Perturbation of Macaque Supplementary Motor Area Produces Context-Independent Changes in the Probability of Movement Initiation

Task and behavior

Two monkeys (Monkeys Ba and Ax) executed radial reaches in eight directions across three contexts. Contexts were cued by target color and differed regarding the cues and task constraints governing when movement should be initiated. SMA has been proposed to contribute preferentially when initiation is prompted more by internal considerations versus external cues (Jenkins et al., 2000; Passingham et al., 2010). We note that goal-directed voluntary movements are essentially never purely self-initiated; initiation will almost always relate to some preceding instruction or information. However, movements vary greatly in the degree to which initiation timing is linked to external sensory cues. We assessed the tightness of that link via the RT: the latency between the cue indicating that movement is allowed and subsequent reach initiation. Shorter/more-tightly distributed RTs were taken to indicate a tighter link between external cues and movement initiation.

In the self-initiated context (Fig. 1A, blue), monkeys were free to reach upon target appearance, but waiting longer yielded increased reward up to a maximum at 1200 ms. Growing reward was mirrored by increasing target diameter, eliminating any need to estimate elapsed time. RTs were long with broad SDs: 1069 ± 142 ms (mean ± SD) for Monkey Ba and 1023 ± 106 ms for Monkey Ax (Fig. 1B,C, blue line). The considerable RT variability presumably reflects competition between internal factors (desire for immediate reward versus desire for large reward) with different factors dominating on different trials. Consistent with this interpretation, the distribution of self-initiated RTs during training was very sensitive to the reward schedule. The self-initiated context does not provide a situation as unrestricted as in Thaler et al. (1995), where monkeys could go minutes between self-initiated movements. Instead, the self-initiated context gives monkeys considerable control over when to initiate while also providing a well-defined temporal window upon which analysis could concentrate.

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Figure 1.

Overview of task and stimulation. A, Overview of the three task contexts. Each context required the monkey to complete a reach from a central position to one of eight targets, arranged radially as shown at right. In the self-initiated context, the target was blue and grew steadily with time. In the cue-initiated context, the target was red and remained small until enlarging suddenly, which provided the go cue. In the quasi-automatic context, the target was yellow and the go cue was the onset of target motion. Left, Timing of key events. Gray bars represent times when stimulation could begin. Tan bars represent a variable-duration delay period, present only for the cue-initiated and quasi-automatic contexts. Black bars represent times when movement initiation was allowed. For the self-initiated context, initiation was allowed anytime from target onset until 300 ms after the target stopped growing at 1200 ms. Thus, visual cues placed only broad constraints on when movement should be initiated. The more important determinant was available reward, which grew as the target grew. For the cue-initiated context, initiation was allowed only from 100 to 500 following the go cue (RTs < 100 ms were disallowed to discourage attempts to anticipate the go cue). These requirements were the same for the quasi-automatic context, although in practice capturing the target mid-flight typically necessitated RTs < ∼300 ms. B, C, Cumulative RT distributions for the three contexts in the absence of stimulation. Blue represents self-initiated. Red represents cue-initiated. Yellow represents quasi-automatic. D, Targeted region of SMA for the left (contralateral) hemisphere. Most stimulation sites lay within the medial wall. E, Distribution of stimulation currents used during experiments.

The cue-initiated context (Fig. 1A, red) emulated the standard instructed-delay paradigm: a variable delay period (0–1000 ms) separated target onset from a go cue, indicated by an instantaneous increase in target size and the simultaneous disappearance of the central touch point. After the go cue, monkeys still had modest leeway regarding the exact moment of initiation; RTs up to 500 ms were allowed. Yet monkeys generally reached promptly out of desire for immediate reward: RTs were 238 ± 49 ms and 222 ± 37 ms (mean ± SD for Monkeys Ba and Ax; Fig. 1B,C, red line). Thus, relative to the self-initiated context, initiation was more tightly locked to an external cue. Initiation occurred closer in time to the key cue (RTs were approximately one-fourth as long) and was less temporally variable (SDs were approximately one-third as wide).

The quasi-automatic context (Fig. 1C, yellow) was similar to the cue-initiated context and also included a 0–1000 ms delay. However, the go cue was the onset of target motion along a radial path toward the screen's edge. Success required executing a reach that intercepted the target mid-flight. Moving targets are known to naturally produce reactive, short-RT, intercepting reaches (Perfiliev et al., 2010; Wong et al., 2017; Lara et al., 2018a). In keeping with that finding, RTs were 199 ± 28 ms and 184 ± 27 ms (mean ± SD for Monkeys Ba and Ax; Fig. 1B,C, yellow line). Essentially no training was required to obtain short RTs; RTs dropped immediately upon the introduction of moving targets. Thus, the quasi-automatic context naturally evoked initiation that was tightly locked to a very salient external cue. Initiation occurred even closer in time to that cue than in the cue-initiated context, with even lower temporal variability. Given sizeable physiological delays (∼130 ms including afferent, efferent, and EMG-to-velocity delays), initiation in the quasi-automatic context occurs with little or no time for internal deliberation. Thus, if SMA plays a specialized role in internally initiated movements, SMA would be expected to make little contribution to initiation in the quasi-automatic context.

