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INTRODUCTION |
The dorsal premotor cortex (PMd) has a hypothesized role in the transformation of sensory stimuli into appropriate motor behaviors (Crammond and Kalaska 1996
; Godschalk et al. 1981; Johnson et al. 1996b; Mushiake et al. 1991; Weinrich and Wise 1982; Wise et al. 1992, 1997). Particular emphasis has been placed on visuomotor transformations, hypothesized to involve pathways from extrastriate visual areas to PMd and the primary motor cortex (MI) via the superior parietal lobule (for reviews see Johnson et al. 1996b; Milner and Goodale 1995; Wise et al. 1997). Neuronal populations in and surrounding the superior parietal lobule are directionally modulated before and during reaching movements (Johnson et al. 1996b; Kalaska et al. 1983), by visual and somatosensory stimulation (Albright 1984; Colby and Duhamel 1991; Steinmetz et al. 1987), and during conditional sensorimotor behavior (Mountcastle et al. 1975). Thus a variety of visuomotor signals reach the PMd.
The discharge of PMd and MI neurons has a pronounced sensorimotor character. In instructed delay tasks, PMd neurons exhibit prominent and prolonged premovement activity. This premovement activity is directionally tuned and modulated by the visual or remembered direction of the target (di Pellegrino and Wise 1993; Wise et al. 1992). Similar premovement discharge has been described in MI (Alexander and Crutcher 1990; Crutcher and Alexander 1990; Georgopoulos et al. 1989a; Johnson et al. 1996b; Tanji and Evarts 1976). Premovement activity in the PMd is highly modulated by visuospatial information that is significant for upcoming motor acts (Crammond and Kalaska 1994; di Pellegrino and Wise 1993; Johnson et al. 1996b; Shen and Alexander 1997a,b; Zhang et al. 1997). In addition, gaze (Boussaoud 1995) and spatial attention (Boussaoud and Wise 1993; di Pellegrino and Wise 1993) modulate the discharge of PMd neurons, as does motor error (Flament et al. 1993). The discharge of PMd and MI neurons is also highly correlated with several parameters of movement including direction, position, amplitude, speed, and force (for reviews see Ashe 1997; Georgopoulos 1986; Wise et al. 1997).
How does this transformation of a visual target into a motor signal occur? Several lines of evidence point to a distributed process by which the visuospatial activity is processed more rostrally (i.e., PMd) and the motor commands more caudally (i.e., MI). Premovement neuronal activity decreases along a rostral-caudal gradient from the PMd to MI, corresponding to a topographically organized input from the superior parietal lobule (Alexander and Crutcher 1990; Johnson et al. 1996b). There is also a rostral-caudal gradient from PMd to MI reflecting the processing of visuospatial to motor information (Shen and Alexander 1997a,b). Evidence also points to a temporal sequencing of the visuomotor transformation in which the more visuospatial aspects of the task are processed earlier and the more motoric features later (Shen and Alexander 1997a,b; Zhang et al. 1997). For example, in tasks in which the visual information is dissociated from the actual movement, the discharge is characterized by an early phase reflecting the direction of the visual cue and a late phase reflecting the direction of the upcoming movement (Crammond and Kalaska 1994; Georgopoulos et al. 1989b; Lurito et al. 1991; Shen and Alexander 1997a,b; Wise et al. 1996; Zhang et al. 1997). The population vector has been shown to rotate from the direction of a visual cue to that of the upcoming movement (Georgopoulos et al. 1989b; Lurito et al. 1991). Also, there is sequential processing of information about the direction, position, and amplitude of a movement in the discharge of PMd and MI neurons (Fu et al. 1993, 1995). Therefore, in PMd and MI, both spatial gradients and temporal sequencing of information appear to contribute to the transformation of a visual stimulus into a limb movement.
A more specific hypothesis states that the role of the PMd in visuomotor transformations is nonstandard mapping (Wise et al. 1996). For reaching movements, standard mapping refers to a sensorimotor transformation in which the stimulus is the object of the reach. Nonstandard mapping is the mapping of an arbitrary stimulus onto an arbitrary movement. The results of imaging, lesioning, and electrophysiological studies support the hypothesis that the PMd plays an important role in nonstandard mapping (for review see Wise et al. 1996). How might nonstandard mapping be achieved? Evidence exists for the learning of complex stimulus-response relationships in the PMd (Boussaoud and Wise 1993; di Pellegrino and Wise 1993). However, learning of all possible stimulus-movement combinations may be computationally prohibitive, and it is possible that neural substrates exist for the more common types of nonstandard mappings. Furthermore, the brain may not distinguish between standard and nonstandard mapping and may use a common neural mechanism for both. For example, consider the processing of movement direction during a visually guided, instructed-delay reaching task. If standard mapping was operative, the prediction is that directional tuning would be constant throughout the task (Wise et al. 1996). Another possibility is that the directional tuning changes throughout the task, consistent with a nonstandard mapping process in which a visual stimulus from one direction can be transformed into movements of a different direction.
To address this question the discharge of PMd and MI neurons was analyzed while monkeys performed a two-dimensional visually guided tracking task with an instructed delay period. Most previous studies have examined motor cortical activity during steplike reaching movements (for review see Ashe 1997; Georgopoulos 1986; Wise et al. 1997). In this report a new paradigm based on two-dimensional pursuit tracking with the arm was used. The paradigm was designed to 1) provide a long instructed delay period that continuously presented visual information about the speed and direction of the upcoming movement, 2) elicit controlled movements of a specified speed and direction in which both parameters were controlled independently, and 3) require continual matching of visual input with motor output to maintain a straight trajectory within an error envelope. Analysis of the directional tuning of the discharge of these neurons (Caminiti et al. 1991; Fu et al. 1993; Georgopoulos et al. 1982; Schwartz 1992) was used to study the neuronal transformation of a dynamic sensory stimulus into a motor output. These results reveal that the directional tuning is not constant across the cue and track periods and that during the cue period the preferred direction gradually changes. A preliminary account of these findings has been presented (Johnson et al. 1996a).
