Cerebellar associative learning underlies skilled reach adaptation

Abstract

The cerebellum is hypothesized to refine movement through online adjustments. We examined how such predictive control may be generated using a mouse reach paradigm, testing whether the cerebellum uses within-reach information as a predictor to adjust reach kinematics. We first identified a population-level response in Purkinje cells that scales inversely with reach velocity, pointing to the cerebellar cortex as a potential site linking kinematic predictors and anticipatory control. Next, we showed that mice can learn to compensate for a predictable reach perturbation caused by repeated, closed-loop optogenetic stimulation of pontocerebellar mossy fiber inputs. Both neural and behavioral readouts showed adaptation to position-locked mossy fiber perturbations and exhibited aftereffects when stimulation was removed. Surprisingly, position-randomized stimulation schedules drove partial adaptation but no opposing aftereffects. A model that recapitulated these findings suggests that the cerebellum may decipher cause-and-effect relationships through time-dependent generalization mechanisms.

Figure 1.

Net population activity in Purkinje cells predicts reach velocity. a. Schematic diagram of conceptual framework and experimental paradigm. Predictions computed by the cerebellum are hypothesized to be learned through reweighting of cerebellar inputs, including copies of motor commands, instructed by changes in climbing fiber activity. PCs of the deep central sulcus were recorded with either single electrodes or Neuropixel probes while the reaching hand was tracked in real-time with high-speed cameras. b. Kinematic regressors in multilinear LASSO regression were used to model firing rates on individual reaches across sessions. c. Examples of 3 PCs fit with LASSO regression. Top: trial-averaged empirical and LASSO predicted firing rates. Bottom: outward position and velocity aligned to firing rate at optimal lag (mean±SEM). d. Modest single-trial R² for single cells in empirical, reach shuffled, and spike shuffled LASSO regressions (Box plot shows median line +/− 25%tiles, center dot is mean, whiskers are 10–90%). e. Absolute model error (empirical vs predicted, across outward, upward and lateral positions) as a function of reach position. Stable error suggests continuous encoding of reach kinematics across reach epoch. Positions binned at 0.1 cm. f. During reach (kinematics, green), PCs group roughly into cells that increase firing rate (red) and cells that decrease firing rate (blue), aligned to the time the hand passed ‘threshold’, 1-cm in the outward direction. g. Simple spike firing rate modulation during reaches grouped by reach speed. Cells that increase (red) and decrease (blue) firing rate both showed lower firing rates during faster reaches. h. Pooling all PCs reveals net firing rate suppression that scales with reach velocity percentile. Top: Binned reach velocities associated with recordings. Bottom: Net PC population firing rate change for each reach velocity bin. i. Magnitude of net firing rate suppression in total PC population as a function of outward velocity. Firing rate during the suppression in population activity was strongly negatively related to reach velocity (mean±SEM). j. Time of population suppression is intermediate between peak outward acceleration and peak outward velocity, preceding deceleration. Plot relates the median timing of reach start, peak outward acceleration, peak outward velocity, and peak outward deceleration to the time of population simple spike suppression for each reach velocity bin shown in i (mean±SEM).

Figure 2.

