spike activity by approximately 180° during natural stimula-tion, leaving the overall reciprocity between complex spikes and simple spikes intact120. Molecular layer interneurons may play a relevant part in maintaining the reciprocity, because the phase of their firing frequency alters together with that of the Purkinje cell activity in Ptf1a::cre;Robo3lox/lox mice (A. Badura and C.I.D.Z., unpublished observations). Such a mediating role would be consistent with the fact that the strength of the paral-lel-fibre inputs to the molecular layer interneurons can be potentiated by climbing-fibre activation103, as described above, and that these interneurons can show activity that is in phase with that of climbing fibres115. Interestingly, in Ptf1a::cre;Robo3lox/lox mice the shift of the simple-spike modulation (that is, rate coding) comes with a change in the CV2 value of the simple-spike activity (that is, tempo-ral coding)120, which again points to a potential interac-tion between rate coding and temporal coding (TABLE 1; BOX 2). Thus, both reciprocity between complex spikes and simple spikes, and regularity of simple-spike firing might be imposed by climbing-fibre activity through mediation by the molecular layer interneurons.

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Read-out of patterns in cerebellar nucleiThe data reviewed above imply that specific temporal patterns of complex spikes and simple spikes may be observed particularly in the sagittally oriented zones and microzones. These spatiotemporal patterns of Purkinje cell activity are only relevant if their information content is read out by the downstream targets. At the level of the cerebellar and vestibular nuclei, tens to several hundreds of Purkinje cells from single microzones converge upon a single neuron121,122, providing a barrage of inhibitory inputs. Therefore, the firing patterns of sets of Purkinje cells must have some level of coherence in their activity to enable cerebellar-nucleus neurons to unravel the code contained in these patterns123,124 (FIG. 5).

Impact of complex spikes on cerebellar-nucleus neu-rons. Complex spikes are transmitted as small bursts of action potentials down the Purkinje cell axon and evoke profound inhibitory postsynaptic potentials (IPSPs) in the target neurons in the cerebellar and vestibular nuclei125,126. After the inhibition, which can last for tens of milliseconds, the nucleus neurons can show a profound increase in firing, known as rebound firing119 (BOX 3). Complex-spike driven rebounds seem to particularly influence the inhibitory feedback from the cerebellar nuclei to the inferior olive, because GABAergic neurons in the cerebellar nuclei show a longer-lasting increase in firing frequency during rebound than the non-GABAer-gic cells127. The rebound firing in the GABAergic nucleus neurons might have a direct role in mediating the cou-pling between olivary nucleus neurons and inhibit-ing their activity41,46,128–130 (FIG. 2). The non-GABAergic neurons in the nuclei also show a deep hyperpolariza-tion and subsequent rebound following complex-spike activation, although these are less prominent than in GABAergic neurons. As these non-GABAergic neurons include the excitatory and glycinergic cerebellar-nucleus neurons that ultimately control downstream extra-olivocerebellar motor and premotor structures131–135, it is tempting to speculate that the complex-spike patterns that can be correlated to the timing and/or direction of ongoing movements35,131 exert their effects through both the hyperpolarizations and rebounds that they evoke in the cerebellar-nucleus neurons (TABLE 2). This possibility is supported by the fact that the rebounds may be cor-related to the timing of movements, especially when the movements are perturbed and rapid correcting reflexes are triggered (BOX 3). Interestingly, if the synchrony and precision in the timing of complex-spike activity are disturbed owing to blockage of olivary coupling, which is likely to have a detrimental impact on the genera-tion of rebound activity, conditioned reflex movements are impaired and their timing is abnormal33. Thus, complex-spike patterns and their rebounds may serve different but related roles in the timing of the activity in the GABAergic and non-GABAergic neurons in the cerebellar and vestibular nuclei.

Impact of simple spikes on cerebellar-nucleus neurons. Purkinje cells fire far more simple spikes than complex spikes. When a single neuron in the cerebellar nuclei is

innervated by 50 Purkinje cells, all firing at 50 Hz, this neuron receives ~2,500 inhibitory events per second. Considering a decay time constant of a few milliseconds for each IPSP126,135–139, the impact of a single simple spike is probably minimal, unless a substantial amount of these events occur synchronously. However, compared with the input of the excitatory mossy-fibre collaterals, inhibitory inputs from Purkinje cells are better placed to control the spiking of neurons in the cerebellar nuclei because they have a higher convergence ratio and preferentially target the cell bodies121,122. In principle, synchronized simple spikes could thus have a big influence on the timing of action potential formation in neurons in the cerebellar nuclei. For example, the first simple spike in a pattern — which can be synchronized with the first simple spike in other Purkinje cells within an ensemble79 — could pro-vide an essential timing signal to the cerebellar nuclei123,138

