A region of the brain known as the cerebellum plays a key role in learning how to anticipate an event. For example, if you know that a puff of air is going to be directed at your eye, it's a good idea to close it in advance. However, how much you need to close it depends on how strong that puff of air is. A very strong puff might require closing the eye completely to protect it. In contrast, it is probably better to only partially close the eye if you know a lighter puff of air is coming, so that you can still see.

Extensive research has focused on how neurons in and around the cerebellum work together to achieve this goal. When an event—such as a puff of air—occurs, signals are sent to large neurons in the cerebellum, called Purkinje cells, by ‘climbing fibers’. However, climbing fibers were thought to be able to respond in only two ways: either they fire in a single burst to signal that an event has occurred, or they don't fire. It was therefore unclear how the finer details of the event (for example, the strength of the puff of air) are transmitted to the cerebellum.

Najafi et al. imaged the level of calcium in the cerebellum of mice, as this indicates how active the neurons are. When a puff of air was directed at the eyes of the mice, Najafi et al. saw that the size of the response of the Purkinje cells corresponded with how big the puff of air was. Najafi et al. show that the size of this response, which is based mostly on input from the climbing fibers, is also influenced by input from an additional unknown source.

These findings show that Purkinje cells of the cerebellum receive detailed information about the nature of an event, such as a puff of air. What remains to be seen is whether the cerebellum uses this information to learn the correct response, that is how hard to blink to avoid the expected puff.

The climbing fiber (CF) input to Purkinje cells (PCs) plays a key role in theories of cerebellar learning (Houk et al., 1996; Ito, 2000) by providing a teaching signal that sounds the alarm when an unexpected sensory event is encountered (Simpson et al., 1996; De Zeeuw et al., 1998; Ito, 2013). Support for this hypothesis comes from studies of Pavlovian eyeblink conditioning (Medina et al., 2000), a simple associative task in which subjects learn to blink to an initially neutral cue if it is repeatedly paired with a blink-eliciting instructive stimulus, such as a periocular airpuff. Previous work has shown that some CFs fire a burst of spikes when the unexpected periocular airpuff is delivered (Sears and Steinmetz, 1991; Nicholson and Freeman, 2003), and that this signal is sufficient for conditioning (Mauk et al., 1986; Thompson et al., 1998). All of these studies indicate that CFs are an important source of instructive signals to the cerebellum. However, we do not understand how CF signals encode even the most basic stimulus features such as the strength of the periocular airpuff, which has a major impact on the magnitude and the rate of learning (Spence, 1953; Smith, 1968).

CFs have peculiar physiological properties that have inspired a number of hypotheses about the underlying neural code (De Zeeuw et al., 2011; Najafi and Medina, 2013). CFs fire bursts spontaneously at ∼1 Hz (Thach, 1968), a low rate that is barely modulated during sensory stimulation (Simpson et al., 1996). Indeed, CFs are often described as binary because they respond by either not firing at all or firing a single burst regardless of how strongly they are stimulated (Crill, 1970; Gibson et al., 2004). Another peculiarity is that in the adult cerebellum, each PC is innervated by only one CF (Simpson et al., 1996). The CF-PC synapse is one of the most powerful and reliable in the brain (Schmolesky et al., 2002; Ohtsuki et al., 2009): each time the CF fires a burst, it evokes in PCs both a burst of sodium spikes in the soma known as a complex spike (Eccles et al., 1966; Thach, 1968), and a massive calcium-based spike in the dendrite (Llinás and Sugimori, 1980).

Based on these observations, it has been suggested that analog information may be encoded probabilistically, in the total number of bursts generated by an individual CF across many repeated presentations of the same stimulus (Fujita, 1982; Kenyon et al., 1998). Others have pointed out that sensory events synchronize CFs (Llinás and Sasaki, 1989; Lou and Bloedel, 1992; Wylie et al., 1995; Ozden et al., 2009; Schultz et al., 2009; Wise et al., 2010), which raises the possibility that stimulus information may be available in the precise timing of CF inputs (Schweighofer et al., 2004; Van Der Giessen et al., 2008), or in the level of co-activation in the CF population (Ghosh et al., 2011; Tokuda et al., 2013). Recent findings suggest an additional possibility: analog information, like the strength of an instructive stimulus, might be encoded post-synaptically by modulating the size of the PC response to individual sensory-driven CF bursts (Maruta et al., 2007; Najafi et al., 2014; Yang and Lisberger, 2014).

