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Multiplexed coding by cerebellar Purkinje neurons

  1. Sungho Hong Is a corresponding author
  2. Mario Negrello
  3. Marc Junker
  4. Aleksandra Smilgin
  5. Peter Thier
  6. Erik De Schutter
  1. Okinawa Institute of Science and Technology, Japan
  2. Erasmus Medical Center, The Netherlands
  3. Hertie Institute for Clinical Brain Research, University of Tübingen, Germany
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Cite as: eLife 2016;5:e13810 doi: 10.7554/eLife.13810

Abstract

Purkinje cells (PC), the sole output neurons of the cerebellar cortex, encode sensorimotor information, but how they do it remains a matter of debate. Here we show that PCs use a multiplexed spike code. Synchrony/spike time and firing rate encode different information in behaving monkeys during saccadic eye motion tasks. Using the local field potential (LFP) as a probe of local network activity, we found that infrequent pause spikes, which initiated or terminated intermittent pauses in simple spike trains, provide a temporally reliable signal for eye motion onset, with strong phase-coupling to the β/γ band LFP. Concurrently, regularly firing, non-pause spikes were weakly correlated with the LFP, but were crucial to linear encoding of eye movement kinematics by firing rate. Therefore, PC spike trains can simultaneously convey information necessary to achieve precision in both timing and continuous control of motion.

https://doi.org/10.7554/eLife.13810.001

eLife digest

The cerebellum is a part of the brain that uses information from the senses to coordinate movement. Cells called Purkinje neurons in the cerebellum produce the final ‘output’ of its cortex. Therefore, Purkinje neurons have to communicate precise information about different aspects of the movement, such as its speed and timing. This information is likely to be represented by patterns of electrical activity within Purkinje neurons, but these patterns are still not fully understood.

Hong et al. recorded and analyzed electrical ‘spikes’, the output activity of Purkinje neurons, while monkeys made rapid eye movements. The recordings showed that occasional pauses in the otherwise regularly firing spikes of Purkinje neurons signaled the start of the eye movements. The pauses were accompanied by a sharp change in the local field potential, another electrical signal that comes from many neurons in the neighborhood. In the same cells, the rate of regularly firing spikes increased and decreased with the direction and speed of eye movements, following a simple relationship and independently of the local field potential.

Purkinje neurons therefore appear to use both the timing and the rate of their spiking activity to represent movement. This resolves conflicting reports in the literature claiming that either rates of spiking or their timing code essential information about movements: both are important. This way of representing information by combining more than one source is known as multiplexed coding.

Next, experiments recording electrical activity from many cells in the cerebellum at the same time are needed to find out how multiple Purkinje neurons can pause their spiking activity at the same time. Future experiments should also uncover how pauses in spiking and firing rates change with learning.

https://doi.org/10.7554/eLife.13810.002

Introduction

Movements are often executed with high precision in timing and trajectory control. The cerebellum is heavily involved in online motor control and should process sensorimotor information with great accuracy. In particular, PCs, which deliver the final output from the cerebellar cortex, should use an appropriate coding strategy for this task, but the nature of their coding mechanism is actively debated (De Zeeuw et al., 2011; Heck et al., 2013). In one view, transmission of timing-sensitive information is performed by precisely timed PC spikes and their synchronized firing (Ebner and Bloedel, 1981; Gauck and Jaeger, 2000; Shin and De Schutter, 2006; de Solages et al., 2008; De Zeeuw et al., 2011; Person and Raman, 2012). In the other, PCs use linear firing-rate coding with weak PC-to-PC correlations to robustly control continuous movement kinematics, where high signal-to-noise ratio is achieved by averaging the rates of many PCs (Shidara et al., 1993; Thier et al., 2000; Roitman et al., 2005; Medina and Lisberger, 2007; Catz et al., 2008; Herzfeld et al., 2015).

In this study, we re-examined this controversy using a new approach to analyze PC spike trains. We classified PC spikes into specific spike categories, and correlated spike categories with the LFP, using the LFP as a proxy signal for local network activity. In particular, we focused on the role of long, infrequent interspike intervals (ISI), called pauses, which abruptly interrupt the rapid and very regular firing of PCs (Schonewille et al., 2006; Shin and De Schutter, 2006; Shin et al., 2007; Yartsev et al., 2009). Pauses in the PC spike train are a well-known phenomenon in many contexts, such as saccades (Ohtsuka and Noda, 1995; Arnstein et al., 2015; Herzfeld et al., 2015), and classical conditioning (Rasmussen et al., 2008), etc. Spikes that initiate and terminate pauses often synchronize sharply across nearby PCs (Shin and De Schutter, 2006). This suggests that pauses can be simultaneously involved in spike coding by individual PCs and with collective encoding in a local network.

Our approach was to examine the relationships among PC spikes, cerebellar LFPs, and eye motion, with a focus on how those relationships change, depending on the spike category. Using this, we demonstrate that PC spikes simultaneously contribute to precision, both in timing and control of motion by adaptive use of synchrony/spike time and rate coding scheme.

Results

Cerebellar LFP and single PC firing correlate to saccadic eye movements

From three rhesus (Macaca mulatta) monkeys (E, H, and N), we simultaneously recorded spikes of single PCs, the slow component of the LFP below low-γ frequency (42 Hz), and eye positions during spontaneous and visually guided saccades (Figure 1A). Only recordings where both simple and complex spikes could be isolated were used. In this study, we focused exclusively on simple spikes, since complex spikes comprised a very small percentage of total spikes (1.71 ± 0.13% with a rate of 0.81 ± 0.07 Hz, mean ± SEM) and their overall effect on firing statistics was not significant (Figure 1—figure supplement 1H, see also below).

Figure 1 with 1 supplement see all
Cerebellar LFP and PC spikes correlate differently with saccadic eye movements.

(A) Left: Schematics of eye motion tasks. Right: Simultaneously recorded eye speed, PC spike train, and LFP. Both the recorded (black) and filtered LFP below the low-γ frequency (red) are shown, but only the latter was analyzed. (B) CCFLFP-EV and CCFSpike-EV computed with EV (Top) and eye speed in the direction with the angle θ (Bottom). Shaded regions represent the 99% confidence interval. Data are normalized as described in the Materials and methods and plotted as mean ± SEM. (C) θ-dependent variability of CCFLFP-EV (x-axis) versus CCFSpike-EV (y-axis). CCFSpike-EV varied significantly more (p<0.05, t-test) than CCFLFP-EV in 74% (= 25; magenta), and less in 15% (= 5; cyan) of all recordings. No difference was found in the rest (= 4; black). Error bars are omitted for clarity. The gray line represents equal variability. The red circle denotes data in A and B.

https://doi.org/10.7554/eLife.13810.003

We first estimated the sensitivity of neural signals to eye motion by computing their cross-correlation functions to eye velocity (EV), CCFLFP-EV and CCFSpike-EV for the LFP and simple spikes, respectively (Figure 1B). Two sharp differences between the LFP and spikes were noticed: First, CCFLFP-EV was significant in recordings from 49 cells (p<0.01, t-test, = 33, 15, 1 from E, H, and N, respectively), but significant CCFSpike-EV was found only in a subset of 34 cells (p<0.01, t-test, = 21, 12, 1 from E, H, and N, respectively). These 34 cells were used in the rest of the analysis. Second, when computed to account for the eye speed component for specific directions, the CCF varied less significantly with the angles of eye movements for the LFP than for spikes, in most cases (Figure 1B,C). We also computed the average LFP and firing rates for saccades with different directions and durations, and found that they shared the same properties, having similar waveforms as the CCFs (Figure 1—figure supplement 1A–F).

We identified eye saccade-related neurons based on CCFLFP-EV and CCFSpike-EV; this is essentially identical to the classical method used to localize eye motion-sensitive cells (Ohtsuka and Noda, 1992). Differences in how LFP and PC spikes relate to eye movements were similar to previously reported differences between multiple PCs versus single units, where the averaged activity of multiple PCs is more robust, but much less direction-dependent (Ohtsuka and Noda, 1995; Thier et al., 2000). This supports the view that the LFP represents the average activity of many neurons with diverse angle-dependencies in the local network (Buzsáki et al., 2012) rather than reflecting the activity of a single PC or a cluster of PCs with similar directional tuning. For this reason, the LFP and spikes apparently do not encode identical information about eye motion.

PCs fire regularly most of the time, but occasionally pause

All recorded PCs fired rapidly (55 ± 18 Hz, mean ± SD) with high regularity. To quantify this regularity, we computed the ISI asymmetry index (AI) and coefficient of variation (CV2) (Shin et al., 2007) for each data set, and compared them with those of control spike trains. In controls, spikes were randomly generated with the same instantaneous firing rates and refractory period (4 ms) as in the reference PC spike train. All of our spike trains contained a significantly higher number of regularly firing spikes (AI ≈ 0, or equivalently CV≈ 0) than the control (p<0.01, one-sided z-test; Figure 2A). ISI distributions had long tails that followed a power law, PISI(x) ~ x-α (α = 3.78 ± 0.64; tail onset = 30.4 ± 13.4 ms; p<0.05, = 32) (Figure 2B). Furthermore, the size of the ISI after each spike quickly diverged as the AI of the spike increased (Figure 2C), implying that deviation from regular firing tends to be associated with long ISIs.

Figure 2 with 1 supplement see all
Regular and pause spikes in the PC spike train.

(A) Left: The ISI asymmetry index (AI) measures local variability at each spike and is related to the local coefficient of variation (CV2). Right: Distribution of AI for PC spikes (black) and rate-matching control spike train (green, mean ± SD). Significantly more PC spikes occurred around AI ≈ 0. (B) The ISI histogram with a fitted power-law tail (red). Inset: the same histogram and tail in linear scales. (C) ISI after each spike vs. AI. The black line represents mean ± SD in each bin (center = [-0.8, -0.6, …, 0.8], width = 0.2). (D) Top: Three types of spiking pattern classified by their AI and associated ISI length. Bottom: Examples of pause and regular spikes in an actual PC spike train. Data are the same as in Figure 1A,B.

https://doi.org/10.7554/eLife.13810.005

Our observations are consistent with previous studies describing the PC spike train as typically composed of prolonged periods of fast and highly regular firing, occasionally interrupted by longer ISIs, called pauses (Schonewille et al., 2006; Shin and De Schutter, 2006; Shin et al., 2007; Yartsev et al., 2009) (Figure 2D). Some previous studies discussed extremely long (>200 ms) pauses and related them to membrane bistability of the PC (Loewenstein et al., 2005; Schonewille et al., 2006). However, the majority of longer ISIs, or pauses, were much shorter (<100 ms), even when they were associated with a moderately large AI (Figure 2C). Note that these were therefore comparable or larger in duration to pauses triggered by complex spikes (Latham and Paul, 1970) (see also Figure 1—figure supplement 1H) and also those following simple spike bursts induced by optogenetic excitation (Lee et al., 2015).

