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European Journal of Neuroscience, Vol. 11, pp. 4433±4445, 1999 ã European Neuroscience Association Encoding of target direction and speed during visual instruction and arm tracking in dorsal premotor and primary motor cortical neurons M. T. V. Johnson,1 J. D. Coltz3 and T. J. Ebner1,2,3 Departments of 1Neuroscience and 2Neurosurgery, and 3The Graduate Program in Neuroscience, University of Minnesota, Lions Research Building, 2001 Sixth Street SE, Minneapolis, MN 55455, USA Keywords: linear regression, Macaca mulatta, primate, pursuit tracking Abstract The encoding of direction and speed in the discharge of dorsal premotor (PMd) and primary motor (MI) neurons was studied during two-dimensional visually-instructed pursuit arm movements in which eight directions and four constant speeds were independently manipulated. Each trial consisted of equal durations of visual observation of target movement without hand movement (cue) and visual pursuit-tracking of the target with the hand (track). A total of 240 neurons was recorded from PMd and MI in two Macaca mulatta monkeys. Two classes of regression analyses were used to relate neuronal ®ring during the cue and track periods to direction and speed. First, the average ®ring from each period was ®tted to target direction or speed. Period-averaged ®ring signi®cantly correlated with direction more frequently in the track than in the cue period. Conversely, correlations with speed (with or without direction) were more common in the cue than in the track period. Secondly, a binwise regression evaluated the temporal evolution of ®ring correlations with direction and speed. Supporting the period-based results, signi®cant binwise correlations of the discharge with speed occurred preferentially during the cue period when there was no hand movement. Prior to movement, correlations of the ®ring with direction became signi®cant and continued through the movement. Both analyses demonstrated a distinct tendency for neurons to be modulated by speed information early and by direction information later. This temporal parcellation re¯ects both the sequential demands of the task and constraints placed on the neural computations. The early representation of target speed is hypothesized to re¯ect the need to calculate a `go signal' for the initiation of movement. Introduction Speed is a critical control parameter for volitional arm movements involving single or multiple joints. Several motor control strategies are based on the speci®cation and control of movement speed (i.e. `speed control hypothesis', Freund & Bundingen, 1978; Enoka, 1983; `speed-sensitive strategy', Corcos et al., 1989). Multijoint reaching movements are characterized by a stereotypic, bell-shaped velocity pro®le that appears to be an organizing feature of limb movement (for review see Georgopoulos, 1986). The control of speed is also interrelated with other movement parameters such as amplitude (Freund & Bundingen, 1978; Viviani & Terzuolo, 1982), error (Fitts, 1954), and trajectory (Soechting & Lacquaniti, 1981; Viviani & Terzuolo, 1982). Thus, several lines of behavioural evidence underscore the necessity of the central nervous system to be informed of, and control, speed of movement. Electrophysiological studies have described speed or velocity modulation of primary motor cortex (MI) neurons during limb movements (Hamada, 1981; Hore & Flament, 1988; Schwartz, 1992, 1993; Ashe & Georgopoulos, 1994). Modulation of neuronal ®ring by limb movement speed/velocity has also been found in the parietal cortex (Motter et al., 1987; Ashe & Georgopoulos, 1994), cerebellum (Mano & Yamamoto, 1980; Marple-Horvat & Stein, 1987; Coltz Correspondence: Professor Timothy J. Ebner/ Dr Michael T. V. Johnson, as above. Email: [email protected] Received 10 May 1999, revised 29 July 1999, accepted 13 August 1999 et al., 1999) and basal ganglia (Georgopoulos et al., 1983). Neuronal ®ring in the extrastriate visual cortices is also modulated by target speed (Colby et al., 1993; Lagae et al., 1993). Thus, a variety of cortical and subcortical structures play a role in the representation and transformation of the sensorimotor aspects of limb movement speed. However, no study of dorsal premotor (PMd) or MI neurons has systematically varied movement speed during multijoint movements and then quanti®ed the associated changes in neuronal discharge. Therefore, the ®rst aim of this study was to determine how the discharge of PMd and MI neurons is modulated in a pursuit-tracking task that independently manipulated speed and direction (Coltz et al., 1999; Johnson et al., 1999). The discharge of motor cortical neurons is also modulated by movement direction (Georgopoulos et al., 1982, 1984; Caminiti et al., 1991; Schwartz, 1992; di Pellegrino & Wise, 1993; Fu et al., 1993, 1995), distance and position (Fu et al., 1993, 1995; Kettner et al., 1988), offset torque (Kalaska et al., 1989), arm posture (Caminiti et al., 1991; Scott & Kalaska, 1997), gaze (Boussaoud, 1995; Boussaoud et al., 1998) and visuomotor aspects of reach (Shen & Alexander, 1997a, b; Zhang et al., 1997). This raises the question of how multiple parameters of movement are encoded without degrading the different types of information. Two multiplexing schemes, vectorial summation (Kalaska et al., 1989; Redish & Touretzky, 1994) and temporal parcellation (Fu et al., 1995) have been demonstrated to occur in the discharge of motor cortical neurons. Therefore, the second aim of this study was to determine the 4434 M. T. V. Johnson et al. timings of any speed, velocity and direction modulation in the discharge of PMd and MI neurons. An abstract of some of these data has been presented (Johnson et al., 1997). Methods Experimentation was conducted according to the National Institutes of Health Guide for the Care and Use of Laboratory Animals and was approved by the Institutional Animal Care and Use Committee of the University of Minnesota. Behavioural task The behavioural paradigm and recording procedures are described fully in a previous publication (Johnson et al., 1999). Brie¯y, two female rhesus monkeys (Macaca mulatta, 4±6 kg) were trained using juice rewards to use a two-joint manipulandum to make visuallyguided arm tracking movements over a horizontal workspace. To begin a trial (Fig. 1A), the animal positioned a cursor (0.5-cm diameter) in a square start box (1.2-cm diameter) located at the centre of the workspace. The duration of the `hold period' was randomly varied between 1 and 2 s. Following the hold period, the `cue period' began with a square target box (1.2-cm diameter) appearing at one of the eight target positions (0±315° in 45° increments), each 5 cm distant from the start box. The target moved at one of four constant speeds (2, 3, 4 or 5 cm/s) along a straight line to intersect the start box. During the cue period, the animal was required to maintain the cursor in the start box while the moving target was observed. When the target reached the central start box, the start box was extinguished and the target continued to move with the same direction and speed for another 5 cm until it reached the workspace periphery. During this `track period' the animal was required to keep the cursor within the target box by making a visually-guided, pursuit-tracking movement. The trial was aborted if at any time the cursor fell outside the start box or the target during the track period. Using a randomized block design, each direction±speed combination was presented 10 times. Figure 1 shows that the animals were able to track at the required speeds (C) using straight handpaths (B). Details of the behaviour including the eye movements and EMG (electromyographic) activity are described in the earlier report (Johnson et al., 1999). Surgical, electrophysiological and histological procedures After the task was learned, chronic recording chambers were placed to straddle the dorsal premotor and