Practice makes perfect in many areas of life, such as playing sport or even just drinking coffee from a cup without spilling any. Our brains can learn and improve these motor skills through trial, error and learning, with such “motor learning” depending on the cerebellum, a part of the brain that helps to coordinate all kinds of movements.

Motor learning is a product of the organization of the cerebellar circuit, which is well understood, and the “plasticity” in the synapses that determine how cerebellar neurons interact with each other. The cerebellum contains cells called Purkinje cells that receive distinctive inputs from two pathways: a pathway involving inputs from many parallel fibers, which convey signals related to sensory events or motor commands; and a pathway involving input from a single climbing-fiber, which conveys signals from a part of the brain called the inferior olive nucleus.

Research on slices of brain has revealed many sites and forms of cerebellar plasticity that could participate in motor learning. In one form of plasticity, the strength of the synapses between the parallel fibers and the Purkinje cell can be changed when a signal sent along the climbing fiber arrives the Purkinje cell.

Yang and Lisberger have now taken the next step by studying the cerebellum of a monkey as it performs a motor learning task. Remarkably these experiments show that the climbing fiber inputs cause plasticity of Purkinje cell activity, just as happens in the experiments on brain slices. Further, some learning in the cerebellum restricts further learning, so that the cerebellum puts boundaries on its own learning. Overall the results make clear how learning is a property of groups of neurons working together in a circuit, rather than simply of changes in the strength of specific synapses.

By shedding light on what happens in the cerebellum during short-term motor learning, the work of Yang and Lisberger will benefit efforts to understand how the cerebellum is involved in motor learning on all time scales.

Learning is an adaptive change in behavior that results from ‘plasticity’ in the cellular mechanisms of synaptic transmission and/or spike generation in the nervous system. Our thinking about how the brain learns has been influenced heavily by the discovery of a form of synaptic plasticity called long-term potentiation (aka ‘LTP’). Through research on reduced preparations, and electrical activation of neural pathways in artificial patterns, we have a remarkable catalog of multiple forms of cellular plasticity in neurons. But a fundamental bridge is missing. We need to monitor the plasticity that occurs in a known circuit when an animal is participating in a learning task, to reveal what actually happens in the brain during behavioral learning.

Our premise is that behavioral learning involves multiple forms of plasticity at multiple sites in an essential neural circuit for the behavior. Different forms of plasticity may be deployed at different sites over different time courses during learning. Circuit dynamics will play a key role in converting plasticity to learning. Thus, it is critical to understand when and where different forms of plasticity contribute to learning, and how circuits transform plasticity into changes in neural activity patterns. We start by analyzing a form of learning that occurs on the time scale of a single learning trial, with the premise that the analysis of short-term events will provide insight into circuit dynamics and plasticity that might play roles during long-term learning.

The cerebellum provides an excellent brain site to ask what happens in a neural circuit during learning. Many forms of cellular plasticity are present in the cerebellum (Hansel et al., 2001; Zheng and Raman, 2010; Carey, 2011; Gao et al., 2012). The cerebellar circuit is understood well, and there is a prominent theory of cerebellar motor learning (Marr, 1969; Albus, 1971; Ito, 1972) based on climbing-fiber induced long-term depression of the synapses from parallel fibers to Purkinje cells (Ito and Kano, 1982). Research in intact, learning animals using neural recordings, inactivation methods, and genetically-altered mice supports the cerebellar learning theory broadly (e.g., Gilbert and Thach, 1977; Lisberger, 1994; Medina et al., 2000; Christian and Thompson, 2003; van Alphen and de Zeeuw, 2002; Boyden et al., 2004; Blazquez et al., 2006; Ke et al., 2009; Wulff et al., 2009). As research on motor learning has advanced, we have come to understand that learning occurs at multiple neural sites and over several time scales (Medina and Mauk, 2000; van Alphen and de Zeeuw, 2002; Jorntell and Ekerot, 2003; Boyden et al., 2004; Yang and Lisberger, 2010).

In the present paper, we use learning in the smooth pursuit eye movements of awake, behaving monkeys to unravel how a neural circuit creates short-term cerebellar learning (Kahlon and Lisberger, 1996, 2000; Medina et al., 2005; Medina and Lisberger, 2008; Yang and Lisberger, 2010). The cerebellar circuit (Figure 1) includes a mossy-fiber/granule-cell/parallel-fiber pathway to Purkinje cells, and a climbing fiber pathway that originates in the inferior olive (IO). The parallel-fiber inputs cause conventional action potentials in Purkinje cells known as ‘simple-spikes’. An action potential on the climbing-fiber input causes an unconventional, long-duration event known as a ‘complex-spike’ or ‘CS’. Our formulation of the cerebellar circuit includes plasticity of Purkinje cell simple-spike responses driven by conjunction of parallel fiber and climbing fiber inputs (light pink shading in Figure 1), a disynaptic pathway from Purkinje cells to the inferior olive that includes two inhibitory synapses (light gray shading in Figure 1), and a disynaptic pathway from Purkinje cells to motoneurons.

Figure 1

Download asset Open asset

We show how the circuit in Figure 1 can explain a number of related observations on the spiking activity of Purkinje cells during short-term behavioral learning. First, we demonstrate that simple-spike firing rate predicts the probability of a complex-spike response to an instruction on a given trial, and we suggest that the disynaptic inhibitory pathway from Purkinje cells to the inferior olive causes this correlation (gray shading in Figure 1, De Zeeuw et al., 1998; D’Angelo, 2010; Bengtsson and Hesslow, 2006). Feedback from Purkinje cells might allow the cerebellum to control some of the error signals that guide synaptic plasticity in the cerebellum (Mauk and Donegan, 1997; Kenyon et al., 1998; Miall et al., 1998; Bengtsson and Hesslow, 2006). Second, we provide evidence that complex-spike-linked trial-over-trial depression of simple-spike responses (Medina and Lisberger, 2008) is an expression of short-term plasticity (pink shading in Figure 1), presumably in the mossy-fiber/parallel-fiber input pathways. Our paper suggests how plasticity interacts with a neural circuit during a form of short-term motor learning, and outlines circuit dynamics that also may play a role in long-term learning.

