elifeeLifeeLife2050-084XeLife Sciences Publications, Ltd5037110.7554/eLife.50371Research ArticleNeuroscienceTemporal cascade of frontal, motor and muscle processes underlying human action-stoppingJanaSumitashhttps://orcid.org/0000-0003-3742-3958s2jana@ucsd.edu1†HannahRiccihttps://orcid.org/0000-0001-5379-3292rhannah@ucsd.edu1†MuralidharanVignesh1AronAdam R1Department of Psychology, University of CaliforniaSan DiegoUnited Statesvan den WildenbergWeryReviewing EditorUniversiteit van AmsterdamNetherlandsIvryRichard BSenior EditorUniversity of California, BerkeleyUnited States

These authors contributed equally to this work

1803202020209e503712007201917032020© 2020, Jana et al2020Jana et alhttp://creativecommons.org/licenses/by/4.0/This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

Action-stopping is a canonical executive function thought to involve top-down control over the motor system. Here we aimed to validate this stopping system using high temporal resolution methods in humans. We show that, following the requirement to stop, there was an increase of right frontal beta (~13 to 30 Hz) at ~120 ms, likely a proxy of right inferior frontal gyrus; then, at 140 ms, there was a broad skeletomotor suppression, likely reflecting the impact of the subthalamic nucleus on basal ganglia output; then, at ~160 ms, suppression was detected in the muscle, and, finally, the behavioral time of stopping was ~220 ms. This temporal cascade supports a physiological model of action-stopping, and partitions it into subprocesses that are isolable to different nodes and are more precise than the behavioral latency of stopping. Variation in these subprocesses, including at the single-trial level, could better explain individual differences in impulse control.

stop signal taskpartial responsesingle trial metricelectromyographyvariabilitybeta burstResearch organismHumanhttp://dx.doi.org/10.13039/100000002National Institutes of HealthNS 106822JanaSumitashHannahRicciMuralidharanVigneshAronAdam Rhttp://dx.doi.org/10.13039/100000002National Institutes of HealthDA 026452JanaSumitashHannahRicciMuralidharanVigneshAronAdam RThe funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.Author impact statementThe sequence of neural and physiological processes underlying action-stopping has been delineated.Introduction

The ability to control one’s actions and thoughts is important for our daily lives; for example: changing gait when there is an obstacle in the path (Wagner et al., 2016), resisting the temptation to eat when on a diet (Sedgmond et al., 2019), and overcoming the tendency to say something hurtful (Xue et al., 2008). While many processes contribute to such forms of control, one important process is response inhibition – the prefrontal (top-down) stopping of initiated response tendencies (Aron, 2007). In the laboratory, response inhibition is often studied with the stop-signal task (Verbruggen et al., 2019). On each trial, the participant initiates a motor response, and then, when a subsequent Stop signal occurs, tries to stop. From the behavioral data one can estimate a latent variable; the latency of stopping known as Stop Signal Reaction Time (SSRT), which is typically 200–250 ms in healthy adults (Verbruggen et al., 2019). SSRT has been useful in neuropsychiatry where it is often longer for patients vs. controls (Alderson et al., 2007; Bari and Robbins, 2013; Lavagnino et al., 2016; Lijffijt et al., 2005; Smith et al., 2014; Snyder et al., 2015). The task has also provided a rich test-bed, across species, for mapping out a putative neural architecture of prefrontal-basal-ganglia-regions for rapidly suppressing motor output areas (Aron et al., 2014; Bari and Robbins, 2013; Schall and Godlove, 2012). Given this rich literature, this task is one of the few paradigms included in the longitudinal Adolescent Brain Cognitive Development study (Casey et al., 2018) of 10,000 adolescents over 10 years.

Against this background, a puzzle is that the relation between SSRT and ‘real-world’ self-reported impulsivity is often weak (Chowdhury et al., 2017; Enkavi et al., 2019; Friedman and Miyake, 2004; Lijffijt et al., 2004; McLaughlin et al., 2016; Skippen et al., 2019b). One explanation is that SSRT may not accurately index the brain’s true stopping latency. Indeed, recent mathematical modelling of behavior during the stop-signal task suggests that standard calculations of SSRT may overestimate the brain’s stopping latency by ~100 ms (Skippen et al., 2019b; also see Bissett and Poldrack, 2019). Further, in a recent study (Raud and Huster, 2017), electromyographic (EMG) recordings revealed an initial increase in EMG activity in response to the Go cue, followed by a sudden decline at ~150 ms after the Stop signal. This decline in EMG could be because of the Stop process ‘kicking in’ to cancel motor output – but the striking thing is that this was 50 ms before the SSRT of 200 ms. This timing is also consistent with experiments using transcranial magnetic stimulation (TMS) to measure the motor evoked potential (MEP) during the stop-signal task (the MEP indexes the excitability of the pathways from motor cortex to muscle). The MEP in the muscle that was-to-be-stopped reduced at ~150 ms (Coxon et al., 2006; van den Wildenberg et al., 2010). Further, other studies that measured the MEP from muscles that were not needed for the task, show there is ‘global suppression’ also at ~150 ms (Badry et al., 2009; Cai et al., 2012; Wessel et al., 2013a; Wessel and Aron, 2013) (i.e. corticospinal activity was suppressed for the broader skeletomotor system). This ‘global MEP suppression’ has been linked to activation of the subthalamic nucleus of the basal-ganglia (Wessel et al., 2016), which is thought to be critical for stopping, and might broadly inhibit thalamocortical drive (Wessel and Aron, 2017).

The potential overestimation of the brain’s true stopping latency by SSRT could arise for several reasons. First, the race model assumes that the Stop process is ‘triggered’ on every trial. But recent research shows that this is not the case (Skippen et al., 2019b), and that failing to account for ‘trigger failures’ inflates SSRT. Second, while the standard ‘race model’ assumes that the Go and Stop processes are independent (Verbruggen et al., 2019), recent research show that violations of this independence underestimates SSRT (Bissett and Poldrack, 2019). Finally, the standard ways of computing SSRT likely do not account for electromechanical delays between muscle activity and the response. In any event, overestimating the brain’s stopping latency would add variance to SSRT which could potentially weaken the above-mentioned across-participant associations between stopping latency and self-report scores (Chowdhury et al., 2017; Lijffijt et al., 2004; Skippen et al., 2019b). Furthermore, if the true stopping latency is ~150 ms, the timing of activation of nodes in the putative response inhibition network should precede this time-point for those nodes to play a causal role in action stopping – and this is important for the interpretation of neuroscience studies. For instance, in electrocorticography, electroencephalography (EEG), and magnetoencephalography (MEG) studies, successful stopping elicits increased beta band power over right frontal cortex in the time period between the Stop signal and SSRT (Castiglione et al., 2019; Schaum et al., 2020; Swann et al., 2009; Wagner et al., 2018; Wessel et al., 2013b). Whether this, and other, neurophysiological markers of the Stop process occur sufficiently early to directly contribute to action-stopping (if SSRT is overestimated) is unknown; yet this is fundamental to our understanding of brain networks underlying response inhibition.

Here we leveraged the insight from the above-mentioned study (Raud and Huster, 2017) which used EMG of the task relevant muscles. We now tested whether we could derive a single trial estimate of stopping latency from EMG (referred to as CancelTime). More specifically, we hypothesized that ‘partial’ EMG bursts on the Successful Stop trials (i.e. small EMG responses that begin but do not reach a sufficient amplitude to lead to an overt response) (de Jong et al., 1990; McGarry et al., 2000) would carry information about the latency of stopping. We tested this in two studies. In a third study we tested if CancelTime would correspond with the measure of putative basal ganglia-mediated global motor suppression, measured with single-pulse TMS. In studies four and five we turned to the cortical process thought to initiate action–stopping, using the above-mentioned proxy of right frontal beta (Swann et al., 2009; Wagner et al., 2018). We measured scalp EEG, derived a right frontal spatial filter in each participant, and then extracted beta bursts (Little et al., 2018) in the time period between the Stop signal and SSRT. We tested how the timing of these beta bursts related to CancelTime.

ResultsStudy 1 (EMG)

10 participants performed the stop-signal task (Figure 1a). On each trial they initiated a manual response when a Go cue occurred, and then had to try to stop when a Stop signal suddenly appeared on a minority of trials. Depending on the stop signal delay, SSD, participants succeeded or failed to stop, each ~50% of the time). We measured EMG from the responding right index and little fingers (Figure 1b inset). Behavioral performance was typical, with SSRT (referred to as SSRTBeh) of 216 ± 8 ms, and action-stopping on 51 ± 1% of Stop trials (Table 1). EMG analysis was performed on the trial-by-trial root-mean-squared EMG (EMGRMS; Figure 1b). On 53 ± 6% of Successful Stop trials (i.e. where no keypress was made) there was a small but detectible EMG response (Partial EMG trials; see Figure 1—figure supplement 1 for RTEMG-RTBeh correlation), while on the remainder of Successful Stop trials there was no detectible EMG response (No EMG trials). The amplitude of EMG responses (mean peak EMG voltage) in the Partial EMG trials was 48 ± 3% smaller than in trials with a keypress (Figure 2a).

Behavioral task and EMG recording.

(a) Stop-signal task. (b) EMGRMS on a Successful Stop trial (Partial EMG) in an exemplar participant. Data are aligned to the Go cue. CancelTime refers to the time from the Stop signal (dotted red line) to when the EMGRMS starts decreasing (blue line). The green and purple line represent the detected onset and offset of the EMG response. (Inset) Recording set-up with a vertical and a horizontal keypad to record keypresses from the FDI and ADM muscles.

EMG responses in study 1 and 2.

(a) RTEMG-RTBeh correlation in the Correct Go trials. Each small dot represents the mean in a participant, color coded by the RTEMG-RTBeh correlation in that participant, while the cross-hairs represent the s.e.m. in that participant. The large dot and cross-hairs represent the mean and s.e.m. across all the participants, again color coded by the mean RTEMG-RTBeh correlation (r = 0.97, p<0.001, BF10 >100; RTEMG = 342 ± 13 ms, RTBeh = 480 ± 12 ms) across all participants. The linear regression fit and its 95% confidence interval is shown as a green line and shaded region respectively. The unity line is represented as a black dotted line. (b) Same as (a) but for the Failed Stop trials (r = 0.97, p<0.001, BF10 >100; RTEMG = 302 ± 11 ms, RTBeh = 439 ± 11 ms).

Mean RT<sub>EMG</sub> and RT<sub>Beh</sub> in the Correct Go and Failed Stop trials for study 1 and 2.

EMG responses in Successful (Partial and No EMG) and Failed Stop trials in study 1 and 2.

(a) Normalized EMGRMS voltage in Failed Stop (orange), Partial EMG (brown), and No EMG trials (purple), aligned to the Stop signal. The lines and the shaded area represent the mean ± s.e.m. across participants. The dotted cyan line and shaded area represent the mean ± s.e.m of SSRTBeh across participants. The dots and cross-hairs represent the mean ± s.e.m. of the Go cue in a participant. Note that the time between the Go cue and the Stop signal (i.e. the SSD) is shortest for the No EMG (purple), then the Partial EMG (brown), and then the Failed Stop trials (orange). (b) Same as (a) but for study 2. (c) (Left) Beeswarm plot of the CancelTime in an exemplar participant from study 1. Each dot represents a trial. The dotted cyan line represents the SSRTBeh. (Right) Same as left but for study 2. (d) Correlation between CancelTime and SSRTBeh in study 1 (light red) and study 2 (yellow). The brown dot, lines and arrows represent the means, while the black dotted line represents the unity line. The linear regression fit and its 95% confidence interval (pooled study 1 and 2) is shown as a brown line and shaded region respectively.

Correlation between CancelTime and SSRTBeh for study 1 and 2.

Behavior (mean ± s.e.m.; All values in ms).

Behavior in the Stop-signal task in all five studies.

Study 1 (EMG)Study 2 (EMG)Study 3 (TMS)Study 4 (EEG)Study 5 (EEG)
Go RTBeh470 (15)493 (15)430 (17)427 (15)405 (6)
Failed Stop RTBeh416 (11)447 (14)391 (12)384 (12)370 (5)
Correct Go %97 (1)98 (0)99 (0)99 (0)99 (0)
Correct Stop %51 (1)52 (1)49 (1)48 (1)50 (0)
Mean SSD237 (20)280 (17)194 (18)191 (21)170 (7)
SSRTBeh216 (8)204 (4)219 (6)214 (9)219 (6)

We hypothesized that the time when the Partial EMG response starts declining after the Stop signal is a readout of the time when the Stop process is implemented in the muscle (hereafter ‘CancelTime’). We observed that, first, CancelTime is much earlier than SSRTBeh (see Figure 2c (left) for all CancelTimes in an exemplar participant; mean CancelTime = 146 ± 3 ms, SSRTBeh = 203 ms); and second, across participants, CancelTime was positively correlated with SSRTBeh (Figure 2d; study 1: mean CancelTime = 152 ± 11 ms, mean SSRTBeh = 216 ± 8 ms; r = 0.71, p=0.020, BF10 = 3.6). This suggests that CancelTime might index the time when stopping is implemented at the muscle.

Study 2 (EMG)

We then ran a new sample (n = 32; see Table 1 for behavioral results). Again, we observed partial EMG responses on 49 ± 2% of Successful Stop trials; where the EMG amplitude was 54 ± 1% smaller than the amplitude in trials with a keypress (Figure 2b). Figure 2c (right) shows the distribution of CancelTimes in an exemplar participant (mean CancelTime = 156 ± 4 ms, SSRTBeh = 218 ms). Again, across participants, mean CancelTime was positively correlated with SSRTBeh (Figure 2d; mean CancelTime = 146 ± 4 ms, mean SSRTBeh = 204 ± 4 ms; r = 0.59, p<0.001, BF10 = 71.7). Intriguingly, in each study, CancelTime was ~ 60 ms less than SSRTBeh. To further explore this, we pooled the data across the two studies.

Pooled studies 1 and 2

Mean CancelTime (147±5 ms) was 60±3 ms shorter than SSRTBeh (t(41) = 18.4, p < 0.001, d = 2.5, BF10 > 100; r = 0.62, p < 0.001, BF10 > 100). However, one must note that the criterion for estimating the stopping latency is different for the two measures, CancelTime uses EMG responses, while SSRTBeh uses the keypress responses. Hence, inherent differences in latencies between the two responses might lead to these incompatible measures of stopping latency. We hypothesized that the difference between SSRTBeh and the time of EMG cancellation (CancelTime) is due to an inherent “ballistic stage” in movements and once the muscle activity crosses the point-of-no-return they can no longer be stopped and a movement is inevitable (de Jong et al., 1990; Mirabella et al., 2006; Osman et al., 1986; Verbruggen and Logan, 2009). [The duration of such ballistic stages has been estimated to be ~15 ms in saccades in non-human primates (Boucher et al., 2007; Kornylo et al., 2003; Purcell et al., 2010) and ~50 ms for reaching movements in humans (Gopal and Murthy, 2016; Jana and Murthy, 2018)]. In other words, the time of EMG cancellation on partial trials reflects a time just before the point-of-no-return, whereby if EMG activity is allowed to continue develop beyond this point it will exceed a critical threshold such that a button press necessarily ensues (we presume this threshold reflects the point at which the inertia of the finger is overcome). In this respect, what is being tracked by the SSD staircasing procedure is the probability of crossing that EMG threshold, but since SSRT is calculated based on button press response times, it inevitably incorporates the ballistic stage that follows the crossing of this threshold. Hence, although our study was not designed to track the SSD staircase based on EMG, we calculated SSRT using the presence of EMG responses (SSRTEMG) instead of the keypress responses (SSRTBeh). The purpose of the SSRTEMG estimation was to test the idea of a ballistic phase by removing the influence of electromechanical delays and inertia in the neuromuscular system and response device, which likely make-up the ballistic stage, on the estimated stopping latency. We thus considered Partial EMG trials as Failed Stop trials and used EMG onset time (RTEMG) on Correct Go trials to recalculate SSRT (i.e. instead of using P(Respond|Stop) from behavior and Go RTBeh as is typical for SSRTBeh calculations; see Materials and methods; see Figure 3a for an exemplar participant). We then performed 1-way repeated measures ANOVA with 'Stop Time' as the dependent measure and the method of estimation as a factor (SSRTEMG, SSRTBeh, and CancelTime). There was a significant main effect of the estimation method on 'Stop Time' (FGG(1.4, 56.1) = 66.3, p < 0.001, ηp2 = 0.6). Pairwise comparisons showed that SSRTEMG (157±7 ms) was significantly faster than SSRTBeh (207±3 ms) (Figure 3b; t(41) = 8.2, pBon < 0.001, d = 1.3, BF10 > 100), but importantly, not significantly different from mean CancelTime (t(41) = 1.5, pBon = 0.270, d = 0.2, BF10 = 0.5). This suggests that SSRTBeh might be protracted by a peripheral delay and that CancelTime might be a better metric of the time of implementation of the Stop process. [Our simulations using a previously described modelling framework (Boucher et al., 2007; Ramakrishnan et al., 2012; Usher and McClelland, 2001) also lead credence to this idea, demonstrating that the duration of the ballistic stage might be ~35 ms or longer (see Figure 3—figure supplement 1 and Appendix 1)].

Peripheral delay associated with SSRT<sub>Beh</sub> and the relationship between CancelTime and BEESTS parameters.

(a) P(Respond|Stop) in an exemplar participant calculated using the behavioral response (dark green dots) and the EMG response (cyan dots). The lines represent the cumulative Weibull fit as w(t)=γ−(γ−δ)e[−(t/α)β] where t is the SSD, α is the time at which the function reaches 64% of its full growth, β is the slope, δ is the minimum value of the function, and γ is maximum value of the function. The difference between δ and γ marks the range of the function. (Inset) Beeswarm plot of the EMG onset (dark green) and the behavioral responses (cyan) used to calculate SSRTEMG and SSRTBeh respectively. (b) Comparison of SSRTBeh (cyan), CancelTime (brown), and SSRTEMG (dark green) across all participants. Each dot represents a participant, while the bar and cross-hair represents the mean ± s.e.m. in a group. (c) The normalized EMG responses aligned to the detected EMG onsets in the Correct Go (green), Failed Stop (orange), and Partial EMG (brown) trials. The line and shaded region represent the mean ± s.e.m. in a group. The dots and cross hairs represent the mean ± s.e.m. of the keypress in a participant. (d) Correlation between CancelTime and mean SSRTBEESTS estimate. Each dot and cross-hair represent the mean ± s.e.m. in a participant. The brown line and the shaded area represent the linear regression fit and its 95% confidence interval. The unity line is represented as a dotted black line. (e) Correlation between SD of CancelTime and SD of the SSRTBEESTS estimate. Other details same as (d). (f) Correlation between percentage Trigger Failures estimated from BEESTS and CancelTime. Other details same as (d).

Peripheral delay associated with SSRT<sub>Beh</sub> and relationship between CancelTime and BEESTS parameters.

Simulation results.

(a) Cumulative Weibull fit of the empirical (solid blue line) and simulated (dotted gray line) behavioral (Beh) inhibition function in an exemplar participant. The dots represent the P(Respond|Stop) data. (Inset) The Stop distribution estimated using the behavioral (Beh) inhibition function and (μSTOP-Beh,σSTOP-Beh) with the black triangle representing the mean. (b) The estimated Stop distribution poorly fits the EMG inhibition function in the exemplar participant (solid green line – empirical, dotted gray - simulated). Other details same as (a). (c) Comparison of the squared error between the simulated and empirical inhibition function when the Stop distribution is estimated from the Beh inhibition function and RTBeh (Beh inhibition function: squared error = 0.10 ± 0.01; EMG inhibition function: squared error = 0.21 ± 0.02; t(41) = 4.8, p<0.001, d = 0.7, BF10 > 100). Each dot represents a participant, and the bar and cross-hairs represent the mean ± s.e.m. (d) Same as (a) but now the Stop distribution (inset) has been estimated from the EMG inhibition function and the (μGO-EMG, σGO-EMG). (e) Similar to (b). The Stop distribution estimated from EMG inhibition function poorly fits the Beh inhibition function (solid cyan line – empirical, dotted gray - simulated). (f) Same as (c) but when the Stop distribution is estimated from the EMG inhibition function (EMG inhibition function: squared error = 0.12 ± 0.02; RT inhibition function: squared error = 0.23 ± 0.02; t(41) = 4.7, p<0.001, d = 0.9, BF10 > 100). (g) Schematic of the architecture underlying a Correct Stop trial. The green accumulator represents the Go process, while the red accumulator, starting at the SSD, represents the Stop process. Both race towards the threshold (orange line at the top), but as the Stop hits the threshold first, no response is elicited. There is a delay at the periphery (EMG onset to keypress) which is partitioned into a non-ballistic and ballistic stage. (h) Same as (g) but for a Partial EMG trial. Here the Go process reaches the threshold first and EMG response is elicited, but the Stop process intervenes during the non-ballistic stage and cancels the drive, thereby preventing a keypress. (i) Same as (g) but for a Failed Stop trial. Here the Stop process is unable to cancel the response as the ballistic stage is impervious to the Stop process. (j) Same as (b) but here the Stop distribution has been estimated using the EMG inhibition function and the model has a ballistic stage (solid cyan line – empirical, dotted cyan line – model with ballistic stage, dotted gray line – model without a ballistic stage). (k) Comparison of the squared error between the simulated and empirical inhibition function for Stop estimated from the EMG inhibition function, with (cyan) and without a ballistic stage (blue-green) (With ballistic stage: squared error = 0.14 ± 0.02; Without ballistic stage: squared error = 0.23 ± 0.02; t(41) = 4.2, p<0.001, d = 0.7, BF10 > 100).

Simulation results.

Partial EMG voltage across SSDs in study 1 and 2.

