Dendritic spikes mediate negative synaptic gain control in cerebellar Purkinje cells

Abstract

Dendritic spikes appear to be a ubiquitous feature of dendritic excitability. In cortical pyramidal neurons, dendritic spikes increase the efficacy of distal synapses, providing additional inward current to enhance axonal action potential (AP) output, thus increasing synaptic gain. In cerebellar Purkinje cells, dendritic spikes can trigger synaptic plasticity, but their influence on axonal output is not well understood. We have used simultaneous somatic and dendritic patch-clamp recordings to directly assess the impact of dendritic calcium spikes on axonal AP output of Purkinje cells. Dendritic spikes evoked by parallel fiber input triggered brief bursts of somatic APs, followed by pauses in spiking, which cancelled out the extra spikes in the burst. As a result, average output firing rates during trains of input remained independent of the input strength, thus flattening synaptic gain. We demonstrate that this “clamping” of AP output by the pause following dendritic spikes is due to activation of high conductance calcium-dependent potassium channels by dendritic spikes. Dendritic spikes in Purkinje cells, in contrast to pyramidal cells, thus have differential effects on temporally coded and rate coded information: increasing the impact of transient parallel fiber input, while depressing synaptic gain for sustained parallel fiber inputs.

A hallmark of active dendrites is their ability to produce regenerative events known as dendritic spikes (1–8). In pyramidal neurons, the inward currents associated with dendritic spikes provide a strong local depolarization that can boost distal synaptic inputs and enhance their effect on axonal action potential (AP) output (1–4), particularly during burst generation (5, 6). Furthermore, dendritic spikes can enhance the precision of axonal APs in hippocampal pyramidal neurons (7) as well as in neocortical pyramidal cells in vivo (8). Dendritic spikes thus have a boosting effect on the output of pyramidal cells, thus enhancing the gain of the synaptic input-output (I/O) function (9, 10). In contrast, the effect of dendritic spikes on AP output in Purkinje cells is not well understood. Purkinje cell dendritic spikes, originally discovered in alligator Purkinje cells (11, 12), can be triggered by strong parallel fiber (PF) activation (11, 13) or climbing fiber activation (14, 15) and are due solely to activation of dendritic voltage-gated calcium channels (13, 16–18), because Purkinje cells lack dendritic voltage-gated sodium channels and active backpropagation of APs (17, 19). Calcium influx driven by dendritic spikes has an important role in triggering synaptic plasticity (20–22) and dendritic release of neurotransmitters and neuromodulators (13, 23, 24). Dendritic spikes triggered by climbing fiber input have virtually no effect on the somatic complex spike waveform, probably due to the large synaptic and intrinsic conductances activated during the complex spike (14). However, the functional role of parallel fiber-driven dendritic spikes in regulating axonal output has not been addressed directly. This distinction is crucial, because the state of the Purkinje cell dendritic tree is very different during climbing fiber and parallel fiber excitation (25), and because climbing fiber input occurs only at ≈1 Hz in vivo (26, 27), whereas parallel fiber input occurs continuously at high rates. We have therefore directly probed the relationship between dendritic spikes and axonal AP output in Purkinje cells by using simultaneous dendritic and somatic whole-cell recordings. Our results show that a dendritic spike transiently increases synaptic efficacy by promoting short bursts of somatic APs but dampen AP output over longer timescales. The interplay between these two effects during sustained parallel fiber input results in a “clamping” of Purkinje cells output over long timescales and, thus, a flattening of synaptic gain, in striking contrast to pyramidal cells (9).

Results

Single Dendritic Spikes Differentially Affect Axonal Output on Different Timescales.

