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(2015) Encoding of Action by the Purkinje Cells of the Cerebellum

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(2015) Encoding of Action by the Purkinje Cells of the Cerebellum LETTER doi:10.1038/nature15693 Encoding of action by the Purkinje cells of the cerebellum David J. Herzfeld1, Yoshiko Kojima2, Robijanto Soetedjo2 & Reza Shadmehr1 Execution of accurate eye movements depends critically on the Purkinje cells project to the caudal fastigial nucleus (cFN), where cerebellum1–3, suggesting that the major output neurons of the cere- about 50 Purkinje cells converge onto a cFN neuron17. For each bellum, Purkinje cells, may predict motion of the eye. However, this Purkinje cell we computed the probability of a simple spike in 1-ms encoding of action for rapid eye movements (saccades) has remained time bins during saccades of a given peak speed, averaged across all 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.Herewe a 400° per s saccade 650° per s saccade 400° per s saccade 650° per s saccade analysed Purkinje-cell discharge in the oculomotor vermis of behav- 500° per s 8,9 200 ing rhesus monkeys (Macaca mulatta) and found neurons that N12 increased or decreased their activity during saccades. We estimated the combined effect of these two populations via their projections to 100 the caudal fastigial nucleus, and uncovered a simple-spike popu- lation response that precisely predicted the real-time motion of 0 the eye. When we organized the Purkinje cells according to each –1000 100 0 100 0 100 0 100 cell’s complex-spike directional tuning, the simple-spike population b 500° per s response predicted both the real-time speed and direction of saccade multiplicatively via a gain field. This suggests that the cerebellum N23 predicts the real-time motion of the eye during saccades via the 100 combined inputs of Purkinje cells onto individual nucleus neurons. 50 A gain-field encoding of simple spikes emerges if the Purkinje cells 0 Firing rate (Hz) Firing rate (Hz) that project onto a nucleus neuron are not selected at random but –1000 100 0 100 0 100 0 100 share a common complex-spike property. Time relative to saccade onset (ms) Previous studies have focused on bursting activity of Purkinje cells ce400° per s saccade 650° per s saccade 6,10,11 Burst during saccadess and found no consistent modulation with sac- 80 60 4,5 5–7 4 12 End cade amplitude , speed or direction . A recent simulation sug- 40 Start 60 Burst gested that Purkinje cells that pause during saccades may be important 20 in understanding the responses observed in the deep cerebellar nucleus Pause 0 neurons. The main question that we wished to address was how the 40 –20 Mean firing rate (Hz) Change in firing rate Purkinje cells encode the real-time motion of the eye. of individual cells (Hz) Pause 20 –40 We analysed simple-spike activity of 72 Purkinje cells in the oculo- 10 15 –100 0 100 –50 0 100 motor vermis (OMV, cerebellar lobules VI and VII) of five monkeys Saccade magnitude (deg) Time relative to peak speed (ms) during saccades. The population included cells that exhibited increased d f activity (bursting; n 5 39, Fig. 1a) or decreased activity (pausing; n 5 33, 800 Speed (deg per s) 5,6,10 Burst Fig. 1b). Consistent with previous reports , most neurons were poorly Simple 600 80 4,000 spikes Speed modulated by saccade amplitude (Fig. 1c and Extended Data Fig. 1); 400 however, the mean firing rate of burst cells (but not pause cells) increased 60 210 200 significantly with saccade peak speed (Fig. 1d, P , 10 ). Previous work 3,000 40 Pause had demonstrated that the population response encoded additional sac- 0 cade-related information that was not reliably present in the responses of Mean firing rate (Hz) 20 2,000 6,13,14 400 650 Rate of spikes generated by a –100 0 100 –50 0 100 individual neurons . To examine the population response, we mea- population of 50 cells (spikes per s) sured change in firing rates (from baseline) for the bursting and pausing Saccade peak speed (deg per s) Time relative to peak speed (ms) cells during slow (400u s21) and fast (650u s21) saccades (Fig. 1e), pooled Figure 1 | Population of burst and pause Purkinje cells together predict eye across all directions. The onset of change in firing rates in both popula- speed in real time. a, b, Perisaccade histograms for a bursting (a) and tions generally led saccade onset bymorethan50ms.Theterminationof pausing (b) Purkinje cell during saccades of various speeds and directions (red activity was also significantly arrow). The trace on the top row is saccade speed. The grey arrow indicates 21 c d later than the saccade: a 650u s saccade was 38 6 1.2 ms in duration saccade end. , , Mean firing rates over the duration of saccade computed across all directions. Changes in speed produced an increase in the firing rate of 6 (mean s.e.m.), whereas activity of burst and pause cells persisted for the burst cells but not the pause cells. e, Change in firing rates (with respect more than 100 ms. Given that the cerebellum is thought to have a critical to baseline) of the bursting and pausing Purkinje cells for two saccade 15,16 role in termination of ipsiversive saccades , it is unlikely that separate speeds. Grey bars are onset and termination of the saccade (width is s.e.m.). populations of burst or pause Purkinje cells control the motion of the eye, f, The total rate of simple spikes produced by a random selection of 50 since their activity persists for much longer than the saccade. Purkinje cells. 