(FIG. 5). The question remains how many Purkinje cells have to participate in the generation of a spatiotemporal pattern for the cerebellar nuclei to respond with a timed signal. This number may depend on the level and direction of short-term plasticity at the Purkinje cell–nucleus-neuron synapse139–141, which may help to convert pattern sig-nals into spike rate codes (FIG. 5c). Simulations based on realistic convergence ratios indicate that epochs of rela-tively constant synaptic conductance can be evoked in cerebellar-nucleus neurons by short-lasting but regular simple-spike patterns, which suggests that these neurons may be able to read out the signal information provided by simple-spike patterns79,123,142,143.

Interaction with collaterals. Mossy fibres provide an excitatory collateral input to cerebellar-nucleus neu-rons, yielding numerous EPSCs per second137. Purkinje cell activity-induced decrements in Ca2+ in the neurons in the nuclei are optimal for driving plasticity of these EPSCs when the excitation by mossy fibres occurs before the inhibition by Purkinje cells137,144,145. Thus, the tim-ing of the collateral input is of crucial importance for the resulting plasticity; indeed, only excitatory synaptic inputs arriving up to several hundred milliseconds before inhibition undergo LTP146 (FIG. 5d). Whether climbing-fibre collaterals, which also target cerebellar-nucleus neurons147, can induce the same level of potentiation remains to be established. Under some circumstances — for example, classical eyelid conditioning involving delays of 100 to 500 ms80 — the potentiation described above might be selective for mossy-fibre collaterals, which mediate signals about the conditioned stimu-lus148. Under other circumstances, such as conditions that require widespread and complex motor responses following sudden locomotion perturbations33,149, it might be advantageous to strengthen climbing-fibre collat-eral synapses with neurons in the cerebellar nuclei to enable fast movements through a short loop involving the nuclei. Conditions requiring a combination of such responses may benefit from modifications in the strength of both mossy-fibre and climbing-fibre collaterals as well as from an overall change in intrinsic excitability, which can be readily induced following bursts of inhibition and rebound activity in the nuclei134,150,151.

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Interestingly, the sequence of spiking events that is required to exert synaptic plasticity at neurons in the nuclei may be consistent with the way in which these neurons use coherent patterning in Purkinje cell activ-ity to filter the impact of the collateral input143 (FIG. 5). According to the mechanism proposed by Sejnowski and colleagues152,153, this would mean that whenever the spa-tiotemporal patterns generated in the cerebellar cortex oscillate at the right intervals with respect to the timing of the collaterals, the efficacy of the excitatory output of the collaterals will increase dramatically143. This mecha-nism is partly independent of plasticity in the neurons in the nuclei; so, if this mechanism is further enhanced by short-term plasticity at the Purkinje cell–nucleus-

neuron synapse, by LTP at the collateral–nucleus-neuron synapse and/or by intrinsic plasticity, the timing of the cerebellar cortical patterns with respect to that of the col-laterals may have an even greater impact on the spiking output of the neurons in the cerebellar nuclei.

Conclusions and future directionsPurkinje cells and neurons in the cerebellar nuclei differ from other principal neurons in, for example, the hip-pocampus and cerebral cortex154,155, in that they show remarkably persistent pacemaking activity, the patterns of which can be shaped by various inhibitory and excita-tory synaptic inputs. Both the Purkinje cells and neu-rons in the cerebellar nuclei are centrally positioned in

Figure 5 | Read-out of patterns in cerebellar nuclei. a | Five different Purkinje cells (PCs) innervating the same cerebellar-nucleus neurons (CNs) fire different simple-spike patterns and complex-spike patterns over time. When the spikes of different PCs occur simultaneously, the level of synchrony increases (shown by the darker shade of the brown bars), the PC jitter decreases and the probability for rebound firing in CNs increases (shown by the black trace; see also BOX 3). Synchronous complex spikes evoke rebound bursts in CNs, whereas synchronous simple spikes evoke timed spiking126. b | As the PC jitter decreases, the gain of the CN responses to the excitatory collaterals of mossy fibres (MFs) and/or climbing fibres (CFs) increases143. The higher the excitatory drive of these collaterals, the higher the gain of CN responses. The shades of brown correspond to the shades of brown in part a. c | In addition, PC–CN synapses in vivo presumably show both short-term depression (STD) and short-term potentiation (STP), depending on the firing frequency modulation of PCs141. The figure shows the normalized efficacy of PC–CN synapses (normalized to inhibitory postsynaptic current (I

IPSC) at 60 Hz) as a function of the normalized interspike interval of PCs (data from REF. 140), which was set at