Although complex spikes triggered pauses, their contribution to pauses in our study remained limited. Complex spikes had a larger average AI than simple spikes (complex: 0.36 ± 0.12, simple: 5.9 × 10-4 ± 7.7 × 10-4), but their standard deviations were comparable (complex: 0.36 ± 0.05, simple: 0.31 ± 0.04). This implies that AI values were widely distributed in both simple and complex spikes. However, durations of complex-spike pauses did not increase as rapidly with AI as those of simple-spike pauses. In all cells, correlations between AI and log10 (ISI) were significantly smaller for complex spikes than simple spikes (complex: 0.24 ± 0.15, simple: 0.66 ± 0.03; p<2.84 × 10-12, Wilcoxon rank-sum test), which made complex-spikes pauses poorly predicted by AI (Figure 2—figure supplement 1A). Therefore, if we select ~10% of all ISIs as representative 'pauses', based on ISI size and the AI value of a preceding spike (see below), only 4.3 ± 2.5% of all pauses would be caused by complex spikes. For this reason, we did not include complex spikes and their associated pauses in our analysis beyond this point.

Pause spikes couple strongly to the LFP and specifically to the β/γ band

Our first question was whether the relationship between spikes of individual PCs and the activity of the local network vary with specific spike categories, i.e., regular-firing or pause-related. To examine this, we first selected three subsets of simple spikes from each cell, representing regular, pause-initiating, and pause-terminating spikes, based on a criterion combining AI and ISI duration (see Materials and methods) that selected ~10% of all spikes in each category (Figure 2—figure supplement 1B). Then, we computed the spike-triggered average LFP (STALFP) (Gray and Singer, 1989; Soteropoulos and Baker, 2006) for each.

We found that the STALFP of spikes that initiated or terminated pauses was sharply different from those of regular spikes: the pause-related STALFP was characterized by strong and sharp peaks around the spike time, whereas the regular spike-related STALFP showed only a weak modulation (Figure 3A left, B). For comparison, if computed with randomly selected, or all simple spikes, the STALFP showed a level of peak correlation similar to that of regular spikes (Figure 3A right, B). This suggests that pause spikes are more strongly and more precisely coupled to network activity than regular spikes, but this fact goes unnoticed if the temporal structure of the spike train is ignored when computing the STALFP (Figure 3A right), because pauses are relatively rare events. The larger amplitude of the STALFP for pause-related spikes was readily observed when we varied the criterion for pause spike selection (Figure 3—figure supplement 1).

Figure 3 with 4 supplements see all
Pause and regular spikes correlate differently with the LFP.

(A) Left: STALFP of the pause-initiating (red), -terminating (cyan), and regular spikes (black). The grey region is the 99% confidence interval. h is the peak-to-peak amplitude and shown for pause-terminating spikes. Right: STALFP of randomly selected spikes (black) and all spikes (green). Data are mean ± SEM. (B) Relative STA amplitude, h, to that of all spikes (hAll) for each spike category. (C) Phase distribution of the β/γ LFP at the pause, regular, and randomly selected spikes (thick: histogram, thin: kernel-estimated density). φ denotes location of the peak, shown for the pause-initiating spike. (D) Pair phase consistency (PPC) for each spike category. (E) Peak phases for the pause-initiating (x-axis) and pause-terminating spikes (y-axis) in all data. Grey and red lines represent φPauseT = φPauseI and φPauseT = φPauseI + 278.3º, respectively. In (C) and (E), **p<10–5 (Wilcoxon rank-sum test). Data in (A), (D), and (E) are the same as in Figure 1A,B.

https://doi.org/10.7554/eLife.13810.007

In a few exceptional PCs, the STALFP of regular spikes had a modulation amplitude comparable to that of pause spikes (>70% in amplitude, = 5; Figure 3—figure supplement 2A), whereas these cells did not show difference in correlation with eye movements (measured by max |CCFSpike-EV|) from the rest (p>0.16, Wilcoxon rank-sum test). However, in most of these cases (= 4), the STALFP of regular spikes developed on a much slower time scale, mostly below the high β frequency (15 Hz). Therefore, when the STALFP was recomputed with the β/γ band (15–42 Hz) LFP, STALFP amplitudes were mostly retained for pause spikes, but significantly diminished for regular spikes, particularly if the original amplitude was large (Figure 3—figure supplement 2B–D). This was observed even when the LFP power spectrum did not have a distinct peak in the β/γ band, implying that it is a property of pause spikes rather than a product of LFP dynamics that generates the β/γ band oscillation.

The preferential coupling of pause spikes to the higher frequency LFP band, not the lower, led us to examine whether pause spikes are phase-locked to the β/γ LFP. This was true in the entire dataset, where pause spikes strongly preferred certain phases of the β/γ LFP while regular spikes showed only a weak dependence on the phase (Figure 3C). To estimate how reliably spikes fired at certain LFP phases, we computed the pairwise phase consistency (PPC), which is an average coincidence between any two spikes in the LFP phase space (see Materials and methods for more details) and provides an unbiased measure of phase locking (Vinck et al., 2010). Again, we found a large difference between pause and regular spikes in their PPC (Figure 3D), specifically for the β/γ LFP (Figure 3—figure supplement 3). Notably, pause-initiating spikes preferentially occurred near the climbing phase, i.e., <φPauseI> = 48.7º ± 45.7º where φPauseI was the most preferred phase for each data set, and pause-terminating spikes were shifted by about 3/4 cycles on average (<φPauseT> = <φPauseI> + 278.3º ± 35.3º) (Figure 3E).

These results clearly show that pauses are not randomly occurring events. On the contrary, their initiating and terminating spikes are temporally locked to specific patterns of network activity, which generate significant and temporally precise fluctuations in the LFP.

Pause spikes and correlated LFP components encode the timing of eye motion

If pause spikes in single PCs are related to specific patterns of network activity, what information do they jointly encode about eye motion? To answer this question, we first probed how the phase of the β/γ LFP evolves during each saccade in recordings for each cell. In many of them, the β/γ LFP was significantly coherent across all saccades, with a phase locking to saccade onsets (Figure 4A,B). We quantified this by computing the average cross-saccade phase coherence during a time window around saccade onset (from −100 ms to 150 ms), which we called LFP phase reliability. Significantly high LFP phase reliability was found in 80% of the data (p<0.01, = 28, one sided t-test to time-shifted control data; <RLFP> = 0.20 ± 0.02, mean ± SEM).

Figure 4 with 1 supplement see all
Pause spikes and β/γ LFP encode motion timing.

(A) Eye speed (Top) and β/γ LFP (Bottom) aligned with saccade onset. Black lines represent an average over all saccades (grey, n = 865). (B) Phases of the β/γ LFP at saccade onset for the same data. (C) Top: Spike trains for pause-initiating, -terminating, and regular spikes aligned with onsets of randomly subselected saccades (= 289). Light colored regions represent periods with significantly reliable firing (jp(t)<0.05, see Materials and methods). Bottom: Z-score for spike occurrence, smoothed by a gaussian kernel (σ = 5 ms). (D) Spike reliability of pause and regular spikes in all data. *p = 0.0229, 0.0193 (Wilcoxon rank-sum test). (E) LFP phase reliability versus spike reliability. The two were significantly correlated (red and black line) for pause-initiating and regular spikes (p = 9.3074 × 10-6, 0.0012; Fisher’s z-test), but not for pause-terminating spikes (p = 0.0912), due to some recordings with low spike reliability but high LFP reliability. Data in (AC) are the same as in Figure 1A,B.

https://doi.org/10.7554/eLife.13810.012

This predicted that pause spikes, which are phase-locked to the β/γ LFP, should reliably code eye movement timing. The most significant pattern that we observed was that pause-initiating spikes encode saccade onsets with a significant and sharp increase in average firing (Figure 4C and Figure 4—figure supplement 1). This could be caused either by a firing rate increase of pause spikes during some saccades, or by a sharp spike-time correlation across most saccade trials, i.e. reliable spiking. To ascertain which, we estimated how many spike coincidence events occurred beyond the prediction from the firing rate, from all possible pairings of spike trains and saccades, which we called the spike reliability: Briefly, for each pair of saccade trials, we counted spike coincidences (|Δt|≤3 ms) between two spike trains within a 50 ms-long moving time window, centered at t (−100 ms ≤t≤150 ms, relative to saccade onset). Then we estimated the probability, jp(t), that two random spike trains with the same firing rates could have the same or more spike coincidences, looking for significant ones (jp(t)<0.05) (Riehle et al., 1997; Denker et al., 2011; Ito et al., 2011). The fraction of those significant coincidences from all cells, summed over all trials and time, became the spike reliability. Significantly coincident spikes were indeed found during significant peaks of firing probability (colored regions in Figure 4C); therefore, spike reliability was significantly higher for pause spikes (Figure 4D), further emphasizing their role in encoding the onset of eye motion. Finally, the LFP phase and spike reliability were much more steeply related to each other for pause-initiating spikes than for regular spikes (Figure 4E). This demonstrates that the fidelity of temporal coding by pauses in individual PCs crucially reflects the reliability of activity and coding of the local network.

PC firing rate linearly encodes eye motion, mostly by regular spikes

So far we have focused on pause spikes, rare events in the spike train that provide timing information. On the other hand, eye velocity-spike correlation (and similarly saccade-triggered average rate) showed firing rate modulation by eye movement kinematics such as direction, duration, etc. (Figure 1B–C and Figure 1—figure supplement 1A–F). This suggests that a firing rate code may also be present in PC spike trains.

To answer this question, we constructed an inverse model that predicts firing rate from eye movements in each cell, based on the linear-nonlinear (LN) model framework (Victor and Shapley, 1980). LN models are widely used in sensory system studies, but have not been applied to PCs to date. First, the eye velocity profile is compared with a preferred pattern (motion feature) estimated from the linear cross-correlation (CCFs in Figure 1B) to generate a linear prediction m of the firing rate, which goes through an additional nonlinear transformation to fit the actually observed firing rate (Figure 5A,B).

