Mechanisms that allow cortical preparatory activity without inappropriate movement

We reveal a novel mechanism that explains how preparatory activity can evolve in motor-related cortical areas without prematurely inducing movement. The smooth eye movement region of the frontal eye fields (FEFSEM) is a critical node in the neural circuit controlling smooth pursuit eye movement. Preparatory activity evolves in the monkey FEFSEM during fixation in parallel with an objective measure of visual-motor gain. We propose that the use of FEFSEM output as a gain signal rather than a movement command allows for preparation to progress in pursuit without causing movement. We also show that preparatory modulation of firing rate in FEFSEM predicts movement, providing evidence against the ‘movement-null’ space hypothesis as an explanation of how preparatory activity can progress without movement. Finally, there is a partial reorganization of FEFSEM population activity between preparation and movement that would allow for a directionally non-specific component of preparatory visual-motor gain enhancement in pursuit.


Introduction
Preparation is an important component of voluntary movement. Throughout the motor system, many neurons show modulation of firing rate that occurs during movement preparation and is linked to parameters of the ensuing movement (Dorris et al., 1997;Glimcher and Sparks, 1992;Hanes and Schall, 1996;Munoz and Wurtz, 1995;Tanaka and Fukushima, 1998;Tanji and Evarts, 1976;Weinrich and Wise, 1982;Wurtz and Goldberg, 1972;Churchland et al., 2006a;Churchland et al., 2006b;Darlington et al., 2018;Hanes and Schall, 1996;Mahaffy and Krauzlis, 2011;Messier and Kalaska, 2000). Importantly, many neurons that seem to be tied to movement still have preparatory activity, even though there is neither movement nor muscle activity during preparation. How can motor and premotor cells in the cerebral cortex and even the brainstem and spinal cord (Glimcher and Sparks, 1992;Munoz and Wurtz, 1995;Prut and Fetz, 1999) show preparatory activity without causing inappropriate movement?
We have addressed the general question of how preparatory activity fails to evoke movement in the smooth eye movement region of the frontal eye fields (FEF SEM ), a critical node in the neural circuit for smooth pursuit eye movements. Neurons in FEF SEM are seemingly tied to pursuit. Inactivation or lesioning of FEF SEM produces dramatic defects in smooth pursuit (Keating, 1991;Shi et al., 1998). Micro-stimulation induces smooth eye movement (Gottlieb et al., 1993). Strong modulation of activity occurs just before the initiation of pursuit (MacAvoy et al., 1991). The modulation is tuned for the direction of visual motion and eye movement and is monotonically related to their speeds (Gottlieb et al., 1994;Tanaka and Lisberger, 2002a;Tanaka and Lisberger, 2002b). Therefore, the activity of FEF SEM cells seems to play an important role in the generation of smooth pursuit eye movement. Importantly, the same cells that discharge in relation to the initiation of pursuit also show an impressive ramp increase in firing rate during fixation, at a time when there is neither visual motion nor smooth eye movement (Mahaffy and Krauzlis, 2011;Tanaka and Fukushima, 1998). The preparatory activity grows over the hundreds of milliseconds preceding visual motion and the onset of pursuit, and its amplitude encodes expectation of upcoming target speed and combines with visual-motion input in a reliability-weighted manner to determine pursuitrelated responses (Darlington et al., 2018).
Several mechanisms have been proposed in various motor systems to explain how preparatory activity can evolve without causing movement. In the arm movement system, the current paradigm suggests that populations of neurons act as a dynamical system in which preparatory activity sets the initial conditions for the progression of movement activity (Churchland et al., 2010;Churchland et al., 2012). Importantly, preparatory population activity in primary motor cortex (M1) and dorsal premotor cortex (PMd) progresses in a way that avoids dimensions related to movement (Kaufman et al., 2014). It remains confined to 'movement-null' dimensions until just before movement initiation, and only then begins to progress along 'movement-potent' dimensions. Indeed, the preparatory and movement-related population responses in M1 and PMd occupy orthogonal dimensions (Elsayed et al., 2016). Furthermore, the use of output-null neural dimensions plays a role in both M1's initial processing of visuomotor feedback during movement as well as short-term forcefield adaptation in PMd (Perich et al., 2018;Stavisky et al., 2017).
In the saccadic eye movement system, movement is prevented during preparation via the action of an all-or-none inhibitory gate created by the action of omnipause neurons in the brainstem (Cohen and Henn, 1972;Keller, 1974;Luschei and Fuchs, 1972). Ramps of preparatory activity in the saccadic region of the frontal eye fields fail to trigger eye movements until the collective descending activity from the frontal eye fields and superior colliculus cause the omnipause neurons to cease firing, releasing the circuits that generate movement (Dorris et al., 1997;Hanes and Schall, 1996). Furthermore, subthreshold activity in the superior colliculus possesses some motor potential when omnipause neurons are inhibited by the trigeminal blink reflex (Jagadisan and Gandhi, 2017). However, there is no evidence that the pursuit system uses the all-or-none gate that controls saccades (Missal and Keller, 2002;Schwartz and Lisberger, 1994).
Here we propose a third, different, mechanism for movement prevention during motor preparation. The outputs from the FEF SEM seem to control the gain of visual-motor transmission for pursuit (Nuding et al., 2009;Tanaka and Lisberger, 2001). Further, visual-motor gain is dialed up in preparation for an imminent smooth eye movement (Kodaka and Kawano, 2003;Tabata et al., 2006). In the present paper, we show striking parallels between the progression of preparatory activity in FEF-SEM and the preparatory enhancement of visual-motor gain in the pursuit system. We argue that the output of FEF SEM dials up visual-motor gain in preparation for a behaviorally-relevant visual motion of a specific direction and speed, and that the use of FEF SEM output as a sensorimotor gain signal allows preparation to proceed without causing movement. We also show that preparatory activity in FEF SEM seems to contradict the major predictions of the dynamical system framework that has arisen from work in arm motor cortex (Churchland et al., 2010;Elsayed et al., 2016;Kaufman et al., 2014).

