Long-Term Predictive and Feedback Encoding of Motor Signals in the Simple Spike Discharge of Purkinje Cells

Purkinje cell simple spike modulation in relation to hand position during the track period. A, Sequence of firing maps in 200-ms steps showing simple spike modulation with hand position. Map colors denote simple spike rate relative to mean firing rate, according to color bar. B, D, R² temporal profiles show the strength of X and Y encoding as function of τ value. Chance level of simple spike encoding determined by trial shuffling, mean (red continuous line) + 4 SD (red dotted line). C, E, β temporal profiles show the simple spike sensitivity to X and Y as a function of τ value. In all figures, negative τ values represent firing leading behavior.

Purkinje cell simple spike modulation in relationship to hand velocity during track period. A, Sequence of firing maps showing simple spike modulation with velocity in 200-ms steps. B, D, R² temporal profile shows the strength of VX and VY encoding as function of time, respectively. C, E, β temporal profiles show the firing sensitivity to VX and VY as a function of τ, respectively. Color scheme of firing maps, τ values, and denotation of chance encoding as in Figure 2.

Purkinje cell simple spike modulation in relationship to position error during track period. A, Sequence of firing maps showing simple spike modulation with position errors in 200-ms steps. B, D, F, R² temporal profile shows the strength of XE, YE, and RE encoding as function of τ, respectively. C, E, G, β temporal profiles show the firing sensitivity to XE, YE, and RE as a function of τ, respectively. Color scheme of firing maps, τ values, and denotation of chance encoding as in Figure 2.

Temporal distribution of simple spike peak and averaged R² values during the track period. A, Distributions of significant R² peaks for position (left panel) and averaged R² (right panel) for each of the predictive and feedback epochs (X, blue; Y, red). B, Similar distributions of significant R² peaks (left panel) and averaged R² (right panel) for velocity (VX, blue; VY, red) and speed (S, green). C, Distributions of significant R² peaks (left panel) and averaged R² (right panel) for position error (XE, blue; YE, red) and radial errors (RE, green). Epochs are P1: -2000 to -1500 ms, P2: -1500 to -1000 ms, P3: -1000 to -500 ms, P4: -500-0 ms, F1: 0-500 ms, F2: 500-1000 ms, F3: 1000-1500 ms, F4: 1500-2000 ms. Same epochs are used in subsequent figures.

Behavioral parameters temporal structure and interactions. A, Autocorrelograms of the simple spike firing and behavioral parameters. B, Cross-correlograms for all pairs of kinematic and error parameters. An * marks the time of a positive or negative correlation between parameters that exceeds a threshold of ρ < -0.1 or ρ > 0.1, respectively. Mean (solid line) ± SD (gray area) of autocorrelograms and cross-correlations computed over entire data set from the 183 Purkinje cells.

Relation between encoding similarity and behavioral interaction for pairs of parameters with significant correlation. A, Scatter plots of encoding similarity minima versus peak negative behavioral interaction for X and VX, VX and XE, and Y and YE, respectively. B, Scatter plots of encoding similarity maximum versus peak positive behavioral interaction for the same parameters in A. Each scatter plot shows data from all 183 Purkinje cells. The times of the peak negative and positive behavioral interactions for each parameter are shown in Figure 6B (*). The Pearson correlation coefficient (ρ) and p value are included in each scatter plot.

Population decoding of VX and YE in different epochs. Distribution of decoded values versus observed values over 25 decoding repeats. The continuous lines illustrate the slope of each distribution. The dotted lines illustrate a slope of 1, corresponding to perfect decoding. In each row, the population decoding is performed using signals from a specific epoch (indicated on the right of each row). In the right column, the gray shaded region denotes the extent of the target.

Decoding performance across all epochs during track period. A, GoF for all parameters as identified on column B. B, Decoding slope for all parameters. For both columns, red illustrates population based decoding and blue illustrates chance decoding.

Analyses used to correlate simple spike activity during the hold periods with the behavior parameters. A, Simple spike firing (upper left inset) from a single trial during the initial hold period (gray shadow) is correlated with X-position at different τ values from 0 to -2000 ms using a sliding window of the same width as the initial hold period. Colored traces illustrate X-position at τ = 0 ms (black), τ = -500 ms (pink), τ = -1000 ms (blue), τ = -1500 ms (green), τ = -2000 ms (red). B, For the same cell in A, the R² temporal profile from the regression with X across all trials as a function of τ. C, Simple spike firing (lower right inset) from a single trial during the final hold period (gray shadow) is correlated with position error (YE) recorded in both track (gray segment) and final hold (black segment) periods using a sliding window with the same width as the final hold period moving from 0-2000 ms. Colored segments illustrate the sliding window at τ = 0 ms (black), τ = 500 ms (pink), τ = 1000 ms (blue), τ = 1500 ms (green), τ = 2000 ms (red). D, For the same cell as in C, the R2 temporal profile from the regression with YE encoding across all trials as a function of τ. Arrows at the bottom of A and C indicate direction of recording time. B, D, Colored dots coded the same as in A and C, respectively. Conventions for τ values, and denotation of chance encoding are as in Figure 2.

Purkinje cell simple spike modulation during the hold periods in relation to errors and kinematics motor. A, Sequence of firing maps in 300-ms steps of the simple spike modulation in the initial hold with error position. B, D, R² temporal profiles show the strength of XE and YE encoding as function of τ value for this example recording. C, E) β temporal profiles show corresponding simple spike sensitivity during the initial hold to XE and YE as a function of τ value. F, Sequence of firing maps in 200-ms steps of the simple spike modulation during the final hold with hand position for another Purkinje cell. G, I, R² temporal profiles show the strength of X and Y encoding as function of τ value for this neuron. H, J, β temporal profiles show simple spike sensitivity to X and Y as a function of τ value. Color scheme of firing maps, τ values, and denotation of chance encoding are as in Figure 2.

Temporal distribution of peak and averaged R² during the hold periods. A–C, Distribution of significant R² peaks for the initial hold period for each parameter (left panels) and averaged R² (right panels) for the predictive epochs. D–F, Distribution of significant R² peaks for the final hold period for each parameter (left panels), and averaged R² (right panels) in the feedback epochs. Epochs and color-code as in Figure 5.

Decoding performance during hold periods. A, B, GoF and decoding slope based on the simple spike firing during the initial hold for each parameter as identified in column B. C, D, GoF and decoding slope based on the simple spike firing during the final hold for each parameter as identified in column D. Epochs as in Figure 5 and color-code as in Figure 9.