Monkeys successfully completed the majority of trials for all three contexts: 94% and 99% of cue-initiated trials (Monkey Ba and Monkey Ax, respectively), 92% and 96% of self-initiated trials, and 86% and 87% of quasi-automatic trials. Reach trajectories were similar across contexts; the primary difference was a tendency for reach velocity to be slightly higher for quasi-automatic reaches (Fig. 2E,F). We have previously shown that these three contexts evoke similar patterns of muscle activity and similar patterns of neural activity in primary motor and premotor cortex (Lara et al., 2018b). In contrast, neural activity in SMA (recorded from sites interspersed with those stimulated in the present study) varies robustly across these three contexts (Lara et al., 2018b). The presence of differential neural activity raises the possibility that SMA could be making differential contributions to initiation across contexts. On the other hand, the fact that SMA is active for all contexts suggests that SMA might contribute to initiation in all contexts.

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Figure 2.

Microstimulation produces complex changes in RT, but not reach kinematics. A, B, Cumulative RT distributions for trials with no stimulation (dashed gray traces), early stimulation (light colored traces), and late stimulation (dark colored traces). C, D, Summary of the above effects in terms of changes in mean RT. Error bars indicate SEs. The mean ± SE were computed across trials. For all comparisons, the RT of nonstimulated trials was computed using only trials where the delay period length and RT would have allowed stimulation to be delivered. This eliminates potential biases; for example, late stimulation might otherwise appear to increase RT simply because late stimulation implies that movement has not yet been initiated. E, F, Mean speed profiles for reaches to one representative target (target located rightward of central position) for the three contexts. Dashed gray represents no stimulation. Light colored traces represent early stimulation. Dark colored traces represent late stimulation. G, Movement kinematics for trials with no, early, and late stimulation. Symbols plot mean values. Error bars indicate SEs, computed across conditions. Initial reach direction was measured relative to target direction. Endpoint variability was measured as the SD of reach endpoint within each condition.

Reach kinematics were largely unaffected by stimulation

We delivered microstimulation (200 ms train of 333 Hz biphasic pulses) at 122 sites in SMA of 2 monkeys (Fig. 1D). Stimulation sites lay within a region where, during separate recordings, we observed robust preparatory and movement-related activity in this task. Task-related activity was observed with approximately equal magnitude both contralateral and ipsilateral to the reaching hand. The impact of stimulation was thus examined for both hemispheres (Monkey Ba: 66 contralateral and 11 ipsilateral sites; Monkey Ax: 24 contralateral and 21 ipsilateral sites). For each site, we first determined the threshold for directly eliciting movement. Thresholds varied broadly (Fig. 1E), from 10 μA to above the highest tested current (150 μA). During experiments, stimulation current was set below threshold. Unless otherwise stated, data are pooled across sites for statistical power. This yielded a total of 9854 and 4591 stimulated trials (Monkeys Ba and Ax), comprising 20% and 20% of all trials. Thresholds, and thus currents, tended to be higher for Monkey Ba. As will be described below, the impact of microstimulation was qualitatively similar for both monkeys, with some effects being larger in Monkey Ba and others being larger in Monkey Ax. Thus, there was not an obvious relationship between higher currents and larger effects.

We wished to assess the impact of stimulation on movement initiation, independent of any impact on the reaches themselves. Conveniently, stimulation had almost no impact on reach kinematics. Velocity profiles on stimulated trials were very similar to those on nonstimulated trials. The correlation between the average velocity trajectories for stimulated and nonstimulated trials was 0.998 and 0.995 (Monkeys Ba and Ax, mean across conditions). The primary effect of stimulation on kinematics was a small increase in reach-speed variability. Across monkeys/contexts, there was a 1.2%–9.9% increase in the SD of peak reach speed. This effect was significant (p < 0.05 for each monkey, paired t test, calculated across 77 and 45 stimulation sites) for the cue-initiated and quasi-automatic contexts only. We also observed small and inconsistent changes in reach angle variability. For Monkey Ba, microstimulation in the self-initiated context caused a small (1%) but significant (p < 0.001, paired t test) tightening of the circular SD of reach angle, yet microstimulation in the other two contexts caused a small increase (2% and 1%, p < 0.001 for both, paired t test). For Monkey Ax, microstimulation had no impact on reach variability in the self-initiated context, caused a modest increase (10%, p < 0.001, paired t test) in the cue-initiated context, and a small decrease (3%, p < 0.001, paired t test) in the quasi-automatic context. Thus, the impact of stimulation on reach kinematics was small and did not interfere with the ability to assess changes in the time of reach initiation.