We made simultaneous somatic and dendritic recordings (average distance 141 ± 11 μm, n = 9, range 102–194 μm) from Purkinje neurons in rat cerebellar slices. Purkinje cells were spontaneously active (28), and somatic APs were severely attenuated at dendritic recording sites (17, 19). To test the effect of dendritic spikes on somatic AP output, we evoked excitatory postsynaptic potentials (EPSPs) by stimulating parallel fibers close to the dendritic recording electrode (Fig. 1A). Stimulus intensity was carefully adjusted to reach dendritic spike threshold (13), such that dendritic spikes were only triggered in some trials at identical stimulus strengths (Fig. 1B). Dendritic spikes triggered a brief burst of somatic APs (2.46 ± 0.18 APs, n = 9; Fig. 1 C and D) at high instantaneous firing rates (maximum firing rate 367 ± 52 Hz with dendritic spikes vs. 236 ± 26 Hz without dendritic spikes, n = 9, P < 0.02; Fig. 1E). However, the burst of APs was followed by a prolonged pause that was not observed in the response to subthreshold EPSPs (Fig. 1C). The longest somatic interspike intervals (ISIs) were identical before and after EPSPs, which did not trigger dendritic spikes (44 ± 4.6 ms vs. 44 ± 5.4 ms, respectively, n = 9, P = 0.99). In contrast, EPSPs which triggered dendritic spikes were followed by substantially longer maximal somatic ISIs (71 ± 11 ms, n = 9; P < 0.02 compared with subthreshold EPSPs; Fig. 1E). The effects of dendritic spikes on somatic firing were independent of the location of the synaptic input (recording distance along the dendrite, range 102–194 μm; r_{(evoked spikes)} = 0.17; r_(pause) = −0.12).

Fig. 1.

Single dendritic spikes enhance AP output on short, but not long, timescales. (A) Simultaneous whole-cell recordings were made from the soma and dendrite of the same Purkinje cell while stimulating PFs close to the dendritic recording site. (B) Stimulating PFs at the threshold for dendritic spike generation resulted in subthreshold EPSPs (black) or dendritic spikes (red, same traces as in C and D). (C) Somatic (dotted line) and dendritic (thick line) voltage recording during a single parallel fiber stimulus (arrow) not triggering a dendritic spike. The raster plot and the PSTH contain 10 trials; bin size is 2 ms. (D) Same as in C, except the synaptic stimulus triggered a dendritic spike. The raster plot shows 10 trials, the PSTH contains 45 trials; bin size is 2 ms. Note the somatic AP burst associated with the dendritic spike and the following pause in somatic firing. (E) Pooled averages of maximum somatic instantaneous firing rates and maximum somatic ISIs (n = 9). Black bars show the effect of EPSPs without dendritic spikes, red bars show the effect of EPSPs with dendritic spikes, and the blue bar represents the average maximal somatic ISI during spontaneous activity showing no significant pauses are present without dendritic spikes. (F) The PSTHs in C and D were integrated then normalized to trial number and spontaneous firing rate, thus only showing the stimulus-evoked spikes. (G) Bar graphs showing the pooled averages of maximum number of stimulus added spikes and the number of sustained added spikes (in a 100-ms window starting 100 ms after the stimulus, n = 9). *P < 0.02.

The net effect of an input on AP output (stimulus-evoked spikes) can be quantified by integrating the poststimulus time histograms (PSTH) and subtracting spontaneous activity (Methods and refs. 29 and 30). This analysis confirmed that dendritic spikes resulted in an increase in the peak number of somatic APs triggered by the stimulus (Fig. 1F). On average, EPSPs triggering dendritic spikes added significantly more somatic APs immediately following the stimulus than subthreshold EPSPs (2.3 ± 0.3 APs vs. 1.7 ± 0.4 APs, n = 9, P < 0.01; Fig. 1F). However, the increase in somatic AP output was transient, because after a few tens of milliseconds, there was no significant difference between the effect of suprathreshold and subthreshold EPSPs (1.6 ± 0.2 APs vs. 1.5 ± 0.4 APs, respectively, n = 9, P = 0.9; Fig. 1G). We also estimated the time window for reading out dendritic spike-related axonal firing changes by comparing the distribution of stimulus evoked spikes with or without dendritic spikes across cells for every 1-ms time bin. This measure was significantly different for 73 ms following the stimulus (n = 9 cells, P < 0.05). Dendritic spikes thus produce a short-term increase in somatic AP output. However, this increase is not reflected in a long-term change in output, because the transient increase in spiking is cancelled out by the succeeding pause in spiking.

Dendritic Spikes Triggered by Synaptic Input Bursts Suppress Somatic Firing.