Results
We present three primary findings to support the conclusion that FEF SEM preparatory activity can evolve without causing smooth pursuit eye movement because its output does not drive smooth eye movement, but rather is used as a gain signal that controls access of visual motion to the oculomotor machinery. First, we demonstrate parallel progression of FEF SEM preparatory activity and an objective measure of visual-motor gain. Second, we show that preparatory activity in FEF SEM evolves in a manner that predicts movement when there is none, precluding for the smooth pursuit eye movement system the 'movement-null' space mechanism proposed for M1 and PMd preparatory activity in the arm movement system (Kaufman et al., 2014). Third, we show that there is some degree of reorganization of the FEF SEM population response, and we link the reorganization to a directionally nonspecific component of preparatory modulation of visual-motor gain. We suggest that gain control should be considered in all movement systems as one of several possible mechanisms to allow preparatory activity without movement. FEF SEM preparatory activity evolves in parallel with a preparatory modulation of visual-motor gain Neurons in FEF SEM are seemingly tied to the generation of smooth pursuit eye movement, yet display preparatory activity in the absence of any eye movement. We recorded single neurons in FEF-SEM while monkeys smoothly tracked moving targets during blocks of trials that presented target motion in a single direction. The example recording in Figure 1A-C shows the response of a neuron with a strong ramp increase in firing rate during fixation of a stationary spot, well in advance of either (1) target motion that starts 800-1600 ms after fixation onset or (2) the initiation of eye movement. The same neuron shows a second increase in firing rate that starts after the onset of target motion, around the time of the initiation of smooth pursuit (arrow in Figure 1C). We observed a wide range of preparatory-and pursuit-related firing rate modulation across our FEF SEM population, and there was a positive relationship between preparatory-and pursuit-related firing rate modulation ( Figure 1D, Monkey Re: Spearman's correlation coefficient = 0.17, p=0.02, n = 187 data points from 80 neurons; Monkey Xt: Spearman's correlation coefficient = 0.55, p=4.5Â10 À10 , n = 110 data points from 66 neurons). As explained in the Materials and methods, we ran multiple blocks of trials on most neurons using different directions of target motion, and each block provided a data point. Thus, more data points than neurons.
We hypothesized that preparatory activity in FEF SEM fails to cause movement because it is used downstream as a visual-motor gain signal. Gain can be dialed up by preparatory activity, but absent a movement-driving visual motion signal there will be no movement. This hypothesis is based on Solid and open symbols plot pursuit-related firing rate modulation as a function of preparatory-related firing rate modulation for the population of neurons recorded in monkeys Xt (Spearman's correlation coefficient = 0.55, p = 4.5 x 10 -10 , n = 110 data points from 66 neurons) and Re (Spearman's correlation coefficient = 0.17, p = .02, n = 187 data points from 80 neurons). The black arrow indicates the example neuron from panel C. Pursuit firing rate modulation was calculated as the average firing rate 51-150 ms after motion onset minus the average firing rate during the last 100 ms of fixation. Preparatory firing rate modulation was calculated as the average firing rate during the last 100 ms of fixation minus the average firing rate during 151-250 ms after fixation onset. Panel D is adapted from Darlington et al. (2018), except that here the analysis is performed during different behavioral conditions from the same data set and slightly different epochs are used to calculate pursuit firing rate modulation. The online version of this article includes the following source data for figure 1: Source data 1. Source data for Figure 1. previous publications showing that FEF SEM output during pursuit initiation is involved in controlling the gain of visual-motor transmission (Tanaka and Lisberger, 2001).
To test whether FEF SEM preparatory activity could be acting as a gain signal, we conducted experiments that measured only pursuit behavior, but were carefully contrived based on knowledge of the properties of preparatory activity in FEF SEM . We probed the state of visual-motor gain in pursuit by delivering a brief (50 ms) pulse of target motion at 5 deg/s during fixations leading up to single-direction pursuit trials. We delivered the pulse at different times during the build-up of preparatory activity and in different states of preparation. Because the test pulses of visual motion were always exactly the same and eye speed was zero at the time of the pulse, any effect of fixation time or preparatory state on the eye movement responses to the probe must reflect a change in the setting of visual-motor gain in the pursuit system.
It is important to note that the visual motion pulse experiments measured eye movement behavior only and were a direct follow-up from the analyses we performed on our neurophysiological data in FEF SEM . We matched all experimental conditions, including the timing of fixation and visual  Darlington and Lisberger. eLife 2020;9:e50962. DOI: https://doi.org/10.7554/eLife.50962 motion onset, in order to maximize the validity of comparisons between the behavioral and neurophysiology data sets. Further, the neurophysiological and behavioral experiments were conducted on the same pair of monkeys.
We found a series of parallels between the amplitude of preparatory activity and the setting of visual-motor gain, as probed by the size of the eye movement response to the pulse. Parallels include: (1) time course during fixation before target motion, (2) effect of variations in the expectation of target speed, and (3) direction specificity.
The behavioral assessment of visual-motor gain increases as a function of fixation time, paralleling the progression of preparatory activity in FEF SEM . Figure 2A illustrates data from one example session showing larger eye speed responses at later fixation times in response to identical, but differently-timed, pulses of visual motion. The same result appeared consistently in both monkeys we tested across multiple behavioral sessions ( Figure 2B). Modulation of FEF SEM preparatory activity showed a very similar time course across fixation for the overwhelming majority of neurons that had positive preparatory firing rate modulation ( Figure 2C, Figure 2-figure supplement 1). We can see the tight link between visual-motor gain and preparatory firing if we plot the behavioral results from Figure 2B against the preparatory firing from Figure 2C for each fixation time and each monkey ( Figure 2D). The relationship is fairly linear with a positive correlation between neural responses and behavior across our population of neurons (slopes were computed for each neuron using linear regression: monkey Re mean = 0.073 degrees/spike, p=2.34Â10 À11 , n = 135 data points from 66 neurons monkey Xt mean = 0.074 degrees/spike, p=2.76Â10 À11 , n = 67 data points from 45 neurons).
The behavioral assessment of visual-motor gain varies in parallel with preparatory activity when we change the expected target speed by changing the blend of target speeds in a block of trials. We showed previously that the amplitude of FEF SEM preparatory activity encodes an expectation of target speed based on experience in blocks of 50 trials with different blends of target speed ( Figure 3A; Darlington et al., 2018). Preparatory firing rate modulation was larger in magnitude ( Figure 3B) during the 'fast-context' (green traces, 80% of trials at 20 deg/s and 20% at 10 deg/s) compared to during the 'slow-context' (blue traces, with 80% of trials at 2 deg/s and 20% at 10 deg/ s). Based on behavioral assessment using pulses of visual motion during fixation, visual-motor gain during the preparatory period also is enhanced in the fast context compared to the slow context. Eye velocity responses were larger during the fast-context versus the slow-context when we presented the same visual motion pulses during fixation at different times (green versus blue in  Figure 3C, scatter plot in Figure 3D). In the fast-context versus slow-context, the mean eye velocity responses to the pulse were 3.02 ± 0.71 deg/s (SD) versus 2.27 ± 0.73 deg/s (SD), and the difference was statistically significant (p=8.30Â10 À6 , paired, two-sided Wilcoxon signed rank test, n = 26 behavioral experiments in two monkeys, z = 4.46, Cohen's d = 1.06).
The directional specificities of preparatory modulation of visual-motor gain and FEF SEM preparatory activity vary in parallel. To assess the directional specificity of preparatory visual-motor gain modulation, we delivered visual motion pulses during fixation again, but now in four different directions relative to the consistent direction of the pursuit target motion in a given single-direction block: 0 deg, 'same-direction';±90 deg, 'orthogonal-direction'; 180 deg, 'opposite-direction'. Across the full duration of fixation, eye speed responses were largest for same-direction pulses, intermediate for orthogonal-direction pulses, and smallest for opposite-direction pulses ( Figure 4A). For all directions, eye speed responses increased as a function of time during fixation for same-, orthogonal-, and opposite-direction pulses. We quantified the effect of fixation time by computing the slope of response amplitudes across pulse times. For the same direction, orthogonal direction, and opposite direction pulses, the mean (+/-S.D.) slopes across 30 experiments in two monkeys were 1.05 ± 0.59 deg/s per s, 0.73 ± 0.40 deg/s per s, and 0.72 ± 0.45 deg/s per s. The effect of fixation time on response amplitude was significant across all directions using 2-sided Wilcoxon signed rank tests: same-direction (p=2.60Â10 6 , z = 4.70); orthogonal-direction (p=1.73Â10 À6 , z = 4.78); and opposite-direction (p=4.78Â10 À6 , z = 4.78). The differences from same-direction were statistically significant using the paired sample, 2-tailed Wilcoxon signed rank test for n = 30 experiments on two monkeys: same versus orthogonal-pulses (p=0.0093, z = 2.60, Cohen's d = 0.63); same-versus opposite-direction pulses (p=0.029, n = 30, z = 2.19, Cohen's d = 0.62). Thus, there is a greater preparatory enhancement of visual-motor gain in the expected direction of the upcoming pursuit trial. Further, the increase in response amplitude over fixation time for all directions of pulses indicates a degree of directionally non-specific preparatory enhancement of visual motor gain.
FEF SEM preparatory activity also is related to the expectation of target direction created by adjusting the preponderance of target directions in a block of trials. We divided our FEF SEM population into three groups according to the relative difference between the preferred direction of each cell and the direction of the experiment: same direction, 0 ± 45 deg; orthogonal, +90 ± 45 deg and À90 ± 45 deg; and opposite, 180 ± 45 deg. Consistent with a larger behavioral preparatory enhancement of visual-motor gain in the expected direction, FEF SEM neurons display the largest modulation of firing rate during fixations leading to target motion towards their preferred direction ( Figure 4B). Preparatory firing rate modulation was smallest for upcoming target motions that were opposite to the preferred direction and intermediate for upcoming target motions that were orthogonal to the preferred direction.
We find even more compelling neural correlates of the behavior shown in Figure 4A using a semi-supervised variant of principal component analysis: demixed principal component analysis (dPCA) (Kobak et al., 2016). The primary difference is that dPCA retains knowledge of experimental conditions when finding components, allowing for identification of different patterns of population activity that are independent of, or dependent on, experimental condition. We performed dPCA on the preparatory responses of a subset of our FEF SEM population (n = 63 neurons) from which we were able to collect data during experiments toward and away from the preferred directions of each neuron. Thus, the sole condition in our dPCA is the direction of the ensuing target motion and eye movement. Our aim was to identify 'direction-dependent' and 'direction-independent' components to test the idea that FEF SEM contributes to the directionally specific and non-specific components of preparatory visual-motor gain enhancement shown in Figure 4A.
FEF SEM population activity can fully account for the directional features of preparatory visualmotor gain enhancement. The first three components obtained via dPCA account for~90% of the variance of our FEF SEM population preparatory response ( Figure 4C). Each of the three primary components predict features of the behavioral data shown in Figure 4A. Component one is directionindependent. The projections of FEF SEM preparatory population activity onto component one both increase across fixation for impending target motion toward and away from the preferred direction ( Figure 4D). The projections onto component one are consistent with the directionally nonspecific enhancement of visual-motor gain observed for the orthogonal and opposite-direction visual motion pulses. Component two is direction-dependent. There are two primary differences between the projections of FEF SEM population activity onto component two during preparation for target motion toward and away from the preferred direction ( Figure 4E). (i) The projections are offset from each other with the projections for toward and away motion sitting above and below each other, respectively. The offset between the projections is consistent with the behavioral finding of an offset between the eye speed responses to brief target motions in the same versus opposite direction from expected target motion: there is a substantial difference in eye speed responses to the same and opposite visual motion pulses even at the earliest fixation times we tested. (ii) The projection for motion toward the preferred direction increases and that for motion away from preferred projection decreases during the latter half of the fixation period. Component three also is direction dependent. The projection of FEF SEM population activity onto component three also shows a ramp increase for impending target motion toward the preferred direction and a ramp decrease for impending target motion away from the preferred direction. The increase and decrease of the projections onto components 2 and 3 are consistent with the larger enhancement of visual-motor gain across fixation time for the same versus opposite direction visual motion pulses. In conclusion, the neural basis for the behavioral preparatory enhancement of visual-motor gain can be fully reconstructed from the first 3 dPCA components of the FEF SEM preparatory population response.