primary motor cortices using aseptic techniques under full anaesthesia (Johnson et al., 1999). Once recovery was complete, conventional techniques were used to record single units with paralyene-coated tungsten microelectrodes (3±10 MW). A neuron was recorded only if its activity was audibly modulated relative to the task or to active reaching movements. Following discrimination, a spike train was digitized (1-ms intervals), and binned to 20 ms. The x and y positions of the hand/cursor (sampled at 1 kHz from the manipulandum potentiometers) were smoothed using a moving average extending 6 20 points. The x, y and tangential velocities were obtained by numerical differentiation. Both position and velocity data were then compressed into 20 ms bins. The spike trains and kinematic data were then aligned on target onset at the start of the cue period and averaged over trials of like direction and speed. Eye movements and EMG activity were also acquired (see Johnson et al., 1999 for details). Analysis Linear regression analyses were used to relate the neuronal discharge to direction and speed. Direction was treated as a unit vector with the origin centred on the workspace. Speed was de®ned as a scalar describing the rate of target movement irrespective of direction. Velocity is a vector with both direction and magnitude (i.e. speed). Operationally, therefore, velocity modulation was de®ned as the simultaneous modulation of a cell's discharge by both direction and speed over a speci®ed time interval (see below: Binwise regression methodology). Period regression methodology FIG. 1. (A) Schema of the tracking paradigm and trial sequence. (B) Hand path trajectories (average of 10 trials in each direction) for the 2 cm/s target speed. (C) Pro®les of the tangential velocity of the hand over the trial sequence for the four target speeds of 5, 4, 3 and 2 cm/s. The tangential velocity traces for movements along 0, 90, 180 and 270° were superimposed with each trace representing an average of 10 trials. The vertical dotted line at time zero indicates the start of the cue period. Target speed is indicated by the interrupted lines. The initial analysis consisted of ®tting the average ®ring in the cue or track periods to each of two predictors, direction and speed, using separate regression models. These are referred to as `period regressions'. For each of these models, the data from all 32 direction±speed combinations (eight directions and four speeds) were used. Because each model (equations 1 and 2) involved 32 data points and two predictors, the criterion for a signi®cant ®t was, in terms of regression, an R2 > 0.2 (F-test, P < 0.05). Regression of the average ®ring to the predictors was determined separately for the cue and track periods. For the linear regression to direction, the mean ®ring, f, for each direction, q, was ®tted to a cosine and sine function, i.e. a cosine tuning model (Georgopoulos et al., 1982; Schwartz, 1992; Fu et al., 1993). f(q) = a0 + a1 cos(q) + a2 sin(q) (equation 1) This equation can be rearranged to f(q) = a0 + c1 cos(q±qpd) in which qpd is the preferred direction and c1 is a measure of the depth of modulation (Georgopoulos et al., 1982). The preferred direction was Ó 1999 European Neuroscience Association, European Journal of Neuroscience, 11, 4433±4445 Motor cortical encoding of direction and speed 4435 referenced to the direction in which the target was moving (Johnson et al., 1999). To determine the relationship between ®ring and speed, the regression model ®tted the mean ®ring, f(s), to target speed, s. f(s) = b0 + b1 s + b2 s2 (equation 2) 2 The s term was included in the model to allow for nonlinearity in the speed coding and to balance the number of terms with those used for direction (equations 1 and 3). Binwise regression methodology To evaluate the temporal evolution of the correlations of the discharge with direction and speed, a multivariate `binwise' regression was performed as used previously (Fu et al., 1995). The model used equation 3 to relate the ®ring rate, on a ®ner scale, to both target direction and speed over time (t). f(t) = d0(t) + d1(t) cos(q) + d2(t) sin(q) + d3(t) s + d4(t) s2 (equation 3) Firing, f(t) and the regression coef®cients, dn(t), are now functions of time. The ®t to the model is calculated bin by bin over the cue and track periods. To calculate the binwise regression (equation 3), the spike data was ®rst smoothed by ®tting a Gaussian function with a standard deviation of 40 ms to each bin. The multiple regression algorithm differed from that used previously (Fu et al., 1995) in that type II sums of squares were used to evaluate the contributions of the partial regression terms to the total model variance rather than a best R2 model optimization procedure (Neter, 1996). The two directional terms [d1(t) cos(q) + d2(t) sin(q)] were combined for the partial R2 for direction and the two speed terms [d3(t) s + d4(t) s2] were combined for the partial R2 for speed. Both partial R2s were directly comparable in terms of the amount of ®ring variability explained because the number of predictors was equal. A highly conservative criterion of 10 consecutive bins (200 ms) with an R2 > 0.2 (P < 0.05) for each bin was required to accept a relationship between the ®ring and a parameter as signi®cant. This strict criterion was used to avoid spurious, shortduration correlations and to take into account the fact that the binwise regression is based on multiple statistical tests. Two approaches were used to compare neuronal ®ring at different speeds (Fig. 2). The ®rst approach was to `clip' the data and evaluate only the 1 s prior to and after the cue-track transition. Although keeping the absolute timing intact, this method ignores large segments of data. The second approach was to `stretch' the temporal pro®le of the neuronal ®ring from the faster speeds (3, 4 and 5 cm/s) to the same number of 20-ms bins as the slowest target (2 cm/s). This was accomplished by ®tting a cubic spline to the ®ring pro®le of the faster three speeds and interpolating to 250 bins, the same number of bins in a 2-cm/s trial. Thus, all target speeds resulted in the same number of instantaneous ®ring frequency bins, such that speed comparisons could be made across each sequential bin. The duration of each bin ranged from 8 ms (5 cm/s) to 20 ms (2 cm/s). The evolution of correlations between ®ring and the parameters was thus evaluated as a function of target travel distance. As this method maps the sequence of ®ring directly onto the workspace, the absolute timing in each trial period is lost. However, by including the complete temporal pro®le, this method preserves the entire task sequence. Because the same period of time (500 ms) was analysed for the hold period, this component of the discharge was not included in the interpolation. Figure 2 compares the results of the temporal regression analysis using the `stretched' vs. the `clipped' data for the ®ring of one neuron. As shown, the stretching of the ®ring frequency histograms faithfully reproduces the temporal pro®le of the discharge pattern and the R2 pro®les. A comparison of the two approaches was undertaken for the ®ring of the 240 neurons and yielded similar R2 pro®les. Also, interpolation to 100 bins, the number of bins in the 5cm/s trial, was also undertaken and resulted in almost identical correlation pro®les (data not shown). The binwise regression results are independent of whether the data was expanded or compressed. Therefore, the stretching methodology was used in this report to permit an analysis of the entire ®ring pro®le, including the hold period. Trade-off of speed and duration FIG. 2. Comparison of the two approaches used to accommodate records of differing durations for the temporal regression analysis. Firing frequency histograms are shown (above) for one neuron during 0° movement trials. The 500-ms hold prior to the cue period was the same length for all target speeds. The remainder