The normalized EMG voltage in the partial EMG trials for the first 5 SSDs (SSD no.) in each participant (SSD1 = 0.206±0.012, SSD2 = 0.212±0.012, SSD3 = 0.237±0.017, SSD4 = 0.234±0.015, SSD5 = 0.260±0.020; rmANOVA: F(4,24) = 3.7, p = 0.018, ηP2 = 0.4). Each dot represents a participant, while the bar and cross-hairs represent the mean and s.e.m. across all the participants.

Partial EMG voltage across SSDs for study 1 and 2.

Next, we examined in more detail the EMG profile on Partial EMG trials. Across all participants, the EMG response in the Partial EMG trials (when aligned to the EMG onset) had a profile similar to the EMG response in the Correct Go and Failed Stop trials, but diverged ~55 ms after EMG onset (55 ms compared to Correct Go, and 56 ms compared to Failed Stop trials, Figure 3c). We surmised that if the Partial EMG trials reflect responses that have been actively cancelled at the muscle-level, then the amplitude of these responses should increase with SSD. The rationale was that, at shorter SSDs, the Go process will have been active for a shorter duration, meaning EMG activity will not have increased much before being inhibited, while at longer SSD, the Go process will have been active for a longer duration, meaning EMG activity will have increased much more before being inhibited. Indeed, the amplitude of the Partial EMG responses increased with SSD (Figure 3—figure supplement 2). A 1-way repeated measures ANOVA with amplitude as the dependent variable and the SSD as the independent variable showed significant effect of SSD on amplitude (F(4,24) = 3.7, p = 0.018, ηp2 = 0.4) (also see Coxon et al., 2006). This suggests that the Partial EMG trials represent inhibited Go responses and not merely a weak Go process (which would presumably not increase across SSDs). In other words, the partial EMG response does not simply reflect a weak Go response, where the individual intended to execute a response but failed to produce sufficient muscle activity to fully depress the button, since the amplitude of such responses would presumably not vary as a function of SSD.

To further validate CancelTime, we modelled the behavior using BEESTS (Bayesian Estimation of Ex-gaussian STop-Signal reaction time distributions; see Table 2 for model estimates). While SSRTBeh produces a single estimate per person, BEESTS uses a Bayesian parametric approach to estimate the distribution of SSRTs (Matzke et al., 2017). Also, for each participant, it provides an estimate of the probability of trigger failures (i.e. stop trials where the stopping process was not initiated Matzke et al., 2017). Across participants, mean CancelTime was positively correlated with the mean SSRTBEESTS (205 ± 3 ms; r = 0.54, p<0.001, BF10 > 100; Figure 3d). More interestingly, the SD of CancelTime (33 ± 2 ms) was positively correlated with the SD of SSRTBEESTS (48 ± 5 ms; r = 0.42, p=0.005, BF10 = 6.9; Figure 3e). Further, the percentage of trigger failures (4 ± 1%) was positive correlated with mean CancelTime (ρ = 0.57, p<0.001, BF10 > 100) suggesting that participants who fail to ‘trigger’ the Stop process more often, are also likely to have longer stopping latency, indicating that there might exist a dependency between the triggering and the implementation of the Stop process (Figure 3f). These relationships between CancelTime and model estimates give further credence to our interpretation that CancelTime on Partial EMG trials reflects a single-trial measure of the time of implementation of the Stop process.

BEESTS estimates (mean ± s.e.m.; All values in ms)

BEESTS estimates for study 1 and 2.

Estimated parametersPooled study 1 and 2
Mean Go RTBeh483 (13)
SD Go RTBeh94 (5)
Mean SSRTBEESTS205 (3)
SD SSRTBEESTS48 (5)
%Trigger Failures4 (1)
Study 3 (TMS)

To further validate CancelTime and relate it to brain processes we turned to a different method – single-pulse TMS over a task-irrelevant muscle representation in the brain. As mentioned above, the reduction of MEPs from task-irrelevant muscles on Successful Stop trials (Badry et al., 2009; Cai et al., 2012; Wessel and Aron, 2013), is thought to reflect a basal ganglia-mediated global suppression (Wessel et al., 2016). Seventeen new participants (see Table 1 for behavioral results) now performed the task with their left hand, while TMS was delivered over the left motor cortex and MEPs were recorded from a task-irrelevant, right forearm muscle. MEPs were recorded at different times after the Stop signal on different trials: 100–180 ms in 20 ms intervals, as well as during the inter-trial interval which served as a baseline. Concurrently, we recorded EMG from the task-relevant left-hand muscles as in studies 1 and 2 above (Figure 4a).

Relationship between global motor system suppression and CancelTime.

(a) Experimental set up and TMS stimulus timings for study 3. Participants performed the Stop signal task with the left hand with concurrent EMG measurement of CancelTime from task-relevant FDI and ADM muscles. On a given trial, a single TMS stimulus over left M1 was delivered at one of 6 possible times to elicit a motor evoked potential (MEP) in the task-irrelevant extensor carpi radialis (ECR) muscle of the right forearm. (b) Global motor system suppression begins at 140 ms after the Stop-signal, and thus ~20 ms prior to the mean CancelTime. Paired t-tests: *, pBon < 0.05 Successful Stop (red; combined Partial and No EMG trials) vs. Correct Go (green); #, pBon < 0.05 Successful Stop vs. Failed Stop (orange). Each dot and cross-hairs represent the mean ± s.e.m. across the population. The black dotted line shows amplitude of MEPs normalized to those at the inter-trial interval. (c) (Top) Schematic representation of an MEP. (Bottom) Beeswarm plot of the mean corticospinal conduction time to a hand muscle, which was established by measuring the onset latency of MEPs in the hand (~23 ms on average). Each dot represents a participant. This conduction time is included in CancelTime. (d) Trial-by-trial analysis of MEP amplitudes organized into 30 ms time bins reflecting the time of TMS expressed relative to CancelTime. Global motor system suppression begins in a window 30-0 ms prior to the CancelTime (gray shaded region). Wilcoxon rank sum test: *, pBon < 0.05 Partial EMG (brown) vs. Correct Go (green); #, pBon < 0.05 Partial EMG vs. Failed Stop (orange); ^, pBon < 0.05 Failed Stop vs. Correct Go. The black dotted line shows amplitude of MEPs normalized to those at the inter-trial interval.

Relationship between global motor system suppression and CancelTime.

MEPs in study 3.

Normalised MEP amplitudes in Successful Stop trials divided according to the presence, or not, of a Partial EMG burst. There was no difference in amplitude of MEPs for trials with (Partial EMG, brown) and without (No EMG, purple) EMG bursts. The squares and cross-hairs represent the mean ± s.e.m. across the population. rmANOVA showed no main effect of trial type (F(1,16) = 1.2, p = 0.288, ηP2 = 0.1) or time (F(4, 64) = 1.1, p = 0.356, ηP2 = 0.1), nor any interaction of trial-type by time (F(4, 64) = 2.3, p = 0.066, ηP2 = 0.1). Therefore, the timing and extent of the global motor system suppression on Successful Stop trials was not influenced by whether or not a partial EMG burst was detected.

The key TMS finding, in keeping with earlier studies (Badry et al., 2009; Cai et al., 2012; Wessel and Aron, 2013), was of suppression of MEPs in the task-irrelevant forearm, indicating global motor system suppression, beginning ~ 140 ms following the Stop signal in Successful Stop trials (Figure 4b; see Figure 4—figure supplement 1 for MEP amplitudes for Partial EMG and No EMG trials separately). A 2-way repeated measures ANOVA with MEP amplitude as the dependent measure and the factors of trial-type (Correct Go, Successful Stop, Failed Stop) and time (100, 120, 140, 160, 180 ms after the Stop signal) showed main effects of both trial-type (F(2,32) = 7.2, p=0.003, ηp2 = 0.3) and time (FGG(2.5, 40.7)=4.8, p=0.008, ηp2 = 0.2), as well as an interaction of trial-type by time (F(8, 128)=3.4, p=0.002, ηp2 = 0.2). Post hoc t-tests across Successful Stop and Correct Go trials showed no difference at 100 ms (t(16) = 0.7, pBon = 1.0, BF10 = 0.3), 120 ms (t(16) = 2.5, pBon = 0.066, BF10 = 2.8), and 160 ms (t(16) = 2.1, pBon = 0.159, BF10 = 1.4). However, MEP amplitudes were significantly suppressed on Successful Stop trials at 140 ms (t(16) = 4.1, pBon = 0.003, BF10 = 39.8) and 180 ms (t(16) = 4.4, pBon < 0.001, BF10 = 65.2) after the Stop signal. Therefore, we estimate the onset of the global motor suppression to be ~ 140 ms after the Stop signal, which places it ~ 20 ms prior to the mean CancelTime (160 ± 9 ms). There were no significant differences in MEP amplitudes between Failed Stop and Correct Go trials at any time point, though MEP amplitudes on Successful Stop trials were also suppressed compared to Failed Stop trials at 160 ms (t(16) = 2.9, pBon = 0.033, BF10 = 4.9).

It makes sense that global motor suppression occurs before CancelTime as motor cortical output takes time to be transmitted along the corticospinal pathway to the muscles. To verify whether the ~20 ms discrepancy in timings could be accounted for by corticospinal conduction delays, we estimated this corticospinal conduction time in a separate phase of the current study by delivering TMS over the hand representation to evoke MEPs in the left, task-relevant, FDI muscle (Figure 4c). This was 23 ± 0.3 ms. Thus, a decline in muscle activity would be expected to be preceded by a reduction in motor cortical output by ~23 ms, which is very similar to the ~20 ms difference between global motor suppression and CancelTime. Note, however, that the onset latency of the TMS-evoked MEP is likely an under-estimate of the mean conduction time of all pathways involved in voluntary movement, because TMS is biased towards recruiting fast conducting corticospinal neurons with mono-synaptic connections to the spinal motorneurons (Day et al., 1989; Edgley et al., 1997). Therefore, the mean latency at which changes in motor cortical output are observable as changes in EMG activity is probably longer than 23 ms by several milliseconds.

To further elaborate the temporal relationship between global motor suppression and CancelTime, we performed a trial-by-trial analysis whereby MEP amplitudes were sorted according to the time at which TMS was delivered, relative to the time at which EMG decreased on Successful Stop, Failed Stop and Correct Go trials (Figure 4d). The suppression of MEPs in Successful Stop trials compared to Correct Go trials began in the 30 ms prior to the EMG decline (−30 to 0 ms: Z = 3.12, pBon = 0.005; 0 to 30 ms: Z = 4.48, pBon <0.001; 30 to 60 ms: Z = 2.45, pBon = 0.045). This lag in the time of EMG decrease relative to the time of the MEP suppression on Successful Stop trials can again be accounted for by the corticospinal conduction time. Thus, these results imply that the brain output to task-relevant muscles declines at approximately the same time as the global motor suppression begins. We note too, that MEPs were also suppressed in Failed Stop versus Correct Go trials, but at some delay relative to Successful Stops and the time of EMG cancellation (Figure 4d). This is consistent with the idea that the Stop process is initiated even in Failed Stop trials, and that part of the reason for the failure to stop is that the Stop process is initiated/implemented later in these trials (the other reason being that the Go process might have been completed particularly quickly).

Study 4 (EEG)

Having established that CancelTime reflects the time of an active stopping process at the muscle (studies 1 and 2, EMG/behavior), which also related tightly with the timing of global motor suppression (study 3, TMS), we then tested whether this EMG measure was also related to the timing of a prefrontal correlate of action-stopping, specifically the increase of beta power (13–30 Hz) before SSRTBeh at right frontal electrode sites (Castiglione et al., 2019; Wagner et al., 2018). We now measured scalp EEG as well as EMG from the hand, in 11 participants (see Table 1 for behavioral results). We derived beta bursts rather than beta power per se, as bursts have richer features (Shin et al., 2017) also see Little et al. (2018); Wessel (2020), such as burst timing and duration.

To identify right frontal electrodes of interest in each participant (i.e. a spatial filter), we used Independent Components Analysis (Bell and Sejnowski, 1995; see Castiglione et al., 2019; Wagner et al., 2018). We selected a participant-specific independent component (IC) based on two criteria; First, the scalp topography (right-frontal, and if not present, frontal); and Second, an increase in beta power on Successful Stop trials (from Stop signal to SSRTBeh; StopWin) compared to activity prior to the Go cue [−1000 to −500 ms aligned to the Stop signal; see Materials and methods; Figure 5—figure supplement 1]. The average scalp topography across all participants is shown in Figure 5b, inset (see Figure 5—figure supplement 2 for average dipoles). For each participant, we estimated beta bursts; First, by filtering the data at the peak beta frequency; and Second, by defining a burst threshold based on the beta amplitude in a baseline period after the Stop signal (500–1000 ms after Stop signal in the Stop trials, and 500–1000 ms after the mean SSD in the Correct Go trials) (see Materials and methods; Figure 5—figure supplement 3).

Relationship between scalp EEG beta bursts and CancelTime (study 4 and 5).

(a) Burst % across time for Successful Stop (red), Failed Stop (orange), and Correct Go (green) trials for an exemplar participant in study 4 from the right frontal spatial filter. The shaded region represents mean ± s.e.m. The CancelTime is shown in brown and the SSRTBeh as a cyan line. (b) The mean burst probability across all participants for Successful Stop (red), Failed Stop (orange), and Correct Go (green) trials and their respective baselines (gray). The bars and cross-hairs represent the mean and s.e.m across participants, while the dots represent individual participants. (Inset top right) The average scalp topography of all the right frontal ICs across all participants. (c) Same as (b) but for study 5. (d) Correlation between mean BurstTime and mean CancelTime. The yellow dots and cross-hairs represent the participants in study 4, while the light red ones represent participants in study 5. The brown line and the shaded area represent the linear regression fit and its 95% confidence interval (pooled study 4 and 5). Other details same as Figure 2d.

Relationship between scalp EEG beta bursts and CancelTime for study 4 and 5.

Beta power in Successful Stop trials for study 4.

(a–k) shows the time course of the peak beta power (solid red line) in the selected IC for each participant. The dotted cyan line represents each participant's SSRTBeh. The inset in each panel shows the scalp topography for the selected IC.

Average dipole location of the ICs selected in study 4 and 5.

(a), (b), and (c) The sagittal, top, and coronal view of the brain respectively, showing the average dipole location. The purple dot represents the mean location and the orange bubble represents the SD.

Illustration of beta burst computation.

(a) The average beta power (13–30 Hz) between the Stop signal and SSRTBeh (top panel) for a participant. The window between mean SSD (dotted pink line) and Stop (dotted black line at 0) represents the baseline time window (BaseWin). The time from Stop signal to SSRTBeh (dotted cyan line) represents the stop time window (StopWin). The burst threshold window is the time period from 500 to 1000 ms after the Stop signal. The bottom two panels show single trial examples of brief bursts of activity with the dotted black and cyan lines represent the Stop signal and SSRTBeh respectively. (b) The histogram of beta amplitude for all trials in a participant i(500 to 1000 ms after the Stop signal in the Stop trials; 500 to 1000 ms after mean SSD in the Go trials). The dotted red line represents the threshold for defining a burst which is estimated as median + 1.5 SD of the beta amplitude. The BurstTime and burst height are the time and amplitude of the peak within a burst respectively. Once a burst is identified using this threshold, the burst % and burst length are estimated using a lower threshold which is median + SD (dotted blue line) (c) The burst raster for all trials in a participant across time. Each black dot represents a burst in that trial. To compute BurstTime we consider the burst times between the Stop signal and SSRTBeh (dotted cyan line).

Dynamics of burst% aligned to the Go cue.

(a) Burst% for the Correct Go (green), Successful Stop (red), and Failed Stop (orange), aligned to the Go cue in Study 4. The bold traces represent the mean across the population, while the shaded region represents the s.e.m. The grey, brown, and cyan shaded regions represent the mean ± s.e.m. of the time of presentation of the Stop signal, CancelTime, SSRTBeh across the population. (b) Same as (a) but for Study 5.

Relationship of CancelTime with other burst parameters.

(a) Correlation between mean burst height (0.9 ± 0.2) and mean CancelTime across participants in study 4 (r = 0.5, p=0.161, BF10 = 0.7). The brown dots and cross-hairs represent the mean ± s.e.m. for individual participants. The brown line and the shaded area represent the linear regression fit and its 95% confidence interval respectively. (b) Across participants correlation between mean burst length (210 ± 20 ms) and mean CancelTime in study 4 (r = −0.1, p=0.801, BF10 = 0.3). Other details are same as in (a). (c) Same as (a) but for study 5. Mean burst height is 0.65 ± 0.05 (r = −0.3, p=0.281, BF10 = 0.5). (d) Same as (b) but for study 5. Mean burst length is 220 ± 15 ms (r = −0.22, p=0.475, BF10 = 0.4).

Relationship between CancelTime and other burst parameters in study 4 and 5.

In an exemplar participant, the burst % increased for Successful Stop compared to both Failed Stop and Correct Go trials prior to SSRTBeh (Figure 5a). To quantify this across participants, we compared the mean burst % among the three trial-types, and for the time window from the Stop signal to the SSRTBeh of a participant (StopWin) and the baseline period before the Stop signal (BaseWin; Go to Stop signal in Stop trials and Go to mean SSD in Correct Go trials). We performed a 2-way repeated measures ANOVA with mean burst % as the dependent measure, with trial-type (Successful, Failed Stop, and Correct Go trials) and time-window (StopWin and BaseWin) as factors. There was a significant main effect of trial-type (F(2,20) = 4.5, p=0.025, ηp2 = 0.3) and a trial-type by time-window interaction (F(2,20) = 4.0, p=0.034, ηp2 = 0.3), but no main effect of time-window (F(1,10) = 3.8, p=0.088, ηp2 = 0.3). Post hoc t-tests showed that in the StopWin there was a significant increase in burst % for Successful Stop (14.6 ± 1.7%) compared to both its baseline (9.9 ± 1.7%; t(10) = 3.3, pBon = 0.022, BF10 = 7.6), and Correct Go (9.6 ± 1.3%; t(10) = 3.7, pBon = 0.015, BF10 = 11.8), but not to Failed Stop (10.3 ± 1.6%; t(10) = 2.1, pBon = 0.198, BF10 = 1.2) (Figure 5b). Thus, burst % increased for the Successful Stop trials which could not be attributed to post-movement beta rebound (see Figure 5—figure supplement 4).

To further clarify the temporal relationship between beta activity and the current EMG measure of action-stopping, we quantified the mean burst time (BurstTime in the StopWin) for each participant. Across participants, the mean BurstTime (115 ± 6 ms) was significantly shorter than mean CancelTime (169 ± 10 ms; t(10) = 8.2, p<0.001, BF10 > 100) and there was also a strong positive relationship between them (ρ = 0.76, p=0.006, BF10 = 10.6; Figure 5d; see Figure 5—figure supplement 5 for correlation between CancelTime and other burst parameters). Further, we show that the observed correlation was not merely an artifact of varying StopWin across participants (permutation test, p<0.05; see Materials and methods). Thus, these results show that participants with an early frontal beta burst also had an early CancelTime.

Study 5 (EEG replication)

We ran a new sample of 13 participants (see Table 1 for behavioral results). As above a right frontal IC was extracted for each participant (average topography Figure 5c inset) and the burst % was compared for the three trial-types (Successful Stop, Failed Stop, and Correct Go) in the two time-windows (StopWin and BaseWin). Again, a 2-way repeated measures ANOVA with burst % as the dependent measure revealed that there was a significant main effect of trial-type (F(2,24) = 6.9, p=0.004, ηp2 = 0.4) and a trial-type by time-window interaction (F(1,12) = 5.8, p=0.009, ηp2 = 0.3; Figure 5c). Here there was also a significant effect of time-window on burst % (F(1,12) = 16.1, p=0.002, ηp2 = 0.6). Post-hoc t-tests confirmed that the burst % was greater for Successful Stop (16.2 ± 2.2%) compared to its baseline (11.3 ± 1.4%; t(12) = 3.3, pBon = 0.021, BF10 = 7.6), and Correct Go (12.0 ± 1.4%; t(12) = 3.0, pBon = 0.030, BF10 = 5.3) but not compared to Failed Stop (15.4 ± 1.4%; t(12) = 1.0, pBon = 0.957, BF10 = 0.34). Across participants, the mean BurstTime (129 ± 7 ms) was again significantly shorter than CancelTime (166 ± 8 ms; t(10) = 5.0, p<0.001, BF10 > 100) and there was a significant positive relationship (ρ = 0.57, p=0.045, BF10 = 1.9; Figure 5d). Again, a permutation test suggested that this correlation was unlikely to result from mere variation in the length of StopWin across participants (p<0.05). Combining data from studies 4 and 5 confirms the strong relationship between right frontal beta BurstTime and CancelTime (ρ = 0.66, p<0.001, BF10 = 29.4).

Discussion

This set of studies provides detailed information about the timing of subprocesses in human action-stopping. We started with the recently published observations that the standard behavioral measure of action-stopping (SSRT) is, an over-estimate of stopping latency (Bissett and Poldrack, 2019; Raud and Huster, 2017; Skippen et al., 2019b). To more precisely delve into this, we validated a trial-by-trial method for estimating stopping latency from EMG. We focused on Successful Stop trials with small impulses (partial bursts) in EMG activity. The amplitude of such partial EMG activity was ~ 50% of the amplitude of EMG activity for outright keypresses, and this decreased at ~160 ms after the Stop signal (CancelTime), which is similar to other studies (Raud et al., 2019; Raud and Huster, 2017). While, one interpretation of this partial EMG activity is that it merely reflects ‘weak’ Go activation that did not run to completion (de Jong et al., 1990), several lines of evidence strongly suggest it is a muscle manifestation of the stopped response. First, CancelTime was positively correlated with SSRTBeh, similar to recent studies (Huster et al., 2019; Thunberg et al., 2019). Second, the variability of CancelTime was positively correlated with the variability of SSRT estimated from the BEESTS modeling framework. Third, the partial EMG activity had a profile which was initially similar to the EMG profile seen when actual keypresses were made, and only diverged at ~55 ms after EMG onset. This initial similarity would not be expected if it were a weak Go activation – since previous research has demonstrated that weak and strong muscle activations have distinct profiles that diverge soon after onset (Bellumori et al., 2011). Fourth, our TMS experiment demonstrated that CancelTime coincided well with the timing of a putative basal ganglia-mediated global motor suppression (Badry et al., 2009; Cai et al., 2012; Wessel and Aron, 2013; Wessel et al., 2016; Wessel and Aron, 2013; Wessel and Aron, 2017). This implies that the smaller amplitude and earlier decline of the partial EMG activity on Successful Stop was due to an active suppression of motor output. Fifth, across participants, on Successful Stop trials, CancelTime correlated strongly with the time of right frontal beta bursts (BurstTime) from scalp EEG. This is consistent with response inhibition being implemented via right prefrontal cortex (Aron et al., 2014), and with previous research showing an increase of beta at right frontal electrode sites before SSRTBeh (Castiglione et al., 2019; Wagner et al., 2018).