One of our previous papers (Medina and Lisberger, 2008) demonstrated that a complex-spike (CS) response on one learning trial leads to a ‘trial-over-trial’ depression of simple-spike responses on the subsequent trial. The depression is expressed selectively over a brief interval centered at the time when the instruction occurred. Another of our papers (Yang and Lisberger, 2010) showed that pursuit eye movements show ‘trial-over-trial’ learning when a monkey pursues a target motion with a change in direction. The eye velocity on one trial undergoes a transient and properly-timed deflection that takes the eyes in the direction of the change in target motion on the previous trial.

Our earlier findings, and the techniques they used, have set the stage for the approach deployed here. Our long-term goal is to understand what happens in the brain to cause motor learning when an instructive target motion is repeated many times. We start toward that goal in the present paper through analysis of events that occur after a single instructive stimulus. We put the approaches from our prior papers together in a way that (i) elucidates the multiple components, including CS-linked short-term plasticity, that cause trial-over-trial depression of simple-spike firing rate, and (ii) provides neural and behavioral evidence that the cerebellum may control its own instructive inputs in a way that would modulate cerebellar learning capacity.

The learning paradigm

We use an experimental design that causes learned changes in the direction of smooth pursuit eye movements (Medina et al., 2005; Yang and Lisberger, 2010). In other words, visual targets start moving in one direction and, 250 ms later, undergo a change in direction. Pursuit learns to anticipate the change in target direction, leading to a small deviation in the direction of eye velocity after a single learning trial, and larger learned changes over blocks of 100 identical learning trials.

Figure 2A uses traces of eye position and velocity as a function of time to provide details about the structure of each learning target trajectory. Target motion began at a speed of 20 deg/s downward, in what we will call the ‘pursuit’ direction. As illustrated in the vertical position traces, the start of the downward ramp of target motion was accompanied by small upward displacement of the target to obviate the need for a catch-up saccade, thereby providing uncontaminated initiation of downward pursuit. Then, 250 ms after the onset of target motion, the target underwent an ‘instructive’ change in direction through the addition of a rightward or leftward ramp of motion at 30 deg/s for 400 ms (horizontal position traces in Figure 2A). The brief addition of horizontal target motion during downward target motion created learning target trajectories in a two-dimensional position space shown by the zigzags at the top of Figure 2A.

Figure 2

Download asset Open asset

In most of the experiments reported here, we used a fixed pursuit direction, but delivered instructions that comprised changes in direction randomly in one of the two directions along the orthogonal, learning axis. This ‘random-order’ learning paradigm has the advantage that it allows us to study trial-over-trial learning while preventing any long-term learning. Trial-over-trial learning causes the eye movement on any given ‘test’ trial to possess a small, properly-timed deflection that takes eye velocity in the direction of the change in target motion on the prior ‘instruction’ trial. In the examples in Figure 2A, the small rightward deflection of horizontal eye velocity (arrowhead) in the red trace (‘n-1’ trial) was learned as the result of a rightward instruction in the prior trial (‘n-2’, not shown); the leftward deflection in the blue trace (‘n’ trial) was learned as the result of the leftward instruction on the ‘n-1’ trial. Because the eye velocity responses start before the instruction, they must be related to the instruction in the prior trial, rather than to that in the current trial.

We realize that trial-over-trial learning is not an adaptive response during a random-order learning block, because it causes an inappropriate learned response half of the time. We also realize that the trial-over-trial effects we report in the present paper probe only the initial phases of behavioral learning. Still, we regard the random-order paradigm as a means to get ‘under-the-hood’ and determine how neural circuits transform cellular changes into behavioral learning in a limited time frame. We expect that the phenomena we are studying also play a role in more natural learning conditions, when the same instructive stimulus occurs repeatedly.

Relationship between simple-spike firing rate and complex-spike probability

Our first observation suggests a causal link between simple-spike firing rate and the probability that a CS response occurs in response to an instruction. Simple-spike firing rate at the time of an instruction was ∼5 spike/s higher on average depending on whether or not a CS occurred later in the trial in response to an off-direction instruction. The relationship between simple-spike and CS responses was restricted to the time interval surrounding the onset of the instruction (vertical dashed line in Figure 3C,D), suggesting that the relationship is not caused by low frequency fluctuations of attention or other top-down influences. Note that the increased simple-spike firing rate preceded the time of the CS response and therefore cannot be attributed to a trivial explanation such as bleed-through of the CS spike into the train of spikes used to calculate simple-spike firing rate.

Figure 3

Download asset Open asset

Similar analysis of the eye velocity responses revealed a tiny difference of ∼0.1 deg/s that was present before the instruction and could be seen only in high-gain records (Figure 3A). The difference in eye velocity probably was too small to cause the presence vs absence of a CS response to the instructive stimulus. Low-gain eye velocity records (Figure 3B) showed that the eye movement responses to the instruction were not related the presence vs absence of a CS response, a control that argues against the possibility that some trials lacked CS responses simply because the monkey was not attending or was being lazy.

Figure 3C,D show that the simple-spike firing rate of a Purkinje cell before an instruction is related to whether or not an off-direction instruction evokes a CS on that learning trial. Because the variation in simple-spike firing rate is present before the CS response, we suspected that simple-spike firing rate could causally modulate the probability of a CS. However, the analysis described so far stops short of assessing how strongly simple-spike firing affects CS probability, and therefore also does not give insight into the possible strength of the proposed modulation. To assess the strength of the relationship, we next used simple-spike firing as the independent variable and assessed its impact on the probability of a CS response for each Purkinje cell. To do so, we created distributions of simple-spike firing rate in each trial averaged across the analysis interval (light pink shading on traces in Figure 3E,F). Then, we trisected the distributions at the mean simple-spike firing rate plus/minus 0.44 standard deviations, grouped the trials for each third of the distribution, and computed the probability of a CS response to the instruction (analysis interval shown by light gray shading in Figure 3E,F) for each third of the distribution.

Each neuron showed a clear relationship between the probability of an instruction-evoked CS and the average simple-spike firing rate at the time of the instruction (Figure 3E). The clouds of points for different neurons move from lower left to upper right as we step from the trials with the lower 1/3 of simple-spike firing rates (yellow symbols) through the trials with the middle 1/3 (blue symbols) to the trials with the upper 1/3 (red symbols). The trend appears in the scatter plot showing three connected symbols for each of the 90 Purkinje cells in our sample, and in the marginal histograms. On average, the magnitude of simple-spike firing rate averaged 66, 84, and 103 spikes/s for the three segments of the distributions and the probability of a CS response averaged 0.26, 0.34, and 0.44. Correlation analysis of the cluster of points in Figure 3E yielded a statistically-significant correlation of 0.33 (p<<0.001). The slope of the means from the marginal histograms indicated that one spike/s of simple-spike firing rate is associated with a difference of 0.005 in the probability of a CS response to the instruction. We conclude that simple-spike firing rate may modulate the probability of CS responses, but weakly.