Microstimulation impacts RT

We grouped data into early-stimulation trials (stimulation delivered well before initiation would typically occur) and late-stimulation trials (stimulation delivered close to when initiation would typically occur). Because the distribution of initiation times differed across contexts, we defined early versus late relative to a common reference: the time when movement had begun on 10% of nonstimulated trials in that context. Early-stimulation trials were those where microstimulation began 700–550 ms before this reference, such that stimulation ended well before movement initiation became likely. Late-stimulation trials were those where microstimulation began 300–150 ms before the reference, such that stimulation occurred just when initiation was becoming likely.

For Monkey Ba, early and late stimulation trials constituted 12% and 17% of stimulated trials (3% and 4% of all trials). There were 1218 early stimulation trials: 353, 442, and 423, for the self-initiated, cue-initiated, and quasi-automatic contexts. There were 1647 late stimulation trials: 426, 631, and 590, for the self-initiated, cue-initiated, and quasi-automatic contexts. For Monkey Ax, early and late stimulation trials constituted 13% and 16% of stimulated trials (3% and 3% of all trials). There were 609 early stimulation trials: 161, 215, and 233, for the self-initiated, cue-initiated, and quasi-automatic contexts. There were 738 late stimulation trials: 170, 318, and 250, for the self-initiated, cue-initiated, and quasi-automatic contexts.

Late stimulation delayed movement initiation, increasing RT relative to nonstimulated trials. This was true for both monkeys and all three contexts (Fig. 2A–D; p < 0.001 for all, two-sample t test). Notably, SMA stimulation increased RT even for the quasi-automatic context, despite initiation being tightly linked to external cues. However, the RT increase was smaller for the quasi-automatic context than for the other two contexts, suggesting some potential interaction between context and the impact of stimulation.

Early stimulation had the opposite effect on RT, and effects depended even more strongly on context. For the self-initiated context, early stimulation advanced movement initiation (p < 0.001 and p = 0.002 for Monkeys Ba and Ax, two-sample t test). This RT reduction was much smaller for the other two contexts: ranging from 1 to 9 ms; p < 0.05 only for the quasi-automatic context.

We wished to rule out the possibility that changes in RT are secondary to changes in reach kinematics (e.g., changes in reach velocity might alter the estimate of movement onset). This is unlikely: we showed above that stimulation has little average impact on kinematics. However, it remains possible that early and late stimulations have sizeable but opposing effects that largely cancel out on average. This was not the case (Fig. 2E,F). Movement duration, initial reach direction, and endpoint variability were not significantly different between no-stimulation, early-stimulation, and late-stimulation trials (Fig. 2G). We did observe a small increase in endpoint error following early stimulation (data not shown): a 0.31 mm increase in mean error in Monkey Ba and a 0.85 mm increase in Monkey Ax (Fig. 2G; p = 0.03 and p < 0.001, respectively, two-sample t test). This increase in endpoint error did not impact task performance: the percentage of trials failed due to a missed target was unchanged (remaining at 1.4% for Monkey Ba and 0.3% for Monkey Ax). We also did not observe any interaction between reach direction and the impact of stimulation on RT. For example, the change in RT with stimulation did not differ between ipsilateral and contralateral targets (p > 0.05 for both monkeys, all contexts, and both early and late stimulation, two-sample t test, calculated across trials).

Thus, SMA microstimulation alters the timing of reach initiation, with negligible impact on the reaches themselves. This is consistent with SMA activity contributing, directly or indirectly, to the computations determining when movement is triggered. SMA stimulation had an effect on all three contexts, arguing that the contribution of SMA to movement initiation is not limited to situations where initiation is less tightly cue-locked. However, the impact of SMA stimulation appears potentially context-dependent. Late-stimulation-driven RT increases were smaller for the quasi-automatic context, and early-stimulation-driven RT decreases were sizeable only for the self-initiated context. Yet as will be detailed below, strong conclusions should not be drawn without first considering that RT may not be the only, or even the most natural, way to measure changes in the tendency to initiate movement.

Movement initiation as a probabilistic process

The central goal of this study is to characterize how perturbations of SMA activity impact the tendency to initiate and to ask whether that impact is context-dependent. We assume that, at each time, underlying movement-initiating computations have produced a particular neural state (Fig. 3, purple box). That neural state, or more precisely the distribution of such states across trials, yields a probability of initiating at that time. As one example, in a diffusion-to-bound model, initiation becomes probable when the state tends to be close to the bound. We refer to the baseline (without stimulation) probability of initiation at time t as P₀(t).

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Figure 3.