Due to the poor spatial resolution of EEG it is not possible to pin down the origin of the bursts recorded on the scalp to any particular frontal cortical area (see Figure 5—figure supplement 2) – these bursts could relate to the rIFC or the presupplementary motor area, preSMA, or both [the rIFC and preSMA are connected via the aslant tract (Catani et al., 2013; Swann et al., 2012)]. We note again that two studies with intracranial EEG showed increases of right frontal beta for rIFC (Swann et al., 2009; Swann et al., 2012) and also that a recent study using source reconstruction of MEG signals based on fMRI in the same subjects showed an especially strong beta power increase for rIFC, that began ~ 140 ms after the Stop-signal (Schaum et al., 2020), consistent with our results.

We also acknowledge that the burst % was quite low on Successful Stop trials (~15%) and that CancelTimes on trials with and without bursts were not different (Study 5: CancelTimeWith Burst = 164 ± 9 ms; CancelTimeNo Burst = 165 ± 9 ms, t(12) = 0.6, p=0.58, d = 0.2, BF10 = 0.3; Study 4: too few trials for meaningful comparisons). While this might indicate that bursts are not necessary or sufficient for action-stopping, we think that the poor signal-to-noise of EEG could explain the low burst %. Further research is needed to test if beta bursts are causal to stopping. On a related point, the presence of beta on Go trials was also interesting. It is possible that beta bursts on Go trials reflected the (partly) spontaneous events that occur periodically (but have some functional consequence) (Shin et al., 2017), or the bursts might have had a role in proactive slowing on Go trials (as the task, after all, required participants to prepare to stop their response).

While several scalp EEG, intracranial EEG, and MEG studies showed increased right frontal beta power for stopping (Castiglione et al., 2019; Schaum et al., 2020; Swann et al., 2009; Swann et al., 2012; Wagner et al., 2018), a recent scalp EEG study focused on the spatial and temporal dynamics of beta bursts (Wessel, 2020). That study saw that burst probability increased for likely dorsomedial frontal cortex (electrode FCz) rather than right frontal cortex, as we do. This discrepancy could be explained by our use of a spatial filter approach whereas that study analyzed the data in channel space. A further observation of Wessel (2020) was that bursts increased over bilateral sensorimotor cortex ~ 25 ms after the frontal area; and this was interpreted as inhibition of the motor system. This fits our observation of a decrease in corticospinal excitability within ~ 20 ms of right frontal bursts. Putting aside methodological differences, these studies together implicate beta bursts in action-stopping.

A puzzle in our results was that CancelTime was ~ 60 ms earlier than SSRTBeh. To better understand this discrepancy, we calculated SSRT based on the EMG response rather than behavior. We saw that SSRTEMG better matched CancelTime than did SSRTBeh. Thus, SSRTBeh could be an over-estimation of the duration of the Stop process in the brain. This extra time in SSRTBeh probably reflects a ‘ballistic stage’ in generation of the button press (de Jong et al., 1990). We suggest that the maximum CancelTime reflects the last point at which a Stop process can intervene to prevent responses. We note that CancelTime (a muscle measurement) is an overestimation of the brain’s stopping latency since it does not include the corticospinal conduction time, which we estimated as ~ 20 ms, and does not include the stopping latencies of the No EMG trials, which presumably reflect the fastest stopping latencies where the Stop process was fast enough to cancel the impending response before it reaches the muscle. Indeed, our TMS results show that global motor suppression, which we take as the time at which motor areas of the brain are suppressed, is ~ 140 ms (which is ~ 20 ms less than CancelTime). One important consequence of our observation that the brain’s stopping latency is ~ 140 ms is that neural events that mediate stopping need to occur before this time. Indeed, we found that right frontal beta activity increased ~ 120 ms after the Stop signal on Successful Stop trials, and also that, across participants, there was a strong positive relationship between mean BurstTime and mean CancelTime.

Taken together, these studies motivate a relatively detailed model of the temporal events of action-stopping (Figure 6; Video 1). First, we suppose the right frontal beta bursts relate to activity of right inferior frontal gyrus (Aron et al., 2014; Swann et al., 2009), and this happens in ~ 120 ms, which then leads via basal ganglia (Wessel et al., 2016) to global suppression of the primary motor cortex (Badry et al., 2009; Cai et al., 2012; Wessel and Aron, 2013; Wessel and Aron, 2013; Wessel and Aron, 2017) at ~140 ms. After a corticospinal conduction delay of ~ 20 ms, this suppression of motor output is then reflected at ~160 ms as a decline in muscle activity (CancelTime). Finally, SSRTBeh occurs at ~220 ms, after, what we suppose is an electromechanical delay of ~ 60 ms. Thus, CancelTime narrows the time window for the causal manipulation of neural structures involved in action-stopping. This is in contrast to previous studies that have proposed that the onset of intramuscularly-recorded antagonist EMG responses (which is longer than SSRT) can be used as an alternative for estimating the stopping latency (Atsma et al., 2018; Corneil et al., 2013; Goonetilleke et al., 2012; Goonetilleke et al., 2010).

Hypothetical model of the temporal cascade of processes underlying human action-stopping.

Following the Stop signal, the right PFC including the rIFC and the preSMA gets activated at ~120 ms. These region/s activate (green connections) the STN of the basal ganglia. This in turn activates the globus pallidus interna which, via its inhibition (red connection) on the motor regions of the thalamus, cuts down the ‘drive’ to the motor cortex. Theoutcome is a global motor suppression at ~140 ms after the Stop signal. This suppression is reflected in the hand muscle at ~160 ms which is measured as the CancelTime. There is a delay of ~60 ms at the muscle level which gets added to the behavioral estimate of SSRT.

Hypothetical model of the temporal cascade of processes underlying human action-stopping.

Following the Go signal, after a delay, the thalamocortical drive starts building up. After a while this drive is sufficient to activate muscles via the corticospinal pathways. Following the Stop signal, the right PFC including the rIFC and the preSMA gets activated at ~ 120 ms. These region/s activate (green connections) the STN of the basal ganglia which in turn activates the globus pallidus interna which via its inhibition (red connection) on the motor regions of the thalamus cuts down the ‘drive’ of the motor cortex. This results in a global motor suppression at ~ 140 ms after the Stop signal. This suppression is reflected in the hand muscle at ~ 160 ms which is measured as the CancelTime. There is a delay of ~ 60 ms at the muscle level which gets added to the behavioral estimate of SSRT.

We acknowledge that the timings in this model are approximations that are dependent on a range of factors (such as averaging across participants, running different experiments, and the particular parameters of detection algorithms). However, we note a striking convergence of timings across the current experiments and in other studies, for example CancelTime (Hannah et al., 2019; Raud et al., 2019; Raud and Huster, 2017), time of MEP suppression (Coxon et al., 2006; van den Wildenberg et al., 2010), corticospinal conduction time (Groppa et al., 2012; Hamada et al., 2013), BurstTimes (Hannah et al., 2019), and the ballistic stage (Gopal and Murthy, 2016; Jana and Murthy, 2018). Together, these all provide support for our model.

This model specifies the possible chronometrics of stopping in more detail than extant human models, and, more generally, raises questions about the timing reported in some other studies where the neural change appears late. For example, movement neurons in monkey Frontal Eye Field decrease activity in less than 10 ms before SSRT (Hanes et al., 1998), dopaminergic neurons in rodent substantia nigra and striatum increase activity only 12 ms before SSRT (Ogasawara et al., 2018), TMS at ~ 25 ms before SSRT over human Intraparietal Sulcus prolongs SSRT (Osada et al., 2019), and P300 human EEG activity ~ 300 ms after the Stop signal relates to the stopping latency (Wessel and Aron, 2015). Whereas the rather late timing of some of these results might be related to processes such as monitoring and feedback (Huster et al., 2019) as has been ascribed to brain signatures that modulate after SSRT (Logan et al., 2015; Schall and Boucher, 2007), our earlier latencies for prefrontal bursts, TMS-MEP and muscle CancelTime are more indicative of a role in stopping itself.

While our study specifically looked at the chronometrics of the Stop process, and tried to better characterize the physiological model underlying action-stopping, we also now speculate how our results relate to computational models of action-stopping (specifically, the independent race model, the interactive race model, the BEESTS model, and the blocked-input model, and the). First, our results are not compatible with a strictly independent model (of the Go and the Stop processes) since we see active inhibition of M1 (the Go process) already some time before SSRT. Second, our results are compatible with the interactive race model which suggests that the Stop process begins late, but implementation is quick (i.e. within the last 1/3th of the stopping latency) (Boucher et al., 2007). Indeed, we observed beta bursts in frontal areas ~ 120 ms after the stop signal followed by rapid cancellation at the muscle within ~ 40 ms. Third, our results are also compatible with the BEESTS model insofar as they point to a trigger process that has a duration of about 80–120 ms (Bekker et al., 2005; Skippen et al., 2019a). Finally, the interactive-race model and blocked-input model are very similar (Logan et al., 2015), so our results do not disambiguate them.

Our results have several important implications. First, whereas several earlier studies of action-stopping recorded partial EMG for various purposes (de Jong et al., 1990; McGarry et al., 2000; McGarry and Franks, 1997), some more recent ones specifically interpreted the time of the partial EMG as related to stopping (Huster et al., 2019; Nguyen et al., 2019; Raud et al., 2019; Raud and Huster, 2017; Thunberg et al., 2019). Our results strongly affirm that partial EMG can be used to estimate the latency of stopping reflected in the muscle. Second, as just noted, they provide temporal constraints on neuroscience studies of stopping in the brain. They suggest that methods with high temporal resolution need to focus on the time after the Stop signal and before CancelTime (indeed CancelTime minus conduction time) rather than before SSRTBeh, and the current study points to the potential of CancelTime as single-trial metric of stopping (please see our recent pre-print; Hannah et al., 2019). Third, our results have clinical implications. Whereas meta-analysis shows that SSRTBeh is longer for patients (e.g. ADHD, OCD, and substance use disorder) vs. controls (Alderson et al., 2007; Bari and Robbins, 2013; Lavagnino et al., 2016; Lijffijt et al., 2005; Smith et al., 2014; Snyder et al., 2015), not all such studies show differences (Clark et al., 2007; Kalanthroff et al., 2017; Lipszyc and Schachar, 2010; Smith et al., 2014). We predict that CancelTime will be more sensitive than SSRTBeh. Furthermore, future studies can easily estimate within-subject variability in CancelTime, which will likely discriminate patients from controls. Fourth, our results provide insight into why SSRTBeh might only have a modest relationship with more ‘real-world’ measures of impulsivity (Chowdhury et al., 2017; Enkavi et al., 2019; Friedman and Miyake, 2004; Lijffijt et al., 2004; McLaughlin et al., 2016; Skippen et al., 2019b). As we show, SSRTBeh includes not only CancelTime but an extra, and variable, 60 ms ballistic stage. We expect that future studies may show stronger correlations between CancelTime and self-report than that seen between SSRTBeh and self-report (also see Skippen et al., 2019b); likewise we predict that right frontal beta burst time might also correlate more tightly with self-report measures. More generally, the detailed timing information of frontal beta at ~ 120 ms, global motor suppression at ~ 140 ms, and CancelTime at ~ 160 ms points to subprocesses of action-stopping that provide potential biomarkers that could better explain individual differences in impulse control.

In conclusion, we propose a detailed timing model of action-stopping that partitions it into subprocesses that are isolable to different nodes and are more precise than the behavioral latency of stopping. At the core of this timing model is a method of measuring the latency of stopping from the muscles. This offers a potential single-trial estimate of stopping latency that could be easily measured with minimal equipment in any lab that studies human participants.

Materials and methodsParticipants

All were adult, healthy, human volunteers provided written informed consent and were compensated at $20/hour. The studies were approved by the UCSD Institutional Review Board (protocol #171285).

Study 1. Ten participants (four females; age 22 ± 1 years; all right-handed).

Study 2. Thirty-six participants (19 females; age 19 ± 0.4 years; all right-handed). Two were excluded for bad behavior (violating the assumptions of the independent race model - Failed Stop RTBeh < Correct Go RTBeh, and P(Stop) increasing monotonically as a function of SSD), and two were excluded for noisy EMG data.

Study 3 (TMS): Eighteen participants (11 females; age 19 ± 0.4 years; 15 right-handed, 2 left-handed) with no contraindications to TMS (Rossi et al., 2011). One was excluded for bad behavior.

Study 4 (EEG). Eleven participants (six females, age 19 ± 0.4 years, all right-handed).

Study 5 (EEG): Fifteen participants (nine females, age 21 ± 0.4 years, all right-handed). Two were excluded from analysis, one for misaligned EEG markers due to a technical issue, while the other lacked a right frontal brain IC, based on our standard method (Castiglione et al., 2019; Wagner et al., 2018).

Stop-signal task

This was run with MATLAB 2014b (Mathworks, USA) and Psychtoolbox (Brainard, 1997). Each trial began with a white square appearing at the center of the screen for 500 ± 50 ms. Then a right or left white arrow appeared at the center. When the left arrow appeared, participants had to press a key on a vertically oriented keypad using their index finger, while for a right arrow they had to press down on a key on a horizontally oriented keypad with their pinky finger (Figure 1b inset), as fast and as accurately as possible (Go trials). The stimuli remained on the screen for 1 s. If participants did not respond within this time, the trial aborted, and ‘Too Slow’ was presented. On 25% of the trials, the arrow turned red after a Stop Signal Delay (SSD), and participants tried to stop the response (Stop trials). The SSD was adjusted using two independent staircases (for right and left directions), where the SSD increased and decreased by 50 ms following a Successful Stop and Failed Stop respectively. Each trial was followed by an inter-trial interval (ITI) and the entire duration of each trial including the ITI was 2.5 s (Figure 1a).

Study 1 and 2. Participants performed the task with their right hand. They performed 40 practice trials before the actual experiment, where their baseline SSD was determined and was subsequently used as the starting SSD in the main experiment. In study 1 and 2, the experiment had 600 trials divided in 15 blocks, such that each block had 40 trials (450 Go trial and 150 Stop trials). At the end of each block the participants were presented a figure showing their mean reaction times (RT) in each block. Participants were verbally encouraged to maintain their mean reaction time constant across the different blocks and between 0.4–0.6 s.

Study 3. Participants performed the task with their left hand. Following 48 practice trials without TMS, participants performed 12 blocks of the experiment with TMS, with each block consisting of 96 trials each (72 Go trials and 24 Stop trials).

Study 4. Participants performed the task with their right hand. Following 160 practice trials, participants performed 4 blocks of 80 trials (240 Go trials and 80 Stop trials).

Study 5. Participants performed the task with their right hand. Following 80 practice trials, participants 24 blocks of 80 trials each (1440 Go trials and 480 Stop trials).

Data recordingEMG

EMG data were acquired using a Grass QP511 AC amplifier (Glass Technologies, West Warwick, RI) with a frequency cut-off between 30 and 1000 Hz. A CED Micro 1401 mk II acquisition system sampled the data at 2 kHz. The EMG data were acquired by CED Signal v4 software (Cambridge Electronic Design Limited, Cambridge, UK) for 2 s following the fixation cue. The data acquisition was triggered from MATLAB using a USB-1208FS DAQ card (Measuring Computing, Norton, MA). In all five experiments, surface EMG was recorded from both the first dorsal interossei (FDI) and the abductor digiti minimi (ADM) muscles of the hand (Figure 1b inset). In the TMS experiment, surface EMG was also recorded from the task-irrelevant right extensor carpi radialis (ECR) muscle (Figure 4a).

TMS

MEPs were evoked using a TMS device (PowerMag Lab 100, MAG and More GMBH, Munich, Germany) delivering full sine wave pulses, and connected to a figure-of-eight coil (70 mm diameter, Double coil PMD70-pCool; MAG and More GMBH, Munich, Germany). During the task, the coil was positioned on the scalp over the left primary motor cortex representation of the ECR muscle and oriented so that the coil handle was approximately perpendicular to the central sulcus, that is at ~45° to the mid-sagittal line, and the initial phase of current induced in the brain was posterior-to-anterior across the central sulcus. Prior to the experiment, the motor hot spot was determined as the position on the scalp where slightly supra-threshold stimuli produced the largest and most consistent MEPs in ECR. The position was marked on a cap worn by the participants. Resting motor threshold (RMT) was defined as the lowest intensity to evoke an MEP of at least 0.05 mV in 5 of 10 consecutive trials while participants were at rest. We then established the test stimulus intensity to be used during task, which was set to produce a mean MEP amplitude of approximately 0.2–0.5 mV whilst the participant was at rest.

MEPs were also evoked in the left FDI muscle prior to beginning the main experiment for the purpose of recording the corticospinal conduction time. The motor hot spot for the FDI was defined in a manner similar to that for the ECR. The active motor threshold (AMT) was defined as the lowest intensity to evoke a discernible MEP in 5 of 10 consecutive trials, while participants maintained slight voluntary contraction (~10% of maximum voluntary EMG amplitude during isometric finger abduction). Then, 10 stimuli were delivered at 150% AMT during slight voluntary contraction (again 10% of maximum), with the coil oriented to induce lateral-medial current in the brain in order to obtain estimates of corticospinal conduction time.

During the task, TMS stimuli were delivered on every Stop trial and on 50% of Go trials. On every Stop trial, a single TMS stimulus at the test stimulus intensity was delivered at one of six time points: inter-trial interval (100 ms prior to fixation; ITI), 100 ms, 120 ms, 140 ms, 160 ms and 180 ms after the Stop signal (Figure 4a). On the Go trials, TMS stimuli were yoked to the time of the Stop signal on the previous Stop trial. Thus, there were 48 trials per TMS time point on Stop trials and 96 trials per time point on Go trials.

EEG

64 channel EEG (Easycap, Brainvision LLC) was recorded in the standard 10/20 configuration at 1 kHz using BrainVision actiChamps amplifier (Brain Products GMBH, Gilching, Germany) and BrainVision Pycorder (Brain Products GMBH, Germany).

Data analysis

All analyses were performed using MATLAB (R2016b, R2018b, R2019a).

Stop signal reaction time

SSRT from the behavioral responses (SSRTBeh) was determined using the integration method (Verbruggen et al., 2019). When calculating SSRT using the EMG responses, SSRTEMG, as the P(Respond|Stop) was often much more than 0.5, we calculated the SSRT individually for all SSDs and then averaged it (Verbruggen and Logan, 2009).

EMG data analysis

EMG data were filtered using a 4th order Butterworth filter (roll-off 24 dB/octave) to remove 60 Hz noise and its harmonics at 120, and 180 Hz. EMG data were full-wave rectified and the root-mean square (RMS) of the signal was computed using a centered window of 50 ms. Any EMG activity which was greater than 8 SD of the mean EMG activity in the baseline period (Fixation to Go cue) was marked, on a trial-by-trial basis. Starting from the peak of that EMG activity, we backtracked and marked the onset at the point where the activity dropped below 20% of the peak for five consecutive ms. This method of adjusting the threshold based on the peak EMG activity, allowed better onset detection than a fixed threshold, especially when the amplitude of the EMG activity was small. The time when EMG started to decline was determined as the time when, following the peak EMG, the activity decreased for five consecutive ms. Visual inspection of individual trials showed that this method provided a reliable detection of both EMG onsets (see Figure 1—figure supplement 1a,b for RTEMG vs. RTBeh correlation) and decline. Any detected EMG timing which was beyond 1.5 times the inter-quartile range (IQR) of the first and third quartile (Q3) of that particular timing distribution was deemed an outlier. This removed < 4% trials. CancelTime was marked as the time of the EMG decline following the Stop signal. For outlier rejection, CancelTimes had a lower cutoff of 50 ms and higher cutoff of Q3+1.5 × IQR. This removed < 3% trials.

As the peak EMG amplitude for the FDI and ADM muscle were quite distinct, before averaging the two EMG activities, we normalized the muscle activity by the peak activity in that particular muscle (VoltageNorm in Figures 2a, b and 3c, Figure 3—figure supplement 2).

Global MEP suppression

MEP amplitudes were measured on a trial-by-trial basis. Data were included for analysis if the following criteria were met: (i) the amplitude of the ECR EMG signal in a 90 ms period prior to the TMS stimulus was < 0.05 mV; (ii) the amplitude of the MEP fell within the mean±1.5× IQR of values for the same time point and trial type (Correct Go, Failed Stop, Successful Stop). Thereafter, MEP amplitudes measured at the ITI were collapsed across trial type (Correct Go, Failed Stop and Successful Stop), averaged and used as a baseline against which to compare other TMS time points. For each of the other TMS time points (100, 120, 140, 160, 180 ms following the Stop signal), data were averaged within each trial type (Correct Go, Failed stop, Successful Stop) and expressed as a percentage of the mean ITI MEP amplitude.

Corticospinal conduction time

Corticospinal conduction time was determined by delivering TMS over the hand representation of left FDI and measuring MEP from the muscle (Figure 4c). The earliest MEP onset latency across 10 trials was identified by visual inspection of the EMG traces (Hamada et al., 2013; Hannah and Rothwell, 2017; Rossini et al., 2015).

