Conservation of preparatory neural events regardless of how movement is initiated

Voluntary movement is believed to be preceded by a preparatory stage. Evidence arises from experiments where a delay separates instruction and execution cues. While this sequence emulates some real-world situations (e.g., swatting a fly upon landing) movements are commonly made at a moment of one’s choosing (reaching for a coffee cup) or are made reactively (intercepting a falling cup). To ascertain whether neural events are conserved across such contexts, we examined motor cortex population-level responses in monkeys when reaches were initiated either after an imposed delay, at a self-chosen time, or reactively with very low latency. We found that the same preparatory and movement-related events were conserved. However, preparation was temporally flexible and could be remarkably brief. Our findings support the existing hypothesis that preparation is an obligatory stage that achieves a consistent state prior to movement. Yet our results reveal that preparation can unfold more rapidly than previously supposed.

that early, putatively preparatory aspects of the response may be conserved. 23 Ambiguity at the neural level is underscored by behavioral results suggesting that preparation may be 24 unnecessary 23 . Preparation has generally been considered to be a time-consuming process that makes a 25 sizeable contribution to the RT 2,4,5,9,10 . Yet under certain circumstance, humans and monkeys display very short 26 RTs 24-26 despite having no time to prepare in advance. Such RTs appear incompatible with a preparatory stage 27 that consumes considerable time. 28 We wished to explore the hypothesis that delay-period activity reflects a preparatory process that also occurs 29 when there is no delay, but displays enough temporal flexibility to allow very short RTs. In principle, this 30 hypothesis is readily tested via a straightforward strategy: by exploiting the delay period to identify putatively 31 preparatory neural activity, then inquiring whether and how similar activity is present in other contexts. 32 estimate of rate was representative, we chose analysis epochs based on typical behavioral performance. For 187 example, in the quasi-automatic context, epochs were selected such that target onset and movement onset 188 were separated by an interval equal to the mean RT. 189 Many neurons showed activity that varied with reach direction during the delay period of the cue-initiated 190 context (e.g., Figure 3, red traces). For this context, we defined a 450 ms 'delay epoch', beginning 50 ms after 191 target onset. Variation of delay-epoch firing rate with target direction was significant (ANOVA, p < 0.05) for the 192 majority of neurons (74/129 and 88/172 for monkey Ba and Ax). We also defined a 300 ms 'movement epoch ', 193 starting 50 ms before movement onset (just after EMG began to change) and ending just after the hand landed 194 on the target. Variation of movement-epoch firing rate with target direction was also significant for the 195 majority of neurons (116/129 and 144/172). 196 As in prior studies, delay-period activity suggests a preparatory process. A natural question -relevant to 197 interpretation of activity in the other two contexts -is when putatively preparation-related activity transitions 198 to movement-related activity. Presumably this must happen following the go cue but before movement. Yet 199 the moment of this hypothesized transition is difficult or impossible to determine via inspection of single-200 neuron responses. For example, the neuron illustrated in Figure 3a shows multiple response phases following 201 the go cue, including a peak ~75 ms before movement onset (higher for rightwards reaches; lighter red traces) 202 and a subsequent peak during movement (higher for leftwards reaches; darker red traces). Should one 203 consider the first peak to be a final strengthening of a preparation-related response, or the beginning of a 204 movement-related response? Is such a distinction even meaningful? These questions are challenging because 205 there is no easily identifiable moment when putatively preparatory activity ends and movement-related 206 activity begins. Similar ambiguity was present even for neurons with simpler response patterns. The neuron 207 illustrated in Figure 3c (red traces) exhibits activity just before movement that is (approximately) a magnified 208 version of delay-period activity. Again, it is unclear whether such activity reflects the culmination of 209 preparation-related activity, or a movement-related burst. 210 These uncertainties highlight a known limitation of the instructed-delay paradigm: although activity between 211 target onset and the go cue is suggestive of a preparatory process, it is more challenging to interpret neural 212 events between the go cue and movement onset 6 . One might wish to define events before a specified time as 213 putatively preparatory, and events after that time as movement-related. Yet when that time should be (or 214 even whether the transition happens at a discrete time) is not clear from inspection of single-neuron 215 responses. This creates a problem: if a delay period is necessary to identify activity as putatively preparatory, 216 how can we test whether putatively preparatory events occur in the absence of a delay? This challenge will 217 become particularly relevant when examining responses during the quasi-automatic context. 218

Single-neuron responses during the self-initiated versus cue-initiated context 219
In the self-initiated context, movement initiation is never demanded by an unpredictable go cue. Rather, the 220 monkey chooses when to reach and can potentially anticipate that choice in advance. Given this, how does 221 activity in the self-initiated context relate to that in the cue-initiated context? There exist at least three 222 possibilities. First, if delay-period activity is primarily suppressive, then a similar pattern of activity should be 223 present in the self-initiated context. That pattern should be strongest shortly after target onset (when reaches 224 should be most strongly suppressed because they yield little reward) and should wane as the time of 225 movement approaches. Second, if delay-period activity is primarily preparatory, then during the self-initiated 226 context, a similar pattern should grow with time as movement nears. Any strengthening could be gradual -227 starting hundreds of milliseconds before movement onset -or rapid -occurring just before movement-related 228 activity. Third, activity in the self-initiated context could look quite unlike activity during the cue-initiated 229 context. Self-initiated movements likely involve a larger role of anterior areas, including the supplementary 230 motor area 30 . If so, the role of motor cortex might be reduced or altered. This could impact pre-movement 231 activity, movement-related activity, or both. 232 Single-neuron responses followed the second prediction: the patterns of pre-movement activity in the self-233 initiated context grew with time and came to resemble the patterns of delay-period activity in the cue-initiated 234 context. For example, in Figure 3a,c, the ordering of traces ~250 ms before movement onset is similar for the 235 cue-initiated (red traces) and self-initiated (blue traces) contexts. The pattern of pre-movement activity in the 236 self-initiated context became stronger rather than weaker with time with time. Across all neurons, the median 237 correlation between self-initiated and cue-initiated activity patterns was low during the first 150 ms after 238 target onset (median r = 0.39 and r = 0.16 for the two monkeys), reflecting the fact that early activity was 239 typically weak in the self-initiated context. This correlation became stronger as movement onset approached 240 (median r = 0.86 and r = 0.74, using a 150 ms window ending 50 ms before movement onset). During 241 movement, the correlation was quite high (median r = 0.92 and r = 0.87). Such strengthening of activity agrees 242 with related results in rodent 31 , and is inconsistent with a suppressive process that relaxes to eventually allow 243 movement. These observations will be further quantified by population-level analyses below. 244