Framework relating the underlying neural state to behavioral measures of movement initiation. The underlying neural state evolves over time (purple box). At each time, there is a probability of initiation, P₀ (yellow box), produced by that underlying state. (More generally, at a particular time, there is a distribution of possible neural states which determine P₀ at that time.) The values of P₀ are not directly observed on a single trial. Rather, one observes multiple time points where initiation does not occur (0 in green box) and then a time when initiation does occur (1 in green box). These observations are summarized as the RT: the time from when movement was first allowed until it was initiated. Across many trials, one can compute the mean RT, which then becomes a summary of the tendency to initiate. However, a more direct summary can be produced by estimating P₀ for each time where sufficient data are available.

On a given trial, one does not directly observe P₀(t). Instead, one observes a stretch of time when movement was not initiated (“0's” in green box) and then a particular time (“1” in green box) when movement was initiated. These observations are often summarized as a single number: the RT. Yet with sufficient trials, one can also estimate P₀(t) at each time. To do so, one takes all trials where movement has not yet occurred by time t and computes the proportion where movement is initiated at time t. This value is also referred to as the hazard rate.

P₀(t) and the RT are intimately related: P(RT = t) = P₀(t)Π_τ=1:t(1 − P₀(t − τ)). Note that P(RT = t), unlike P₀(t), reflects the entire history of initiation tendencies and thus the entire history of neural states. This creates some interpretational complexities. Suppose that a perturbation alters the neural state at time t and, in doing so, changes the probability of initiation. The resulting change in mean RT is a function not only of that change but of the initiation probabilities at all preceding times. Furthermore, stimulation at time t_s implies RT > t_s, resulting in a longer mean RT even if stimulation has no effect. This can be accounted for (as was done in the analyses in Fig. 2C,D), but doing so adds a layer of complexity. Another complication is that, to properly compare changes in RT, one has to match (across contexts) the time of stimulation. We did so above by defining a common reference time based on when initiation tended to normally occur. This is a reasonable choice, but other reasonable choices are possible. Given these complexities when interpreting changes in the RT, we found it desirable to directly assess changes in the probability of initiation. Doing so allows one to simply inquire, for a given baseline probability, whether one observes a context-dependent change in that probability following stimulation.

Baseline probabilities of initiation

For each context, we estimated P₀(t), the baseline (without stimulation) probability that initiation occurs soon after time t, given that it has not occurred before time t. We plot that probability as a heat-map (Figs. 4, 5, top left, bars). One challenge when assessing P₀(t) is a need for high trial counts. For large values of t, there may be few trials where movement initiation has not yet occurred, preventing a reasonable estimate of P₀(t). Still, by pooling across multiple sites, we were able to estimate P₀(t) across a sizeable domain for every context (all non-gray values).

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Figure 4.

Impact of microstimulation on initiation probability for Monkey Ba. A, Heat-plots of P₀ (top) and P_stim (bottom) for the self-initiated context. Time is plotted relative to target onset. For P_stim(t,t_s), each row plots the probability of initiation, as a function of time since target onset, for a particular time of stimulation. White line indicates the onset of microstimulation for each row. Gray and black contour lines indicate P = 0.25 and P = 0.65, respectively. B, ΔP_stim for the self-initiated context. C, D, P₀, P_stim, and ΔP_stim for the cue-initiated context. Time is plotted relative to the go cue. E, F, P₀, P_stim, and ΔP_stim for the quasi-automatic context. Time is plotted relative to the go cue.

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Figure 5.

A–F, Impact of microstimulation on initiation probability for Monkey Ax. Same format as in Figure 3.

For the self-initiated context, P₀(t) remains low for ∼600 ms after target onset (Figs. 4A, 5A; Monkey Ba and Monkey Ax, respectively). The optimal strategy in the self-initiated context is to reach when the presently available reward exceeds the temporally discounted future reward. This idealized strategy would involve selecting a particular time (or equivalently, a particular target size) upon which to initiate, resulting in a step-like increase in P₀(t). Monkeys did not follow this strategy; P₀(t) increased more gradually, reaching values >0.9 only around the time of maximal reward (1200 ms after target onset). Thus, at least from an external perspective, monkeys behaved probabilistically: P₀(t) increased monotonically with the juice value of the target.

In the cue-initiated context, P₀(t) increased rapidly soon after the go cue (Figs. 4C, 5C). For the quasi-automatic context, P₀(t) evolved similarly, but the increase was more sudden, occurred slightly earlier, and more swiftly reached values near unity (Figs. 4E, 5E). This underscores the degree to which initiation was tightly locked to target-motion onset in the quasi-automatic context: P₀(t) was essentially unity shortly after motion onset.

The step-like increase in P₀(t), especially for the quasi-automatic context, carries potential implications regarding whether perturbations of neural activity have behavioral consequences. As one example, there may be floor/ceiling effects when P₀(t) is near zero/unity. Such considerations are a major motivation for considering P₀(t) directly, rather than relying only on RT measurements. We will return to this point below. For now, we simply stress that the temporal epoch where movement initiation is likely yet uncertain (red zones) has a different duration for the three contexts.