Figure 5 with 1 supplement see all
PC firing rate linearly encodes motion kinematics.

(A) Schematics of the eye motion-to-rate inverse model. (B) Example motion feature. (C) Predicted vs. measured firing rate for all (green), regular (black), and pause (red) spikes. The rates of pause and regular spikes are rescaled to match those of all spikes to compensate for subsampling. The dotted line represents equality. (D) Goodness of fit R2 for the linear prediction to actual rate. **p<10-30 (Wilcoxon rank-sum test). (ER2 for all cells. Error bars are omitted and box plots are for means. *p<10-6, **p<10-11 (Wilcoxon rank-sum test). Error bars represent SEM. Data in B–D are the same as in Figure 1A,B.

https://doi.org/10.7554/eLife.13810.014

We found that the linear rate prediction m followed the actual rate very closely (R= 0.92 ± 0.07, mean ± SD); therefore, the effect of the nonlinear transformation is small (Figure 5C–E). This made the linear rate prediction m alone a good predictor of the time-course of average firing rate modulation during saccades and it was used exclusively in the rest of the analysis. Importantly, correlation with the firing rate remained high (R= 0.81 ± 0.17) when we computed the linear prediction with only regular spikes, which comprised about 20% of all spikes. Conversely, the firing rate of pause spikes (both pause-initiating and –terminating spikes) did not modulate as linearly or steeply as for regular spikes (R= 0.35 ± 0.25). This suggests that information encoded by the whole firing rate is very different from eye movement features related to pause spikes such as onsets (Figure 4C), but this information can be captured well by a subset of the full spike train, regular spikes.

This led us to further inquire into the similarity between rate coding by regular spikes and the full spike train. For this, we imposed different thresholds on CV2 (=2|AI|) for selecting the regular spikes, computed the direction-dependent CCFSpike-EV of those selected spikes (Figure 1B), and estimated its similarity to that of the full spike train by computing their correlation coefficient ρ. We found that ρ quickly grew as we increased the CV2 threshold, whereas the fraction of regular spikes increased more slowly (Figure 5—figure supplement 1). For example, when we select ~47% of all spikes as regular spikes by imposing CV< 0.4, their CCFSpike-EV is very similar (ρ ≈ 0.93 in average) to that of the full spike train. Even at 20%, CCFSpike-EV of these regular spikes had ρ ≈ 0.85 on average, similar to the linear coding property (Figure 5C). Note that ρ for pause spikes behaved very differently; it was not significant for a reasonable fractions of pause spikes (Figure 5—figure supplement 1 inset).

The combination of Figure 5 and Figure 5—figure supplement 1 demonstrates that regular spikes dominate rate coding. Regular spike and full spike trains respond to similar motion features and also share the linear coding property. Our results resemble those of a previous report in which 'patterns' of regularly firing spikes dominate the rate responses of PCs to sensory stimuli (Shin et al., 2007). Nevertheless, pause spikes can make small contributions to rate coding. With all spikes, the LN model is empirically linear, but the rate coding of regular spikes predicted by the model is slightly less linear (Figure 5D,E). Pause spikes, which by definition represent fast rate changes, must compensate for this.

One regular spike is inexpensive from the standpoint of information content, because a small and very regular subset can already provide a good approximation of the full rate modulation (Figure 5—figure supplement 1). Furthermore, regular spikes are weakly coupled to network activity (Figure 3). This evidence strongly suggests linear rate coding as the primary role of regular spikes.

Discussion

Examples in sensory and motor systems (Riehle et al., 1997; Panzeri et al., 2010; Gire et al., 2013) and theoretical analysis (Ratté et al., 2013) have shown that neurons can use multiplexed coding strategies, where each spike in a single spike train can differentially couple to local network activity and encode different information about sensory stimuli or behavior. This study presents the first evidence for multiplexed coding in cerebellar Purkinje cells. Specifically, spikes that initiate pauses are strongly coupled to the β/γ band of the LFP and are therefore probably synchronized among nearby PCs. These spikes form a temporally reliable signal to initiate saccadic eye motion. Conversely, regular spikes in the same spike trains are desynchronized among nearby PCs and form a rate code that predicts direction selective eye kinematics. Use of a multiplexed code resolves the perceived contradiction between temporal and rate coding that has dominated recent discussions about PC spiking (De Zeeuw et al., 2011; Heck et al., 2013).

Pauses in the spike train are observed in many tonically firing neurons in various contexts. In striatal cholinergic interneurons, synchronized pauses after bursts encode a salient stimulus (Aosaki et al., 1995). Since pause-initiating and -terminating spikes can synchronize sharply (Jaeger, 2003; Shin and De Schutter, 2006), PCs can potentially operate by a similar coding mechanism. In fact, spike synchronization by PCs is a powerful mechanism to control their postsynaptic targets in the cerebellar nucleus (CN). With exceptionally fast GABAergic synapses (Person and Raman, 2012), CN neurons can reliably generate time-locked rebound spikes in response to synchronized inputs followed by simultaneous disinhibition, even at moderate levels of synchrony (≤50%) (Person and Raman, 2012) and spike time jitter (≤20 ms) (Gauck and Jaeger, 2000; Sudhakar et al., 2015). Furthermore, recent optogenetic experiments have shown that synchronous pauses induced either by direct/indirect inhibition or at the offset of direct excitation, can reliably trigger firing in CN neurons, and importantly, at movement onset (Heiney et al., 2014; Lee et al., 2015). Crucially, excitation-induced pauses were short (~35 ms), but effective, and even shorter pauses from direct inhibition caused similar effects (Lee et al., 2015).

Synchronized pause spikes (Shin and De Schutter, 2006) can not only represent timing information, but also can complement a rate code. Previous studies have analyzed PC firing collected over many trials and neurons, and found that a collective representation of time and motion emerges as a form of burst firing alone (Thier et al., 2000) or together with suppressed/paused firing of many PCs (Catz et al., 2008; Arnstein et al., 2015; Herzfeld et al., 2015). Our results suggest that pause spikes can enhance temporal fidelity of such population-level representations since their temporal consistency across different PCs (e.g. Figure 4—figure supplement 1B) can offer a reliable representation, despite large heterogeneity in rate coding schemes of different PCs. For example, Herzfeld et al. (2015) found that population PC coding of saccade direction depends critically on the timing of pause onset, which varies only up to ~10 ms. Here we showed that pause spikes of individual PCs can indeed fire with a reliability of a few milliseconds. This can be particularly important at the single trial/saccade level, but averaging over multiple trials and cells may not be a suitable approach to probe it. Instead, we evaluated the correlation between simultaneously recorded PC spikes and LFP, and also trial-to-trial correlation (reliability) of those signals, for each cell. Our results show that synchronized pause spikes constitute the most significant population signal in PCs despite their sparse appearance in individual spike trains, suggesting that they can be a specific signaling mechanism in the PC-CN part of the motor pathway.

The spike-LFP relationship indicates that pause spikes are generated by the local network. While firings by presynaptic afferents, granule cells, Golgi cells, as well as by the postsynaptic targets, are clearly related to the LFP (Soteropoulos and Baker, 2006; Dugué et al., 2009; Ros et al., 2009), PCs only occasionally or weakly modulate their simple spike firing with the LFP (Courtemanche et al., 2002; Ros et al., 2009), except for the very high frequency component (~200 Hz) (de Solages et al., 2008). Here we found that the β/γ LFP robustly and preferentially couples to pause spikes and that both can reliably encode time information in a correlated way. Considering that cerebellar LFP is coherent with neocortical LFP (Courtemanche and Lamarre, 2005; Soteropoulos and Baker, 2006; Ros et al., 2009) and also plays a critical role in maintaining LFP coherence between the sensory and motor cortex, particularly in the low γ band (Popa et al., 2013), pause spikes may also have a special relationship with the LFP in the cerebral cortex.

We did not attempt to resolve the origin of the time encoding LFP signal due to limitations of the experimental setup. However, there are multiple possible primary sources. One is the dense activation of mossy fibers and granule cells that accompanies the significant LFP in the granular layer (Morissette and Bower, 1996; Roggeri et al., 2008; Diwakar et al., 2011). Because our electrodes are probably too far from the granular layer to detect the signal directly, it is likely that that localized massive activity propagates via ascending and parallel fibers to activate many interneurons and ultimately PCs. In particular, molecular layer interneurons (MLI) could provide significant feedforward inhibition (Mittmann et al., 2005), causing PCs to pause (Mittmann and Häusser, 2007). If simultaneous activation of local MLIs (and/or their synaptic inputs to the local population of PCs) contributes to the LFP, this would explain our observed correlation of the fast LFP signal and pauses in PCs. However, the time-encoding signal components we observed seem to be highly localized in the cerebellar cortex. In LFPs recorded ~1 mm horizontally from the spike electrode, STALFP amplitude, particularly of pause spikes was greatly diminished to absent (Figure 3—figure supplement 4). This suggests that the pause-related β/γ LFP signal originates from localized sources and decays quickly with distance, spreading at most a few hundred microns. This is consistent with the fact that PCs are rarely synchronized unless they are very close to each other (<100 μm) (Ebner and Bloedel, 1981; Jaeger, 2003; Shin and De Schutter, 2006).

We also found that the effect of complex spikes was minimal since pauses triggered by complex spikes (Latham and Paul, 1970) had a distinct distribution compared to simple-spike pauses (Figure 2—figure supplement 1A). The overall impact of complex spikes was negligible, most probably because none of our tasks involved sensorimotor learning where complex spikes are crucial (Catz et al., 2005; Medina and Lisberger, 2008), as they tend to occur after saccades, triggered by significant saccade errors (Herzfeld et al., 2015).

Many studies have reported significant correlated spiking in similar settings. In the motor and visual cortex, synchronized spikes have larger STALFP and better phase locking to the motion-related LFP β oscillation (Denker et al., 2011; Ito et al., 2011). In another part of the cerebellum, Medina and Lisberger found that firing rate variability and cross-correlation of PC firing both peaked at the onset of smooth-pursuit eye motion (Medina and Lisberger, 2007). Our findings are consistent with their observations since pause spikes, which fire reliably with respect to motion onset, have higher ISI variability, and significant coupling to the LFP implies correlated firing. Medina and Lisberger also suggested that such correlated spiking is due to common input to PCs (Medina and Lisberger, 2007), which can significantly contribute to the LFP signal (Denker et al., 2011) and trigger synchronized pauses (Jaeger, 2003).

