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The inferior olive projects climbing fiber axons to cerebellar Purkinje neurons, where they trigger calcium-based dendritic spikes. These responses dynamically shape the immediate spike output of Purkinje cells as well as provide an instructive signal to guide long-term plasticity. Climbing fibers typically fire about once a second, and the instructive role is distributed over many such firing events. However, transmission of salient information on an immediate basis needs to occur on a shorter time scale during which a Purkinje cell would typically be activated by a climbing fiber only once. Here we show using in vivo calcium imaging in anesthetized mice and rats that sensory events are rapidly and reliably represented by momentary, simultaneous co-activation of microbands of adjacent Purkinje cells. Microbands were sagittally oriented and spanned up to 100 microns mediolaterally, representing hundreds of Purkinje cells distributed over multiple folia. Spontaneous and sensory-evoked microbands were similar in structure to one another and were desynchronized by olivary injection of the gap junction blocker mefloquine, indicating that excitation to the olive is converted to synchronized firing by electrical coupling. One-time activation of microbands could distinguish a sensory response from spontaneous activity with up to 98% accuracy. Given the anatomy of the olivocerebellar system, microband synchrony may shape the output of neurons in the cerebellar nuclei either via powerful inhibition by Purkinje cells or by direct monosynaptic excitation from the inferior olive.
The inferior olive is thought to transmit information to the cerebellum and guide movement via the climbing fiber (CF) pathway, which has two major effects on its target, cerebellar Purkinje cells (PCs). The two effects are driven by calcium-based action potentials that occur in the PC dendrite every time the CF fires (Llinas and Sugimori, 1980), triggering widespread dendritic calcium entry and a somatic “complex” spike. First, CF activity immediately modifies the sodium action potential (simple spike) output of the PC (Sato et al., 1992; Simpson et al., 1996). Second, CF activity also instructs long-term plasticity at synapses that are repeatedly co-activated with the CF (Ito and Kano, 1982; Ito, 2001). Both an instructive and an online role for CF function occur under the constraint that CFs fire about once per second, suggesting that information is carried in the timing of complex spikes.
In the case of immediate effects on brain function, models for the role of complex spikes need to be reconciled with the fact that individual PCs do not always respond to single events. Complex spike firing occurs only with low probability after single occurrences of any of a variety of sensorimotor events, including facial touch (Brown and Bower, 2001), movements ( Kitazawa et al., 1998; Welsh et al., 1995), changes in sensory load (Gilbert and Thach, 1977), and visual feedback error signals (Stone and Lisberger, 1986). Typical single-trial firing probabilities are 0.3 or less (though see also (Gilbert and Thach, 1977)), so that event-related firing consists largely of shifts in the timing of one complex spike against a continuing background stream of simple and complex spikes. This stream of spikes provides inhibition to the output structures of the cerebellar cortex, the deep nuclei.
One means of distinguishing events from background is synchronization of firing among cells (Hopfield and Brody, 2001; Singer and Gray, 1995). In the cerebellum, natural sensory stimuli (Wylie et al., 1995) and trained movements (Welsh et al., 1995) are associated with increases in complex spike synchrony. This synchrony originates in the inferior olive. Dendrodendritic gap junctions lead neighboring olivary neurons to fire at the same time (Devor and Yarom, 2002; Long et al., 2002); and in connexin-36 knockout mice, olivary neurons are desynchronized (Long et al., 2002). CFs from neighboring olivary neurons project in a remarkably precise map to well-defined parasagittal zones of Purkinje cells (Apps and Garwicz, 2005; Sugihara and Shinoda, 2007). This mapping suggests that immediately neighboring PCs should show a high degree of simultaneous activation.
In the present work we measured the representation of sensory events by complex spikes in local ensembles of PCs and the degree to which co-activation contributed to the representations. We monitored cerebellar activity in anesthetized mice and rats using two-photon imaging, which can record calcium spike activity in essentially all the PC dendrites in a region of neuropil (Ozden et al., 2008; Sullivan et al., 2005). We found that the degree of co-activation in neighboring PCs is an order of magnitude larger than previously reported from more sparsely sampling methods. The strongest co-activation was found under sensory stimulation, indicating that PC ensemble synchrony can convey the occurrence of salient events.
Experimental procedures were approved by the Princeton University Institutional Animal Care and Use Committee and performed in accordance with the animal welfare guidelines of the National Institutes of Health. C57/BL6 mice (P21-42) or Wistar rats (P21-28) were deeply anesthetized with ketamine/xylazine and a small craniotomy of diameter 2 mm was made over folium crus IIa. Purkinje cells were loaded with calcium indicator Oregon Green BAPTA-1/AM (Invitrogen Corporation, Carlsbad, CA) as previously described (Sullivan et al., 2005).