of the records vary in length from 5 to 2 s for the 2 and 5 cm/s target speeds, respectively. The shorter trials can be `stretched' (left) using spline interpolation or `clipped' (right) to the shortest 2 s length common to all target speeds marked by the vertical dotted lines. The binwise regressions resulted in pro®les of the total R2, direction partial R2 and speed partial R2, which were similar for both methods. The `stretching' method was used only for the binwise regressions. Speed and duration were inversely related because tracking distance was constant. Consequently, the duration of each cue or track period ranged from 1 to 2.5 s for the extremes of target speed from 5 to 2 cm/ s, respectively. This raises the question of whether the speed±duration trade-off could lead to false positive or negative results. For ®ring characterized by relatively constant increases or decreases with speed this does not present a problem because the analyses were based on average ®ring, which was normalized to time. However, for transients of ®ring the speed±duration trade-off could lead to erroneous results. Such transient responses to a visual target presentation are found in a minority of PMd and MI neurons classi®ed as `signal cells' (di Pellegrino & Wise, 1993; Johnson et al., 1996; Johnson et al., 1999). Therefore, several additional analyses were undertaken to insure that neither the period nor the binwise regressions were corrupted. Figure 3A illustrates the problem for a worst-case hypothetical `signal' response in the cue period of 40 spikes/s for a duration of Ó 1999 European Neuroscience Association, European Journal of Neuroscience, 11, 4433±4445 4436 M. T. V. Johnson et al. from the speed regression for the partial and entire cue or track periods (Fig. 3A) shows that two methods yielded almost identical ®ndings. To allow for the response latency and the fact that timelocked `signal' transients occurred most frequently just after the reaction time, a comparison was made between ®rst 150±650 ms and the full cue period. The two slopes were almost identical with an R2 of 0.82 and a slope of 1.0 (Fig. 3A). For the track period, comparison of the slopes from the ®rst 500 ms vs. the entire period resulted in an R2 of 0.71 and a slope of 0.7 (Fig. 3A). Therefore, the potential problem of ®ring transients causing erroneous speed regressions did not occur. For simplicity, only the results from the period regression based on the ®ring in the entire cue and track periods are reported. The speed±duration trade-off could also affect the ®ndings based on the binwise regressions. For the same hypothetical neuronal response, the stretching procedure alters the location of time-locked transients (Fig. 3B). Staggering of this transient produces spurious speed correlations, causing the temporal pro®le of the speed slope to rapidly switch from negative to positive, which makes little physiological sense. Therefore, the occurrence of biphasic slopes was taken to indicate a time-locked component in the ®ring and these neurons (n = 31) were removed from the binwise analysis. All 31 neurons had time-locked ®ring transients, usually in the initial 200± 300 ms of the cue period. Results Neuronal database FIG. 3. Due to the use of equal 10-cm target travel distances for the four target speeds, a speed±duration trade-off resulted. (A) (Left) The distortions to the period-averaged ®ring speed correlation slopes are shown for a worst-case `signal' neuron which ®res only for a ®xed duration (200 ms) transient of 40 spikes/s. The cue period averages span 2.5±1 s (striped boxes). However, because the transient is of ®xed duration and frequency and no other ®ring occurs, the resultant averages divide this ®xed instantaneous frequency by the number of observations which ranges from 125 (2-cm/s trials) to 50 (5-cm/s trials), resulting in an apparent speed slope of 1.6 spikes/cm. (Right) Comparison of speed slopes (b1, equation 2) calculated using averages over the total cue or track period to those calculated using a ®xed duration. For the cue period, a ®xed subperiod from 150 to 650 ms was used to allow for reaction time. For the track period, the ®rst 500 ms were used. For the cue period, the comparison regression is ®tted by Full cue = ±0.3 + 1.0 3 150±650ms cue (R2 = 0.82). For the track period, the regression is ®tted by Full track = ±0.03 + 0.7 3 0±500-ms track (R2 = 0.71). (B) (Left) The distortions to the binwise speed correlation are shown for the same hypothetical neuron as in A. The shorter durations are all spline-interpolated to the same number of bins (250) as the longest duration (2 cm/s) trials. This results in a staggering of the transient as a function of target distance. (Right) The binwise speed regression slope is shown as a function of target distance. 200 ms at a latency of 200 ms. The average ®ring over the four speeds is 8.0, 6.4, 4.8 and 3.2 spikes/s due to the unequal time periods (1.0, 1.25, 1.67 and 2.5 s), yielding a false-positive speed regression slope of 1.6 spikes/cm/s. In contrast, the average ®ring calculated over a ®xed duration (in this case the ®rst second of the cue period) results in 8.0 spikes/s at each speed and no correlation to speed exists. Therefore, the magnitude of the problem may be ascertained by comparing the slopes of the regressions to speed from the entire cue period with those based on a ®xed duration. As the shortest cue period duration was 1 s, regressions to speed were performed for ®ring averaged over the different 500-ms epochs of the cue and track periods and the slopes were compared to the results from the entire period. As described in Results section, signi®cant speed modulation (with or without direction modulation) was found in 79 cue periods and 46 track periods (out of a total of 240 cells). Comparison of the slopes The discharge of 240 neurons from two animals and three hemispheres was studied. This sample of neurons has been previously analysed, addressing the question of how directional tuning changed across the cue and track periods (Johnson et al., 1999). The neurons studied were located in the PMd and MI (for the locations of electrode penetrations, see ®g. 5 of Johnson et al., 1999). The population of neurons recorded did not include cells in the frontal eye ®elds or the ventral premotor area. Examples of direction, speed, and velocity modulation in PMd/ MI neurons The ®ring of 226 neurons (94%) had signi®cant directional ®ts of their ®ring in either the cue (n = 14), track (n = 41) or both periods (n = 171) to the 32-point cosine tuning model (equation 1) with or without speed modulation. The ®ring of 101 neurons (42%) had a signi®cant ®t to speed (equation 2) with or without directional modulation in the cue (55), track (22) or both (24) periods. Examples of direction- and speed-modulated neuronal ®ring are illustrated in Figs 4±6. The ®ring frequency histograms are depicted with a change in time scale for each of the speeds as they were normalized to target travel distance. However, the regressions of average ®ring in the cue or track period were not dependent on this stretching (see Methods section). The spike frequency histograms shown in Fig. 4 are from a neuron in which the ®ring was signi®cantly modulated by target speed in the cue period and by movement direction in the track period. During the cue period, while the monkey viewed the target, the ®ring was inversely related to target speed. This inverse relation occurred along all tracking directions. During the track period the neuronal ®ring was not modulated by target speed but exhibited broad directional tuning with the greatest ®ring for movements around 225° and decreased ®ring for tracking at 45°. The graphs in the centre are the directional tuning curves derived from the regressions to the cosine tuning model (upper) and the linear component of the regressions to target speed (lower) for the cue (right) and track (left) periods. The average ®ring