Modulation of FEF SEM preparatory activity occurs along movementpotent dimensions
Studies of arm movement have shown that population preparatory activity in M1 and PMd evolves in a manner that does not predict movement (Kaufman et al., 2014). Movement is prevented during preparation because the population activity resides in 'movement-null' neural dimensions. We now test this idea on our population of FEF SEM neurons. A priori, such a mechanism could generalize to the smooth pursuit eye movement system, especially since humans and monkeys can initiate smooth pursuit in the absence of visual motion under certain conditions (Freyberg and Ilg, 2008;de Hemptinne et al., 2006;Kowler et al., 2019). Even if the output of FEF SEM truly is used as a gain signal, noise immunity might be enhanced if population activity resided in an output null state until there is a believable visual motion signal to drive pursuit initiation. Two mechanisms for preventing unwanted movement might be better than one.
We established the movement-potent dimensions for our sample of FEF SEM neurons from blocks of trials where the monkey pursued a patch of dots that moved in each of 8 randomly chosen directions ( Figure 5A). The population average of FEF SEM firing across our full sample of neurons was strongly tuned to the direction of target motion and pursuit ( Figure 5B), with a large increase in firing rate in the 'preferred direction' of the cell, a smaller increase when motion was at +/-45 degrees from the preferred direction, no modulation for visual motion orthogonal to the preferred direction, and decreases in firing rate for +/-135 degrees and 180 degrees from the preferred direction. We represented the movement-potent dimension for our population by computing the optimal linear model that related the pursuit-related firing of our sample of FEF SEM neurons to the eye movements evoked during the initiation of pursuit in eight directions. The linear model optimized two weights for each neuron: one related the neuron's firing rate to horizontal eye velocity and the second related the neuron's firing rate to vertical eye velocity. Our fitting procedure assigned a continuous distribution of weight magnitudes to the members of our population ( Figure 5C), showing that the model used the entire FEF SEM population and did not simply pick out a few particularly informative cells. The model worked well on data from pursuit trials that were not used to compute the weights: target motion at three different speeds (2, 10, and 20 deg/s) and two different contrasts (12% and 100%) from a separate block of trials that presented visual motion in a single, repeated direction. It produced fairly accurate predictions for horizontal eye velocity ( Figure 5D, slope = 1.09, r 2 = 0.85) and accurately predicted zero vertical eye velocities (data not shown). Because a model based on the responses to 8 directions of motion was able to predict well the responses in a different block of trials with a single direction of motion, we conclude that it is valid to use a single model across different blocks of behavior.
FEF SEM preparatory activity does not avoid movement-potent neural dimensions. The optimal linear model predicts movement when there is none, during fixation and preparatory activity. When we passed the trial-averaged population preparatory firing rate modulation from a single-direction block of pursuit trials through the model, we obtained a non-zero prediction for change in eye velocity across fixation ( Figure 6A and B). Importantly, the output of the linear model predicts eye movement in a direction that is appropriate for the upcoming target motion according to how neurons across experimental sessions were combined into a pseudo-population (see below): a large positive horizontal component and relatively smaller vertical component.
We obtained similar results when we asked whether we could verify the failings of the movementnull hypothesis for FEF SEM in neural responses from single trials. We generated 1000 single-trial pseudo-population responses by randomly sampling preparatory firing rate modulations from each cell for fixation-duration matched trials across our population. We passed each pseudo-population response into the optimal linear model to predict the change in horizontal and vertical eye speed across fixation, and computed eye direction and speed during fixation on each 'trial'. Consistent with the findings of Figure 6A and B, the single trial analysis predicts non-zero eye velocity with a significant projection in the direction of the subsequent pursuit trial ( Figure 6C and D). The mean predicted direction was À1.3 deg with a 95% bootstrap interval of À65.8 to +71.8 deg; the mean predicted eye speed was 2.9 deg/s. Thus, for the motor system we study, the data do not fulfill one important prediction of the null-space hypothesis: the optimal linear model for pursuit initiation predicts significant non-zero eye velocities driven by preparatory activity.
We made a number of modifications in adapting the analyses performed in Kaufman et al. (2014) to our data. These modifications were made due to a key difference in our behavioral paradigm: the upcoming direction of arm movement was explicitly cued in Kaufman et al. (2014); the direction of the upcoming visual motion was not explicitly cued in our task. Therefore, only the single-direction block allows for accurate preparation, as the monkey is able to anticipate the upcoming visual motion. However, the eight-direction block provides a more rigorous mapping of FEF SEM pursuit-related firing rate to eye velocity. Thus, we chose to find the optimal mapping of FEF SEM firing rate to eye movement in the 8-direction block and test preparatory activity in the single-direction block.
Our strategy was then to create as large of a population response as we could, without excluding data points or neurons. We also did not wish to bias our data collection for the single-direction experiment towards any part of the direction tuning curve of our recorded neurons, for example by only running the single-direction experiment in the preferred direction of our neurons. To this end, we ran multiple single-direction blocks of trials for each neuron that we recorded using target directions that were different from each other and at various points on each neuron's tuning curve. We then rotated each neuron's direction tuning curves while fitting the linear model to the 8-direction block in a manner that made it seem like all of the single-direction experiments were run in the same direction (0 degrees, rightward). We included multiple single-direction blocks from the same neurons       as if they were independent under the relatively safe assumption that there is a different neuron with a tuning curve that is naturally aligned in the manner that we rotated our data.
We performed several control analyses to confirm that none of our analytical choices produced our results. First, the findings of Figure 6 are not a product of oversampling the preferred directions of our FEF SEM cells during the single-direction experiments ( Figure 6-figure supplement 1). Second, we obtained the same results when we used only a single block of trials from each neuron so that our conclusions are strengthened statistically but do not depend on the use of multiple data points from each neuron as independent units (Figure 6-figure supplement 2). Third, a supplementary analysis that is more congruent with the analysis performed in Kaufman et al. (2014), and that uses a model based on the single-direction block, arrives at the same conclusions ( Figure 6figure supplement 3).
Partial reorganization of population activity from preparatory-to pursuit-related dimensions If preparatory and pursuit-related activity resided in orthogonal dimensions, then we would say that the population activity in FEF SEM reorganized completely in the transition from preparation to action. If they resided in parallel dimensions, then we would say that they did not reorganize at all. We now show that the truth lies between these two extremes by using principal component analysis to compare the neural dimensions related to preparation and movement. The existence of a partial reorganization explains why we find that preparatory activity predicts movement and still allows the operation of our system to align to some degree with the operation of the arm movement system, where there is a full reorganization.
After reducing the dimensionality of our preparatory-and pursuit-related population responses during the single-direction trial blocks, we analyze the first preparatory and pursuit PCs (PC Prep1 and PC Purs1 ), each of which captures more than 70% of the variance ( Figure 7A), the same amount captured by the dimensionality reduction in Elsayed et al. (2016). We validated PC Purs1 by showing that the projection of pursuit-related activity onto the PC Purs1 captures differences in both the speed of target motion and the contrast of the target: in parallel with the neural responses, the projections scaled with target speed and are larger in magnitude and shorter in latency for high-compared to low-contrast targets ( Figure 7B). As expected, given the results in the previous section using the optimal linear model, the projection of preparatory activity onto PC Purs1 shows a ramp increase across fixation ( Figure 7D). The main difference between the preparatory and pursuit projections is that the preparatory projection ramps up more slowly to a smaller magnitude compared to the pursuit projections.
We demonstrate a partial reorganization of population activity between preparation and pursuitrelated activity by computing the angle between PC Prep1 and PC Purs1 . We used a bootstrap approach that sampled trial-averaged neurons from our population, independently found PC Prep1 and PC Purs1 for the sampled population, and calculated the angle between them. We used a sampling procedure that created 1000 simulated population responses, each with 160 units having a uniform representation of preferred directions (see Materials and methods and Supplementary Figure 1 for more details). We find that the mean angle between PC Prep1 and PC Purs1 is 65.2 degrees and is significantly different from both 0 and 90 ( Figure 7C, p<0.001, two-sided bootstrap statistics, 95% bootstrap interval = 61.4-69.2 deg, n = 1000 iterations). Therefore, preparatory-and pursuit-related neural dimensions are neither aligned nor completely orthogonal in our population of FEF SEM neurons. As with the linear model, our findings were not influenced by our choice to treat multiple data points from each neuron as independent units in our pseudo-population (Figure 7-figure supplement 1).
To understand what features of the neural responses caused the reorganization of the population response, we examined how the PCA component loadings, defined as the weights relating each neuron's response to the principal component, changed between PC Prep1 and PC Purs1 . The distribution of the ratios between the PCA component loadings of PC Prep1 and PC Purs1 , generated from the bootstrap in Figure 3B, is significantly bimodal ( Figure 8A, Hartigan's Dip Test, Dip statistic = 0.0794, p=0.001). One peak is at a positive ratio and a smaller peak is at a negative ratio. A positive ratio indicates that a given unit behaves in a similar manner during preparation and movement, whereas a negative ratio indicates a change in behavior between preparation and pursuit. We conclude that there are two subpopulations in FEF SEM , and that the one with negative PC Prep1 /PC Purs1 ratios may be responsible for the partial reorganization of population activity between preparation and movement.
To test our hypothesis about the role of neurons with negative PC Prep1 /PC Purs1 ratios, we separated our population into units with positive (Subpopulation 1) and negative (Subpopulation 2) ratios and compared a number of properties of the two subpopulations. (1) Preferred directions ( Figure 8B): Subpopulation 1 consistently made up a larger proportion of units in our bootstrap analysis and contains a higher proportion of units with a preferred direction towards the direction of the single-direction experiment. Conversely, Subpopulation 2 contains a higher proportion of units with preferred directions away from the direction of the experiment. (2) Preparatory versus pursuit modulation: When we redid principal component analysis on the full (non-bootstrapped) data, neurons in Subpopulation 1 had statistically larger amplitudes of both preparatory-and pursuit-related modulation (compare red and black data points in Figure 8C; preparatory activity: p=0.019, Cohen's d = 0.34, pursuit activity: p=2.7Â10 À12 , Cohen's d = 0.95, 2-sided Wilcoxon rank sum tests). There is a significant positive correlation between preparatory and pursuit modulation in Subpopulation 1 ( Figure 8C, Spearman's correlation coefficient = 0.59, p=7.8Â10 À21 , n = 207 samples from 130    Figure 8G). These facts suggest that Subpopulation 2 is responsible for the partial reorganization of population activity between preparation and movement, and that the large difference in response amplitudes between the two populations is at least partly responsible for a lack of full reorganization between preparatory-and movement-related dimensions.
The existence of two subpopulations of FEF SEM neurons allows for a directionally-nonspecific component of preparatory visual-motor gain enhancement. In Subpopulation 1, preparatory modulation of firing rate has conventional direction tuning. It is large and positive when the upcoming target motion will be in the preferred direction of the cell, smaller when it will be orthogonal to the preferred direction, and negative when it will be opposite to the preferred direction of the cell ( Figure 8D,E). In Subpopulation 2, preparatory modulation of firing rate has weaker and non- (B) Black and red symbols summarize the distributions of preferred directions relative to the direction of the single-direction experiment for units in Subpopulations 1 and 2 in the bootstrap analysis. Error bars represent the middle 95% distribution obtained from our bootstrap analysis (n = 1000 iterations). (C) Black and red symbols plot preparatory-versus pursuit-related firing rate modulations for Subpopulations 1 and 2 in our full FEF SEM data set (n = 207 data points from 130 neurons for Subpopulation 1 and n = 90 data points from 65 neurons for Subpopulation 2). Panel C plots the same data from Figure 1D, except here it has been separated into Subpopulations 1 and 2 (D) Black and red symbols plot data for subpopulations 1 and 2 and show the normalized preparatory modulation of firing rate versus the direction of the experiment relative to the preferred direction of the cell. Error-bars represent the middle 95% of the bootstrapped distribution (n = 1000 iterations). (E), (F) Black, magenta, and blue traces plot normalized modulation of preparatory firing rate as a function of time from fixation onset when experiments were run in the same, orthogonal, and opposite direction as the preferred direction of the neuron. Data were averaged separately across neurons in Subpopulations 1 (E) and 2 (F). For each direction, the middle trace is the average and the flanking traces border the middle 95% of the bootstrapped distribution, n = 1000 iterations). (G) Black and red histograms plot the distribution of the angle between the first pursuitrelated and preparatory principal components for Subpopulations 1 and 2 across 1000 bootstrapped iterations. The online version of this article includes the following source data for figure 8: Source data 1. Source data for Figure 8. conventional direction tuning. Modulation is positive when the upcoming target motion is orthogonal or opposite to the preferred direction and absent when target motion will be toward the preferred direction ( Figure 8D,F). Together, the two subpopulations can explain two features of Figure 4A. The preparatory activity in Subpopulation 1 explains why preparatory enhancement of visual-motor gain is largest in the direction of the upcoming target motion. The smaller preparatory activity in Subpopulation 2 might explain the directionally-nonspecific, and smaller, component of preparatory visual-motor gain enhancement in orthogonal and opposite directions relative to the upcoming target motion.
To further examine differences between the two subpopulations, we repeated the optimal linear model analysis from Figures 5 and 6 separately on each subpopulation. Linear models generated from the two subpopulations perform roughly the same in predicting eye velocity during the single direction block ( Figure 9A,D). Subpopulation 1 predicts eye movement during preparation in the same direction as the upcoming visual motion and eye movement ( Figure 9B,C). Subpopulation 2 predicts no significant eye movement during preparation ( Figure 9E,F). However, it is worth pointing out that the spread around zero for horizontal and vertical eye velocities is quite large. These features are consistent with Subpopulation 2 dialing up visual-motor gain in a directionally-nonspecific manner and they suggest that the nonspecific component of visual-motor gain is fairly uniform across directions.
In our system, we not only characterize the population activity during preparation and movement, but also understand why it reorganizes in the way that it does and how that reorganization improves the performance of pursuit eye movements. A full analysis of FEF SEM neural responses during pursuit eye movements shows that (1) there is a partial reorganization of the population between preparation and movement, (2) the reorganization is not complete enough to place the population activity in a movement-null dimension during preparation, (3) output control of the gain of visual-motor transmission rather than of movement kinematics allows the reorganization to be incomplete without causing movement, and (4) the existence of two subpopulations of neurons explains the partial reorganization of population activity and allows the behavior to be preferentially prepared for target motion in an expected direction with a lower level of readiness for all directions of motion.

