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. Author manuscript; available in PMC: 2007 Aug 8.
Published in final edited form as: Neuron. 2006 Dec 21;52(6):1085–1096. doi: 10.1016/j.neuron.2006.10.034

A central source of movement variability

Mark M Churchland 1, Afsheen Afshar 2, Krishna V Shenoy 1
PMCID: PMC1941679  NIHMSID: NIHMS15491  PMID: 17178410

Summary

Movements are universally, sometimes frustratingly, variable. When such variability causes error, we typically assume that something went wrong during the movement. The same assumption is made by recent and influential models of motor control. These posit that the principal limit on repeatable performance is neuro-muscular noise that corrupts movement as it occurs. An alternative hypothesis is that movement variability arises before movements begin, during motor preparation. We examined this possibility directly by recording the preparatory activity of single cortical neurons during a highly-practiced reach task. Small variations in preparatory neural activity were predictive of small variations in the upcoming reach. Effect magnitudes were such that at least half of the observed movement variability likely had its source during motor preparation. Thus, even for a highly-practiced task, the ability to repeatedly plan the same movement limits our ability to repeatedly execute the same movement.

Introduction

In 1990, Larry Bird made 71 consecutive free throws. While a remarkable feat, one wonders why he missed the 72nd? Why could he not simply do what he had done the last 71 times? As humans, we take for granted that our behavior is variable, and that repeated attempts will have variable results, but what is the source of this variability? When we err, we often assume that something went wrong during the movement. But might variability also arise during motor preparation, well before the first muscle contracted? Answering such questions is critical to the study of motor control. Not only is variability part of the behavior to be explained, but hypotheses regarding motor-control strategies are fundamentally linked to hypotheses regarding the noise those strategies combat. Furthermore, different hypotheses can make similar predictions regarding mean behavior, such that deciding between candidate models requires examining movement variability (Kawato, 2004; Todorov, 2004; Todorov and Jordan, 2002). For these reasons, a body of recent work has suggested possible noise sources and proposed control strategies that could limit their harm (Harris and Wolpert, 1998; Haruno and Wolpert, 2005; Todorov, 2002; Todorov and Jordan, 2002; van Beers et al., 2004).

Due to their elegance and explanatory power, these models have been very influential. Though they differ in some important ways, all assume that movement variability is generated ‘online’, during movement. Typically it is assumed that the relevant noise stems from the periphery, especially at the neuromuscular junction. Recent studies (Hamilton et al., 2004; Jones et al., 2002; Osu et al., 2004; Sosnoff et al., 2005) have sought to characterize online neuromuscular noise precisely because it is proposed to be the key factor limiting performance. Yet there is little direct evidence that online noise is the main source of variability or the principal limit on accuracy. Indeed, some recent observations support the opposite conclusion. Osu et al. (2004) found that EMG variability was higher, yet movements less variable, when co-contraction was increased. Van Beers et al. (2004) found that variability in reach velocity was not accounted for by standard online noise models. This led them to propose more elaborate forms of online noise, but a more straightforward explanation is that considerable variability arises during motor preparation. Variability in motor preparation (and/or related sensorimotor transformations) has been previously considered important (Gordon et al., 1994), particularly when a target must be remembered (McIntyre et al., 1997; Messier and Kalaska, 1999; Soechting and Flanders, 1989). On the other hand, it has been recently argued that preparatory variability makes a negligible contribution for straightforward tasks using visible targets (van Beers et al., 2004).

The current study seeks to address this question: for a straightforward and well-practiced task, does motor preparation make a sizeable contribution to the observed behavioral variability? Comparisons of behavior with model predictions must contend with interpretational difficulties. Thus, we chose to address the issue directly, by recording from neurons in dorsal premotor cortex (PMd) and primary motor cortex (M1) as monkeys performed a delayed reach task. We compared trial-by-trial fluctuations in delay-period ‘preparatory’ activity (well before reach onset) with trial-by-trial fluctuations in the subsequent reach velocity. We chose this comparison because 1) velocity variability is a ubiquitous feature of reaching, and 2) most delay-active neurons in PMd/M1 are strongly modulated by instructed speed (Churchland et al., 2006a; Cisek, 2006). That modulation suggests that preparatory activity might also relate to the natural fluctuations in velocity. Of course, this is not guaranteed: trial-by-trial preparatory variability might be minimal, and contribute only a small proportion of the eventual behavioral variability. But in fact we did find that velocity variability was predicted by variability in the preceding delay-period activity. The sign and steepness of the relationship scaled, on average, with the sign and intensity of the tuning for instructed speed. From the strength of this scaling, we estimate that at least half the observed movement variability had its source in movement preparation rather than in online noise. Thus, variability in motor preparation is a major source of movement variability, even for a well-practiced and straightforward task.

Results

Behavior and example responses

Two rhesus monkeys performed a delayed-reach task (figure 1A). Figure 1B illustrates the flow of a single trial: a delay period separates target appearance from the go cue, after which a reach is made. Monkeys were trained to reach at different speeds (‘instructed-fast’ or ‘instructed-slow’) depending on target color (red or green). Figure 1C plots hand velocity and position for reaches to a rightwards target (12 cm distance, ∼15 reaches/instructed-speed). As desired, peak velocities were higher for red targets, and lower (though still fairly rapid) for green targets. Figure 1D plots the peak velocity for all reaches to that target location for that day. Lines give the criteria for success. Performance was generally excellent, particularly as the two instructed speeds were randomly interleaved (humans typically require training to achieve similar performance). Nevertheless, there was still measurable variability in peak velocity within each category. Such variability is a normal, presumably endemic feature of reaching. It has been explicitly noted previously (e.g., Messier and Kalaska, 1999; e.g., van Beers et al., 2004), and is also reflected in the universally-observed variability of movement duration (e.g., Crammond and Kalaska, 2000; Hocherman and Wise, 1991). Similar levels of velocity variability are seen in motivated human subjects. The central question of this study is whether this velocity variability can be predicted by ‘preparatory’ neural activity recorded during the delay period, well before movement initiation.