Mefloquine (National Cancer Institute, Bethesda, MD), a potent blocker of the olivary gap junction connexin36 (IC50=0.3 μM) (Cruikshank et al., 2004) was dissolved in DMSO (100 mM), diluted in artificial cerebrospinal fluid (500 μM) and pressure-injected into the inferior olive by a 6–10 MΩ saline-filled glass recording micropipette at 1–2 psi for 10 min at 0.05–0.1 μl/min. Harmaline (Sigma Chemical Co., St Louis, MO, USA), which enhances tremor and provides net excitation to olivary neurons (de Montigny and Lamarre, 1973; Miwa, 2007), was dissolved in sterile saline with acetic acid and given intraperitoneally at a dose of 1 mg/kg. Extracellular single-unit recordings from Purkinje cells were made using using a NeuroData IR-283A amplifier (Cygnus Technology, Inc., Delaware Water Gap, PA) and glass micropipettes pulled to 6–10 MΩ and filled with artificial cerebrospinal fluid containing (in mM) 135 NaCl, 5.4 KCl, 5 NaHEPES, 1 MgCl2, 2 CaCl2 (pH 7.3 with HCl).
In vivo calcium imaging was performed using a custom-built multiphoton microscope as described previously (Ozden et al., 2008; Sullivan et al., 2005). Data were collected as movies of 64×64 (128 ms/frame) or 128×128 (256 ms/frame) pixel frames, letterbox scans of 10×128 (20 ms/frame), or line scans at 2 ms/line. In movies, the fast-scan direction was oriented parasagittally. In letterbox scans the fast-scan direction was oriented mediolaterally. Distances between dendrites in both mediolateral and rostrocaudal directions were determined from the centroids of the parts of dendrites that were visible within the field of view.
Data analysis was performed as described (see Supplementary Movies and (Ozden et al., 2008)). All code was written in MATLAB version 7.1 (MathWorks) and is available at http://synapse.princeton.edu/programs.
A pixel correlation-based approach was used to exclude less correlated pixels, thereby increasing the likelihood that the final selected pixels belonged to the same cellular structure. Each filtered movie was examined to find candidate dendritic arbors, as judged by the co-occurrence of signals in the shape and orientation of PC arbors, and by the criterion that a candidate structure fire by itself and all at once. For each arbor a region was selected slightly larger than the bright pixels. Pixels were then selected for the final region of interest using a rule requiring each selected pixel to have a correlation value above a threshold rth with at least nth pixels in the selected region.
Event detection was done by using a template-and-threshold algorithm on fluorescence traces averaged from the selected region. Each trace was first convolved using a 4-point filter taken from the time course of the 10 largest peaks. Then local maxima were classified as events if they exceeded a human user-determined threshold. In experiments where calcium transients were confirmed as being of climbing fiber origin by simultaneous extracellular recording of complex spikes, the peak ΔF/F for events was 19.8 ± 6.9% in line scans (29 dendrites in 4 experiments). The peak ΔF/F was 7.0 ± 2.8% (817 events) in movies with 256 ms frame time, as expected (Ozden et al., 2008) and much larger than the background fluctuation of 1.6 ± 0.4% ΔF/F (standard deviation of dendritic fluorescence, mean ± SD, 14 dendrites). Using these methods the true-positive rate was 95% and the false-positive rate was 8%.
In harmaline experiments, event detection was unreliable in frame scans because the frequency of complex spike firing exceeded the frame rate. Therefore correlations were calculated not from event times, an approach that effectively counts the number of coincident firing events, but directly from continuous fluorescence traces. In fast (line and letterbox) scans in which events were reliably resolved, fluorescence-based correlations showed very similar spatial dependence and patterns compared with event-based correlations.
For an arbor aligned in the fast-scan direction, a complex spike during scanning of a frame could occur after the beam had already finished scanning the arbor, leading to a one-frame delay in detecting the corresponding calcium transient and thus affecting the detection of simultaneous spike events. Such scan position-dependent error was corrected with a statistical correction of event times (Ozden et al., 2008) to reduce artifactual, apparent distance-dependent decreases of correlations when dendrites fire together but are far from one another in the field of view. Every detected peak in sample i, which before correction was represented by a value of 1 at one timepoint in the event trace, was represented by x/L and the (i−1)th time point was set to 1−x/L, where x is the time from the beginning of the frame for the scan beam to reach the dendrite and L is the time taken to scan the whole frame..
In brief, a movie with M arbors and N time points was represented as M points in an N-dimensional space, where each point represents the activity of a single dendritic arbor over the entire movie. The “activity distance” between arbors was defined as d=1−r where r is the Pearson correlation between activity sequences. r was calculated from corrected event times or, for harmaline experiments, from fluorescence traces. A Pearson correlation of zero corresponds to the number of simultaneous events that would occur by chance.
