Cerebellar Control of Reach Kinematics for Endpoint Precision

Abstract

The cerebellum is well appreciated to impart speed, smoothness, and precision to skilled movements such as reaching. How these functions are executed by the final output stage of the cerebellum, the cerebellar nuclei, remains unknown. Here, we identify a causal relationship between cerebellar output and mouse reach kinematics and show how that relationship is leveraged endogenously to enhance reach precision. Activity in the anterior interposed nucleus (IntA) was remarkably well aligned to reach endpoint, scaling with the magnitude of limb deceleration. Closed-loop optogenetic modulation of IntA activity, triggered on reach, supported a causal role for this activity in controlling reach velocity in real time. Relating endogenous neural variability to kinematic variability, we found that IntA endpoint activity is adaptively engaged relative to variations in initial reach velocity, supporting endpoint precision. Taken together, these results provide a framework for understanding the physiology and pathophysiology of the intermediate cerebellum during precise skilled movements.

Keywords: cerebellar nuclei; closed-loop optogenetics; dysmetria; forelimb; interposed; kinematics; motor control; motor variability; precision; reaching.

Figure 1.. IntA Neurons Are Modulated Near Reach Endpoint

(A) Schematic of in vivo electrophysiological recording mouse reach paradigm. A tetrode drive was targeted to IntA (right). Example extracellular voltage trace from a single lead and average spike waveforms across tetrode leads for a single cell (far right). (B) Raster (top) and peri-event time histogram (PETH; bottom) of an example IntA neuron aligned to reach endpoint. (C) Population PETH including all cells recorded in IntA(n = 84) aligned to reach endpoint and sorted by time of peak mean firing rate (top). Firing rate is normalized to maximum on a per cell basis. Asterisk indicates example neuron in (B). Average (±SE) reach velocity in the outward direction, aligned to reach endpoint (bottom). The deceleration phase of the outreach is highlighted in magenta; endpoint is defined as time when outward reach velocity crosses zero (dashed line). (D) Histogram of the timing of peak mean firing rates relative to reach endpoint for all cells.

Figure 2.. Brief, Closed-Loop Activation of IntA during Reach Reduces Outward Velocity and Causes Hypometric Reaches

(A) Schematic of kinematic closed-loop system, in which real-time tracking of mouse reach kinematics is used to trigger optogenetic stimulation. (B) Example mouse 3D reach trajectory tracked in real time. “Upward,” “lateral,” and “outward” represent the three spatial dimensions monitored, with “outward” being in the direction toward the food pellet target. (C) Examples of complete unstimulated reach trajectories (top 3) that extend fully to the target location (dashed line), stimulated reach trajectories that return fully after stimulation (middle 3), and stimulated reaches that continue out toward the target following the initial direction reversal (“continued,” bottom 3). (D) Reach trajectories from a single behavioral session at their initial maximum extent in the outward direction (endpoint). Reaches are grouped by type (unstimulated or stimulated) and ordered for visual clarity. (E) Average (±SE) initial endpoint of unstimulated and stimulated reaches (p = 0.0039). (F) Example (single animal) of average outward velocity of unstimulated and stimulated reaches aligned to time of stimulation. Blue bar indicates the stimulation epoch (50 ms, 2 ms pulses, 100 Hz). All velocity profiles display mean (solid line) ± SE (dashed lines). (G) Population average of outward velocity profiles across animals. The linearly interpolated Z score (color bar) shows the time course of statistical divergence between the unstimulated and stimulated reach velocities, with the latency to first effect marked and labeled in gray (inset; see STAR Methods). (H) Difference (Stim. – Unstim.) of population average velocity profiles plotted in (G) (top). Heatmap of p values associated with Wilcoxon rank-sum tests conducted for each animal (rows) at 10 ms intervals (columns). (I) Two-dimensional (2D) plot of average change in outward (x axis) and upward (y axis) velocity for each animal (Stim. – Unstim.; gray dots and lines indicate mean and SE, respectively). Values at the origin would indicate no difference between stimulated and unstimulated reaches. The three NTSR1-Cre/FLEX-ChR2 animals tested are indicated in black. The average 2D effect size across animals is indicated by the tip of the blue arrow (p = 0.0039 for both outward and upward directions).