Discussion Preparatory activity without movement
Preparatory activity is ubiquitous in motor systems. In advance of all but the most short-latency and reflexive movements, preparatory activity appears at least in the primary motor cortex (Tanji and Evarts, 1976), the premotor cortex (Weinrich and Wise, 1982), the frontal eye fields for both saccades and pursuit (Bruce and Goldberg, 1985;Mahaffy and Krauzlis, 2011;Tanaka and Fukushima, 1998), the parietal cortex (Mazzoni et al., 1996;Shadlen and Newsome, 2001), the cerebellum (Gao et al., 2018), the superior colliculus (Dorris et al., 1997;Glimcher and Sparks, 1992;Munoz and Wurtz, 1995;Wurtz and Goldberg, 1972), and even in last-order interneurons in the spinal cord (Prut and Fetz, 1999). It seems clear that preparatory activity plays a crucial role in setting the state of the nervous system leading up to movements. Many of the neurons that show preparatory changes in firing rate seem to play key roles in selecting, initiating, and/or guiding movement. Yet, preparatory activity evolves without actually causing movement. Why? Different mechanistic explanations, all supported by data, have been proposed for different motor systems. The earliest solution, proposed for saccadic eye movements, is a 'gate' or 'switch' (Keller, 1974). The neural circuit that implements the switch is in the brainstem (Cohen and Henn, 1972;Evinger et al., 1982;Luschei and Fuchs, 1972). It has known internal connectivity, documented by electrophysiology and anatomical tracing with horseradish peroxidase (Hikosaka et al., 1978;Langer and Kaneko, 1990). The connectivity leads to switching behavior in computational models and the output pathways from the brain's switching circuit are appropriate to prevent saccades during preparation until it is time for the movement (Fuchs et al., 1985;Robinson, 1973).
A more recent solution, proposed for arm movements, suggests that the population of neurons in the motor cortex operates as a dynamical system (Churchland et al., 2010;Churchland et al., 2012). During the preparation of a movement, the population activity evolves within a set of dimensions that are 'movement-null' in the sense that population output is orthogonal to a later set of states that exists in 'movement-potent' dimensions (Elsayed et al., 2016;Kaufman et al., 2014). Analysis of population activity in the motor and pre-motor cortex supports the dynamical system explanation.
A third mechanism, based on our and others' research in smooth pursuit eye movements, involves the use of motor cortical output signals not to drive movement, but instead to modulate the strength of sensory-motor transmission. In the pursuit system, several lines of evidence, most notably the effects of microstimulation, imply that the output from the FEF SEM modulates the gain of visualmotor transmission (Nuding et al., 2009;Tanaka and Lisberger, 2001).
We imagine that all these mechanisms could be used in different blends by different motor systems. So, the challenge is to identify the mechanisms that prevent preparatory activity from causing movement in as many different movements as possible, explore the blend of mechanisms deployed by each motor system, and find the neural substrates of the different mechanisms.