Granule cells, whose axons form the parallel fibers, can respond to sensory stimulation with bursts of APs in vivo (31, 32). To determine how dendritic spikes triggered by bursts of parallel fiber input affect somatic output, we applied 10 PF stimuli at 100 Hz while monitoring somatic AP output. Somatic AP firing rate progressively increased during the train (Fig. 2A), due to the facilitation of PF transmission and summation of synaptic potentials (33). Sufficiently strong synaptic stimulation triggered dendritic spikes (Fig. 2B). Strikingly, initiation of dendritic spikes was associated with a decrease in the average somatic firing rate, despite the presence of continuous parallel fiber synaptic input (Fig. 2C). To quantify this result, we compared somatic AP output in the first and last 50 ms of the train, because dendritic spikes were usually triggered late in the train. When no dendritic spikes were triggered, the average somatic firing rate between the first and second half of the train increased from 148 ± 16 Hz to 190 ± 13 Hz (P < 0.001; n = 5; Fig. 2D). When dendritic spikes were triggered, however, the average somatic firing rate decreased from 241 ± 8 Hz to 187 ± 12 Hz (P < 0.005, n = 5; Fig. 2E) during the train. Dendritic spikes thus reduced average axonal output. These results indicate that dendritic spikes triggered by trains of parallel fiber synaptic input can paradoxically inhibit somatic firing.

Fig. 2.

Multiple synaptically triggered dendritic spikes suppress AP output. (A) Somatic (gray) and dendritic (red) voltage traces during 10 PF stimuli delivered at 100 Hz. The instantaneous somatic firing rate (blue) is increasing as long as the synaptic input is active. (B) Same as in A except with stronger synaptic stimulus. The onset of dendritic spikes (*) in the dendritic voltage trace (orange line) coincides with a sharp drop in the somatic instantaneous firing rate. (C) Overlay of instantaneous somatic firing rates with and without dendritic spikes. (D) Comparison of the average somatic firing rate during the first and last 50 ms of the stimulus when no dendritic spikes were triggered, showing a clear increase during the stimulus (five cells). (E) Same as in D, except for trials with dendritic spikes (five cells).

Dendritic Spikes Reduce the Gain of the I/O Function.

To characterize the effect of dendritic spikes on the I/O function using a direct measure of input strength, we substituted synaptic stimulation with dendritic injection of synaptic-like currents. The injected current waveforms approximated the temporal dynamics of PF transmission (34), and an I/O curve was constructed by varying the mean amplitude of the injected current from sweep to sweep over a wide range (Fig. 3 A and D). Low levels of synaptic input increased the average somatic firing rate in a manner linearly related to the amount of injected current (r = 0.98 ± 0.01, n = 5; Fig. 3 G and H). In contrast, for current injections above the dendritic spike threshold, the average somatic firing rate was independent of the amount of injected current (r = −0.08 ± 0.18, P < 0.005 compared with no dendritic spikes, n = 5; Fig. 3 G and H), essentially flattening the f/I (firing rate vs. injected current) curve. As a result, the average somatic firing rate during dendritic spiking was clamped at 214 ± 23 Hz (n = 5; Fig. 3H) across a wide range of input strengths.

Fig. 3.

Current injection-evoked dendritic spikes suppress AP output. (A) Somatic (gray) and dendritic (red) voltage trace during dendritic injection of synaptic-like current (green). (B) Superimposed somatic (gray) and average dendritic (red) traces triggered by the current injection. AP probability (blue) follows the input strength. (C) Histogram of somatic interspike intervals triggered by current injection below dendritic spike threshold. (D) As in A but with stronger current injection triggering dendritic spikes (asterisks). (E) Superimposed somatic (gray) and average dendritic (red) traces triggered at dendritic spikes. Somatic AP probability (blue) is strongly reduced following dendritic spikes. (F) Histogram of somatic interspike intervals triggered by current injection above dendritic spike threshold. (G) Average (black), maximal (red), and minimal (blue) somatic firing rates and the number of dendritic spikes (green) during the current injection is plotted versus the average injected current. Note the linear f/I relationship before dendritic spikes occur and the input independence of somatic firing during dendritic spikes. (H) Pooled data from five cells demonstrating the linearity of the f/I curve below (weak input) and above (strong input) dendritic spike threshold and the firing rate where dendritic spikes appear ensuing the clamping effect. Average values marked with red, filled circles. Dotted lines connect measurements from the same cell (black, open circles). (A–G) Data from the same cell.