Reaches with Cspks have erroneous kinematics and elevated simple spike rates. a. Cspks are positively modulated in the 500 ms before reach before dropping close to baseline values. Top: Mean velocity of reaches with Cspks recorded. Bottom: PETH of Cspk activity relative to the time of threshold crossing (mean±SEM, asterisk indicates p < 0.05 for post-hoc Dunnett’s multiple comparisons test with mean Cspk firing rate). b. Positional profiles from an example session separated into reaches with (red) and without Cspks (black) during or shortly after outreach (mean±SEM). c. Endpoint of reaches relative to session median in the outward and upward directions (top) and outward and lateral directions (bottom) for trials with and without Cspks. Large red or grey dot indicates mean and SEM from Cspk and non-Cspk reaches. d. Session endpoints relative to session median for Cspk and non-Cspk reaches for each recorded cell with Cspks during or after outreach (n = 58 cells). Grey line links Cspk endpoint average with non-Cspk endpoint average for an individual session with the recorded cell. Left: outward and upward endpoint position. Right: outward and lateral endpoint position. e. Reach endpoints on Cspk trials were significantly further from session median compared to non-Cspk trials. f. Peak outward velocity was not significantly different between Cspk and non-Cspk trials. g. PC simple spikes (Sspk) on Cspk and non-Cspk trials aligned to threshold crossing (mean±SEM). h. PC simple spike (Sspk) rates were significantly higher during outreach in trials with Cspks (n = 58 cells). i. Ratio of simple spike rate to outward velocity was significantly higher during outreach in trials with Cspks. j. Simple spike rate aligned to the time a Cspks, or simple spikes aligned to the same time relative to threshold crossing on the previous trial showed simple spike increases shortly before the Cspk (mean±SEM). k. Quantification of simple spike rates in the 100 ms before a Cspk on a Cspk trial or a the previous/next trial aligned to the same time of the Cspk relative to threshold crossing.

Figure 3.

Adaptation to mossy fiber stimulation during reach. a. Headfixed mice expressing ChR2 in pontocerebellar mossy fibers were trained to reach for food pellets while the hand was tracked with high-speed cameras. On laser trials, light directed to cerebellar primary fissure through an implanted fiber was triggered in closed loop after the hand crossed a plane 1 cm outward from reach start position. Bottom: Perturbation schedule followed canonical adaptation structure, with a baseline (no-stimulation) block, stimulation block with stimulation on every reach, followed by a washout block with stimulation omitted. b. Hand position 100 ms after threshold crossing in the first stimulated (blue) and washout (red) reaches heading to the target (white), after Guo et al. (2021). c. Hand position during baseline (grey), compared to hand position measured across the adaptation and washout blocks in an example mouse (n = 20 sessions; mean±SEM). Blue shading denotes the time of mossy fiber stimulation. d. Summary of stimulation-induced kinematic effects, which decay over the adaptation block and show opposing aftereffects. Baseline subtracted hand position, rectified relative to the direction of kinematic effect of stimulation, is shown for reaches in the early (first reach), middle (middle 5), and late (last 5) phases for both stimulation (blue) and washout (red) blocks (N=5 mice; 104 sessions; mean±SEM). e. Summary of adaptation effects across animals and sessions. Relative change in outward position was assessed in the 50-ms window following the end of stimulation. Asterisks indicate statistically significant differences between blocks (p values reported in main text; Box and whiskers denote median, 25%, 75%, max and min, circle indicates mean). f. Same as e, but with outward velocity assessed in the 50-ms following the start of stimulation. g. The magnitude and direction of early stimulation effect was related to aftereffects. Plot shows linear regression relating the magnitude of the early stimulation outward position effect and early washout outward position effect compared to baseline reaches.

Figure 4.

PCs show electrophysiological correlates of behavioral adaptation over the stimulation and washout blocks. a. Mossy fibers were stimulated at threshold crossing during outreach while recording PCs with Neuropixel probes. b. Mossy fiber stimulation effect during reach of all reach-modulated PCs. The difference in simple spike rate during the stimulation window is compared to the same epoch during baseline reaches (n = 159 cells). Significant differences are denoted by the color map on the right. c. Population summary of activity of PCs firing rate adaptation over stimulation block for all PCs positively modulated by stimulation. Top: mean reach velocity for all sessions (mean±SEM). Bottom: Average change in simple spike rates for the last 5 baseline reaches (black) and the first 5 (cyan), middle 5 (light blue), and last 5 (dark blue) stimulated reaches. n = 17 cells.. d. Same as in c but for the population of PCs negatively modulated by stimulation. n = 25 cells. e. Same as in c but measuring the magnitude of stimulation across stim increase and stim decrease cells. Here the effect of stimulation is measured in the direction of the initial stimulation effect, thus a positive deflection for stimulation increase cells means an increase in firing rate relative to baseline, and a positive deflection for stimulation decrease cells means a decrease in firing rate relative to baseline. f. Quantification of the data shown in e. (mean±SEM).. g. Population activity across all reach modulated cells. The first stimulated trial shows a negative deflection in net firing rate relative to baseline. Conversely, the first washout reach shows a net positive deflection. Grey box indicates the time of stimulation or analogous time in the washout block. h. Quantification of simple spike firing rates in the stimulation window for the data shown in g and the last 5 stimulated reaches and washout reaches.