On the other hand, PCs also use linear rate coding of eye movements and here non-pause regular spikes are predominant. Linear coding of motion kinematics by the PC firing rate has been repeatedly observed (Shidara et al., 1993; Roitman et al., 2005; Medina and Lisberger, 2007; Herzfeld et al., 2015). If correlations with other PCs are weak, as is the case for regular spikes, rate coding by individual PCs can precisely control continuous movements since CN neurons receive inputs from many PCs and can average away noise in individual inputs.

Because different stages of a movement may demand that some aspects of the motion be controlled more precisely than others, it is useful for PCs to use different spike codes. Our study demonstrates that PCs can use both temporal- and rate-coding schemes to multiplex their population output with different types of information (De Schutter and Steuber, 2009; Ratté et al., 2013), so that precision in motion timing and continuous control can be managed adaptably. We conclude that multiplexed coding is used for sensorimotor coordination in the cerebellar cortex.

Materials and methods

Electrophysiological recording and behavioral procedure

All animal experiments were approved by the local animal care committee (Protocol number: Regierungpräsidium Tübingen N1/08 and N6/13), conducted in accordance with German law and the National Institutes of Health's Guide for the Care and Use of Laboratory Animals and carefully monitored by the veterinary administration (Regierungspräsidium and Landratsamt Tübingen). Three adult male rhesus (Macaca mulatta) monkeys (E, H, and N; 10, 11, and 15 years old, respectively) were subjects in this study. They were implanted with a magnetic scleral search coil to record the eye position (Judge et al., 1980), a titanium head post to painlessly immobilize the head during experiments, and a circular titanium recording chamber located over the midline of the cerebellum to allow electrophysiological recordings (Thier and Erickson, 1992). Position and orientation of the implants were carefully planned using pre-surgical MRI and confirmed using postsurgical MRI that helped to direct electrodes to the oculomotor vermis. All surgical procedures were conducted using aseptic techniques under the full anesthesia consisting of isofluorane supplemented with remifentanil (1–2 μg/kg/min). All relevant physiological parameters such as body temperature, heart rate, blood pressure, pO2, and pCO2 were monitored. Postoperatively, buprenorphine was given until no sign of pain was evident. Animals were allowed to fully recover before starting the experiments.

Animals made saccades either without (= 16) or with visual cues (= 18), but we analyzed all data combined. In the spontaneous saccade paradigm, animals made eye movements freely in the absence of any given visual stimulus. In the visually guided task, animals first focused on a fixation spot at the center of the monitor for periods of time that varied randomly between 1000 and 1500 ms. As soon as the fixation spot disappeared, a target for the primary saccade appeared randomly in one of eight possible locations in the periphery with the angle θ = 0º, 45º,... , 315º at a constant distance from the center, varying between 2.5º and 20º in separate blocks.

Processing and selection of recording data

Extracellular potentials were initially high- and low-pass filtered online and recorded separately. The band pass-filtered (300 Hz–3 kHz) channel was used to identify single-unit activity. Single-PC units were distinguished by the presence of simple and complex spikes via online sorting, but all spikes were resorted offline and semi-automatically via a neural network trained on manually selected spike waveform prototypes as in (Yartsev et al., 2009).

The LFP from the low-pass filtered (<150 Hz) channel went through a series of additional filtering steps to remove influences from spike waveforms. First, an online notch filter at 50 Hz was applied to reduce line noise. An additional offline low-pass filter at 42 Hz was applied. Then, the LFP was resampled at 90 Hz and oversampled back to 1 kHz to minimize the effect of spike waveforms.

Eye velocity was computed from recorded eye position using a Savitzky-Golay filter of the fifth order with a 25 ms time window. Saccade onsets were detected from eye speed using a custom adaptive detection algorithm described in Appendix 1.

We first selected data based on recording quality both in neural and eye motion recordings and then based on statistical significance of CCFEV-LFP and CCFEV-Spike (see below).

Calculation of cross-correlation function and spike triggered averages

When the signal for the quantity A and B are x(t) and y(t), respectively, the cross-correlation function CCFAB is computed by

CCFAB(t)=1ZABs=0Lx(s+t)y(s)1Mshiftm=1Mshift(1ZABs=0Lx(s+t)ymT(s)),

where L is the signal length. ymT(t) is y(t) shifted by m·T, ymT(t) = y(t + m·T). The second term is a shift-correction that estimates the baseline and average of possible uncontrolled correlation. We used T = 1 s and Mshift ~ 200 depending on L and whether the variance of the shift corrections stabilized. Assuming this variance corresponds to the standard error of the CCF both for the original and shifted data, we computed the t-score for the one-sided test for whether the CCF becomes significant (p<0.01), particularly from = −100 ms to = 100 ms.

For the normalization ZAB, we used two different schemes depending on whether A and B were both continuous (eye velocity and LFP) or one of them was a spike train. In the former, the 'CCF-like' convention, ZAB = (Var[x]·Var[y])1/2 (L−|t|), was used. In the latter, we used the 'STA-like' normalization ZAB = Var[x]1/2·Nspike where Nspike was the number of spikes. Therefore, STALFP(t) = CCFLFP-Spike(t) where y(s) was a spike train with 1 ms wide time bins, up to a constant factor.

Saccade-angle dependence of the LFP and PC spikes

We estimated dependence of the LFP and spikes on saccade angle θ by computing their CCF(θ) with the component of the eye velocity vector v, vθ = (v·eθ)+ where eθ = [cos θ, sin θ] (θ = 0º, 45º, …, 315°) and ()+ represents rectification. Then, we computed the matrix CCF = [CCF(0º); CCF(45º); …] and the noise-to-signal ratio, NSR = Tr Cov[CCF]/||Mean[CCF]||2, which was used as an estimate of θ-dependence in CCF(θ). About 200 control CCF(θ) were made from time-shifted data (see above) and their variance was used in the t-test for differences in NSR between the LFP and spikes.

Estimation of spike train statistics and selection of pause/regular spikes

The ISI-asymmetry index (AI) was computed as in Figure 2A. For each data set, we generated 200 rate-matching artificial spike trains in a similar way to Shin et al. (2007). We first computed ISIs, {ISIk} (k = 1,…Nspike-1), from experimental data. At each k, we computed the local firing rate from the nearest five ISIs as rk = 5/(ISIk-2 + ISIk-1+ ... ISIk+2). The k-th artificial ISI, Tk, was drawn from the gamma distribution P(Tk) ~ rk2 Tk exp(-rk Tk) with a refractory period 4 ms imposed. From these, we computed the mean histogram and its variance. The tail shape of the ISI distribution was tested using the powerlaw Python package (http://pypi.python.org/pypi/powerlaw), which provided a fitting algorithm to the power-law tail and statistical tests to compare the result with the alternative hypothesis of an exponential tail.

For pause-initiating spikes, we first selected 15% of spikes having the largest AI values. Then, we removed 25% of spikes with the shortest pause ISI. Pause-terminating spikes were selected similarly, but with the smallest AI. Minimal pause duration varied with the average firing rate of the cell, but was in general ~20% larger than the ISI corresponding to the mean firing rate. Regular spikes were selected based only on their CV2, and their number was matched to those in comparison groups.

LFP phases in the β/γ band and their cross-saccade reliability

The β/γ LFP was obtained by band-pass filtering the LFP between 15–42 Hz. Phases were extracted by the Hilbert transformation (MATLAB function hilbert). From the phase and spike times, we computed pairwise phase consistency (PPC) in the following way (Vinck et al., 2010). When the phase of the β/γ LFP at spike times is {φn} (n = 1,…, Nspike), PPC is given by

PPC=2Nspike(Nspike1)m=1Nspike1n=m+1Nspikeexp(i(ϕmϕn))

LFP phase reliability RLFP is measured by phase coherence of the β/γ LFP across saccades. When φi(t) is the LFP phase at t, time relative to saccade onset (= 0 at the onset), for the i-th of N saccades, RLFP is given by

RLFP=1TeTbTbTeZ(t)dt,Z(t)=|1Ni=1Kexp(iϕi(t))|,

where we used T= −100 ms and Te = 150 ms. We also computed RLFP of time-shifted data in the same way as CCF and their mean and variance were used for the one-sided t-test.

Cross-saccade spike reliability

Spike reliability Rspike was evaluated using the fraction of significant cross-saccade synchronization events, following Denker et al. (2011). We first collected spike trains during the same time window as for RLFP. Then, within a 50 ms-wide moving window centered at t in each saccade period (t = 0 at the onset), we counted the number of spike coincidences up to ± 3 ms time difference, nemp(t). In the same moving window, rate prediction of the coincidence probability and expected number of coincidences nexp(t) were computed from firing rates based on summing all possible spike train/saccade pairings. With a null hypothesis of Poisson statistics, the probability of nemp(t) is

jp(t)=P(nemp(t)|nexp(t))=r=0nemp(t)nemp(t)rr!exp(nexp(t)).

The criterion for significant synchronization was jp(t)<0.05 and if this was satisfied, all coincidence events in the window were regarded as spike synchronization from 'unit events' (Riehle et al., 1997; Denker et al., 2011; Ito et al., 2011). Then, Rspike is a fraction of synchronization events versus all coincidences,

Rspike=jp(t)<0.05nemp(t)tnemp(t).

Eye motion-to-rate inverse model

Our inverse model consists of two parts: a motion feature f acts as a receptive field that linearly transforms eye velocity history to the linear rate prediction, m. Then, a nonlinear function P(spike|m) gives the spiking probability. f was estimated from the spike-triggered average of the rectified eye velocity in four directions (θ = 0º, 90º, etc.) from −300 ms to 300 ms around the spike time. We computed the rate prediction, m, by linear filtering the rectified eye velocity by f, and estimated P(spike|m) by comparing m with actual firing rate. See Appendix 2 for more mathematical details.

Statistical analysis

When z- and t-tests were used, we checked normality of sample distribution using D'Agostino's K2 test (significance level = 0.05). In some cases that failed the normality test, we estimated a p-value by computing an empirical upper bound of the type I error rate by using control data sets. We increased 400~2000 control data sets, depending on computing time, evaluated the quantity of interest, and made one-sided comparisons with an estimate from original data. The p-value was estimated to be an error rate of the comparisons.