We have imaged PC dendrites of awake mice to investigate how CF-triggered calcium events encode information about the strength of a periocular airpuff stimulus. Because each PC receives input from a single CF (Simpson et al., 1996), we were able to discriminate the post-synaptic calcium events corresponding to individual pre-synaptic CF bursts and analyze their amplitude, timing and probability. Two-photon imaging also allowed us to analyze ensembles of PC dendrites whose CF inputs were co-activated by the periocular airpuff. Thus our experiments provide a unique opportunity to evaluate a variety of calcium-based codes in PCs, both at the individual dendrite and population levels.

We used a two-photon microscope to image calcium signals triggered by sensory-driven activation of climbing fiber (CF) inputs to Purkinje cell (PC) dendrites of awake mice. Mice were head-fixed on top of a freely rotating cylindrical treadmill and allowed to locomote in place while we delivered airpuffs of varying pressures and durations to the periocular area. In some experiments we used airpuffs of four different durations (12 experiments, 4 mice, 97 dendrites; durations: 8, 15, 30, 45 ms; pressure: 30 psi); in other experiments we used airpuffs of two different pressures (6 experiments, 3 mice, 39 dendrites; pressures 10, 50 psi; duration: 30 ms). We will refer to these two datasets as duration and pressure data, respectively.

CF-triggered calcium events in PC dendrites

As in previous reports (Sullivan et al., 2005; Ozden et al., 2008), PC dendrites in our experiments appeared as parasagittally aligned, tube-like structures (Figure 1A), in which large calcium transients (Figure 1B, circles) occurred spontaneously and in response to periocular airpuff stimuli (Figure 1B, triangles). We have previously shown that these calcium transients are triggered in each individual PC dendrite by activation of its one-and-only climbing fiber (CF) input, which also evokes a complex spike in the PC somata (Ozden et al., 2008). Hereafter, we will use the term ‘calcium event’ to refer to these CF-triggered calcium transients.

Figure 1

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A number of features confirmed the CF origin of the calcium events in our experiments. First, they occurred spontaneously at about 1 Hz (0.4–1.4 Hz; median 0.7 Hz; Figure 1C), which is similar to the characteristic spontaneous firing rate of CFs reported previously in awake animals (Thach, 1968). Second, they had a fast rise (∼10 ms Figure 1D), as observed for CF-triggered signals in other calcium imaging studies (Miyakawa et al., 1992; Eilers et al., 1995; Schmidt et al., 2003), and a slower decay t_1/2 of 74 ± 13 ms (mean ± SD), which is in the midrange of previously observed kinetics using synthetic indicators (decay t_1/2 = 25–170 ms; [Sullivan et al., 2005; Sarkisov and Wang, 2008; Ozden et al., 2009; Kitamura and Häusser, 2011]). Third, the probability of observing two spontaneous calcium events at the same time was highest for adjacent PC dendrites, and decreased rapidly as the mediolateral distance between dendrites increased (Figure 1E, black). This finding is consistent with previous studies demonstrating the prevalence of synchronous CF input to neighboring PCs in the same parasagittal microzone (Bell and Kawasaki, 1972; Sasaki et al., 1989; Ozden et al., 2009; Schultz et al., 2009).

Location of imaging sites

We imaged 101 sites on the surface of cerebellar cortex in 22 mice, including paravermal locations in lobules V, VI, and more lateral locations in simplex (Figure 2A,B). We were less frequently able to image the most medial parts of simplex due to the high density of blood vessels in that area. Consistent with the location of trigeminal CFs reported in previous studies (Miles and Wiesendanger, 1975a, 1975b; Manni and Petrosini, 2004), we found that many dendrites in the paravermal regions of lobules V and VI responded to periocular airpuff stimulation with a CF-triggered calcium event (Figure 2C,D). In contrast, dendrites on the surface of lobule simplex were mostly unresponsive, which is expected given the deep location of periocularly-related CF zones in this lobule (Hesslow, 1994; Mostofi et al., 2010; Heiney et al., 2014).