The use of FEF SEM output as a gain signal allows preparation to progress without causing movement
In the present paper, we present evidence that the smooth pursuit eye movement system emphasizes gain-modulation as a mechanism to allow preparation to progress without causing movement. Even though preparatory activity in FEF SEM is movement-potent in the sense that it shares dimensions with pursuit-related activity of the same population, preparatory activity fails to cause smooth eye movement because its role is to modulate the strength of movement-potent visual motion signals that are not present during preparation. Without the visual motion signal that it acts upon, gain can be dialed up without causing movement. The smooth eye movement output of the system will remain zero.
In contrast, our population analysis fails to support the dynamical systems explanation of orthogonal preparatory-and movement-related neural dimensions. The preparatory-and pursuit-related neural dimensions are neither completely orthogonal nor completely overlapping. Thus, there is a reorganization of the population activity in FEF SEM between preparation and pursuit, but the reorganization is not complete enough to push preparatory activity into a movement-null dimension. In our system, we are able to understand in terms of the responses of its constituent neurons why the population reorganizes partially rather than fully, and we have a functional explanation for why the system might operate in this regime. We identified two subpopulations of cells in our data and one of them ('Subpopulation 2') seems to be responsible for the partial reorganization of neural dimensions between preparation and pursuit ( Figure 4D). Because the reorganization is not sufficient to prevent movement during preparation, we propose that Subpopulation 1 creates a highly-directional enhancement of visual-motor gain while Subpopulation 2 is responsible for a directionally non-specific component of preparatory visual-motor gain enhancement, in effect providing a rigid and fairly uniform prior for the direction of target motion. A potential benefit of the regime created by the two Subpopulations is that the system will be fully ready for an expected direction of target motion and never be caught entirely flat-footed if target motion occurs in a completely unexpected direction.
Previous work suggests that gating mechanisms play minor roles for pursuit. The discharge of the neurons involved in the switch for saccades is incompatible with the idea that pursuit might use the same switch circuit (Missal and Keller, 2002). The firing of omnipause neurons pauses completely during the execution of saccades of any direction and amplitude but exhibits directionally-tuned decrements of firing rate that are graded according to eye speed during smooth pursuit eye movement. While one could argue that the use of an absolute versus a dynamic gate to prevent activity from causing movement is a matter of semantics, we are suggesting something fundamentally different in this paper: movement is not prevented during modulation of FEF SEM activity by the action of an inhibitory gate, rather FEF SEM output is controlling the gate. Indeed, it is possible that FEF SEM output interacts with omnipause neurons. Omnipause neurons are anatomically connected to at least the saccadic frontal eye fields and their responses during pursuit align closely with properties of visual-motor gain (Langer and Kaneko, 1990;Missal and Keller, 2002;Schwartz and Lisberger, 1994).
Our findings are not due to the trivial conclusion of a lack of importance of FEF SEM in the generation of pursuit eye movement. Lesioning and inactivating FEF SEM results in large decrements of pursuit speed and an increase in the number of catch-up saccades (Keating, 1991;Shi et al., 1998). The output of FEF SEM (and possibly partner areas such as the Supplementary Eye Fields Missal and Heinen, 2001) is necessary to allow visual motion signals to drive the oculomotor machinery (Tanaka and Lisberger, 2001). Furthermore, there are trial-by-trial correlations between FEF SEM activity during pursuit and eye velocity (Schoppik et al., 2008). The fact that microstimulation of FEF SEM causes smooth eye movement seems to contradict our conclusion that the output from FEF-SEM is modulatory. We suspect that the artificial situation created by micro-stimulation will drive activity in brainstem oculomotor neurons simply because FEF SEM is anatomically connected to the motor system. Beyond general anatomical connectivity, micro-stimulation-generated smooth eye movements may say little about how FEF SEM output is actually used downstream.