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METHODS |
Behavioral task
Experimentation was conducted according to the Guiding Principles for Research Involving Animals and Human Beings as endorsed by the American Physiological Society and was approved by the Institutional Animal Care and Use Committee of the University of Minnesota. Two female rhesus monkeys (Macaca mulatta, 4-6 kg) used a two-joint manipulandum to make visually guided arm tracking movements in the horizontal plane (Fu et al. 1993; Ojakangas and Ebner 1992). The task was performed on a workspace based on a modified center-out, eight target design (Georgopoulos et al. 1982), and its trial sequence is schematized in Fig. 1. The movements of the hand/manipulandum were displayed as a cross-shaped cursor on a computer monitor that was placed vertically, ~50 cm in front of the animal. The center of the monitor was aligned with the animal's sagittal plane, as was the center of the task workspace. The dimensions and size of the screen workspace and targets were identical to those of the actual physical workspace; however, horizontal movements were guided by visual cues mapped on a vertical plane. The task required the animal to track square targets that moved at constant speeds on the screen. The task sequence began by the animal positioning the center of the cursor (0.5 cm diam) in a square start box (1.44 cm2) at the center of the workspace for a random period ranging 1-2 s. After this hold period, a square target box of the same size appeared at the periphery of the workspace at one of eight target positions (0-315° in 45° increments) at a distance of 5 cm. This target then moved at one of four constant speeds (2, 3, 4, and 5 cm/s) along a straight line toward the start box. The time between target appearance and intersection with the start box is the "cue" period, and is analogous to the instructed delay period of other paradigms (for example, Crammond and Kalaska 1994; Georgopoulos et al. 1989a; Johnson et al. 1996b). During the cue period, the animal was required to maintain the center of the cursor within the start box. The animal could view its hand and manipulandum, but the tracking requirements of the task demanded that the animal concentrate on the screen.
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| FIG. 1.
Schematic of the pursuit tracking task. Cue and track periods are shown. Arrow denotes the direction of the constant speed target. Plus sign shows the location of the cursor through the trial sequence. See METHODS for further details.
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When the cue target reached the central start position, the start box was extinguished, and the target continued to move along the same trajectory at the same speed for 5 cm. During this interval, called the "track" period, the animal was required to make an arm tracking movement at one of four constant speeds (2, 3, 4, 5 cm/s) for a distance of 5 cm. At all times during the track period, the animal was required to maintain the center of the cursor entirely within the confines of the target box. At any point in the trial sequence, deviation of the cursor from the target aborted the trial and initiated a new trial sequence. All successful trials were followed by a juice reward, and after an interval of 4-8 s, a new trial was initiated. This trial sequence was repeated over the eight directions and four target speeds in a randomized block design, and the discharge of each neuron was evaluated over 10 trials for each direction-speed combination. The cue and track periods were equal in duration, with each period lasting 2.5, 1.67, 1.25, and 1 s for the target speeds of 2, 3, 4, and 5 cm/s, respectively.
Surgical, electrophysiological, and histological procedures
Once the monkeys had learned the tracking task, a chronic recording chamber (19 mm ID) was stereotaxically placed, and a head fixation halo was implanted (for details see Fu et al. 1993). The chamber was positioned to straddle the premotor and primary motor cortices. Anesthesia was induced and maintained with ketamine (20 mg·kg
1·h1 im) and xylazine (1-2 mg·kg1·h1 im) during the aseptic surgical procedure. Postoperatively, buprenorphine (0.05 mg/kg im) was administered for 5 days. Chambers were placed over three cortical hemispheres of the two monkeys (right and left in animal CR and left in DN).
After the animal's recovery, extracellular single-unit recording began using paralyene-coated tungsten microelectrodes (3-10 M
) and conventional electrophysiological techniques (Fu et al. 1993). A neuron was recorded if its activity was audibly modulated during the performance of the task or related to active reaching movements. After isolation of a single unit, the action potentials were time-amplitude discriminated. The output of the discriminator was digitized and stored at 1-ms intervals. The digitized data were analyzed in bin sizes of 20 ms and averaged over the number of trials. These binned firing frequencies were used in the period regressions of cell discharge as a function of direction. For contour plots of cell activity and calculations of a cell's preferred direction trajectory (see Analysis), each bin was convolved with a Gaussian function with a standard deviation of 20 ms.
The animal's tracking movements were calculated by recording the time-varying position of the manipulandum. The x and y positions of the manipulandum were calculated geometrically using angular data sampled from the output of the manipulandum potentiometers. The position data were sampled at 1 kHz and smoothed with the use of a 21-point moving average to prepare the position data for numeric differentiation. Differentiation yielded the x,y velocities from which the tangential velocity was computed. Position and velocity data were then compressed into 20-ms bins. Averaging of the position and velocity data over the 10 trials was performed after smoothing, differentiation, and compression. Eye movements were recorded using an infrared oculometer (Bouis Instruments, Karlsruhe, Germany). The vertical and horizontal position data were digitized at 200 samples/s and also compressed into 20-ms bins, but not smoothed. Electromyographic (EMG) activity was acquired using percutaneously inserted intramuscular wire electrodes. The signal was amplified, filtered (10-1,000 Hz band-pass), and digitized at 2,000 samples/s. The EMG signal was digitally rectified, compressed into 20-ms bins, and averaged over 10 trials. Eight muscles were recorded in both monkeys: pectoralis major (n = 7 records), spinal deltoid (n = 7), clavicular deltoid (n = 9), biceps (n = 10), triceps (long and lateral heads, n = 17), extensor carpi radialis (n = 11), and flexor carpi ulnaris (n = 12). Both the eye movement and EMG recordings were obtained during experimental sessions in which single-unit recordings were not undertaken.
After the completion of all electrophysiological and behavioral recordings, various positions in the chamber were marked by electrolytic lesions. Then each animal was initially anesthetized with ketamine (20 mg/kg im) and xylazine (1 mg/kg im), followed by a lethal dose of pentobarbital sodium (150 mg/kg ip). Intracardiac perfusion with saline containing heparin was followed by perfusion with Zamboni's fixative (4.3 g NaOH, 20 g paraformaldehyde, 18.8 g NaH2PO4, and 150 ml picric acid in 850 ml H2O). After removal of the brain, 50-µm frozen sections perpendicular to the longitudinal cerebral fissure were cut on a microtome throughout the areas of interest and stained with thionin. Recording tracks and electrolytic lesions were identified to map the microelectrode penetrations. The number of large (>29 µm) pyramidal cells in layer V was determined in each section to estimate the boundary between the premotor and primary motor cortex and for comparison of the recording locations with previous reports (Dum and Strick 1991; Fu et al. 1993; Weinrich and Wise 1982). Specifically, the number of large pyramidal cells was averaged along the cortical surface of each slice in 3-mm increments. Density maps of the large pyramidal cells across the cortical surface were constructed, and the isodensity contour line of eight large pyramidal cells was taken as an estimate of the boundary between PMd and MI.