Figure 2

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As observed in electrophysiological work (Hesslow, 1994; Mostofi et al., 2010), we found two types of periocular PC dendrites that could be classified according to the receptive field properties of their CF inputs: some dendrites responded with a CF-triggered calcium event only after ipsilateral periocular airpuffs (Figure 2B,C), while others had bilateral CF receptive fields and responded after ipsi- and contralateral periocular airpuffs (Figure 2B,D). In all the analyses presented below, we only evaluated the data for ipsilateral airpuffs. Our results were the same for both types of dendrites.

CF probability

Previous studies indicate that the likelihood of eliciting a response in an individual CF is proportional to stimulus intensity (Eccles et al., 1972b; Bosman et al., 2010). Thus, we first examined if individual CFs encode information about the strength of the periocular airpuff probabilistically, across repeated presentations of the stimulus. The raster plots of all the PC dendrites in our entire duration dataset demonstrate that CF-triggered calcium events occurred more reliably as the duration of the airpuff was increased (Figure 3A bottom; top: average). On average across all the PC dendrites, we found that the probability of calcium events increased gradually with increasing airpuff duration (Figure 3B, left; two-way ANOVA: F[496] = 238.5, p < 0.0001; Tukey's HSD, p < 0.01 for all pairwise comparisons), and pressure (Figure 3B, right; two-way ANOVA: F[238] = 58.93, p < 0.0001; Tukey's HSD, p < 0.001 for all pairwise comparisons).

Figure 3

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The graded increase of calcium event probability with airpuff duration, which is shown averaged across all dendrites in Figure 3B, was evident in 58% of the individual dendrites (Figure 3C, top row), in which the probability and the stimulus duration increased with the same rank order. The remaining 42% of the dendrites were relatively unresponsive to all airpuffs below a certain threshold (Figure 3C, arrowheads), and responded with similar probability for all durations higher than the threshold (Figure 3C, rows 2–5). These latter CFs may encode duration information about stimulus strength in a binary manner, by providing a signal that tells the post-synaptic PC if the periocular airpuff lasted longer than a certain threshold. In summary, the response probability of individual CFs showed monotonic (i.e., non-decreasing) dependence on stimulus duration, with a dependency that ranged from graded to threshold-like.

CF latency

In agreement with previous electrophysiological reports of sensory-driven CFs (Ekerot et al., 1987; Kobayashi et al., 1998), we found that calcium events were evoked in PC dendrites at a wide range of latencies relative to the onset of the airpuff stimulus (onset latency: ∼25–150 ms; Figure 4A,D). Increasing the duration of the periocular airpuff resulted in progressively more long-latency calcium events (Figure 4A–C left; 67.1 ± 1.5, 71.8 ± 1.8, 78.8 ± 1.4, and 80.9 ± 1.4 ms for d1–d4 respectively; two-way ANOVA: F[393] = 11.85, p < 0.0001; Tukey's HSD: p < 0.05 except for d1–d2 comparison and d3–d4 comparison). The temporal jitter, as quantified by median absolute deviation from median latency (Figure 4C, right), was also reduced (23.3 ± 1.2, 21.1 ± 1.0, 19.3 ± 0.7, and 18.0 ± 0.8 ms for d1–d4 respectively; two-way ANOVA: F[393] = 5.42, p < 0.01; Tukey's HSD: p < 0.05 for d1–d3, d1–d4, d2–d4 comparisons). The analysis shown in Figure 4B confirmed that long-duration airpuffs evoked significantly more calcium events than short-duration airpuffs in the interval 75–150 ms after the periocular stimulation (Figure 4B; Kolmogorov–Smirnov test, p < 0.0001) but not in the interval 0–75 ms (Figure 4B; Kolmogorov–Smirnov test, p = 0.8). In summary, responses to airpuffs of increased duration are characterized by a higher likelihood of calcium events as the stimulus continues over time.