For each statistical test, we computed statistical power by estimating an upper bound of the type II error rate from the resampled data sets: we generated 400~2000 randomly resampled data sets with replacement, performed the same statistical test on them, and counted how many passed the test at a given significance level, which gave our estimate of the power. We regarded the original test result as significant only when the power is sufficiently high (>0.8),

All analyses were done with MATLAB 2012a (Mathworks, VA) and custom scripts in Python 2.7, which will be available on our homepage (http://groups.oist.jp/cnu).

Appendix 1: Adaptive detection algorithm for saccade onsets

We first imposed a threshold vth = 10μ+2.576 σ on the eye speed v, where μ and σ2 are the mean and variance of log10v. This is based on our observation that the statistics of log v is approximately normal with jumps; therefore, log10vth corresponds to the threshold for outliers of p<0.01. Then, we detected the threshold breaking points, upward and downward. If the interval between the neighboring downward and upward breaking point was smaller than 75 ms, we removed those points altogether, which made all the inter-saccade intervals greater than 75 ms.

From these selected saccades, we detected candidate onsets. The eye speed, v, was high-pass filtered above 15 Hz and we looked for a negative peak in the filtered speed, u, within a 15 ms time window before the upward threshold breaking. This point, tonset marked the transition point to rapid eye motion and became the onset.

A small fraction of detected saccades had drifting eye motion before tonset. We found the maximal eye speed between 12 ms and 2 ms before tonset, which we call vmax, and excluded eye motions where vmax exceeded an empirical threshold given by vmax,th = Median[vmax]+2Δvmax where Δvmax = |Median[vmax]-Min[vmax]|. This criterion worked well empirically and removed 3.87 ± 3.80% of all detected saccades, which were ill-formed with slow drifting.

Appendix 2: Construction of the inverse model and comparison with linear coding

Inverse model

Our inverse model is based on the linear-nonlinear model scheme (Victor and Shapley, 1980) composed of a stimulus feature f, which acts as a linear filter on the incoming stimulus, v, to produce the 'motion variable', m(t), and a nonlinear function P(spike|m) that gives the probability to spike given m(t), at each time bin (width = 1 ms) (Figure 5C).

Given eye velocity u(t) = [ux(t), uy(t)], we computed the rectified eye velocity in four directions, v(t) = [v(t); v90º(t); v180º(t); v270º(t)], where vθ(t) = (u∙eθ)+, eθ = [cos θ, sin θ], and ()+ represents rectification. Then, the motion variable m(t) is

m(t)=dτv(tτ)f(τ)TTdτv(tτ)f(τ),

where T is a time window size and we used T = 300 ms.

Estimation of the motion feature

First, we estimated the motion feature f by STA of the rectified eye velocity, v, i.e. STAv, equivalent to CCGv-Spike. This is similar to the linear regression approach for smooth eye movements (Shidara et al., 1993; Roitman et al., 2005; Medina and Lisberger, 2007; Herzfeld et al., 2015), whereas here our regression variables are the history of eye velocity for a extended period of time, not a small number of the motion variables, such as eye position, speed, acceleration, etc. In our case, eye position and speed or acceleration components correspond to the motion feature, f, being a broad integration kernel, a delta function-like single peak function or a biphasic differentiation kernel, respectively.

In practice, the spike train was converted to the firing rate series r(t) by convolution with a Gaussian kernel with σ = 10 ms, and the STA was computed with the weight of the smoothed firing rate. Then, f was estimated by the standard least square,

f(τ)=dτdt Wα(τ,τ)v(tτ)r(t),

where Wα is the Ridge-regularized whitening matrix that compensates the autocorrelation of v,

Wα(τ,τ)=[C(τ,τ)+α1δ(ττ)]1,
C(τ,τ)=dt vT(tτ)v(tτ).

For α, we used the smallest eigenvalue of C among those that together captured 90% of the total variance, i.e., α=λn where i=1nλi/Tr C≈ 0.9 (λi>λj for i<j). This choice gave us empirically good regularization, meaning that f was decorrelated, but still relatively free of artifacts (Figure 5B).

Estimation of the nonlinearity

After obtaining the feature, f, we computed the linear rate prediction, m(t), by filtering the rectified velocity v with f, and compared it with the rate r(t) to get P(spike|m). First, we computed P(m|spike) and P(m) via kernel density estimation, where the former was weighted by the firing rate. Then, by Bayes' theorem,

P(spike | m)=P(m | spike)P(spike)P(m).

We repeated this procedure 500 times with randomly chosen bootstrap samples of r(t) and m(t) to get the bootstrap mean and SD of P(spike|m) (Figure 5C).

In practice, finite size sampling noise in P(spike|m) increases with P(m) and thus P(m|spike) becomes small. To prevent this, we only used a range of the linear prediction variable, [m1, m2], where P(m|spike)>pth for a threshold pth. The threshold was lowered until the range contains as much as 99% of all samples of m at spike times, i.e. m1m2dm P(m | spike)0.99.

Testing for the linear coding model

Within the range [m1, m2], we carried out a linear regression, P(spike|m) ~ αm + β, for each of the bootstrap samples (see above), and computed the mean and SD of α and β, as well as the goodness of fit, which was the coefficient of determination, R2 (Figure 5C,D).

So far the linear prediction, m, in fact described the prediction of the rate fluctuation around the mean firing rate. For better illustration in Figure 5C, we rescaled and shifted m as αm + βm so that m represents the prediction of the actual firing rate.

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Decision letter

  1. Fred Rieke
    Reviewing Editor; Howard Hughes Medical Institute, University of Washington, United States

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

Thank you for submitting your work entitled "Multiplexed coding by cerebellar Purkinje neurons" for consideration by eLife. Your article has been favorably evaluated by Timothy Behrens as the Senior editor and three reviewers, one of whom, Fred Rieke, is a member of our Board of Reviewing Editors.

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

Consensus review (discussed by all reviewers):

This is an interesting paper that suggests that cerebellar Purkinje cells exhibit multiplexed coding – in which spikes at the onset or offset of pauses in spike activity signify the onset of an eye movement, while spikes part of more regular firing patterns represent eye movement properties. The reviewers felt the paper had the potential to provide key insights into Purkinje cell coding and to resolve some issues in the literature. Several issues, however, limited enthusiasm and need to be dealt with before considering the paper further. These are listed below in rough order of importance.

1) Importance of complex spikes. Complex spikes are described in the Discussion as having effectively no impact on the conclusions of the paper. However, it is not clear to what extent the results presented reflect complex-spike-triggered pauses in Purkinje cell firing (see Reviewer #2 comments). This issue needs to be clarified, presumably by additional analyses.

2) Event selection. All of the reviewers had concerns about how spikes were selected for analysis. The core issue is whether the selection process used in the paper biased the results by focusing on a small subset of spikes and omitting others. Controls to test for such biases and to assess the generality of the reported result are needed. These include a more straightforward analysis to identify pauses (see Reviewer #3 comments) and analysis that are more inclusive of all the spikes (see Reviewer #1 comments).

3) LFP phase reliability and Purkinje cell synchrony. How confident can we be that the reliability of the LFP phase is due to synchrony? The reviewers did not feel this point necessarily needed to be resolved by data from cell populations, but instead that any caveats of the interpretation needed to be discussed carefully.

4) Writing. The results could be presented in a more accessible manner, which will be particularly important give eLife's broad readership. See reviewer comments for specific suggestions.

These, and other, issues are detailed below in the comments from the individual reviewers.

Reviewer #1:

I am not an expert in Purkinje cell coding, so will leave comments about significance of the findings and relation with other work on the cerebellum to the more expert reviewers. The comments below deal specifically with more general coding issues and overall presentation of the work. My main concerns had to do with the selection of data to analyze, and how that selection influences the results and interpretation of the findings as well as some writing issues.

Data selection.

I was concerned about several issues about the data included or excluded from analysis. First, in a subset of recordings (subsection “Cerebellar LFP and single PC firing correlate to saccadic eye movements”, second paragraph) spike times and eye velocity exhibited significant correlations. The other recordings were apparently omitted from subsequent analysis. Is that because these are likely cells that do not participate in the control of eye movements? It would be helpful to indicate why that selection of data is justified.

Second, related to above, some selection of recordings was apparently made based on LFP coherence (subsection “Pause spikes and their correlated LFP component encode the timing of eye motion”, second paragraph) – but the details are also unclear.

Third, the identification of pause spikes and regularly firing spikes omits the majority of the recorded spikes. Given the large differences in properties of the pause and regular spikes, the question of what the other spikes are doing comes up immediately. I think this is a key issue with respect to the multiplexing concept – is there a continuum between the extremes represented by the pause and regular spikes, or is there a more discrete transition? I think of multiplexing as being about a set of discrete signals rather than a continuum. It is important to know how much the results extend to encompass all of the Purkinje cell spikes. This issue comes up in particular with regard to Figure 5.

Writing.

I think the writing can be improved in several places. A partial list follows:

Abstract, second sentence could be split into two.

Abstract, last sentence unclear.

In the third paragraph of the subsection “Pause spikes couple to the LFP strongly and specifically to the β/γ band”, last sentence "This effect […]" is unclear.

In the last paragraph of the subsection “Pause spikes couple to the LFP strongly and specifically to the β/γ band”, define pairwise phase consistency in a sentence.

In the last paragraph of the subsection “Pause spikes and their correlated LFP component encode the timing of eye motion”, explain estimate of extra coincident events in a bit more detail.

In the last sentence of the subsection “Pause spikes and their correlated LFP component encode the timing of eye motion” – I'm not sure why you say that the fidelity depends on the local network – perhaps "reflects" is a better word? What if a set of nearby cells received highly synchronized inhibitory input (not necessarily local) and hence generated high fidelity, synchronized pauses?

In the third paragraph of the subsection “PC firing rate linearly encodes eye motion, mostly by regular spikes”, you describe the pause spikes as exhibiting a high degree of nonlinearity, but it seems to me like that the firing rate is just not very dependent on eye movements. In other words, how do you separate nonlinearity from lack of correlation?

The third paragraph of the Discussion seems a bit repetitive.

In the sixth paragraph of the Discussion, "Exclusion of the complex spikes causes minuscule.…" – can you be more specific about what minuscule means?

Reviewer #2:

This manuscript tackles the very general question of how neurons encode information in their spike trains, and, in particular, the contribution of coding by the precise time of spikes within a train vs. a rate code. The experimental systems used by the authors (cerebellum and saccadic eye movements) offer some powerful advantages for analyzing this issue. The manuscript builds on the De Schutter group's previous work suggesting that brief, synchronized pauses in Purkinje cell firing may play a key role in cerebellar function. The current manuscript expands significantly on what had been done previously by 1) building a tighter link to behavior by examining pauses in the context of saccadic eye movement behavior and 2) examining the relationship between the LFP and the spikes bounding the pause.