Figure 1.

Figure 1

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Illustration of the basic task. A. Movements began and ended with the hand touching the display. The hand was a few mm from the screen while in flight. The white trace shows the reach trajectory for one trial. B. Timeline of the task and behavior for the same trial. The target jittered slightly (2 mm standard deviation) upon first appearing, and continued to do so throughout the delay period. The cessation of jitter provided the go cue, at which time the central spot was also extinguished. The plot ends at the time the reward was delivered. C. Horizontal hand velocity and position for instructed-slow (green) and fast (red) reaches (0°, 12 cm distant target). During this session, the monkey performed ∼70 trials for each instructed speed at this target location. Data in this panel are plotted for every 5th trial, with one trace per trial. D. Peak hand velocity is plotted as a function of trial number for every reach to that target location.

We recorded, from PMd and M1, the responses of 136 neurons with tuned delay-period activity. We concentrate exclusively on the response during the delay period, which is known to relate to target direction and distance (Godschalk et al., 1985; Kurata, 1989; Messier and Kalaska, 2000; Riehle and Requin, 1989; Tanji and Evarts, 1976; Weinrich and Wise, 1982; Weinrich et al., 1984). Delay-period activity also depends upon the instructed speed (Churchland et al., 2006a). Figure 2A shows example responses from an ‘instructed-fast preferring’ neuron, tested at 5 target distances in its preferred direction. This neuron responds during the delay-period, and ceases responding around movement onset. Delay-period activity is higher for instructed-fast reaches than for instructed-slow reaches (red versus green traces). The central question is whether, for trials of a given instructed-speed, higher peak velocities are preceded by higher delay-period firing rates. To illustrate this issue, figure 2B plots the occurrence of action potentials for 22 instructed-fast trials, all employing the 6 cm distant target. Reach velocity (black traces) is plotted on top of the mean reach velocity across all trials (grey traces). For presentation, trials are ordered from the fastest to the slowest. If velocity variability results entirely from online noise (e.g., in the muscles) then it should not correlate with the spike-rate during the preceding delay-period. However, if velocity variability is partly due to preparatory variability, then such a correlation should exist. By visual inspection alone, it is difficult to determine whether a correlation exists. The natural variability in peak velocity is small and the spiking of the neuron is, like that of most cortical neurons, irregular even within a trial. We discuss below how these features impact our analyses, and how statistical power can be improved by the appropriate pooling of data.

Figure 2.

Figure 2

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Responses of one example neuron (B24). A. Firing rate versus time. Each subpanel plots the response for 1 of the 5 distances (labeled at top). Dots show the time of target onset (T), the go cue (G), and the median time of movement onset (M). Mean firing rates were computed with data locked to the target onset, and again with data locked to the go cue. These two means are plotted with a break between them, a necessity given the variable delay period. Trace widths show +/- SE. B. Raster plots showing individual-trial responses for the same neuron (all for the instructed-fast, 6 cm target). Ticks show spike times. Data are time-aligned to peak reach velocity. The reach velocity on each trial (black trace) is superimposed on the mean reach velocity across all trials (grey trace). The vertical scale is 1 m/s. Trials are ordered from fast to slow.

Measuring trial-by-trial relationships

Figure 3A illustrates the range of possible effects. Each dot corresponds to one hypothetical trial, and plots the delay-period neural response versus peak velocity for instructed slow (green) and fast (red) trials. If the neural response can be measured exactly, and indicates precisely the ‘planned’ reach speed, then expectations are clear (top panels). Presuming movement variability is not due to preparatory variability (left panel), there should be no preparatory variability, and thus no trial-by-trial correlation. Alternately, if movement variability is entirely due to preparatory variability (right panel), there should be a perfect correlation. Furthermore, the slope of a linear regression (black lines) should match the ‘predicted slope’: the grey line with slope:

(R‒instructed-fast−R‒instructed-slow)∕(V‒instructed-fast−V‒instructed-slow) eqn 1.

where R and V are the mean firing rate and mean peak velocity.

Figure 3.

Figure 3

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Possible results. A. Simulations assuming that velocity variability is unrelated (left column) or entirely related (right column) to preparatory variability. Top and bottom rows correspond to simulations with no spiking noise or Poisson spiking noise. Each dot plots the simulated firing rate versus peak velocity on a given trial. Crosses plot the means for the instructed slow (green) and fast (red) conditions. The grey line plots the predicted slope based on those means. Black lines plot slopes obtained by linear regression. Simulations were based on measurements from neuron B24, using the 6 cm distance. On each trial, the peak velocity was drawn from a Gaussian distribution with the empirical mean and SD. The underlying rate then either did (right column) or did not (left column) co-vary about its mean with that velocity. For the top row, the underlying rate is realized exactly, while for the bottom row it is corrupted by Poisson-distributed noise. B. Similar format, but for the actual data recorded from neuron B24 (6 cm distance).

Unfortunately, neural firing rates cannot be measured exactly. Cortical neurons have noisy spiking statistics that approximate a Poisson process (Churchland et al., 2006b; Tolhurst et al., 1983). Poisson spiking statistics will greatly reduce both trial-by-trial correlation coefficients (r) and the subjective impression of effect strength. Yet regression slopes still approximate the predicted slope (compare the two right panels in Fig. 3A). Thus, if behavioral variability is not due to preparatory variability, we expect correlation coefficients and regression slopes near zero. If behavioral variability is due solely to preparatory variability, we expect modest correlation coefficients and regression slopes that approximate the predicted slope. Finally, given noisy spiking statistics, moderately large numbers of trials may be necessary to determine the presence or absence of effects.