Trial-by-trial analysis of CancelTime and time of global motor suppression

To compare the temporal association between the EMG decline and MEP suppression, we performed a trial-by-trial analysis of Stop-signal task data only on trials where an EMG burst was detected. We first normalized the time of TMS on a given trial by subtracting the time of EMG decline from the time of the TMS pulse. Hence, negative values mean that TMS was delivered before the EMG decline and positive values mean that TMS was delivered after. We then plotted MEP amplitudes for each of the three response types (Correct Go, Failed Stop, and Successful Stop) against the normalized times binned into 30 ms windows. This analysis meant that for a given individual there were relatively few trials per time bin, and some bins would occasionally contain no data. Therefore, we combined data across all individuals. Prior to this, MEP amplitudes for each individual were normalized to the mean MEP amplitude at the inter-trial interval, to account for inter-individual variability in absolute MEP amplitudes at baseline. We restricted our analysis to time bins that contained at least 50 trials, which resulted in time range −90 ms to 60 ms.

EEG preprocessing

We used EEGLAB (Delorme and Makeig, 2004) and custom-made scripts to analyze the data. The data were downsampled to 512 Hz and band-pass filtered between 2–100 Hz. A 60 Hz and 180 Hz FIR notch filter were applied to remove line noise and its harmonics. EEG data were then re-referenced to the average. The continuous data were visually inspected to remove bad channels and noisy stretches.

ICA analysis

The noise-rejected data were then subjected to logistic Infomax ICA to isolate independent components (ICs) for each participant separately (Bell and Sejnowski, 1995). We then computed the best-fitting single equivalent dipole matched to the scalp projection for each IC using the DIPFIT toolbox in EEGLAB (Delorme and Makeig, 2004; Oostenveld and Oostendorp, 2002). ICs representing non-brain activity related to eye movements, muscle, and other sources were first identified using the frequency spectrum (increased power at high frequencies), scalp maps (activity outside the brain) and the residual variance of the dipole (greater than 15%) and then, subtracted from the data. A putative right frontal IC was then identified from the scalp maps (if not present then we used frontal topography) and the channel data were projected onto the corresponding right frontal IC. The data on Successful Stop trials were then epoched from −1.5 s to 1.5 s aligned to the Stop signal. We estimated the time-frequency maps from 4 to 30 Hz, and −100 to 400 ms using Morlet wavelets with three cycles at low frequencies linearly increasing by 0.5 at higher frequencies. The IC was selected only if there was a beta power (13 to 30 Hz) increase in the window between the Stop signal and SSRTBeh compared to a time-window prior to the Go cue (−1000 to −500 ms aligned to Stop signal). In each participant, the beta frequency which had the maximum power in this time window was used in the beta bursts computation (Figure 5—figure supplement 1).

Beta bursts

To estimate the beta bursts, the epoched data were first filtered at the peak beta frequency using a frequency domain Gaussian window with full-width half-maximum of 5 Hz. The complex analytic envelope was then obtained by Hilbert transform, and its absolute value provided the power estimate. In each participant, to define the burst threshold, the beta amplitude within a period of 500 to 1000 ms (i.e. after the Stop signal in the Stop trials, and after the mean SSD in the Correct Go trials) was pooled across all trials [Note that compared to the ICA analysis here we picked a different time-window to estimate the burst threshold to keep the analysis unbiased. However, picking the same time-window also yielded similar results]. The threshold was set as the median + 1.5 SD of the beta amplitude distribution (Figure 5—figure supplement 3). Once the burst was detected, the burst width threshold was set as the median + 1 SD. We binary-coded each time point where the beta amplitude crossed the burst width threshold to compute the burst % across trials. For each detected burst, the time of the peak beta amplitude was marked as the BurstTime.

Statistical analysis

For pairwise comparisons, the data were first checked for normality using Lilliefors test, and if normally distributed a two-tailed t-test (t-statistic) was performed, else a Wilcoxon signed rank test (Z-statistic) was performed. We interpret the effect sizes as small (Cohen’s d: 0.2–0.5; Bayes Factor in favor of the alternate hypothesis, BF10: 1–3), medium (d: 0.5–0.8; BF10: 3–10), large (d > 0.8; BF10 > 10). For comparisons across multiple levels, repeated-measures ANOVA was used, followed by Bonferroni corrected t-tests for pairwise comparisons (Bonferroni corrected p-value: pBon). The Greenhouse-Geisser correction was applied where the assumption of sphericity in ANOVA was violated (corrected F-statistic: FGG). Effect sizes for ANOVAs were interpreted as small (partial eta-squared, ηp2: 0.01–0.06), medium (ηp2: 0.06–0.14), and large (ηp2 : 0.14). For correlational analyses, Pearson’s correlation coefficient (r) was usually used, but Spearman’s correlation coefficient (ρ) was used when the data was bounded in a closed interval. All data are presented as mean ± s.e.m.

In testing the relationship between BurstTime and CancelTime, we performed a permutation test. We sampled BurstTimes randomly from a uniform distribution between 0 and SSRTBeh for a given participant for 3000 iterations. For each iteration, we then computed the correlation (r) between the mean BurstTime and the mean CancelTime across participants. This generated a distribution of r ranging between −1 and 1. The p-value for our analysis was determined as the P(r ≥ rObs|H0) in the permuted data.

Bayesian modelling of behavioral data

We used the BEESTS model developed by Dora Matzke and colleagues (run in R Studio 1.1.463) which assumes a race between two stochastically independent process, a Go and a Stop processes. This model estimates the distribution of the SSRT by using the participant’s Go RTBeh distribution, and by considering the Failed Stop RTBeh as a censored Go RTBeh distribution. The censoring points are sampled randomly from the SSRT distribution on each Stop trial. The RTBeh distributions underlying the Go and Stop processes are assumed to have a Gaussian and an exponential component and is described by three parameters (μGo, σGo, τGo and μStop, σStop, τStop). For such ex-Gaussian distributions, the mean and variance of the RTBeh distributions are determined as μ + τ and μ2 + τ2, respectively. The model also estimates the probability of trigger failures for each participant. The model uses Bayesian Parametric Method (BPE) to estimate the parameters of the distributions. We used a hierarchical BPE, where individual subject parameters are modeled with the group-level distributions. This approach is thought to be more accurate than fitting individual participants and is effective when there is less data per participant (Matzke et al., 2013). We pooled the subjects across both study 1 and 2 to estimate the individual parameters. The priors were bounded uniform distributions (μGo, μStop: U(0,2); σGo, σStop: U(0,0.5) τGo, τStop: U(0,0.5); pTF: U(0,1)). The posterior distributions were estimated using the Metropolis-within-Gibbs sampling and we ran multiple chains. We ran the model for 5000 samples with a thinning of 5. The Gelman-Rubin (R̂) statistic was used to estimate the convergence of the chain. Chains were considered converged if R̂<1.1.

Data and scripts

A core element of this paper is a novel method of calculating single-trial stopping latency from EMG. Accordingly, we provide the EMG and behavioral data from all participants in study 1 and 2, along with analysis scripts, and a brief description of how to execute the scripts (https://osf.io/b2ng5/). All other EMG, TMS-MEP and EEG data and scripts are also provided at the above link.

Acknowledgements

We thank Dora Matkze for sharing the scripts for BEESTS modelling, Sven Bestmann for insightful comments on data, Simon Little for sharing the beta-burst analysis script, Kelsey Sundby for sharing some EEG and EMG data, and Xinze Yu and Hunter Robbins for help in data recording. We gratefully acknowledge our support from NIH: NS106822 and DA026452.

Additional informationCompeting interests

Reviewing editor, eLife

No competing interests declared

Author contributions

Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing

Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing

Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing

Conceptualization, Resources, Formal analysis, Supervision, Funding acquisition, Validation, Visualization, Writing - original draft, Project administration, Writing - review and editing

Ethics

Human subjects: All human volunteers provided written informed consent prior to their participation. The participants were compensated at $20/hour. The University of California San Diego Institutional Review Board approved all the studies (protocol #171285).

Additional filesData availability

A core element of this paper is a novel method of calculating single-trial stopping speed from EMG. Accordingly, we provide the EMG and behavioral data from 10 participants in study 1, along with analysis scripts, and a brief description of how to execute the scripts (https://osf.io/b2ng5/).

The following dataset was generated:

JanaSHannahRMuralidharanVAronA2019Temporal cascade of frontal, motor and muscle processes underlying human action-stoppingOpen Science Frameworkb2ng5

ReferencesAlderson RMRapport MDKofler MJ2007Attention-deficit/hyperactivity disorder and behavioral inhibition: a meta-analytic review of the stop-signal paradigmJournal of Abnormal Child Psychology3574575810.1007/s10802-007-9131-617668315Aron AR2007The neural basis of inhibition in cognitive controlThe Neuroscientist1321422810.1177/107385840729928817519365Aron ARRobbins TWPoldrack RA2014Inhibition and the right inferior frontal cortex: one decade onTrends in Cognitive Sciences1817718510.1016/j.tics.2013.12.00324440116Atsma JMaij FGu CMedendorp WPCorneil BD2018Active braking of Whole-Arm reaching movements provides Single-Trial neuromuscular measures of movement cancellationThe Journal of Neuroscience384367438210.1523/JNEUROSCI.1745-17.201829636393Badry RMima TAso TNakatsuka MAbe MFathi DFoly NNagiub HNagamine TFukuyama H2009Suppression of human cortico-motoneuronal excitability during the Stop-signal taskClinical Neurophysiology1201717172310.1016/j.clinph.2009.06.02719683959Bari ARobbins TW2013Inhibition and impulsivity: behavioral and neural basis of response controlProgress in Neurobiology108447910.1016/j.pneurobio.2013.06.00523856628Bekker EMOvertoom CCKooij JJBuitelaar JKVerbaten MNKenemans JL2005Disentangling deficits in adults with attention-deficit/hyperactivity disorderArchives of General Psychiatry621129113610.1001/archpsyc.62.10.112916203958Bell AJSejnowski TJ1995An information-maximization approach to blind separation and blind deconvolutionNeural Computation71129115910.1162/neco.1995.7.6.11297584893Bellumori MJaric SKnight CA2011The rate of force development scaling factor (RFD-SF): protocol, reliability, and muscle comparisonsExperimental Brain Research21235936910.1007/s00221-011-2735-721656219Bissett PPoldrack R2019Severe violations of independence in response inhibition tasks are pervasive and consequentialPsyArXivhttps://psyarxiv.com/kpa65/Boucher LPalmeri TJLogan GDSchall JD2007Inhibitory control in mind and brain: an interactive race model of countermanding saccadesPsychological Review11437639710.1037/0033-295X.114.2.37617500631Brainard DH1997The psychophysics toolboxSpatial Vision1043343610.1163/156856897X003579176952Cai WOldenkamp CLAron AR2012Stopping speech suppresses the task-irrelevant handBrain and Language12041241510.1016/j.bandl.2011.11.00622206872Casey BJCannonier TConley MICohen AOBarch DMHeitzeg MMSoules METeslovich TDellarco DVGaravan HOrr CAWager TDBanich MTSpeer NKSutherland MTRiedel MCDick ASBjork JMThomas KMChaarani BMejia MHHagler DJDaniela Cornejo MSicat CSHarms MPDosenbach NUFRosenberg MEarl EBartsch HWatts RPolimeni JRKuperman JMFair DADale AMABCD Imaging Acquisition Workgroup2018The adolescent brain cognitive development (ABCD) study: imaging acquisition across 21 sitesDevelopmental Cognitive Neuroscience32435410.1016/j.dcn.2018.03.00129567376Castiglione AWagner JAnderson MAron AR2019Preventing a thought from coming to mind elicits increased right frontal beta just as stopping action doesCerebral Cortex292160217210.1093/cercor/bhz01730806454Catani MMesulam MMJakobsen EMalik FMartersteck AWieneke CThompson CKThiebaut de Schotten MDell'Acqua FWeintraub SRogalski E2013A novel frontal pathway underlies verbal fluency in primary progressive aphasiaBrain1362619262810.1093/brain/awt16323820597Chowdhury NSLivesey EJBlaszczynski AHarris JA2017Pathological gambling and motor impulsivity: a systematic review with Meta-AnalysisJournal of Gambling Studies331213123910.1007/s10899-017-9683-528255940Clark LBlackwell ADAron ARTurner DCDowson JRobbins TWSahakian BJ2007Association between response inhibition and working memory in adult ADHD: a link to right frontal cortex pathology?Biological Psychiatry611395140110.1016/j.biopsych.2006.07.02017046725Corneil BDCheng JCGoonetilleke SC2013Dynamic and Opposing Adjustment of Movement Cancellation and Generation in an Oculomotor Countermanding TaskJournal of Neuroscience339975998410.1523/JNEUROSCI.2543-12.2013Coxon JPStinear CMByblow WD2006Intracortical inhibition during volitional inhibition of prepared actionJournal of Neurophysiology953371338310.1152/jn.01334.200516495356Day BLRothwell JCThompson PDMaertens de Noordhout ANakashima KShannon KMarsden CD1989Delay in the execution of voluntary movement by electrical or magnetic brain stimulation in intact man. Evidence for the storage of motor programs in the brainBrain11264966310.1093/brain/112.3.6492731025de Jong RColes MGHLogan GDGratton G1990In search of the point of no return: the control of response processesJournal of Experimental Psychology: Human Perception and Performance1616418210.1037/0096-1523.16.1.164Delorme AMakeig S2004EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysisJournal of Neuroscience Methods13492110.1016/j.jneumeth.2003.10.00915102499Edgley SAEyre JALemon RNMiller S1997Comparison of activation of corticospinal neurons and spinal motor neurons by magnetic and electrical transcranial stimulation in the lumbosacral cord of the anaesthetized monkeyBrain12083985310.1093/brain/120.5.8399183254Enkavi AZEisenberg IWBissett PGMazza GLMacKinnon DPMarsch LAPoldrack RA2019Large-scale analysis of test-retest reliabilities of self-regulation measuresPNAS1165472547710.1073/pnas.181843011630842284Friedman NPMiyake A2004The relations among inhibition and interference control functions: a Latent-Variable analysisJournal of Experimental Psychology: General13310113510.1037/0096-3445.133.1.101Goonetilleke SCDoherty TJCorneil BD2010A within-trial measure of the stop signal reaction time in a head-unrestrained oculomotor countermanding taskJournal of Neurophysiology1043677369010.1152/jn.00495.201020962073Goonetilleke SCWong JPCorneil BD2012Validation of a within-trial measure of the oculomotor stop processJournal of Neurophysiology10876077010.1152/jn.00174.201222592305Gopal AMurthy A2016A common control signal and a ballistic stage can explain the control of coordinated eye-hand movementsJournal of Neurophysiology1152470248410.1152/jn.00910.201526888104Groppa SOliviero AEisen AQuartarone ACohen LGMall VKaelin-Lang AMima TRossi SThickbroom GWRossini PMZiemann UValls-Solé JSiebner HR2012A practical guide to diagnostic transcranial magnetic stimulation: report of an IFCN committeeClinical Neurophysiology12385888210.1016/j.clinph.2012.01.01022349304Hamada MMurase NHasan ABalaratnam MRothwell JC2013The role of interneuron networks in driving human motor cortical plasticityCerebral Cortex231593160510.1093/cercor/bhs147Hanes DPPatterson WFSchall JD1998Role of frontal eye fields in countermanding saccades: visual, movement, and fixation activityJournal of Neurophysiology7981783410.1152/jn.1998.79.2.8179463444Hannah RMuralidharan VSundby KKAron AR2019Temporally-precise disruption of prefrontal cortex informed by the timing of beta bursts impairs human action-stoppingbioRxiv10.1101/843557Hannah RRothwell JC2017Pulse duration as well as current direction determines the specificity of transcranial magnetic stimulation of motor cortex during contractionBrain Stimulation1010611510.1016/j.brs.2016.09.00828029595Huster RJMessel MSThunberg CRaud L2019The P300 as marker of inhibitory control – fact or fiction?bioRxiv10.1101/694216Jana SMurthy A2018Task context determines whether common or separate inhibitory signals underlie the control of eye-hand movementsJournal of Neurophysiology1201695171110.1152/jn.00085.201829924711Kalanthroff ETeichert TWheaton MGKimeldorf MBLinkovski OAhmari SEFyer AJSchneier FRAnholt GESimpson HB2017The Role of Response Inhibition in Medicated and Unmedicated Obsessive-Compulsive Disorder Patients: Evidence from the Stop-Signal TaskDepression and Anxiety3430130610.1002/da.22492Kornylo KDill NSaenz MKrauzlis RJ2003Cancelling of pursuit and saccadic eye movements in humans and monkeysJournal of Neurophysiology892984299910.1152/jn.00859.200212783947Lavagnino LArnone DCao BSoares JCSelvaraj S2016Inhibitory control in obesity and binge eating disorder: a systematic review and meta-analysis of neurocognitive and neuroimaging studiesNeuroscience & Biobehavioral Reviews6871472610.1016/j.neubiorev.2016.06.04127381956Lijffijt MBekker EMQuik EHBakker JKenemans JLVerbaten MN2004Differences between low and high trait impulsivity are not associated with differences in inhibitory motor controlJournal of Attention Disorders8253210.1177/10870547040080010415669600Lijffijt MKenemans JLVerbaten MNvan Engeland H2005A meta-analytic review of stopping performance in attention-deficit/hyperactivity disorder: deficient inhibitory motor control?Journal of Abnormal Psychology11421622210.1037/0021-843X.114.2.21615869352Lipszyc JSchachar R2010Inhibitory control and psychopathology: a meta-analysis of studies using the stop signal taskJournal of the International Neuropsychological Society161064107610.1017/S135561771000089520719043Little SBonaiuto JBarnes GBestmann S2018Motor cortical beta transients delay movement initiation and track errorsbioRxiv10.1101/384370Logan GDYamaguchi MSchall JDPalmeri TJ2015Inhibitory control in mind and brain 2.0: blocked-input models of saccadic countermandingPsychological Review12211514710.1037/a003889325706403Matzke DDolan CVLogan GDBrown SDWagenmakers E-J2013Bayesian parametric estimation of stop-signal reaction time distributionsJournal of Experimental Psychology: General1421047107310.1037/a0030543Matzke DLove JHeathcote A2017A bayesian approach for estimating the probability of trigger failures in the stop-signal paradigmBehavior Research Methods4926728110.3758/s13428-015-0695-826822670McGarry TInglis JTFranks IM2000Against a final ballistic process in the control of voluntary action: evidence using the Hoffmann reflexMotor Control446948510.1123/mcj.4.4.46911020674McGarry TFranks IM1997A horse race between independent processes: evidence for a phantom point of no return in the preparation of a speeded motor responseJournal of Experimental Psychology: Human Perception and Performance231533154210.1037/0096-1523.23.5.1533McLaughlin NCKirschner JFoster HO'Connell CRasmussen SAGreenberg BD2016Stop signal reaction time deficits in a lifetime Obsessive-Compulsive disorder sampleJournal of the International Neuropsychological Society2278578910.1017/S135561771600054027334752Mirabella GPani PParé MFerraina S2006Inhibitory control of reaching movements in humansExperimental Brain Research17424025510.1007/s00221-006-0456-016636792Nguyen ATAlbrecht MALipp O Marinovic W2019Motor output matters: evidence of a continuous relationship between stop/No-go P300 amplitude and response force on failed inhibitions at the Trial-LevelbioRxiv10.1111/psyp.13558Ogasawara TNejime MTakada MMatsumoto M2018Primate Nigrostriatal Dopamine System Regulates Saccadic Response InhibitionNeuron1001513152610.1016/j.neuron.2018.10.025Oostenveld ROostendorp TF2002Validating the boundary element method for forward and inverse EEG computations in the presence of a hole in the skullHuman Brain Mapping1717919210.1002/hbm.1006112391571Osada TOhta SOgawa ATanaka MSuda AKamagata KHori MAoki SShimo YHattori NShimizu TEnomoto HHanajima RUgawa YKonishi S2019An essential role of the intraparietal sulcus in response inhibition predicted by Parcellation-Based networkThe Journal of Neuroscience392509252110.1523/JNEUROSCI.2244-18.201930692225Osman AKornblum SMeyer DE1986The point of no return in choice reaction time: controlled and ballistic stages of response preparationJournal of Experimental Psychology: Human Perception and Performance1224325810.1037/0096-1523.12.3.243Purcell BAHeitz RPCohen JYSchall JDLogan GDPalmeri TJ2010Neurally constrained modeling of perceptual decision makingPsychological Review1171113114310.1037/a002031120822291Ramakrishnan ASureshbabu RMurthy A2012Understanding how the brain changes its mind: microstimulation in the macaque frontal eye field reveals how saccade plans are changedJournal of Neuroscience324457447210.1523/JNEUROSCI.3668-11.201222457494Raud LWesterhausen RDooley NHuster RJ2019Differences in unity: the go/no-go and stop signal tasks rely on different inhibitory mechanismsbioRxiv10.1101/705079Raud LHuster RJ2017The temporal dynamics of response inhibition and their modulation by cognitive controlBrain Topography3048650110.1007/s10548-017-0566-y28456867Rossi SHallett MRossini PMPascual-Leone A2011Screening questionnaire before TMS: an updateClinical Neurophysiology122168610.1016/j.clinph.2010.12.03721227747Rossini PMBurke DChen RCohen LGDaskalakis ZDi Iorio RDi Lazzaro VFerreri FFitzgerald PBGeorge MSHallett MLefaucheur JPLangguth BMatsumoto HMiniussi CNitsche MAPascual-Leone APaulus WRossi SRothwell JCSiebner HRUgawa YWalsh VZiemann U2015Non-invasive electrical and magnetic stimulation of the brain, spinal cord, roots and peripheral nerves: basic principles and procedures for routine clinical and research application. an updated report from an I.F.C.N. committeeClinical Neurophysiology1261071110710.1016/j.clinph.2015.02.00125797650Schall JDBoucher L2007Executive control of gaze by the frontal lobesCognitive, Affective, & Behavioral Neuroscience739641210.3758/CABN.7.4.39618189013Schall JDGodlove DC2012Current advances and pressing problems in studies of stoppingCurrent Opinion in Neurobiology221012102110.1016/j.conb.2012.06.00222749788Schaum MPinzuti ESebastian ALieb KFries PMobascher AJung PWibral MTuescher O2020Cortical network mechanisms of response inhibitionbioRxiv10.1101/2020.02.09.940841Sedgmond JLawrence NSVerbruggen FMorrison SChambers CDAdams RC2019Prefrontal brain stimulation during food-related inhibition training: effects on food craving, food consumption and inhibitory controlRoyal Society Open Science618118610.1098/rsos.18118630800367Shin HLaw RTsutsui SMoore CIJones SR2017The rate of transient beta frequency events predicts behavior across tasks and specieseLife6e2908610.7554/eLife.2908629106374Skippen PFulham WRMichie PTMatzke DHeathcote AKarayanidis FFulham RMichie PTMatzke DHeathcote AKarayanidis F2019aReconsidering electrophysiological markers of response inhibition in light of trigger failures in the stop-signal taskbioRxiv10.1101/658336Skippen PMatzke DHeathcote AFulham WRMichie PKarayanidis F2019bReliability of triggering inhibitory process is a better predictor of impulsivity than SSRTActa Psychologica19210411710.1016/j.actpsy.2018.10.01630469044Smith JLMattick RPJamadar SDIredale JM2014Deficits in behavioural inhibition in substance abuse and addiction: a meta-analysisDrug and Alcohol Dependence14513310.1016/j.drugalcdep.2014.08.00925195081Snyder HRKaiser RHWarren SLHeller W2015Obsessive-compulsive disorder is associated with broad impairments in executive function: a meta-analysisClinical Psychological Science330133010.1177/216770261453421025755918Swann NTandon NCanolty REllmore TMMcEvoy LKDreyer SDiSano MAron AR2009Intracranial EEG reveals a time- and frequency-specific role for the right inferior frontal gyrus and primary motor cortex in stopping initiated responsesJournal of Neuroscience29126751268510.1523/JNEUROSCI.3359-09.200919812342Swann NCCai WConner CRPieters TAClaffey MPGeorge JSAron ARTandon N2012Roles for the pre-supplementary motor area and the right inferior frontal gyrus in stopping action: electrophysiological responses and functional and structural connectivityNeuroImage592860287010.1016/j.neuroimage.2011.09.04921979383Thunberg CNMessel MSRaud LHuster RJ2019Stimulating stopping? Investigating the effects of tDCS over the inferior frontal gyri and visual corticesbioRxiv10.1101/723296Usher MMcClelland JL2001The time course of perceptual choice: the leaky, competing accumulator modelPsychological Review10855059210.1037/0033-295X.108.3.55011488378van den Wildenberg WPBurle BVidal Fvan der Molen MWRidderinkhof KRHasbroucq T2010Mechanisms and dynamics of cortical motor inhibition in the stop-signal paradigm: a TMS studyJournal of Cognitive Neuroscience2222523910.1162/jocn.2009.2124819400674Verbruggen FAron ARBand GPBeste CBissett PGBrockett ATBrown JWChamberlain SRChambers CDColonius HColzato LSCorneil BDCoxon JPDupuis AEagle DMGaravan HGreenhouse IHeathcote AHuster RJJahfari SKenemans JLLeunissen ILi CRLogan GDMatzke DMorein-Zamir SMurthy AParé MPoldrack RARidderinkhof KRRobbins TWRoesch MRubia KSchachar RJSchall JDStock AKSwann NCThakkar KNvan der Molen MWVermeylen LVink MWessel JRWhelan RZandbelt BBBoehler CN2019A consensus guide to capturing the ability to inhibit actions and impulsive behaviors in the stop-signal taskeLife8e4632310.7554/eLife.4632331033438Verbruggen FLogan GD2009Models of response inhibition in the stop-signal and stop-change paradigmsNeuroscience & Biobehavioral Reviews3364766110.1016/j.neubiorev.2008.08.01418822313Wagner JMakeig SGola MNeuper CMüller-Putz G2016Distinct β band oscillatory networks subserving motor and cognitive control during gait adaptationThe Journal of Neuroscience362212222610.1523/JNEUROSCI.3543-15.201626888931Wagner JWessel JRGhahremani AAron AR2018Establishing a right frontal beta signature for stopping action in scalp EEG: implications for testing inhibitory control in other task contextsJournal of Cognitive Neuroscience3010711810.1162/jocn_a_0118328880766Wessel JRConner CRAron ARTandon N2013aChronometric electrical stimulation of right inferior frontal cortex increases motor brakingJournal of Neuroscience33196111961910.1523/JNEUROSCI.3468-13.201324336725Wessel JRReynoso HSAron AR2013bSaccade suppression exerts global effects on the motor systemJournal of Neurophysiology11088389010.1152/jn.00229.201323699058Wessel JRGhahremani AUdupa KSaha UKalia SKHodaie MLozano AMAron ARChen R2016Stop-related subthalamic beta activity indexes global motor suppression in Parkinson's diseaseMovement Disorders311846185310.1002/mds.2673227474845Wessel JR2020β-Bursts reveal the Trial-to-Trial dynamics of movement initiation and cancellationThe Journal of Neuroscience4041142310.1523/JNEUROSCI.1887-19.201931748375Wessel JRAron AR2013Unexpected events induce motor slowing via a brain mechanism for action-stopping with global suppressive effectsJournal of Neuroscience33184811849110.1523/JNEUROSCI.3456-13.201324259571Wessel JRAron AR2015It's not too late: the onset of the frontocentral P3 indexes successful response inhibition in the stop-signal paradigmPsychophysiology5247248010.1111/psyp.12374Wessel JRAron AR2017On the globality of motor suppression: unexpected events and their influence on behavior and cognitionNeuron9325928010.1016/j.neuron.2016.12.01328103476Xue GAron ARPoldrack RA2008Common neural substrates for inhibition of spoken and manual responsesCerebral Cortex181923193210.1093/cercor/bhm22018245044Appendix 1