Ó 1999 European Neuroscience Association, European Journal of Neuroscience, 11, 4433±4445 Motor cortical encoding of direction and speed 4437 FIG. 4. Firing frequency histograms from a neuron that was modulated by target speed during the cue period and directionally-tuned during the track period. Firing frequency histograms for each target speed are arranged by direction (0° to 315°) around the workspace. The 500-ms hold period is shown to the left of each histogram. The cue and track periods of the histograms are shown at different time scales for the different tracking speeds, as they were normalized to target travel distance. The ticks on the x-axis represent 500 ms intervals. Time axis for each target speed is shown for the 0° direction. The upper inset graphs in the centre display the average ®ring data points and the 32-point cosine tuning curves for the eight directions over the four target speeds. The lower inset graphs display the regression ®t to the ®ring for the four target speeds (2, 3, 4 and 5 cm/s) over the eight directions. Calibration line (to the right of the 270°, 2 cm/s ®ring histogram) indicates ®ring rate in spikes/s. in the cue period was signi®cantly modulated by target speed (R2 = 0.66, b1 = ±3.0 spikes/cm); however, the ®t to the cosine tuning model was not signi®cant. During the track period the ®ring was directionally tuned (R2 = 0.79, c1 = 2.3) with a preferred direction of 243° but the relationship between ®ring and target speed was not signi®cant. This cell was, therefore, modulated by speed in the cue period and direction in the track period. Decreases in ®ring with increased target speed (a negative regression slope) occurred in 42% of the 101 neurons in which the period regressions to target speed yielded a signi®cant ®t. The remaining 58% of the cells increased ®ring with increasing speed (positive regression slope, b1). An example of such a cell is shown in Fig. 5. The histograms and regression results reveal increased ®ring for greater target speeds during the cue period (R2 = 0.45, b1 = 2.4 spikes/cm). However, the cue period discharge was not tuned to target direction. Conversely, during the track period the ®ring was not modulated by target speed but was directionally tuned (R2 = 0.91, c1 = 23.7) with a preferred direction of 81.2°. Thus, during the cue period this neuron responded to increases in target speed with increased ®ring, in contrast to the speed±discharge relationship shown in Fig. 4. Two common features of the ®ring of both cells were the presence of signi®cant speed modulation only in the cue period and directional tuning only in the track period, thus the lack of velocity modulation. The ®ring of a large fraction of the cells (n = 79 out of 240, 33%) and periods (n = 91 out of 480, 19%) was signi®cantly modulated by both parameters within at least one of the task periods. An example of such a neuron is shown in Fig. 6. Signi®cant speed modulation occurred during the cue period (R2 = 0.34) and the discharge increased with increasing target speed (b1 = 5.0). Signi®cant directional tuning was present for both the cue (R2 = 0.48, c1 = 11.7) and the track (R2 = 0.47, c1 = 10.5) periods. The cell's preferred direction Ó 1999 European Neuroscience Association, European Journal of Neuroscience, 11, 4433±4445 4438 M. T. V. Johnson et al. FIG. 5. Firing frequency histograms and direction and speed regression results from the discharge of a neuron demonstrating increased ®ring with increasing speed in the cue period and directional tuning in the track period. The ticks on the x-axis represent 500-ms intervals. Time axis for each target speed is shown for the 0° direction. Conventions as in Fig. 4. was nearly identical for the cue and track periods (112.9° and 117.1°, respectively). The discharge was not signi®cantly modulated by speed during the track period. Therefore, the overlap between direction and speed modulation was con®ned to the cue period. Summary of the period-based direction and speed modulation The database included 240 neurons, so the ®ring in a total of 480 cue and track periods was analysed using the period regressions to direction (equation 1) or speed (equation 2). The ®ring in 125 of 480 periods (26%) demonstrated speed modulation and the ®ring in 399 of 480 (83%) periods demonstrated directional tuning. Directional tuning alone was the most common ®nding (Fig. 7). The average discharge in 64% (308 out of 480) of the periods demonstrated a signi®cant ®t only to direction without speed modulation (131 cue and 177 track periods). Therefore, directional tuning (without speed modulation) was more common in the track than in the cue period. Modulation of the discharge by direction and speed was the second most common group. The ®ring in 19% of the periods (91 out of 480) had signi®cant correlation with both direction and speed (53 cue and 38 track periods). A signi®cant ®t limited to target speed was found in 7% of the periods (26 cue and 8 track periods). Therefore, speed or the combination of direction and speed modulation was more common in the cue than in the track period. This difference in the relative proportions of direction, direction plus speed, and speed modulation between the cue and track periods was signi®cant (P < 0.001, c2 3 3 2 table). Spatial distribution of speed-modulated neurons Of interest was whether there was any spatial distribution over the cortical surface to the neurons whose discharge was modulated by speed. This was evaluated by dividing the neurons with signi®cant speed modulation into three groups: those with speed modulation (i) only in the cue period; (ii) only in the track; and (iii) in both periods. The relative percentages of these three groups in the PMd and MI was evaluated ®rst. Of the 55 neurons modulated by speed in the cue period, 39 were located in the PMd and 16 were in the MI. Of the 22 neurons modulated by speed in the track period, three were found in the PMd, whilst 19 were found in the MI. The 24 neurons modulated Ó 1999 European Neuroscience Association, European Journal of Neuroscience, 11, 4433±4445 Motor cortical encoding of direction and speed 4439 FIG. 6. Firing frequency histograms and direction and speed regression results from a neuron demonstrating increased ®ring with increasing target speed in the cue period and directional tuning in both cue and track periods. Conventions as in Fig. 4. FIG. 7. Summary of results from the period regressions of the average ®ring from the cue and track periods to speed and direction. The numbers of periods with signi®cant correlations to only direction, direction and speed, and to only speed are speci®ed for the cue (black bars) and track (white bars) periods. in both periods were evenly distributed (12 were in the MI and 12 were in the PMd). The change in relative proportions of these three functional groups between the two cortical areas was signi®cant (P < 0.001, c2 3 3 2 table). The percentages of cells falling into each category were also assessed as a function of distance from the central sulcus (Fig. 8A). The relative percentages of cells with signi®cant speed modulation in the cue period increased from 36% at 0±4 mm from the central sulcus to 60% at 4±8 mm and 67% at 8±12 mm. The percentages of cells with speed modulation in the track period decreased from 31% at 0±4 mm to 25% at 4±8 mm and 11% at 8± 12 mm. Figure 8A does not extend to 12±16 mm as only eight cells fell in this range; however, all were modulated by speed in the cue period. These trends also suggest that cells modulated by speed in the cue period were located more anteriorly in PMd and cells modulated by speed in the track were located more posteriorly in MI. A spatial distribution also existed for neurons modulated by direction. This gradient was shown for similar functional categories using a different directional regression methodology (see ®g. 11 of Johnson et al., 1999). Based on the 32-point regression methodology used in this