Empirically, statistical power is indeed a challenge. Figure 3B plots the delay-period response versus peak velocity for one example neuron / target-location (same as in Fig 2B). For the instructed-slow condition, the correlation coefficient was 0.42 and the regression slope was 138 spikes/s per m/s (exceeding the predicted slope: 42 spikes/s per m/s). For the instructed-fast condition, the correlation coefficient was 0.31 and the regression slope was 40 spikes/s per m/s (roughly equal to the predicted slope). Yet given only 22 trials per condition, neither effect was statistically significant (p = 0.054 and 0.16). Thus, while there appear to be strong trial-by-trial effects, statistical power is poor at the level of a single neuron and single target location.

Gaining statistical power

Might statistical power be greater if we considered variability in reach distance or direction, rather than velocity? As is discussed further below, behavioral variability in velocity, relative to the strength of ‘speed tuning’, is considerably greater than that for distance or direction. As can be seen in Figure 3B, the principal problem is not effect magnitude. The basic effect of instructed speed is 20 spikes/s, and regression slopes are 138 and 40 spikes/s per m/s. These are sizeable effects, given that delay-period modulations in PMd/M1 are typically only a few tens of spikes/s (e.g., Crammond and Kalaska, 2000; Lecas et al., 1986). Rather, statistical power is limited by the measurement of noisy spiking over a finite time (the 400-800 ms delay-period). One might attempt to reduce that measurement variability using a much longer (e.g., 5 second) delay, but there is no guarantee the state of motor preparation would remain stationary across that time. Alternately, measurement variability would matter less if we could encourage greater behavioral variability. This would certainly increase correlation coefficients and statistical power. However, it would also undermine the scientific purpose of the study. Certainly one can create behavioral variability by planning different movements on different trials. The central issue is whether performance, when near its best, still contains significant variability due to movement preparation. During training, considerable effort was expended to encourage monkeys to perform consistently, with velocity variability comparable to that of a human trying their best. An ironic consequence of this accurate behavior is that correlation coefficients and statistical power are expected to be low.

In summary, those design features that limit statistical power are essential. Improving statistical power therefore necessitates analyzing more trials. In principal, one could employ a single target location, so that ∼500 trials of the same type could be analyzed per neuron. However, that design renders the target completely predictable, allowing motor preparation to begin well before the delay (the analyzed epoch). We therefore tested each neuron using a range of target directions and distances (see methods). For statistical power, trials are pooled across target locations with the same preferred instructed-speed (e.g., the different target distances in Fig. 2A). To allow meaningful pooling, we express each trial’s firing rate and peak velocity relative to the mean for that target location (see Methods). Figure 4A plots the results of this analysis for neuron B24. Results are similar to those in Figure 3B, but effects are now statistically significant. Correlation coefficients are 0.33 and 0.30, and regression slopes (72 and 37 spikes/s per m/s) compare favorably with the mean predicted slope (38 spikes/s per m/s, averaged across target locations). Figure 4B plots the same analysis for a second example neuron (A06). This neuron preferred the instructed-slow condition for all target locations. In agreement, trial-by-trial correlations are negative (-0.20 and -0.24). Regression slopes are -11 and -13 spikes/s per m/s, slightly less than the mean predicted slope of -15 spikes/s per m/s.

Figure 4.

Figure 4

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Scatterplots of firing rate versus peak reach velocity for two example neurons. A. Neuron B24. Presentation is similar to that in Figure 3B, but trials are pooled across all target locations for statistical power (instructed-fast was preferred at all locations). Each dot plots, for one trial, the delay-period firing rate versus the subsequent peak velocity (474 total trials). Both are expressed as the difference from their mean (which was different for different target locations). Black lines show the result of a linear regression. Data for the two instructed speeds (green and red) are plotted with vertical and horizontal offsets so that the grey line connecting their means has a slope equal to the predicted slope (averaged across target locations). B. Similar plot for neuron A06, which had a consistent preference for instructed slow (384 total trials). For both neurons/speeds, p-values are based on the regression, but were also significant (p<0.01 in every case) using a nonparametric test (Spearman’s rank correlation).

Population analyses

The analysis in Figure 4 was repeated for all neurons where a robust instructed-speed preference spanned enough target locations to allow pooling of ≥50 trials (see Methods). Correlation coefficients (Figure 5A) and regression slopes (Figure 5C) are expressed as positive values if they had the same sign as the predicted slope. Distributions were shifted significantly in the expected direction, and all individually significant effects (black bars) were in the expected direction. The prevalence of significant effects at the level of single neurons is notable, given the large number of neurons that presumably participate in motor preparation. This suggests considerable correlation among neurons, something addressed further below.

Figure 5.

Figure 5

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Population analyses using correlation (top panels) and regression (bottom panels). A. Distributions of correlation coefficients for cases where sufficient data from a given neuron (>50 trials) could be pooled across target locations with a robust (>10 spikes/s) instructed-speed preference (see Methods for details). Data are plotted so that correlation coefficients are positive if they agree with the predicted slope and negative if they do not. The arrow gives the mean of the distribution (significance via t-test). Black bars indicate individually significant correlations (p<0.05). B. Relationship of trial-by-trial correlations to the predicted slope. For each bin on the x-axis, we pooled data from all neurons/target locations where the predicted-slope (eqn. 1) fell within that range. This included data for both instructed speeds (which shared a predicted slope). Black symbols plot the correlation coefficient for each bin; flanking traces give 95% confidence intervals. The grey histogram plots the number of trials/bin. For most neurons there were target locations (e.g., non preferred directions) with a weak impact of instructed speed. Thus, predicted slopes near zero were the most common, but all bins had >100 trials. The rightmost interval was expanded with this intent. 0.1% of the data falls outside the range of the bins. C. Distribution of regression slopes (similar analysis/format as in A.) D. Relationship of trial-by-trial regression slopes to the predicted slope (similar analysis/format as in B). For the pooled data in each bin a regression was applied. T resulting slopes are given by the solid circles (with flanking 95% confidence intervals). Open symbols plot a control analysis where all the same peak velocities and firing rates were used, but where each trial’s peak velocity was randomly reassigned to a new trial. This was done within each condition, before pooling data across conditions, and was repeated 100 times with different random seeds.