Analysis
Neuronal spike trains and kinematic trajectories were aligned on the target onset at the start of the cue period, before averaging. Firing and kinematic data were then averaged over 10 repetitions for each of the 8 directions over the 4 target speeds. Neuronal firing frequency histograms with 20-ms bin increments were constructed from the averages. The firing was analyzed over three time intervals: the hold, cue, and track periods. The "hold" period represented the 500 ms before the appearance of the cue target, corresponding to the time in which the monkey held the cursor in the center start box. In addition to determining the mean firing from the trial averages, the standard deviation of the firing from the individual trial was calculated for the different periods.
Analysis of variance (ANOVA) based on the firing in individual trials was used as the initial step in assessing task-related modulation (Alexander and Crutcher 1990; Crammond and Kalaska 1996; di Pellegrino and Wise 1993; Georgopoulos et al. 1982; Shen and Alexander 1997a). The ANOVA was used to determine whether direction had a significant effect on the discharge in the cue or track periods and to detect significant changes in firing over the trial sequence from the hold, cue, to track periods. The criterion for either a direction or period effect was P < 0.01 (Tukey multiple comparisons). A neuron was considered task related if direction or period had a significant effect on its discharge.
Having identified the cells with a significant direction effect using the ANOVA, regression analyses were used to determine whether the discharge could be fit to a cosine model (Georgopoulos et al. 1982; Mardia 1972). For each target speed, the mean firing rate (f) for each cue or track direction (
), was fitted to a cosine function
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(1)
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Alternatively, this can be expressed as
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(2)
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The peak of the cosine function, referred to as the preferred direction (PD), is given as pd in Eq. 2 (for further details see Georgopoulos et al. 1982, 1984; Mardia 1972). Regression coefficients b0 and c1 denote the mean discharge over all directions and the modulation of the firing as a function of direction, respectively. Goodness-of-fit of the data to the cosine model (Eq. 1) was expressed as R2, with model significance (P < 0.05) requiring R2 > 0.7. The depth of directional modulation, Idir, was calculated by normalizing the slope of the regression, c1, to the averaged firing over all directions, b0 (Georgopoulos et al. 1982, 1988). Neurons whose discharge fit significantly to the cosine model will be referred to as "directionally tuned."
The PD was referenced to the direction of the moving target for all analyses. For example, in the diagram of the paradigm shown in Fig. 1, the direction of the moving target is 45° for both the cue and track periods. Therefore, if a cell's discharge during the cue period was highest for targets moving from the periphery at 225° toward 45°, it was referred to as having a PD of 45°. Similarly, if a cell's discharge during the track period was highest for movements from the center of the workspace out toward 45°, the PD was defined as 45°.
For further analysis of the directional tuning, the cue and track periods were halved into early and late epochs. Equivalent analysis of the PD of discharge for each of these smaller epochs was performed. To increase the temporal resolution of the directional tuning, cosine regressions (Eq. 1) were also performed over sequential 20-ms bins (Mason et al. 1998). This provided a nearly continuous estimate of the PD as a function of time and was referred to as the "PD trajectory." Here, discharge in each time bin was evaluated for a significant fit using a criterion of R2 > 0.7. An additional criterion was required of the PD trajectories to ensure that the determination of the PDs based on 20-ms bins reflected the directional tuning as a function of time. The depth of modulation (Idir) for each bin was required to be characteristic of the Idir obtained from the tuning curves based on the cue or track period averages. The Idir for each bin was required to be greater than the Idir -1 SD obtained from the entire cue or track period. The 5-95% confidence interval for the location of the PD for each 20-ms bin was also calculated based on the von Mises distribution (Batschelet 1981).
As shown in RESULTS the PD trajectories had a pronounced rotational character. To characterize this property of the PD trajectories, the latency, duration, and rotational velocity were calculated for the neurons demonstrating significant cue and track period PDs. Latency to directional discharge was defined as the time at which three contiguous 20-ms bins demonstrated significant directional tuning. Latency values were restricted to 1,000 ms to allow for comparison over the different cue period lengths. The duration of significant directional discharge was defined as the number of bins with significant directional tuning, expressed as a percentage of the total trial duration. The instantaneous rotational velocity of the PD trajectory was calculated between contiguous significant bins. Also, the maximal and mean rotational velocities were determined for each neuron and averaged over the population.
The EMG activity in the cue and track periods was also analyzed for significant directional effects using the single trial ANOVA (P < 0.01, Tukey multiple comparisons), similar to that undertaken for the cell discharge. The timing of the EMG activity was estimated using a binwise procedure for detecting a significant change in the EMG level, defined as exceeding the mean hold period activity by ±3 SD.
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RESULTS |
Characteristics of the tracking task performance
Tangential velocity profiles and hand trajectories resulting from the tracking of the four constant speed targets are shown in Fig. 2. During the cue period, there were no systematic excursions in the hand velocity at any target speed. For the slowest 2-cm/s target speed trials, there were occasional increases in hand velocity while in the start box 100-200 ms before the onset of the track period. The hand velocity increased over the initial 200-400 ms of the track period to approach the target velocity. The initial rise in hand velocity was followed by an overshoot and several subsequent crossings of the target velocity. Small fluctuations in the hand velocity were present at all target speeds, but the paradigm limited these excursions to within the target area, otherwise the trial was aborted. The slight irregularities in the hand velocity reflect frequent feedback-dependent error corrections required for visually guided pursuit tracking. For the fastest 5-cm/s target speed trials, hand velocity could increase ~100-200 ms before the complete superposition of the start and target boxes. The hand velocity climbed to a value of 5 cm/s over the initial 300-400 ms of the track period and then fluctuated around the target velocity. Further examples of the tangential hand velocity are shown superimposed on the firing data in Figs. 6-8. The tracking trajectories for the eight directions were remarkably straight and similar for the four different target speeds. This was due to the fact that the paradigm constrained both speed and path.
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| FIG. 2.
Tangential velocities are shown (left) for 4 tracking directions (0, 90, 180, and 270°) and 4 target speeds (2, 3, 4, and 5 cm/s). Movement trajectories for all 8 directions and 4 target speeds are also shown (right). All traces are the averages of 10 trials. Dashed horizontal lines indicate the tangential target velocity during the cue and track periods (i.e., ideal tracking speed during the track period). All traces were aligned on the initiation of the cue period, which is marked by dashed vertical lines. The onset of the track period is denoted by solid vertical lines.