The main conclusion is that the pause-related spikes are synchronized and encode movement onset, whereas the other, "regular" spikes encode movement kinematics.

I think this paper makes a significant contribution to the field. The idea that different spikes within a train may encode different information and be read out differently (through synchronized action with other cells vs. rate averaging) should be of broad interest to the neuroscience community.

There are three main areas where I have questions or concerns.

First, the authors claim in the Discussion "Exclusion of the complex spikes caused minuscule changes in our results." This is an important issue that should be more thoroughly documented to rule out that the pause spikes are not reflecting the effect of complex spikes. Pause beginning spikes are defined so that they are 10% of all spikes. Complex spikes are nearly 2% of all spikes, so could potentially account for ~20% of the pause beginning spikes-if pause beginning spikes associated with a complex spike are removed, do the results still hold? If so, that would strengthen the authors' claim that the effects they report are not related to the complex spikes. But the opposite result would also be interesting.

Second, it would be nice to see a more systematic analysis of different frequency bands in the LFP to determine whether it is really just the 15-42 Hz band that couple with the pause spikes.

Based on Figure 5C, the authors conclude that the regular spikes more linearly encode eye velocity than the pause spikes. Although this appears to be true, it also appears that there is a nonlinearity in the encoding of eye velocity by the regular spikes, which is compensated by the pause spikes in a way that makes the population as a whole more linear re eye velocity. Is this a reasonable interpretation? If so, it seems worth mentioning.

Reviewer #3:

The manuscript by Hong et al. describes analyses of Purkinje neuron spike trains that shed light on the potential population encoding strategies of this cell population with respect to movement kinematics. They analyze LFPs and simple spikes during saccadic eye movements and find that LFP measurements are more tightly correlated with eye movement onset than single-spike trains, and that long interspike interval – "pauses" – phase-locked with these predictive LFPs. The conclusion from these pause-related data is that pauses encode saccade onsets. On the other hand, overall firing rate is highly correlated with eye velocity, with the "regular" spikes within this population. Pairing these observations, the authors conclude that multiplexed coding occurs with Purkinje firing.

I like the direction taken here and find most of the analyses important. There are some important missing pieces of information, however, that make evaluating the findings challenging and therefore a strong recommendation for accepting or rejecting the manuscript is premature. Of paramount importance is the selection of spikes beginning long pauses: "we selected 15% of largest AI values. […] then removed 25% of the spikes with the shortest pause ISI." Since this process operates on ISI ratios, it is unclear what the ISI durations are that are being analyzed as pauses. Moreover, because this analysis relies on ratios and not overall ISI duration, (which would seem a more natural criterion for long ISIs), it is selecting for essentially bursty sequences of short-then-longish spikes. Interpreting the data through this light seems different than interpreting it through the lens of 'pauses' or longest ISIs. While I acknowledge that there may be no perfect solution to identifying pauses, I am not provided enough information to evaluate their claims because I don't know if the pauses they have chosen are unique in any way, or are alternatively unique in ways they do not highlight. In addition to the distribution of 'pause' ISIs vs. all ISIs, a plot of ISIn vs. ISIn+1 would provide non-ratioed data that may help reveal unique characteristics of the 'pause' population.

An important assumption to the interpretation of the data advanced by the study is that the LFP correlation with pause onset spikes reflects synchronous firing. Since LFPs reflect synaptic and spiking currents, it may be that correlation detected is simply a readout of the fact that pushing the ISI off of the basal firing rates reflects synaptic input, which is also reflected in the LFP. I am not confident that any data analysis short of multi single-unit array recordings could resolve whether single spikes are temporally aligned at the onset of a pause to the degree necessary for synchrony coding in the nuclei, but I could be persuaded by experts of LFP interpretation.

Overall I think this manuscript could really help resolve an ongoing debate and find many of their observations tantalizing. The information and caveats I raise above prevent me from providing overwhelming support.

https://doi.org/10.7554/eLife.13810.021

Author response

This is an interesting paper that suggests that cerebellar Purkinje cells exhibit multiplexed coding – in which spikes at the onset or offset of pauses in spike activity signify the onset of an eye movement, while spikes part of more regular firing patterns represent eye movement properties. The reviewers felt the paper had the potential to provide key insights into Purkinje cell coding and to resolve some issues in the literature. Several issues, however, limited enthusiasm and need to be dealt with before considering the paper further. These are listed below in rough order of importance.

1) Importance of complex spikes. Complex spikes are described in the Discussion as having effectively no impact on the conclusions of the paper. However, it is not clear to what extent the results presented reflect complex-spike-triggered pauses in Purkinje cell firing (see Reviewer #2 comments). This issue needs to be clarified, presumably by additional analyses.

In the revised manuscript, we have included expanded statistics and discussion about the impact of complex spikes on our results (see also our response to Reviewer #2). We found that the effect of complex spikes was almost negligible, mainly because pauses triggered by complex spikes have different characteristics from simple-spike pauses that we selected.

This is demonstrated in Author response image 1 based on the cell used in Figure 2C. In A(included as Figure 2—figure supplement 1A in the revision), we plot the asymmetry index (AI) versus post-spike ISI where “pauses” selected by our criterion are in light blue, complex spike pauses in orange, and the rest in purple. First, the AI distribution of complex spikes was slightly shifted to the right but widely spread. In all cells, complex spikes had a larger average AI (complex: 0.36 ± 0.12, simple: 5.9 × 10-4 ± 7.7 × 10-4, mean ± SD) whereas their standard deviations were comparable (complex: 0.36 ± 0.05, simple: 0.31 ± 0.04). Therefore, many complex spikes had smaller AI than the thresholds. Second, durations of complex-spike pauses did not increase as rapidly as those of simple spike pauses with the asymmetry index. In all the cells, the correlation between AI and log10(ISI) was significantly larger for simple spikes than complex spikes (complex: 0.24 ± 0.15, simple: 0.66 ± 0.03, p = 2.84 × 10-12, Wilcoxon rank-sum test), which made the complex-spikes pauses poorly predicted by the asymmetry index. This led to only a small overlap between the orange and light blue dots. In all the cells, the overlap, or the fraction of the complex spike-triggered pauses in selected pauses, was only 4.3 ± 2.5% (B).

Even in the few cases where complex spikes contributed more than 10% of selected pauses, removing complex spikes improved our signal-to-noise ratio. This is because the LFP triggered by complex spikes have a large positive peak while other pause-initiating simple spikes tend to be associated with a sharp negative peak, as shown in the Author response image 2 (PauseI, PauseT, and Regular stand for pause-initiating, -terminating, and regular spikes, respectively).

In the revised version, we write in Results “PCs fire regularly most of the time, but occasionally pause”:

“Although complex spikes triggered pauses, their contribution to pauses in our study remained limited. […] For this reason, we did not include complex spikes and their associated pauses in our analysis beyond this point.”

Also in Discussion:

“We also found that the effect of complex spikes was minimal since pauses triggered by complex spikes (Latham and Paul 1970) had a distinct distribution compared to simple-spike pauses (Figure 2—figure supplement 1A). The overall impact of complex spikes was negligible, most probably because none of our tasks involved sensorimotor learning where complex spikes are crucial (Catz et al. 2005; Medina and Lisberger 2008), as they tend to occur after saccades, triggered by significant saccade errors (Herzfeld et al. 2015).”

2) Event selection. All of the reviewers had concerns about how spikes were selected for analysis. The core issue is whether the selection process used in the paper biased the results by focusing on a small subset of spikes and omitting others. Controls to test for such biases and to assess the generality of the reported result are needed. These include a more straightforward analysis to identify pauses (see Reviewer #3 comments) and analysis that are more inclusive of all the spikes (see Reviewer #1 comments).

We checked whether including more spikes would change our results. In the selection criterion for pause spikes described in the original submission, we chose 15% of the spikes with larger CV2 values and removed 25% of those that were associated with shorter pauses. Previously we used a simpler criterion, the CV2 criterion, which gave very similar results as in Author response image 3, which shows the STALFPs for the same cell as in Figure 3A. Because we received feedback that this resulted in the inclusion of rather short pauses, we added the short pause removal step to the selection criterion.

As an additional control, we varied the fraction of the initial choice from 10% to 50% by steps of 10%, and also applied the 25% removal of short pauses. Therefore, the fraction of pause spikes varied from 7.5% to 37.5% in increments of 7.5%. Figure 3—figure supplement 1A shows how the STALFP in Figure 3A varied with different number of spikes chosen. In pause spikes, the fast fluctuating initial part of the STALFP is quite invariant in shape while the amplitude slightly decreases as we include more spikes. In the regular spike case, there was almost no difference.

For all data, we computed STAs specifically with the β-γ LFP (Figure 3—figure supplement 1) and their amplitude relative to the STA of all spikes (as in Figure 3B). Figure 3—figure supplement 1B shows how they change when more spikes are included. Amplitudes for the pause spike case again tended to decrease with more spikes, but they were still much larger than those for regular spikes. Therefore, conservatively speaking, if we choose about 25% of all spikes as pause-initiating or -terminating spikes, based on our criterion, their behavior will be qualitatively similar to the more extreme selections of ~10% in the paper. However, the distinction shows a gradient rather than a clear cut.

A similar analysis was already included in the original submission for linear encoding of motion kinematics by regular spikes (Figure 5—figure supplement 1).

We would like to stress that the lack of a clear separation between pause and regular spikes in our data – which is compatible with the multiplexing hypothesis – was one of the motivations to compare the three extreme cases in our analysis. This also addresses Reviewer #3’s comments about the pause criterion: we have tried multiple criteria for pauses, and as long as we can obtain a sufficient sample size in each group, all of them resulted in qualitatively more or less the same results. Therefore, we decided to settle on one of the simplest ones.