The above analyses reveal the presence of trial-by-trial effects, but do not examine whether those effects scale as predicted. Are correlations stronger and regression slopes steeper when predicted slopes are steeper? This question can be addressed if we pool data not within each neuron, but across neurons and target-locations that share a similar predicted slope. This approach also allows us to include data from all neurons, including those where the effect of instructed speed was weak, or present for only a few target locations. We pooled single-trial data across all neurons/target-locations with a similar predicted slope (in bins from -60 to 110 spikes/s per m/s). As above, means were subtracted before pooling. Figure 5B plots, for each bin, the correlation between velocity and firing rate. All correlation coefficients have the predicted sign, and most were significant (i.e., the 95% confidence intervals don’t overlap zero). Furthermore, correlation coefficients scaled in magnitude with the predicted slope, and for the extrema were -0.36 and 0.19.

This analysis was repeated for measurements of the regression slope (Figure 5D). That slope differed significantly from zero for 11 of 15 bins, and for every bin had a sign that agreed with the predicted slope. However, the trial-by-trial slope was quite convincingly smaller than the predicted slope, with 12/16 bins plotting significantly below the line of unity slope. The mean ratio of the trial-by-trial to predicted slope (the ‘slope-ratio’) was 0.47, and was similar (means of 0.43 and 0.50) for negative and positive predicted slopes. This analysis highlights a critical component of our experimental design: the use of instructed speeds allows quantitative comparison of the measured and predicted slopes. The empirical slope-ratios fall, on average, halfway between the extremes illustrated in Figure 3A.

Muscle activity and peak velocity

We also analyzed the trial-by-trial relationship between peak velocity and perimovement muscle activity. Twenty-four EMG recordings were made from the deltoid, biceps brachii, triceps brachii, trapezius, latissimus dorsi, and pectoralis major. Figure 6A plots representative single-trial recordings from the deltoid. As expected, EMG differed between the two instructed speeds. Regardless of the ultimate cause (preparatory or online, central or peripheral), trial-by-trial variations in muscle activity are presumably the direct cause of peak-velocity variations. It was thus unsurprising to observe significant trial-by-trial relationships between EMG and velocity. Figure 6B plots, for this same recording, the mean EMG magnitude on each trial versus the peak velocity (EMG activity was rectified and averaged from -75 to +250 ms relative to movement onset). Trial-by-trial slopes are clearly present but are less than the predicted slope.

Figure 6.

Figure 6

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Muscle activity. A. Example EMG traces (deltoid of monkey A). Data are for one ‘fast’ and one ‘slow’ reach (red and green traces) to a 12 cm distant rightwards target. Black traces show hand velocity (calibration = 1 m/s). Arrows indicate target onset and the go cue. B. Trial-by-trial relationship for the same muscle recording. Each dot plots, for one trial, average EMG activity versus peak velocity. As before, means were subtracted before pooling trials across target locations. The vertical scale is arbitrary. C. Relationship of trial-by-trial regression slopes to the predicted slope (similar analysis/format as for neural data in Fig. 5D). Data were pooled (in bins) from muscles/target-locations with similar predicted slopes. Solid black symbols plot the regression slope for each bin. Flanking traces give 95% confidence intervals. Blue symbols plot the same analysis but for delay-epoch EMG (averaged from 50 ms after target onset until 50 ms after the go cue).

Analyzed across all muscle recordings and target locations, correlation coefficients ranged from -0.03 to 0.45 and the mean slope-ratio was 0.41 (Figure 6C). A slope-ratio less than one is not necessarily unexpected. There are likely differences between the instructed-fast and slow EMG, beyond the differences related to peak velocity per se (e.g., greater co-contraction for the instructed-fast reaches, beyond that expected given their greater velocity). If so, the trial-by-trial slope will tend to underestimate the predicted slope (see the Discussion and the Supplementary analysis for further consideration of this phenomenon). Still, it is noteworthy how similar the results were for neural data recorded during the preparatory period (mean slope-ratio = 0.47) and for EMG recorded during the movement (mean slope-ratio = 0.41).

The analysis in figure 6B and C was based on the average EMG in a window (-75 to +250 ms r.e. movement onset) that included the entire movement. Assuming that motor preparation involves ‘planning’ of the entire movement, this is a reasonable window to use when comparing results for EMG and preparatory activity. However, we note that very similar results (mean slope-ratio = 0.42) were obtained using a shorter window (-75 to +50 ms) that preceded peak velocity. In a related analysis, instead of taking the average EMG for each trial, we took the projection of each trial’s EMG onto the direction defined by the difference in mean EMG between the two instructed speeds. Slope-ratios were similar to those found when using the average, and this was true whether we used the long (-75 to +250 ms, mean slope-ratio = 0.36) or short (-75 to +50 ms, mean slope-ratio = 0.44) analysis period.

As a control, we analyzed delay-period EMG activity. Trial-by-trial slopes are all near zero, and did not scale with the predicted slope (blue symbols in figure 6C, mean ratio of -0.11). As changes in the EMG signal during the delay were rare, one would not expect delay-period EMG to predict upcoming reach velocity.

Additional controls

If monkeys regularly ‘mistake’ an instructed-slow trial for an instructed-fast trial (and vice-versa), that could create a trial-by-trial relationship where one might not otherwise exist. However, most violations of the peak-velocity constraints involved reaching only slightly too fast or too slow. Large ‘categorical’ errors were uncommon, and were excluded from further analysis (see methods). We also re-computed the most critical analysis (figure 5D) using both stricter criteria (even minor peak-velocity violations rejected) and looser criteria (no rejections). Results were essentially identical to those originally obtained (mean slope-ratios of 0.49 and 0.42 respectively).