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| FIG. 6.
Firing and speed profiles of a neuron with significant and congruent directional tuning in both cue and track periods. Histograms of average firing rates binned in 20-ms intervals are plotted over the trial sequence of hold, cue, and track periods for the 8 target directions and 4 target speeds (2, 3, 4, and 5 cm/s). Dashed vertical line denotes cue period onset, and solid vertical line denotes track period onset. Note that at the higher speeds the histograms appear less dense due to the smaller number of 20-ms bins being displayed. Averaged tangential hand velocity is superimposed on the firing rate. Below each set of histograms are plotted the cosine tuning curves ( ) of the averaged firing ( ) in the cue (left) and track (right) periods. The vertical bar above each averaged data point indicates 1 SD for the firing from the 10 trials.
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There was little directionally tuned EMG activity during the cue period in the eight arm muscles tested. The patterns of the arm and shoulder EMG are shown in Fig. 3 for two shoulder muscles (pectoralis major and posterior deltoid), an elbow extensor (long head of the triceps), and a wrist flexor (flexor carpi ulnaris). In the cue period the directional modulation in EMG activity was extremely small to nonexistent, a result also found for other instructed delay tasks (Georgopoulos et al. 1989a). ANOVA demonstrated no significant direction effect for the cue period (P > 0.01) for all eight muscles sampled (n = 73 records). As expected, the EMG activity was highly modulated during the track period in all muscles (P < 0.01). The ANOVA was based on the EMG activity in the entire cue period and may have missed changes in EMG activity that occurred before the onset of movement. Therefore an additional binwise procedure was performed to detect the timing of any changes in EMG activity. A significant change was defined as that exceeding the mean hold period activity by ±3 SD. The times of significant change invariably occurred at the cue-track period transitions (Fig. 3). Over all directions and muscles, the binwise procedure detected significant EMG changes at an average of 37 ± 71 and 112 ± 124 ms before track onset for the 5- and 2-cm/s trials, respectively. There were no significant differences in the onset of the EMG changes across the eight muscles recorded (P > 0.1, ANOVA). Therefore, as shown previously (Turner et al. 1995), the EMG activity during the cue period was modulated at most for a brief period (~100 ms) before track onset.
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| FIG. 3.
R e c t i f i e d e l e c t r o m y o g r a p h i c (EMG) activity from 4 muscles during the cue and track periods. Eight directions (0-315°, in 45° increments) of the slowest 2-cm/s target speed are shown. All traces result from averages of 10 trials aligned on cue signal onset and are shown for each muscle using the same scale. Dashed vertical lines denote the end of the hold period and cue onset; solid vertical lines divide the cue and track periods. Triangles above the traces indicate when the EMG activity differed by >3 SD from the mean activity during the hold period. Averaged epoch EMG activity as a function of direction is shown below the time course records.
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Eye movements, although unconstrained by the experimental paradigm, were also measured. Figure 4 details the horizontal and vertical position traces and the workspace trajectories of the left eye for four of the eight directions of arm tracking. For the slowest target speed of 2 cm/s, the eye tracking behavior may be summarized by a series of five stages, best appreciated in the time plots of horizontal (x) and vertical (y) eye position. First, before the appearance of the target while the hand was in the start box, saccades subtending up to 10-20° were directed over the entire workspace, apparently as the animal searched for the target. The saccades covered an area of the workspace larger than the 10 cm diam of the circular target array. Second, ~100-200 ms after the appearance of the target, the saccades stopped and the moving target was smoothly pursued for 400-500 ms. Third, after this period of smooth pursuit of the target, a second phase of saccades occurred, lasting ~1,000-1,200 ms. It should be stressed that in some trials the animal maintained smooth pursuit throughout the entire cue period and that this period of saccadic eye movement was highly dependent on the target speed. Fourth, ~700-900 ms before the track period, smooth pursuit of the target was resumed and continued through the first half of the track period. Fifth, during the final portion of the tracking period, the saccades resumed.
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| FIG. 4.
Horizontal (x) and vertical (y) components of the eye movements are shown over the temporal trial sequence and as trajectories over the workspace. Four of the 8 directions of the tracking task (0, 90, 180, and 270°) for the 2 extremes of target speeds, 2 cm/s (left) and 5 cm/s (right), are shown. An additional 1,000-ms period of eye movement data was included at the end of the tracking period. Leftmost dashed vertical lines mark the end of the hold period; solid vertical lines divide the cue and track periods. Rightmost dashed vertical lines mark the end of the track period. Single trials of unsmoothed eye movements are shown.
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The faster target speed of 5 cm/s resulted in a simplified eye movement behavior, summarized as three stages through the trial sequence (Fig. 4). As for slower tracking, the monkey initially made large amplitude saccades during the hold period until ~200 ms into the cue period. This was followed by the eyes moving to the target and smooth pursuit. The smooth pursuit continued through the cue period well into the track period, at which point the saccades resumed. For the faster target velocities, few saccades occurred during the cue period. Apparently, there was not sufficient time to allow for saccades in the cue period and still perform the task at the highest tracking velocities.
Directional modulation of neural activity
Neuronal activity was recorded in two animals, CR and DN. Of the total 240 neurons, 57 were obtained from the right hemisphere of DN, 103 from the left hemisphere of CR, and 80 from the right hemisphere of CR. Of these 240 neurons, the discharge of 201 (84%) showed a significant period effect, and the discharge of 228 (95%) showed a significant direction effect based on the trial-by-trial ANOVA (P < 0.01). All 240 neurons were task related, that is their discharge exhibited either a significant period or direction effect. The ANOVA is a highly sensitive test of a directional effect (Crammond and Kalaska 1996) but does not define the form of the directional modulation. Therefore to define the type of directional modulation, the average firing in the cue and track periods was fit to the cosine model (Eq. 1). Significant directional tuning as defined by the cosine model was found for 212/240 (88%) neurons. In 132, significant directional tuning was found for both the cue and track periods. In 26 neurons, significant directional tuning was present only during the cue period, and in another 54, the directional tuning was significant only in the track period. The majority of the analysis focused on the relationship of the directional tuning in the cue and track periods for cells in both PMd and MI.
Based on the histological findings, the cells in this study were recorded in PMd and MI. The locations of the penetrations corresponding to neurons with significant directional tuning are shown in Fig. 5 for the three hemispheres. In the left hemisphere of monkey CR (Fig. 5A), the recordings were located primarily in PMd. The penetrations in the right hemisphere of monkey CR (Fig. 5B) covered both PMd and MI. In the right hemisphere of monkey DN (Fig. 5C), the penetrations were predominantly in MI.
