Encoding of action by the Purkinje cells of the cerebellum

Abstract

Execution of accurate eye movements depends critically on the cerebellum1,2,3, suggesting that the major output neurons of the cerebellum, Purkinje cells, may predict motion of the eye. However, this encoding of action for rapid eye movements (saccades) has remained unclear: Purkinje cells show little consistent modulation with respect to saccade amplitude4,5 or direction4, and critically, their discharge lasts longer than the duration of a saccade6,7. Here we analysed Purkinje-cell discharge in the oculomotor vermis of behaving rhesus monkeys (Macaca mulatta)8,9 and found neurons that increased or decreased their activity during saccades. We estimated the combined effect of these two populations via their projections to the caudal fastigial nucleus, and uncovered a simple-spike population response that precisely predicted the real-time motion of the eye. When we organized the Purkinje cells according to each cell’s complex-spike directional tuning, the simple-spike population response predicted both the real-time speed and direction of saccade multiplicatively via a gain field. This suggests that the cerebellum predicts the real-time motion of the eye during saccades via the combined inputs of Purkinje cells onto individual nucleus neurons. A gain-field encoding of simple spikes emerges if the Purkinje cells that project onto a nucleus neuron are not selected at random but share a common complex-spike property.

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Figure 1: Population of burst and pause Purkinje cells together predict eye speed in real time.
Figure 2: Determination of complex-spike properties of Purkinje cells.
Figure 3: A cluster of Purkinje cells, organized by their complex spikes, produced a population response that predicted in real time the motion of the eye.
Figure 4: Population response of Purkinje cells predicted saccade speed and direction in real time as a gain field.

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Acknowledgements

These data were collected in the laboratory of A. Fuchs. The authors are grateful to his generosity. The authors would like to thank S. du Lac for comments. The work was supported by NIH grants R01NS078311, R01EY019258, R01EY023277 and F31NS090860.

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Authors

Contributions

Y.K. and R.So. conceived, designed and performed all experiments. D.J.H. and R.Sh. formed the conceptual model. D.J.H. analysed the data and made all figures. R.Sh. and D.J.H. wrote the paper.

Corresponding authors

Correspondence to David J. Herzfeld or Reza Shadmehr.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Firing rates of individual Purkinje cells as a function of saccade amplitude and peak speed.

a, Increase in saccade amplitude produced robust increases in mean and peak saccade speed (mean: R2 = 0.86, P < 10−4; peak: R2 = 0.99, P < 10−9). Error bars indicate s.e.m. b, For each neuron, we correlated the average firing rate and the peak firing rate (computed over the saccade duration and averaged over all directions) with saccade amplitude. Some neurons increased their firing rates with increasing saccade amplitude (positive slope) and some neurons decreased their responses (negative slope). However, mean and peak firing rates of a majority of neurons (47 of 72) were not significantly modulated with saccade amplitude. As a result, activity of neither the burst nor the pause cells showed a significant modulation with saccade amplitude (Fig. 1c, main manuscript). c, Most neurons (45 of 72) had a significant linear relationship between firing rates and peak saccade speed. In particular, mean and peak response of burst cells showed a significant increase with peak speed (Fig. 1d).

Extended Data Figure 2 Complex spikes encode direction of error, not direction of saccade that preceded that error.

a, The response of the same cell shown in Fig. 2 as a function of direction of saccade and direction of error. The probability of complex spikes is high when the direction of error is at − 45°, despite the fact that saccade direction may be at − 45° or + 135°. b, Population statistics from n = 39 Purkinje cells in which the probability of complex spikes was quantified as a function of direction of the error vector and direction of the saccade that preceded that error. Probability of complex spikes depended on direction of error, not direction of saccade.

Extended Data Figure 3 The simple-spike population response of Purkinje cells, organized by their complex-spike properties (Fig. 3a), correlated with motion of the eye in real time.

a, Population response for saccades in direction CS-off for three different peak speeds. b, Temporal lead of the population response with respect to saccade speed as computed by finding the temporal shift that maximized the cross-correlation. c, Correlation between the population response and the temporally shifted eye speed trace (measured as R2). Error bars in all panels indicate s.e.m. across bootstrapped populations.