Single-neuron responses during the quasi-automatic context 245
Before considering putatively preparatory events, we note that movement-related responses in the quasi-246 automatic context closely resembled those in the other two contexts. This can be appreciated by visually 247 comparing, across rows in Figure 3, activity from just before movement onset until the end of the trial. These 248 example neurons were representative: the median correlation between movement-epoch activity patterns 249 during the quasi-automatic and cue-initiated contexts was 0.85 and 0.85 (monkey Ba and Ax). The primary 250 difference in movement-epoch response patterns was a tendency for some features to be slightly magnified in 251 the quasi-automatic context (e.g., the central peak in Fig. 3b). This observation is consistent with the slight 252 increase in reach speed, and with the slight increase in the magnitude of muscle activity. The similarity in 253 movement-related activity across contexts was not a given. Because there may be subcortical contributions to 254 very short-latency movements 25,26 , movement-related cortical activity could have been different or reduced 255 during the quasi-automatic context relative to the other two contexts. 256 The similarity of movement-related responses makes it sensible to ask whether those responses are preceded 257 by similar patterns of preparatory activity. Is the very first portion of the response in the quasi-automatic 258 context potentially preparatory? Or does that initial response simply constitute the beginning of movement-259 related activity? We saw no way of addressing this question using individual-neuron analyses. Consider the 260 neurons illustrated Figure 3a,c. For both, the very first pattern of activity to emerge in the quasi-automatic 261 context resembled that seen shortly before movement onset in the cue-initiated context. Interpretation thus 262 hinges on whether activity at that time in the cue-initiated context reflects the culmination of preparation or 263 the beginning of movement-related activity. As discussed above, this is difficult or impossible to infer from 264 individual-neuron responses. We therefore turn to analyses that leverage population-level properties. 265

Segregating preparatory and movement responses at the population level 266
We employed a recently developed analytical method to segregate the population response into putatively 267 preparatory and movement-related response patterns. This method leverages the observation that the 268 correlation structure between neurons changes dramatically between delay-period and movement-period 269 epochs 27 . Specifically, the 'neural dimensions' that best capture delay-epoch activity do not capture 270 movement-epoch activity, and vice versa. That observation was unexpected; it occurs because neurons with 271 related response properties during preparation become unrelated during movement, something predicted by 272 no existing model 27 . Yet the finding has considerable utility from the standpoint of the present study. Although 273 putatively preparatory and movement-related processes are not separable at the single-neuron level, they are 274 potentially separable at the population level. Our strategy is to use the cue-initiated context to identify a set of 275 neural dimensions that captures putatively preparatory activity and an orthogonal set of dimensions that 276 captures movement-related activity. These dimensions can then be used to examine the population response 277 in the other contexts. If delay-period activity indeed reflects preparation, then dimensions that capture delay-278 period activity in the cue-initiated context may similarly capture preparatory processing in the other two 12 contexts. Alternatively, if delay-period activity reflects some non-preparatory process (e.g., suppression) or a 280 process specific to the presence of an experimenter-imposed delay, then the dimensions that captured delay-281 period activity will either not capture activity during the other two contexts, or will capture activity with 282 structure that is very different from that observed during the delay. 283 Based on neural responses during the cue-initiated context only, we isolated twelve preparatory dimensions, 284 collectively the 'preparatory subspace'. The preparatory subspace captured 80% of firing rate variance (i.e., 285 firing-rate structure across all neurons) during the delay epoch, but only 3% of variance during the movement 286 epoch. We isolated twelve movement dimensions (collectively the 'movement subspace') which together 287 captured 85% of variance during the movement epoch, but only 3% of variance during the delay epoch. The 288 above percentages are for monkey Ba and were similar for monkey Ax (72% versus 4% and 83% versus 3%). 289 The ability to achieve this near-perfect segregation is not a general feature of neural data. It is a consequence 290 of the dramatic change in covariance between the delay and movement epochs. 291 We projected the population response, for the cue-initiated context, onto the preparatory and movement 292 dimensions. This revealed putatively preparatory and movement-related activity patterns (Figure 4, middle). 293 Each projection is a weighted sum of single-neuron responses (weights are the elements of the vector defining 294 the dimension). Yet unlike a generic linear readout, weights were optimized to capture response structure. 295 Projections are thus not only readouts but also building blocks of single-neuron responses, much as for 296 principal component analysis. Indeed, the dimensions we found span a space similar to the top principal 297 components. Using these building blocks, it becomes possible to estimate putatively preparatory and 298 movement-related contributions to each neuron's response. For example, the response of neuron 88 (Fig. 4, 299 rightmost column) is accurately approximated as the sum of a preparatory-subspace pattern (a weighted sum 300 of preparatory projections, orange) and a movement-subspace pattern (a weighted sum of movement 301 projections, purple). The reconstruction is not perfect -the pattern in Figure 4 (right) differs slightly from the 302 true response in Figure 3a -but is quite good (R 2 = 0.93). High reconstruction accuracy reflects the high 303 proportion of firing-rate variance captured. Do the dimensions found using the cue-initiated context -in 304 particular the preparatory dimensions -similarly capture variance during the other two contexts? 305

