Cerebellar Representations of Errors and Internal Models

Abstract

After decades of study, a comprehensive understanding of cerebellar function remains elusive. Several hypotheses have been put forward over the years, including that the cerebellum functions as a forward internal model. Integrated into the forward model framework is the long-standing view that Purkinje cell complex spike discharge encodes error information. In this brief review, we address both of these concepts based on our recordings of cerebellar Purkinje cells over the last decade as well as newer findings from the literature. During a high-dimensionality tracking task requiring continuous error processing, we find that complex spike discharge provides a rich source of non-error signals to Purkinje cells, indicating that the classical error encoding role ascribed to climbing fiber input needs revision. Instead, the simple spike discharge of Purkinje cells carries robust predictive and feedback signals of performance errors, as well as kinematics. These simple spike signals are consistent with a forward internal model. We also show that the information encoded in the simple spike is dynamically adjusted by the complex spike firing. Synthesis of these observations leads to the hypothesis that complex spikes convey behavioral state changes, possibly acting to select and maintain forward models.

Keywords: Complex spike; Forward internal model; Kinematics; Performance error; Prediction error; Purkinje cell; Simple spike.

Figure 1

Change is simple spike encoding is coupled to CS occurrence. a During pseudo-random tracking, plots of simple spike firing (mean-subtracted) with hand velocity (VX and VY) aligned on CS occurrence (t = 0 msec). Simple spike modulation with velocity increases following CS discharge. Also, the lead and lag modulations encode opposite directions. b Plots of simple spike modulation strength (R²) with VY as function of time relative to CS discharge. c Corresponding increase in simple spike sensitivity (β) to VY as function of time relative to CS discharge. b and c blue traces pre-CS, red traces post-CS. Examples in a, b, and c are from the same Purkinje cell. With permission from [30].

Figure 2

Simple spike encoding of performance errors. a Example of simple spike modulation (mean subtracted) with position error at different lead/lags in 200 msec steps showing strong modulation at both lead and lag times. Note the opposite modulation direction at lead and lag times. Black circle denotes the edge of the moving target. Negative τ values represent neural activity leading behavior. b-c Examples of simple spike encoding strength (R²) of individual position error parameters as function of lead/lag. Examples in a-c are from the same Purkinje cell. d Distribution of the simple spike error encoding strength relative to the kinematic encoding strength. Error encoding strength (Error R²_adj) was determined using a multilinear regression model including position error, radial error and directional error as independent variables. Kinematic encoding strength (PVS R²_adj) was determined using a multilinear regression including position, velocity and speed (magnitude of the velocity vector) as independent variables. b-d are from [35, 36], with permission.

Figure 3

Simple spike predictive and feedback encoding of performance errors consistent with a forward internal model. a Example simple spike encoding of performance errors at lead/lag timing during baseline conditions (black trace) and a visual feedback delay of 200 milliseconds (green trace). Note the shift in lead encoding to more negative timing, while the timing of peak lag encoding is not affected. b Population summary data of the change in peak lead/lag encoding for two different experimental delays. The shift of the timing in lead encoding is approximately equal to the duration of the experimental delay, while the timing of lag encoding is unaffected. c Example simple spike encoding of performance errors at lead/lag timing during baseline (black trace) and visual feedback reduction (red trace) paradigms, illustrating a strong reduction in lag encoding. d Population summary data of the magnitude of simple spike lead and lag encoding. Visual feedback reduction significantly decreases the magnitude of lag, but not lead simple spike encoding of performance errors. With permission from [36].