paper and the same three functional categories de®ned above for speed modulation, the distribution of directional modulation as a function of trial period and distance from the central sulcus was constructed (Fig. 8B). The gradient of increasing incidence of directional modulation in the cue period paralleled that found for speed, increasing from 1% at 0±4 mm to 4% at 4±8 and 17% at 8± 12 mm. The percentage of neurons with directional modulation in the track period decreased as a function of distance from the central Ó 1999 European Neuroscience Association, European Journal of Neuroscience, 11, 4433±4445 4440 M. T. V. Johnson et al. FIG. 8. (A) Locations of neurons relative to the central sulcus with three functional types of speed coding. The proportions of neurons with (i) speed coding in only the cue period (black bars) (ii) speed coding in only the track period (white bars), and (iii) speed coding in both cue and track periods (grey bars). The proportions of the three groups add to 100% for each 4-mm distance segment. (B) Proportions of neurons with (i) direction coding in only the cue period (black bars) (ii) direction coding in only the track period (white bars), and (iii) direction coding in both cue and track periods (grey bars). FIG. 9. The temporal R2 pro®les from the multivariate binwise regressions over the trial period are shown for the three neurons in Figs 4±6. The partial R2 for speed (d3(t) s + d4(t) s2) and direction (d1(t) cos(q) + d2(t) sin(q)) were plotted as a function of the trial sequence. The total R2 pro®le over the trial is also plotted. To the far right, the speed slope d3(t) was plotted over the trial. The lengths of the cue and track periods were normalized as described in Fig. 2. Dashed vertical lines represent the end of the hold period. Solid vertical lines represent the cue±track transition. Vertical hatching of the R2 pro®les indicate signi®cant correlations (P < 0.05 for 10 consecutive bins, see Methods section). sulcus (31 to 17 to 10% in these same intervals). A similar trend was also observed for speed (Fig. 8A); however, the percentage of neurons with directional modulation in both periods was greater than for speed modulation. Analysis of the temporal multiplexing of direction and speed To obtain a temporal pro®le of the correlation of the discharge with direction and speed, a binwise multivariate regression was performed (equation 3, Methods section). More precise timing relations are obtainable with the binwise regressions than with the period average regressions; however, results from the two were in general agreement. Of particular interest was the presence of velocity modulation in the discharge of single neurons. Figure 9 shows the results from the binwise regression of ®ring to speed and direction for the three neurons shown in Figs 4±6. The partial R2 for speed reached signi®cance and peaked in the cue period for each neuron. This is in agreement with the period regression results in which the discharge of each of these cells had a signi®cant ®t with speed in the cue period. The partial R2 for speed did not reach signi®cance in the track period for the ®rst two neurons (A and B), also in agreement with the results from the period regressions. For the third cell shown in C the partial R2 for speed was signi®cant only for 1 cm of the track period. However, this brief period of speed modulation was not suf®cient to yield a signi®cant relationship with speed when the average ®ring of the track period was regressed to speed (Fig. 6). The temporal pro®les of the partial R2 for direction differed from the partial R2 for speed in that signi®cance was not reached until later in the cue period (C) or until the track period (A and B). As predicted from the period regressions, the cue period ®ring of the cell shown in C was modulated by both direction and speed. The partial R2 for direction was signi®cant throughout almost the entire track period (A±C). The temporal pro®le of the speed slope (d3, equation 3) was monophasic, negative for the cell in A and positive for the cells in B and C, in agreement with the period regressions. A negative speed slope indicated that the cell in A increased its ®ring for decreasing target speeds. A positive speed slope indicated that the cells in B and C increased ®ring for increasing target speeds. This coincides with the speed slopes based on the period regressions shown in the insets of Figs 4±6. The lack of rapid sign changes in the speed slope in A±C demonstrated that spurious regressions were not present (see Methods section). Complete speci®cation of the velocity vector requires both direction and speed modulation. From the binwise regression results, the cell shown in A lacked simultaneous correlation to direction and speed and therefore this cell was not modulated by velocity at any time through the trial sequence. In contrast the cell shown in C had a period of overlap of speed and direction modulation beginning in cue and extending into early track. This cell had a temporal ordering of the modulation by the three parameters, speed modulation ®rst, then velocity, and direction last. For the cell shown in B, speed modulation occurred ®rst and direction modulation later with a short epoch of velocity modulation between. Therefore, signals encoded in the ®ring of these three cells generally exhibited a serial ordering of speed, then direction. In 159 cells, the binwise regression results for speed yielded a signi®cant ®t and in 223 the ®t to direction was signi®cant. As 31 cells produced biphasic slopes in the speed partial regression, only 128 cells with signi®cant speed correlations were used in subsequent analyses (see Methods section). Partial R2 temporal pro®les for speed and direction for these data were averaged and are shown in Fig. 10A. The average partial R2 for speed reached signi®cance early in the cue period and became nonsigni®cant before movement onset. This ®nding parallels the greater number of signi®cant ®ts of averaged discharge to target speed in the cue period (Fig. 7). In contrast, the average temporal pro®le of the partial R2 to direction reached signi®cance approximately midway through the cue period, and continued to rise throughout the cue period. The average partial R2 for direction remained signi®cant throughout the entire track period. This predominance of directional tuning in the track period was found as well using the period regressions to direction. The points along the trial sequence at which the partial R2 for speed and direction reached signi®cance (B) as well as the points at which the maximum R2 occurred (C) are shown in histogram form. Each bar represents a target travel distance of 0.2 cm. Signi®cant speed encoding occurred Ó 1999 European Neuroscience Association, European Journal of Neuroscience, 11, 4433±4445 Motor cortical encoding of direction and speed 4441 FIG. 10. Population average pro®les of the trial sequence binwise regressions. For each speed or direction partial R2 record to be included in the average, the criterion of 10 sequential bins with signi®cant (P < 0.05) regressions had to be met. (A) The averaged trial sequence binwise regressions are shown for the speed partial R2 and direction partial R2. The mean (thick line) and the +1 SD boundary (thin line) are shown. The solid horizontal line at R2 = 0.2 denotes the P < 0.05 signi®cance level. The dashed vertical line marks the end of the hold period. The solid vertical line marks the cue±track transition. (B) The distance of target travel at which the speed and direction partial R2 sequences became signi®cant is plotted in histogram form. (C) The distance at which the R2 sequences for speed and direction reached a maximum is shown. The mean 6 SD for each distribution is plotted above each histogram. as early as 0.4 cm in the cue period, with the average distance of onset at 1.5 6 0.9 cm into the trial sequence. The average distance at which the peak R2 for speed occurred was 