Figure 3.. The Magnitude of IntA Activation Scales Reach Kinematics

(A) Average (±SE) outward velocity of unstimulated and stimulated reaches with decreasing optical power of optogenetic stimulation (“ChR2”)from high (1.0 mW; far left) to low (0.1 mW; far right). (B) Heatmap of relative frequency of unstimulated and stimulated reach velocity values from data in (A). Individual frequency heatmaps for unstimulated reaches and stimulated reaches were normalized and subtracted (stimulated – unstimulated) to view the relative prevalence of reach velocity values in each distribution. (C) Summary of the magnitude (left) and direction (right) of average changes in outward reach velocity (Stim. – Unstim.; mean ± SE) in response to graded levels of excitation. (D) Average (±SE) initial endpoint of stimulated reaches in response to graded levels of excitation.

Figure 4.. The Timing of IntA Activation Does Not Alter Directionality

(A) Images of paw at three kinematic landmarks used to trigger IntA stimulation (left) and the associated positional and velocity characteristics at each landmark (mean ± SE; right). (B) Average (±SE) outward velocity of reaches stimulated with ChR2 at the kinematic landmarks in (A), overlaid with unstimulated reaches. Insets: schematic of stimulation trigger points. (C) Summary of the magnitude (left) and direction (right) of average changes in outward reach velocity (Stim. – Unstim.; mean ± SE) in response to stimulation at different kinematic landmarks during reach.

Figure 5.. IntA Exerts Directional Control on Reach Kinematics

(A) Schematic of observed and predicted effects of IntA excitation under the directional control and gain control hypotheses. Images of paw position during outreach and return (top). The observed stimulation effects on movement velocity during outreach are consistent with either gain or directional control, but the two hypotheses make opposite predictions for the direction of kinematic effects (blue arrows) in response to stimulation during the return phase of reach (bottom, right-hand column). For a gain controller, decreased return velocity is predicted (shorter gray arrow); for a directional controller, increased return velocity is predicted (longer gray arrow). (B) Average (±SE) outward velocity of reaches stimulated during the outreach phase (left) or return phase of reach (right). Insets: schematic of stimulation trigger points. (C) Summary of the magnitude of average changes in outward reach velocity (Stim. – Unstim.; mean ± SE) in response to stimulation during the outreach and return phases of reach. “Late” data are replotted from Figure 4C for comparison with “return.” Paired data are indicated with a connecting line; one animal was unpaired each for late and return experiments.

Figure 6.. Effects of IntA Activation Are Gated by Behavioral Context

(A) Example of the effect of optogenetic stimulation outside of reach behavior (e.g., standing, feeding; see STAR Methods) on average (±SE) paw position (p > 0.05). Each paired point represents the outward position before and after stimulation, reflecting the lack of dependence on initial starting position. (B) Example of the effect of optogenetic stimulation during non-reach behavior on average (±SE) paw velocity (p > 0.05). (C) Summary of average (±SE) maximum velocity effect magnitudes of stimulation during non-reach (Stim. – Unstimulated; outward, three of three animals, p > 0.05; upward, two of three animals, p > 0.05) in each of the three spatial dimensions across subjects (gray dots). (D) For comparison with (C). Replotted summary of average (±SE) maximum velocity effect magnitudes of stimulation during reach (Stim. – Unstim.; outward, nine of nine animals, p < 0.05; upward, nine of nine animals, p < 0.05) in each of the three spatial dimensions across subjects (gray dots).