Reconstruction of neural responses across contexts 306
The dimensions found using the cue-initiated context continued to capture a high percentage of response 307 structure in the self-initiated and quasi-automatic contexts. In the self-initiated context, the total variance 308 captured by both preparatory and movement subspaces was 89% and 84% (monkey Ba and Ax) of that in the 309 cue-initiated context. In the quasi-automatic context, the variance captured was 87% and 84% of that in the 310 cue-initiated context. The high percentage of captured variance is reflected in accurate reconstruction of 311 neural responses in the self-initiated and quasi-automated contexts. For example, the response of neuron 88 312 ( Fig. 3a) was accurately reconstructed not only in the cue-initiated context (Fig. 4, right) but also in the self-313 initiated (Fig. 5a) and quasi-automatic (Fig. 5b) contexts. 314 These successful reconstructions involved contributions from both preparatory and movement subspaces. For 315 example, the reconstruction for neuron 88 included a robust preparatory-subspace pattern during the self-316 initiated context (Fig. 5a, orange) and a short-lived but strong preparatory-subspace pattern during the quasi-317 automatic context (Fig. 5b, orange). Within this preparatory-subspace patterns, the ordering of conditions was 318 similar across contexts: for neuron 88 the pattern was most positive for rightwards reaches (light traces) and 319 most negative for leftwards reaches (dark traces). To facilitate quantitative comparison, for each neuron we 320 measured the preparatory pattern 100 ms before movement onset, yielding a vector with one value per 321 direction. This vector captures the directionality of the preparatory pattern. To assess whether directionality 322 was similar across contexts, for each neuron we regressed the preparatory patterns for the self-initiated and 323 quasi-automatic contexts against that observed for the cue-initiated context. If the two patterns are the same, 324 then regressing one versus the other will yield a slope of one. In contrast, an average slope of zero would 325 indicate no consistent relationship between the preparatory patterns across contexts. 326 When comparing self-initiated and cue-initiated contexts, slopes were strongly positive (Fig. 5c,