Activation of dendritic spikes was also associated with a change in the output firing pattern (compare Fig. 3 B and E). The maximal and minimal somatic firing rates during the train were differentially affected by dendritic spikes (Fig. 3 C and F). When dendritic spikes were triggered, maximal firing rates were higher but were independent of input strength, indicating that dendritic spikes cause an all-or-nothing rather than a gradual increase in maximal firing rate (Fig. 3G). In contrast, the minimal firing rate, reflecting the pauses following dendritic spikes, decreased with increasing input and increasing number of dendritic spikes (Fig. 3G). The pause was also prominent in the somatic interspike interval distributions (Fig. 3F): When no dendritic spikes were evoked, somatic interspike intervals adopted a unimodal distribution with the peak corresponding to the average firing rate. However, when dendritic spikes were triggered the ISI distribution showed two distinct peaks, one corresponding to faster than average ISIs (i.e., bursts triggered by the dendritic spikes) and a second peak corresponding to pauses in somatic firing. These longer ISI values always followed dendritic calcium spikes (Fig. 3E), consistent with the idea that dendritic spikes promote pauses in somatic AP firing (cf. Fig. 1).

BK Channel Activation Underlies the Pause Following Dendritic Spikes.

To probe the mechanism underlying the pause and the clamping of the f/I relationship triggered by dendritic spikes, we tested the involvement of high conductance calcium-activated potassium (BK) channels, which contribute to the afterhyperpolarization (AHP) of somatic APs (35) and dendritic spikes (13, 36) in Purkinje cells (Fig. S1). We therefore measured the I/O relationship of Purkinje cells after blocking BK channels. When dendritic spikes were triggered in the presence of penitrem A, a selective antagonist of BK channels (37), the clamping effect of dendritic spikes on somatic output disappeared (Fig. 4 A and B). The relationship between dendritic current injection and somatic firing rate remained linear (although with a slightly reduced slope) after the appearance of dendritic spikes (r = 0.78 ± 0.12, n = 3, P = 0.2 compared with no dendritic spikes; Fig. 4C). Furthermore, dendritic spikes were no longer associated with pauses in somatic spiking in the presence of penitrem A. Accordingly, when dendritic spikes were evoked in the presence of penitrem A, the somatic ISI distribution remained unimodal but shifted to the left (Fig. 4D), consistent with the continuing increase in average somatic firing rate with increasing injected current. These results show that the activation of BK channels by dendritic spikes (resulting in long dendritic AHP) is responsible for the pause in somatic firing, clamping the average somatic firing rate.

Fig. 4.

The clamping of the input-output relationship by dendritic spikes requires BK channels and maintains axonal output below the propagation limit. (A) Somatic (gray) and dendritic (red) recording during dendritic current injection (green). BK channels were blocked by 100 nM penitrem A. Note the lack of dendritic afterhyperpolarization and somatic pause following dendritic spikes. The slow AHP of somatic spikes is also reduced. (B) Average somatic firing rate (black) and the number of dendritic spikes (red) during the current injection is plotted versus the peak of the injected current. Note that with the appearance of dendritic spikes, the somatic output continues to correlate positively with the input, although with a reduced gain. (C) Pooled values of the linearity of the f/I curve below (black) and above (red) dendritic spike threshold (n = 3). (D) The interspike interval histogram is shifted to the left and remains unimodal with the appearance of dendritic spikes when BK channels are blocked. (A, B, and D) Data from the same cell. (E) Somatic (gray) and dendritic (red) voltage trace during synaptically triggered dendritic spikes. BK channels were blocked by 100 nM penitrem A. The instantaneous somatic firing rate (blue) keeps increasing when the synaptic input is active despite the presence of dendritic spikes. (F) Pooled average of maximal sustained somatic firing rates during synaptic-like current injections. (G) Pooled average of the maximal somatic instantaneous firing rates. Here again, the BK channel-dependent dampening mechanism invoked by dendritic spikes keeps the instantaneous somatic firing rate below the axonal propagation limit.

BK Channel Block Shifts the Balance of Inward and Outward Currents Associated with Dendritic Spike.