For each movie the k-means algorithm (Hartigan and Wong, 1979) was run 1000 times by initializing k=3 clusters at random locations in N-space; going through a cycle of adding arbors one at a time to the nearest cluster and recalculating the cluster center; and iterating the cycle, starting with the new cluster centers; until membership did not change. For each pair of dendritic arbors i and j, the number of times arbors i and j were clustered together, Cij, was determined. C always had a structure similar to that of the correlation matrix. Working clusters were then defined as the maximum set of arbors such that Cij was greater than 800 for every (i,j) within the cluster. This procedure usually found 6 to 8 working clusters in a dataset. Working clusters were then combined iteratively to maximize Dunn’s index, which emphasizes individual cluster tightness and the distance between adjacent clusters and is defined as DI=Dmin/dmax, where Dmin is the smallest distance between two points in different clusters and dmax is the diameter of the widest cluster (Maulik and Bandyopadhyay, 2002). The final clustering did not change with successive runs of meta-k-means. In some datasets meta-k-means achieved a higher DI than the most successful single run of k-means due to the exclusion of outliers.
The correlation between two dendritic signals x(t) and y(t) was calculated as the Pearson correlation
where T is the total recording time and Δt is the sampling time. For discrete event times,
where N is the number of frames, C is the number of coincidences, ex = N·px and ey = N·py are the expected number of events in each dendrite for probabilities px and py, , and . r is zero when dendrites x and y fire independently and ranges from (no coincidences) to 1 (identical sequences).
Facial whisker stimulation was delivered by Pressure System IIe (Toohey Co., Fairfield, NJ) as 40 ms pulses at 20–40 psi. Dendrites were scored as responding based on all sensory trials if the number of events detected in two movie frames (or 10 letterbox scans) immediately following a stimulus exceeded a baseline rate determined from the seven frames (or 100 letterbox scans) preceding the stimulus, as determined by a chi-square test (2 d.f., P<0.05). The response probability was defined as pr = (Nresp − Nprestim)/(Ntotal − Nprestim), where Nresp is the number of trials in which an event occurred in the response period, Nprestim is the number of trials in which an event occurred in a prestimulus period of equal duration, and Ntotal is the total number of trials. The number of dendrites responding at once was calculated from two frames in movie scans and one frame in letterbox scans.
A train of PC events at times ti was assumed to trigger an enhancement process with time course F(t) = 1 + A Σi H(t−ti) e(ti−t)/τ dt, where H is the Heaviside step function, A=3, and τ =140 ms. For each timepoint tj in which at least one PC event occurred, neurotransmitter release R was defined as the sum of F(tj) over all active PCs and converted to a postsynaptic response using the sigmoidal relationship O(tj)=1/(1+e(R0−R(tj)/ρ), where R0 ranged from 0.5 to 2 N and ρ ranged from 0.1 to 1 N, where N was the total number of dendrites. R0 and ρ were varied to optimize the ROC by minimizing the distance between the left top corner (point (0,1)) and ROC curve. The decoder output was taken as the sum of all O(tj) in a 512 ms following the sensory stimulus.
Averages are given as mean ± standard deviation unless otherwise noted.
We used in vivo two-photon microscopy (Figure 1A) to monitor spontaneous and sensory-evoked PC complex spikes in mouse and rat crus II, a cerebellar region that receives peri-oral and other somatotopic sensory information (Brown and Bower, 2001). We bulk-loaded the molecular layer of the intact cerebellum with the fluorescent indicator dye Oregon Green BAPTA-1/AM (Sullivan et al., 2005).
This preparation allowed us to record calcium transients optically 90–120 μm above the PC body layer in fields of view up to 270 μm wide, where the observed calcium signals come mainly from PC dendritic arbors (Sullivan et al., 2005). PC dendritic arbors are finely branched and fill a flat, fan-like, parasagittally-oriented space about 200 μm wide and 6–10 μm thick, (Palay and Chan-Palay, 1974). In mice and rats, arbors appear in transverse section as uninterrupted tube-like structures (Johnston, 2005) separated by 4–8 μm from the nearest neighbor with minimal intermingling. The nonoverlapping arrangement of PC arbors is visible in transgenic mice expressing GFP under the PC-specific L7 promoter (Figure 1A).
Anatomical separation of dendritic arbors made it possible for pixels from calcium imaging experiments to be assigned to specific PCs. Because bulk-loading with Oregon Green-1/AM (Figure 1B) gave lower contrast than GFP, pixels were classified using correlations in the pixel time courses (Ozden et al., 2008) that arose from CF-evoked dendritic action potentials, which trigger calcium entry throughout the PC dendritic arbor (Ross and Werman, 1987; Tank et al., 1988). Between 15 and 40 neighboring PC arbors were visible per field of view.