d black bars in 327
left subpanel). When comparing quasi-automatic and cue-initiated contexts, slopes were again strongly 328 positive ( Fig. 5c,d dark bars in right subpanel). For monkey Ba, the slope was slightly greater than unity, 329 consistent with preparatory-subspace activity being slightly stronger in the quasi-automatic context. A 330 potential concern is that this strong similarity might not be specific to the preparatory pattern. For example, if 331 neurons have similar directionality at all times, then similarity would be high even when comparing a 332 preparatory pattern in one context and a movement pattern in another context. This was not the case: there 333 was no consistent relationship between the preparatory-subspace contribution in the cue-initiated context and 334 the movement-subspace contribution (assessed 150 ms after movement onset) in the other two contexts (Fig.  335 5c,d, gray bars). In summary, the dimensions that captured delay-period activity also made strong 336 contributions to firing rates during all three contexts, and had a similar pattern across all three contexts. The 337 nature of that pattern will be further investigated below. 338 If preparatory-subspace activity is truly preparatory, then it should exhibit a time-course consistent with that 340 role. Is this true across all three contexts? For each time, we measured the across-condition variance (the 341 strength of selectivity) of preparatory-subspace activity. This variance reflects the size of the envelope 342 describing the orange patterns in Figure 4. We refer to this measure as the 'preparatory-subspace occupancy'. 343 An important question is whether putatively preparatory events consistently precede movement-related 344 events. We therefore similarly computed the movement-subspace occupancy. Movement-subspace occupancy 345 ( Fig. 6, purple traces) had a similar time-course across contexts: it was negligible until ~110 ms before 346 movement onset and reached a peak just after movement onset (the peak occurred between 30 and 80 ms 347 after movement onset across both monkeys and all contexts). 348 Preparatory-subspace occupancy (Fig. 6, orange traces) followed a very different time course for each context. 349 In the cue-initiated context, there was an initial rapid rise that was sustained (at a lower level) throughout the 350 delay period. Preparatory-subspace activity then declined rapidly just before movement onset, reaching 351 baseline levels around the time the reach began. It is worth stressing that, by construction, preparatory 352 subspace occupancy is high during the delay period of the cue-initiated context. However, no further structure 353 is imposed; occupancy could have declined following the go cue, could have stayed the same, or could have 354 become stronger. 355 In the self-initiated context, the rise in preparatory subspace occupancy following target onset was weaker 356 (monkey Ba) or much weaker (monkey Ax) than for the cue-initiated context. Preparatory-subspace occupancy 357 remained weak from 200-400 ms after target onset. Occupancy then grew as movement approached, and 358 reached a peak before movement onset (at 120 ms and 160 ms for monkey Ba and Ax respectively). Occupancy 359 at that time was then similar to occupancy in the cue-initiated context at the same time (slightly greater for 360 monkey Ba and slightly smaller for monkey Ax). These observations concur with the hypothesis that, in the self-361 initiated context, monkeys do not consistently prepare their reach immediately following target onset, but 362 instead wait until nearer the time they choose to move. Whether the ramp of increasing occupancy reflects 363 ramping on individual trials cannot be inferred from the present data. It is equally plausible that preparation 364 has a sudden onset that is variable relative to movement onset, resulting in a ramp in the averaged data. 365 In the quasi-automatic context, preparatory-subspace occupancy rose rapidly following target onset and was 366 short-lived: occupancy peaked 70 ms and 80 ms (monkey Ba and Ax respectively) before movement onset and 367 then declined. The magnitude of this peak in preparatory-subspace occupancy was similar to, but slightly 368 higher than, the peak observed in the other two contexts just before movement onset. These observations are 369 consistent with the hypothesis that a preparatory stage is present even for low-latency intercepting reaches. 370 However, preparation appears to be very rapid: preparatory subspace occupancy precedes movement-371 subspace occupancy by only a few tens of milliseconds: 33 ms for monkey Ba and 42 ms for monkey Ax. 372 (Latency was measured as the time occupancy crossed a 10% threshold, and a shorter filter was used to 373 minimize the influence of filtering on latency, see methods). 374 Comparing between monkeys, there was one obvious difference in the time-course of preparatory subspace 375 occupancy. For monkey Ax, the initial, post-target peak during the cue-initiated context was larger than at any 376 other time, for any context. (Occupancy is plotted in normalized form, and thus the large initial peak for the 377 cue-initiated context necessarily means that all other peaks are plotted with values below unity.) In contrast, 378 for monkey Ba, the post-target and pre-movement peaks in the cue-initiated context were closer in magnitude. 379 When comparing the peak just before movement across contexts, the two monkeys were more similar. For 380 both monkeys, the pre-movement peak in preparatory subspace occupancy was a similar size across contexts, 381 and was slightly larger for the quasi-initiated context. We now ask whether the events within that subspace are 382 conserved across contexts. 383 Preparatory and movement events in state space 384  Fig. 2 shows similar snapshots for monkey Ax). Within 386 each snapshot, each trace plots the evolution of the neural state for one reach direction over a 150 ms period, 387 beginning at the indicated time. For this task, preparatory-subspace activity was quite low-dimensional: the 388 first two dimensions captured much more variance than subsequent dimensions. E.g., for monkey Ba, the third 389 preparatory dimension captured only 14% as much variance as the first. Thus, the preparatory subspace 390 projections in Figure 7a give a reasonably complete view of the preparatory state, and subsequent 391 quantification is based on those dimensions. Movement subspace activity was considerably higher 392 dimensional: there were many dimensions with structure that was clearly not noise. The projections in Figure  393 7b thus yield only a partial view. Subsequent quantification therefore employed all twelve dimensions. 394 There was a remarkable consistency, across contexts, in the patterns of the neural trajectories. The most 395 notable differences across contexts regarded not the patterns per se, but the time-course of preparatory-396 subspace events. In the cue-initiated context, target onset prompted preparatory-subspace activity to become 397 strongly selective for reach direction (red traces in reach, the preparatory-subspace pattern became more robust until it was approximately as strong as that in 402 the cue-initiated context. For the quasi-automatic context, the preparatory-subspace pattern was very short-403 lived: it grew rapidly following target onset then immediately collapsed prior to movement onset. However, 404 while present, the preparatory-subspace pattern during the quasi-automatic context closely resembled that in 405 the other two contexts (compare across contexts in the third-to-last column of Fig 7a). For example, the 406 dependence of the neural state on reach direction was similar across contexts (lighter / darker traces indicate 407 rightwards / leftwards movements). 408 Movement-subspace patterns were very similar across contexts, in both their pattern and their timing. Target 409 onset produced essentially no separation of movement-subspace states for the cue-initiated or self-initiated 410 contexts. This is consistent with finding that target onset produced little or no change in EMG activity. 411 Movement-subspace states started to differentiate between reach directions ~110 ms before movement 412 onset. This occurred at a similar time and in a similar way across contexts. During movement, the neural state 413 evolved according to rotational dynamics, as previously reported 19 and in a manner predicted by neural 414 network models 32 . As for such models, rotational dynamics were present in a subset of dimensions; the 415 dimensions shown here were chosen specifically to capture such dynamics for the cue-initiated context, and 416 naturally captures similar dynamics for the other two contexts. 417 Comparing between subspaces reinforces and extends the results described in Figure 6. Across all contexts, 418 preparatory-subspace activity always emerged before movement-subspace activity began. Preparatory-419 subspace activity and movement-subspace activity then showed considerable overlap: the former declined as 420 the latter emerged. Just before and during that period of overlap, the pattern of preparatory subspace activity 421 was similar across all three contexts. We explore this finding quantitatively below. 422

Quantification of similarity across contexts 423
A central question of this study is whether similar movement-subspace events are preceded by similar 424 preparatory subspace events. To quantify movement-subspace similarity, we measured the correlation (per 425 dimension) between time-evolving patterns measured during a 150 ms window starting at movement onset. To address this question, we focused on the preparatory subspace state at a specific moment: 70 ms before 436 movement onset. At this moment, movement-related activity is just starting to emerge. We have previously 437 hypothesized that the preparatory state seeds movement-related dynamics 10,18,19,21,27,32 . Under this hypothesis, 438 the preparatory state when movement-related activity begins is critical. This hypothesis thus predicts that the 439 preparatory subspace state at that time should be very similar across contexts, given that subsequent patterns 440 of movement-related activity are similar. We refer to that potentially critical preparatory state as the 'final' 441 preparatory state; after that moment, movement-subspace activity becomes strong and preparatory-subspace 442 activity declines to near-baseline levels. 443 The final preparatory state was similar across contexts. For each reach direction, the neural states across 444 contexts formed a cluster (these are grouped via covariance ellipses in Fig. 8a,b). Clusters were quite tight for To assess the time-course of similarity, at each time we computed the covariance, for a pair of contexts, 453 between the neural states in the preparatory space. Covariance reflects both similarity and strength, and is 454 thus expected to peak at a time when preparatory patterns are both similar and robust. When comparing the 455 self-initiated and cue-initiated contexts (Fig. 8c,d; blue) covariance rose as movement approached, peaking 120 456 ms and 130 ms (monkey Ba and Ax) before movement onset. This is consistent with what can be observed in 457 earlier figures: in the preparatory subspace, the pattern of states in the self-initiated context generally 458 resembles that in the cue-initiated context, but is weaker until the time of movement onset nears. 459 When comparing the quasi-automatic and cue-initiated contexts (Fig. 8c,d; blue) covariance rose rapidly, 460 peaking 80 ms and 90 ms (monkey Ba and Ax) before movement onset. These peaks occur just after activity in 461 the movement-subspace first begins to change, which occurred 90 ms (monkey Ba) and 94 ms (monkey Ax) 462 prior to movement onset in the quasi-automatic context. The narrowness of the peak underscores that the 463 similarity in preparatory subspaces states was short-lived; it was high for only a few tens of milliseconds, 464 around the time that movement-subspace activity was beginning to develop. Thus, while the pattern of 465 preparatory subspace activity in the quasi-automatic context comes to closely match that in the cue-initiated 466 context, this similarity occurs late (just as movement-subspace activity is developing) and is not sustained. This 467 is consistent with a preparatory process that is observed across all contexts, but that unfolds very rapidly in the 468 quasi-automatic context. 469