Microstimulation alters initiation probability

For each context, we estimated P_stim(t,t_s): the probability that initiation occurs soon after time t, given that it has not occurred before time t and given stimulation near time t_s. We first consider data for Monkey Ba, beginning with the self-initiated context (Fig. 4A). Each row of the bottom heat plot shows P_stim(t,t_s) for a particular value of t_s. Each such row resembles a slightly altered version of P₀(t); differences reflect the impact of stimulation. Early stimulation increased the probability of initiation (the red area extends further leftward). In contrast, late stimulation reduced the probability of initiation (the red area extends further rightward).

To assess these effects, we computed the change in the probability of initiation due to microstimulation: ΔP_stim(t,t_s) = P_stim(t,t_s) − P₀(t). ΔP_stim(t,t_s) was not a simple function (Fig. 4B). There were regions where initiation became more likely (red) and regions where it became less likely (blue). For early stimulation during the self-initiated context, ΔP_stim(t,t_s) was largely positive (top rows). Conversely, for late stimulation, ΔP_stim(t,t_s) was largely negative (bottom rows). This structure agrees with the finding that self-initiated RTs were advanced by early stimulation and delayed by late stimulation.

For the cue-initiated context, late stimulation extended the region where the probability of initiation was low (Fig. 4C, the black trace indicating the 65th percentile bows to the right). This resulted in negative values of ΔP_stim(t,t_s) (Fig. 4D, blue region). This movement-inhibiting effect agrees with the finding that late stimulation increased RT. Notably, early stimulation had the opposite effect and was movement-promoting (Fig. 4D, red region). This movement-promoting effect is barely detectable at the level of RTs (Fig. 2C) but becomes apparent when assessing ΔP_stim(t,t_s). Notably, ΔP_stim(t,t_s) shared some features between the self-initiated and cue-initiated contexts. In both contexts, early stimulation was movement promoting and late stimulation was movement inhibiting.

For the quasi-automatic context, ΔP_stim(t,t_s) appears by inspection to differ only slightly from P₀(t). In both cases, the probability of initiating underwent a rapid increase, approaching unity, shortly after the go cue (Fig. 4E). Yet examining ΔP_stim(t,t_s) reveals that early stimulation was movement promoting (Fig. 4F, red regions in top rows) and late stimulation was movement inhibiting (blue regions in bottom rows). These changes are not small, but they are restricted to a narrow temporal window.

For all three contexts, similar effects were observed for Monkey Ax (Fig. 5). One difference was the presence of fewer positive values of ΔP_stim(t,t_s), especially for the self-initiated and cue-initiated contexts. Thus, movement-promoting effects were less strong in Monkey Ax, consistent with the more modest advancement of self-initiated RTs by early stimulation. Nevertheless, for both monkeys, ΔP_stim(t,t_s) shared basic features across contexts: early stimulation was largely initiation-promoting and late stimulation was largely initiation-inhibiting.

The above results thus reveal a commonality in ΔP_stim across contexts. However, all effects were more temporally restricted for the cue-initiated and quasi-automatic contexts, relative to the self-initiated context. A straightforward possibility is that this occurs because only the self-initiated context produces a broad range of times where P₀ had intermediate values (i.e., neither zero nor unity). Might stimulation have a common impact across contexts, with that impact becoming patent only when the probability of initiation lies within a range amenable to modulation? We explore this possibility below.

A simple model captures changes in initiation probability in the self-initiated context

We considered a simple model where stimulation impacts the odds of initiation. The odds of initiation is the ratio of the probability of initiating to the probability of not initiating: O₀(t) = . We model the impact of microstimulation as follows:

The kernel k(t − t_s) describes the impact of stimulation, delivered at time t_s, on the odds of initiating at time t. Under this model, the impact of stimulation depends only on the elapsed time since stimulation and not on the overall time within the trial. Using odds provides a natural way of modeling the hypothesis that microstimulation tilts the balance toward or against initiation. The odds of an event can be doubled regardless of baseline probability. For example, for baseline initiation probabilities of 1%, 50%, and 98% (odds of 1/99, 1, and 49), doubling the odds would result in poststimulation probabilities of ∼2%, 67%, and 99% (odds of 2/99, 2, and 98). The central question is whether it is possible for a single kernel to capture effects across all combinations of t and t_s. We first considered each context separately, optimized the kernel, and examined the resulting fit.