Figure 5.

Dissociation of adaptation and aftereffects with randomized stimulation position. a. Stimulation location during outreach was distributed pseudorandomly between 0.3 and 1.8 cm in the outward direction during the stimulation block. b. Examples of reaches stimulated at 5 different locations during outreach. Each stimulated reach is compared to the last 5 baseline reaches of each session. The horizontal dashed line indicated the threshold crossing that triggered stimulation. c. Summary data of relative change in outward position for stimulation reaches in the early, middle, and late block. N=5 mice; 60 sessions. d. Quantification of stimulation effect on outward position across adaption block. For each reach, the analysis window was the 50–100 ms after stimulation onset aligned to the time of threshold crossing for each reach (inset). Quantification of aftereffects on outward position during washout block. Here, the analysis window is the 50–100 ms after crossing the 1-cm threshold for each reach – the same as the analysis in fixed-position stimulation experiments. e. Same as d but instead quantifying of outward velocity in the stimulus window, and aftereffects in the 50 ms after crossing the 1-cm threshold for each reach.

Figure 6.

A cerebellar model accounts for adaptation and aftereffect dissociation. a. Schematic diagram of the temporal cerebellar-learning model. The model input is a population of 2000 cells, divided into 2 balanced populations of 1000 parallel fibers and 1000 interneurons, activated during a brief window during a simulated 400-ms movement. The output of the PC module that receives this information is compared to the input in the cerebellar nuclei. At equilibrium, the 2 populations are perfectly balanced (parallel fibers cause net activation of the PC, and the interneurons cause a net decrease; bottom) and the PC module outputs an activity curve (Gaussian that mimics the firing rate suppression observed in empirical data) that spans the movement. Positive deviations from this curve (errors) lead to mismatch in the nuclei and subsequent activation of the inferior olive, which reduces the weights of parallel fibers active shortly before the error. To simulate optogenetic perturbation experiments (bar-code like pattern at 200 ms), a step of activity was added to a subset of parallel fibers and interneurons for 50 ms in the center of the movement (fixed stim) or randomized across the block (random stim). Note that stimulation can either activate a cell twice (e.g. parallel fiber 1257, *) or overlap with endogenous activity (e.g. 1490, #), and non-stimulated neurons can be endogenously active during the stimulus window (e.g. 1561, arrow). b. PC simple spike activity during the stimulation block (top, blue) and washout block (bottom, red) showing progressively adapting response magnitudes during the adaptation block and progressively decaying aftereffects during washout. c. Parallel fiber weight changes at the end of the fixed-position stimulation block. Top: change in weights of “artificially” stimulated and non-stimulated parallel fibers plotted by time of endogenous activation. Bottom: heatmap of parallel fiber weight changes on top and unchanged interneurons on bottom. Note population weight change concentrated at time of stimulation, seen in both artificially stimulated and unstimulated fibers during stimulation epoch. d. Comparison of model output to empirical observations for fixed-position stimulus conditions (Fig. 3). Model closely matches behavioral adaptation. e. Same as b but here the stimulation window is randomized across the reach. f. Same as c but for random position stimulation experiments. Note the absence of clustered weight changes in unstimulated parallel fibers. g. Comparison of model output to empirical observations for random-position stimulus conditions (Fig. 5) showing that both model and empirical observations show adaptation but not directional aftereffects.