Figure 7.. Brief Inhibition of IntA Increases Outward Velocity and Causes Hypermetric Reaches

(A) Example (single animal) of average (±SE) outward velocity of unstimulated and stimulated reaches aligned to time of stimulation. Green bar Indicates the stimulation epoch (50 ms). (B) Population average (±SE) of outward velocity profiles across animals, with linearly interpolated Z score (color bar) displaying the time course of statistical divergence between the unstimulated and stimulated reach velocities. (C) Difference (Stim. – Unstim.) of population average (±SE) velocity profiles plotted in (B) (top). Heatmap of p values associated with Wilcoxon rank-sum tests conducted for each animal (rows) at 10 ms intervals (columns). (D) Two-dimensional (2D) plot of average change in outward (x axis) and upward (y axis) velocity for each animal (Stim. – Unstim.; gray dots and lines indicate mean and SE, respectively). The average 2D effect size across animals is indicated by the tip of the green arrow (outward, p = 0.0039; upward, p = 0.0078). (E) Average (±SE) distance traveled over time following stimulation for both stimulated and unstimulated reaches (70 ms time point; p = 0.0002, paired t test). (F) Average (±SE) initial endpoint of unstimulated and stimulated reaches (p = 0.023, paired t test).

Figure 8.. Endogenous IntA Activity Is Scaled to Enhance Endpoint Precision

(A) Schematic of the protocol for burst-triggered average analysis. The timing of IntA bursts (Z score ≥ 2.5 for 5 ms) was identified and used to align paw kinematics. Red shading indicates burst identification example. Raw extracellular voltage trace of an example burst is displayed in gray, with detected spikes marked below. (B) Example of individual (gray) and average (±SE) (red) burst-aligned kinematics for a single IntA neuron for bursts occurring during the reach epoch. (C) Population average (±SE) (all “endpoint” neurons, n = 35; see STAR Methods) of burst-aligned kinematics during reach. (D) Population average (±SE) of burst-aligned kinematics during non-reach (top) and for random alignments (bottom). (E) Left: binned instantaneous firing rates (x axis) and the average (±SE) change in outward reach velocity (y axis) for all neurons during the reach epoch (*p < 0.05 and **p < 0.01, Wilcoxon signed rank test; H₀: no change). Right: linear regression relating instantaneous firing rate and change in outward velocity for an example neuron (top) and for the population (bottom). The grand mean of regression coefficients is plotted in black (bottom) with its associated equation. (F) Grand mean outward reach velocity profiles aligned to endpoint for reaches grouped by activity level in IntA neurons (deceleration [decel.] epoch neurons, n = 17; see STAR Methods). Reaches were sorted per cell on the basis of peak instantaneous firing rate within the deceleration epoch, segregated into sliding quintiles (see color bar, right) and averaged and then combined across cells to generate grand means. The “deceleration epoch” was the analysis window for peak instantaneous firing rates. (G) Kinematic comparison between high peak instantaneous firing rate reaches (red) and low peak instantaneous firing rate reaches (blue) for each cell (gray dots) and the population (bars). Comparisons include the difference in pre-deceleration velocity (left; p = 0.015), the change in outward velocity during the deceleration epoch (middle; p = 0.002), and the final endpoint distance (right; p = 0.071). Bars indicate ±SE. (H) Inverse relationship between pre-deceleration velocity (left axis, filled circles) and change in velocity (right axis, open circles) across quintile groups, as separated across the range of low to high peak instantaneous firing rates (percentile color scale as in F). Linear regressions in (H) and (I) are for display. (I) Calculated endpoints on the basis of kinematic parameters at the beginning of the deceleration epoch (100 ms prior to endpoint) across quintile groups, as separated across the range of low to high peak instantaneous firing rates. Endpoints were calculated from grand mean kinematic data for each quintile using either the actual deceleration for that quintile (“actual”) or the average deceleration across all reaches (“simulated”). Gray bar indicates the SE of endpoints across quintiles for “actual” endpoints.