Following the request of Reviewer #3, we made a pre-spike ISI versus post-spike ISI plot (same cell as Figure 3) (A) (included as Figure 2—figure supplement 1B). Here, the red, cyan, and black dots represent, pause-initiating, -terminating, and regular spikes, based on our criterion, while the gray dots are the rest of the spikes. Contours represent log10(density) and become quickly triangular as we move to the tail part of the ISI distribution (pauses), which is captured by the selected pause spikes. We previously wrote “The minimal pause duration varied with the average firing rate of the cell, but was in general ~20% larger than the ISI corresponding to the mean firing rate.” We see this more explicitly in the ISI histograms, normalized by their peaks (B). Post-spike ISIs of pause-initiating spikes (red solid line) are significantly larger than those corresponding to the mean firing rate (18.4 ms, blue dot and vertical line). Pre-spike ISIs (red dotted line) are the shortest of all, but it is still within the overall spike distribution that peaks around 10-15 ms.

3) LFP phase reliability and Purkinje cell synchrony. How confident can we be that the reliability of the LFP phase is due to synchrony? The reviewers did not feel this point necessarily needed to be resolved by data from cell populations, but instead that any caveats of the interpretation needed to be discussed carefully.

Unfortunately, we don’t have any data to resolve how much of the LFP signal originates from Purkinje cell synchrony and we do not wish to suggest that Purkinje cell synchrony is a direct cause of the LFP signal. The contribution of other cells, providing inputs to the Purkinje neurons, could also be substantial. Therefore, we instead argue that Purkinje cell pausing reflects this temporary, sharp, circuit-wide activity and that accordingly, synchrony of pause spikes may be a part of it. Previous studies observed similar LFP phenomena in the granular layer (Morisette and Bower, Exp Brain Res, 1996; Roggeri et al., J Neurosci 2008), which seems to arise from dense synchronous activation of granule cells (Diwakar et al., PLOS One 2011). We do not have any means to probe whether our LFP signal was conducted from the granular layer, but even if not, we think it is likely that such a synchronous activation of mossy fibers and granule cells could spread to many cells, including molecular layer interneurons and ultimately Purkinje cells. Strong activation of interneurons will provide feedforward inhibition to Purkinje cells (Mittmann et al., J Physiol, 2004). This inhibition can cause simple-spike pausing (Mittmann and Häusser, J Neurosci, 2007) while significantly contributing to the LFP signal.

In the revised manuscript, we have now modified the Discussion to state:

“We did not attempt to resolve the origin of the time encoding LFP signal due to limitations of the experimental setup. […] If simultaneous activation of local MLIs (and/or their synaptic inputs to the local population of PCs) contributes to the LFP, this would explain our observed correlation of the fast LFP signal and pauses in PCs.”

4) Writing. The results could be presented in a more accessible manner, which will be particularly important give eLife's broad readership. See reviewer comments for specific suggestions.

We made all the changes that reviewers suggested. Also, to improve readability of our manuscript extensively, OIST’s technical editor has twice reviewed the manuscript. We have substituted the phrases “pause-initiating” and “pause-terminating” for “pause beginning” and “pause ending.” Because the editor streamlined and simplified the language, we believe that our paper is now as accessible as possible, given the subject’s technical complexity.

These, and other, issues are detailed below in the comments from the individual reviewers.

Reviewer #1:

I am not an expert in Purkinje cell coding, so will leave comments about significance of the findings and relation with other work on the cerebellum to the more expert reviewers. The comments below deal specifically with more general coding issues and overall presentation of the work. My main concerns had to do with the selection of data to analyze, and how that selection influences the results and interpretation of the findings as well as some writing issues.

Data selection.

I was concerned about several issues about the data included or excluded from analysis. First, in a subset of recordings (subsection “Cerebellar LFP and single PC firing correlate to saccadic eye movements”, second paragraph) spike times and eye velocity exhibited significant correlations. The other recordings were apparently omitted from subsequent analysis. Is that because these are likely cells that do not participate in the control of eye movements? It would be helpful to indicate why that selection of data is justified.

The reviewer is right about our assumption that cells with non-significant responses do not participate in encoding eye motion. The eye saccade-related area in the cerebellar vermisVIc (oculomotor vermis, OMV) is limited to a tiny subregion of lobuli VIc and VIIA, the OMV proper (Prsa and Thier, Eur J Neurosci, 2011), and the classical studies on which our study builds used activity-based techniques to identify eye motion-related responses, such as 1) identifying saccade-related background activity, 2) saccade-related Purkinje cell discharge, and 3) saccade-triggering microstimulation, to locate this subregion (Ohtsuka and Noda, Neurosci Res, 1992). Our criteria based on significant correlations of eye speed to LFP and Purkinje cell firing are equivalent to 1 and 2.

We explain this in the updated manuscript:

“We identified eye saccade-related neurons based on CCFLFP-EV and CCFSpike-EV, because this is essentially identical to the classical method used to localize eye motion-sensitive cells (Ohtsuka and Noda 1992). Differences in how the LFP and PC spikes relate…”

Second, related to above, some selection of recordings was apparently made based on LFP coherence (subsection “Pause spikes and their correlated LFP component encode the timing of eye motion”, second paragraph) – but the details are also unclear.

We regret that this part was not clear. We did not sub-select data sets based on the LFP coherence, but showed results for recordings from all 34 cells. Therefore, for example, there is a wide range of variation in LFP phase reliability (=LFP coherence across trials), while a majority of data shows statistical significance compared to the controls (Figure 4E).

Third, the identification of pause spikes and regularly firing spikes omits the majority of the recorded spikes. Given the large differences in properties of the pause and regular spikes, the question of what the other spikes are doing comes up immediately. I think this is a key issue with respect to the multiplexing concept – is there a continuum between the extremes represented by the pause and regular spikes, or is there a more discrete transition? I think of multiplexing as being about a set of discrete signals rather than a continuum. It is important to know how much the results extend to encompass all of the Purkinje cell spikes. This issue comes up in particular with regard to Figure 5.

Our original intent in selecting small subsets of spikes was that we wanted to probe differences between extreme cases. We performed extra analyses by including more spikes in the selection, which is described in our response to consensus review 2. To summarize our conclusion, our observations are quite robust to variation. The transition seems quite continuous, just like many other aspects of our data. For example, there is no discrete transition between the regular ISI and longer pauses, but they form a unimodal distribution with a long tail (Figure 2C in the manuscript). The reliability of pause spikes in encoding saccade onset is not distinguishably higher than that of regular spikes in some PCs, but it varies with LFP reliability (Figure 4E). We believe that for efficient multiplexing it may be beneficial if a population of PCs differ in the degree to which each behavior is expressed. This should be more advantageous in encoding eye motion since there is a continuous gradient from short and tiny to long and large saccadic eye motion. For effective coding, Purkinje cell pauses should have variable sizes and effects.

Writing.

I think the writing can be improved in several places. A partial list follows:

Abstract, second sentence could be split into two.

Abstract, last sentence unclear.

In the third paragraph of the subsection “Pause spikes couple to the LFP strongly and specifically to the β/γ band”, last sentence "This effect.…" is unclear.

In the last paragraph of the subsection “Pause spikes couple to the LFP strongly and specifically to the β/γ band”, define pairwise phase consistency in a sentence.

In the last paragraph of the subsection “Pause spikes and their correlated LFP component encode the timing of eye motion”, explain estimate of extra coincident events in a bit more detail.

We thank reviewer for these specific suggestions. We have revised the manuscript accordingly.

In the last sentence of the subsection “Pause spikes and their correlated LFP component encode the timing of eye motion” – I'm not sure why you say that the fidelity depends on the local network – perhaps "reflects" is a better word? What if a set of nearby cells received highly synchronized inhibitory input (not necessarily local) and hence generated high fidelity, synchronized pauses?

We agree with the reviewer that “reflects” is better. Highly synchronized inhibitory inputs are definitely possible, and can be a source of the LFP signal related to pauses.

In the third paragraph of the subsection “PC firing rate linearly encodes eye motion, mostly by regular spikes”, you describe the pause spikes as exhibiting a high degree of nonlinearity, but it seems to me like that the firing rate is just not very dependent on eye movements. In other words, how do you separate nonlinearity from lack of correlation?

We used “nonlinearity” to simply describe the lack of a linear relationship between the linear prediction and the actual firing rate. The reason why the firing rate of pause spikes does not look very dependent on eye movements is that we computed motion features (Figure 5B) from all spikes. Pause spikes do correlate with eye motion (e.g. Figure 4C), but very differently from the full spike train for which the correlation to eye motion is dominated by regular spikes, as we argued in Figure 5—figure supplement 1 and the related text. Therefore, the firing rate of pause spikes has a weak and nonlinear dependence along the direction of those motion features. To further illustrate this, we plotted a figure (included as an inset of Figure 5—figure supplementary 1 in the revision) how similar (measured by the correlation ρ) the CCFSpike-EV for pause spikes is to that of the full spike train, as we change thresholds for pause spikes, similarly to Figure 5—figure supplement 1. In contrast to Figure 5—figure supplement 1, the CCFSpike-EV of pause spikes is still unmatched to that of all spikes, even when we classify more than 50% of the spikes as pause spikes.

In the revised text, we clarified this point in Results – PC firing rate linearly encodes eye motion, mostly by regular spikes:

“On the other hand, pause spikes (both pause-initiating and -terminating spikes) showed high degrees of nonlinearity (R2 = 0.39 ± 0.25) as their firing rate did not vary as steeply as for regular spikes (Figure 5C–E). This suggests that information encoded by the whole firing rate is very different from eye movement features related to pause spikes such as onsets (Figure 4C), but this information can be captured well by a subset of the full spike train, regular spikes.”

and in next paragraph:

“Note that ρ for pause spikes behaved very differently; it was not significant for reasonable fractions of pause spikes (Figure 5—figure supplement 1 inset).”

The third paragraph of the Discussion seems a bit repetitive.

Fixed.

In the sixth paragraph of the Discussion, "Exclusion of the complex spikes causes minuscule.…" – can you be more specific about what minuscule means?

This part has been replaced with an expanded discussion about complex spikes (see our response to consensus review 1).

Reviewer #2:

This manuscript tackles the very general question of how neurons encode information in their spike trains, and, in particular, the contribution of coding by the precise time of spikes within a train vs. a rate code. The experimental systems used by the authors (cerebellum and saccadic eye movements) offer some powerful advantages for analyzing this issue. The manuscript builds on the De Schutter group's previous work suggesting that brief, synchronized pauses in Purkinje cell firing may play a key role in cerebellar function. The current manuscript expands significantly on what had been done previously by 1) building a tighter link to behavior by examining pauses in the context of saccadic eye movement behavior and 2) examining the relationship between the LFP and the spikes bounding the pause.