Another fact argues that simple-spike firing rate merely modulates CS probability and does not exert obligatory control. For the interval at the end of the pulse of instructive target motion in the on-direction for simple-spike responses, the relationship is quite weak between the probability of a CS and simple-spike firing rate at the time of the instruction (Figure 3F). The cluster of points in Figure 3F yielded a correlation of −0.028 that was not statistically significant (p=0.65) In this interval, stopping the target during on-direction eye motion causes image motion (relative to the retina) in the off-direction and evokes the CS responses. But this is not a strong learning situation, and that may explain the absence of a relationship between CS probability and simple-spike firing rate.

We have named the relationship between CS probability and simple-spike firing rate ‘same-trial facilitation’, to distinguish it from CS-linked ‘trial-over-trial depression’ (e.g., Medina and Lisberger, 2008). The existence of same-trial facilitation (Miall et al., 1998) raises the possibility we will consider in our ‘Discussion’, that same-trial facilitation reflects an important feature of cerebellar learning (Mauk and Donegan, 1997; Kenyon et al., 1998).

Evidence for trial-over-trial plasticity in simple-spike firing

Our second observation shows that plasticity of simple-spike firing is linked to the occurrence of a CS response to an instruction. We showed in a prior publication that a CS response to an instruction on one trial is linked to a depression of simple-spike firing rate on the next trial (Medina and Lisberger, 2008). We demonstrated trial-over-trial depression there (and here) by dividing the stream of learning trials into pairs where the first trial of the pair delivered an off-direction instruction. In each pair, we called the first trial the ‘instruction’ trial, and the second trial a ‘test’ trial. We computed the millisecond-by-millisecond difference between the simple-spike firing rates on the two consecutive trials. We tagged the trial-over-trial difference in firing rate for each pair according to whether or not the instruction trial contained a CS response to the instruction. A ‘1-0’ pair, for example, meant that the instruction trial contained a CS response to the instruction and the test trial did not. We then averaged the trial-over-trial changes in simple-spike firing rate, first for all like pairs of trials within a single Purkinje cell, and then across Purkinje cells.

Trial-over-trial depression in simple-spike firing rate appeared if the instruction trial contained a CS response to the instruction and the test trial did not (Figure 4A, red trace, ‘1-0’ pairs); trial-over-trial depression did not appear when neither trial contained a CS response (Figure 4A, blue trace, ‘0-0’ pairs). It was tempting to assume that the depression was caused by CS-linked plasticity of simple-spike firing. However, the existence of ‘same-trial facilitation’ means that trial-over-trial depression could appear simply because of elevated simple-spike firing rate on the instruction trial, but not on the test trial. Thus, our next step is to take advantage of a dramatically larger dataset than we had before (Medina and Lisberger, 2008) to show that CS-linked short-term plasticity is one component of trial-over-trial depression.

Figure 4

Download asset Open asset

We isolated a contribution of CS-linked plasticity by comparing the trial-over-trial depression of simple-spike firing for pairs of consecutive trials that both had CS responses (‘1-1’ pairs) with that for pairs of consecutive trials that both lacked CS responses (‘0-0’ pairs). Because the ‘1-1’ and ‘0-0’ pairs have the same CS response on each trial, they also should have the same amount of same-trial facilitation on each trial; same-trial facilitation would be ‘nulled’ and would not contribute to trial-over-trial depression. Even with the effect of same-trial facilitation nulled, the upper graph of Figure 4A shows a difference in trial-over-trial depression of about 5 spikes/s between ‘1-1’ pairs (green trace) and ‘0-0’ pairs (blue trace). We attribute this component of trial-over-trial-depression to CS-linked plasticity that occurs during trial-over-trial behavioral learning, because it persists after we control for same-trial facilitation.

Overall, Figure 4A shows a complicated progression of differences between the different-colored traces because it summarizes the combined effects of same-trial facilitation and CS-linked plasticity of simple-spike firing rate. We can see the effect of same-trial facilitation by comparing pairs of trials that had the same CS response on the instruction trial, to hold trial-over-trial plasticity constant, but different CS responses on the test trial. For example, the simple-spike firing rate was the same in both trials of the pair when neither included a CS response (‘0-0’), so the trial-over-trial change in firing rate was almost flat (Figure 4A, blue trace). When only the test trial included a CS response (‘0-1’, yellow trace), simple-spike firing rate was higher in the test trial and the trial-over-trial change in simple-spike firing rate was more positive. The same effect appears when a CS response always occurred in the instruction trial. The simple-spike firing rate was higher in test trials that contained a CS response (Figure 4A, ‘1-1’, green trace), and the trial-over-trial change in firing rate was more positive, compared to pairs that did not contain a CS response in the test trial (Figure 4A, ‘1-0’, red trace).

Finally, trial-over-trial learning in eye velocity (Figure 4D) is closely aligned to the trial-over-trial changes in simple-spike firing rate (Figure 4A) for the 4 pairs of trials, supporting a causal link between trial-over-trial depression in neural firing and trial-over-trial learning in behavior. As we have noted elsewhere (Medina and Lisberger, 2008), the fact that the learned eye velocities track the trial-over-trial changes in simple-spike firing rate implies that the CS responses are highly correlated across the Purkinje cell population. If the CS responses occurred with independent probabilities in different Purkinje cells, then the average across the population of Purkinje cells would be independent of the pattern of CS responses in the different pairs of trials. The learned eye velocity would be present for all pairs, and would not differ according to the pattern of CS responses.

To perform statistical testing, we averaged firing rate across the analysis interval for simple-spike firing rate in individual neurons. Comparison of different pairs revealed statistically significant differences among the four types of pairs of trials (multiple comparisons in a two-way ANOVA, n = 90 neurons, simple-spike firing, p<0.01; eye velocity, p<0.05).