Figure 4

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To test whether CF timing can provide a code for stimulus strength under conditions of constant stimulus duration, we varied the pressure of the airpuff. This led to a modest reduction in onset latency (81.3 ± 2.4 vs 79.6 ± 3.4 ms for p1 and p2 respectively) that was not significant (Figure 4D–F left; two-way ANOVA: F[134] = 0.98, p = 0.3), and did not alter temporal jitter (Figure 4F right; two-way ANOVA: F[134] = 0.13, p = 0.7). Higher-pressure airpuffs evoked more calcium events throughout the analysis window, both in the 0–75 ms interval (Figure 4E; Kolmogorov–Smirnov test, p < 0.01), and in the 75–150 ms interval (Figure 4E; Kolmogorov–Smirnov test, p < 0.001). These findings indicate that the onset latency of an individual CF input cannot be used to encode the pressure of the airpuff. However, additional information about stimulus strength may be available in the timing of the CF population (population co-activation). This question is addressed next.

CF co-activation

Previous work has demonstrated that groups of CFs converging on the same zone of cerebellar cortex become synchronized in response to sensory stimulation (Lou and Bloedel, 1992; Ozden et al., 2009; Schultz et al., 2009; Wise et al., 2010; Ghosh et al., 2011). We examined if the level of co-activation in the CF population provides information about the strength of the periocular airpuff stimulus. In 16 experiments in which we were able to image at least six PC dendrites simultaneously (Figure 5), we found that the number of synchronized calcium events in a 150 ms window after stimulus onset increased in response to airpuffs of longer durations (Figure 5A,B, top: two-way ANOVA, F[4394] = 199.75, p < 0.0001; Tukey's HSD, p < 0.05 for all pairwise comparisons), and higher pressures (Figure 5B, bottom: two-way ANOVA, F[2209] = 106.56, p < 0.0001; Tukey's HSD, p < 0.0001 for all pairwise comparisons).

Figure 5

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Since stronger airpuffs increase the probability of calcium events in individual PC dendrites (Figure 3), it is possible that the gradual increase in the number of synchronized calcium events (Figure 5A,B) simply reflects an increase in probability in a group of otherwise independent dendrites. To assess this possibility, we measured the joint probability for every pair of dendrites in each one of our experiments, that is the probability of observing a CF-triggered calcium event in both dendrites within the same 150 ms time window, and compared it to the joint probability expected for independent dendrites (P_ij = P_i × P_j, where P_i and P_j represent the calcium-event probability of dendrites i and j in that same time window). We found that joint probability deviated significantly from the independence assumption for all airpuff strengths (Figure 5C; two sample t test, p < 0.001). We call this deviation ‘extra synchrony’ because it represents the synchrony beyond that expected solely from the calcium-event probability of two independent dendrites. Figure 5D shows that there was a gradual boost in the amount of extra synchrony as the airpuff duration or pressure was increased (Duration data: two-way ANOVA: F[4361] = 113.49, p < 0.0001; Tukey's HSD: p < 0.0001, except for d3–d4 comparison. Pressure data: two-way ANOVA: F[2136] = 10.27, p < 0.0001; Tukey's HSD: p < 0.05, except for p1–p2 comparison). In other words, the degree to which CFs are dependent on each other scales up smoothly with their overall response probability. These results suggest that CF co-activation may be controlled upstream, perhaps in the inferior olive, in a way that provides information about stimulus strength at the level of the PC population.