Relative timing of movement-related events 470
Our subspace-based analysis method isolates a movement subspace that is, by construction, occupied during 471 movement for the cue-initiated context. However, our method imposes no additional constraints on the timing 472 of movement-subspace events: they could begin well before movement onset, at the time of movement onset, 473 or after movement onset. We were particularly interested in the relationship between movement-subspace 474 occupancy and the onset of muscle activity. Does movement-subspace occupancy occur with timing 475 appropriate given a role in producing descending commands that cause muscle activity? For both movement-476 subspace occupancy and EMG, we assessed latency by measuring the moment when activity surpassed 10% of 477 its peak. To minimize the impact of filtering on latency, these analyses employed a 10 ms Gaussian filter (rather 478 than 20 ms for all other analyses) for both neural and EMG data. 479 Across monkeys and contexts, the movement subspace always became occupied just before the onset of 480 changes in EMG, with an average latency of 21 ms. For comparison, the conduction delay from cortex to 481 muscles, assessed via spike-triggered averages, can be as little as 6 ms from the time of a spike to the peak of 482 the EMG response 33 . This delay would be slightly reduced (to ~4 ms for the lowest-latency neurons) when 483 considering the beginning rather than the peak EMG response. Thus, activity in the movement subspace rises 484 early enough to potentially account for the onset of muscle activity. This was consistently true across contexts, 485 although with slight variability. The latency between the onset of movement-subspace activity and muscle 486 activity was, for monkey Ba and Ax, 27 and 20 ms (cue-initiated), 33 and 22 ms (self-initiated) and 19 and 6 ms 487 (quasi-automatic). These exact latencies should be interpreted with some caution: latencies are notoriously 488 difficult to assess because high thresholds overestimate latency while low thresholds are sensitive to noise. 489 Still, our best estimates indicate that, if cortico-motoneurons draw from movement-subspace activity, the 490 onset of such activity occurs early enough to plausibly account for the onset of muscle activity. 491

Is delay-period activity a reflection of motor preparation? 493
Early studies generally viewed delay-period activity as preparatory, but noted that directional selectivity often 494 reverses between delay and movement epochs, suggesting a suppressive role 34 . Subsequent experiments 495 revealed that delay-period and movement-related activity patterns typically differ 6,18,27,35 , ruling out the 496 hypothesis that preparation involves a subthreshold version of movement-related activity. A different 497 preparatory role for delay-period activity was suggested: serving as the initial state of a neural dynamical 498 system whose evolution produces movement 10,18,21 . In support, one can directly observe that the phase and 499 amplitude of movement-related dynamics flow from the state achieved during the delay 19 . Under this 500 hypothesis, preparatory activity is a necessary precursor to movement-related activity. Yet a recent study 501 yielded mixed evidence regarding the presence of a consistent preparatory state with and without a delay 22 . 502 That mixed evidence highlighted the longstanding uncertainty regarding whether delay-period activity 503 represents a true preparatory process, a facilitatory but non-obligatory process, or a suppressive process 504 specific to an artificial imposed delay 23 . 505 Our results reveal that the neural process present during a delay-period is not specific to that situation, but is 506 consistently observed in other contexts. This putatively preparatory process has the following properties. First, 507 activity occupies a neural subspace orthogonal to that occupied during movement. Second, such activity 508 consistently occurs before activity in the movement-related subspace. Third, regardless of the presence of an 509 imposed delay period, the neural state in the preparatory subspace achieves a similar movement-specific state 510 before movement onset. That similarity is maximal at the critical moment when movement-subspace activity is 511 just beginning. These results essentially rule out the hypothesis that delay-period activity is primarily 512 suppressive. The suppressive hypothesis cannot explain the presence of preparatory-subspace activity in the 513 quasi-automatic context, or the rising profile of preparatory-subspace occupancy in the self-initiated context. 514 That said, our results do not prove that preparatory-subspace activity is preparatory -they only show that it 515 follows the major predictions of that hypothesis. Proving that hypothesis would require specifically perturbing 516 activity in that subspace and observing the impact on behavior -something not currently feasible. That said, it 517 is known that a non-specific disruption of premotor cortex activity, at the end of the delay period, impacts RT 518 in a manner consistent with disruption of a preparatory process 17 . Given that evidence and the present 519 observations, we tentatively interpret preparatory subspace activity as preparatory and ask what conclusions 520 might follow. 521 20