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| FIG. 5.
Locations of the penetrations corresponding to neurons with significant directional tuning for the 3 hemispheres studied. The left (A) and right (B) hemispheres from monkey CR and the right hemisphere from monkey DN (C) are shown. Electrode penetrations () and marking lesions ( ) are shown. The line drawn on the cortical surface is the estimate of the dorsal premotor cortex and primary motor cortex boundary.
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An example of a neuron with significant directional tuning for both the cue and track periods is shown in Fig. 6. The discharge during the cue and track periods exhibited broad directional tuning with increased firing for directions 270° to 45°. There was a reduction in firing below baseline at 180° for both the cue and track periods. The fit to the cosine tuning model in the cue period was highly significant over the four target speeds, with the R2 ranging from 0.94 to 0.99. The directional tuning during the track period was also highly significant with the R2 ranging from 0.97 to 0.99. The consistency of the firing on a trial-by-trial basis is demonstrated by the small standard deviations in the firing for each direction. Furthermore, the tuning curves demonstrated similar average PDs for the cue (358 ± 6°, mean ± SD) and track (355 ± 4°) periods over the four target speeds. The depth of directional modulation was less for the cue period than for the track period. The Idir averaged over the four speeds was 0.50 ± 0.06 for the cue period and 0.90 ± 0.03 for the track period.
The PD of the discharge of a cell was not generally constant through the trial sequence, an example of which is shown in Fig. 7. The discharge increased in the cue period for directions 45-180°, an increase that persisted up to the initial part of the track period. For directions ranging from 225° to 0°, there was considerably less activity above background in the cue period. The average PD during the cue period was 92 ± 12° (mean ± SD) for the four speeds. During the track period, the firing was tuned to the opposite direction. The average PD of the track period was 320 ± 4° over the four target speeds. The average absolute PD difference in the cue and track period was 132° for this cell, and the population data summarized in Fig. 10 shows that ~50% of the cells had an absolute PD difference of >45°. Again, the small standard deviations of the firing illustrate the consistency of the discharge over the individual trials. As for the discharge of the neuron shown in Fig. 7, the depth of modulation for the cue period was less than that for the track period. The Idir for the cue period was 0.46 ± 0.05 and for the track period 0.66 ± 0.04. For the subpopulation of 132 neurons with significant directional tuning in both the cue and track periods, the Idir for the cue period, 0.34 ± 0.21, was significantly less than that for the track period, 0.67 ± 0.31 (P < 0.00001, n = 132, paired Student's t-test).
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| FIG. 7.
Neuron with significant but directionally noncongruent mean firing in the cue and track periods. Discharge histograms with superimposed tangential hand velocity traces and cosine tuning curves use the same conventions as Fig. 6.
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| FIG. 10.
Distribution of the preferred directions, fractionated into early and late cue (cue 1 and cue 2) and track (track 1 and track 2) periods, for all neurons with significant directional tuning in 3 or 4 contiguous periods including the final track 2 (top row). Absolute differences between cue 1, cue 2, and track 1 relative to track 2 are shown (bottom row). The circular means ± SD are shown as a wedge superimposed on the absolute difference distributions.
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Neurons responding transiently to the onset of the cue target have been found in the premotor cortex and have been referred to as "signal neurons" (di Pellegrino and Wise 1993; Johnson et al. 1996b). These neurons, like that illustrated in Fig. 8, may show directional tuning (di Pellegrino and Wise 1993; Johnson et al. 1996b). For the cell shown in Fig. 8, firing transiently increased for ~500 ms after the onset of the cue target. This signal-related firing was directionally tuned with a significant cosine fit for three target speeds and had an average PD of 145 ± 17°. Directionality of the firing was less pronounced relative to the "set neurons" shown in Figs. 6 and 7 as judged by the smaller proportion of the variance accounted for by the cosine model and the increased standard deviations of the averaged data points. Overall, firing decreased in the track period for all directions and was not significantly directionally tuned at any target speed. In the second half of the cue period and the whole track period, the neuronal discharge was lower than that during the initial baseline period. Of the 26 PMd neurons with directional tuning only in the cue period, all demonstrated initial firing transients (i.e., signal-related). In the 132 neurons directionally tuned over both cue and track periods, firing continued throughout the cue period. Thus the distinction made by Weinrich and Wise (1982) between signal-related and set-related activity has clear parallels in the present data.
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| FIG. 8.
Neuron with increased firing confined to the cue period. Discharge histograms with superimposed tangential velocity traces and cosine tuning curves use the same conventions as Figs. 6 and 7. A solid line is drawn only through those data points with significant directional tuning (R2 > 0.7).
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Differences in directional tuning as a function of the task sequence
Of the 132 neurons demonstrating significant directionality in both cue and track periods, many had PDs that differed between the cue and track periods (see Fig. 7). The distributions of the period PDs for the cue (Fig. 9A) and track (Fig. 9B) periods are shown in Fig. 9. Because both left and right hemispheres were used for recording, the PDs were normalized to a right hemisphere convention by mirror-reversing the PD of each left hemisphere neuron about the vertical meridian (Funahashi et al. 1989; Georgopoulos et al. 1982; Steinmetz et al. 1987). For the cue and track periods, the distributions of PDs were uniform about the workspace (Rayleigh test for uniformity, P > 0.1 in both cases). For a given neuron, the absolute difference in PDs (a range from 0 to 180°) between the cue and track period was calculated (Fig. 9C). A predominance of vectors was in the 0 to 90° range, with a mean of 45.2 ± 44.9°. Almost one-half (47%) of the neurons had an absolute PD difference of >45°. The PD distributions obtained from the cue and track periods were significantly different (P < 0.001, n = 132, Hotelling's paired test) (Batschelet 1981). Furthermore, the relative difference distribution (Fig. 9D) was significantly different from zero along the x-axis (P < 0.001), but not along the y-axis (P > 0.2, Student's t-test on the sine and cosine fractions with Bonferroni correction). This y-axis symmetry implies that clockwise or counterclockwise deviations of the cue PD relative to the track PD were equally probable. The relative difference plot (Fig. 9D) further demonstrates the equal probability of clockwise and counterclockwise differences between the cue and track PDs.
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| FIG. 9.