2.3 6 1.2 cm into the trial sequence. Based on the binwise regressions, speed modulation occurred primarily in the cue period. Signi®cant direction modulation had an average onset distance of 2.5 6 1.7 cm into the trial sequence which was later in the cue period than for speed. However, the peak R2 for directional tuning occurred during the track period, after the target had travelled 7.4 6 1.6 cm, approximately halfway through the track period. Therefore, speed modulation occurred preferentially in the cue and directional tuning dominated the track period. How are subpopulations of directional- and speed-modulated neurons recruited through the trial sequence? Using indices based on the binwise regression, the sampled population of the 223 directionally-modulated and 128 speed-modulated neurons was analysed as a function of trial sequence. Onsets of initial signi®cance for direction and speed correlations were plotted as the cumulative percentage of modulated neurons in Fig. 11A. The subpopulation of speed-modulated neurons reached signi®cance rapidly during the ®rst 2 cm of target travel in the cue period. The subpopulation of directionally-modulated neurons reached signi®cance more gradually over the entire cue period. However, both subpopulations were active in the cue period. Profound differences were apparent at the positions in the trial sequence at which each subpopulation reached maximal signi®cance (Fig. 11B). Speed-modulated cells were recruited to maximal signi®cance in the cue period while the direction-modulated cells reached maximal signi®cance in the track period. From the perspective of reaching maximal signi®cance, the two subpopulations were almost completely segregated over the trial sequence. FIG. 11. (A) Cumulative percentage of neurons signi®cantly modulated to direction (squares) and speed (circles) as a function of the trial sequence. (B) Cumulative percentage of direction- and speed-modulated neurons reaching peak signi®cance (maximal R2) as a function of the trial sequence. The dashed vertical line marks the end of the hold period. The solid vertical line marks the cue±track transition. The horizontal axis shows the distance of target travel. FIG. 12. Average binwise regression pro®les for neurons with both distance and speed partial R2 pro®les that were signi®cant. First, the partial R2 pro®les from individual neurons had the nonsigni®cant portion (R2 < 0.2) removed. An estimate of the velocity partial R2 pro®le was constructed using the regions of simultaneously signi®cant direction and speed partial R2 pro®les. The partial R2 pro®les were averaged (thick line) and the +1 SD boundary (thin line) calculated. The temporal R2 pro®les for speed and direction (Figs 10 and 11) show that, across the population of cells, direction and speed modulation both occurred in the cue period. A similar result emerged Ó 1999 European Neuroscience Association, European Journal of Neuroscience, 11, 4433±4445 4442 M. T. V. Johnson et al. from the period regressions, that direction and speed modulation in the cue period was prevalent (Fig. 7). However, neither of these analyses answers the question to what extent direction and speed are simultaneously modulated in the ®ring of single cells. To answer this, neurons with signi®cant partial R2 pro®les for direction and speed were ®rst chosen. Secondly, the nonsigni®cant portion (R2 < 0.2) of the partial R2 pro®les from each individual neuron were removed. Lastly, an estimate of the partial R2 pro®le for velocity was constructed from the regions of simultaneously signi®cant direction and speed R2 pro®les. Once processed for each neuron, the partial R2 pro®les were averaged. Figure 12 shows the averaged direction, speed and velocity partial R2 pro®les as a function of target travel distance for this group of neurons. The direction partial R2 pro®le rises through the cue reaching a maximum in the track period, characteristically similar to the direction pro®les shown in Figs 9 and 10. The speed partial R2 pro®le peaks during the middle of the cue period, similar to the speed pro®les of Figs 9 and 10. The estimated velocity partial R2 pro®le was half that of the speed and rose slightly later than the speed partial R2. Using the increased resolution of the binwise regressions, the presence of velocity modulation in individual neurons proved to be limited. Discussion The discharge of PMd and MI motor cortical neurons was studied during a pursuit-tracking task in which the direction and the speed of the target were systematically varied. Several characteristics of the paradigm dictated the analysis and interpretation of the results. First, the paradigm explicitly varied direction and speed, and con®ned the tracking to straight, radially-directed movements. Therefore, speed was independent of tracking direction. In other tasks, direction and speed continuously covaried (Schwartz, 1992, 1993) and precluded an independent assessment of the effects of these two parameters on the neuronal discharge. Secondly, two sources of information, target direction and speed, were presented continuously through the trial sequence. Thus, the temporal pro®le of the correlation of the ®ring with direction and speed could be determined. Thirdly, the instructed delay design of the paradigm allowed the neuronal ®ring to be recorded during a visuomotor transform in which the animal was required to map the direction and speed of the moving target in the cue period onto the upcoming track period. This permitted an evaluation of the evolution of the PMd and MI discharge during a cue period consisting of a dynamic visual stimulus and during a track period consisting of error-constrained pursuit tracking. Relating neuronal ®ring comparisons to task parameters: regression methodologies In the literature, three classes of regression techniques have been used to determine how movement parameters (i.e. direction, velocity and acceleration) are encoded in neuronal ®ring. These classes will be referred to as `period average', `time course' and `binwise' regressions. Each approach has certain advantages and disadvantages. Period average regressions were the ®rst utilized to relate the ®ring during a behaviourally relevant epoch to peak velocity or acceleration of step movements (Hamada & Kubota, 1979; Hamada, 1981; Burbaud et al., 1991). More recently, multiple linear regression models have been used for period average data (Fu et al., 1993; Coltz et al., 1999). In the present study, period average regressions were used extensively to determine if direction, speed or both (i.e. velocity) modulated the average ®ring in the cue and track periods. Time course regressions have been used to ®t the temporal pro®le of the discharge to the temporal pro®le of the movement kinematics, introducing time lags and leads to optimize the R2 of the model. This method was used by Marple-Horvat & Stein (1987) to analyse the ®ring of cerebellar cells and by Ashe & Georgopoulos (1994) for motor cortical and parietal neurons. The former used separate regressions to position, velocity or acceleration while the latter used a multivariate regression model, ®tting ®ring to target direction and hand position, velocity and acceleration. However, great care must be exercised when using time course regressions due to the high prevalence of spurious signi®cant regressions resulting from nonstationarity (i.e. nonconstant means and changing variances over time) and auto-correlated errors in the residuals (Granger & Newbold, 1974). The problem of auto-correlated errors in the regression analysis of time series has been recognised (Ashe & Georgopoulos, 1994). A limitation of both epoch and time course regression is that the correlation of the ®ring to the task parameters can be time-dependent (Fu et al., 1995). Binwise regression addresses this limitation. It is essentially an extension of epoch regression methodology wherein the ®ring in a brief time bin is ®tted to the parameters