Author response: Multiplexed coding by cerebellar Purkinje neurons
2016-05-04

Full text Figures and data Side by side Abstract eLife digest Introduction Results Discussion Materials and methods Appendix 1: Adaptive detection algorithm for saccade onsets Appendix 2: Construction of the inverse model and comparison with linear coding References Decision letter Author response Article and author information Metrics 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 Download asset Open asset 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% (n = 25; magenta), and less in 15% (n = 5; cyan) of all recordings. No difference was found in the rest (n = 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, n = 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, n = 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 CV2 ≈ 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, n = 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 Download asset Open asset 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 Download asset Open asset 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, n = 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 (n = 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, information do they encode about eye To this we first how the phase of the β/γ LFP during each saccade in recordings for each In many of the β/γ LFP was significantly across all with a phase locking to saccade onsets (Figure We this by computing the average phase during a time around saccade onset to ms), which we called LFP phase Significantly high LFP phase was found in of the data (p<0.01, n = one to control = ± mean ± Figure 4 with 1 supplement see all Download asset Open asset Pause spikes and β/γ LFP encode motion timing. (A) speed (Top) and β/γ LFP with saccade lines represent an average all saccades n = (B) of the β/γ LFP at saccade onset for the same data. (C) Top: trains for pause-initiating, and regular spikes with onsets of randomly saccades (n = regions represent periods with significantly reliable firing see Materials and Bottom: for spike by a = (D) of pause and regular spikes in all data. = (Wilcoxon rank-sum test). (E) LFP phase versus spike The two were significantly correlated and black for pause-initiating and regular spikes = × but not for pause-terminating spikes = to recordings with spike but high LFP Data in are the same as in Figure 1A,B. 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 and Figure supplement 1). This could be caused either by a firing rate increase of pause spikes during or by a sharp correlation across most saccade reliable To we estimated how many spike coincidence occurred beyond the from the firing from all of spike trains and which we called the spike for each of saccade we spike ms) between two spike trains within a time at to saccade we estimated the that two spike trains with the same firing rates could have the same or more spike for significant et al., et al., 2011; et al., The of those significant from all cells, all and time, the spike Significantly spikes were found during significant peaks of firing regions in Figure spike was significantly higher for pause spikes (Figure their role in encoding the onset of eye motion. the LFP phase and spike were much more related to each for pause-initiating spikes than for regular spikes (Figure This that the of temporal coding by pauses in individual PCs the of activity and coding of the local network. PC firing rate eye motion, mostly by regular spikes we have focused on pause spikes, rare in the spike train that provide timing On the eye correlation average showed firing rate modulation by eye movement kinematics such as etc. (Figure and Figure 1—figure supplement 1A–F). This suggests that a firing rate code also be in PC spike trains. To this we an inverse model that firing rate from eye movements in each cell, based on the model and are widely used in but have not to PCs to First, the eye velocity is compared with a preferred pattern estimated from the linear cross-correlation in Figure to generate a linear of the firing which goes an to the observed firing rate (Figure Figure with 1 supplement see all Download asset Open asset PC firing rate motion (A) Schematics of the eye inverse (B) motion (C) vs. firing rate for all regular and pause (red) spikes. The rates of pause and regular spikes are to those of all spikes to for The line represents (D) of for the linear to actual rate. (Wilcoxon rank-sum test). (E) for all Error bars are omitted and are for (Wilcoxon rank-sum test). Error bars represent SEM. Data in are the same as in Figure 1A,B. We found that the linear rate followed the actual rate very = ± mean ± the effect of the is small (Figure This made the linear rate a of the of average firing rate modulation during saccades and it was used exclusively in the rest of the analysis. correlation with the firing rate remained high = 0.81 ± when we computed the linear with only regular spikes, which comprised about of all spikes. the firing rate of pause spikes pause-initiating and did not as or as for regular spikes = ± This suggests that information by the firing rate is very different from eye movement related to pause spikes such as onsets (Figure but this information can be by a subset of the spike train, regular spikes. This led us to into the between rate coding by regular spikes and the spike train. For this, we different on CV2 for the regular spikes, computed the direction-dependent CCFSpike-EV of those selected spikes (Figure and estimated its to that of the spike train by computing their correlation coefficient We found that quickly as we increased the CV2 whereas the of regular spikes increased more (Figure supplement 1). For when we select of all spikes as regular spikes by CV2 their CCFSpike-EV is very similar ≈ in to that of the spike train. at CCFSpike-EV of these regular spikes had ≈ on similar to the linear coding property (Figure Note that for pause spikes very it was not significant for a of pause spikes (Figure supplement 1 The of Figure and Figure supplement 1 that regular spikes rate coding. Regular spike and spike trains to similar motion and also the linear coding Our results those of a previous in which of regularly firing spikes the rate of PCs to (Shin et al., pause spikes can small to rate coding. all spikes, the model is but the rate coding of regular spikes predicted by the model is less linear (Figure Pause spikes, which by represent fast rate for regular spike is from the of information because a small and very regular subset can provide a of the rate modulation (Figure supplement 1). Furthermore, regular spikes are weakly coupled to network activity (Figure 3). This strongly suggests linear rate coding as the role of regular spikes. Discussion Examples in and motor et al., et al., et al., and analysis et al., have shown that neurons can use multiplexed coding where each spike in a single spike train can couple to local network activity and encode different information about or This study the first for multiplexed coding in cerebellar Purkinje spikes that initiate pauses are strongly coupled to the β/γ band of the LFP and are therefore synchronized among nearby These spikes a temporally reliable signal to initiate saccadic eye motion. regular spikes in the same spike trains are among nearby PCs and a rate code that direction eye of a multiplexed code resolves the between temporal and rate coding that about PC spiking (De Zeeuw et al., 2011; Heck et al., 2013). Pauses in the spike train are observed in many firing neurons in In synchronized pauses after bursts encode a et al., pause-initiating and -terminating spikes can synchronize sharply Shin and De Schutter, PCs can by a similar coding In spike by PCs is a mechanism to control their in the cerebellar fast and Raman, neurons can reliably generate spikes in response to synchronized followed by even at of and Raman, 2012) and spike time ms) and Jaeger, 2000; et al., 2015). Furthermore, optogenetic experiments have shown that pauses induced either by or at the of can reliably firing in neurons, and at movement onset et al., et al., 2015). pauses were ms), but and even shorter pauses from