Does preparation necessarily consume time? 522
Early behavioral investigations leveraged and supported the assumption that it takes considerable time to 523 'plan' or 'specify' the desired movement 2,5 . Influenced by this framework, subsequent physiology and modeling 524 studies proposed that preparation involves the time-evolving strengthening and shaping of neural activity 525 directly specifying movement parameters 9,36,37 . We have argued that movement is specified more implicitly, by 526 achieving a preparatory state that seeds movement dynamics 18,19,21,27,32 , but found evidence that it takes time 527 (100-200 ms) to consistently prepare 10 . Thus, a time-consuming preparatory process has often been considered 528 to be a major determinant of RT. This traditional framework has enjoyed explanatory power, and has 529 motivated successful comparisons of trial-to-trial RT variability with trial-to-trial variability of putatively 530 preparatory activity 4,[8][9][10]16 . 531 Yet there have been compelling recent arguments against the necessity of a time-consuming preparatory 532 process 23,26 . The present study supports those arguments. RTs in the quasi-automatic context were on average 533 221 and 208 ms, and were frequently 170-200 ms on individual trials. These short RTs occur despite the 534 inability to prepare in advance, and cannot be explained by anticipation: monkeys had no fore-knowledge of 535 target direction and did not attempt to 'jump the gun'. Given a delay of at least 50 ms for visual information to 536 reach motor cortex, and an afferent delay of at least 75 ms (including the sizeable lag between muscle activity 537 and movement onset), there cannot exist an obligatory preparatory process that necessarily takes 100-200 ms 538 to complete. That conclusion is further supported by the neural data. In the quasi-automatic context, 539 preparatory subspace activity lead movement-subspace activity by only ~40 ms, and the preparatory-subspace 540 state came to match that in the cue-initiated context in ~70 ms. These findings rule out the idea of a slow, 541 cognitive planning process that must complete before movement. These findings support our prior proposal 542 that preparatory activity is necessary to seed movement-generating dynamics. However, the development of 543 such activity can occur much faster than previously supposed. 544 Nevertheless, the influential idea that motor preparation tends to consumes time may have some merits. It 545 may be that preparation often, or even typically, spans time. In the self-initiated context, putatively 546 preparatory activity begins hundreds of milliseconds before movement-related activity. This raises a central 547 question: if preparation can be fast, why is it ever extended? Why do monkeys not simply wait to prepare until 548 just before movement onset? We can only speculate, but the ability to rapidly and consistently achieve the 549 correct preparatory state may not be something that can be counted on in all real-world situations, especially 550 for less familiar or more challenging movements. The motor system may thus have developed the conservative 551 strategy of preparing in advance when possible, allowing time for errors to be corrected before movement 552 generation begins 10,17 . We did indeed find that accuracy was slightly reduced in the quasi-automatic context, as 553 would be expected if movement is sometimes triggered before preparation has fully converged on the 554 appropriate preparatory state. 555

Putatively preparatory and movement-related processes overlap 556
Preparatory subspace activity overlapped with movement subspace activity by slightly more than 100 ms. This 557 overlap is consistent with (and indeed required by) the hypothesis that preparatory-subspace activity seeds 558 movement-subspace dynamics. Aspects of the overlap explain a seeming discrepancy between our results and 559 the recent finding of Ames et al. 22 that the neural state for no-delay trials does not pass through the state 560 achieved during the delay of long-delay trials. This might seem at odds with our finding that a consistent 561 preparatory-subspace state is achieved across all contexts. In fact, our results are fully compatible. 562 Preparatory-subspace activity in the quasi-automatic context achieves its maximal match with that in the cue-563 initiated context slightly after movement-subspace activity emerged. Thus, at the moment the match is 564 achieved, the full neural state contains both preparation-related and movement-related contributions. The 565 neural state at this moment will therefore not match that during the delay-period of the cue-initiated context, 566 when there is no contribution from movement-related dimensions. 567 With this conflict resolved, the present results support and extend two key conclusions of Ames et al. First, the 568 initial response to target onset can be similar with and without an imposed delay (compare the initial 569 development of preparatory subspace activity between cue-initiated and quasi-automatic contexts in Fig. 7). 570 However, this early response is unlikely to be an inevitable visual response: it is considerable weaker in the 571 self-initiated context. Second, when under time pressure, the neural state does not momentarily pause at a 572 stable state prior to the onset of movement-related activity (also see 8 ). Indeed, in the quasi-automatic context, 573 events are so compressed that preparatory-subspace activity is still developing as movement-subspace activity 574 is beginning. 575

Preparing versus deciding 576
Although our data argue against the conception of preparation as an intrinsically slow, cognitive process, they 577 are quite consistent with the idea that slow cognitive processes influence preparatory activity. It is well 578 established that preparatory activity in a variety of brain regions can reflect decisions regarding when or where 579 to move 31,[38][39][40][41][42] . Such decisions can sometimes unfold slowly or vacillate with time. In motor cortex, preparatory 580 subspace activity may therefore sometimes evolve slowly simply because the overall movement goal is being 581 decided slowly. 582 In the present study, the rising strength of pre-movement activity in the self-initiated context is somewhat 583 reminiscent of the rise of choice-related activity in decision tasks. However, in the present case the target was 584 always fully specified; target choice did not become more certain with time. Thus, strengthening pre-585 movement activity is unlikely to be related to target choice per se, and is more likely to reflect preparation to 586 execute a choice that was clear from the outset (also see 31,43 ). This suggests that having a clear movement goal 587 does not necessarily mean that low-level preparatory processes are fully engaged. Whether or not preparatory 588 activity develops may depend on whether it is reasonably likely that movement will be initiated soon. 589 Consistent with this interpretation, studies that use a fixed, predictable delay typically find that delay-period 590 activity ramps up with time (e.g., 9 ) while studies that use an unpredictable delay tend to find delay-period 591 activity that reaches a rough plateau after a burst following target onset (e.g., 10 ). 592 Thus, the processes of deciding what to do, preparing to do it, and actually initiating, may occur with variable 593 timing relative to one another. This hypothesis is potentially relevant to the finding that there exist neural 594 events that are predictive of movement initiation, yet precede movement by more than the typical reaction 595 time, and also precede self-report of the decision to initiate movement 43,44 . This is consistent with our finding 596 that preparatory subspace activity, in the self-initiated context, develops hundreds of milliseconds before 597 movement onset, and potentially before a definitive choice to execute movement has been made. 598