Given that physiological synaptic input can produce changes in membrane conductance that can affect excitability and synaptic integration (6, 38–40), we tested the effect of BK channel block on the I/O function associated with parallel fiber synaptic input. In the presence of penitrem A, no dampening of somatic output was observed for synaptic input suprathreshold for dendritic spikes (Fig. 5A), with the instantaneous firing rate increasing monotonically during the synaptic stimulus (cf. Fig. 2C). Furthermore, there were no pauses in somatic AP firing following dendritic spikes. Thus BK channels underlie the inhibitory effect of dendritic spikes on somatic output, regardless of how they are triggered.

To understand the functional relevance of this clamping mechanism, we compared the maximal somatic firing rates measured with and without dendritic spikes to the frequency limit for reliable axonal propagation of APs in Purkinje cells. The maximal sustained firing rate was below the axonal propagation limit (236 ± 15 Hz; refs. 41 and 42), both when the input was subthreshold for dendritic spike generation (225 ± 13 Hz, n = 5) and when dendritic spikes were activated (214 ± 23 Hz, n = 5; Fig. 5B). However, when BK channels were blocked, the sustained somatic firing rate could reach up to 320 Hz (average 293 ± 13 Hz; n = 3), which would result in failures of AP propagation during sustained spike firing.

Purkinje cell axons can propagate short bursts of APs more efficiently than sustained firing (41, 42), with the axonal propagation limit being 438 ± 37 Hz for short bursts (42). The highest burst frequency observed in the absence of dendritic spikes was 380 Hz (average 303 ± 26 Hz; n = 5), below the axonal limit for short bursts. However, when dendritic spikes were triggered, the fastest somatic bursts reached an instantaneous firing rate of 461 ± 36 Hz, a value comparable to the axonal propagation limit for short bursts (41, 42). When BK channels were blocked, the fastest bursts reached frequencies of 669 ± 73 Hz (n = 3; Fig. 5C), well above the frequency limit for axonal propagation. Thus, both for sustained somatic firing and for short somatic AP bursts, dendritic spikes maintain somatic firing below the level at which failures of axonal transmission occurs.

Evaluating the Downstream Consequences of Dendritic Spikes.

We have shown that dendritic spikes, generated by parallel fiber input, alter the temporal pattern of Purkinje cell output. To determine how this altered pattern is relayed to the postsynaptic neurons in the deep cerebellar nuclei (DCN), we fed the AP patterns recorded from Purkinje cells into a deterministic model of the Purkinje cell to DCN synapse (ref. 43 and Fig. S2A). The extra APs triggered by single PF inputs caused a brief increase in the inhibitory synaptic conductance in the DCN neuron (Fig. S2B). When dendritic spikes were triggered, the peak synaptic conductance change was larger (P < 0.01; n = 7) and followed by a larger trough (P < 0.05; n = 7; Fig. S2C). The change in AP pattern caused by the dendritic spike thus improves the signal-to-noise of the postsynaptic conductance change in the downstream DCN neurons. Similar results were observed when using a more prolonged PF stimulus (10 PF stimuli delivered at 100 Hz; Fig. S2D). Again, the occurrence of dendritic spikes increased the peak synaptic conductance (P < 0.01; n = 5) and enhanced the period of decreased synaptic inhibition following the PF input train (P < 0.05; n = 5; Fig. S2E). These modeling results suggest that the short–term effect of dendritic spikes on Purkinje cell output (burst followed by pause) is further amplified by the properties of the Purkinje-DCN synapse.

Discussion

We have shown that synaptically evoked dendritic spikes in Purkinje cells serve a dual role: They enhance axonal output on brief timescales but paradoxically inhibit average axonal firing rates over longer timescales. This inhibitory effect presents a striking contrast to cortical pyramidal cells, where dendritic spikes are purely excitatory, increasing the gain of synaptic input. We demonstrate that the mechanism of this paradoxical inhibition caused by dendritic spikes in Purkinje cells involves the activation of dendritic calcium-activated BK-type calcium channels, which balance the inward current provided by calcium channel activation. These results indicate that the complement of dendritic voltage-gated conductances determines the functional signature of dendritic spikes. This signature is cell-type specific and may reflect the opposite polarity of neuronal output in pyramidal cells and Purkinje cells.

Dendritic Spikes Trigger Pauses in Axonal Output.