The difference between SSRTBeh and the time of EMG cancellation (CancelTime) might be attributed to an inherent ‘ballistic stage’ in movements, and once the muscle activity crosses the point-of-no-return they can no longer be stopped, making the movement inevitable (de Jong et al., 1990; Mirabella et al., 2006; Osman et al., 1986; Verbruggen and Logan, 2009). The duration of such ballistic stages has been estimated to be 10–25 ms in saccades in non-human primates (Boucher et al., 2007; Kornylo et al., 2003; Purcell et al., 2010) and 40–50 ms for reaching movements in humans (Gopal and Murthy, 2016; Jana and Murthy, 2018). In other words, the time of EMG cancellation on partial EMG trials reflects a time just before the point-of-no-return, whereby if EMG activity is allowed to develop beyond this point it will exceed a critical threshold such that a button press necessarily ensues (we presume this threshold reflects the point at which the inertia of the finger is overcome). In this respect, what is being tracked by the SSD staircasing procedure is the probability of crossing that EMG threshold, but since SSRT is calculated based on keypress response times, it inevitably incorporates the ballistic stage that follows the crossing of this threshold.

To test the idea that there might be a ballistic stage in responses which inflates SSRTBehwe simulated the independent race model with a Go and Stop accumulator which raced to a threshold, where the activity of each accumulator could be described by the mean drift rate (μ) and the SD of the drift rate (σ) (Boucher et al., 2007; Ramakrishnan et al., 2012; Usher and McClelland, 2001). First, we tested whether the independent race model without a ballistic stage could fit the behavioral results. For each participant, we fitted the RTEMG and RTBeh distributions in the Correct Go trials, to estimate the (μGO-EMG, σGO-EMG) and (μGO-Beh, σGO-Beh). Next, using the estimated Go parameters, we estimated the (μStop,σStop), which would best fit the inhibition function. This estimation of the Stop parameters (μStop,σStop) was performed separately for EMG (μSTOP-EMG,σSTOP-EMG) and keypresses (μSTOP-Beh,σSTOP-Beh). We reasoned that if the only difference between the two inhibition functions is due to the difference in the Go processes (RTEMG vs RTBeh) then the μSTOP-EMG should be similar to μSTOP-Beh. However, this was not the case. First, Stop distributions estimated from the EMG and keypresses were quite distinct, where μSTOP-EMG (188 ± 8 ms) was significantly less than μSTOP-Beh (207 ± 5 ms; t(41) = 2.7, p=0.009, d = 0.4, BF10 = 4.4). Second, the difference between the simulated and experimental inhibition function was much greater when (μSTOP-EMG,σSTOP-EMG) was used to fit the behavioral inhibition function compared to the EMG inhibition function (Figure 3—figure supplement 1a,b). To quantify this, we computed the squared difference between the experimental and simulated P(Respond|Stop) data (Figure 3—figure supplement 1c; EMG inhibition function, squared error between experimental and simulated data = 0.15 ± 0.02; RT inhibition function, squared error = 0.23 ± 0.02, t(41) = 2.7, p=0.011, d = 0.6, BF10 = 3.7). Conversely, the difference between the simulated and experimental inhibition function was much greater when μSTOP-Beh was used to fit the EMG inhibition function compared to the behavioral inhibition function (Figure 3—figure supplement 1d,e,f; behavioral inhibition function, squared error = 0.10 ± 0.01; EMG inhibition function, squared error = 0.22 ± 0.02, t(41) = 4.7, p<0.001, d = 0.7, BF10 >100). This incompatibility suggests that some change needs to be made to the model such that one Stop distribution is able to fit both the EMG and keypress inhibition functions. Hence, we tested whether incorporating a ballistic stage in the delay between RTEMG and RTBeh could rescue the model.

To check this, we used a model previously used to study stopping of reaching movements in the context of coordinated eye-hand movements (Gopal and Murthy, 2016; Jana and Murthy, 2018). Here, the Go process comprises an accumulation phase, and once the accumulator hits the threshold, EMG responses can be observed, and then following a peripheral delay, the EMG builds up enough (i.e. the point-of-no-return) to be able to cross the inertia of the limb and generate a movement (see Figure 3—figure supplement 1g,h,i). If the Stop reaches the threshold before the Go reaches the threshold, then no EMG is elicited (no EMG trial). Further, if the Stop reaches the threshold early during the delay period when the EMG has not built up to a critical level (point-of-no-return) it will be able to inhibit the response resulting in a partial EMG trial. However, if the Stop reaches the threshold after the EMG has reached the point-of-no-return a movement is inevitable, resulting in a Failed Stop trial. We used this model to estimate the duration of the ballistic stage. Across participants, the mean ballistic stage was 34 ± 4 ms. Incorporation of this ballistic stage allowed μSTOP-EMG to fit the behavioral inhibition function much better than a model without a ballistic stage (Figure 3—figure supplement 1j,k; squared error = 0.14 ± 0.02, t(41) = 4.2, p<0.001, d = 0.7, BF10 > 100). Thus, based on our model, there exists a ballistic stage in keypress responses, which might be responsible for the difference between CancelTime and SSRTBeh. While this measure was less than our estimate of ~60 ms, we note that some participants did not have a sigmoidal inhibition function (as the task was designed to have a P(Stop)=0.5 such that SSRTBeh could be well estimated) leading to suboptimal estimation of the Stop parameters. Indeed, when we considered only those participants who had lower than the population median error, the duration of the ballistic stage was 47 ± 3 ms which is closer to our estimate of ~60 ms.

Methods

The rate of accumulation is governed by the differential equations (Boucher et al., 2007; Ramakrishnan et al., 2012; Usher and McClelland, 2001):daGO= dtτ μGO-k.aGOt+ dtτξGOdaSTOP= dtτ μSTOP-k.aSTOPt+ dtτξSTOPwhere daGO and, daSTOP represents the change in accumulation within a time-step dt and a time constant τ; μGO and μSTOP is the mean drift rate; ξGO and ξSTOP is a Gaussian noise term with mean 0 and SD equal to the σ of the associated accumulator, which represents the noise in the input signal; k is the leakage parameter. k was set to 0, dtτ was set to 1.

Parameter estimation of the independent race model with a ballistic stage

Step 1 was to estimate the (μGO-EMG, σGO-EMG), that is the mean and SD that would generate RTEMG distribution (Figure 3c inset green beeswarm plot) for each participant. A range of values, representing the parameter space for (μGO-EMG, σGO-EMG), which could generate behaviorally relevant distributions were uniformly and ‘coarsely’ sampled, to simulate distributions for 2000 trials. The top 20 parameters which generated a distribution with a mean and SD within 30 ms of the mean and SD of the empirical RTEMG distribution and had the minimum least-squared error between the empirical and simulated cumulative distribution function, were fed into MATLAB’s fmincon function for optimization. The MATLAB function tried to minimize the least-squared difference between the empirical and simulated cumulative distribution functions (this method of coarse sampling followed by fmincon minimization of the top 20 parameters was used for all the subsequent steps). Additionally, for the optimization, a nonlinear constraint was imposed such that the absolute difference between the mean of the empirical and simulated RT distribution was < 10 ms.

For each participant we were able to estimate the (μGO-EMG, σGO-EMG) well, such that the simulated distribution had a mean similar to the empirical one. Within each participant, the simulated RTEMG closely matched the mean of the simulated RTEMG (2-tailed unpaired t-test: all p>0.05; BF10: min = 0.06, max = 0.85, mean = 0.08 ± 0.01). Across all participants, the estimated EMG onset distribution closely matched the empirical mean (Empirical: 343 ± 12 ms, Simulated: 343 ± 13 ms, t(41) = 0.6, p=0.532, d = 0.1, BF10 = 0.2).

Step 2 was to estimate a delay which could be added to the RTEMG which would result in the RTBeh distribution. In other words, the sum of the Go-EMG accumulation process described by (μGO-EMG, σGO-EMG) and the delay would yield the RTBeh distribution. A range between 10–300 ms was coarsely sampled, and then the top 20 parameters were fed into fmincon for optimization. Additionally, a nonlinear constraint was imposed such that the absolute difference between the mean of the empirical and simulated data was < 10 ms.

At single participant level, the estimated (μDelay, σDelay) yielded distributions that closely matched the mean (of the empirical RTBeh distribution (2-tailed unpaired t-test: all p>0.05; BF10: min = 0.06, max = 0.13, mean = 0.074 ± 0.003). Thus, we were able to estimate all the parameters (μGO, σGO, and μDelay, σDelay) describing the putative Go process. Across the population, the simulated RT distributions closely matched the empirical mean (Empirical: 478 ± 12 ms, Simulated: 478 ± 13 ms, t(41) = 0.04, p=0.967, d = 0.01, BF10 = 0.2). Further, across the population, the simulated delay period (133 ± 3 ms) was not significantly different than the empirical delay between the RTEMG and RTBeh (135 ± 3 ms; t(41) = 1.9, p=0.068, d = 0.3, BF10 = 0.8).

Step 3 was to estimate the (μStop,σStop) from the EMG responses using the independent race model (we assumed that the true Stop distribution could be estimated from the EMG inhibition function). Thus, the end of the Go-EMG process marked the onset of the EMG response (described by the estimated (μGO-EMG,σGO-EMG)). The EMG inhibition function was calculated based on whether EMG was detected (thus partial EMG responses were considered as error responses), and was fitted with a cumulative Weibull function (Hanes et al., 1998; Ramakrishnan et al., 2012):w(t)= γ−(γ−δ)e[−(t/α)β]

(where t is the SSD, α is the time at which the function reaches 64% of its full growth, β is the slope, δ is the minimum value of the function, and γ is maximum value of the function. The difference between δ and γ marks the range of the inhibition function). The optimization process tried to minimize the least-squared error between the fits of the empirical and simulated inhibition functions. Additionally, a nonlinear constraint was imposed that the least-squared error between the empirical and simulated data was < 0.2.

Step 4 was to estimate the duration of the ballistic stage. Here the duration of the Go process (keypress response time) would be the sum of the (μGO-EMG,σGO-EMG) accumulation and the delay (μDelay,σDelay). The Stop process was the same as that estimated from EMG, and we used these parameters to simulate a race model that would best fit the keypress inhibition function. The ballistic stage was assumed to have a normal distribution and again the least-squared error between the fits of the empirical and simulated inhibition functions was minimized. A range between 5–200 ms was coarsely sampled, and then the top 20 parameters were fed into fmincon for optimization. Additionally, a nonlinear constraint was imposed that the least-squared error between the empirical and simulated data was < 0.2.

To simulate the independent race model without a ballistic stage (i.e. when considering RTBeh as the Go process, and directly fitting the RT inhibition function to estimate the underlying Stop distribution), we followed Step 1 to estimate the Go parameters, and Step 3 to estimate the Stop parameters.

10.7554/eLife.50371.sa1Decision lettervan den WildenbergWeryReviewing EditorUniversiteit van AmsterdamNetherlandsvan den WildenbergWery ReviewerUniversiteit van AmsterdamNetherlandsHusterRené ReviewerUniversity of OsloNorwayBissettPatrick GReviewerStanford UniversityUnited States

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Thank you for submitting your article "Temporal cascade of frontal, motor and muscle processes underlying human action-stopping" for consideration by eLife. Your article has been reviewed by three peer reviewers, including Wery van den Wildenbert as the Reviewing Editor and the evaluation has been overseen by Richard Ivry (Senior Editor).

The Reviewing Editor, Wery van den Wildenberg, drafted this letter based on the detailed evaluation reports. As you will see, the reviewers are generally positive about the broad scope and they commend the use of different methodological approaches.

Several issues, detailed below as major points, deserve attention when preparing a revision of your manuscript. Of these, we would like to highlight the tendency to not give sufficient credit to prior relevant publications of others (some of which are listed under major point 1). The inclusion of relevant previous work on partial EMG and beta-burst analyses (major point 10) might lead to a more balanced rating of the acclaimed novelty of the methods and conclusions.

Given that this paper addresses questions about when and where stopping occurs, major points 6 and 11 seem to be particularly fundamental. Major point 6 might be viewed as a fundamental challenge to the temporal cascade as proposed by the authors (i.e., about when stopping occurs). Major point 11 seems to fundamentally challenge the attempt to spatially localize a stop command that is necessary and sufficient for stopping (i.e., about where stopping occurs).

The work is presented as if it "confirms a detailed model of action-stopping" [Abstract]. In general, the reviewers seem to be in agreement in their impression that this should better be toned down (see also major point 4). In its current form, which in and of itself represents elaborate work, such claims might better be framed in terms of tentative evidence for a neural model for stopping.

Summary:

The in-depth content and broad scope of the manuscript are impressive. The five empirical studies cover different neurocognitive levels of the information processing chain when healthy participants are cued to stop a motor action. Not only is stopping investigated at different stages during processing (from the brain to muscles, and behavior), the lineup of the methods, including EEG, single-pulse TMS, EMG, and modeling techniques, provide a full account of the temporal dynamics and the neural mechanisms that are at play during action stopping. The fact that the extent of these comments go far beyond the recommendation of 500 words reflects the width of methods and topics touched by this manuscript. Whereas some interpretations and claims should be toned down a bit, and the bulk of the comments refer to these rather conceptual issues, the work is considered very important and an innovative contribution to the study of action cancellation.

Essential revisions:

Relevant Background Literature:

1) The authors are kind to mention work by Huster et al. on residual or partial EMG in successful stop trials. It should be noted though that earlier work already went into a similar direction yet does not seem to receive enough credit (in general, and not specifically with respect to this manuscript). The authors may thus consider including references to this earlier work. Some examples:

- de Jong et al., 1990.

- McGarry (1999). On the nature of stopping a voluntary action. Dissertation, University of British Columbia, Canada. (see also McGarry's articles from 2003 in Motor Control and Q J Exp Psychol).

- Goonetilleke et al. (2010). A within-trial measure of the stop signal reaction time in a head-unrestrained oculomotor countermanding task. J Neurophysiol.

- And last but not least, some more recent articles/manuscripts:

- Atsma et al. (2018). Active Braking of Whole-Arm Reaching Movements Provides Single-Trial Neuromuscular Measures of Movement Cancellation. J Neurosci.

- Raud et al. (submitted). Differences in unity: the go/no-go and stop signal tasks rely on different inhibitory mechanisms. bioRxiv 705079; doi: https://doi.org/10.1101/705079

- Huster et al. (submitted). The P300 as marker of inhibitory control – fact or fiction? bioRxiv 694216; doi: https://doi.org/10.1101/694216

- Thunberg et al. (submitted). Stimulating stopping? Investigating the effects of tDCS over the inferior frontal gyri and visual cortices. bioRxiv 723296; doi: https://doi.org/10.1101/723296

- In light of this relatively rich prior history, the authors may want to consider to tone down their claim on this approach (E.g., "We predict that our new single-trial method of CancelTime will be more sensitive than SSRTBeh.").

SSRTEMG measure of Stopping:

2) I am admittedly torn when it comes to the SSRTEMG. On the one hand, one may argue that it could avoid rather unspecific biases associated with the use of different response systems for the estimation of the SSRT. Then again, whereas plausible, it is not really clear that this is the case as little research systematically assessed the influence of response devices on the shape and timing of the EMG. Also, I see no good justification for classifying partial response EMG trials as failed stop trials; no overt response was produced, which is the instruction given to the participants, and I think there is no good justification to only classify trials without any EMG response as successful stop trials. In the end, I am unsure about how to interpret this measure meaningfully, and whether it can be used to "validate" the CancelTime (as is implied here). Not least, the calculation of the SSRTEMG relies on a rather small subset of SSDs (three per subject), as described in the subsection “Data analysis”, whereas usually a wide sampling of SSDs is recommended.

3) When testing the partial response EMG against different SSDs, the H0 of no difference is justified by means of "weak go processes". I am wondering though what that implies: a very slow response (i.e., shallow slope), or one with a high threshold (thus unlikely to cause a button press), or a relatively delayed onset?

Functional interpretation of CancelTime:

4) The authors stress repeatedly that the CancelTime can be considered or is used as single-trial measure of the stop process. I suggest to tone this claim down, because:

- it is not really used as a single-trial measure in the vast majority of analyses (with exceptions being the SD-based correlations of CancelTime and SSRTBEESTS, or the CancelTime-MEP alignment).