Comparative advantages of different mechanisms for preventing movement during preparation
We suggest that the brain uses multiple mechanisms to prevent preparatory activity from causing unwanted and premature movement, and that the primary mechanism used by any particular movement system will depend on the organization of that particular system. Further, a system could use multiple mechanisms at the same time, perhaps emphasizing one or another.
The short latency and sensory-driven features of pursuit may mitigate in favor of a system where preparatory activity is used to modulate sensory-motor transmission. In pursuit, movement initiation is driven directly, with relatively short latencies, by sensory inputs from extrastriate visual area MT (Komatsu and Wurtz, 1989;Newsome et al., 1988). Outputs from MT and FEF SEM converge downstream in the pursuit circuit to control the activity of motoneurons (Lisberger, 2010;Mustari et al., 2009). Importantly, preparatory modulation of visual-motor gain is a genuine preparatory signal. FEF SEM preparatory responses encode the expected speed and direction of the upcoming target motion and FEF SEM seems to set the state of the pursuit system during preparation in a way that sculpts the subsequent visual motion signals (Darlington et al., 2018).
In the arm movement system and the motor cortex, it may be difficult to prevent activity in the motor cortex from affecting the firing of motoneurons, and so it is ideal to nullify the preparatory activity by contriving for it to reside in a movement-null dimension. Here, the link from sensory input to motor output is less direct than for pursuit and the output from the primary motor cortex and the premotor cortex affect the firing of motoneurons directly, over monosynaptic and disynaptic pathways (Dum and Strick, 1991;Griffin et al., 2015;Kuypers and Brinkman, 1970). That said, it is possible that gain control mechanisms also operate in arm movements, both to implement the essential function of adjusting to different contexts, and to allow preparatory activity without movement. Just as we think that FEF SEM is responsible for the preparatory aspects of pursuit and area MT is responsible for the movement drive, recent work in the mouse motor system revealed subpopulations of motor cortex neurons with distinct roles in preparation and movement . Furthermore, last-order interneurons in the spinal cord show arm-movement-related preparatory activity that could reflect motor cortical modulation of the gain of spinal reflex circuits (Prut and Fetz, 1999).
In saccadic eye movements, the need for high degrees of accuracy and precision in a totally open-loop movement probably requires the preparatory activity that exists at least in the frontal eye fields, the superior colliculus, and the parietal cortex, but also requires an absolute brake on movement until all the brain's ducks are in a row (Glimcher and Sparks, 1992;Hanes and Schall, 1996;Mazzoni et al., 1996). Here, the switching circuit in the brainstem prevents any movement until the activity that guides the direction and amplitude of the impending saccade is fully prepared to make a movement that is at the same time really quick and accurate (Robinson, 1973). For example, a monkey executes a 20 deg saccade in 40 ms with accuracy of better than 5% (Fuchs, 1967). By contrast, pursuit eye movements are much slower and less accurate, and arm movements rely partly on feedback to achieve maximum accuracy.
Preparatory activity is ubiquitous, but the different features of different motor systems may require different mechanisms to prevent movement during preparation. A switching circuit could exist for movements other than saccades, perhaps in a softer, more compliant form. Gain control, may be an ideal way to establish context sensitivity and adjust the responsiveness to descending signals in systems with short latencies and graded responses. The dynamical system regime may be specialized for neural systems where the neurons involved in preparation make synaptic connections directly onto final motor pathways.