Figure 6 illustrates model predictions for the self-initiated context for Monkey Ba. Optimization resulted in a kernel with a negative lobe followed by a positive lobe (orange trace at top). To illustrate the impact of this kernel, we first consider the effect of stimulation delivered 220 ms after target onset (Fig. 6A). Stimulation caused a leftward shift in the empirical probability of initiation: P_stim (black trace) rises earlier than P₀ (gray trace). This effect is captured by the model (dashed orange trace). The predicted values, P̂_stim exhibit a leftward shift because the positive lobe of k occurs when P₀ is >0 but not yet maximal. Conversely, the negative lobe has little impact because P₀ is essentially zero at the relevant times. Stimulation 570 ms after target onset (Fig. 6B) caused a mixed effect: an initial reduction in initiation probability, followed by a small elevation. The model captures this mixed effect, due to the biphasic kernel. Stimulation 740 ms after target onset (Fig. 6C) caused a rightward shift in P_stim. This is again captured by the model; the negative lobe of k aligns with times when initiation probability is >0 but not unity. The fit of P̂_stim to P_stim had an R² > 0.98 for each of these 3 cases. Thus, effects could be captured by a model where stimulation had an immediate movement-inhibiting effect (decreasing the odds of initiation) followed by a movement-promoting effect (increasing the odds of initiation).

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Figure 6.

A single, multiplicative kernel predicts P_stim for early, middle, and late stimulation in the self-initiated context. A, Data and predictions for stimulation delivered starting 220 ms after target onset. Gray trace represents P₀(t), the baseline probability of initiation without stimulation, for all values of t. Black trace represents P_stim(t,220): the probability of initiation following stimulation starting 220 ms after target onset. Dashed orange trace represents P̂_stim(t,220), the predicted effect of stimulation at that time. This prediction is based on the kernel, k, plotted at top (orange trace) aligned to stimulation onset. The log of the kernel is shown, such that a doubling and halving of odds are plotted equidistant from 0, which indicates no change in odds. B, Similar plot for stimulation starting 570 ms after target onset. The kernel is thus shifted to begin at 570 ms. C, Similar plot for stimulation starting 740 ms after target onset.

Still focusing on the self-initiated context, we next asked whether fits were similarly good across all tested stimulation times. To provide a more stringent test of the model, we concentrated on the fit to ΔP_stim, rather than P_stim as above. Many features of P_stim are simply inherited from P₀; the key question is how well one can account for the differences. The model provided a good fit to ΔP_stim(t,t_s) across the full range of tested values of t and t_s (Figs. 7C, 8C; compare in the middle subpanel with ΔP_stim in the left subpanel). For both monkeys, R² (Figs. 7, 8C, left blue bar) approached an upper benchmark based on the sampling error of the data (gray line, computed via bootstrap; see Materials and Methods). These results confirm that, for the self-initiated context, the impact of SMA microstimulation can be explained by an initial suppression of initiation probability, followed by a weaker facilitation.

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Figure 7.

Model predictions of ΔP_stim for Monkey Ba. A, Context-specific kernels, found when fitting to each context separately: self-initiated (blue), cue-initiated (red), and quasi-automatic (yellow). As in Figure 6, the log of the kernel is plotted. Dashed line at 0 thus indicates no change in initiation odds. B, Unified kernel, found when fitting to all contexts simultaneously. Shaded region represents 95% CIs of kernels fit to dummy stimulation data (see Materials and Methods). C, Empirical (left) and predicted changes in the probability of initiation following stimulation in the self-initiated context. Predictions in the middle heat plot are based on the context-specific kernel (A, yellow kernel). Predictions in the right heat plot are based on the unified kernel (B, black kernel). Prediction performance is quantified at right. A rough benchmark on the fit performance that could be provided by a good model was estimated via bootstrap. Horizontal line and shaded region represent mean and 95% CIs of that estimate. D, Same as for C, but for the cue-initiated context. E, Same as for C, but for the quasi-automatic context.

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Figure 8.

A–E, Model predictions of ΔP_stim for Monkey Ax. Same format as in Figure 7.

Similar kernels explain the impact of stimulation across contexts

Assessed in terms of RT, SMA stimulation had a context-dependent effect. Is this also true when considering initiation probability? Three results are possible. First, a similar kernel may account for effects across all contexts. Second, the same model may be successful across contexts but may require a different kernel for each. Third, the model may provide a good fit for some contexts but not others, regardless of the kernel used. We found that the first possibility held.

We fit the kernel separately for each monkey and each context. In all cases, the produced by the model provided a good fit to the empirical ΔP_stim (Figs. 7, 8, compare middle and leftmost heat-plots). R² ranged from 0.76 to 0.89 (Figs. 7, 8, bars at right) and was always close to the upper benchmark. The kernels that provided the optimal fit were similar across contexts (Figs. 7A, 8A), even though fitting was independent for each context. In all cases, there was an initial negative phase followed by a shallow positive phase. The correlation of kernel shape between contexts, for a given monkey, ranged from 0.80 to 0.95. To estimate correlations expected by chance, for each context, we fit kernels to dummy-stimulation data drawn from nonstimulated trials (see Materials and Methods) and computed the percentage of repetitions where correlations between the three contexts were as high as the empirical values. For both monkeys, empirical correlations were significant (p < 0.001).