- a proper metric should undergo testing in terms of its psychometric properties (reliability, validity, objectivity etc.). This is too often overlooked, not only but especially with psychophysiological measures.

Thus, whereas I am also hopeful that the CancelTime may serve us as such a measure one day, I think we should not make this claim yet.

5) In order to validate CancelTime, the authors show high correlations with other stop task measures including SSRTbeh and BEESTs model estimates. Along with other traditional measures, CancelTime was positively correlated with trigger failure rate. This seems to challenge the discriminant validity of CancelTime (and/or trigger failure rate). CancelTime was calculated on trials in which a stop signal has been triggered, reaches the muscle of the hand, but a behavioral response is not emitted. It is also intended to be a purer measure of response inhibition. Trigger failures are putative failures of attention and should only occur on failed stop trials. I suggest that the authors discuss this relationship between CancelTime and trigger failure rate.

Concerning Temporal Dynamics:

6) If I am understanding correctly, CancelTime is computed exclusively from partial EMG trials. Additionally, it is intended to be an alternative to SSRTbeh, which is a measure of the central tendency of SSRT across all trials. When CancelTime is compared to SSRTbeh, CancelTime is ~60ms shorter. The authors argue that CancelTime is shorter than SSRTbeh because CancelTime does not include the (~60ms) electromechanical delay and therefore is a purer measure of stopping. However, I would like to suggest another explanation for why CancelTime is shorter than SSRTbeh.

Assuming (1) a race model architecture, (2) variability in the go RT and (3) variability in SSRT, then failed stops will tend to occur when SSD is long, go RT is fast, and SSRT is slow. Successful stops will tend to occur when SSD is short, go RT is slow, and SSRT is fast. Partial EMG trials, which I understand to be trials in which the go process doesn't win as decisively as a successful stop trial or fail as decisively as a failed stop trial, should have SSD, go RT, and SSRT values between these two extremes. However, ~1/2 of trials are failed stop, ~1/4 of trials as partialEMG, and ~1/4 of trials are successful stops. Therefore, partialEMG trials should be preferentially sampled from the half of trials with shorter SSD, slower go RT, and faster SSRT. If this is the case, then CancelTime being faster than SSRTbeh may be partially or completely explained by CancelTime being selectively sampled from faster SSRT trials whereas SSRTbeh is computed across all stop trials.

To concretize my suggestion in an example, if we assume an SSRT distribution with variability such that the first quantile has a mean of 120 ms, the second 160 ms, the third 250, and the fourth 350 ms. When the first quantile is sampled, these should preferentially result in successful stops, when the second is sampled these should preferentially result in partialEMG trials, and when either of the latter two are sampled these should preferentially result in failed stop. However, if you computed CancelTime on these data it should be closer to 160ms (as a result of preferentially sampling the 2nd quantile) but the overall central tendency of the SSRT distribution would be ~220ms.

This alternative implies that the average neural latency for stopping may not differ from SSRTbeh, or may differ less than the ~60 ms suggested here. One tool for evaluating this alternative explanation may be to simulate stop trials with variability in go, stop and SSD and evaluate whether computing SSRT only (or preferentially) on trials sampled from the 2nd quartile of SSRT can produce significant differences from the traditional method of computing SSRTbehav. If it may be useful, here is some openly available code that instantiates the interactive race framework and would allow varying go, stop, and SSD: https://github.com/bissettp/SharingContextDependence/blob/master/interactive_race.ipynb).

7) The authors stress that parts of their model of the processing sequence is supported by the fact that the temporal distance between cortical reduction in excitability (TMS) and the CancelTime corresponds to the corticospinal conduction time (here about 23 ms). The difference between the CancelTime and the reduced motorcortical excitability is about 15 ms (155 – 140). However, the onset of decreased motorcortical excitability, which would best correspond to the onset of the decline in MEP amplitude, does start before that, as can be seen in Figure 4A. An only somewhat smaller effect is apparent already at 120ms, with an onset probably even before that. This would add another 20+ ms to the equation, thus contrasting 23ms vs. 35+ms. The point I want to make is that, even though I find the interpretation of the findings interesting and plausible, care has to be taken not to over-interpret these measures since they are heavily dependent on our statistical procedures (sample size, size of presumably relevant effect, parameterization of onset times etc.).

8) The validity of the reduced TMS-MEPs as indicators of the stopping process is derived from the strong reduction in successful stop relative to go trials around 140 ms, a notion further supported by Figure 4D. It is not discussed, however, that MEPs also are reduced for unsuccessful stop trials around 140 ms locked to the stop signal (a reduction similar to that of successful stop trials; Figure 4B; the effect does not seem to be that much smaller). How to reconcile these findings?

9) In the fourth paragraph of the Discussion, the authors cite papers showing that in monkey, rats, and humans that neurons that are putatively related to stopping change close to SSRT. This seems like considerable evidence against the chronometric framework presented here that assumes that the stop command is sent from brain to muscle well before SSRT (~60 ms + conduction time). I think it would be helpful to understand the authors' position on how these seemingly contradictory findings relate to this current framework.

Functional Significance of Beta Burst Activity:

10) How does the work presented in Study 4 relate to the recent preprint of a paper by Wessel on the role of beta bursts in stopping? [Wessel, J.R., "β-bursts reveal the trial-to-trial dynamics of movement initiation and cancellation", https://www.biorxiv.org/content/10.1101/644682v1].

11) Study 4 finds an increase in beta bursts for successful stops relative to baseline and go trials, an effect interpreted as indicator of the engagement of the right inferior frontal stopping processes. This is a very interesting finding, but its interpretation is not without some conceptual problems.

- Given that EEG is plagued with the inverse problem, it seems somewhat unjustified to claim that this signature originates in the right frontal cortex. But even if one would agree that a rough deduction of the source from its topography is possible, I would have a hard time to associate the rather midfrontal topography with a right frontal source close to the sylvian fissure. Beyond, the authors performed dipole fitting on the independent component topographies, and thus could easily check if the individual dipoles of these components at least roughly are fitted to such a position.

- Βeta burst activity is depicted and analyzed relative to the pre-stop period. If we leave the IC-selection aside for a moment, the resulting time courses may still be in accordance with an effect akin to motor beta: around the time of the stop signal, beta activity would be similarly low for all three categories due to motor preparation, followed by rebound-effects that might be earlier in case of successful stops (cancelled), succeeded by unsuccessful stops and go trials (rebound after execution).

The IC selection states, however, that a component needed to show a beta power increase between the stop signal and the SSRT compared to a time window prior to the go cue. This should exclude potential motor beta components with typical time courses delineated above. The time course for the go activity supports this assumption. Nevertheless, given the conceptual importance of this beta component in this context, it would be nice to also see the go-locked time courses for the stop-related conditions.

12) I understand the presented beta burst data to be the probability that a beta burst occurred on any given trial. Assuming this, beta bursts, which are taken as evidence of the frontal (perhaps rIFG) signal to stop, only occur on ~15% of stop trials (14.6% in Experiment 4 and 16.2% in Experiment 5). Additionally, beta bursts often occur on go and stop-failure trials, sometimes at similar rates to successful stop trials (e.g., 15.4% in Experiment 5 for stop-failure rates). Therefore, beta bursts happen on few stop trials and almost as many go trials as stop trials. How does this signal that is neither necessary or sufficient for stopping explain stop success generally? Might there be differences between stop success trials with and without beta bursts? Could trials with beta bursts be edge cases of some sort (e.g., when proactive control is low and reactive stopping is therefore particularly essential) that are not indicative of the general mechanism for stopping on the other 85% of stop success trials?

Theoretical Implications:

13) I agree with the authors that these results have potentially striking implications for existing models of stopping. However, I think the paper could be improved by laying out these implications more explicitly. For instance, how does this framework relate to existing models including the original Independent Race Model (Logan and Cowan, 1984 / Psych Review), updated Independent Race Models including blocked input models (Logan et al., 2014; Logan et al., 2015), the Interactive Race Model (Boucher et al., 2007), the BEESTs model and trigger failures (Matzke et al., this relates to comment 5), and perhaps recent work suggesting violations of independence that can be accounted for by variable, sometimes weak inhibition (Bissett, Poldrack and Logan, in revision https://psyarxiv.com/kpa65).

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Thank you for submitting the revised version of your article "Temporal cascade of frontal, motor and muscle processes underlying human action-stopping" for consideration by eLife. Your revised article has been reviewed by two peer reviewers. The reviewers have discussed the reviews. The evaluation has been overseen by a Reviewing Editor (Wery van den Wildenberg) and Richard Ivry as the Senior Editor. The Reviewing Editor has drafted this decision to help you prepare a revised submission.

The thorough review reports of the previous review round match the vast nature and the wide scope of the original manuscript. The resulting rebuttal letter that accompanied the revision also reflects a broad discussion, which is commendable. Concerning the revised manuscript, there are a few issues left to be discussed.

These issues are addressed in detail at the end of this letter. Here I provide a brief summary:

The first remaining issue concerns the request to not merely acknowledge connecting studies by citing them, but to also address and integrate the findings of these relevant studies vis-a-vis the current work. In this respect, the rebuttal letter provides a more balanced account, and that tone might be extended to the manuscript.

The second issue concerns the timing when stopping reaches the muscle in relation to the model. This point has been brought to your attention by the Senior Editor, a few days before this decision letter, to facilitate the exchange process. Below you can find the whole line of reasoning (main point 2). More data, additional analyses or simulation studies are not required (or even asked) at this point. A discussion of the seemingly controversial time-courses would be sufficient.

Elaboration on these issues:

1) The authors wrote a detailed and insightful response, which essentially clarified my methodological questions. Some of the more conceptual issues were answered well in the response letter, yet the changes in the manuscript were less substantial than what one might have expected.

a) E.g., regarding Wessel's beta-burst analysis: the authors now cite this work (Results), but rather casually so. The manuscript does not try to compare or integrate the presented findings with Wessel's.

b) The same goes for the partial EMG work. Most of the studies we provided in the first round of the review are cited, but again rather offhand. The manuscript does not really integrate the different studies. Several studies already used an estimate essentially the same to what the authors still refer to as "our idea of CancelTime" (although admittedly these claims have been toned down), yet no attempt is made to compare these estimates, their correlations with SSRTs etc.

c) In some ways, I find that some of the claims made are not founded well enough in data, and the authors seem to be aware of it: "we agree that the temporal cascade model that we have constructed is only approximate as it is averaged across participants who had different stopping latencies, and is also contingent on, as the reviewers' rightly point out, on statistical procedures."

Yet again, the manuscript has not really been changed in accordance with this. Still, it is not properly discussed, for example, that the exact timing estimates heavily rely on the choice of latency estimates (EMG/MEP onsets or peak, of which each again can be calculated in many different ways.

2) I reviewed the initial submission of this manuscript. The manuscript is significantly improved in many ways. The editor requested that we evaluate whether claims have been toned down, previous work on EMG and beta-bursts have been acknowledged, and main point 6 regarding the timing estimate of CancelTime and a ballistic phase have been addressed. I think the first two points have been sufficiently addressed. However, the authors response to Main Point 6, especially their point 3, has raised new concerns about their claims about timing of stopping.

The authors present a 3-part response to main point 6. Part 1 points out that SSRTemg is similar to CancelTime and argues that this is consistent with the remaining ~60ms difference between CancelTime and SSRTbeh being a ballistic stage. Part 2 presents simulations consistent with a ballistic stage that is 34-47ms long (which is perhaps less than the ~60ms difference between canceltime and SSRTbeh). Point 3 argues that the real end of the race (at least as a criterion for evaluating CancelTime) is when EMG amplitude exceeds the threshold set on PartialEMG trials. They show that on correct go trials this threshold is exceeded ~100ms after the average stop signal would occur. Given the SSD tracking algorithm that ensured that the race between going and stopping is roughly tied, then the real latency of the stop process (as measured by EMG) may be ~100ms, so CancelTime may actually be an overestimate of the average stop latency.

The part 3 simulation results seem to conflict with multiple pieces of evidence in the manuscript and the literature. It appears that the authors are suggesting that the ballistic stage may be ~120ms (~220ms SSRTbeh minus the ~100ms stop process), which is both inconsistent with the simulation results in part 2 and inconsistent with the previous literature presented in the manuscript (e.g., Gopal and Muphy, 2016; Jana and Murthy, 2018 suggested 50ms for reaching movements). It also seems to bring into question the entire temporal sequence presented in the manuscript. Why would the end of the race be observable in muscles at 100ms if the signal to stop from cortex (perhaps rIFG) occurs 20ms later at 120ms?

Additionally, none of the 3 parts of the response have directly addressed the reviewers' main point 6. To briefly reiterate, assuming a race model, the ~50% of trials that are true failed stops (an overt response occurs) should tend to have the longest SSDs, fastest go RTs, and slowest SSRTs. The ~25% of trials that are successful stops with no EMG should be the opposite: shortest SSDs, slowest go RTs, and fastest SSRTs. This leaves the ~25% of trials that are successful stops with EMG, which should be in between these extremes. However, because there are ~twice as many stop failures as stop successes, the partial EMG trials will tend have shorter SSDs, slower go RT, and faster SSRTs than each measure's overall average. Therefore, CancelTime may be an underestimate of the true central tendency of SSRT across all stop trials.

In the text, the authors seem to agree with parts of this point, at least in part. They say "CancelTime… does not include the stopping latencies of the No EMG trials, which presumably reflect the fastest stopping latencies where the Stop process was fast enough to cancel the impending response before it reaches the muscle". However, they do not point out that CancelTime also does not include stop-failure trials, which presumably reflect the slowest stopping latencies, leaving CancelTime to reflect stopping latencies that are faster than the slowest half of stop trials but slower than the fastest quarter of stop trials. Also, in Figures 1G-I in their response, they illustrate how they believe correct stops with No EMG, correct stops with partial EMG, and failed stops arise from an accumulator model framework. No EMG has the fastest stop process, failed stop has the slowest stop process, and partial EMG is in between.

To conclude, I do not think that the response to main point 6 addressed the original concern, and I believe that the new simulations bring up new questions about the temporal cascade of processes in stopping. Does the stop process reach the muscle ~150-160ms after the stop signal, as suggested by CancelTime and SSRTemg, or is it ~100ms after the stop signal, as seemingly suggested by their part 3 in response to Main Point 6? If the latter, then how does this fit in with TMS evidence of motor suppression at ~140ms or beta-burst in cortex (perhaps rIFG) at 120ms? Also, if the argument from Main Point 6 is valid (and the authors do not address its validity directly), how can this be synthesized with the Part 3 response suggesting that CancelTime is an overestimate of the latency of the stop process?

10.7554/eLife.50371.sa2Author response

Essential revisions:

Relevant Background Literature:

1) The authors are kind to mention work by Huster et al. on residual or partial EMG in successful stop trials. It should be noted though that earlier work already went into a similar direction yet does not seem to receive enough credit (in general, and not specifically with respect to this manuscript). The authors may thus consider including references to this earlier work. Some examples:

- de Jong et al., 1990.

- McGarry (1999). On the nature of stopping a voluntary action. Dissertation, University of British Columbia, Canada. (see also McGarry's articles from 2003 in Motor Control and Q J Exp Psychol).

- Goonetilleke et al. (2010). A within-trial measure of the stop signal reaction time in a head-unrestrained oculomotor countermanding task. J Neurophysiol.

- And last but not least, some more recent articles/manuscripts:

- Atsma et al. (2018). Active Braking of Whole-Arm Reaching Movements Provides Single-Trial Neuromuscular Measures of Movement Cancellation. J Neurosci.

- Raud et al. (submitted). Differences in unity: the go/no-go and stop signal tasks rely on different inhibitory mechanisms. bioRxiv 705079; doi: https://doi.org/10.1101/705079

- Huster et al. (submitted). The P300 as marker of inhibitory control – fact or fiction? bioRxiv 694216; doi: https://doi.org/10.1101/694216

- Thunberg et al. (submitted). Stimulating stopping? Investigating the effects of tDCS over the inferior frontal gyri and visual cortices. bioRxiv 723296; doi: https://doi.org/10.1101/723296

- In light of this relatively rich prior history, the authors may want to consider to tone down their claim on this approach (E.g., "We predict that our new single-trial method of CancelTime will be more sensitive than SSRTBeh.").

The reviewers are correct to point out that there is a long history of studies evaluating EMG in the context of stopping. We now better acknowledge all of the above-mentioned papers in the revised manuscript and we have toned down our claims over ownership of the approach (Introduction, and Discussion).

SSRTEMG measure of Stopping:

2) I am admittedly torn when it comes to the SSRTEMG. On the one hand, one may argue that it could avoid rather unspecific biases associated with the use of different response systems for the estimation of the SSRT. Then again, whereas plausible, it is not really clear that this is the case as little research systematically assessed the influence of response devices on the shape and timing of the EMG. Also, I see no good justification for classifying partial response EMG trials as failed stop trials; no overt response was produced, which is the instruction given to the participants, and I think there is no good justification to only classify trials without any EMG response as successful stop trials. In the end, I am unsure about how to interpret this measure meaningfully, and whether it can be used to "validate" the CancelTime (as is implied here). Not least, the calculation of the SSRTEMG relies on a rather small subset of SSDs (three per subject), as described in the subsection “Data analysis”, whereas usually a wide sampling of SSDs is recommended.

First, we would like to sincerely apologize for an erroneous reporting in the Materials and methods section of the manuscript, all SSDs were considered for calculation of SSRTEMG, and not 3 SSDs per subject. The results mentioned for SSRTEMG thus considered the whole range of SSDs per subject. In fact, when the 3 most frequent SSDs are selected, mean SSRTEMG = 163 ± 6 ms, as opposed to 157 ± 7 ms in the manuscript. We have accordingly changed this in the revised manuscript (subsection “Data analysis”).

The reviewers point out that the use of SSRTEMG could potentially avoid biases in the determination of stopping latency associated with different response devices, but question whether this is likely to be the case because we don’t know how EMG profiles and onsets differ across devices. However, SSRTEMG relies mainly on being able to detect an increase in EMG above baseline, and not really on the shape of the EMG after onset. EMG onsets can be reliably detected (Gopal et al., 2015; Jana et al., 2016) and correlate well with response times across a range of response devices (Botwinick and Thompson, 1966) (Figure 1—figure supplement 1), despite differences mechanical responses and thus electromechanical delays, supporting their use as a criterion measure. Thus, for simple movements (e.g. single joint) one might expect EMG onsets, but not electromechanical delays, to remain relatively consistent across devices, and consequently that SSRTEMG might be less susceptible to device-related differences in estimations of stopping latency.

Moreover, our contention is that a large part of the difference between SSRTBeh and the time of EMG cancellation (CancelTime) is due to an inherent “ballistic stage” in movements, and once the muscle activity crosses the point-of-no-return they can no longer be stopped, and a movement is inevitable (De Jong et al., 1990; Mirabella et al., 2006; Osman et al., 1986; Verbruggen and Logan, 2009). The duration of such ballistic stages has been estimated to be 10-25 ms in saccades in non-human primates (Boucher et al., 2007; Kornylo et al., 2003; Purcell et al., 2010) and 40-50 ms for reaching movements in humans (Gopal and Murthy, 2016; Jana and Murthy, 2018). In other words, the time of EMG cancellation on partial trials reflects a time just before the point-of-no-return, whereby if EMG activity is allowed to continue beyond this point it will exceed a critical threshold such that a button press necessarily ensues (we presume this threshold reflects the point at which the inertia of the finger is overcome). In this respect, what is being tracked by the SSD staircasing procedure is the probability of crossing that EMG threshold, but since SSRT is calculated based on keypress response times, it inevitably incorporates the ballistic stage that follows the crossing of this threshold. The purpose of the SSRTEMG estimation was to test the idea by essentially removing the influence of any potentially ballistic phase (incorporating any electromechanical delays and inertia in the neuromuscular system and response device), on the estimated stopping latency. In order to do this, we re-classified successful and failed stops on the basis of the absence or presence of an EMG activation. The results of this analysis produce an estimate of stopping latency that very closely approximates our estimate based on CancelTime, and that are considerably shorter than the button-based estimate of SSRT. We have now added a few lines explaining the rationale in the revised manuscript (Results).

We admit that this was a post hoc analysis of data and that the task was designed to titrate SSD based on button presses, and not on the basis of whether EMG was detected. However, we believe it is reasonable to classify a response as the presence or not of EMG. Although participants were not explicitly trying to prevent EMG from being emitted, ~50% of successful stop trials contained no EMG, and so it seems reasonable to ask how quick the stopping latency has to be to prevent any EMG from being emitted. Also, in the wider context of action stopping, the choice of what is considered a response is rather arbitrary and depends on the question at hand. For example, whilst most studies, including ours, tend to use button presses, others have used continuous force or displacement measures and defined a response as anything exceeding a fixed force (25% maximum, (De Jong et al., 1990)), displacement threshold (0.01 m radius, (Atsma et al., 2018)) or velocity threshold (10% of peak velocity, (Jana and Murthy, 2018)). Therefore, we feel that this analysis is still informative, though we now acknowledge in the manuscript that our analysis of SSRTEMG would potentially benefit from further validation in future, basing the SSD staircasing on whether EMG was present or not (Results).

In effect, the SSRTEMG measure also might provide a solution to a long-standing puzzle in the literature where global motor suppression, i.e. the time when the Stop is implemented in the brain, is seen at ~150 ms of the Stop signal (Cai et al., 2012; Wessel et al., 2013) while SSRTBeh, i.e. the actual stopping of the response,is ~ 60 ms greater. The difference between SSRTEMG and SSRTBeh suggests that this discrepancy might be due to a ballistic stage.

3) When testing the partial response EMG against different SSDs, the H0 of no difference is justified by means of "weak go processes". I am wondering though what that implies: a very slow response (i.e., shallow slope), or one with a high threshold (thus unlikely to cause a button press), or a relatively delayed onset?