The main conclusion is that the pause-related spikes are synchronized and encode movement onset, whereas the other, "regular" spikes encode movement kinematics.

I think this paper makes a significant contribution to the field. The idea that different spikes within a train may encode different information and be read out differently (through synchronized action with other cells vs. rate averaging) should be of broad interest to the neuroscience community.

There are three main areas where I have questions or concerns.

First, the authors claim in the Discussion that "Exclusion of the complex spikes caused minuscule changes in our results." This is an important issue that should be more thoroughly documented to rule out that the pause spikes are not reflecting the effect of complex spikes. Pause beginning spikes are defined so that they are 10% of all spikes. Complex spikes are nearly 2% of all spikes, so could potentially account for ~20% of the pause beginning spikes-if pause beginning spikes associated with a complex spike are removed, do the results still hold? If so, that would strengthen the authors' claim that the effects they report are not related to the complex spikes. But the opposite result would also be interesting.

We thank the reviewer for calling our attention to this important issue. We have added a more detailed account of why the effect of complex spikes is limited in our response to consensus review 1.

Second, it would be nice to see a more systematic analysis of different frequency bands in the LFP to determine whether it is really just the 15-42 Hz band that couple with the pause spikes.

Since the STALFP of pause spikes fluctuates transiently, it triggers a high coherence in a wide frequency band, following the time-frequency uncertainty principle. However, the coherence peak was located at higher frequencies (28.2 ± 5.7 Hz, 29.2 ± 4.6 Hz for pause-initiating and -terminating spikes, respectively), which was the most consistent pattern that we observed. In the lower frequency band (< 15Hz), coherence peaks tend to be smaller, by a factor of 0.36 ± 0.66 and 0.16 ± 0.23 for pause-initiating and -terminating spikes, respectively. This made the average coherence less than 0.05 in the lower frequency band, which predicted much weaker phase-locking in this band.

Our measure of spike-LFP phase locking, pairwise phase consistency (PPC; Figure 3D), indeed showed this. Figure 3—figure supplement 3 shows the PPC of each frequency band and type of spikes, normalized by the β-γ case. The PPC sharply dropped as we moved to lower frequency bands such as the low β (12-15 Hz), theta (4-10 Hz), and δ (0-4 Hz), except for a few outliers, in pause-spike cases. Compared to this, regular spikes showed an inconsistent pattern.

In summary, the 15-42 Hz band was the only frequency band in which we observed robust coupling to pause spikes.

Based on Figure 5C, the authors conclude that the regular spikes more linearly encode eye velocity than the pause spikes. Although this appears to be true, it also appears that there is a nonlinearity in the encoding of eye velocity by the regular spikes, which is compensated by the pause spikes in a way that makes the population as a whole more linear re eye velocity. Is this a reasonable interpretation? If so, it seems worth mentioning.

It is indeed reasonable since we are testing how the LN model constructed from all spikes can predict the firing rate of each group. Therefore, if the coding by all spikes is really linear, nonlinearity in one group should be compensated by those of other groups. As the reviewer remarks, we show that linearity is indeed slightly smaller for regular spikes, and pause spikes should compensate. The revised text now reads,

“Nevertheless, pause spikes can make small contributions to rate coding. […] Pause spikes, which by definition represent fast rate changes, should compensate for this. However, overall rate coding is dominated by regular spikes.”

Reviewer #3:

The manuscript by Hong et al. describes analyses of Purkinje neuron spike trains that shed light on the potential population encoding strategies of this cell population with respect to movement kinematics. They analyze LFPs and simple spikes during saccadic eye movements and find that LFP measurements are more tightly correlated with eye movement onset than single-spike trains, and that long interspike interval – "pauses" – phase-locked with these predictive LFPs. The conclusion from these pause-related data is that pauses encode saccade onsets. On the other hand, overall firing rate is highly correlated with eye velocity, with the "regular" spikes within this population. Pairing these observations, the authors conclude that multiplexed coding occurs with Purkinje firing.

I like the direction taken here and find most of the analyses important. There are some important missing pieces of information, however, that make evaluating the findings challenging and therefore a strong recommendation for accepting or rejecting the manuscript is premature. Of paramount importance is the selection of spikes beginning long pauses: "we selected 15% of largest AI values.[…] then removed 25% of the spikes with the shortest pause ISI." Since this process operates on ISI ratios, it is unclear what the ISI durations are that are being analyzed as pauses. Moreover, because this analysis relies on ratios and not overall ISI duration, (which would seem a more natural criterion for long ISIs), it is selecting for essentially bursty sequences of short-then-longish spikes. Interpreting the data through this light seems different than interpreting it through the lens of 'pauses' or longest ISIs. While I acknowledge that there may be no perfect solution to identifying pauses, I am not provided enough information to evaluate their claims because I don't know if the pauses they have chosen are unique in any way, or are alternatively unique in ways they do not highlight. In addition to the distribution of 'pause' ISIs vs. all ISIs, a plot of ISIn vs. ISIn+1 would provide non-ratioed data that may help reveal unique characteristics of the 'pause' population.

For the plots, please see our response to consensus review 2. The ISIn versus ISIn+1 plot shows that the distribution of (ISIn, ISIn+1) is stretched along the x- and y-axes, particularly for longer ISIs. In combination with the ISI distribution with pause ISIs vs. all ISIs, this shows that indeed our criterion selects the tail of the distribution. Selected pauses are indeed longer than average ISIs, but they are not all at extreme durations.

Choosing the longer ISIs following shorter ones, by using ratios, is important to us, since they occurred at saccade onsets in many Purkinje cells. Some Purkinje cells show relatively long periods of very low firing far after saccade onset, and long ISIs there should have a different role than our pauses in encoding eye movements, such as contributing to a rate code. Long pauses that follow short ISI are also likely to release cerebellar nucleus neurons from inhibition, which has been shown to encode motion onsets (e.g., Lee et al., Neuron, 2015).

An important assumption to the interpretation of the data advanced by the study is that the LFP correlation with pause onset spikes reflects synchronous firing. Since LFPs reflect synaptic and spiking currents, it may be that correlation detected is simply a readout of the fact that pushing the ISI off of the basal firing rates reflects synaptic input, which is also reflected in the LFP. I am not confident that any data analysis short of multi single-unit array recordings could resolve whether single spikes are temporally aligned at the onset of a pause to the degree necessary for synchrony coding in the nuclei, but I could be persuaded by experts of LFP interpretation.

We think it is unlikely that the LFP reflects only synaptic events in recorded cells. For example, Figure 1B and Figure 1—figure supplement 1 show that, although the LFP signal more or less stays the same for different saccade angles, the direction of firing modulation can flip completely. Our conclusion is that the LFP signal should reflect a certain network event that involves many neurons (but not necessarily only Purkinje neurons). We provide a more detailed discussion in our response to consensus review 3.

https://doi.org/10.7554/eLife.13810.022

Article and author information

Author details

  1. Sungho Hong

    Computational Neuroscience Unit, Okinawa Institute of Science and Technology, Okinawa, Japan
    Contribution
    SH, Conception and design, Analysis and interpretation of data, Drafting or revising the article
    For correspondence
    shhong@oist.jp
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon 0000-0002-6905-7932
  2. Mario Negrello

    1. Computational Neuroscience Unit, Okinawa Institute of Science and Technology, Okinawa, Japan
    2. Department of Neuroscience, Erasmus Medical Center, Rotterdam, The Netherlands
    Contribution
    MN, Analysis and interpretation of data, Drafting or revising the article
    Competing interests
    The authors declare that no competing interests exist.
  3. Marc Junker

    Department of Cognitive Neurology, Hertie Institute for Clinical Brain Research, University of Tübingen, Tübingen, Germany
    Contribution
    MJ, Acquisition of data, Drafting or revising the article
    Competing interests
    The authors declare that no competing interests exist.
  4. Aleksandra Smilgin

    Department of Cognitive Neurology, Hertie Institute for Clinical Brain Research, University of Tübingen, Tübingen, Germany
    Contribution
    AS, Acquisition of data, Drafting or revising the article
    Competing interests
    The authors declare that no competing interests exist.
  5. Peter Thier

    Department of Cognitive Neurology, Hertie Institute for Clinical Brain Research, University of Tübingen, Tübingen, Germany
    Contribution
    PT, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article
    Competing interests
    The authors declare that no competing interests exist.
  6. Erik De Schutter

    Computational Neuroscience Unit, Okinawa Institute of Science and Technology, Okinawa, Japan
    Contribution
    EDS, Conception and design, Analysis and interpretation of data, Drafting or revising the article
    Competing interests
    The authors declare that no competing interests exist.

Funding

Okinawa Institute of Science and Technology Graduate University

  • Sungho Hong
  • Mario Negrello
  • Erik De Schutter

Deutsche Forschungsgemeinschaft (Research Unit FOR 1847/1, Project A3 (TH 425/13-1))

  • Peter Thier

Bundesministerium für Bildung und Forschung (Joint project Bernstein Center for Computational Neuroscience, 01GQ1002A, Project C3)

  • Marc Junker
  • Aleksandra Smilgin
  • Peter Thier

European Commission (PITN-GA-2009-238214-C7)

  • Aleksandra Smilgin
  • Peter Thier

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We thank Sonja Grün, Chris De Zeeuw, Steve Prescott, Javier Medina, and Fahad Sultan for helpful discussions. We thank OIST Graduate University for its generous support of the Computational Neuroscience Unit. This work was also supported by grants from the Deutsche Forschungsgemeinschaft (Research Unit FOR 1847/1, project A3–TH 425/13-1, P Thier), the European Union (Marie Curie Training Network PITN-GA-2009-238214-C7, P Thier and A Smilgin) and the German Federal Ministry of Education and Research (Bernstein Center for Computational Neuroscience 01GQ1002A, project C3, P Thier, M Juncker and A Smilgin).

Ethics

Animal experimentation: All animal experiments were approved by the local animal care committee (Protocol number: Regierungpräsidium Tübingen N1/08 and N6/13), conducted in accordance with German law and the National Institutes of Health's Guide for the Care and Use of Laboratory Animals and carefully monitored by the veterinary administration (Regierungsprääsidium and Landratsamt Tübingen).

Reviewing Editor

  1. Fred Rieke, Reviewing Editor, Howard Hughes Medical Institute, University of Washington, United States

Publication history

  1. Received: December 15, 2015
  2. Accepted: June 13, 2016
  3. Version of Record published: July 26, 2016 (version 1)

Copyright

© 2016, Hong et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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