PC dendritic arbors generated calcium transients at 0.2–1 Hz, as expected from observed rates of CF firing (Brown and Bower, 2001). Line scans (2 ms/line; Figure 1A, bottom, green trace) across dendrites showed that calcium transients, which span the arbor, rose in about 10 ms and fell with a half-maximal decay time of 170 ± 50 ms and an exponential decay time constant of 280 ± 60 ms (mean ± SD, 29 dendrites in 4 experiments), consistent with previous reports in vivo (Sullivan et al., 2005). These slow decay times and the low rate of calcium transients (0.48 ± 0.15 Hz) made it possible to detect individual events even at frame acquisition times as long as 256 ms.
In movies with low frame rates (128 ms/frame and 256 ms/frame), the orientation of the scan pattern was adjusted to align dendritic arbors in the direction of fast scanning, thus establishing a precise within-frame time at which each dendritic arbor was scanned. Because transients might not be detected until the following frame, event times were adjusted using a likelihood-based correction (Ozden et al., 2008). For line scans and letterbox (10-line frame) scans, the line scan direction was set perpendicular to the dendrite orientation to allow many dendrites to be monitored at once.
To confirm the complex spike origin of transients, simultaneous optical and electrophysiological recordings were performed (Figure 1A, green and black traces respectively). Fluorescence transients in a dendritic arbor were almost always associated with complex spikes recorded near the originating cell body. Fluorescence transient events identified by a template matching-and-thresholding algorithm (Ozden et al., 2008) (Supplementary Movies 1 and 2) were associated with 95.4 ± 3.0% of electrophysiologically recorded complex spikes (mean ± SD, 16 recordings in 5 rats, 850 complex spikes). Conversely, 92.2 ± 5.1% of detected transients (835 transients) were accompanied by a complex spike in the associated electrophysiological recording. Thus in vivo imaging of PC dendritic calcium transients is a reliable means of monitoring complex spike activity.
Climbing fibers originate from inferior olivary neurons, which are electrically coupled to one another (Devor and Yarom, 2002; Llinas et al., 1974) and frequently generate simultaneous action potentials (Devor and Yarom, 2002), suggesting that PC complex spike firing should manifest a high degree of synchrony. In populations of PCs we found that nearby arbors often fired at the same time (Figure 1B and 1C).
The rapid rise time of calcium transients allowed complex spike times to be determined with a precision of a few milliseconds. Line scans (2 ms/line) showed that calcium transients in multiple arbors often began at the same time (Figure 1B), even in arbors that were separated mediolaterally and thus would not be expected to receive input from the same CF (Sugihara et al., 1999; Sugihara et al., 2001). Arbor-arbor cross-correlations (see Figure 1C, left) were highest at a relative timing of 4 ms or less in 190 out of 213 pairs of dendrites (Figure 1C, right, n=8, 4 rats and 4 mice). In these experiments, which spanned 9 ± 2 dendritic arbors per field of view, 90% of all calcium events were associated with events in at least one other PC. Thus PC complex spike firing almost always occurs in groups, presumably driven by the activity of multiple olivary neurons (Wylie et al., 1995).
Previous measurements done with electrodes spaced hundreds of microns apart (Welsh et al., 1995) suggested that PC-PC correlations were low, typically no more than 0.2. In our recordings, which sampled every PC in a field of view, we observed much higher arbor-arbor event time cross-correlations (maximum correlation 0.88, interquartile range 0.12 to 0.42; Figure 1D). The highest correlations corresponded to pairs of arbors closely spaced in the mediolateral and parasagittal (Figure 1D) directions. These correlations were considerably larger than reported by (Welsh et al., 1995) (indicated by arrowheads in Figure 1D) and consistent with measurements from pairs of neurons separated by tens of microns (Bell and Kawasaki, 1972). Thus complex spike co-activation is strongest on a local scale, less than 100 microns.
We tested for several potential errors of interpretation. On average, the size of cross-correlations was not affected by the rate of scanning, as might be expected for frame rates comparable to or lower than the event rate (Supplementary Figure 1A). We also tested the extent to which high correlations could be ascribed to misidentification of dendritic arbor boundaries. Such misidentification could lead to mixing of signals between pairs of neighboring arbors. We compared the cross-correlation of fluorescence signals from outer one-thirds of arbors with one another and with parasagitally neighboring arbors from different PCs. The average correlation between the end of an arbor and that arbor’s closest neighbor was 0.28 ± 0.13, much smaller than the correlation between opposite ends of the same arbor (0.78 ± 0.09; P < 0.01, t-test; Supplementary Figure 1B). We also tested whether the end of an arbor showed detectable calcium transients when its closest neighbor fired but its own parent arbor did not. In this case the peak fluorescence change was 3 ± 12% the size of the full signal seen when its own arbor fired (Supplementary Figure 1C), a level that did not lead to any falsely detected events in the arbor end. Taken together, our analysis indicates that correlations in our frame scan movies measure the true amount of synchrony and that cross-talk between neighboring dendritic arbors emanating from different PCs is low.