Additional evidence for the existence of CS-linked plasticity during learning comes from analysis of trial-over-trial changes in simple-spike firing rate at the offset of on-direction instructive target motion. Same-trial facilitation is very weak at the offset of on-direction instructions (Figure 3F). However, comparison of the trial-over-trial changes in firing rate for ‘1-0’ pairs and ‘0-0’ pairs revealed about 5 spikes/s of CS-linked trial-over-trial depression in simple-spike firing rate (bottom graph in Figure 4A, also Medina and Lisberger, 2008). The difference in the firing rate averaged across the simple-spike analysis interval was statistically-significant (paired t-test, p=0.002, n = 90). The presence of trial-over-trial depression in conditions that lack same-trial facilitation, albeit with a slightly different time course, implies that trial-over-trial depression is caused partly by plasticity of simple-spike firing that is linked to CS responses.

Computational analysis of cerebellar operation during trial-over-trial depression and learning

Our data suggest that a number of features of cerebellar organization and function collaborate to create the specific fingerprint of cerebellar learning revealed in Figures 3 and 4. However, the most stringent test for the logic of our conclusions comes from analysis of a computational model that includes the features we think are important. The data we strove to mimic with the model were: the trial-over-trial changes in simple-spike firing rate and eye velocity for all pairs of trials with and without the CS responses to an instructive stimulus (Figure 4A,D); the absolute firing patterns for the relevant trios of trials (Figure 4B,C,E,F); and the relationship between CS probability and simple-spike firing rate (Figure 3).

We created a population of 1000 Purkinje cells and 100 inferior olive neurons and connected them according to the architecture outlined by the cartoon in Figure 5. The cartoon retains the two inhibitory synapses between Purkinje cells and inferior olive neurons to emphasize the sign of the putative pathway in the brain, even though the neuron in the deep cerebellar nucleus was not actually modeled (Equations appear in the ‘Materials and Methods’). The model incorporated a number of features that were designed to allow it to reproduce our data, and that were suggested by data from our research and others’:

• The simple-spike responses of each Purkinje cell varied from trial-to-trial. Each individual response, meant to reflect the simple-spike firing rate averaged across the analysis interval used for our data, was drawn from a distribution with a mean of 100 spikes/s and a standard deviation of 18 spikes/s, in agreement with our recordings (data not shown).

• The trial-to-trial variation in simple-spike firing rate was correlated at a level of ∼0.16 between pairs of model Purkinje cells. This level of neuron-neuron correlation enables the neuron-behavior correlations found 250 ms after the onset of pursuit by Medina and Lisberger (2007).

• Each inferior olive neuron provided a climbing fiber to 10 Purkinje cells (Sugihara et al., 2004 visualized at least 5).

• The probability that an off-direction change in target motion will evoke a response in a particular inferior olive neuron on a given trial is modulated by the simple-spike firing rate of floccular Purkinje cells on that trial. On-direction instructions never evoke the CS responses in model Purkinje cells.

• If a model Purkinje cell receives an input from its climbing fiber on a given trial, its simple-spike firing rate on the subsequent trial is reduced by 5 spikes/s through CS-linked plasticity.

• CS-linked plasticity relaxes back to zero over 2 trials when the instruction-test interval is 2.5 s (Yang and Lisberger, unpublished data).

• The responses of model inferior olive neurons were synchronized enough so that the trial-by-trial correlation in the occurrence of a CS between model Purkinje cells was ∼0.25 on trials that delivered an off-direction instruction.

Figure 5

Download asset Open asset

We ran the model for 800 trials, each of which delivered a randomly selected on-direction or off-direction instruction. We analyzed the ‘data’ from the model using the same approach we had used for the real Purkinje cells. We assumed that the eye movement on each trial was defined by the average of the responses of all 1000 Purkinje cells on that trial, scaled arbitrarily so that the full model produced eye velocities of the amplitudes in our data. Because we did not simulate the responses in each trial as a function of time, the outputs from the model are scalars on each trial. For demonstration purposes, we have used those scalars as gains on the relevant simple-spike firing rate and eye velocity traces from our data in Figure 4.

Analysis of the ‘data’ produced by the model yielded results that captured most of the features of our recordings from monkeys. The trial-over-trial changes in simple-spike firing rate (Figure 5A) and eye velocity (Figure 5D) showed the same progression as the data in Figure 4A,D. Simple-spike firing rate mimicked Figure 4A almost perfectly, but there are minor differences in polarity of the eye velocities for ‘0-1’ and ‘0-0’ pairs. We suspect that these differences are related to correlations in the CS responses across the population of Purkinje cells that we have not captured fully in our model. Figure 5B,C,E,F shows excellent agreement between the performance of the model and the data in Figure 4B,C,E,F. The model also reproduced our finding that each spike/s of simple-spike firing rate is associated with an increase of ∼0.005 in the probability of a CS response to an off-direction instruction (data not shown).

Analysis of the sensitivity of the model to its parameters revealed that almost all of the features of the model were necessary to reproduce the data. In Figure 6, we have plotted the scalar results of each of 20 runs of the model, with different configurations shown at different locations along the x-axis. The predictions for trial-over-trial changes in simple-spike firing rate broke down if we eliminated either CS-linked plasticity (‘NO plast’) or same-trial facilitation (‘NO SStoCS’). Trial-over-trial depression of simple-spike firing rate was fairly normal for all other configurations of the model, and also did not depend strongly on whether the response of an inferior olive neuron to the instruction was controlled by 1, 20, or all 1000 model Purkinje cells (‘F1’, ‘F20’, ‘F1000’). Trial-over-trial changes in eye velocity were quite sensitive to the presence of neuron–neuron correlations in the simple-spike firing rate and the CS responses across the population of Purkinje cells. Thus, the model supports the intuition outlined earlier about the likely high-degree of correlation in the presence and absence of CS responses across the population of Purkinje cells.

Figure 6

Download asset Open asset

We conclude that the features included in our model are at least sufficient to reproduce the trial-over-trial changes in simple-spike firing rate and eye velocity in our data. Even though the features of the model are supported by knowledge of the organization of the cerebellar circuit, it is possible that other, quite different, models would make similar predictions. We also note that the model does not reproduce the absence of same-trial facilitation at the end of an on-direction learning stimulus, when CS-linked plasticity persists. Clearly, we do not understand completely the basis for CS-related same-trial facilitation.