A second concern regards potentially non-stationary behavior over the 1000-4000 trials performed during a session. Peak velocities were often slightly lower overall near the end of a session, presumably due to minor fatigue or waning motivation. This non-stationarity in behavior could, if there were a parallel non-stationarity in the neural response, produce artifactual trial-by-trial correlations. However, on the timescale of a given recording behavior was typically quite stationary (e.g., Figure 1D). Furthermore, effects scaled with the predicted slope, something not expected given the potential artifact. Finally, we recomputed the analysis in figure 5D, regressing firing rate against both velocity and trial number (the latter minus its mean to allow pooling). This did not weaken the relationship of firing rate with velocity (mean slope-ratio = 0.46).

A third potential concern regards the pooling of data across target locations. Simulations (not shown) indicate that artifacts resulting from pooling are unlikely, as velocity and firing rate were expressed relative to their intra-condition means. We also performed three controls. The first addresses the concern that we pool across reach distances with different peak-velocity variances. All experiments employed the 12 cm distance, allowing us to repeat the analysis in figure 5D restricted to that distance, without a serious loss of statistical power. Results were very similar to those obtained initially, with a mean slope-ratio of 0.40. For the second control, we shuffled (before pooling) the intra-condition trial-by-trial relationship between velocity and firing rate. If the observed effects are artifacts related to pooling, shuffling should have no impact, as such artifacts (by definition) don’t result from true trial-by-trial relationships. In fact, shuffling completely eliminated effects (open circles in figure 5D). Finally, we computed the trial-by-trial slope directly for each neuron/target-location/instructed-speed (i.e. with no pooling). In the original analysis, we sought to pool enough data so that each regression would provide a meaningful value. Here we were willing to accept that individual measurements would be very noisy. Indeed, when plotting the trial-by-trial versus the predicted slope (Figure 7) the scatter is considerable. Still, given the large number of points, it is possible to perform a ‘meta-regression’, (black line, slope of 0.36, 95% CI = 0.25-0.47). Thus, the presence of trial-by-trial relationships that scale with the predicted slope can be detected without pooling.

Figure 7.

Figure 7

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Scatterplot of the trial-by-trial slope versus the predicted slope, with one point per neuron/target-location/instructed-speed (i.e., with no pooling). To limit the unreliability of individual measurements, this analysis was applied only where there were >15 trials for a given neuron/condition (1094 data points passed this test). The black line plots the results of a ‘meta-regression’ of the trial-by-trial versus the predicted slope, and reveals a significant ‘meta-slope’ (p<10-9, p<10-12 via a non-parametric Spearman’s rank correlation; y-intercept not significantly different from zero).

A final concern is that trial-by-trial relationships might arise from extensive experience with instructed-speeds. We therefore analyzed data from a third monkey (G), trained only on the basic instructed-delay task. Responses were recorded using an implanted electrode array, yielding 13 single-unit isolations with tuned delay-period activity. As illustrated by the examples in figure 8A,B, we observed statistically significant trial-by-trial relationships of both signs. Pooling across target locations, significant slopes (p<0.05) were found for 7/13 neurons. Although pooling increases statistical power, it may wash out effects if the ‘speed preference’ differs between target locations (something that can’t be known without instructed speeds). We therefore also computed the trial-by-trial slope for each individual target-location and neuron. Slopes ranged from -38 to 43 spikes/s per m/s, with 16% of the 182 regressions showing a significant effect at p<0.05. Figure 8C plots the distribution of the absolute slopes (top). The distribution expected by chance (due to measurement error) can be estimated using a bootstrap procedure (see Methods) and subtracted, yielding the black trace at bottom. This reveals a dearth of small observed slopes, and an excess of large observed slopes, relative to that expected by chance. This effect was statistically significant (the measured distribution was shifted to the right of the bootstrapped distribution; p<0.05, Mann-Whitney rank sum test). Slightly weaker (but also statistically significant), results were obtained for multi-unit recordings (34) from the same array (data not shown). We also repeated this analysis for the data from the instructed-speed-trained monkeys (gray trace). Direct comparison is somewhat problematic, given differences between the experiments, but it certainly does not appear that the effect in the untrained monkey is smaller. If anything the reverse is true.

Figure 8.

Figure 8

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Trial-by-trial relationships for a monkey (G) trained without instructed-speeds. A. An example neuron (G12) with a negative relationship. Responses are pooled (after subtracting means) across all 14 target locations. The regression slope was -13 spikes/s per m/s (r = -0.17). B. An example neuron (G17) with a positive relationship (slope = 10 spikes/s per m/s; r = 0.19). C. Histogram (using a logarithmic x-axis) of the frequency with which we observed different magnitude slopes. For each neuron (13) and target location (14, an average of 58 trials each) we regressed delay-period firing rate versus peak reach velocity and took the absolute slope. The top panel plots the distribution of those slopes, while the black trace at bottom plots the difference between this distribution and that expected by chance (see Methods). The grey trace plots the same analysis for data from monkeys A and B, based on the absolute distribution of trial-by-trial slopes seen in Figure 7.

As a final note, one would expect that, when two neurons exhibit a trial-by-trial correlation with behavior, they ought also exhibit a trial-by-trial correlation with each other, something that can be addressed using the array-recorded data. We used half the trials to ascertain whether each single neuron had a significant (p<0.05) trial-by-trial correlation with behavior. Using the other half, we then asked whether each pair had a correlation with one another. A correlation in the expected direction (positive for similarly ‘tuned’ neurons, negative for oppositely ‘tuned’ neurons) was found for 24/25 such pairs (p<0.05 for 10 of these, correlation coefficients ranged from -0.16 to 0.29).