Size of CF-triggered calcium events

We have recently shown that the amplitude of CF-triggered calcium events is enhanced during sensory stimulation (Najafi et al., 2014). Here, we examined if the magnitude of this sensory-driven enhancement is graded according to periocular airpuff strength. Compared to the average fluorescence traces for spontaneous calcium events (Figure 6A, ‘sp’), the average fluorescence traces for sensory-driven calcium events revealed a gradual enhancement as the duration or the pressure of the airpuff was increased (Figure 6A top; only duration data is displayed). Note that the fluorescence trace of each individual dendrite was normalized to the peak value of its mean spontaneous calcium event (‘Materials and methods’). However, calcium events occurred with variable latency after the periocular airpuff, and for this reason the peaks of the average fluorescence traces in Figure 6A are substantially lower than ‘1’ (for comparison purposes, the ‘sp’ trace is plotted with the same temporal jitter as the d1–d4 traces).

Figure 6

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To quantify the gradual enhancement in Figure 6A (top), we measured the size of each individual calcium event by computing the integral of its fluorescence trace over a 100 ms time window after the peak (‘ΔF/F-integral’), and normalizing this value to the average ΔF/F-integral of all the spontaneous calcium events of the corresponding PC dendrite. Note that we only examined the fluorescence traces of individual calcium events and excluded trials in which the periocular stimulation resulted in two or more calcium events separated from each other by less than 100 ms (this occurred in <2% of trials and did not affect our results). This analysis confirmed that periocular airpuffs of longer duration and higher pressure evoked progressively larger calcium events (Figure 6A, bottom; Duration data: two-way ANOVA: F[496] = 80.74, p < 0.0001; Tukey's HSD: p < 0.05 except for d2–d3 comparison. Pressure data: two-way ANOVA: F[238] = 62.88, p < 0.0001; Tukey's HSD: p < 0.01 for all pairwise comparisons). Thus, the calcium elevation evoked in PC dendrite after activation of its CF input provides information about the strength of peripheral stimulation.

Our results demonstrate that climbing fibers (CFs) represent information about the strength of a periocular airpuff in a number of ways, both at the individual-CF and population level. Consistent with previous reports of CF activity in awake animals (Gibson et al., 2004), we found no evidence for rate coding in our experiments: each presentation of the periocular airpuff resulted in either zero or one calcium event in the Purkinje cell (PC) dendrite, which would indicate that the pre-synaptic CF was activated at most once in virtually all trials (multiple activation in <2% of all trials). In the absence of a rate code, our results indicate that analog information about airpuff strength was encoded in: (1) the probability and latency distribution of individual CF inputs across repeated stimulus presentations, (2) the amplitude of the stimulus-evoked calcium event in individual PC dendrites, and (3) the level of co-activation of the CF population.

Below, we evaluate these different codes, and make a number of predictions about the underlying mechanisms and their potential role in regulating the efficacy of instructive signals during cerebellar learning.

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Author details

1. Farzaneh Najafi

   Department of Biology, University of Pennsylvania, Philadelphia, United States

   Present address

   Cold Spring Harbor Laboratory, Cold Spring Harbor, United States

   Contribution

   FN, Designed experiments, Established behavioral and imaging set-up, Acquired data in laboratory of Dr Samuel Wang, Developed analysis, Analyzed data, Wrote first draft of manuscript, Edited manuscript

   Competing interests

   The authors declare that no competing interests exist.

2. Andrea Giovannucci

   1. Department of Molecular Biology, Princeton University, Princeton, United States
   2. Princeton Neuroscience Institute, Princeton University, Princeton, United States

   Contribution

   AG, Designed experiments, Established behavioral and imaging set-up, Developed analysis, Edited manuscript

   Competing interests

   The authors declare that no competing interests exist.

3. Samuel S-H Wang

   1. Department of Molecular Biology, Princeton University, Princeton, United States
   2. Princeton Neuroscience Institute, Princeton University, Princeton, United States

   Contribution

   SS-HW, Designed experiments, Developed analysis, Edited manuscript

   Competing interests

   The authors declare that no competing interests exist.

4. Javier F Medina

   Department of Psychology, University of Pennsylvania, Philadelphia, United States

   Contribution

   JFM, Conception, Designed experiments, Developed analyses, Wrote first draft, Edited manuscript

   For correspondence

   jmed@psych.upenn.edu

   Competing interests

   The authors declare that no competing interests exist.

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