We found that correlations were strongest at distances of tens of microns, declining steeply in the mediolateral direction (Figure 1D, left) with a characteristic half-maximal distance of 29 ± 13 μm (11 fields of view in 3 mice and 3 rats; for rats 30 ± 18 μm and for mice 29 ± 11 μm). Correlations dropped more gradually in the parasagittal direction (Figure 1D, right). Using the centers of visible dendrites as the PC location, half-maximal correlations were reached at a distance of 102 ± 21 μm (50 dendrite pairs in 3 mice), which is an underestimate of the true distance since in many cases only part of a dendritic arbor was visible. Correlations among dendrites showed an overall preference for the parasagittal direction (parasagittal half-maximal distance greater than mediolateral half-maximal distance, p<0.01, two-tailed test). In summary, synchronized firing of PCs is organized predominantly parasagittally with the strongest correlations occurring on a scale of tens of microns, a distance largely unexplored in previous physiological reports.
Despite the overall strength of short-distance correlations, correlations between immediately adjacent pairs of PC dendritic arbors ranged from 0.08 to 0.83. This wide range of correlations suggested that pairwise coupling was not smoothly varying but instead organized to form discrete groups. To test this idea, recordings were made from up to 40 dendritic arbors at once (Figure 2A and Figure 2B). In these recordings, plots of all pairwise correlations (Figure 2C) revealed an emergent pattern in which groups of neighboring dendritic arbors often fired at the same time, but were less correlated with nearby groups.
We identified groups computationally using meta-k-means (Ozden et al., 2008), a robust clustering procedure based on repeated runs of the k-means algorithm (d’Haeseleer, 2005). K-means is used widely to find structure in gene expression datasets when the number of clusters is known in advance. Meta-k-means addresses the absence of a priori information on the number of clusters by aggregating many runs of k-means to determine the number and composition of clusters. This approach is robust, versatile, and produces consistent results when applied to calcium imaging datasets (Ozden et al., 2008). We applied meta-k-means to matrices of likelihood-corrected event times recorded from all dendrites. We defined a distance metric based on dendrite-dendrite correlation, so that identical event sequences are separated by zero distance. Use of this “pattern distance” metric identifies clusters in which co-activation is high within groups and low between groups.
Identified groups (Figure 2D) took the form of microbands that extended across the field of view parasagittally. Microbands included 3 to 19 arbors that were near one another, usually in a contiguous region, and spanned 3 to 11 arbors in the mediolateral direction. To quantify the degree to microbands were distinct entities, we found that the mean correlation in pairs of arbors within a microband (0.25 ± 0.12, 266 pairs, 35 microbands in 10 mice) was higher than the mean dendrite-dendrite correlation in pairs of neighbors across microband borders (0.17 ± 0.08, 22 pairs; p<0.01).
In cases where both boundaries of a band were visible, the microband spanned 6.3 ± 2.0 dendritic arbors mediolaterally in mice (15 fields of view, 10 animals) and 6.8 ± 1.9 dendritic arbors in rats (9 fields of view, 4 animals). The thickness of microbands was also similar between mice (61 ± 23 microns) and rats (64 ± 19 microns). In summary, olivocerebellar projections show local modular coupling structure on a scale of less than 100 microns as measured in the molecular layer.
Microband identity might be determined by the strength and pattern of electrical coupling among olivary neurons. We therefore examined how microbands were altered by pharmacological manipulation of the inferior olive. Infusion into the inferior olive of mefloquine, which blocks the gap junction channels connexin-36 and connexin-50 (Cruikshank et al., 2004) to decouple olivary neurons (Urbano et al., 2007), reduced correlations within microbands from 0.23 ± 0.09 to 0.08 ± 0.07 (Figure 3A, left; n=49 dendrites in 3 mice; mefloquine smaller than pre-drug, P<0.01, paired t-test) and modestly reduced the mean frequency of dendritic calcium transients from 0.33 ± 0.07 events/s/dendrite to 0.19 ± 0.07 events/s/dendrite (n=49 dendrites, P<0.01). Microband structure was also disrupted, leaving only lone uncorrelated dendrites and pairs of correlated dendrites (Figure 3A, lower left).
In contrast, harmaline, which also interferes with olivary signaling by a different mechanism, modulation of intrinsic neuronal conductances (de Montigny and Lamarre, 1973), did not strongly affect clustering patterns (Figure 3B and 3C) or the distance-dependence of dendrite-dendrite fluorescence correlations (Figure 3B, right), even though correlations were increased from 0.26 ± 0.10 to 0.44 ± 0.15 (n=116 dendrites in 2 mice and 3 rats, p<0.01 by paired t-test) and the electrophysiologically recorded complex spike rate increased from 0.84 ± 0.56 Hz to 2.03 ± 0.56 Hz as (n=3 in 1 mouse and 2 rats, P<0.05 by paired t-test). Harmaline observations were confirmed in scans done at higher sampling rates (data not shown). These results indicate that the organization of microbands specifically requires electrical coupling in the inferior olive.