Cortical involvement despite fast RTs 599
Reaching can involve very rapid, nearly involuntary corrections that are likely to have a subcortical 600 contribution 25 . It has thus been suggested that entire movements may sometimes be produced subcortically, 601 perhaps with minimal cortical involvement 26 . In particular, a loud, startling sound can release a pre-planned 602 movement (the 'StartReact' phenomenon) with EMG-based RTs of 70-100 ms. While this short latency is due in 603 part to the use of a highly salient auditory stimulus (which suffers less sensory delay than a visual stimulus), it 604 also depends on the subcortically generated startle reflex. Given that the triggering impetus likely arises 605 subcortically, it has been suggested that movement generation itself may not depend on cortical involvement. 606 Yet a recent study argued against a reduction of cortical involvement in StartReact 45 . The authors instead 607 interpreted StartReact as a subcortical triggering of movement-generating dynamics that span cortical and 608 subcortical circuits in the same way as conventionally triggered movements. Our findings indicate that cortical 609 events are not necessarily slow, and are thus compatible with this view. EMG activity in the quasi-automatic 610 context could begin changing as early as 90 ms following target onset, with a mean of 150 ms and 130 ms for 611 the two monkeys. This is not as fast as during StartReact, but is only slightly slower when one considers the 612 additional sensory delay incurred by a visual stimulus (also note that in StartReact, movements are planned 613 ahead of time while in the quasi-automatic context they are not). The fastest RTs in the quasi-automatic 614 context are thus likely to be near the physiological limit. Yet we saw no evidence of reduced cortical 615 involvement. Indeed, the patterns of cortical movement-related activity in the quasi-automatic context were 616 very similar to those in the other two contexts. As in 45 , we do not suggest an absence of sub-cortical 617 involvement, merely a conservation of cortical involvement. 618 The conservation of neural events across contexts in motor cortex should not be taken to imply that events 619 other cortical or subcortical areas will be similarly conserved. Monkeys were clearly aware of the differences 620 between contexts, and behaved appropriately. It must therefore be the case that some brain areas perform 621 different computations in different contexts as necessary to initiate movement at the appropriate time. We 622 have indeed observed that neural activity in the supplementary motor area differs across contexts not only 623 during movement, but even before target onset (unpublished observations) and one suspects that this will be 624 true of a variety of cortical and subcortical areas. However, motor cortex appears to be playing a more 625 mechanical role: similar movements are driven by similar patterns of movement-related activity, following 626 similar patterns of preparatory activity, across a broad range of timing constraints. 627 24 Methods 628

Subjects and task 629
Subjects were two adult male macaque monkeys (Macaca mulatta) aged 10 and 14 years and weighing 11 -13 630 Kg at the time of the experiments. Daily fluid intake was regulated to maintain motivation to perform the task. 631 All procedures were in accord with the US National Institutes of Health guidelines and were approved by the 632 Columbia University Institutional Animal Care and Use Committee. 633 Subjects sat in a primate chair facing an LCD display and performed reaches with their right arm while their left 634 arm was comfortably restrained. The timing of stimulus presentation was controlled using a photodetector 635 (Thorlabs) to track individual frames on the display, such that the exact moment (within ~1 ms) of all events 636 was known. This allows accurate assessment of reaction times and neural response latencies relative to visual 637 events. Hand position was monitored using an infrared optical system (Polaris; Northern Digital) to track (~0.3 638 mm precision) a reflective bead temporarily affixed to the third and fourth digits. Each trial began when the 639 monkey touched and held a central touch-point. Touch-point color indicated context (Fig. 1). After the touch-640 point was held for 450 -550 ms (randomized) a colored 10 mm diameter disk (the target) appeared in one of 641 eight possible locations radially arranged around the touch point. Target distance was 130 mm for cue and self-642 initiated contexts and 40 mm for the quasi-automatic context (Fig. 1). Trials for different contexts / directions 643 were interleaved using a block-randomized design. 644 In the cue-initiated context, after a variable delay period (0-1000ms) the target suddenly grew in size to 30 mm 645 and the central touch point simultaneously disappeared. These events served as the go-cue, instructing the 646 monkey to make the movement. Reaches were successful if they were initiated within 500 ms of the go cue, 647 had a duration < 500 ms, and landed within an 18 mm radius window centered on the target. Juice was 648 delivered if the monkey held the target, with minimal hand motion, for 200 ms (this criterion was also shared 649 across all three contexts). 650 In the self-initiated context, the target slowly and steadily grew in size, starting upon its appearance and ending 651 when the reach began. Growth continued to a maximum size of 30 mm, which was achieved 1200 ms after 652 target appearance (most reaches occurred before this time). The reward for a correct reach grew exponentially 653 starting at 1 drop and achieved a maximum of 8 drops after 1200 ms. Monkeys were free to move as soon as 654 the target appeared. However, monkeys essentially always waited longer in order to obtain larger rewards. In 655 rare instances where no movement was detected 1500 ms after target onset, the trial was aborted and flagged 656 as an error. Requirements for reach duration and accuracy were as for the cue-initiated context. 657 deviation of 20 ms and averaged across trials to produce peri-stimulus time histograms. For measurements of 688 latency, we used a 10 ms Gaussian to minimize the impact of filtering on latency. 689 We recorded electromyogram (EMG) activity using intramuscular electrodes from the following 690 muscles: lower and upper aspects of the trapezius, medial, lateral and anterior aspects of the deltoid, medial 691 and outer aspects of the biceps, brachialis, pectoralis and latismus dorsi. The triceps were minimally active and 692 were not recorded. EMG signals were bandpass filtered (10 -500 Hz), digitized at 1kHz, rectified, smoothed 693 with a Gaussian kernel with standard deviation of 20 ms, and averaged across trials to produce peri-stimulus 694 time histograms. 695 Data pre-processing prior to population analyses 696 As in our previous work, we employed two pre-processing steps 19 . First, the responses of each neuron were 697 soft-normalized so that neurons with high firing rates had approximately unity firing-rate range (normalization 698 factor = firing rate range+5). This step ensures that subsequent dimensionality reduction (see below) captures 699 the response of all neurons, rather than a handful of high firing-rate neurons. Second, the responses for each 700 neuron were mean-centered at each time as follows: we calculated the mean activity across all conditions of 701 each neuron at each time point, and subtracted this mean activity from each condition's response. This step 702 ensures that dimensionality reduction focuses on dimensions where responses are selective across conditions, 703 rather than dimensions where activity varies in a similar fashion across all conditions 46 . 704