17 ms. d | The timing of the excitatory input from the MF collaterals relative to the rebound evoked by synchronous patterns of complex spikes and/or simple spikes greatly influences the synaptic plasticity and spike rate of CNs. Following synchronous activity (left panel, shown in green) in the inferior olive (IO), PCs respond with synchronous complex spikes (left panel, shown in red) evoking rebound firing in CNs (left panel, shown in black). Four examples of mossy-fibre input (middle panel, shown by the light blue square, triangle, circle and star) are shown with a particular timing relative to the rebound (shown by the grey bar). The MF–CN synapses undergo long-term potentiation (LTP) or long-term depression (LTD) if the MF signals arrive before or after the CN rebound, respectively137 (right panel). Finally, structural plasticity may also occur at the level of the inputs of the collaterals, in that they may expand and sprout following associative motor learning202. Thus, various short-term and long-term processes may ultimately constitute a mechanism for flexible signal routing in the cerebellar neural circuitry. The circuitry may exploit sparsely synchronized network oscillations and temporal filtering by feedforward inhibition to extract the spatiotemporal patterns of Purkinje cell activities at the cerebellar-nucleus neurons and turn them into rate coding124,143,203. EPSP, excitatory postsynaptic potential. All figure parts are schematic drawings that represent mechanisms proposed in the field124,126,137,143,144.

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olivocerebellar modules, each of which is involved in controlling a particular motor domain118,147 (BOX 1). As reviewed here, all cellular components of the olivo-cerebellar modules have characteristics that enable them to contribute to fine-tuning the spiking activity of Purkinje cells and cerebellar-nucleus cells and thereby to create spatiotemporal patterning. Many manipula-tions, pharmacological or genetic, lead to a change in the spatiotemporal firing pattern within the olivocer-ebellar system and concomitantly to some change in motor behaviour (TABLE 1); these include cell-specific targeting of phosphatases, kinases and receptors, as well as global defects in gap junction channels and calcium channels. Remarkably, those manipulations that merely affect the spatiotemporal patterning (for example, CV and CV2 values) result in impairments in motor learning and consolidation, whereas those that also affect rate coding (for example, a change in simple-spike firing) consistently also result in ataxic motor behaviour (TABLE 1).

We propose that the combined read-out — in the cerebellar nuclei — of the pattern of complex- and/or simple-spike activity, and the pattern of the mossy-fibre and/or climbing-fibre collateral activity, is essential or permissive for the adaptive regulation of movements (FIG. 5). An accurate read-out of complex-spike patterns and activity of the climbing-fibre collaterals may lead to appropriate, quick reaction movements (for example, unconditioned responses or speeding up of movements) within 100 ms, whereas an accurate read-out of simple-spike patterns and the activity of mossy-fibre collaterals may lead to improved conditioned reaction movements (or combined sets of movements) that operate at inter-vals between 100 and 500 ms. Interactions between the two pathways and related patterns of Purkinje cell activity may be particularly relevant when both types of movements are combined — for example, when initial quick reaction movements are required but must be fol-lowed by dampening of oscillatory activity in the same set of muscles156.

Depending on the sensorimotor task, the read-out of the spatiotemporal patterns may be combined with a read-out of changes in the average firing frequencies (that is, the rate code) of Purkinje cells within the same microzone and module. Such a combination may be relevant, for example, for the start of the consolidation process during adaptation of the vestibulo-ocular reflex, whereby the consolidation requires the patterning medi-ated by feedforward inhibition72, whereas the ongoing movements are presumably controlled by changes in the modulation of the peak-to-peak amplitude of activity in the same Purkinje cells157 (see also the peristimulus time histogram in the left column of BOX 2). Thus, this concept of temporal coding in the cerebellum does not exclude, but instead embraces, many of the current theories that are based on rate coding principles8–14. In fact, the spa-tiotemporal activity patterns in a selective population of Purkinje cells (shaped by activity in the molecular layer interneurons) may be extracted in the cerebellar nuclei when the Purkinje cell activity in the appropriate part of the module switches from an asynchronous to an

Box 3 | Rebound firing — occurrence and relevance

Rebound firing is an excitatory response to an inhibitory stimulus (see the figure; shown in red in parts a and b). It has been assumed to occur in neurons in the cerebellar nuclei (CNs) following Purkinje cell activation170–173 (see the figure, shown by the arrows). However, it remains to be shown to what extent this rebound firing is functional126,174–176 (TABLE 2). In addition, the relative contributions of the hyperpolarization-activated depolarizing current134,177–180 (I