Extended Data Figure 4 Mean and peak/trough firing rate of the burst and pause cells were poorly modulated by saccade direction.

a, Maximum, minimum and mean firing rates averaged across burst or pause cells with respect to saccade direction, relative to CS-on direction of each cell. b, Mean firing rates of the burst and pause cells, as measured across all saccades, were not significantly different for saccades in the CS-on versus CS-off direction (burst P > 0.10, pause P > 0.05). c, Mean firing rates of the burst and pause cells as a function of saccade speed, for saccades in the CS-on versus CS-off direction. Saccade speed modulated the mean firing rates of the burst cells, but there were no significant interaction between saccade direction and speed (P > 0.6), nor a significant effect of saccade direction (P > 0.7). d, Peak (maximum) firing rates of the burst cells and the minimum firing rate of the pause cells as a function of saccade speed, for saccades in the CS-off and CS-on directions. We asked whether the maximum response of the burst cells or the minimum response of the pause cells was significantly modulated by direction. Separate repeated measures ANOVAs showed that for the burst cells, peak activity increased as a function of saccade peak speed (P < 0.001), but this relationship was unaffected by saccade direction (P > 0.4). For the pause cells, the response was not affected by saccade speed (P > 0.6), and this relationship was not modulated by saccade direction (P > 0.4). We found that saccade direction did not significantly alter the encoding of peak speed in either the mean or minimum/maximum activity of Purkinje cells. Error bars in all panels represent s.e.m. across neurons.

Extended Data Figure 5 A population of Purkinje cells, organized by their complex spike properties, predicted the real-time speed of the eye better than activity of individual cells.

a, We used equation (S2) (see Supplementary Information for details) and used the measured population response s(t) of Purkinje cells to predict the real-time speed of the eye . The plot shows the predicted speed for saccades of 400, 525 and 650° s−1. The predicted speed led the actual speed by 19 ms. MSE is the mean squared error between the predicted and actual eye trajectory at the optimal value of Δ. b, The result of fitting equation (S2) (see Supplementary Information) to the response of individual neurons. c, The result of fitting equation (S2) (Supplementary Information) to the discharge of a population composed exclusively of burst cells. d, The result of fitting equation (S2) (Supplementary Information) to the discharge of a population composed exclusively of pause cells.

Extended Data Figure 6 Change in saccade direction was associated with a change in the timing of the reduction of discharge in the pause cells (that is, pause onset) (see Fig. 4f).

a, Timing of pause onset with respect to saccade onset for saccades of various speeds and directions. We computed the pause onset as the time when the neuron’s response reached 20% of its minimum response. Positive numbers indicate that the pause onset occurred before saccade onset. b, Within-neuron measure of pause onset for saccade in direction CS-on, minus onset from saccades in direction CS-off. Negative numbers indicate that the pause onset occurred earlier for saccades in the CS-on direction. Error bars in all panels indicate s.e.m. across neurons.

Extended Data Figure 7 Complex-spike-dependent organization of the Purkinje cells.

a, Hypothesized anatomical organization of the oculomotor vermis (OMV). Bursting and pausing Purkinje cells are organized into clusters, with the cells in each cluster sharing a common complex-spike direction. Neurons on the right side of the OMV project to right cFN neurons and have CS-off directions to the right. b, Distribution of the CS-off directions from recorded neurons in chamber coordinates. Vertical dotted line shows the line that best separates rightwards CS-off direction neurons (blue) from leftwards CS-off direction neurons (red). c, Probability of having a rightwards (blue), up/down (green), or leftwards CS-off direction as a function of chamber coordinates. Purkinje cells with CS-off to the left were more probable on the left side of the cerebellum. Purkinje cells with CS-off to the right were more probable on the right side of the cerebellum. d, Pause (red) and burst (blue) Purkinje cells were equally likely at all recorded locations.

Extended Data Figure 8 The population response was sensitive to the fraction of pause and burst cells that composed a cluster of Purkinje cells.

In our data set, 54% of the population was composed of burst cells. We computed the population response under the assumption that the membership of a cluster was 54% burst cells. Here, we tested how sensitive the population response was to this membership ratio. The vertical lines indicate saccade onset and offset for all saccades pooled across direction and speed. As the percentage of burst cells in the cluster becomes larger than 70%, or smaller than 50%, the population response no longer returns to baseline at saccade offset.

Extended Data Figure 9 Gain-field encoding of saccade kinematics in the population response of the Purkinje cells disappeared if the Purkinje cells were organized by their simple-spike activity.

a, In this analysis we assumed that a collection of 50 Purkinje cells projected onto a single cFN neuron, with the property that all the Purkinje cells shared a similar simple-spike preferred direction. Therefore, the cluster was organized based on the simple-spike properties of the Purkinje cells, not their complex-spike properties. b, The population response for saccades made in the direction for which each Purkinje cell showed the largest mean firing rate (simple spikes), for various saccade peak speeds. The peak population response was not modulated with saccade speed. Error bars are boot-strap-estimated s.e.m. c, The population response for saccades made in the direction of maximal modulation. For burst cells, this was the direction for which the Purkinje cell showed the largest mean firing rate, whereas for pause cells, this was the direction associated with the minimum activity (largest pause). The peak population response was not modulated with saccade speed when clusters were organized based on the direction of maximal simple-spike modulation.

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Herzfeld, D., Kojima, Y., Soetedjo, R. et al. Encoding of action by the Purkinje cells of the cerebellum. Nature 526, 439–442 (2015). https://doi.org/10.1038/nature15693

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