Consistent with the above results, fit quality decreased only slightly when the model was constrained to use an identical kernel for all contexts (Figs. 7B, 8B, unified kernel). The rightmost heat-plots show the predicted using this kernel. Predictions were very similar to those when using a different kernel for each context (middle column). Fits were nearly as good when using the unified kernel as when using context-specific kernels (Figs. 7, 8, compare bars at right). The average reduction in R² was 7.8%. Thus, the same kernel, a negative initial lobe and a subsequent shallow positive lobe, accounted for effects across all contexts. The negative lobe of the kernel was more prominent, but both lobes were important in accounting for effects. We used the resampling procedure described above to ask whether the area within each lobe was greater than expected by chance. This was indeed the case (positive lobe: p < 0.001 and p < 0.001; Monkeys Ba and Ax; negative lobe: p < 0.001 and p < 0.001). Resampling also verifies that effects are due to stimulation itself and not to interactions between behavioral tendencies and incidental properties of stimulated trials (e.g., in the quasi-automatic context, late stimulation implies a longer delay, which could have made monkeys anxious to move).

In summary, effects across all contexts could be accounted for by a simple model where the impact of stimulation depended only on the time since stimulation was delivered. Put differently, we saw no evidence for the hypothesis that perturbation of SMA activity impacts initiation in different ways depending on how tightly initiation is linked to external cues. For a given baseline probability of initiation, the change in that probability due to stimulation was similar regardless of context. This lack of context dependence is potentially surprising. For example, the quasi-automatic context produces highly reactive movements, a situation where initiation might have been expected to bypass any influence of SMA. Put differently, the transition from low to high initiation probability in the quasi-automatic context might have been expected to be unaltered by stimulation. Yet it was altered and in a manner that was captured by the same model that captured effects in the other two contexts. Conversely, the self-initiated context engages internal considerations more heavily, and perturbations of SMA activity might thus have been expected to have a larger impact. Yet this was not the case: changes in initiation probability were consistent with the same model that captured effects in the other contexts.

That said, it certainly is true that a given change in the odds of initiation can impact RT to a greater or lesser degree depending on other factors. For example, the positive lobe of the kernel (which produces an increase in the odds of initiation) will have a larger impact on RT if there is a broad range of times when initiation is possible but far from certain. There is thus no paradox in observing context-independent changes in initiation probability but context-dependent changes in the RT. This is explored quantitatively below.

Kernels that account for initiation probability predict RT changes

As noted above, the probability of observing a particular RT can be derived from the probability of initiating at each time. This remains true after stimulation: P(RT = t | stimulation at t_s) = P_stim(t,t_s)Π_τ=1:t(1 − P_stim(t − τ,t_s)). We used this relationship to obtain the predicted changes in RT given the values of P̂_stim(t,t_s) produced by the model. To test whether a single kernel could account for the diverse RT effects, we used the unified kernel (Figs. 7B, 8B) and computed the predicted RT distribution. We then computed the mean change in RT (relative to no stimulation) for early and late stimulation. The model, although entirely context-independent, reproduced the context-dependent impact of stimulation on mean RT (Fig. 9). The variance in ΔRT accounted for (across the 6 cases for both monkeys) by the fit was 0.88.

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Figure 9.

Predicting ΔRT from P̂_stim. Predicted ΔRT following early or late stimulation. Predictions were made using the unified kernel (found by fitting simultaneously to all contexts). To mirror the analysis in Figure 2, the values of t_s used to predict the effect of early and late stimulation were 700 and 300 ms, respectively, before the reference time: the time when movement had begun on 10% of nonstimulated trials in that context. Because of the 150 ms window used when originally estimating ΔP_stim, this effectively produced stimulation windows of 700–550 ms and 300–150 ms before the reference time, matching the windows used in the original analysis.

The model captured the advancement of self-initiated RTs following early stimulation. This can be understood in terms of the stimulation-induced change in P_stim. The positive lobe of the stimulation kernel occurs when initiation is gradually becoming likely. A small increase in the odds of initiation during this extended period produces a sizeable change in mean RT. For the other two contexts, the transition from low to high baseline initiation probability is more rapid. Even though these contexts also involve a sizeable increase in initiation probability (e.g., Fig. 8E, red regions), the impact on RT is small due to the restricted temporal window where that effect matters.

The model also captured the increased RT following late stimulation. For late stimulation, the negative lobe of the kernel occurs when initiation is becoming likely. As for the empirical data, the RT increase was less pronounced for the quasi-automatic context. This is again a consequence of the rapid increase in baseline initiation probability during the quasi-automatic context.

Despite these successes, the model underestimated some effect sizes. This is unsurprising for two reasons. First, the model reproduces the empirical ΔP_stim well but not perfectly. Second, the kernel was optimized to minimize mean-squared error between ΔP_stim and , rather than ΔRT and . If the former error is zero, the latter will also be zero, but in in general the optimal kernel will differ slightly depending on which error is minimized. We can reduce this second contribution by adding, to the cost function, the error between ΔRT and , producing a kernel that minimizes both errors. Doing so resulted in small but noticeable improvements in the model predictions of RT (R² increased to 0.96). For example, the predicted RT reduction in the self-initiated context following early stimulation was 13 and 14 ms larger (Monkeys Ba and Ax) when using the revised cost function, better matching the empirical magnitude.