Experimental model and subject details
As described in Darlington et al. (2018), two male rhesus monkeys aged 8-10 years and weighing between 12 and 14 kg were used in the neurophysiology experiments (Darlington et al., 2018). The same two monkeys were used for the new behavioral experiments presented here. The monkeys underwent surgeries to implant head-restraining hardware onto the skull and a scleral search coil to track eye movements. Following recovery, monkeys were trained to fixate and smoothly track moving visual targets. During experiments, analog signals produced by the scleral search system recorded vertical and horizontal eye position. Eye velocity-related signals were obtained by passing the position-related signals through an analog circuit that differentiated signals from DC to 25 Hz and rejected signals at higher frequencies (À20 dB/decade). Eye position and velocity signals were sampled at 1 kHz and stored for offline data analysis. After training, monkeys underwent another surgery in which a craniotomy was performed in an area centered over the smooth eye movement region of the frontal eye fields (FEF SEM ). A sealable, titanium chamber was fixed to the skull over the craniotomy. All procedures received prior approval by Duke's Institutional Animal Care and Use Committee and complied with the National Institutes of Health's Guide for the Care and Use of Laboratory Animals.

Method details Neurophysiological experiments
We present new analyses of neural data that were collected using methods detailed in Darlington et al. (2018). Briefly, we made extracellular single unit recordings in awake, behaving monkeys. Three Thomas Recording tetrodes were introduced into FEF SEM for isolation of single units. Visual stimuli were displayed on a 24-inch gamma-corrected CRT monitor with a refresh rate of 80 Hz placed 40 centimeters from the monkeys' eyes, creating a field of view that spanned 62 (horizontal) by 42 (vertical) degrees.
Each experiment was divided into discrete trials. All trials began with the monkey fixating a central black spot for 800-1600 ms, after which the fixation target was replaced with a pursuit target. The pursuit target was either a patch of 72 dots within a 4-degree aperture or a Gabor function see Darlington et al. (2018). The pursuit target initially underwent 100 ms of coherent local pattern motion at a defined speed and direction within a stationary, invisible aperture. The target and aperture subsequently moved en bloc with the same parameters as the previous local motion. The initial use of local motion followed by global motion helps avoid early catch-up saccades and has similar advantages as the Rashbass 'step-ramp' used in pursuit paradigms for spot-targets (Rashbass, 1961). Monkeys were rewarded with juice for successfully tracking the center of the target within a 4 Â 4 degree window.
During neurophysiological recording, we ran two different behavioral experiments. In the '8-direction' experiment, targets moved at 15 deg/s in a direction randomly chosen from the four cardinal and four oblique directions. In the 'single direction' experiment, targets moved in only one direction (chosen from the four cardinal and oblique directions). Thus, target direction was perfectly predictable. The 'single-direction' task was split up into blocks of trials that provided visual motion of different blends of speed. In the fast-context, 80% of the trials moved at 20 deg/s and 20% of the trials moved at 10 deg/s. In the slow-context, 80% of the trials moved at 2 deg/s and 20% of the trials moved at 10 deg/s. In a control-context, 100% of the trials moved at 10 deg/s. In both of the experiments, pursuit targets of high-(100%) and low-contrast (6 or 12%) were interleaved randomly.

Behavioral assessment of gain of visual-motor transmission
We performed two separate sets of behavioral experiments, without neurophysiological recordings, as a modified version of the single-direction experiment described above. We presented the same blends of targets, directions, and speeds but the pursuit target was present through the entire trial, including during fixation before the onset of target motion. On approximately half of the trials, the pursuit target delivered a brief pulse that comprised a 5 deg/s step of target speed for 50 ms. Pulses occurred at a random time during fixation, 550-1350 ms after fixation onset. In the speed context experiment, pulses provided motion in the same direction as the impending target motion. In an experiment that tested direction selectivity, pulses provided motion in one of four directions, the same direction, opposite direction, or one of the two directions orthogonal to the direction of target motion in the single-direction experiment. The purpose of the pulse in target velocity was to probe the state of visual-motor gain in the pursuit system. We confirmed that the brief pulse of target velocity evokes responses with all the same features discovered before with sinusoidal perturbations (data not shown), and we chose to use the pulse to better assess directional specificity of gain modulation during fixation (Schwartz and Lisberger, 1994).

Comparison with arm movement paradigm
Our behavioral paradigm for defining movement potent dimensions was very similar to the behavioral paradigm used in Kaufman et al. (2014). The random 8-direction pursuit task is the eye movement analogue to the center out reaching task. One notable difference is that we used a singledirection task to probe the preparatory activity whereas Kaufman et al. used the preparatory epoch during the center out task. We did not use explicit cues during the 8-direction block to allow for preparation to occur. Instead we used the single-direction block to allow for expectation-driven preparation. Several benefits to our approach include the use of single-direction eye movement epoch data for cross validation ( Figure 5D) and prevention of confounding variables like visual cues. There were no differences in the methods by which we collected neurophysiological data. Most neurons were recorded during different experimental sessions. This is consistent with half of the data presented in Kaufman et al. (2014) and all of the data presented in Elsayed et al. (2016).

Demixed principal component analysis
The method of demixed principal component analysis (dPCA) is described in detail by Koback et al. (2016). Briefly, dPCA is a semi-supervised dimensionality reduction technique that in addition to capturing the majority of the variance present in the data (e.g. PCA) pulls out, or 'demixes', features of the data that are task-dependent (i.e. stimulus, decision, etc.). It does so by first decomposing a neural matrix, X, with n rows that is mean-centered on zero into a sum of averages taken over various task parameters, f.
The core of dPCA is to then find a low dimensional encoding/decoding model (FD) for each X f that minimizes the loss function: FD produces an n x n matrix A, which could normally be solved via classical regression, yielding the ordinary least squares solution. However, A is not full rank and is instead solved as a reducedrank regression problem via singular value decomposition.
We used the MatLab code publicly provided from the Machen's lab to perform the dPCA presented in Figure 4 (https://github.com/machenslab/dPCA). Our goal in using dPCA was to discover features of the FEF SEM population response during preparation that are related to the expectation of upcoming direction of visual motion and eye movement. As direction is not predictable during the eight-direction block, we relied on data from the single-direction task to probe reliable preparatory responses. In this way, expectation of direction is implicit and built from experience as monkeys tracked targets in the same direction typically for about 700-800 consecutive trials. The direction of the single-direction task varied across experiments and was chosen at various points relative to the preferred direction of the neurons under study. In order to get a sense for the neural representation of expected upcoming target direction and to pool as much of our data together, we subsampled our population of FEF SEM neurons, limiting ourselves to neurons where we ran multiple single-direction experiments with target motion both toward and away from their preferred directions. Toward the preferred direction was considered to be any single-direction experiment run within 90 degrees of the preferred direction and away from the preferred direction was considered to be any experiment run greater than 90 degrees away from the preferred direction. Preferred directions were calculated from pursuit responses of each neuron to trials in a direction tuning block of trials (see Statistics section). Thus, the sole condition used in our dPCA is the expected (and impending) direction of target motion relative to the preferred direction.
Of the 146 neurons that we recorded, we were able to collect single-direction experiments run both toward and away from the preferred direction in 63 of our neurons. We used 1400 ms of firing rate during fixation for each of the two conditions (towards and away from preferred direction). Therefore, the X in our analysis was a 63 x 2800 matrix.