Testing predictions of the postulated pathway from Purkinje cells to the inferior olive

The microcircuit in Figure 1, and its success in modeling our observations on simple-spike firing rate (Figure 5), supports the hypothesis that a learned decrease in simple-spike firing rate may cause a decrease in the probability of CS responses to the instruction, and thereby reduce the magnitude or speed of learning. It could do so through the pathway from Purkinje cells through the deep cerebellar nucleus to the inferior olive. This pathway contains two inhibitory synapses so that increases or decreases in simple-spike firing rate would facilitate or inhibit responses of neurons in the inferior olive. The possibility that such a pathway exists and plays a functional role makes three testable predictions.

Prediction #1

For a random-order learning block, a CS in response to an off-direction instruction on one trial will cause trial-over-trial depression of simple-spike firing rate on the next trial. If the second trial of a pair delivers an off-direction instruction, then the probability of a CS on that trial should be reduced. We tested this prediction by finding all pairs of trials that delivered successive off-direction instructions and asking whether the probability of ‘1-1’ pairs was lower than predicted by the independent probability of a CS response to an off-direction instruction. For the full sample of 90 Purkinje cells, the probability of ‘1-1’ pairs was 0.11 and the probability predicted by independent occurrence of CS responses was 0.12. Even though the difference between the actual and independent probabilities was only 0.01, it was highly significant (two tailed paired t-test, p<<0.01). There was a commensurate slight excess in the probability of ‘1-0’ pairs. The actual probability of 0.24 was significantly higher than the probability of 0.22 predicted by independence (two tailed paired t-test, p<0.01). The model in Figure 5 showed the same small effects.

Prediction #2

For a learning block where the same instruction occurs on multiple repeated trials, a gradual learned decrease in simple-spike firing should be associated with a gradual decrease in the probability that a CS occurs in response to an off-direction instruction. Figure 5B of Medina and Lisberger (2008) verifies this prediction, and our data agree with theirs (not shown).

Prediction #3

Past behavioral learning should inhibit future behavioral learning. After some number of trials that deliver an off-direction instruction, both eye movements and simple-spike firing rate would learn. The neural learning would be expressed as a transient decrease in simple-spike firing rate surrounding the time of the instruction. Lower simple-spike firing should cause a reduction in the probability of CS responses to the instruction (see ‘Prediction #2’). The reduced probability of CS responses should partially inhibit future learning. In the next paragraph, we describe a behavioral experiment that is consistent with the prediction that some past learning inhibits future learning.

To induce some learning but leave headroom for future learning, we delivered a series of learning trials that repeated the same direction of instruction, but with an instruction-test interval of 6 s instead of the usual interval of 2.5 s. The longer instruction-test interval supports less long-term and trial-over-trial learning than does a shorter instruction-test interval (Yang and Lisberger, unpublished data). Thus, in Figure 7A,B, the learning in the first 50 trials is lower in amplitude for the 6 s instruction-test interval (open blue symbols) than for the 2.5 s instruction-test interval (open red symbols). After the 50^th learning trial, we switched to an instruction-test interval of 2.5 s. The learning curve (Figure 7A,B, filled blue symbols) initiated an increase in learning after the switch from long to short instruction-test intervals, but the magnitude of learning never caught up to the learning obtained when we used the short instruction-test interval for the entire learning block (filled red symbols). We assessed the effect of past learning on future learning by measuring the size of the learned eye velocity in the last 10 trials of each 100-trial block (gray shading in Figure 7A,B). The effect of past learning was instantiated by as 10 trials of learning, and became slightly stronger as a function of the number of trials that delivered the longer instruction-test interval in the early phase of learning blocks (Figure 7C,D). We conclude that some past learning inhibits future learning, as predicted if a learned depression of Purkinje cell simple-spike responses inhibits instructive climbing-fiber inputs.

Figure 7

Download asset Open asset

In vitro studies have identified plasticity at multiple sites in the cerebellar cortex and the deep cerebellar nucleus, and have outlined many intricacies of the cerebellar circuit. The studies of neural responses in intact animals have measured neural representations of motor memories and have inferred what happened in the cerebellum during motor learning. There are numerous examples where genetic ablation of specific forms of cellular plasticity cause altered-learning phenotypes. Still, prior studies have stopped short of ‘monitoring’ what happens in the cerebellum during behavioral learning.

We have made the next step of creating a quantitative description of how CS-linked plasticity of simple-spike firing interacts with the cerebellar circuit in a behaving monkey to create motor learning. By combining the approaches from two of our prior studies (Medina and Lisberger, 2008; Yang and Lisberger, 2010) we have made four observations that relate to cerebellar operation during short-term motor learning:

1. A single CS causes short-term CS-linked plasticity of simple-spike firing during motor learning, perhaps due to synaptic depression at the parallel fiber to Purkinje cell synapse.

2. Higher simple-spike firing rate at the time of an instructive stimulus for learning is correlated with, and might cause, a higher probability of a CS response.

3. Learned depression of simple-spike responses is associated with, and might cause, a reduced probability of a CS response to an instruction.

4. Some past learning inhibits future learning.

The model in Figures 5 and 6 reproduced most of the features of our data by simulating CS-linked short-term plasticity of simple-spike firing, a disynaptic, disinhibitory pathway from Purkinje cells to the inferior olive, neuron–neuron correlations in simple-spike firing rate, and correlations in the occurrence of CS responses across the population of Purkinje cells. The success of the model shows that these four features of cerebellar anatomy and physiology are sufficient to create the physiological observations we have detailed in the present paper. The necessity of including all four features shows how plasticity and circuit organization could work together to create a complex but quantifiable set of relationships among different neural and behavioral phenomena.

We think our model might reflect the actual operation of the cerebellar learning system, because available knowledge supports the existence of the four critical features of the model. CS-linked trial-over-trial depression of simple-spike firing was demonstrated before (Medina and Lisberger, 2008), and we have verified here that trial-over-trial depression results partly from single-trial plasticity. The present paper demonstrates CS-related same-trial facilitation of simple-spike firing rate during learning, and Miall et al. (1998) showed the same phenomenon during quiescence. Medina and Lisberger (2007) provided evidence for moderate neuron–neuron correlations in simple-spike firing rate within the population of floccular Purkinje cells, and a number of papers have outlined the case for synchrony across the climbing-fiber inputs (Llinas et al., 1974; Welsh et al., 1995). Thus, our measurements have created a hypothesis for the operation of the cerebellar microcircuit during behavioral learning that is validated by experimental data and computer simulations. Still, we are aware that other models also could reproduce our data. For example, the probability of a CS and the simple-spike firing rate at the time of the instruction could be subject to top-down influences in parallel, a situation that would not require a pathway from Purkinje cells to the inferior olive, and might alter the implications for what happens in the cerebellum during motor learning.