Identifying preparatory and movement dimensions 705
We recently developed a method that leverages the finding that neural responses in the delay-epoch are 706 nearly orthogonal to responses in the movement epoch 27  The optimization objective is normalized (by the singular values) to be insensitive to the relative dimensionality 726 and amount of response variance in the two subspaces. This normalization is particularly important in our case 727 since movement activity is stronger and typically has higher dimensionality than the preparatory activity. For 728 visualization, we need to choose two dimensions spanned by * +,-+ and * ./0-to define the plotted projections 729 (e.g., in Fig. 7). For * +,-+ we chose the basis so that the top two dimensions captured the most variance (with 730 all others ranked accordingly). For * ./0-the basis was chosen using the jPCA method 19 to capture movement-731 related oscillatory activity patterns. 732

Projections and reconstructions 733
For a given time V and for condition _, the projection of the population response onto the `Y Z preparatory 734 dimension is simply a weighted sum of all single-neuron responses: ? a +,-+ V, _ = * b,a +,- where 735 * b,a +,-+ is the element in the [ YZ row and `Y Z column of * +,-+ (see previous section) and < b V, _ is the 736 response of the [ YZ neuron. This is illustrated in Figure 4, where the orange weights w are taken from * +,-+ . 737 The projection onto each movement dimension is defined analogously. The response of a given neuron can

Latency of physiological events 752
To measure the latency of preparatory-and movement-subspace occupancy, we filtered the spike trains of all 753 neurons using a Gaussian kernel with 10 ms standard deviation. We recomputed the preparatory and 754 movement dimensions using these data and calculated the subspace occupancy as before. We measured the 755 latency as the first moment in time in which occupancy reached 10% of peak occupancy. 756 Similarly, to calculate the latency of the EMG with respect to movement onset, we filtered EMG activity of all 757 muscles using a Gaussian kernel with a 10 ms standard deviation. We then performed PCA on the EMG activity 758 for each context separately and projected the corresponding EMG responses onto the first PC. We measured 759 the latency as the first moment in which activity in the first PC reached 10% of peak activity. 760 Figure 1. Behavioral task. Monkeys performed the same set of reaches under three initiation contexts. a) Cueinitiated context. Trials started when the monkeys touched a red central point on the screen. After a brief delay (450 -550 ms) a red target appeared in one of eight possible locations (white dashed circles, not visible to the monkey) 130 mm from the touch point. After a variable delay period (0 -1000ms) the target suddenly increased in size providing the go cue to initiate the reach. b) Self-initiated context. Trials began as above, but the central point was blue. Subsequently, a small blue target appeared and gradually grew in size. Monkeys were free to initiate the reach as soon as the target appeared on the screen. However longer waiting times were rewarded with larger amounts of juice. c) Quasi-automatic context. The central point was yellow. Yellow targets appeared in one of eight possible locations. The initial appearance of the target was 40 mm from the touch point. Immediately after appearing, the target moved radially outward. Monkeys had to initiate the reach quickly in order to intercept the target before it reached the edge of the screen and disappeared. Targets were intercepted at a location near the location of the targets in the other two tasks (dashed circles). Each column shows the responses of a single neuron for the three initiation contexts. Each trace plots the trial-averaged firing rate for one reach direction (same color scheme as in Fig. 2). Gray shaded regions indicate the delay and movement epochs, used to define the preparatory and movement dimensions in subsequent analyses. All traces contain data that was aligned to target onset for the left-hand side of the trace, and to movement onset for the right-hand side of the trace. Individual trials had these two intervals spliced together before filtering and averaging. The sizes of these intervals and the moment of splicing were chosen to imitate the typical timing between target onset and movement onset (keeping in mind that this was variable across trials). For the cue-initiated context, the lefthand side contains data from -200 -450 ms relative to target onset (only trials with delays >400 ms were analyzed). The right-hand side contains data from -350 ms before movement to 400 ms post movement. The indicated time of the go cue is based on the mean reaction time. For the self-initiated context, spliced averages were computed using the same timing as above, to aid visual comparison. For the quasi-automatic context, the first 150 ms of the response is aligned to the target onset and the subsequent response is aligned to movement onset. Splicing was performed so that the interval from target onset to movement onset matched the mean reaction time. All vertical calibration bars indicate 20 spikes/s.