Linear model relating FEF SEM to eye velocity
We analyzed neurophysiological data and eye velocity from the random 8-direction block of trials to generate a linear model relating the modulation of firing rate of our population of FEF SEM neurons to changes in eye velocity: Here, E is a 2 Â 2000 matrix of eye velocity (horizontal, vertical velocity x eight directions, 250 ms of data per direction) averaged across all experiments. N 8D is a 297 Â 2000 matrix of firing rate modulation during the random 8-direction experiment (297 single-direction neural recordings from 146 neurons x eight directions, 250 ms of data per direction). W is the 2 Â 297 wt matrix that relates the firing rate of each neuron to modulation of horizontal and vertical eye velocity.
We took several steps to combine neural data collected during different experiments. The singledirection experiments were run in different directions for different cells in an attempt to sample the full tuning curve of our population. Because we were interested in how modulation of our population of cells predicts changes of eye velocity relative to the single direction, we rotated the tuning curves of each cell so that they were aligned according to the direction of the single-direction experiment. For example, if the single-direction experiment was run at 90 degrees, then 90 degrees during the random 8-direction experiment was considered 0 degrees, 180 degrees was considered to be 90 degrees, 270 degrees was considered to be 180 degrees, and 0 degrees was considered to be 270 degrees. We rotated eye velocity in the same way and averaged across experiments to get the 2 Â 2000 E matrix. For each neuron, firing rate responses to motion in each of the eight directions were averaged across trials, smoothed with a Gaussian filter (s = 20 ms, similar results were obtained using s = 10 ms), subtracted to have a mean of zero across all conditions, and normalized to the range across all conditions. To accommodate known lags between firing rate and movement, behavioral data was shifted forward in time by 25 ms. We repeated the analysis with shifting by 50 and 0 ms, but 25 ms yielded the best cross validation shown in Figure 5D. Nevertheless, repeating the analysis with the other temporal shifts yielded similar conclusions (data not shown). The weight matrix, W, was solved using regularized (ridge) regression.
Firing rates during fixation from the single-direction paradigm were processed in a similar manner. For each neuron, we averaged firing rate across trials, aligned to fixation onset. Each trial contributed data up to the time of the onset of target motion in that trial. We discarded the first 150 ms of averaged data to avoid any effects from the beginning of the trial and/or the saccade back to the center of the screen from the previous trial. We also discarded the last 50 ms of averaged data since there were too few trials with long enough fixation durations to generate a meaningful average. Again, firing rates were subtracted to have a value of zero at the start of the trial and normalized using the same ranges that were used for the normalization of the random 8-direction firing rates. The firing rates during fixation then were passed through the linear model generated from solving W of Equation (1) to obtain PE, the eye velocity predicted from preparatory modulation of firing rate: Here, N 1D is a 297 Â 1400 matrix of firing rates (297 data points from 146 neurons x 1400 ms of fixation data; firing rates were trial-averaged, Gaussian-smoothed, s = 20 ms, similar results with s = 10 ms) and PE is a 2 Â 1400 matrix of predicted eye velocity (horizontal, vertical velocity x 1400 ms of fixation). Predicted speeds (PS) were computed using standard trigonometry based on the horizontal and vertical components of the predicted eye velocity.
For the single trial analysis performed in Figure 6C and D, we used the same W matrix obtained from Equation (1). However, we computed preparatory firing rate modulation on single trials for each neuron as the average firing rate during the last 100 ms of fixation minus the average firing rate 150-250 ms after fixation-onset. Trials were matched by fixation time across cells and then randomly sampled (one trial per cell). These single trial data were normalized to the same range used to normalize N 8D and N 1D and passed through the linear model. For each of 1000 repetitions of the analysis, we computed the predicted eye direction as the arctangent of the predicted vertical and horizontal components of eye velocity and predicted eye speed as the square root of the sum of the squares of the predicted horizontal and vertical components.

Principal component analysis
We performed dimensionality reduction independently on preparatory-and pursuit-related firing rates using Principal Component Analysis (PCA) on their respective data matrices (N prep and N purs ). N prep is a 297 neuron x 1400 ms of preparatory-related firing rate matrix and N purs is a 297 neuron x 750 ms of pursuit-related firing rate matrix (125 ms x 2 contrasts x two target speeds). All firing rates were trial-averaged and Gaussian smoothed (s = 20 ms, similar results were obtained with s = 10 ms). As is standard for PCA, we preprocessed each data matrix by normalizing rows (firing rates for each neuron) to have unity range and then centering firing rates on their means by subtracting off the row means. Each PC represents an orthogonal vector in N = 297 (or N = 160 for the bootstrap analyses) dimensional neural space. We chose to focus all of the subsequent analysis on the first identified PC for preparation and movement (PC Prep1 and PC Purs1 ), because they each captured at least 70% of the variance of the full responses (Elsayed et al., 2016). The angle between PC Prep1 and PC Purs1 was calculated as: We also determined how the PCA component loadings for each unit changed between PC Prep1 and PC Purs1 by calculating the ratio PC Prep1 /PC Purs1 .

Pulse analysis
Trials with saccades, detected with a combination of acceleration and velocity thresholds, in the window from pulse onset to 200 ms after visual motion onset were discarded before averaging the eye speed responses to pulses in matched conditions. The magnitude of the eye speed response was estimated as the maximum eye speed achieved across the 200 ms following pulse onset.

Statistics
We did not use formal tests to predetermine sample size, but our sample sizes are comparable to those reported in previous studies. Data were collected from two rhesus monkeys and consist of 321 data points collected from 164 neurons across 95 experimental sessions. We used only cells for which at least four trials/direction were collected during a direction-tuning block. This brought the sample size to 297 data points from 146 neurons: 80 neurons (187 data points) from monkey RE and 66 neurons (110 data points) from monkey XT. For the behavioral pulse experiments, 26 experiments were run in two monkeys for the speed context analysis ( Figure 3) and 30 experiments were run in two monkeys for the effect of pulse direction experiments (Figure 4). Of the 30 pulse direction experiments, 27 had an early pulse onset time point of 400 ms for the same direction ( Figure 2). Hypothesis testing was accomplished using a mix of two-sided bootstrap statistics, two-sided Wilcoxon signed rank tests, and two-sided Wilcoxon rank sum tests. Parametric hypothesis testing led to the same conclusions. The bootstrap procedure used in Figures 7 and 8 and Supplementary Figure 1 randomly sampled 20 units from each of the eight groups with different preferred directions relative to the direction of the experiment. We randomly sampled without replacement to avoid rank issues when performing the linear fitting and PCA. We chose 20 units because the smallest number of units in one of the 8 groups of preferred directions is 24. Preferred direction was calculated for each neuron as the weighted circular mean of the responses during the 8-direction block. This gives the mean parameter of a von Mises distribution fit to the direction tuning data. Our bootstrap approach was chosen to generate populations with a uniform distribution of preferred directions as a way of controlling for any biases of preferred direction in our data collection. The bootstrap was repeated for 1000 iterations.

Ethics
Animal experimentation: All procedures received prior approval by Duke's Institutional Animal Care and Use Committee (protocol A085-18-04) and were in compliance with the National Institutes of Health's Guide for the Care and Use of Laboratory Animals.