The relationship between simple-spike firing rate on a given trial and the probability of a CS response to an instructive stimulus on the same trial has multiple implications. One implication is caution in assuming that trial-over-trial depression is due to CS-linked plasticity. Indeed, our analysis indicates that CS-linked plasticity is responsible for only half of trial-over-trial depression. The other half of trial-over-trial depression on ‘1-0’ pairs of trials is related to the tendency for simple-spike firing rate to be higher on trials with a CS. A second implication concerns a possible role in learning. If simple-spike firing rate acts through inhibitory neurons in the deep cerebellar nucleus to modulate the response of inferior olive neurons to a given instruction, then a learned response in the cerebellum could modulate its own instructive inputs (Schweighofer, et al., 2013). There are two inhibitory synapses in the pathway from Purkinje cells to the inferior olive (De Zeeuw et al., 1998; D’Angelo, 2010), so higher (lower) simple-spike firing could cause a higher (lower) probability of CS responses, in agreement with the data of Miall et al. (1998) during quiescence and with our data during learning. Importantly, the climbing fiber axons from the inferior olive to the cerebellum and the pathway from the deep cerebellar nucleus back to the inferior olive both cross the midline, so that Purkinje cells can control their own climbing-fiber inputs (Ruigrok, 1997).

Three features of our data support the idea that learned changes in the responses of Purkinje cells could modulate their own instructive climbing fiber inputs (Mauk and Donegan, 1997; Kenyon et al., 1998; but see Zbarska, et al., 2008). (1) There is a correlation between CS probability and simple-spike firing rate on learning trials. (2) Learned decreases in simple-spike firing are associated with a reduction in the probability of CS responses to an instruction, both during learning blocks that repeat the same instruction on many trials (Medina and Lisberger, 2008) and during single-trial learning. (3) Past learning inhibits future learning, presumably by causing a learned decrease in the simple-spike responses of Purkinje cells (Medina and Lisberger, 2008) that could reduce the probability of the CS responses that would instruct learning. In addition, anatomical and physiological studies have documented the required neural pathway (Ruigrok, 1997; Bengtsson and Hesslow, 2006).

We suggest that the cerebellar learning circuit is set up to be conservative by allowing only a finite amount of learning in the cerebellar cortex. Learning may need to be transferred to the deep cerebellar nucleus (Ohyama et al., 2006) so that plasticity can relax back to baseline in the cerebellar cortex before further plasticity is allowed in the input pathways to Purkinje cells. Still, we are aware that there are multiple possible explanations for the observation that past learning inhibits future learning in pursuit eye movements. Thus, our data add support for, but do not obligate the conclusion that Purkinje cells modulate their own climbing-fiber inputs.

We have used physiological techniques to create a hypothesis (Figure 8) that starts to outline how the cerebellar circuit architecture and plasticity might interact during motor learning. Consider a sequence of trials that delivers the same instruction on 50 consecutive trials. A CS response on trial ‘1’ leads to a properly-timed depression of simple-spike firing on trial ‘2’. Because of the decreased simple-spike firing, there is a lower probability of a CS response on trial ‘2’. On trial ‘3’, the random variation in simple-spike firing rate leads to some trials with the same or higher firing than trial ‘1’ and a higher probability of a CS response to the instruction; other trials have lower simple-spike firing rate and a lower probability of a CS response. Finally, our analysis predicts that by trial ‘50’, sustained learning has depressed simple-spike firing rate substantially (Medina and Lisberger, 2008), so that the probability of a CS response is below control values and further learning is limited in the cerebellar cortex. Additional learning might become possible at a later time if some of the changes in the cerebellar cortex are transferred to the deep cerebellar nucleus, allowing a relaxation of the depression in the cerebellar cortex.

Figure 8

Download asset Open asset

We expect that the CS-linked plasticity of simple-spike responses in our data is a product of CS-driven depression of the synapses from parallel fibers to Purkinje cells. For example, cannabinoid-dependent synaptic depression seems to have the requisite brief time course (Brown et al., 2003; Brenowitz and Regehr, 2005). However, other forms of cellular plasticity may contribute, either within the cerebellar cortex (Hansel et al., 2001; Carey, 2011) or in the deep cerebellar nucleus (Miles and Lisberger, 1981; Zhang and Linden, 2006; Zheng and Raman, 2010). The oculomotor vermis also could play a role in pursuit learning (Suzuki and Keller, 1988; Takagi et al., 2000). We expect that future work will provide positive evidence of specific roles during learning for other forms of plasticity and other brain sites of learning. Indeed, we hope that we have outlined an approach that might be used to establish roles for other forms of plasticity in the cerebellar circuit.

1. 1. Albus JS

   (1971) A theory of cerebellar function

   Mathematical Biosciences 10:25–61.

   https://doi.org/10.1016/0025-5564(71)90051-4

   • Google Scholar
2. 1. Bengtsson F
   2. Hesslow G

   (2006) Cerebellar control of the inferior olive

   Cerebellum 5:7–14.

   https://doi.org/10.1080/14734220500462757

   • Google Scholar
3. 1. Blazquez PM
   2. Hirata Y
   3. Highstein SM

   (2006) Chronic changes in inputs to dorsal Y neurons accompany VOR motor learning

   Journal of Neurophysiology 95:1812–1825.

   https://doi.org/10.1152/jn.01061.2005

   • Google Scholar
4. 1. Boyden ES
   2. Katoh A
   3. Raymond JL

   (2004) Cerebellum-dependent learning: the role of multiple plasticity mechanisms

   Annual Review of Neuroscience 27:581–609.

   https://doi.org/10.1152/jn.01061.2005

   • Google Scholar
5. 1. Brenowitz SD
   2. Regehr WG

   (2005) Associative short-term synaptic plasticity mediated by endocannabinoids

   Neuron 45:419–431.

   https://doi.org/10.1016/j.neuron.2004.12.045

   • Google Scholar
6. 1. Brown SP
   2. Brenowitz SD
   3. Regehr WG

   (2003) Brief presynaptic bursts evoke synapse-specific retrograde inhibition mediated by endogenous cannabinoids

   Nature Neuroscience 6:1048–1057.

   https://doi.org/10.1038/nn1126

   • Google Scholar
7. 1. Carey MR

   (2011) Synaptic mechanisms of sensorimotor learning in the cerebellum

   Current Opinion In Neurobiology 21:609–615.