Distribution of the preferred directions of all neurons with significant directional tuning (R2 > 0.7). Preferred directions were calculated from averaged firing of the cue or track periods relative to the direction of the moving target. A: distribution of the preferred direction (PD) vectors obtained from the cue period shown with the magnitude equal to the R2. B: distribution of the track period PD vectors with magnitude equal to R2. The outer circle in A and B denotes an R2 = 1. C: distribution of the absolute differences between cue and track PDs (range of distribution is 0-180°). D: distribution of the relative differences between the cue and track PDs.
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Evaluation of the PD differences between cue and track periods was performed at a higher temporal resolution by dividing equally each period and recalculating the PDs for each half period. The population distributions of the PDs calculated from each of the four epochs (i.e., cue 1, cue 2, track 1, and track 2) shown in Fig. 10 demonstrate uniform directional tuning (P > 0.1, Rayleigh test for uniformity). For each neuron, absolute differences of the PDs were calculated for each period (cue 1, cue 2, track 1) relative to the final tracking period (track 2). Relative to the late track period, the mean change in PDs was greatest for the early cue (79.2°), less for the late cue (45.7°), and least for the early track (22.3°) periods. The distributions differed significantly (P < 0.001 in all cases, Hotelling's paired test). The decreasing differences in the PD from the early cue to the late track epochs suggests that a sequential, and not abrupt, convergence of PDs is occurring. A similar analysis comparing cue 1 and cue 2 to track 1 yielded a similar systematic decrease in the mean differences in the PD as the trial progressed. The mean differences in the PDs from cue 1 to track 1 and from cue 2 to track 1 were 42.1 and 23.5, respectively. The difference between cue 1 and track 1 was significant (P < 0.001, Hotelling's paired test).
Functional-anatomic correlations
Of the 212 neurons with significant directional tuning in either cue or track periods, 122 neurons were recorded in PMd and 84 were in MI. Five penetrations resulting in six directional neurons were located in the vicinity of the supplementary motor area (see Fig. 5A) and thus removed for the comparisons of PMd and MI. Most of the neurons with significant cosine tuning limited to the cue period were located in PMd (20 of a total of 26). For the 54 neurons with significant directional tuning only in the track period, 26 were located in PMd, whereas 28 were in MI. Neurons with directional tuning in both cue and track periods (n = 132) were also found in both PMd (n = 73) and MI (n = 54). The proportions of these three types of directional neurons showed significant differences between the PMd and MI (P < 0.001, 
2 3 × 2 table). Thus directional activity limited to the cue period was more frequently found in PMd cortex, consistent with previous observations (Alexander and Crutcher 1990; Johnson et al. 1996b; Weinrich et al. 1984).
Several other findings demonstrate that there is a gradient of directional tuning properties across PMd and MI. The prevalence of four properties of directional tuning were mapped in 2-mm increments on the cortex from the central sulcus (Fig. 11): 1) directional tuning occurring only during the cue period, 2) directional tuning occurring only during the track period, 3) directional tuning occurring in cue and track that was <45° divergent between the two periods, and 4) directional tuning in both periods that was >45° divergent. As shown in Fig. 11A, neurons with significant directional tuning only in the track period comprised 45% of the total at 2 mm from the central sulcus, and the percentage decreased to 16% at the most anterior recording position in the PMd. Conversely, the percentage of neurons with significant directional tuning only in the cue period increased from posterior to anterior with only 10% near the central sulcus and 28% in the region of the PMd. As shown in Fig. 11B, the percentage of neurons with <45° difference in cue and track period PDs reached a maximum of 50% at 6 mm from the central sulcus and decreased to ~20% at 10 mm from the central sulcus. Neurons with >45° difference increased from 20% posteriorly to 37% anteriorly. It should be noted that the percentage of total neurons with a cue-track period PD difference of <45° decreased near the central sulcus because the number of neurons with track only directional tuning increased dramatically (see Fig. 11A). The changes in these directional tuning properties as a function of distance were statistically significant (P < 0.005, 2 4 × 4 table). A 4 × 4 table (4 directional tuning properties by 4 distance bins) was constructed by binning the data in 4-mm increments. A 4-mm binning was necessary so that all expected cell counts were >5, as required by the 2 statistic (Devore and Peck 1993).
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| FIG. 11.
Locations relative to the central sulcus of 4 functional types of directional tuning. A: proportions of neurons with directional tuning only in the cue period (Cue) and directional tuning only in the track period (Track). B: proportions of neurons with PD differences between the cue and track periods of <45° and >45°. Although shown in 2 graphs, the proportions of the 4 groups add to 100% for each 2-mm distance.
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Temporal profiles of the preferred directions of individual neurons
To evaluate the directional tuning of individual cells with increased temporal resolution, the firing rate of these cells was fitted to the cosine model (Eq. 1) in sequential 20-ms bins. As described in METHODS, a significant fit (R2 > 0.7) to the cosine model was required for each bin and a minimum depth of modulation criterion within 1 SD of the average Idir from the cue and track periods was imposed. Thus the minimum Idir of a bin for the cue or track period was required to be larger than 0.13 or 0.36, respectively. The resulting significant PDs were used to map the temporal sequence of the PDs, or PD trajectory through the trial. The PD trajectory is referenced to the direction of the moving target for both the cue and track periods (see METHODS).
To define the temporal evolution of the PD, Fig. 12A details the construction of a PD trajectory from the discharge of one cell. Figure 12 also shows the PDs based on the average firing for comparison. Tuning curves with the actual data points for each consecutive 20-ms bin in the hold, cue, and track periods are shown. The firing modulation during the 1st 10 bins (200 ms) while the cursor was held in the center hold period did not significantly fit the cosine tuning model (dashed green lines). The fits of the 1st 10 of the tuning curves (200 ms) in the cue period also did not meet either the model fit (R2 > 0.7) or depth of modulation (Idir > 0.13) criterion. Over the next 16 bins (320 ms), the fit of the data met both criteria (solid red lines), and the PD sequentially shifted from 90 to 0°. Over the next 10 bins the PD shifted further from 0 to 270°, after which the PD stabilized at 270°, and the depth of modulation progressively increased over the next 14 bins until the start of the track period. The maximum depth of modulation occurred 140 ms (7 bins) before the onset of the track period. Through the majority of the track period (solid blue lines), the PD remained constant at 270°, and the tuning curves gradually decreased in modulation. During the last 100 ms of the track period, there was a shift in the PD toward 225°. Note that for 3 bins in the track period, the fit did not meet both criteria (dashed blue lines).