Variability in reach distance

Given the natural scaling of reach velocity with distance, might the observed trial-by-trial relationship with velocity be secondary to a relationship with distance? More deeply, can the variability in reach distance (e.g., figure 1C) also be predicted by variability in motor preparation? To address the first question, we repeated the analyses in figure 5D using a multiple regression against peak velocity and reach distance (between hand position 100 ms before movement onset and 100 ms after movement completion). If the relationship with velocity were secondary to one with distance, then including distance in the regression should weaken that relationship. In fact, the mean slope-ratio was if anything slightly higher: 0.57. There were also clear individual cases where the speed and distance preference ‘disagreed’ (e.g., a preference for the greater distance but the slower instructed-speed). Thus, the trial-by-trial relationship between preparatory activity and velocity cannot be secondary to a relationship with distance. This also rules out any concern that the trial-by-trial relationship with velocity might be indirectly due to sensory mis-estimation of target distance (perhaps due to the target ‘jitter’ used during the delay), and/or initial hand position. This possibility was unlikely to begin with: trial-by-trial effects scaled with the instructed-speed preference (Fig. 5B,D), which would not be expected if those effects were artifacts of distance variability/tuning, or were somehow related to the use of target jitter. We also note that target jitter was not used for monkey G, who nevertheless showed trial-by-trial relationships with speed. More generally, the small amount of very rapid jitter we used is expected to have negligible impact on the ability to accurately estimate target location. Indeed, reaches of these monkeys on this task were at least as accurate as those of other monkeys in our laboratory trained using other cues (data not shown).

The above control doesn’t address the deeper question of whether distance variability might itself have a preparatory source. To do so we employed the analysis in figure 5D, but with the trial-by-trial slope computed with respect to reach distance, and the predicted slope computed from each neuron’s ‘distance tuning’. The mean slope-ratio for distance was similar to that for velocity: 0.41 (data not shown). However, statistical reliability was poor: for most (8/10) bins the 95% confidence interval overlapped zero. Alternately, when distance was analyzed as in figure 7, the ‘meta-slope’ was positive (0.71), but of unclear statistical significance (significant given a parametric correlation, but not given Spearman’s rank correlation). It thus appears likely that variability in reach distance also has a significant contribution from motor preparation (which in this case might be inherited from sensory sources). However, even for this large dataset (∼48,000 trials), there is insufficient statistical power to address this issue with confidence. The lack of power results from the fact that there is relatively little variability in reach endpoint, relative to the strength of distance tuning.

Discussion

Even in a highly-practiced task that provides a strong incentive for consistency, repeated reaches to the same target show fluctuations in peak velocity. Remarkably, these fluctuations are correlated with neural variability during a preparatory period, hundreds of milliseconds before movement onset. Thus, variability in some process active at that time – presumably motor preparation – is a source of the subsequent movement variability. Of course, one cannot conclude that a given recorded neuron plays a causal role in driving movement variability; it may merely correlate with one that does. Furthermore, our results cannot address whether the relevant variability arises in PMd/M1, or whether it is merely reflected there. Finally, there may be other relevant sources of preparatory variability that are uncorrelated with PMd/M1 activity. If so, our results will underestimate the true contribution of motor preparation to behavioral variability.

Our ability to detect effects depended on a novel task employing instructed speeds (Churchland et al., 2006a). The robust impact of instructed speed yielded predicted slopes as high as 100 spikes/s per m/s. This led to non-trivial changes in firing rate, even over the rather tight (a few 10’s of cm/s) range of natural variability. In contrast, analysis of reach distance yielded effects that, while not small, were not statistically reliable. Thus, the success of this study hinged on the novel instructed-speed task, which evoked tuning that was strong relative to the natural velocity variability.

Proportion of variability due to motor preparation

One cannot draw caveatless conclusions from our data regarding the proportion of movement variability that is due to preparatory variability. Doing so would require recording simultaneously from many neurons, and ‘decoding’ activity so as to predict velocity on a trial-by-trial basis. Presuming that sufficient neurons (potentially thousands) could be recorded, and presuming an optimal decode method were known, that approach could provide an unambiguous answer. While the current approach cannot do so, some reasonable estimates can be made with moderate confidence. The measured slope ratio of ∼0.5 lies halfway between the extremes illustrated in figure 3A. Intuition suggests that this will occur if ∼50% of the behavioral variability arises during motor preparation, something confirmed by simulations (supplementary materials). Those simulations further reveal that the measured slope-ratio typically provides a lower bound on the preparatory contribution. This occurs if the effect of instructed-speed is not truly due to ‘tuning’ for peak velocity, but for a factor that correlates with peak velocity. One presumes that this must be the case. Indeed, this is presumably the reason why the slope-ratio for the EMG recordings was on average only 0.41: EMG activity does not truly ‘code’ peak velocity, even if it causes it. Simulations never revealed circumstances where the slope-ratio overestimated the contribution. Thus, preparatory variability almost certainly contributes 50%, and probably more, of the behavioral variability. Certainly it is not surprising that there exists some variability (beyond just noisy spiking statistics) in the preparatory activity, and also not surprising that such variability has an effect on the subsequent movement. However, it was at the outset far from clear that preparatory variability makes more than a minimal contribution to movement variability. Indeed, many models/studies assumed that it did not make a significant contribution, certainly not one as high as ∼50% or more. Of the remaining ∼50%, our results cannot address what proportion is due to online noise generated in the periphery, what proportion might be online but central, and what proportion might arise from preparatory sources extrinsic to PMd/M1.

A sensory source of variability?

Might some of the observed movement variability have a sensory source (Osborne et al., 2005)? One presumes that endpoint variability is due in part to sensory uncertainty regarding target and hand location. This is especially true of tasks where the target is memorized (McIntyre et al., 1997; Messier and Kalaska, 1999; Soechting and Flanders, 1989). However, there is no obvious sensory source for the variability in reach velocity. The target was always either red or green; we did not vary the shade and monkeys were not asked to provide a graded response. The hand was stationary during the delay period, so its velocity (if not location) should be reasonably certain. Velocity variability could in theory be secondary to variability in reach distance (which could have a sensory source). However, the trial-by-trial relationship with velocity was preserved when distance was included in the regression. It is thus most likely that the preparatory variability in reach velocity has no simple sensory source.