   https://doi.org/10.1016/j.conb.2011.06.011

   • Google Scholar
8. 1. Christian KM
   2. Thompson RF

   (2003) Neural substrates of eyeblink conditioning: acquisition and retention

   Learning & Memory 10:427–455.

   https://doi.org/10.1101/lm.59603

   • Google Scholar
9. 1. D’Angelo E

   (2010) Rebuilding cerebellar network computations from cellular neurophysiology

   Frontiers in Cellular Neuroscience 4:131.

   https://doi.org/10.3389/fncel.2010.00131

   • Google Scholar
10. 1. De Zeeuw CI
    2. Simpson JI
    3. Hoogenraad CC
    4. Galjart N
    5. Koekkoek SK
    6. Ruigrok TJ

    (1998) Microcircuitry and function of the inferior olive

    Trends in Neurosciences 21:391–400.

    https://doi.org/10.1016/S0166-2236(98)01310-1

    • Google Scholar
11. 1. Gao Z
    2. van Beugen BJ
    3. De Zeeuw CI

    (2012) Distributed synergistic plasticity and cerebellar learning

    Nature Reviews Neuroscience 13:619–635.

    https://doi.org/10.1038/nrn3312

    • Google Scholar
12. 1. Gilbert PF
    2. Thach WT

    (1977) Purkinje cell activity during motor learning

    Brain Research 128:309–328.

    https://doi.org/10.1016/0006-8993(77)90997-0

    • Google Scholar
13. 1. Hansel C
    2. Linden DJ
    3. D’Angelo E

    (2001) Beyond parallel fiber LTD: the diversity of synaptic and non-synaptic plasticity in the cerebellum

    Nature Neuroscience 4:467–475.

    https://doi.org/10.1038/87419

    • Google Scholar
14. 1. Ito M

    (1972) Neural design of the cerebellar motor control system

    Brain Research 40:81–84.

    https://doi.org/10.1016/0006-8993(72)90110-2

    • Google Scholar
15. 1. Ito M
    2. Kano M

    (1982) Long-lasting depression of parallel fiber-Purkinje cell transmission induced by conjunctive stimulation of parallel fibers and climbing fibers in the cerebellar cortex

    Neuroscience Letters 33:253–258.

    https://doi.org/10.1016/0304-3940(82)90380-9

    • Google Scholar
16. 1. Jorntell H
    2. Ekerot CF

    (2003)

    Receptive field plasticity profoundly alters the cutaneous parallel fiber synaptic input to cerebellar interneurons in vivo

    The Journal of Neuroscience 23:9620–9631.

    • Google Scholar
17. 1. Kahlon M
    2. Lisberger SG

    (1996)

    Coordinate system for learning in the smooth pursuit eye movements of monkeys

    The Journal of Neuroscience 16:7270–7283.

    • Google Scholar
18. 1. Kahlon M
    2. Lisberger SG

    (2000)

    Changes in the responses of Purkinje cells in the floccular complex of monkeys after motor learning in smooth pursuit eye movements

    Journal of Neurophysiology 84:2945–2960.

    • Google Scholar
19. 1. Ke MC
    2. Guo CC
    3. Raymond JL

    (2009) Elimination of climbing fiber instructive signals during motor learning

    Nature Neuroscience 12:1171–1179.

    https://doi.org/10.1038/nn.2366

    • Google Scholar
20. 1. Kenyon GT
    2. Medina JF
    3. Mauk MD

    (1998) A mathematical model of the cerebellar-olivary system I: Self-regulating equilibrium of climbing fiber activity

    Journal of Computational Neuroscience 5:17–33.

    https://doi.org/10.1023/A:1008874209991

    • Google Scholar
21. 1. Lisberger SG

    (1994)

    Neural basis for motor learning in the vestibuloocular reflex of primates. III. Computational and behavioral analysis of the sites of learning

    Journal of Neurophysiology 72:974–998.

    • Google Scholar
22. 1. Lisberger SG
    2. Fuchs AF

    (1978)

    Role of primate flocculus during rapid behavioral modification of vestibulo-ocular reflex. I. Purkinje cell activity during visually guided horizontal smooth pursuit eye movements and passive head rotation

    Journal of Neurophysiology 41:733–763.

    • Google Scholar
23. 1. Lisberger SG
    2. Pavelko TA

    (1986)

    Vestibular signals carried by pathways subserving plasticity of the vestibulo-ocular reflex in monkeys

    The Journal of Neuroscience 6:346–354.

    • Google Scholar
24. 1. Llinas R
    2. Baker R
    3. Sotelo C

    (1974)

    Electrotonic coupling between neurons in cat inferior olive

    Journal of Neurophysiology 37:560–571.

    • Google Scholar
25. 1. Marr D

    (1969)

    A theory of cerebellar cortex

    The Journal of Physiology 202:437–470.

    • Google Scholar
26. 1. Mauk MD
    2. Donegan NH

    (1997) A model of Pavlovian eyelid conditioning based on the synaptic organization of the cerebellum

    Learning & Memory 4:130–158.

    https://doi.org/10.1101/lm.4.1.130

    • Google Scholar
27. 1. Medina JF
    2. Lisberger SG

    (2007) Variation, signal, and noise in cerebellar sensory-motor processing for smooth-pursuit eye movements

    The Journal of Neuroscience 27:6832–6842.

    https://doi.org/10.1523/JNEUROSCI.1323-07.2007

    • Google Scholar
28. 1. Medina JF
    2. Lisberger SG

    (2008) Links from complex spikes to local plasticity and motor learning in the cerebellum of awake-behaving monkeys

    Nature Neuroscience 11:1185–1192.

    https://doi.org/10.1038/nn.2197

    • Google Scholar
29. 1. Medina JF
    2. Mauk MD

    (2000) Computer simulation of cerebellar information processing

    Nature Neuroscience 3:1205–1211.

    https://doi.org/10.1038/81486

    • Google Scholar
30. 1. Medina JF
    2. Carey MR
    3. Lisberger SG

    (2005) The representation of time for motor learning

    Neuron 45:157–167.

    https://doi.org/10.1016/j.neuron.2004.12.017

    • Google Scholar
31. 1. Medina JF
    2. Nores WL
    3. Ohyama T
    4. Mauk MD

    (2000) Mechanisms of cerebellar learning suggested by eyelid conditioning

    Current Opinion In Neurobiology 10:717–724.