We demonstrate that in Purkinje cells, dendritic spikes exert a dual role on axonal output. On short timescales, they enhance AP firing, triggering a brief burst of spikes. This effect is similar to pyramidal cells, where dendritic spikes are also associated with enhanced axonal AP generation (1, 6, 7), often leading to bursts of spikes (5, 6). In contrast, on longer timescales, the dendritic spike leads to a prolonged pause in spontaneous firing following the parallel fiber synaptic input, an inhibitory effect that cancels out the effect of the burst of spikes on the average axonal firing rate. Thus, the net effect of dendritic spikes on average axonal output rate is neutral. When trains of synaptic inputs activate multiple dendritic spikes, this inhibitory effect can summate, leading to the clamping of the output firing rate at a fixed value. Interestingly, spike synchronization (a timing code) and spike rate modification (a rate code) have been shown to relay different information in another motor area, the primary motor cortex of macaque monkeys (44), suggesting the two coding strategies can coexist and complement each other. The climbing fiber input in Purkinje cells also triggers dendritic spikes, which have recently been shown to regulate the postcomplex spike pause in axonal firing (14). However, the dendritic spikes activated by the complex spike are global, and their effect on axonal output is weakened by the strong synaptic and intrinsic conductances active during the complex spike. In contrast, here we show that dendritic spikes triggered by single parallel fiber stimuli, which produce highly localized spikes (13), can still produce a significant effect on axonal spiking, both in terms of burst generation and the subsequent pauses. This pausing effect of dendritic spikes, an intrinsic counterpart to feed-forward inhibition, is particularly significant given that they are superimposed on top of the high spontaneous firing rate of Purkinje cells (28, 45, 46), and may contribute to the pauses in Purkinje cell spiking seen in vivo (45, 47) and following synchronous PF stimulation in vitro (48).

Relative Contribution of Voltage-Gated Conductances Driven by Dendritic Spikes.

What is the mechanism driving the enhanced pause following a dendritic spike and the clamping effect produced during multiple dendritic spikes? We demonstrate that a selective blocker of BK-type calcium-activated potassium channels, which strongly reduces the dendritic AHP following a dendritic spike (13, 36), can prevent the clamping effect. This result indicates that the outward current mediated by BK channels is sufficiently strong to counteract the net effect of the inward current delivered by activation of P-type calcium channels during the dendritic spike. This finding is consistent with voltage clamp experiments in isolated Purkinje cell somata showing that the net effect of blocking calcium channels is to remove an outward current (49), indicating that calcium-activated potassium currents predominate over calcium currents (at least in the somatic membrane). To most effectively influence the shape of the dendritic spike, and its afterhyperpolarization, the BK channels must be localized close to the source of the calcium entry triggered by the dendritic spikes, i.e., in the dendrite; this assumption is consistent with anatomical (50) and electrophysiological evidence for the dendritic location of BK channels in Purkinje cells (51). Once the threshold for dendritic spiking is reached, this balancing of inward and outward conductances remains effective over a wide range of input strengths, producing a flat I/O curve. Thus, the relative density and dynamics of activation and inactivation of calcium channels and BK-type channels (and possibly other conductances; refs. 39 and 52–57) must be carefully calibrated to produce this robust balancing effect, which is independent of input strength. The balancing of inward and outward currents driven by a dendritic spike appears to be a distinctive signature of Purkinje cells, because in pyramidal cells, inward currents appear to predominate and pausing is not observed.

Consequences for Cerebellar Function.

Our results are consistent with two modes of integration of parallel fiber synaptic input in cerebellar Purkinje cells. At low input strengths, the relationship between maximal firing frequency and parallel fiber input is linear (29, 33, 58), enabling the simplest possible encoding strategy for parallel fiber input strength. Dendritic properties may contribute to, but are not required for this linearity, because the f/I curve of Purkinje cells remains linear after the removal of the dendrites (59). Above threshold for generation of dendritic spikes, however, the f/I relationship becomes flat, with average firing rate remaining clamped at ≈220 Hz, independently of the input intensity. This clamping is in sharp contrast to pyramidal cells, where recruitment of dendritic voltage-gated calcium channels during dendritic synaptic input produces an increased gain of the f/I function (9). The clamping or saturation of the I/O curve at high levels of synaptic input can also be observed in pyramidal cell I/O curves, but it is thought to be due primarily to shunting by synaptic conductances. In contrast, Purkinje cells exhibit an intrinsic mechanism based on balanced voltage-gated conductances for regulating synaptic gain and limiting dynamic range at high input intensities. This rapid, real-time mechanism will complement other ways to limit output gain, such as feedforward inhibition (30), which is active over a wider range of input strengths, and retrograde endocannabinoid-dependent suppression of parallel fiber input (13), which provides negative feedback over longer timescales. Recent advances in calcium imaging (4) and whole-cell recording in awake, freely behaving animals (60) should eventually help make it possible to determine under which conditions this mechanism is called into action during behavior.