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| FIG. 12.
Sequence of tuning curves derived from sequential 20-ms bins are shown in A for the hold (green), cue (red), and track (blue) periods. All records are averages of 10 trials for the fastest 5-cm/s target speed. Solid sinusoidal tuning curves are shown for significant fits (R2 > 0.7 and Idir > period Idir  1 SD), whereas dotted curves signify fits not satisfying both criteria. Data points from which the tuning curves were derived are superimposed. Shown below the sequence of binned tuning curves are the tuning curves and firing data averaged over the hold, cue, and track periods. The firing rate calibration bar applies to both binned and period tuning curves. The x-axis denotes the PD convention based on the direction of the moving target. In B, PD trajectories as a function of time are shown for averages based on the even (blue symbols) and odd trials (purple symbols) for the same neuron. The y-axis is time (the cue to track period sequence lasts 2 s for the 5-cm/s target speed), and the x-axis is the PD (ranging from 0 to 360°). The PD trajectories were referenced to the direction of the moving target (see METHODS). Therefore for this cell the PD trajectory pointed to 90° initially in the cue period and rotated clockwise to 270° at the start of the track period.
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Figure 12 demonstrates that there were smooth, gradual shifts in the PD and in the depth of modulation over the course of the trial. The correspondences between the peaks in actual firing and the maxima of the tuning curves demonstrate that the model fits were not spurious. Furthermore, the fits during the center hold period were invariably nonsignificant, as would be expected. The tuning curves and the firing data, averaged over the hold, cue, and track periods are also shown. The average discharge during the center hold period was not significantly modulated. However, the directional tuning curves obtained from the cue (R2 = 0.89, Idir = 0.53, PD = 312°) and track periods (R2 = 0.82, Idir = 0.85, PD = 278°) were significant and fit the cosine tuning model. The difference between the cue and track period PDs based on the average firing in these two periods was 34°, which minimizes the approximate 170° shift (80° at the beginning of the cue period to 270° at the onset of track period) evident in the PD trajectory that occurred over the cue period. The calculation of the PD based on the average firing failed to capture these temporal features of the directional tuning.
An additional analysis was undertaken to validate the PD trajectories. The PD trajectory was calculated from averages of odd and even trials taken from the randomized trial sequence for a single cell. The two PD trajectories as a function of time resulting from this split averaging are shown in Fig. 12B for the same cell. In both sets of trials, the cue period PD trajectory began around 80° and rotated clockwise to 0° and finally to 270° to converge with the PD trajectory of the track period. The tracking PD trajectory in both cases continued along 270° until the last third of the period. The PD trajectory based on the entire set of trials is quite similar (see Fig. 13B). Similar results were obtained for other cells.
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| FIG. 13.
Contour plots of the firing and PD trajectories for 4 neurons. The neurons are ordered in increasing difference between cue and track epoch based PDs (ranging from 33 to 123°). The x-axis is the trial sequence from cue to track (a total duration of 2 s, corresponding to a 10-cm target travel). The PD is mapped on the y-axis, ranging from 0 to 360°. The amplitude of firing relative to the hold period is coded by color (peak orange, minima purple). Significant preferred directions (by R2 and Idir criteria) calculated in 20-ms bins are marked by solid symbols. Confidence intervals (5-95%, based on the von Mises distribution) for the location of the PD are marked by smaller symbols on either side of the PD trajectory. All records are averages of 10 trials for the fastest 5-cm/s target speed.
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Therefore several points establish the validity and reproducibility of the PD trajectory calculation based on 20-ms bins. Previously, PD trajectories had been based on the calculation of the population vector and not the discharge of individual cells (Georgopoulos et al. 1984, 1989a; Schwartz 1993). First, the criteria used to calculate the PD trajectory were more stringent than typically used for epoch-based determinations of a cell's PD (Caminiti et al. 1991; Fu et al. 1993; Georgopoulos et al. 1982; Schwartz 1992). In this report we required not only statistical significance (R2 > 0.7) but also a minimum depth of modulation. Therefore the directional tuning based on 20-ms bins is as rigorous and valid (if not more so) than the directional tuning defined over longer epochs. Second, as shown in Fig. 12, the individual tuning curves were nearly continuous and in complete agreement with the PD calculations. Third, the determinations based on odd and even trials yielded similar results. Over the 320 movement trials necessary to generate a complete data set in which the speed and direction of the trial were randomized, the similarity of the results from the odd and even trials reveals the reproducibility of the PD trajectory. Fourth, the fits based on the firing during the center hold period were invariably nonsignificant, demonstrating that the results from the cue and track period were not artifactual. Fifth, at least three reports from other investigators using steplike reaching tasks have documented similar rotations in the PD trajectory when calculated on a finer time scale (Baker et al. 1997; Mason et al. 1998; Scott and Kalaska 1996). Also, because these other reports were based on a steplike reach, the observed rotations in the PD trajectory were not simply a function of the moving targets employed in this paradigm.
The PD trajectories ranged from those that were relatively unidirectional over the cue and track periods to trajectories that were nearly opposite in the cue relative to track periods. Examples of PD trajectories from four neurons are shown in Fig. 13. In this figure, the neurons are presented in terms of increasing absolute difference between the cue and track period PDs, with differences of 33, 34, 47, and 123° in A, B, C, and D, respectively. The PD trajectories reveal that the similarities and differences in the directional tuning during the cue and track periods are much more complex than revealed by the period average PDs. For the example shown in Fig. 13A, the PD trajectory became significant (R2 > 0.7) ~300 ms after the onset of the cue period. The PD was initially 90° but shifted to 160° by the end of the cue period, rotating counter clockwise with an average velocity of 100°/s. During the track period, the PD trajectory initially rotated another 20° counterclockwise before maintaining a constant direction of ~180° for the remaining two-thirds of the period. For the last 150 ms of the track period, the PD calculations were not significant. Examination of the firing profile reveals a similar picture. Firing relative to the hold period increased ~200 ms after the cue period onset but did not become directionally tuned for another 100 ms. The PD trajectory followed the ridge of increased firing (orange-red pseudocolor) with remarkable fidelity. The confidence interval was initially ±70°, reflecting the smaller depth of modulation in the early cue period. During the cue period the confidence interval constricted to ±30° and decreased to approximately ±10° midway through the track period. The confidence interval confirms that the changes in PD in the cue period exceed the uncertainty of the estimate.