    https://doi.org/10.1016/S0959-4388(00)00154-9

    • Google Scholar
32. 1. Miall RC
    2. Keating JG
    3. Malkmus M
    4. Thach WT

    (1998) Simple spike activity predicts occurrence of complex spikes in cerebellar Purkinje cells

    Nature Neuroscience 1:13–15.

    https://doi.org/10.1038/212

    • Google Scholar
33. 1. Miles FA
    2. Fuller JH

    (1975) Visual tracking and the primate flocculus

    Science 189:1000–1002.

    https://doi.org/10.1126/science.1083068

    • Google Scholar
34. 1. Miles FA
    2. Lisberger SG

    (1981) Plasticity in the vestibulo-ocular reflex: a new hypothesis

    Annual Review of Neuroscience 4:273–299.

    https://doi.org/10.1146/annurev.ne.04.030181.001421

    • Google Scholar
35. 1. Ohyama T
    2. Nores WL
    3. Medina JF
    4. Riusech FA
    5. Mauk MD

    (2006) Learning-induced plasticity in deep cerebellar nucleus

    The Journal of Neuroscience 26:12656–12663.

    https://doi.org/10.1523/JNEUROSCI.4023-06.2006

    • Google Scholar
36. 1. Ramachandran R
    2. Lisberger SG

    (2005) Normal performance and expression of learning in the vestibulo-ocular reflex (VOR) at high frequencies

    Journal of Neurophysiology 93:2028–2038.

    https://doi.org/10.1152/jn.00832.2004

    • Google Scholar
37. 1. Rashbass C

    (1961)

    The relationship between saccadic and smooth tracking eye movements

    The Journal of Physiology 159:326–338.

    • Google Scholar
38. 1. Ruigrok CJ

    (1997) Cerebellar nuclei: the olivary connection

    Progress in Brain Research 114:167–192.

    https://doi.org/10.1016/S0079-6123(08)63364-6

    • Google Scholar
39. 1. Schweighofer N
    2. Lang EJ
    3. Kawato M

    (2013) Role of the olivo-cerebellar complex in motor learning and control

    Frontiers in Neural Circuits 7:94.

    https://doi.org/10.3389/fncir.2013.00094

    • Google Scholar
40. 1. Stone LS
    2. Lisberger SG

    (1990)

    Visual responses of Purkinje cells in the cerebellar flocculus during smooth-pursuit eye movements in monkeys. II. Complex spikes

    Journal of Neurophysiology 63:1262–1275.

    • Google Scholar
41. 1. Sugihara I
    2. Ebata S
    3. Shinoda Y

    (2004) Functional compartmentalization in the flocculus and the ventral dentate and dorsal group Y nuclei

    The Journal of Comparitive Neurology 470:113–133.

    https://doi.org/10.1002/cne.10952

    • Google Scholar
42. 1. Suzuki DA
    2. Keller EL

    (1988)

    The role of the posterior vermis of monkey cerebellum in smooth-pursuit eye movement control. II. Target velocity-related Purkinje cell activity

    Journal of Neurophysiology 59:19–40.

    • Google Scholar
43. 1. Takagi M
    2. Zee DS
    3. Tamargo RJ

    (2000)

    Effects of lesions of the oculomotor cerebellar vermis on eye movements in primate: smooth pursuit

    Journal of Neurophysiology 83:2047–2062.

    • Google Scholar
44. 1. van Alphen AM
    2. de Zeeuw CI

    (2002) Cerebellar LTD facilitates but is not essential for long-term adaptation of the vestibulo-ocular reflex

    European Journal of Neuroscience 16:486–490.

    https://doi.org/10.1046/j.1460-9568.2002.02094.x

    • Google Scholar
45. 1. Welsh JP
    2. Lang EJ
    3. Suglhara I
    4. Llinas R

    (1995) Dynamic organization of motor control within the olivocerebellar system

    Nature 374:453–457.

    https://doi.org/10.1038/374453a0

    • Google Scholar
46. 1. Wulff P
    2. Schonewille M
    3. Renzi M
    4. Viltono L
    5. Sassoè-Pognetto M
    6. Badura A
    7. Gao Z
    8. Hoebeek FE
    9. van Dorp S
    10. Wisden W
    11. Farrant M
    12. De Zeeuw CI

    (2009) Synaptic inhibition of Purkinje cells mediates consolidation of vestibulo-cerebellar motor learning

    Nature Neuroscience 12:1042–1049.

    https://doi.org/10.1038/nn.2348

    • Google Scholar
47. 1. Yang Y
    2. Lisberger SG

    (2010) Learning on multiple timescales in smooth pursuit eye movements

    Journal of Neurophysiology 104:2850–2862.

    https://doi.org/10.1152/jn.00761.2010

    • Google Scholar
48. 1. Zbarska S
    2. Bloedel JR
    3. Bracha V

    (2008) Cerebellar dysfunction explains the extinction-like abolition of conditioned eyeblinks after NBQX injections in the inferior olive

    The Journal of Neuroscience 28:10–20.

    https://doi.org/10.1523/JNEUROSCI.3403-07.2008

    • Google Scholar
49. 1. Zhang W
    2. Linden DJ

    (2006) Long-term depression at the mossy fiber-deep cerebellar nucleus synapse

    The Journal of Neuroscience 26:6935–6944.

    https://doi.org/10.1523/JNEUROSCI.0784-06.2006

    • Google Scholar
50. 1. Zheng N
    2. Raman IM

    (2010) Synaptic inhibition, excitation, and plasticity in neurons of the cerebellar nuclei

    Cerebellum 9:56–66.

    https://doi.org/10.1007/s12311-009-0140-6

    • Google Scholar

Author details

1. Yan Yang

   Department of Neurobiology, Duke University School of Medicine, Durham, United States

   Contribution

   YY, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

2. Stephen G Lisberger

   1. Department of Neurobiology, Duke University School of Medicine, Durham, United States
   2. Howard Hughes Medical Institute, Duke University School of Medicine, Durham, United States

   Contribution

   SGL, Conception and design, Analysis and interpretation of data, Drafting or revising the article

   For correspondence

   lisberger@neuro.duke.edu

   Competing interests

   The authors declare that no competing interests exist.

• 1,526

  views

• 261

  downloads

• 26

  citations

Views, downloads and citations are aggregated across all versions of this paper published by eLife.