By “weak Go process” we mean one in which the individual intended to execute a response but failed to reach the threshold level of muscle activity required to fully depress the button. We have clarified this in the manuscript (Results).

Functional interpretation of CancelTime:

4) The authors stress repeatedly that the CancelTime can be considered or is used as single-trial measure of the stop process. I suggest to tone this claim down, because:

- it is not really used as a single-trial measure in the vast majority of analyses (with exceptions being the SD-based correlations of CancelTime and SSRTBEESTS, or the CancelTime-MEP alignment).

- a proper metric should undergo testing in terms of its psychometric properties (reliability, validity, objectivity etc.). This is too often overlooked, not only but especially with psychophysiological measures.

Thus, whereas I am also hopeful that the CancelTime may serve us as such a measure one day, I think we should not make this claim yet.

We agree with the reviewers’ assessment that in the majority of the analyses in the manuscript the single-trial capability of CancelTime has not been utilized. We chose to mention this to highlight the possibility of using CancelTime as a single-trial measure in future experiments. Indeed, we are currently exploring the possibility of using CancelTime as a single-trial measure (see Hannah et al., 2019 for single-trial correlations with right frontal beta bursts), and using the shape of the CancelTime distribution to better understand the network underlying human action-stopping. Likewise, we admit that the measure has not undergone thorough evaluation of its psychometric properties. Therefore, in line with the reviewers’ suggestion, we have toned down such statements (Abstract and Discussion). However, as alluded to above we have recently submitted a new manuscript (Hannah et al., 2019), in which we use single pulse TMS over the right inferior frontal cortex while concurrently measuring CancelTime from the hand. We show that real vs. sham TMS elongates CancelTime, and especially in those participants for whom the time of the pulse came closer to Cancel Time. This was a double-blind study, and the Sham coil was roughly equally as uncomfortable. The fact that real TMS elongated CancelTime reaffirms that it is a metric of stopping, and the single-trial correlations with frontal beta bursts supports its use on a single-trial basis.

5) In order to validate CancelTime, the authors show high correlations with other stop task measures including SSRTbeh and BEESTs model estimates. Along with other traditional measures, CancelTime was positively correlated with trigger failure rate. This seems to challenge the discriminant validity of CancelTime (and/or trigger failure rate). CancelTime was calculated on trials in which a stop signal has been triggered, reaches the muscle of the hand, but a behavioral response is not emitted. It is also intended to be a purer measure of response inhibition. Trigger failures are putative failures of attention and should only occur on failed stop trials. I suggest that the authors discuss this relationship between CancelTime and trigger failure rate.

Trigger failure trials ostensibly reflect those trials where the participant failed to detect the Stop signal or initiate the Stop process (Band et al., 2003). Unfortunately, there is no established physiological metric of this detection (although the N1 ERP during auditory SST might hold some promise), hence we relied on the BEESTS output which provides a single estimate of the probability of observing trigger failures (p(TF)) in a participant. The relationship we observed between CancelTime and trigger failure rate might be due to several factors. First, the reviewers’ point relies on the assumption that the detection of the stop signal and implementation of the stop process are independent processes, but they might not be. In other words, it is possible that a participant who is more likely to fail to detect the Stop Signal, is also likely to be slower to initiate the stop process which would result in a relationship between p(TF) and CancelTime. Second, it is not entirely obvious that so-called “trigger failures” truly reflect a failure to trigger the Stop process. Another interpretation could be that the measure reflects the “strength” of the Stop process once activated, in other words activation of the Stop network (Band et al., 2003) [but see (Matzke et al., 2017)]. One could imagine that a stronger Stop process would be quicker to stop a response leading to a relationship between p(TF) and CancelTime. We have commented on these issues in the Discussion section.

Concerning Temporal Dynamics:

6) If I am understanding correctly, CancelTime is computed exclusively from partial EMG trials. Additionally, it is intended to be an alternative to SSRTbeh, which is a measure of the central tendency of SSRT across all trials. When CancelTime is compared to SSRTbeh, CancelTime is ~60ms shorter. The authors argue that CancelTime is shorter than SSRTbeh because CancelTime does not include the (~60ms) electromechanical delay and therefore is a purer measure of stopping. However, I would like to suggest another explanation for why CancelTime is shorter than SSRTbeh.

Assuming (1) a race model architecture, (2) variability in the go RT and (3) variability in SSRT, then failed stops will tend to occur when SSD is long, go RT is fast, and SSRT is slow. Successful stops will tend to occur when SSD is short, go RT is slow, and SSRT is fast. Partial EMG trials, which I understand to be trials in which the go process doesn't win as decisively as a successful stop trial or fail as decisively as a failed stop trial, should have SSD, go RT, and SSRT values between these two extremes. However, ~1/2 of trials are failed stop, ~1/4 of trials as partialEMG, and ~1/4 of trials are successful stops. Therefore, partialEMG trials should be preferentially sampled from the half of trials with shorter SSD, slower go RT, and faster SSRT. If this is the case, then CancelTime being faster than SSRTbeh may be partially or completely explained by CancelTime being selectively sampled from faster SSRT trials whereas SSRTbeh is computed across all stop trials.

To concretize my suggestion in an example, if we assume an SSRT distribution with variability such that the first quantile has a mean of 120 ms, the second 160 ms, the third 250, and the fourth 350 ms. When the first quantile is sampled, these should preferentially result in successful stops, when the second is sampled these should preferentially result in partialEMG trials, and when either of the latter two are sampled these should preferentially result in failed stop. However, if you computed CancelTime on these data it should be closer to 160ms (as a result of preferentially sampling the 2nd quantile) but the overall central tendency of the SSRT distribution would be ~220ms.

This alternative implies that the average neural latency for stopping may not differ from SSRTbeh, or may differ less than the ~60 ms suggested here. One tool for evaluating this alternative explanation may be to simulate stop trials with variability in go, stop and SSD and evaluate whether computing SSRT only (or preferentially) on trials sampled from the 2nd quartile of SSRT can produce significant differences from the traditional method of computing SSRTbehav. If it may be useful, here is some openly available code that instantiates the interactive race framework and would allow varying go, stop, and SSD: https://github.com/bissettp/SharingContextDependence/blob/master/interactive_race.ipynb).

The reviewers raise an interesting point, however, there are several reasons why we think our interpretation that the extra 60 ms reflects an electromechanical delay, rather than us sampling preferentially from the faster portion of the stopping distribution.

1) As we hopefully clarified in an earlier response, our calculation of SSRTEMG produces an estimate of stopping latency that is similar to CancelTime. Since the SSRTEMG calculation utilized all the SSDs it is unlikely that our results are a manifestation of preferential sampling of the faster half of the true Stop distribution, and instead suggests that the difference between the two measures is due to a ballistic stage in responses that is insensitive to the Stop process. We now better describe our rationale behind calculating SSRTEMG in the revised manuscript (Results).

2) We further tested the idea that there might be a ballistic stage in responses which inflates SSRTBeh by simulating the independent race model. Here, the Go and Stop accumulator raced to a threshold, and the outcome of the trial was determined by which accumulator reached the threshold first. The activity of each accumulator could be described by the mean drift rate (μ) and the SD of the drift rate (σ) (Boucher et al., 2007; Ramakrishnan et al., 2012; Usher and McClelland, 2001) [Please note that although the interactive race model might be more appropriate, we choose the independent race model for simplicity. Future studies might investigate these issues further]. First, we tested whether the independent race model without a ballistic stage could fit the empirical results. It provided a poor fit suggesting that a modification to the model is needed. We then added a ballistic stage to the model and observed a better fit indicating that the difference between CancelTime and SSRTBeh might be a reflection of this ballistic stage. Below we describe our steps.

To test the independent race model without a ballistic stage, for each participant, we estimated the Go parameters, (μGO-EMG, σGO-EMG) and (μGO-Beh, σGO-Beh) which best fit the RTEMG (Go cue to EMG onset) and RTBeh (Go cue to keypress) distributions in the Correct Go trials, respectively [further details outlined in Appendix 1]. Next, using the estimated Go parameters (μGO-Beh, σGO-Beh), we estimated the Stop parameters (μSTOP-Beh,σSTOP-Beh) that best fit the behavioral inhibition function (Figure 1A). Similarly, for EMG, we used its respective Go parameters (μGO-EMG, σGO-EMG) to estimate the Stop parameters (μSTOP-EMG,σSTOP-EMG) using the EMG inhibition function (Figure 1D). We reasoned that the Stop distribution underlying the inhibition of both the EMG and keypresses should be the same as both are part of the same response, and thus μSTOP-EMG should be similar to μSTOP-Beh. Additionally, the observed difference between the EMG and behavioral inhibition functions might be attributed to the difference in the underlying Go processes (RTEMG vs. RTBeh). However, this was not the case. The Stop distributions estimated from the EMG and keypresses were distinct, where μSTOP-EMG (188 ± 9 ms)was significantly less than μSTOP-Beh (207 ± 5 ms; t(41) = 2.7, p = 0.011, d = 0.4, BF10 = 3.7). Second, the difference between the two inhibition functions could not be attributed to just the difference between the two Go processes. To check this, we used (μSTOP-Beh,σSTOP-Beh) as the Stop distribution and (μGO-EMG, σGO-EMG) as the Go distribution, and simulated the EMG inhibition function. We observed that the simulated EMG inhibition function did not match the empirical one (Figure 1B). To quantify this, we compared the squared error between the simulated and empirical EMG inhibition functions to the squared error between the simulated and empirical behavioral inhibition functions. The difference was significantly greater for the EMG inhibition functions compared to the behavioral ones (Figure 1C; behavioral inhibition function, squared error = 0.10 ± 0.01; EMG inhibition function, squared error = 0.21 ± 0.02, t(41) = 4.8, p < 0.001, d = 0.7, BF10 > 100). Conversely, when we used (μSTOP-EMG, σSTOP-EMG) as the Stop distribution and (μGO-Beh, σGO-Beh) as the Go distribution, and simulated the EMG inhibition function we again did not observe a good fit (Figure 1E, F; EMG inhibition function, squared error between experimental and simulated data = 0.12 ± 0.02; RT inhibition function, squared error = 0.23 ± 0.02, t(41) = 4.7, p < 0.001, d = 0.9, BF10 > 100). This incompatibility suggests that some change needs to be made to the model such that a single Stop distribution is able to fit both the EMG and behavioral inhibition functions. Hence, we made two changes based a model previously used to describe stopping of reaching movements (Gopal and Murthy, 2016; Jana and Murthy, 2018). First, we added a peripheral delay to the Go process reflecting the observed delay between RTEMG and RTBeh. Second, we partitioned this delay period into a non-ballistic and ballistic stage. And we then tested whether this model with a ballistic stage fit the empirical results better than the one without a ballistic stage.

In this physiologically relevant model, the Go process comprises an accumulation phase and a delay phase. Once the accumulator hits the threshold, EMG responses can be observed, and then following a peripheral delay, the EMG builds up enough (i.e. the point-of-no-return) to be able to cross the inertia of the limb and generate a movement (Figure 1G). If the Stop reaches the threshold before the Go reaches the threshold, then no EMG is elicited (no EMG trial; Figure 1G). Further, if the Stop reaches the threshold early during the delay period when the EMG has not built up to a critical level (point-of-no-return) it will be able to inhibit the response resulting in a partial EMG trial (Figure 1H). However, if the Stop reaches the threshold after the EMG has reached the point-of-no-return a movement is inevitable, resulting in a Failed Stop trial (Figure 1I). Thus, the point-of-no-return partitions the delay phase into a non-ballistic (where Stop can act) and a ballistic stage (where Stop cannot act). We tested whether this model provides a better fit compared to the model without a ballistic stage. Indeed, this was the case, as incorporation of a ballistic stage allowed μSTOP-EMG to fit the behavioral inhibition function much better (Figure 1J). We quantified this by comparing the squared error between the simulated and empirical behavioral inhibition functions (Figure 1K; Model with ballistic stage: squared error = 0.14 ± 0.02; Model without ballistic stage: squared error = 0.23 ± 0.02; t(41) = 4.2, p < 0.001, d = 0.7, BF10 > 100). Across participants, the mean ballistic stage was estimated to be 34 ± 4 ms. Thus, based on our model, there exists a ballistic stage in keypress responses, which we think is responsible for the difference between CancelTime and SSRTBeh (we now mention this in the Results, and add Figure 3—figure supplement 1 to the revised manuscript, and have added the simulation methods and results as an Appendix 1). While this measure was less than our estimate of ~60 ms, we note that some participants did not have a sigmoidal EMG inhibition function leading to suboptimal parameter estimation. Indeed, when we considered only those participants who had lower than the population median squared error, the duration of the ballistic stage was 47 ± 3 ms which is closer to our estimate of ~60 ms.

3) In a similar vein, we carried out another analysis which provides a similar answer, and is based on the idea that there is a critical EMG threshold that once exceeded will inevitably result, after some electromechanical delay, in a button press (i.e. a ballistic stage). Consider Author response image 1 showing theoretical distributions of the end of the Go and Stop processes assuming that button presses reflect the end of the Go process (solid lines). Due to the SSD staircasing procedure employed in the studies, on average, the Go and Stop processes should end at the same time. By contrast, on the Failed Stop trials the Go process ends earlier than the Stop process. Going by definition of SSRT, on average, the Go process across all Go trials ended (i.e. button was pressed) ~220 ms after the stop signal (computed using the keypress RT minus the mean SSD). Now note that our mean CancelTime preceded SSRT by ~60 ms. At first glance, this might be taken to suggest that the reviewer is correct and CancelTime samples from the left half of the stop end time distribution. However, such comparisons are unfair because the criterion for the end time is different in each case: button press versus EMG.

If there is a ballistic stage, then the end time of the Go process ought to be the time at which EMG crosses the putative threshold. We therefore estimated the end time of the Go process on Failed Stop trials and Go trials as the time at which EMG activity exceeded the mean of the EMG amplitude recorded on Partial trials (as our estimate of the threshold for a response, see Author response image 1). We expressed this relative to the time of the Stop signal for Failed Stop and Go trials, respectively. When we do this, the mean end time of the Go process for the Correct Go trials is ~100 ms, while CancelTime is ~150 ms. While these timings are only rough estimates, it suggests that, as the reviewers propose, CancelTime only samples from a part of the whole Stop distribution, but it does not seem to be sampling from the faster half. If anything, this analysis suggests it samples the slower half of the Stop distribution. This makes sense as CancelTime does not include the stopping latency in the No EMG trials, where the Stop process was presumably quick (or the Go process was slow). This also lines with our TMS evidence where we detect MEP suppression (ostensibly marking the implementation of the Stop process) ~30 ms prior to CancelTime. Thus, we believe that while CancelTime is much shorter than SSRTBeh, it is still an overestimation of the true stopping latency. We note this in the revised manuscript (Discussion).

Thus, taken together, these results provide additional evidence that, 1) CancelTime preferentially subsamples the true Stop distribution, but in contrast to the reviewers’ suggestion, we think that it likely samples from the center or potentially the slower half of the true Stop distribution; and, 2) The difference between CancelTime (and SSRTEMG) and SSRTBeh might be due to a ballistic stage.

End time of the Stop process using keypress and EMG amplitude.

(a) Schematic of the distributions of the mean end time of the Go and Stop process in the Correct Go (green), Failed Stop (orange), and the Successful Stop (red) trials, while considering the keypress as the response. The CancelTime distribution is represented in brown. Note that CancelTime is an EMG measure and preceded SSRTBeh calculated using keypresses. (b) Same as (a) but here the response is considered as the time when the EMG reaches the mean amplitude of that in the partial EMG trials. Note that the all distributions other than CancelTime shift to the left. (Inset) Mean EMG amplitude in the Failed Stop (orange) and partial EMG (brown) trials in Study 1. (c) Histogram showing the distribution of the Failed Stop and Correct Go responses when considering response as the time when the EMG in these trials cross the mean amplitude of that in the partial EMG amplitude. Histogram of CancelTime is shown on the inverted y-axis for better visualization. The triangle and cross-hairs represent the mean ± s.e.m. Colors are the same as in (a). (d) Same as (c) but for all participants in Study 1 and 2. The histogram of the population is shown at the top. Note that CancelTime probably overestimates the mean of the true Stop distribution.

7) The authors stress that parts of their model of the processing sequence is supported by the fact that the temporal distance between cortical reduction in excitability (TMS) and the CancelTime corresponds to the corticospinal conduction time (here about 23 ms). The difference between the CancelTime and the reduced motorcortical excitability is about 15 ms (155 – 140). However, the onset of decreased motorcortical excitability, which would best correspond to the onset of the decline in MEP amplitude, does start before that, as can be seen in Figure 4A. An only somewhat smaller effect is apparent already at 120ms, with an onset probably even before that. This would add another 20+ ms to the equation, thus contrasting 23ms vs. 35+ms. The point I want to make is that, even though I find the interpretation of the findings interesting and plausible, care has to be taken not to over-interpret these measures since they are heavily dependent on our statistical procedures (sample size, size of presumably relevant effect, parameterization of onset times etc.).

Firstly, we would like to apologize as there was a minor error in the reporting of the data, and the actual mean CancelTime was 160 ms, not 155 ms as reported previously. The difference was due to slightly different cut-off and outlier rejection procedures compared to the other experiments. These procedures are now consistent across experiments. We have rectified this in the revised manuscript (Results, and in Figure 4B).

To the reviewers’ point, we agree that the temporal cascade model that we have constructed is only approximate as it is averaged across participants who had different stopping latencies, and is also contingent on, as the reviewers’ rightly point out, on statistical procedures. For example, there is a degree of uncertainty even in our estimates of corticomotor conduction latency. The reason for this is that the conduction delay measured by TMS-evoked MEP is biased towards assessing the fastest corticospinal pathways: large-diameter, fast-conducting corticospinal neurons with mono-synaptic connections to the spinal motoneurons (Day et al., 1989; Edgley et al., 1997; Groppa et al., 2012). Yet conduction velocities in the (primate) pyramidal tract vary hugely (Firmin et al., 2014) and we presume that voluntary motor commands recruit a mixture of both faster and slower conducting (i.e. smaller diameter neurons and/or poly-synaptic connections to the spinal motorneurons) pathways. This would mean our estimate of conduction time is an underestimate and that the mean time at which changes in motor cortical output are observed at the level of the muscle (i.e. in the electromyogram) is probably several milliseconds longer than our estimate of 23 ms. In line with the reviewers’ comments, we have acknowledged a degree uncertainty in our temporal model on the whole, as well as in relation to this particular issue concerning the timing of the MEP and EMG suppression (Results, Discussion).

8) The validity of the reduced TMS-MEPs as indicators of the stopping process is derived from the strong reduction in successful stop relative to go trials around 140 ms, a notion further supported by Figure 4D. It is not discussed, however, that MEPs also are reduced for unsuccessful stop trials around 140 ms locked to the stop signal (a reduction similar to that of successful stop trials; Figure 4B; the effect does not seem to be that much smaller). How to reconcile these findings?

We thank the reviewers’ for making this observation. Indeed, we do see a relative reduction in MEPs in the Failed Stop trials. The fact this happens doesn’t invalidate our use of the MEPs as an indicator of the Stop process. In fact, it seems to make some sense if we think that the Stop process is initiated (nearly) every time a Stop signal is presented (as the signal is quite salient and the studies were conducted on young, healthy adults), and that failure to stop generally occurs when the Go process is particularly fast or the Stop process is particularly slow. Thus, the MEP reduction in Failed Stop trials is the expression of the Stop process, i.e. it crossing the line, despite the fact that the Go process has already crossed the point-of-no-return. Indeed, the reviewers pointed out that in Successful Stops the MEP suppression might even begin a little earlier than in Failed Stops (120 ms versus 140 ms), which would be consistent with the idea that some stops fail because of a slower Stop process (rather than a particularly fast Go). Bear in mind too, that the suppression we are observing here is in a task-irrelevant muscle. A benefit of this is that we can observe the timing of the Stop-related suppression in the absence of any Go-related muscle activity that would otherwise overlap and potentially blur the true timing. We have included a few lines in the manuscript discussing this issue (Results).

9) In the fourth paragraph of the Discussion, the authors cite papers showing that in monkey, rats, and humans that neurons that are putatively related to stopping change close to SSRT. This seems like considerable evidence against the chronometric framework presented here that assumes that the stop command is sent from brain to muscle well before SSRT (~60 ms + conduction time). I think it would be helpful to understand the authors' position on how these seemingly contradictory findings relate to this current framework.

Although we acknowledge that additional evidence may be required, based on our current results, we believe that some of the brain signatures previously reported might not be causally-related to the initiation/implementation of the Stop per se [for example, the intraparietal sulcus which has been described to be important for stopping movements (Osada et al., 2019) might not be so (Hannah and Jana, 2019)]. They could instead reflect some other aspect of the Stop, for example, monitoring or feedback related to the implementation of the Stop as has been ascribed to certain brain signatures that modulate after SSRT (Logan et al., 2015; Schall and Boucher, 2007). We now discuss this in the revised manuscript (Discussion).

Relatedly, a recent study in non-human primates performing the Stop signal task has demonstrated that the premotor cortical network dynamics in the Successful Stop trials diverge from that seen in the Failed Stop and Go trials within 70-120 ms of the Stop signal (Pani et al., 2019). This again highlights that rapid action-stopping might be implemented in the motor system much earlier than that observed at the behavioral end point.

Functional Significance of beta Burst Activity:

10) How does the work presented in Study 4 relate to the recent preprint of a paper by Wessel on the role of beta bursts in stopping? [Wessel, J.R., "β-bursts reveal the trial-to-trial dynamics of movement initiation and cancellation", https://www.biorxiv.org/content/10.1101/644682v1].