of interest (Fu et al., 1995). In this study, binwise regressions were used to determine the time course of the correlations with direction and speed. An interesting variant of binwise regression methodology was employed by Schwartz (1992) to determine the correlation of the ®ring of MI neurons with the tangential velocity of continuous ®nger tracing movements. The neuronal ®ring residual from the directional regression was found to vary with ®nger speed. Firing correlations to direction and speed In the present study, the ®ring of both PMd and MI neurons was found to signal target direction and speed. Using the period average regressions, neurons were found to be modulated by direction, speed or both in the cue, track or both periods. Irrespective of period, neurons modulated by only direction were by far the most numerous. The second largest group comprised neurons modulated by both direction and speed. The smallest group were neurons modulated only by speed (see Fig. 7). Direction encoding has been demonstrated repeatedly in the ®ring of PMd and MI neurons (Georgopoulos et al., 1982, 1984; Caminiti et al., 1991; Schwartz, 1992; Fu et al., 1993; Johnson et al., 1999). Speed/velocity coding has been reported for the discharge of MI neurons (Hamada & Kubota, 1979; Hamada, 1981; Schwartz, 1992, 1993; Ashe & Georgopoulos, 1994). However, there has been little information available concerning the PMd. While the present ®ndings con®rm and extend these earlier results, particularly to the PMd, there are some important differences. The previous studies used primarily step-type movements and did not systematically vary both direction and movement speed. The only other tracking study (Schwartz, 1992, 1993) employed a task in which the trajectories were characterized by continuously changing direction and speed. Speed and curvature varied inversely; the residuals could thus correlate with either. This confound did not exist in the current task, which minimized angular velocity by using straight, error-constrained movements. Another difference from previous reports is the differentiation between speed and velocity coding. Neurons with simultaneous direction and speed modulation were operationally de®ned as coding velocity. The higher temporal resolution of the binwise regression demonstrated that the overlap between direction and speed in single neurons was minimal. The conjunction of the partial R2 pro®les of direction and speed explained only half of the variability that the partial R2 to speed did (Fig. 12). Therefore, while the ®ring of single neurons signals both speed and direction, the two signals are not combined. Presumably, other structures combine these two signals Ó 1999 European Neuroscience Association, European Journal of Neuroscience, 11, 4433±4445 Motor cortical encoding of direction and speed 4443 into a velocity vector as recently shown for cerebellar Purkinje cells (Coltz et al., 1999). In agreement with previous studies, speed modulation, in either the cue or track periods, had an equal probability of having either a positive or negative slope. Bivalent modulation by speed or velocity appears to be the rule rather than exception in the central nervous system. Positive and negative speed/velocity slopes were found for the ®ring of pyramidal tract neurons (Hamada, 1981), cerebellar Purkinje cells (Marple-Horvat & Stein, 1987; Coltz et al., 1999) and for neurons in the globus pallidus (Georgopoulos et al., 1983). One possibility is that the positive and negative slopes re¯ect different uses or targets of this information. Temporal parcellation of speed and direction The results from the period regressions suggested strongly that the neural encoding of target speed was more prominent while the monkey viewed the target during the cue period than during the actual hand movement in the track period. Conversely, directional modulation was more prominent in the track period. The percentage of periods that were modulated only by direction increased by 26% from cue to track. The percentage of periods modulated by both direction and speed decreased by 28% from cue to track. Neurons modulated only by speed decreased by 69% from the cue to track periods. The binwise regression model con®rmed this ®nding, demonstrating that the partial R2 for speed became signi®cant early in the cue period and became nonsigni®cant by the track period onset (Fig. 10). The correlation with direction became signi®cant about halfway through the cue period and increased over the cue period to become the major determinant of the ®ring in the track period. The cumulative percentage of neurons with correlations to direction and speed (Fig. 11) shows that the recruitment of neurons modulated by speed occurred earlier in the trial sequence than the recruitment of those modulated by direction. A previous study of identi®ed pyramidal tract neurons reported that the ®ring of a majority (21 out of 41) was correlated to wrist ¯exion velocity during movement, but in only one neuron was there a correlation with velocity prior to movement onset (Hamada, 1981). The present ®nding of prominent speed modulation in the instructed delay period would seem to be in sharp contrast. However, the ®nding of little velocity modulation during the instructed delay period in the earlier study may be instructive in terms of task and behavioural demands on neuronal processing. The paucity of velocity or speed signals may be attributed to two task differences. First, in the previous study the `go' signal was explicit and movement onset was not contingent on the intersection of a dynamically displayed cue target with the hold box. Therefore, there was no need for the animal to use speed to estimate the onset of the actual movement. Secondly, in the previous study speed was not presented as a moving target, but was symbolically displayed as three levels of lights. Therefore if, prior to movement, speed is visually presented as a moving target and the processing of this information is required to determine movement onset, speed becomes an important determinant of the ®ring of PMd and MI neurons. It was assumed in the design of the paradigm that the monkeys would use both speed and direction information presented during the cue period to prepare the upcoming movement. The presence of correlations to both direction and speed during the cue period strongly suggests that both sources of information were used, possibly re¯ecting the visuomotor transform required in preparation for the movement phase of the task. PMd and MI neurons have been shown to modulate according to go/no-go instructions (Wise et al., 1983; Sakagami & Niki, 1994; Kalaska & Crammond, 1995). As the `go' signal was implicit in this study, the visually deduced speed or rate of closure of the moving target with the central hold box becomes important for timing the onset of tracking. It is hypothesized that target speed information is transformed into an internal `go' signal. This would explain why the cortical neurons were modulated initially by speed information, then by direction. Psychophysical studies have lead to the hypothesis that different parameters of movement are processed separately, including direction and distance (Rosenbaum, 1980; Favilla et al., 1990; Soechting & Flanders, 1991). However, at the level of the PMd and MI, information about several parameters of movement is not segregated into different neurons. The ®ring of PMd and MI neurons is modulated by direction and distance (Fu et al., 1993, 1995) and the discharge of MI neurons is modulated by direction and changes in angular velocity or speed (Schwartz, 1993). Likewise, this study found that PMd and MI neurons signal both direction and speed during pursuit-tracking, but segregate this information in the temporal domain. Therefore, temporal parcellation appears to be a general multiplexing strategy in the PMd and MI. Potential experimental and analytic confounds The possibility