To test whether coupling-dependent microband membership was stable over time, microbands were compared from five-minute periods comprising the first and second halves of recordings (n=16 fields of view from 10 mice and 4 rats). Between the halves microbands were nearly unchanged, with only 5% (22 out of 477) dendrites changing their assigned membership (Figure 3D). Membership-changing dendrites were usually found at boundaries between microbands and were comparable in number to those changing membership after harmaline injection, but far fewer in number than seen under mefloquine or when cluster structures were compared from unrelated experiments to provide a bootstrap measure of the maximum possible change (Figure 3D; p<0.01, all four pairwise comparisons, one-tailed test). Thus microband membership was stable for the duration of recordings and during consecutive recordings from the same field of view (range of inter-movie intervals 6–113 minutes).
The existence of strong, clustered electrical coupling in the inferior olive suggested that sensory-driven complex spike responses could be synchronized across PCs within a microband. To test this idea, PC dendrites were monitored under delivery of airpuff stimuli to the ipsilateral whisker pad. On each trial, airpuffs triggered responses in some but not all dendrites in a field of view, with different dendrites responding from trial to trial (Figure 4A). Consistent with previous mapping studies (Brown and Bower, 2001), dendrites fired within the first two full scan frames (512 ms) or 25 box scans (500 ms) after presentation of the airpuff with response probabilities ranging from 7 to 72% (29 ± 15 %, 150 out of 195 dendrites in 8 mice, 8 fields of view; Figure 4A).
Application of clustering analysis to sensory response data revealed a microband structure that was almost identical to that measured under spontaneous conditions during the same experiment (Figure 4B). Nearly all dendrites showed the same membership between spontaneous and sensory conditions. Only 10% of dendrites (15 out of 153 dendrites in 12 microbands, 5 full-scan fields of view in 5 mice) changed membership, usually at the boundaries between bands. The sensory response probability pr was not correlated with mediolateral position within a microband (absolute value of rank correlation 0.31 ± 0.19, 12 microbands of 6 to 20 dendrites; correlations not significant by two-tailed test with correction for multiple comparisons), suggesting that olivocerebellar sensory input was not mapped more finely than the microband level. Responding dendrites were, however, distributed heterogeneously between microbands within a field of view (Figure 4C–E), with 77 ± 13 % of the variance in pr accounted for by cluster membership (n=5; Figure 4D). Compared with the microband with the highest overall average pr (0.32 ± 0.04, mean ± SEM, n=5), the nearest microband had a significantly higher average pr than the next one out (0.12 ± 0.05 vs. 0.01 ± 0.01, mean ± SEM, n=5, P<0.01, one-tailed test; Figure 4D), indicating that responsiveness to the stimulus tended to vary in a gradient across multiple microbands.
Airpuff stimulation triggered responses in an average of 8.8 ± 4.7 dendrites out of 32.8 ± 5.0 dendrites at once in a field of view (457 trials in 5 mice) compared with an average of 2.9 ± 3.5 dendrites responding at once spontaneously (5112 events; different from airpuff-evoked stimulation, P<0.01). Because of the low time resolution of movies (256 ms/frame) these measurements may have combined asynchronous responses or, conversely, assigned synchronous events to different frames (Ozden et al., 2008). It was therefore necessary to scan dendrites at higher time resolution. We scanned smaller fields of view, containing 10 to 20 dendrites, at high speed (20 ms/frame, n=3 mice, 184 stimuli; Figure 5A). In these experiments, airpuffs triggered responses in 4.9 ± 1.8 dendrites (35 ± 2 % of the total) at once, compared with 1.5 ± 0.2 dendrites (11 ± 3%) during spontaneous activity (1209 events; numbers and percentages of dendrites both different by one-tailed test, P<0.05, n=3). Therefore information about the occurrence of a sensory stimulus was conveyed in part by the number of synchronously responding dendrites.
Fast scanning also revealed that sensory responses were characterized by repeated firing during each response. Airpuffs evoked multiple calcium transient events in single dendrites, each of which was also synchronized across dendrites (Figure 5A, top). Within each burst of events, synchronous events could occur in some or all responding dendrites at once (Figure 5A, top, inset). The overall response pattern was a burst of 2 to 5 transients occurring at a frequency of ~10 Hz (Figure 5A, bottom), with the first event occurring within 40–100 ms of the stimulus.