There are some clear similarities between the Wessel, 2019 study and ours. First, similar to what we have reported, he observes an increase in bursts% in frontocentral electrodes prior to SSRT in the Successful Stop trials compared to the Failed Stop trials. Second, this increase seems to occur quite early after the Stop signal and much before the SSRT (Figure 2B, 25-75 ms and 75-125 ms bin). In fact, the difference between the Successful and Failed Stop trials seems to subside close to SSRT (see Figure 5—figure supplement 4 for the burst% modulation across time). Thus, the average timing of beta bursts in the Successful Stop trials might be similar in both studies. However, we would also like to highlight some differences between the two studies. First, while Wessel analyzed the EEG channel space, we analyzed beta bursts in a frontal spatial filter. Indeed, the signal-to-noise observed in a spatial filter is much improved (Muralidharan et al., 2019; Wessel, 2018). This allowed us to detect beta bursts despite having far fewer number of subjects (N = 11, 13 vs. N = 234). In fact, we were unable to detect enough beta bursts in the channel space in our pool of subjects at all to make any predictions about the timings of the bursts (see Author response image 2 for exemplar subject where beta burst probability is computed over the entire channel space as in Wessel’s case). Second, while we defined bursts based on the beta power during a baseline period prior to the presentation of the Stop Signal, Wessel defined it based on the beta power in a channel across time. Third, Wessel does not show if the increase beta burst% in the Successful Stop trials prior to SSRT is greater than that observed before the Stop signal. Indeed, if beta bursts were to play a role in movement cancellation then one might expect it to increase once the Stop signal is presented. Thus, taking all these together, we believe that our method might be better suited for detection of beta bursts in future EEG studies. Nevertheless, despite all these differences, the study by Wessel, 2019, reinforces our observation that the timing of beta bursts in the frontal cortex might have a key role during movement cancellation.

Beta burst analysis in the channel space.

Please note that the SNR is far worse than that observed using a spatial filter.

11) Study 4 finds an increase in beta bursts for successful stops relative to baseline and go trials, an effect interpreted as indicator of the engagement of the right inferior frontal stopping processes. This is a very interesting finding, but its interpretation is not without some conceptual problems.

- Given that EEG is plagued with the inverse problem, it seems somewhat unjustified to claim that this signature originates in the right frontal cortex. But even if one would agree that a rough deduction of the source from its topography is possible, I would have a hard time to associate the rather midfrontal topography with a right frontal source close to the sylvian fissure. Beyond, the authors performed dipole fitting on the independent component topographies, and thus could easily check if the individual dipoles of these components at least roughly are fitted to such a position.

While we have converging evidence that beta bursts might have originated from the right frontal cortex (Swann et al., 2009, 2012), we agree that it is inappropriate to establish the origin of the beta bursts from EEG due to its poor spatial resolution. However, as suggested, we performed a dipole localization analysis of the right-frontal ICs which were selected from both Study 4 and Study 5 and plotted the average dipole location along and its variability in an average MNI space. The dipole is fronto-central (but biased towards the right) which roughly estimates the origin of this beta from the mid to right frontal cortex. However, future studies are required to establish whether the beta bursts recorded at the scalp do originate from the right inferior frontal gyrus, a key node in the stopping network, or rather to preSMA or to both (note that these are connected via white matter (Catani et al., 2013; Swann et al., 2012)). We discuss this in the revised manuscript (Discussion, and have added Figure 5—figure supplement 2 to the revised manuscript).

Beta burst activity is depicted and analyzed relative to the pre-stop period. If we leave the IC-selection aside for a moment, the resulting time courses may still be in accordance with an effect akin to motor beta: around the time of the stop signal, beta activity would be similarly low for all three categories due to motor preparation, followed by rebound-effects that might be earlier in case of successful stops (cancelled), succeeded by unsuccessful stops and go trials (rebound after execution).

The IC selection states, however, that a component needed to show a beta power increase between the stop signal and the SSRT compared to a time window prior to the go cue. This should exclude potential motor beta components with typical time courses delineated above. The time course for the go activity supports this assumption. Nevertheless, given the conceptual importance of this beta component in this context, it would be nice to also see the go-locked time courses for the stop-related conditions.

We thank the reviewer for raising this issue. While it is possible that the motor beta rebound might contaminate the increase in burst% following the Stop signal, we think that this is unlikely to explain our results. First, as mentioned above, the dipole localization does not support a sensorimotor source for the generation of this beta and points to a frontal source. Secondly, post-movement beta rebound occurs at least ~500 ms after the EMG offset. However, in the frontal spatial filter, when the burst% is time-locked to the Go cue (see Figure 5—figure supplement 4), the increase in burst% in the Successful Stop trials starts well before both CancelTime (average time when EMG activity starts decreasing) and SSRTBeh (average time of movement execution). In addition, there is either no modulation of burst% in the Go trials (Study 5) or the modulation occurred after the average RT (Study 4). We mention this in the revised manuscript (Results) and add Figure 5—figure supplement 4 to the revised manuscript).

12) I understand the presented beta burst data to be the probability that a beta burst occurred on any given trial. Assuming this, beta bursts, which are taken as evidence of the frontal (perhaps rIFG) signal to stop, only occur on ~15% of stop trials (14.6% in Experiment 4 and 16.2% in Experiment 5). Additionally, beta bursts often occur on go and stop-failure trials, sometimes at similar rates to successful stop trials (e.g., 15.4% in Experiment 5 for stop-failure rates). Therefore, beta bursts happen on few stop trials and almost as many go trials as stop trials. How does this signal that is neither necessary or sufficient for stopping explain stop success generally? Might there be differences between stop success trials with and without beta bursts? Could trials with beta bursts be edge cases of some sort (e.g., when proactive control is low and reactive stopping is therefore particularly essential) that are not indicative of the general mechanism for stopping on the other 85% of stop success trials?

Indeed, it is quite curious why beta bursts are observed on a small percentage of trials. One potential explanation could be that we are not able to detect a burst reliably on every trial. This could be due to the low SNR of EEG and if we were recording directly from these brain regions, we could get a better estimate of the percentage of bursts in Successful Stop trials. However, the presence of beta bursts in the Go trials does raise a question about the role of beta bursts. It is possible that beta bursts are (partly) spontaneous events that occur all the time (but have some functional consequence) (Shin et al., 2017), or it might have a role in proactive slowing in the Go trials (as they are embedded in a task where the participants have to stop their response in a minority of trials). Nevertheless, we did an additional analysis of looking at CancelTimes in the Successful Stop trials with and without bursts between Stop signal and SSRTBeh. There was no difference in the CancelTimes between these trial types (CancelTimeWith Burst = 164 ± 9 ms; CancelTimeNo Burst = 165 ± 9 ms, t(12) = 0.57, p = 0.58, d = 0.2, BF10 = 0.32) We now discuss this in the revised manuscript (Discussion).

Theoretical Implications:

13) I agree with the authors that these results have potentially striking implications for existing models of stopping. However, I think the paper could be improved by laying out these implications more explicitly. For instance, how does this framework relate to existing models including the original Independent Race Model (Logan and Cowan, 1984 / Psych Review), updated Independent Race Models including blocked input models (Logan et al., 2014; Logan et al., 2015), the Interactive Race Model (Boucher et al., 2007), the BEESTs model and trigger failures (Matzke et al., this relates to comment 5), and perhaps recent work suggesting violations of independence that can be accounted for by variable, sometimes weak inhibition (Bissett, Poldrack, and Logan, in revision https://psyarxiv.com/kpa65).

Our study sheds light on the temporal profile of the physiological/network model underlying action-stopping (Aron et al., 2014). To this end we characterize the chronometrics of the Stop process and observe, frontal beta activity at ~120 ms, followed by decreased M1 excitability at ~140 ms, and cancellation of the muscle response at ~160 ms. As we have not formally tested all the computational models existing in the literature, it is probably premature to comment on the computational relationship between the Go and the Stop process. However, we can conjecture as to which models might best explain our results. Our results are not compatible with a strictly independent model since we see active inhibition of M1 (the Go process) already some time before SSRT. We think that the interactive race model (Boucher et al., 2007) best explains out data, but we must note that this model was originally tested on inhibition of saccades on over-trained non-human primates (SSRT ~90 ms), whereas our results are on inhibition of keypresses in naïve human participants (SSRT ~220 ms). Boucher et al. considered SSRT as a sum of DelayStop (delay in activation of the Stop process, ~60 ms, i.e. ~70% of the SSRT), Stopinterrupt (duration in which the Stop process is implemented, starting from the accumulation to the inhibition of the Go process, ~20 ms), and GoBallistic (ballistic stage preceding movement initiation, ~10 ms). First, frontal beta bursts occur ~120 ms after the Stop while CancelTime is ~160 ms, i.e. the DelayStop is ~75% of the duration of the Stop duration, which is similar to that reported by Boucher et al., 2007. Second, frontal beta bursts are followed by decrease in M1 excitability within ~20 ms. This is similar to the Stopinterrupt value reported by Boucher et al., 2007. However, the duration of the ballistic stage is probably longer for manual responses (~50 ms for reaching movements (Gopal and Murthy, 2016; Jana and Murthy, 2018)). Our simulations also support this (see response to a previous question). Thus, we believe that, SSRTBeh = DelayStop + Stopinterrupt + DelayCorticospinal + GoBallistic.

The initial delay in activation of the Stop process might relate to the triggering/detection of the Stop process [which might take about 80-120 ms (Bekker et al., 2005)] which is a key component of the BEESTS model. Another support of the interactive race model is that, we observe a decrease in corticomotor excitability in task-unrelated muscles at ~140 ms which persists for at least ~60 ms. This probably reflects an active inhibition of the Go process to directly suppress the output neurons of the primary motor cortex, but we presume that there is also a suppression of upstream drive to the motor cortex. For example, exogenous suppression of motor cortical output with TMS over the primary motor cortex seems only to delay voluntary motor output, rather than abolish it (Day et al., 1989). Thus, while we favor the interactive race model where the initial delay is related to the triggering/detection of the Stop signal. We note that the interactive-race model and blocked-input model are very similar (Logan et al., 2015), so our results do not disambiguate them. We now discuss this in the revised manuscript (Discussion).

References:

Band GPHH, van der Molen MW, Logan GD. 2003. Horse-race model simulations of the stop-signal procedure. Acta Psychol (Amst) 112:105–142. doi:10.1016/S0001-6918(02)00079-3

Botwinick J, Thompson LW. 1966. Premotor and motor components of reaction time. J Exp Psychol 71:9–15. doi:10.1037/h0022634

Firmin L, Field P, Maier MA, Kraskov A, Kirkwood PA, Nakajima K, Lemon RN, Glickstein M. 2014. Axon diameters and conduction velocities in the macaque pyramidal tract. J Neurophysiol 112:1229–1240. doi:10.1152/jn.00720.2013

Gopal A, Viswanathan P, Murthy A. 2015. A common stochastic accumulator with effector-dependent noise can explain eye-hand coordination. J Neurophysiol 2033–2048. doi:10.1152/jn.00802.2014

Hannah R, Jana S. 2019. Disentangling the role of posterior parietal cortex in response inhibition. J Neurosci 39:6814–6816. doi:10.1523/JNEUROSCI.0785-19.2019

Jana S, Gopal A, Murthy A. 2016. Evidence of common and separate eye and hand accumulators underlying flexible eye-hand coordination. J Neurophysiol 117:348–364. doi:10.1152/jn.00688.2016

Matzke D, Hughes M, Badcock JC, Michie P, Heathcote A. 2017. Failures of cognitive control or attention? The case of stop-signal deficits in schizophrenia. Attention, Perception, Psychophys 79:1078–1086. doi:10.3758/s13414-017-1287-8

Muralidharan V, Yu XY, Cohen MX, Aron AR. 2019. Preparing to Stop Action Increases Beta Band Power in Contralateral Sensorimotor Cortex Vignesh. J Cogn Neurosci 31:657–668. doi:10.1162/jocn

Pani P, Giamundo M, Giarrocco F, Mione V, Brunamonti E, Mattia M, Ferraina S. 2019. Neuronal population dynamics during motor plan cancellation in non-human primates. bioRxiv 774307. doi:10.1101/774307

Wessel JR. 2018. Testing Multiple Psychological Processes for Common Neural Mechanisms Using EEG and Independent Component Analysis. Brain Topogr 31:90–100. doi:10.1007/s10548-016-0483-5

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

The thorough review reports of the previous review round match the vast nature and the wide scope of the original manuscript. The resulting rebuttal letter that accompanied the revision also reflects a broad discussion, which is commendable. Concerning the revised manuscript, there are a few issues left to be discussed.

These issues are addressed in detail at the end of this letter. Here I provide a brief summary:

The first remaining issue concerns the request to not merely acknowledge connecting studies by citing them, but to also address and integrate the findings of these relevant studies vis-a-vis the current work. In this respect, the rebuttal letter provides a more balanced account, and that tone might be extended to the manuscript.

The second issue concerns the timing when stopping reaches the muscle in relation to the model. This point has been brought to your attention by the Senior Editor, a few days before this decision letter, to facilitate the exchange process. Below you can find the whole line of reasoning (main point 2). More data, additional analyses or simulation studies are not required (or even asked) at this point. A discussion of the seemingly controversial time-courses would be sufficient.

Elaboration on these issues:

1) The authors wrote a detailed and insightful response, which essentially clarified my methodological questions. Some of the more conceptual issues were answered well in the response letter, yet the changes in the manuscript were less substantial than what one might have expected.

We apologize for not integrating a more substantial discussion of these issues and hope that the new changes are much better.

a) E.g., regarding Wessel's beta-burst analysis: the authors now cite this work (Results), but rather casually so. The manuscript does not try to compare or integrate the presented findings with Wessel's.

We now include a more fulsome discussion of Wessel’s beta-burst study in the revised manuscript (Discussion).

b) The same goes for the partial EMG work. Most of the studies we provided in the first round of the review are cited, but again rather offhand. The manuscript does not really integrate the different studies. Several studies already used an estimate essentially the same to what the authors still refer to as "our idea of CancelTime" (although admittedly these claims have been toned down), yet no attempt is made to compare these estimates, their correlations with SSRTs etc.

We have removed the phrase “our idea”. We also discuss the previous studies in more detail (Discussion).

c) In some ways, I find that some of the claims made are not founded well enough in data, and the authors seem to be aware of it: "we agree that the temporal cascade model that we have constructed is only approximate as it is averaged across participants who had different stopping latencies, and is also contingent on, as the reviewers' rightly point out, on statistical procedures."

Yet again, the manuscript has not really been changed in accordance with this. Still, it is not properly discussed, for example, that the exact timing estimates heavily rely on the choice of latency estimates (EMG/MEP onsets or peak, of which each again can be calculated in many different ways.

We agree with the reviewer that there is some uncertainty in our timing estimates. We did previously mention in the revised manuscript that the timings for the temporal model were approximate (Discussion), and as such Figure 6 is described as a “hypothetical” model of the temporal cascade of process underlying human action-stopping. We also previously had a section noting the imprecision in our estimates of MEP latencies (Results). We have now amended the manuscript to further acknowledge some of the likely sources of imprecision in our timing estimates (Discussion). We would like to point out too, that despite these uncertainties, our estimates do seem broadly consistent with those from numerous other studies, e.g. “CancelTime” (Hannah et al., 2019; Raud et al., 2019; Raud and Huster, 2017), time of MEP suppression (Coxon et al., 2006; van den Wildenberg et al., 2010), corticomotor conduction time (Groppa et al., 2012; Hamada et al., 2013), BurstTimes (Hannah et al., 2019), and the ballistic stage (Gopal and Murthy, 2016; Jana and Murthy, 2018). We now mention this explicitly in the revised manuscript (Discussion).

2) I reviewed the initial submission of this manuscript. The manuscript is significantly improved in many ways. The editor requested that we evaluate whether claims have been toned down, previous work on EMG and beta-bursts have been acknowledged, and main point 6 regarding the timing estimate of CancelTime and a ballistic phase have been addressed. I think the first two points have been sufficiently addressed. However, the authors response to Main Point 6, especially their point 3, has raised new concerns about their claims about timing of stopping.

The authors present a 3-part response to main point 6. Part 1 points out that SSRTemg is similar to CancelTime and argues that this is consistent with the remaining ~60ms difference between CancelTime and SSRTbeh being a ballistic stage. Part 2 presents simulations consistent with a ballistic stage that is 34-47ms long (which is perhaps less than the ~60ms difference between canceltime and SSRTbeh). Point 3 argues that the real end of the race (at least as a criterion for evaluating CancelTime) is when EMG amplitude exceeds the threshold set on PartialEMG trials. They show that on correct go trials this threshold is exceeded ~100ms after the average stop signal would occur. Given the SSD tracking algorithm that ensured that the race between going and stopping is roughly tied, then the real latency of the stop process (as measured by EMG) may be ~100ms, so CancelTime may actually be an overestimate of the average stop latency.

The part 3 simulation results seem to conflict with multiple pieces of evidence in the manuscript and the literature. It appears that the authors are suggesting that the ballistic stage may be ~120ms (~220ms SSRTbeh minus the ~100ms stop process), which is both inconsistent with the simulation results in part 2 and inconsistent with the previous literature presented in the manuscript (e.g., Gopal and Muphy, 2016; Jana and Murthy, 2018 suggested 50ms for reaching movements). It also seems to bring into question the entire temporal sequence presented in the manuscript. Why would the end of the race be observable in muscles at 100ms if the signal to stop from cortex (perhaps rIFG) occurs 20ms later at 120ms?

Additionally, none of the 3 parts of the response have directly addressed the reviewers' main point 6. To briefly reiterate, assuming a race model, the ~50% of trials that are true failed stops (an overt response occurs) should tend to have the longest SSDs, fastest go RTs, and slowest SSRTs. The ~25% of trials that are successful stops with no EMG should be the opposite: shortest SSDs, slowest go RTs, and fastest SSRTs. This leaves the ~25% of trials that are successful stops with EMG, which should be in between these extremes. However, because there are ~twice as many stop failures as stop successes, the partial EMG trials will tend have shorter SSDs, slower go RT, and faster SSRTs than each measure's overall average. Therefore, CancelTime may be an underestimate of the true central tendency of SSRT across all stop trials.

In the text, the authors seem to agree with parts of this point, at least in part. They say "CancelTime… does not include the stopping latencies of the No EMG trials, which presumably reflect the fastest stopping latencies where the Stop process was fast enough to cancel the impending response before it reaches the muscle". However, they do not point out that CancelTime also does not include stop-failure trials, which presumably reflect the slowest stopping latencies, leaving CancelTime to reflect stopping latencies that are faster than the slowest half of stop trials but slower than the fastest quarter of stop trials. Also, in Figures 1G-I in their response, they illustrate how they believe correct stops with No EMG, correct stops with partial EMG, and failed stops arise from an accumulator model framework. No EMG has the fastest stop process, failed stop has the slowest stop process, and partial EMG is in between.

To conclude, I do not think that the response to main point 6 addressed the original concern, and I believe that the new simulations bring up new questions about the temporal cascade of processes in stopping. Does the stop process reach the muscle ~150-160ms after the stop signal, as suggested by CancelTime and SSRTemg, or is it ~100ms after the stop signal, as seemingly suggested by their part 3 in response to Main Point 6? If the latter, then how does this fit in with TMS evidence of motor suppression at ~140ms or beta-burst in cortex (perhaps rIFG) at 120ms? Also, if the argument from Main Point 6 is valid (and the authors do not address its validity directly), how can this be synthesized with the Part 3 response suggesting that CancelTime is an overestimate of the latency of the stop process?

We appreciate the insightful comments here and apologize for the confusion caused by our response. A key tenet of the paper, and our response to Main Point 6, is that SSRT may overestimate stopping latency by virtue of an inherent ballistic stage. All three of the additional analyses in Point 6 of our response provide further evidence of this: #1 the EMG-based calculation of SSRT very closely approximates CancelTime; #2 our simulation supported the notion of a ballistic stage, implying that SSRTBeh might be an overestimate of the true stopping latency; and #3 used a crude estimate of the end of the Go process relative to a theoretical stop cue, and suggested the mean was ~100 ms, which is closer to CancelTime than it is SSRTBeh.

To be clear about #3, the idea we were attempting to illustrate with this analysis was that comparing the SSRTBeh distribution with the CancelTime distribution is inappropriate because the former includes an electromechanical delay that the latter does not. The fact that the center of the Go distribution does not line up perfectly with the center of the CancelTime distribution probably reflects the particular EMG threshold chosen for the end of the Go process. This is a conservative estimate because the EMG amplitude on ~50% of the Partial EMG trials exceeded this value without generating an overt keypress, implying that there is actually a significant buffer. We note that raising the threshold slightly to account for this would bring the estimates of the end of the Go process closer to that of CancelTime.

We also note that unlike timing, the amplitude of EMG is quite variable and probably not the only determinant of response time (e.g. the rate of EMG rise as well as synergist and stabilizer muscle activity may contribute). This is evident in the fact that the tails of the EMG amplitude distributions for Partial EMG and Go trials overlap. Given these issues, we would urge against using this #3 analysis to infer the latency of stopping and thus do not feel that this analysis invalidates our temporal model of the processes contributing to stopping. We hope this allays the reviewer’s concerns.

In relation to the reviewer’s original point about whether CancelTime sub-samples from the true Stop distribution, our #1 response was intended to deal specifically with this issue. The point we were trying to make was that SSRTEMG is calculated in the same manner as SSRTBeh, only the definition of a response differs. Thus, SSRTEMG is calculated from the whole distribution, i.e. it does not sub-sample, and yet it still gives a similar estimate of stopping latency as CancelTime. This seems contrary to the reviewer’s suggestion that CancelTime underestimates the central tendency of the true Stop distribution.

In summary, our analyses provide converging evidence that SSRTBeh seems to include a ballistic stage and thus may overestimate stopping latency. This creates a temporal disparity between SSRTBeh and neurophysiological measures of stopping latency which appear much earlier. CancelTime measures the latency of stopping at the level of the muscle and bridges this temporal disparity. Thus, a main contribution of the paper is in demonstrating the temporal relationship between brain signatures and the muscle (CancelTime) and behavioral markers of stopping latency (SSRTBeh). [Another main contribution is that CancelTime is a potentially single trial estimate of the speed of stopping – which has big implications for our field].