What is the functional purpose of the clamping effect of dendritic spikes on axonal output? Axonal spiking is energetically expensive (61; see also ref. 62), and given the high spontaneous firing rates exhibited by Purkinje cells, this intrinsically imposed ceiling on activity may represent an energy-saving measure. Furthermore, the close match between the firing rates at which dendritic spikes clamp somatic output and the maximal frequency for faithful transmission of spiking (41, 42) suggests that the clamping of axonal output may be required to maintain optimal transmission of spikes along the axon by obviating generation of spikes which cannot be transmitted.

Finally, the temporal dynamics of the axonal spiking pattern associated with dendritic spikes—a burst of APs followed by a pause—may also have important consequences for information transfer at the Purkinje cell to deep cerebellar nuclei (DCN) relay (47) by improving the discriminability of learned patterns in Purkinje cells (48) and producing an improved signal-to-noise at the synaptic connection with DCN neurons, due to the short-term dynamics of Purkinje cell synapses (63, 64). This effect will further be amplified by the summation of postsynaptic IPSPs (65) and consequently also the rebound excitability of DCN neurons (54, 66, 67). In this way, even though parallel fiber-triggered dendritic spikes experience marked attenuation toward the soma (13), they can still profoundly influence axonal output and its downstream consequences.

Methods

All procedures were carried out with approval from the UK Home Office. Sagittal brain slices (200–250 μm thick) were prepared from the cerebellum of 18–25 d postnatal Sprague–Dawley rats (68). ACSF for slicing and recording contained 125 mM NaCl, 26 mM NaHCO₃, 25 mM glucose, 2.5 mM KCl, 1.25 mM NaH₂PO₄, 2 mM CaCl₂, and 1 mM MgSO₄ (305 mOsm). All recordings were carried out at 34 ± 1 °C. Simultaneous somatic and dendritic whole-cell patch clamp recordings were made from Purkinje neurons under visual control using differential interference-contrast optics (13, 68). Patch electrodes (soma: 5–6 MΩ; dendrite: 6–10 MΩ) were filled with 130 mM methanesulfonic acid, 7 mM KCl, 2 mM Na₂ATP, 2 mM MgATP, 0.5 mM Na₂GTP, 0.05 EGTA and 0.4 wt/wt% biocytin at pH 7.30 with KOH (285 mOsm). Recordings were made by using a Multiclamp 700A amplifier (Molecular Devices). PF inputs were stimulated (10–90 V, 0.1–0.2 ms) using ACSF-filled patch pipettes placed under visual control ≈100 μm directly beneath the dendritic recording site. EPSPs were mimicked by injection of current waveforms shaped like EPSCs, consisting of a double-exponential function with t_rise = 0.6 ms and t_decay = 6 ms. To mimic physiological PF trains, the dynamics of the EPSC amplitudes were calculated based on a modified facilitation-depression model (ref. 34 and Dataset S1). Different input amplitudes were randomized from sweep to sweep. Recordings were low-pass filtered at 8 kHz and sampled at 20–50 kHz by using an Instrutech ITC18 DAC-board controlled by Axograph, and were analyzed by using Igor Pro. To determine the net spike output in response to synaptic input with or without dendritic spikes, poststimulus time histograms (PSTH) were computed and integrated. To account for spontaneous firing, a linear fit to 200–600 ms prior the stimulus was extrapolated over the entire trial duration and subtracted from the integral to yield the spontaneous activity corrected cumulative spike count, which we called “stimulus evoked spikes” (29, 30). For the synaptic conductance modeling, we used the deterministic model of ref. 43 implemented in Igor Pro. Methanesulfonic acid was obtained from Fluka, penitrem A from Alomone Labs; all other chemicals were obtained from Sigma or Tocris. Linearity was assessed by using Pearson's correlation coefficient (P_r), significance by Student's t test, and all data are given as average ± SEM.