Bursts contained 2.94 ± 0.77 events (n=365 bursts) during airpuff stimulation, in contrast with spontaneous activity, in which multiple firing at 100-ms intervals was largely absent (1.17 ± 0.46 transients per response, n=1017 events; different from airpuff stimulation, P<0.05). Extracellular microelectrode recordings from single PCs (Figure 5B) confirmed that airpuff stimuli could trigger complex spikes separated by ~100 ms (n = 4 mice). The timing of complex spikes was similar from trial to trial, consistent with the synchrony among PCs observed in imaging experiments.
To test whether stimulus-evoked synchrony relied on electrical coupling, we imaged sensory responses before and after injecting mefloquine into the inferior olive. Pairwise correlations among all responding dendritic arbors were 0.15 ± 0.06 before injection and 0.03 ± 0.04 after injection (Figure 5C; n=156 pairs of arbors in 2 mice; mefloquine smaller than pre-drug, P<0.01, paired t-test). The discrete 10 Hz repetitive nature of sensory responses was replaced by a continuous period of enhanced probability of calcium transients (Figure 5D). These observations indicate that sensory-evoked excitatory input to the inferior olive is converted by a gap junction-dependent mechanism to synchronous output firing.
To quantify how multidendrite complex spike firing and bursting in PC ensembles might distinguish stimuli from spontaneous activity, we plotted the distributions (Figure 6A and 6B) of activity parameters (the number of dendritic arbors responding and the number of calcium transients per response) during sensory-evoked activity. In addition, plots of cumulative true positives vs. cumulative false positives, starting from the highest values of the parameters, defined receiver operating characteristic curves (ROCs; Figure 6D and 6E). An ROC based solely on the number of simultaneously active dendrites (Figure 6D) indicated an optimum accuracy in which 69 ± 13% of stimuli were detected with a false-positive rate of 17 ± 5%. Analysis of burst length alone gave a similar optimum accuracy of 64 ± 4%, with a false-positive rate of 14 ± 3% (Figure 6E). Therefore, both bursting and synchrony carry information about the occurrence of a sensory event.
To quantify the degree to which stimuli were encoded in activity patterns, we designed a two-stage decoder (see Methods for details). In the first stage, any spike in a PC enhanced the effect of subsequent spikes occurring in the same PC with a decaying time constant. In the second stage, the resulting responses from all PCs were summed through a sigmoidal input-output function (Figure 6C). The resulting output had an ROC (Figure 6F) that rejected 95 to 98% of spontaneously occurring events. In three fields of view containing 10, 12, and 20 dendrites, the decoding rule detected 87 ± 10% of of airpuffs. The highest accuracy (98%) and lowest false-positive rate (2%) occurred for the 20-dendrite case, suggesting that discrimination was limited by the number of dendrites monitored. Thus event-related information is present in the ensemble activity patterns of PC dendrites.
Our findings show that Purkinje cells (PCs) are co-activated in microbands of many neighboring dendritic arbors at once. Correlations among PCs in microbands were high enough to accurately represent single events. Correlations were similar in amplitude and structure when measured with line scans and frame scans, indicative of synchrony on the time scale of at most a few milliseconds, and were sensitive to gap junction blockers. Our measurements furthermore show that complex spike activity is organized into microbands with a characteristic thickness of 30 to 100 microns. This distance provides a scale for the microzonal organization of the cerebellum.
Previous studies using anatomical tracing (Groenewegen et al., 1979; Pijpers et al., 2005; Sugihara et al., 2001), antigen staining (Herrup and Kuemerle, 1997; Sugihara and Shinoda, 2007), electrophysiological recording (Bell and Kawasaki, 1972; Sasaki et al., 1989), and low-resolution imaging (Chen et al., 1996; Dunbar et al., 2004) revealed a parasagittal organization of climbing fiber (CF) projections into bands several hundred microns thick (Chen et al., 1996; Oscarsson, 1979). We do not know at present whether microband boundaries, which are more closely spaced, coincide with one or more of the previously found types of boundary. Reconciling these various observations of zonation will require further investigation.
Microbands of PCs comprise one component of a three-part system connecting Purkinje cells, the inferior olive, and the deep nuclei (Apps and Garwicz, 2005; Sugihara and Shinoda, 2007). The olivonuclear projection links well-defined subregions of the olive to counterparts in the deep nuclei, which in turn send a reciprocal connection back to the inferior olive (Voogd and Glickstein, 1998). Each olivonuclear axon gives rise to multiple CFs that innervate a parasagittal “microzone” of PCs (Oscarsson, 1979). The organization of the projection from synchronized olivary neurons to the cerebellar cortex would account for the local correlations that we have observed. Also, since calcium transients in PCs closely reflect activity in olivary neurons, the activity patterns we observe are also transmitted as direct excitation to neurons of the cerebellar nuclei via the olivonuclear pathway.
