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Encoding of error and learning to correct that error by the Purkinje cells of the cerebellum

Nature Neurosciencevolume 21pages736743 (2018) | Download Citation


The primary output cells of the cerebellar cortex, Purkinje cells, make kinematic predictions about ongoing movements via high-frequency simple spikes, but receive sensory error information about that movement via low-frequency complex spikes (CS). How is the vector space of sensory errors encoded by this low-frequency signal? Here we measured Purkinje cell activity in the oculomotor vermis of animals during saccades, then followed the chain of events from experience of visual error, generation of CS, modulation of simple spikes, and ultimately change in motor output. We found that while error direction affected the probability of CS, error magnitude altered its temporal distribution. Production of CS changed the simple spikes on the next trial, but regardless of the actual visual error, this change biased the movement only along a vector that was parallel to the Purkinje cell’s preferred error. From these results, we inferred the anatomy of a sensory-to-motor adaptive controller that transformed visual error vectors into motor-corrections.

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These data were collected in the laboratory of A. Fuchs. The authors are very grateful for his generosity. The work was supported by NIH grants R01NS078311 (R. Shadmehr), R01EY019258 (R. Soetedjo), R01EY023277 (Y.K.), the Johns Hopkins Science of Learning Institute (D.J.H.), and the Office of Naval Research (N00014-15-1-2312, R. Shadmehr).

Author information


  1. Department of Biomedical Engineering, Laboratory for Computational Motor Control, Johns Hopkins University School of Medicine, Baltimore, MD, USA

    • David J. Herzfeld
    •  & Reza Shadmehr
  2. Department of Neurobiology, Duke University School of Medicine, Durham, NC, USA

    • David J. Herzfeld
  3. Department of Physiology and Biophysics, Washington National Primate Center, University of Washington, Seattle, WA, USA

    • Yoshiko Kojima
    •  & Robijanto Soetedjo


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Y.K. and R. Soetedjo conceived, designed, and performed all experiments. D.J.H. analyzed the data and made all figures. R. Shadmehr and D.J.H. wrote the paper.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to David J. Herzfeld.

Integrated supplementary information

  1. Supplementary Figure 1 Single-cell complex spike probability shows a directional tuning for error.

    Error was measured via a vector that pointed from eye position at saccade termination to the current location of the target. The time plot shows probability of CS across trials at 1ms time bins for various error directions relative to this cell’s preferred direction. The polar plot shows probability of CS over the 50–200 ms post-saccadic time period as a function of error direction for this P-cell (error bars are standard deviation across trials). For each P-cell, we determined the preferred error direction (CS-on) as the direction which elicited the highest probability of CS across trials in the 50–200 ms period following saccade termination (right).

  2. Supplementary Figure 2 Increasing error magnitude modulates CS timing.

    The median time of complex spikes in the 250 ms period following saccade termination decreased with error magnitude (left) as the distribution in Fig. 1e changed from uniform to unimodal. In addition, CS timing became more precise, resulting in decreased jitter (median absolute deviation from the median, center) and decreased variance (right). Error bars are SEM across neurons.

  3. Supplementary Figure 3 Complex spikes elicit changes in behavior in the CS-on direction of the P-cell even when the error is orthogonal to CS-on.

    The difference in trial-to-trial change in behavior when a CS is present vs. when it is absent is indicated by the blue traces. This difference has a large component in the CS-on direction of the P-cell that produced the CS, and a non-significant component along the actual error direction (which was CS-on+90). Shaded regions denote standard error of the mean (SEM) across all neurons (n = 67).

  4. Supplementary Figure 4 CS-dependent learning is linked to the CS-on direction and not SS-on.

    Analysis of trial-to-trial change in velocity for trials in which a CS was present (green) or absent (magenta). We projected the trial-to-trial change in velocity onto the preferred simple spike direction (SS-on, left) or the direction orthogonal to the preferred simple spike direction (SS-on+90°). Presence of a CS did not modulate learning in either of these axes, indicating learning due to complex spikes is specific to a direction CS-on, not SS-on. Error bars denote standard error of the mean (SEM) across all recorded neurons (n = 67).

  5. Supplementary Figure 5 Heterogeneous responses of Purkinje cells during saccade execution.

    Perisaccade histograms for exemplar neurons that burst (left) and pause (right). Data were aligned relative to saccade onset. The durations of P-cell bursting and pausing responses outlast the saccadic duration. See4 for details.

  6. Supplementary Figure 6 Purkinje cell population responses during adaptation without considering CS-on show little effect of adaptation.

    We computed the population response without regard for each cell’s preferred error direction (CS-on). a. There is little apparent change in the population response between the beginning (blue) and end of adaptation (red) when the response is not organized by the CS-on direction (Fig. 4). b. The population response across all adaptation trials. Data is smoothed as in Fig. 4b. Error bars represent standard error of the mean (SEM) across all neurons (n = 67).

  7. Supplementary Figure 7 Schematic diagram of cerebellar contributions to control of a saccade following experience of an error.

    Following a saccade to the right, the target is moved inward, resulting in an error. This single error (vector pointing leftwards), results in changes on two sides of the oculomotor vermis. For the P-cells on the right side, this error is CS-on, producing a reduction in simple spikes. For the P-cells on the left side, the same error is in direction CS-on+180, producing a small increase in simple spikes. The two sides of the cerebellum project to different deep cerebellar nuclei, but their combined effect is a synergistic reduction in the gain of the saccade: reducing the activity of the agonist and increasing the activity of the antagonist muscles. Black filled circles represent inhibitory neurons and white filled circles represent excitatory neurons.

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