1Department of Biomedical Engineering, Laboratory for Computational Motor Control, Johns Hopkins University School of Medicine, Baltimore, Maryland 21205, USA. 2Department of Physiology and Biophysics, Washington National Primate Center, University of Washington, Seattle, Washington 98195, USA. 15 OCTOBER 2015 | VOL 526 | NATURE | 439 G2015 Macmillan Publishers Limited. All rights reserved RESEARCH LETTER directions. We then chose 50 Purkinje cells at random and computed ab the total number of simple spikes generated by the population at each 90° millisecond, resulting in an estimate of the rate of presynaptic spikes 0.6 converging onto a cFN cell. The results (Fig. 1f) revealed a real-time Error 0.4 encoding of the speed of the eye: the peak of the activity preceded peak 0.2 speed, increased in magnitude when speed increased, and returned to 0o baseline just before saccade termination (R2 at the optimal delay, 21 2 222 21 2 243 400u s : R 5 0.52, P , 10 ; 650u s : R 5 0.62, P , 10 ). It N1 CS-on appeared that the simple spikes of the pause and burst cells combined Primary target Pr(CS) together to predict motion of the eye. Back-step target Let us hypothesize that the Purkinje cells that project to a nucleus 0 100 200 0 100 200 neuron are not selected randomly, but are organized by their inputs from the inferior olive18. That is, suppose that the olive projections 0 100 200 divide the Purkinje cells into clusters where each cluster of Purkinje cells Time relative to primary saccade termination (ms) projects onto a single nucleus neuron. The input from the olive produces complex spikes in the Purkinje cells. We found that if we organized the Figure 2 | Determination of complex-spike properties of Purkinje cells. simple spikes of the Purkinje cells based on each cell’s complex-spike a, Response of a Purkinje cell during the 250-ms period after completion of a properties, additional features of the population activity were unmasked. saccade (simple spikes are grey; complex spikes are red). CS-on was We measured complex-spike properties of each Purkinje cell by determined via a back-step paradigm in which the target was jumped (unfilled target to filled target) during saccade execution. Black arrow inducing a post-saccadic error through displacement of the target indicates saccade vector, red arrow indicates error vector. We computed the during the saccade, and then measured the probability of complex probability of complex spikes in the 50–200-ms period after saccade spikes as a function of the direction of this error (Fig. 2 and termination. b, The probability of a complex spike (Pr(CS)) as a function of Supplementary Information section 2). For each Purkinje cell, the the direction of the error vector. For this neuron, the highest probability (CS-on) direction of error that produced the largest probability of complex occurred when the error vector was in direction 245u. The direction of spikes during the 50–200-ms post-saccade period was labelled as CS-off for this cell was 135u. CS-on, and the opposite direction was labelled as CS-off9 (Extended Data Fig. 2). We then made the assumption that the Purkinje cells that repeated measures analysis of variance (ANOVA) with main effects projected onto a nucleus neuron all had the same CS-on direction 215 27 of peak speed, P , 10 ; CS-direction P , 10 ; and a speed by (Fig. 3a). Under this assumption, we computed the rate of presynaptic 215 CS-direction interaction, P , 10 ). simple spikes that a nucleus neuron would receive from the cluster of To examine the effects of saccade direction more closely, we plotted Purkinje cells (Supplementary Information section 3). We did this by the population response across saccade directions with respect to convolving each Purkinje cell simple-spike train with a 2.5 ms stand- CS-on (Fig. 4c). We found that the population response was highest ard-deviation normalized Gaussian, approximating the temporal for saccades made in the CS-off direction, with an encoding of direction characteristics of the inhibition produced in the nucleus neuron due that resembled a cosine function (Fig.
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