H), sodium current126,179,181,182 and calcium current137,175,178,182–

186 to rebound firing are still disputed137,178,184,185. For example, the IH current seems to

boost rebound178 without being strictly necessary for all rebound responses179,184, whereas activation of voltage-gated calcium channels may mainly control the response of nuclear neurons to synchronous complex spikes137,183,185. Likewise, at the behavioural level, rebound responses may only be relevant during particular tasks187–189. For example, no rebound firing can be detected in neurons during slow sinusoidal movements190,191, but pauses with subsequent increases in firing rate can be identified in CNs following sudden perturbations in locomotion149 or fast saccadic eye movements149,192 (see the figure, part a), following unexpected natural or artificial peripheral nerve stimulation193 (see the figure, part b (top panel)), or following direct stimulation of the inferior olive (IO)126,193–197(see the figure, part b (middle panel)). Whether these pause–increase responses reflect true rebound membrane depolarizations following inhibitory responses is difficult to determine owing to the ongoing activity of various excitatory synaptic inputs198 and/or the potential influences of anaesthesia and recording techniques that are involved126,174. The bottom panels in parts a and b show schemes of the olivocerebellar system to illustrate how the experimental stimuli (shown by arrows) activate the IO and lead to increases in firing frequency in neurons of CNs. For experiments in part b, electrical stimulation was used (shown by the lightning symbol in the bottom panel). CF, climbing fibre; Ctx, cerebellar cortex; contra, contralateral; ipsi, ipsilateral; MF, mossy fibre; NRTP, nucleus reticularis tegmenti pontis; PCN, precerebellar nuclei. Part a, top three panels are reproduced, with permission, from REF. 192 © (1991) American Physiological Society. Part b, top and middle panels are reproduced, with permission, from REF. 193 © (1973) Elsevier.

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oscillatory state143 while the other Purkinje cells of the same module fire asynchronously at the same time and mediate a rate code that contributes to the amplitude of ongoing movements124,157 (FIG. 5). The frequency and extent of occurrence of these switches — and thereby the ratio of the use of spatiotemporal coding versus rate coding — may differ substantially between different cer-ebellar tasks. It is possible to imagine that the vestibu-locerebellum — which controls slow compensatory eye and head movements — heavily uses rate coding, whereas the neocerebellum — which controls, for example, high-frequency whisker movements — preferentially employs spatiotemporal coding. Unipolar brush cells could be elementary in this respect, because they are particularly prominent in the vestibulocerebellum and because they

show slow and long-lasting responses158,159, befitting a rate coding system.

The network principles reviewed above favour a role for spatiotemporal patterning in cerebellar processing. Testing the main mechanisms underlying this hypothesis would require simultaneous recordings from multiple Purkinje cells and cerebellar-nucleus neurons in awake, behaving animals during training, and identification of the activity patterns of these neurons during different types of motor behaviour. This approach would make it possible to investigate the relationship between the rel-evance of spike timing and spatiotemporal patterning on the one hand, and average firing rate coding on the other hand during fast and slow, and dynamic and adaptive sensorimotor responses.

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Table 2 | Occurrence of rebound firing in experimental paradigms

Type of recording

Type of stimulus Rebound firing did occur (refs) Rebound firing did not occur (refs)

In vitro extracellular Electrical stimulation – 174, 183

In vitro intracellular

Electrical stimulation 133, 151, 170, 175, 178, 180, 185,186 136, 138, 174

Current inputs 133, 136, 138, 143, 170, 174, 175, 177, 178, 183 –

In vivo extracellular Electrical stimulation 125, 193, 194, 197 174

Non-electrical stimulation 195–197 –

During behaviour 149, 192 187–191

In vivo intracellular Electrical stimulation 126, 170 –

Current inputs 126, 170 –

–, no experiments have been reported

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AcknowledgementsWe kindly thank the following organizations for their financial support: the Netherlands Organization for Medical Sciences (ZonMw) to C.I.D.Z., the Netherlands Organization for Life Sciences (ALW) to C.I.D.Z., F.E.H., M.S. and S.K.K., Fonds Economische Stuurversterking (NeuroBasic project) to C.I.D.Z., the Erasmus University Fellowship to F.E.H. and M.S., the Prinses Beatrix Fonds to C.I.D.Z., and the SENSOPAC (sensorimotor structuring of perception and action for emergent cognition), CEREBNET and C7 programs of the European Community to C.I.D.Z. We also thank our laboratory members for valuable discussions.

Competing interests statementThe authors declare no competing financial interests.

FURTHER INFORMATIONErasmus MC Department of Neuroscience homepage: http://www.neuro.nl/research.phpChris I. De Zeeuw’s homepage: http://www.nin.knaw.nl/research_groups/de_zeeuw_group

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Spatiotemporal Firing Patterns in the Cerebellum