In examples B, C, and D, the PD trajectories in the cue period demonstrated initial rotations covering up to 180° of the workspace and then aligned during the cue period to approximate the direction of the track PD trajectories. These examples have several common features. First, the direction modulation of the discharge was delayed relative to the appearance of the target by 150-200 ms. Baseline firing values evolved into significant directional tuning, and, subsequently, a PD trajectory developed. Second, the rotations of the PD trajectories were most marked in the cue period. The PD trajectory rotated in the clockwise direction in two of the cells (B and D) and counterclockwise in two (A and C). Third, the PD trajectories during the track period were relatively straight and approximated the track period average PD. In B the PD trajectory was initially directed to 90° and rotated at ~200°/s to 270° by the end of the cue period. The 180° shift of the PD trajectory in the cue period was larger than the 5-95% confidence limit. In C the PD trajectory started at 135°, shifting to 300° after a rotation of ~200°/s. Once the track period began, the trajectory remained within ±45° of the period average PD of 301°. In D the PD trajectory shifted clockwise from 45 to 300° with a rotational velocity of 210°/s. The PD trajectory continued to shift clockwise another 70° until the initial third of the track period, stabilizing around the period average PD of 226°. The confidence intervals demonstrate that the shifts during the cue period were statistically significant.
Temporal characteristics of the PD trajectories
From the slowest to fastest target speeds, the available time allowed for the transformation of directional visual information into directional motor commands ranged from 2.5 to 1 s. Because temporal constraints were found in the oculomotor behavior, the temporal profiles of the PD trajectories were also analyzed for similar constraints. The average latency of the directional discharge ranged from 299 to 388 ms for the fastest to slowest target speeds, respectively (Table 1). Linear regression analysis demonstrated that the average onset latencies significantly increased with decreasing target speed, with a slope of 33.3 ms per cm/s (F-ratio = 11.5, P < 0.001). Thus the detection of target directionality was delayed in the longer cue periods resulting from slower target speeds. Conversely, when the cue period was limited to 1 s by the 5-cm/s target, the onset of directional tuning occurred earlier. Directional tuning was maintained for a larger fraction of the trial duration as the target speed increased, resulting in a significant linear regression relationship (slope = 3.6% trial duration per cm/s, F-ratio = 15.3, P < 0.0001). Thus, when the cue period was limited by faster target speeds, directional tuning occurred 20% earlier and occupied 20% more of the time allotted before movement. These target speed-related changes in the onset and duration of directional tuning paralleled the changes seen in oculomotor behavior. As the cue period became longer, smooth pursuit was present for a smaller fraction of the cue period (Fig. 4).
Rotations of the PD trajectories were prominent, particularly in the cue period (see Figs. 12 and 13). Group averages of the maximal rotational velocity ranged from 438 to 552°/s and from 297 to 323°/s for the cue and track periods, respectively (Table 1). The difference in PD trajectory rotational velocity between the cue and track periods was highly significant (P < 0.001, at all target speeds, paired Student's t-test), whereas the differences due to target speed were not. Linear regression of the mean rotational velocity to target speed did not result in a significant relationship for the cue or track periods (P > 0.4, in both cases). Thus the rotational velocity of the PD trajectory was a function of the visuomotor processing occurring in the cue relative to the track periods but not the target speed, further supporting the conclusion that the PD trajectory was relatively invariant with respect to speed. Furthermore, a fixed rotational velocity would explain the increase in the relative duration of the PD trajectory during the shorter cue periods.
Composite profiles of the PD trajectories
A composite of PD trajectories is shown for the extremes of target speed in Fig. 14A to illustrate the temporal evolution of directional tuning. These trajectories were obtained from 20 neurons selected from the sampled population on the basis of having the largest number of contiguously significant PD trajectories. The selected sample had a uniform distribution of PDs in both cue and track periods (Rayleigh test for uniformity, P > 0.3 in both cases) and was characteristic of the entire population of cells (Fig. 14B). The track period PD was first rotated to align on 0°, and the PD trajectories for the cue and track periods were rotated by an equal amount.
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| FIG. 14.
Temporal profiles of contiguously significant PD trajectories from 20 neurons. PD as a function of time throughout the trial sequence is shown in A for the fastest 5-cm/s and slowest 2-cm/s target speeds. Vertical line at time 0 denotes onset of the track period. The PD trajectories were rotated such that the track period PD trajectory was aligned with 0°. The distributions of the average PDs from the cue and track periods are shown in B using the convention of Figs. 9 and 10. Comparison of the PD trajectories from the 2- and 5-cm/s target speed trials is shown in C. The 2-cm/s speed trials were reduced to 100 bins, the same size as the 5-cm/s trials. Bins with significant directional tuning from the 2- and 5-cm/s trials were plotted as x-y pairs. The linear regression line and the 99% confidence intervals are shown. The R2 was 0.80. Axes are normalized as in A to 0 ± 180°.
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This population of trajectories confirms that the PD differed during the cue and track periods. During the initial cue period, the PD could differ by as much as 180° from the track PD. For both 5- and 2-cm/s target speeds, the PD trajectory reached initial significance 100-200 ms after onset of the cue target, corresponding to the initiation of oculomotor smooth pursuit (Fig. 4). At either extreme of target speed, the PD trajectories during the cue period characteristically rotated over one to two quadrants of the workspace until the cue-track transition. Around this point, the PD trajectory converged to that of the track period PD (normalized to 0°), and the PD trajectories during the track period were relatively straight.
For the fastest target speed (Fig. 14A, top), the PD trajectories converged at the onset of the track period to a zone of ±30° of the normalized track period PD. For the slowest target speed (Fig. 14A, bottom), the PD trajectories did not fully converge to within ±30° of the normalized average until 500 ms after the track period onset. It follows from the design of the error constraint of the paradigm and the observed kinematics that the monkey did not have to move at the exact start of the track period for the slower target speeds. Movements could be delayed as much as 600 ms, corresponding to an error window of 1.2 cm for a target speed of 2 cm/s. The kinematic records revealed that movement was commonly delayed, and the hand did not reach target speed until 500 ms after the onset of the track period (see Figs. 2 and 5-7). Thus convergence of the PD trajectories to the preferred direction of the track period occurred in the time period in which the movement was being initiated. It has been shown that the discharge of premotor neurons is modulated by gaze angle (Boussaoud 1995). However, it should be stressed that the angular rotation of the cue period PD trajectories was not simply due to the eye movements because the sacc
Abstract
Introduction
Abstract