Relevance to the role of PMd

The presence of a strong relationship with movement variability suggests that PMd/M1 preparatory activity plays a relatively low-level role in movement preparation/production. Prior work has found evidence for a higher-level (Lebedev and Wise, 2001; Wise et al., 1997) and/or visuo-spatial (Johnson et al., 1999; Shen and Alexander, 1997) role. Yet this does not necessarily constitute a contradiction. The act of movement planning may necessitate a mixture of high and low-level signals. The current results indicate only that any representation employed is not purely visuo-spatial. However, whether the observed trial-by-trial relationships reflect tuning for something abstract (such as intended speed) or something lower level (such as muscle activity) cannot be determined from our data. Indeed, the answer may be different for different neurons. However, it is worth noting that the observed trial-by-trial relationships are unlikely to be related to expected reward (Roesch and Olson, 2004), which would predict opposing slopes for the two instructed speeds.

Sources of movement variability

One expects planning variability to be substantial for novel or complex tasks, or when the target must be remembered. But for simple highly-practiced movements, it is often assumed that the movement plan is essentially identical on every trial. After all, movement planning should be ‘easy’ under such circumstances, and is therefore an unlikely source of variability. Given such expectations, it is surprising that we found that roughly half, and perhaps more, of the variability in reach speed appears to be due to movement planning. This is especially so as the task was so well practiced (hundreds of thousands of trials) and behavior so consistent. Under similar circumstances, prior work has argued (van Beers et al., 2004) or assumed (Todorov and Jordan, 2002) that variability in motor preparation plays a negligible role. van Beers et al. (2004) specifically argues that velocity variability is due not to movement planning, but to online noise, and posits a unique form of such noise. One can understand this expectation: looking at the small variations in reach velocity in figure 1C, they seem like noisy instantiations of a single ‘plan’. Yet our recordings reveal that those small fluctuations were, to a substantial degree, predetermined by events that occurred before the reach began. In general, when we fail at a well-practiced movement (e.g., a dart throw or golf swing) we tend to assume that something went wrong during execution. Our results indicate that it is at least as likely that something went wrong during motor preparation.

Relevance to models of optimal control

A large and influential body of theory is based on efforts to infer optimal strategies of motor control (Hamilton et al., 2004; Hamilton and Wolpert, 2002; Harris, 2004; Harris and Wolpert, 1998; Haruno and Wolpert, 2005; Iguchi et al., 2005; Simmons and Demiris, 2006; Todorov, 2002; Todorov, 2004; Todorov and Jordan, 2002; van Beers et al., 2002). These approaches explain the features of real movements by inferring optimal strategies in the presence of noise. Their conclusions sometimes depend critically on the assumption of ‘signal-dependent’ noise arising during the movement (e.g., at the neuromuscular junction). However, until now this assumption had been based on behavioral observations and muscle recordings and had not been investigated at the neural level. Our results certainly do not rule out a contribution of signal-dependent noise during execution. They do indicate that significant amounts of movement variability arise in the motor preparation stage. The contribution of preparatory variability would presumably be larger still for a more difficult and/or less-practiced task. Thus, we must reconsider those conclusions that depended on the assumption that signal-dependent execution noise is the key limiting factor. For example, reaches may exhibit smooth velocity profiles to minimize the impact of signal-dependent noise (Harris and Wolpert, 1998). Alternately, smooth movements may be ‘easier’ to plan and may incur less variability at the motor preparation stage.

In a larger sense, our results are entirely compatible with models of optimal control, which certainly can incorporate sensory or other noise sources (Todorov, 2004; Todorov and Jordan, 2002). Indeed, some such models are naturally extended to incorporate variability in motor preparation. For example, the model of Todorov and Jordan (2002) necessitates that the online controller be precisely ‘customized’ for different movements. This is an implicit form of motor preparation and a natural place to assume some degree of variability. This is especially true because the computations that determine the optimal controller are – for most models – far more challenging than those actually performed by the controller. Furthermore, a very general feature of optimal control models – using feedback to optimize, but allowing variability to accumulate in harmless dimensions – applies naturally to the domain of motor preparation. We have previously argued that motor preparation involves the optimization of neural activity over time (Churchland et al., 2006b). This view suggests that motor preparation involves potentially difficult and time-consuming optimizations. If so, it should not be surprising that motor preparation is a significant source of movement variability.

Experimental Procedures

Task and training

Animal protocols were approved by the Stanford University Institutional Animal Care and Use Committee. Our basic methods have been described previously (Churchland et al., 2006a; Churchland et al., 2006b). Briefly, three adult male monkeys (Macaca mulatta, ∼10 kg) sat in a customized chair with head restraint and performed the task on a fronto-parallel screen. Hand position was tracked optically (60 Hz, accuracy of 0.35 mm). Most data were collected from two monkeys (A and B) using an instructed-speed task. Green and red targets instructed ‘slow’ and ‘fast’ reaches respectively, with success determined by peak hand speed falling within a window (for slow) or above a threshold (for fast, see Fig. 1D). These criteria scaled according to the natural progression of reach velocity with distance.

We typically employed 2 target distances / 7 directions. Some data (41 neurons from monkey B) were collected using 5 distances / 2 directions. From the standpoint of the current study, the exact configuration matters little. The key comparisons are made between instructed-speeds at a given target location and among trials for a given instructed speed. Ocular fixation was not enforced, but monkey A typically fixated the central spot throughout the delay. In contrast, monkey B typically fixated the target from ∼200 ms after its appearance until after the reach was executed. Delay period durations were randomized on each trial either from 400-800 ms (most experiments) or 500-900 ms (experiments with 5 distances).

We also analyzed data from a third monkey (G) not trained on the instructed speed task, using 2 target distances / 7 directions, with a 200-700 ms range of delay-period durations. For this task, the target never ‘jittered’. The go cue was instead a slight increase in target size and the simultaneous disappearance of the central touch point. For this monkey, fixation was enforced near the target from shortly after its onset until after the go cue.