Thus olivary neurons can influence the deep cerebellar nuclei in two ways, by indirect disynaptic inhibition via PCs and by direct excitatory synaptic connections. This circuit arrangement provides several means by which olivary synchrony could be processed in the cerebellar cortex and nuclei. First, synchronous complex spiking might trigger powerful inhibitory responses in nuclear cells. Each olivary axon distributes approximately 10 CFs arranged parasagittally across multiple folia (Hrycyshyn et al., 1989; Sugihara et al., 1999). Therefore an observed microband of 3–19 dendrites is likely to represent as many as several hundred additional simultaneously firing PCs outside the field of view. Each PC axon in turn projects to dozens of deep nuclear neurons (Palkovits et al., 1977), and PCs outnumber deep nuclear neurons by about 20-fold (Alvarez-Otero et al., 1996; Caddy and Biscoe, 1979; Gould and Rakic, 1981). Thus a deep nuclear neuron may receive input from up to several hundred PCs. Consistent with this hypothesis, olivary activation has been shown to trigger large IPSPs in deep nuclear neurons as in vivo by whole-cell recording (H. Jorntell, personal communication).
Microbands of simultaneously active PCs may have additional effects beyond simple inhibition. Each complex spike is followed by a pause in simple spiking that lasts tens of milliseconds, thus briefly vetoing the influence of the mossy fiber/granule cell pathway (Steuber et al., 2007). The pause is often followed by a depolarizing rebound (Molineux et al., 2008); in addition, a second depolarizing effect arises from direct monosynaptic excitation (Llinas and Muhlethaler, 1988) since each olivary neuron projects directly to the deep nuclei (Apps and Garwicz, 2005; Voogd and Glickstein, 1998). Thus synchrony among olivary neurons may act through several routes to evoke a strong and stereotyped effect on nuclear neurons that mixes inhibition, excitation, and silencing or modulation of simple spikes.
In addition to providing a way of distinguishing stimulus-evoked complex spike events from spontaneous firing, synchrony also provides a way of combining unreliable single-PC responses to make a more reliable ensemble response. In addition, meaning may be conveyed by the specific combinations in which PCs fire, either within or across microbands.
In awake animals, synchrony is a prominent feature of complex spike-based signaling. Lang et al. (1999) reported that awake animals show slightly lower complex spike firing rates but similar distance-dependent correlations as compared with ketamine/xylazine anesthesia. However, ketamine/xylazine anesthesia has also been reported to depress evoked climbing fiber responses as monitored by field potential recording in decerebrated rats (Bengtsson and Jorntell, 2007). It remains to be determined how synchrony will be manifested on short distance scales under awake conditions.
Awake patterns of PC activation are potentially more complex than the anesthetized case. Under anesthesia, sensory-evoked microbands follow very similar boundaries as those observed from spontaneous activity. If olivary gap junctions are concentrated in glomeruli (Sotelo et al., 1974), olivary neurons receiving common synaptic drive might contribute to a single microband of PCs with well-defined anatomical boundaries. The similarity suggests that in our experiments, external excitatory drive is not sufficient to overcome the synchronizing effects of electrical coupling. However, under some conditions microband structure might be modulated by external excitation, as well as reciprocal inhibitory input from the cerebellar nuclei to the inferior olive (de Zeeuw et al., 1989; Lang, 2002). Consistent with this idea, we found that pairs of neighboring bands were more strongly correlated and had more similar probabilities of sensory response than more widely spaced microbands. It remains to be seen whether temporal variation in nuclear firing can modulate synchronization across multiple microbands.
Microbands fit into the microzone model of cerebellar organization (Oscarsson, 1979), in which projections among the inferior olive, PCs, and deep nuclei are thought to form precisely interconnected modules that can work separately or in concert (Lang et al., 1996; Welsh et al., 1995). A teaching role for the CF pathway has been suggested by the fact that it drives associative long-term plasticity at PC synapses after many pairings (Coesmans et al., 2004; Wang et al., 2000). Microband synchrony provides information in a single trial that could be useful for online function and also provide a teaching signal to the deep nuclei (Ohyama et al., 2006). Synchrony-based coding suggests that moment-to-moment guidance and teaching may coexist as roles for the inferior olive in processing sensation and refining movement and cognition.
We thank S.J. Cruikshank for advice on mefloquine sources, the National Cancer Institute for a gift of mefloquine, J.I. Simpson, E.F. Civillico, T.M. Hoogland, and D.W. Tank for reading the manuscript, and members of the Wang laboratory for advice and discussion. This work was supported by National Insitutes of Health grant R01 NS045193, a National Science Foundation Career Development Award, a Distinguished Young Investigator Award from the W.M. Keck Foundation, the Human Frontier Science Project, the National Alliance for Autism Research, and the New Jersey Governor’s Council on Autism (S.S.-H.W.).