Thus, a simple context-independent model reproduces the diverse changes in RT. The direction of all effects was correctly predicted, and effect magnitudes were reasonably well predicted. The model assumes that changes in the probability of initiation depend only on the time since stimulation and not on context or the overall time since target onset. Because this parsimonious explanation is naturally expressed in terms of the probability of initiation, subsequent analyses focus on ΔP_stim.

Initiation-promoting effects were more prominent for early stimulation trials

The impact of microstimulation can fade with time (Churchland and Shenoy, 2007). To explore the possibility that some effects may be more prominent when a site is first stimulated, we separately fit stimulation kernels to data for the first 25 stimulation trials at each recorded site (Fig. 10A,E, black kernel). Kernels changed only modestly following this restriction. However, one subtle effect was present for both monkeys: the positive lobe was slightly more prominent when considering only the first 25 trials.

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Figure 10.

Movement-enhancing effects of microstimulation are strongest when a site is first stimulated. A–D, Results for Monkey Ba. E–H, Results for Monkey Ax. Kernels were the “unified” kernel fit to all contexts simultaneously. A, Stimulation kernel fit to first 25 stimulation trials at each site (black line) and all stimulation trials (gray line). B, Empirical (left) and predicted (right) changes in the probability of initiation following stimulation in the self-initiated context, after restricting to the first 25 stimulation trials at each site. C, Same as for B, but for the cue-initiated context. D, Same as for B, but for the quasi-automatic context. E–H, Same as for A–D, but for Monkey Ax.

Examination of the data revealed why the fitting procedure used a more prominent positive lobe: positive values of ΔP_stim, corresponding to initiation-promoting effects, were more common when analyzing trials early at a stimulation site. This can be seen by noting that bright red/orange regions are more prominent in Figure 10 (where analysis is restricted to the first 25 stimulation trials) than in Figures 7 and 8 (which consider all trials). This effect was particularly noticeable for Monkey Ax in the self-initiated and cue-initiated contexts.

The above results predict that the ability to advance RTs, via stimulation early within self-initiated trials, should be enhanced for the first 25 stimulation trials. This was indeed the case. We repeated the analysis in Figure 2C, D, restricted to the first 25 trials at each site. RT advancement grew for both monkeys. This increased advancement was sizeable for Monkey Ax (a 24 ± 9 ms increase relative to the effect for all trials, p = 0.04, two-sample t test) and quite modest for Monkey Ba (a 6 ± 13 ms increase, p = 0.75). Thus, the movement-promoting impact of SMA stimulation tended to be modestly stronger when a site was first stimulated.

Effects of SMA stimulation across hemispheres and sites

The kernels above were estimated after pooling data across stimulation sites. Pooling was essential to provide sufficient trials so that ΔP_stim(t,t_s) could be estimated for every combination of t and t_s. However, effects may potentially vary across sites. We first considered that sites in one hemisphere might differ systematically from those in the other. This was not the case; kernels were similar when fit separately to data from each hemisphere (Fig. 11A,B). The bilateral impact of stimulation presumably relates to the fact that SMA is active for movements of both the contralateral and ipsilateral arm (Kermadi et al., 1998; Nakayama et al., 2015). However, we note that suprathreshold stimulation typically produced movement only of the contralateral arm. Thus, the initiation-altering effects of stimulation are likely unrelated to the more direct impact of suprathreshold stimulation.

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Figure 11.

Analysis of potential heterogeneity of effects across sites. A, Stimulation kernels for stimulation sites in contralateral (left subpanel) and ipsilateral (right subpanel) SMA. Kernels were the “unified” kernel fit to all contexts simultaneously. Data are for Monkey Ba. B, Same as for A, but for Monkey Ax. C, Reliability of stimulation kernel estimated by resampling stimulation sites. Black trace represents the original stimulation kernel. Gray region represents the 95% CI across resamplings. Data are for Monkey Ba. D, Same as for C, but for Monkey Ax.

We were also curious whether effects differed across sites within each hemisphere yet found this impossible to address. Trial counts for a single site were insufficient to provide robust estimates of effects, making it unclear whether site-to-site variability was real or due to sampling error. Given this, we stress that the kernels we report should be considered a summary of the central tendency across all sites. Effects at individual sites may (or may not) vary around this central tendency.

Importantly, site-to-site variability did not limit our ability to estimate the central tendency. We resampled our stimulation sites, with replacement, and recomputed the kernel (fitting a single kernel to the data for all contexts). A similar kernel was consistently found, as indicated by the 95% CIs in Figure 11C, D.