exists that other behaviours such as eye movement (Boussaoud, 1995; Boussaoud et al., 1998) or spatial attention (di Pellegrino & Wise, 1993) may differentially modulate neuronal ®ring in the cue relative to the track periods. Eye movements consisted initially of saccades followed by smooth pursuit of the target (see ®g. 4 of Johnson et al., 1999). However, eye movement behaviour was symmetric in the cue and track periods. Selective attention would be expected to follow a similarly symmetric behaviour over the trial sequence, initially directed over the entire workspace, then directed at the moving target, and becoming again diffuse at the end of the trial. Neither the modulation with direction nor the modulation with speed demonstrated such symmetric behaviour between the cue and track periods, demonstrating that neither eye movements nor attention can account for the discharge modulation observed. As can be seen by the tangential velocity pro®les (Fig. lC), the initial track period was marked by an acceleration of the hand as it went from rest to the constant target speed. The regressions to target speed performed in this study did not take this parameter into consideration. Two ®ndings downplay a potential relationship between the ®ring and acceleration. First, ®ring transients during the initial track period were virtually nonexistent. Secondly, regressions comparing the speed slopes (b1) taken from ®rst 500 ms with those from the last 500 ms of the track period demonstrated that they were highly correlated. Is the speed modulation in the cue period a confound due to the coexisting directional tuning? Speci®cally, the directional tuning during the cue has been shown to rotate and converge toward the eventual preferred direction (PD) of the track period (Johnson et al., 1999). Could this rotation of the PD, which is most pronounced in the cue period, artifactually produce a correlation with target speed? Two observations argue that this is not the case. First, the PDs resulting from period average and binwise regressions do not systematically change with changing target speed (Johnson et al., 1999). Secondly, one last analysis was undertaken. Binwise regressions (equation 3) were performed on two groups of neurons, those with PDs diverging little between cue and track (< 45°) and those with greatly divergent PDs (> 45°). The resultant binwise pro®les of speed and direction correlations were almost identical to those shown for the entire population in Fig. 10. Therefore, the presence of directional tuning in the cue period did not effect the speed coding. Ó 1999 European Neuroscience Association, European Journal of Neuroscience, 11, 4433±4445 4444 M. T. V. Johnson et al. Neural substrate for direction and speed coding Direction and speed information must reach the PMd/MI during the cue period, prior to movement onset. It has been postulated that the source of the visual information is mediated through two channels. One possible route is the transfer of this information via the pontocerebellar pathway and then to the motor cortex (Stein & Glickstein, 1992). Most recently, it has been hypothesized that the dorsal stream mediates the transfer of visual information from the parietal areas to the PMd and MI, with the parietal cortex serving as the bridge between vision and movement (Milner & Goodale, 1995; Johnson et al., 1996; Wise et al., 1997; Battaglia Mayer et al., 1998). Both pathways may contribute; however, this discussion will focus on the potential contribution of the dorsal stream. Most parietal input to the PMd/MI originates from the superior parietal lobule with additional projections from the inferior parietal lobule and the parieto-occipital sulcus (Johnson et al., 1996; Wise et al., 1997). Direction and speed relationships to neuronal ®ring have been characterized for several of these extrastriate visual association areas. Early visual directional responses (`signal' and `set' responses) were found to be most prominent in the intermediate and ventral part of the intraparietal sulcus (Johnson et al., 1996). Neurons in the ventral intraparietal area are highly responsive to the direction and speed of moving visual targets (Colby et al., 1993). The adjacent middle temporal visual area also responds to directionally-moving visual targets (Albright, 1984; Lagae et al., 1993). Neurons with foveal receptive ®elds have low-pass speed tuning curves with a peak at 1 °/s while those with peripheral receptive ®elds have broad speed tuning curves with peaks around 10 °/s (Lagae et al., 1993). Not only visual, but also limb movementrelated neurons have been characterized in the parietal cortex. Movement-related directional responses were most prominent in the dorsal medial wall of the intraparietal sulcus (Johnson et al., 1996). Neurons in the intraparietal sulcus are also modulated by the direction and velocity of wrist joint movement (Burbaud et al., 1991). Therefore, a variety of parietal and extra-striate cortical regions could provide direction and speed information during the cue period. Speed modulation during the visual instruction was found in cells located predominantly in the PMd. Speed modulation during the movement was preferentially seen in cells located in MI. Speed coding during cue, track or both periods was equally probable in the region close to the central sulcus. In the region 8±12 mm rostral to the central sulcus, the percentage of speed-modulated cells in the cue period increased to 67%, while the speed-modulated cells in both periods or during only track fell to 23 and 11%, respectively (see Fig. 8A). Thus a rostral±caudal gradient exists for the modulation of cells by speed information from the visual instruction to the actual movement phases of the trial sequence. This temporal±spatial gradient parallels that seen for directional information in this same task (Fig. 8B). Furthermore, this rostral±caudal gradient is similar to that found for the prevalence of premovement activity (Weinrich et al., 1984; Riehle & Requin, 1989; Alexander & Crutcher, 1990; Johnson et al., 1996) and the prevalence of visuospatial vs. movement encoding (Shen & Alexander, 1997a,b). This supports the view that the PMd and MI are a rostral extension of the distributed visuomotor system begun as the dorsal stream (Godschalk et al., 1985; Johnson et al., 1996; Battaglia Mayer et al., 1998). The ®nding that, prior to movement, visual target speed and direction are processed in the PMd and MI further underscores the visuomotor nature of the processing in these areas. During the cue period, visual input has been shown to be an important contributor to the ®ring of neurons within the PMd and MI. During instructed-delay reaching tasks, the discharge of these cells is highly modulated for prolonged periods prior to movement onset by both the visual and motoric aspects of the task (Tanji & Evarts, 1976; Weinrich & Wise, 1982; Crammond & Kalaska, 1994; Johnson et al., 1996; Shen & Alexander, 1997a,b; Zhang et al., 1997). Even more complex sensorimotor processes occur in these traditionally motor areas, including the control of visuospatial attention (di Pellegrino & Wise, 1993), registration of the sequences of successive visual directional stimuli (Kettner et al., 1996; Carpenter et al., 1999), quantization of vibrotactile stimulation speeds (Salinas & Romo, 1998), and mental rotation (Georgopoulos & Pellizzer, 1995). Therefore, the visuomotor transforms begun in the caudal dorsal stream are far from completed in the parietal cortex, as considerable processing occurs in the frontal motor areas. Acknowledgements We wish to thank Mike McPhee for assistance with graphics and histology and Joan Bailey and Linda King for help with manuscript preparation. Ezra Ebner assisted in programming. The work was supported by NIH grants 5R01NS31530, 2R01-NS18338 and 5F31-MH11430 and a grant from the Human Frontier Science Program. 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