Datasets

For monkeys A and B, neural data were recorded from PMd and from the adjacent part of M1 (supplementary figure 1), using single microelectrodes and conventional techniques. Of 189 single-neuron recordings 136 passed our criteria for robust and tuned delay-period activity (Churchland et al., 2006a). Defining cylinder zero (approximately the middle of the precentral dimple, see supplementary figure 1) to be (very roughly) the PMd/M1 ‘border’, 53% (47%) of analyzed neurons were recorded from PMd (M1). Data from monkey G were recorded using an electrode array (Cyberkinetics, Foxborough, MA) chronically implanted in caudal PMd. 13 single-neuron isolations passed the inclusion criteria.

Data analysis

Analyses are largely based on two measurements: peak hand velocity and delay-period firing rate. The first was computed by differentiating, for each trial, the horizontal and vertical hand position signals, and applying a low-pass (25 Hz) filter. Peak hand velocity was then based on the velocity component in the direction of the target (virtually identical results were obtained if we instead analyzed peak speed). For each trial, the mean delay-period firing rate was computed from 50 ms after target onset until 50 ms after the go cue (∼50 ms being the minimum latency of the cortical response). Delay-period durations were different for each trial. Although mean firing rates are often fairly stationary over the course of the delay (e.g., figure 2A) they are rarely perfectly so. This raises the question of whether one should prefer to compute firing rate over the entire delay or over the same period for every trial: perhaps from 50 ms after target onset until 50 ms after the minimum delay. In prior analyses we have generally found that statistical power is better for the first method; any variability due to non-stationarity is more than compensated by improving the estimate of spike rate by averaging across more time. From the standpoint of the present analysis, variability in spike rate right before the go cue might be most critical in driving subsequent behavior, something that would be lost for most trials using the ‘minimum-delay’ method. Thus, we performed all analyses based on the mean spike rate across the entire delay for each trial. We then repeated key analyses using the minimum-delay method. As might be expected, effect sizes were somewhat reduced (∼20%, but still easily reaching statistical significance).

Trials aborted because the hand moved during the delay (or never moved) were not saved but comprised at most a few percent of all trials. Saved trials were analyzed if the target was hit accurately and held until the time of the reward (∼98% of saved trials). Most failures of the instructed-speed aspect of the task involved peak velocity being only slightly too fast or slow. These failures presumably did not reflect a lack of effort on the part of the monkey but simply the natural variability on this challenging task. We therefore analyzed all trials so long as the peak velocity did not intrude on the accepted range for the other instructed-speed. This method included >90% of trials and was intended to strike a balance between including the natural variability in peak velocity and excluding overt failures where the monkey might have planned or intended a reach of the wrong speed. Analysis was based on peak hand velocity measured offline (in the interests of greater accuracy), rather than the judgment made by the software during the trial. However, the two estimates are very strongly correlated, and results were essentially identical (mean slope-ratio of 0.45) if the latter was used.

Many analyses involved pooling data across target locations and/or neurons. Mean firing rates differ across target-locations/neurons, and different target distances have different peak velocities. Before pooling, we therefore subtracted, from each trial’s delay-period firing rate, the mean for that neuron / target-location / instructed-speed. The same was done for peak velocity.

When pooling data for a given neuron, we wished to focus on neurons with a consistently strong effect of instructed speed, for which detectable trial-by-trial effects might be expected. We first determined a neuron’s speed preference. Data were then pooled across target locations where the preferred speed evoked the larger response by at least 10 spikes/s, and where this difference was statistically reliable using generous criteria (p<0.1 via a one-tailed t-test). A second pool was formed for the non-preferred instructed-speed, so long as there were target locations with a mean firing rate >5 spikes/s (else many trials could have no spikes during the delay). Note that pools for both instructed speeds share the same predicted slope (see Fig. 4). A given pool was analyzed further if it contained >50 trials. This procedure led to 44 usable pooled datasets, 33 for fast-preferring neurons and 11 for slow-preferring neurons. In principal, a given cell could contribute pooled data for both speed preferences (if the preferred speed depended on target location) but in practice sufficient trials were never pooled for both preferences. It was common for a given neuron to contribute pooled data for both instructed speeds (as for both examples in Fig. 4).

For the analyses in figure 5B,D we pooled data across neurons/target-conditions with a similar predicted slope (in bins from -60 to 110 spikes/s per m/s). Data were included for every neuron/target-condition with ≥5 trials/condition. That criterion ensured we could make a reasonable estimate of the predicted slope (3174 of 3480 cases satisfied this condition, with a mean of 15 trials). Data for the two instructed speeds share the same predicted slope and were thus always pooled together.

For one analysis (figure 8) we computed the distribution of regression slopes expected by chance. For each neuron, target-location, and (if appropriate) instructed speed, we randomly shuffled the relationship between firing rate and peak velocity. We did this 20 times for each neuron/target-location, and took the absolute slope of the regression for each shuffle. We then computed the distribution of slopes across all repetitions, neurons, target-locations and instructed speeds, and subtracted this ‘correction’ from the observed distribution.

EMG recordings

EMG activity was recorded using hook-wire electrodes (44 ga w/ 27 ga.canula, Nicolet Biomedical, Madison, WI) placed in the muscle for the duration of single dedicated recording sessions. Voltages were conventionally amplified, filtered at 150-500 Hz and digitized at 1000 Hz. Before taking means, digitized voltages were differentiated (to eliminate any low frequencies surviving the analog filtering) and rectified.

Supplementary Material

01

Acknowledgements

We thank Gopal Santhanam, Stephen Ryu, and Byron Yu for contributing data from monkey G. We thank Melissa Howard for animal care and Sandra Eisensee for administrative assistance. Research was supported by a Burroughs Wellcome Fund Career Award in the Biomedical Sciences (MMC), a Helen Hay Whitney postdoctoral fellowship (MMC), an NIH postdoctoral training fellowship (MMC), the Stanford MSTP (AA), a BioX Graduate Student Fellowship (AA) and the following sources for KVS: Burroughs Wellcome Fund Career Award in the Biomedical Sciences, the Stanford Center for Integrated Systems, the NSF Center for Neuromorphic Systems Engineering at Caltech, ONR, the Sloan Foundation and the Whitaker Foundation.

Footnotes

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