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The Journal of Neuroscience, March 14, 2007, 27(11):2760-2780; doi:10.1523/JNEUROSCI.3147-06.2007
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Behavioral/Systems/Cognitive
Relationship between Unconstrained Arm Movements and Single-Neuron Firing in the Macaque Motor Cortex
Tyson N. Aflalo andMichael S. A. Graziano Department of Psychology, Princeton University, Princeton, New Jersey 08544-1010
Abstract
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Abstract
Introduction
The activity of single neurons in the monkey motor cortex was studied during semi-naturalistic, unstructured arm movements made spontaneously by the monkey and measured with a high resolution three-dimensional tracking system. We asked how much of the total neuronal variance could be explained by various models of neuronal tuning to movement. On average, tuning to the speed of the hand accounted for 1% of the total variance in neuronal activity, tuning to the direction of the hand in space accounted for 8%, a more complex model of direction tuning, in which the preferred direction of the neuron rotated with the starting position of the arm, accounted for 13%, tuning to the final position of the hand in Cartesian space accounted for 22%, and tuning to the final multijoint posture of the arm accounted for 36%. One interpretation is that motor cortex neurons are significantly tuned to many control parameters important in the animal's repertoire, but that different control parameters are represented in different proportion, perhaps reflecting their prominence in everyday action. The final posture of a movement is an especially prominent control parameter although not the only one. A common mode of action of the monkey arm is to maintain a relatively stable overall posture while making local adjustments in direction during performance of a task. One speculation is that neurons in motor cortex reflect this pattern in which direction tuning predominates in local regions of space and postural tuning predominates over the larger workspace.
Key words: primary motor; reaching; grasping; posture; direction tuning; motor control
Introduction
Neurons in the motor cortex of the monkey brain are active during arm movements. This activity is correlated with a range of movement parameters, including force, muscle activity, the direction, speed, and position of the hand, joint rotation, the multijoint posture of the arm, and other aspects of movement (Evarts, 1968; Georgopoulos et al., 1982
One limitation in previous studies is a tendency to use highly constrained movement sets and animals that are extensively trained. We recorded from neurons in the motor cortex of untrained monkeys. The arm was free to move spontaneously and naturalistically while the movements were measured. One goal of this study was to compare the results of a naturalistic, untrained movement set with the previous results obtained with structured, trained movement sets. Can the previous findings be replicated in the present movement set, or will removing the behavioral control also remove the previously obtained neuronal tuning curves?
A second goal of this study was to assess the proportion of total neuronal variance attributable to different movement parameters. In most previous experiments, the constrained movement sets were designed to focus on one or a small number of movement parameters. Once all other sources of variance have been removed, minimized, or averaged out of the data, then the particular parameter under study may account for most of the remaining neuronal variance, with an R2 value that may be as high as 0.9. Such studies, although legitimately addressing a variety of questions, do not address a certain fundamental question. If most sources of neuronal variance are left in the data by using a more natural range of movement, then what proportion of the total neuronal variance can be explained by any single parameter? Are neurons primarily tuned to one parameter, with the majority of their total variance explained by that parameter, or instead are neurons partially tuned to a diversity of parameters, with each parameter capturing a small portion of the total variance?
Of the 25 analyses included here, five overlap with a preliminary report (Aflalo and Graziano, 2006
Materials and Methods
All procedures were approved by the Princeton University Institutional Animal Care and Use Committee and the attendant veterinarian and were in accordance with National Institutes of Health and United States Department of Agriculture guidelines. We studied the motor cortex in the left hemispheres of two adult male Macaca fascicularis.Surgery. For each monkey, an initial surgical operation was performed under isoflurane anesthesia and strict aseptic conditions, during which an acrylic skullcap was fixed to the skull with bone screws. A steel bolt for holding the head and a 2.5 cm diameter steel chamber for neuronal recording were also imbedded in the acrylic. The recording chamber was positioned for a vertical (dorsoventral) approach to the precentral gyrus. Each animal recovered from the surgery within 1 week but was given 2 additional weeks to allow the skull to grow tightly around the skull screws. In a subsequent procedure, also under deep anesthesia and aseptic conditions, the recording chamber was opened and a hole
10 mm in diameter was drilled through the layer of acrylic and the bone, exposing the dura.
Neuronal recording. During the daily recording sessions, the monkey sat in a Lexan primate chair with the head restrained by the head bolt. A hydraulic microdrive (Narishige, Tokyo, Japan) was mounted to the top of the recording chamber. A steel guide tube (a 22 gauge syringe needle) was lowered through the hole in the skull and into the granulation tissue that lay over the dura. Then the varnish-coated tungsten microelectrode (impedance of 0.5–2 M
; Frederick Haer Company, Bowdoinham, ME) was advanced from the guide tube through the dura and into the brain. Neural signals were amplified (model 1800 amplifier; A-M Systems, Carlsborg, WA), filtered (300–5000 Hz), and recorded at 25,000 Hz. An off-line spike-sorting algorithm was used to assign spikes to individual neurons. Typically one to three neurons could be reliably isolated on the electrode at one time.
Single-neuron activity was sampled at various depths within the motor cortex ranging from the first depth at which any neurons could be isolated to the depth at which the neurons disappeared and the white matter was presumed to begin. A systematic test of different layers of cortex was not attempted in the present experiment. We saw no clear distinction in the tuning properties reported here for shallow or deeper recordings within motor cortex and therefore included all neurons into one analysis population. Neurons were not preselected in any way based on response properties. Instead, all neurons that were encountered by the electrode and that could be held long enough for collection of a full dataset were included.
Location of recording sites. Neither monkey was killed at the termination of this experiment. For monkey 1, after the experiment, the implant was removed and the brain was scanned in a 3-T Siemens (Munich, Germany) Allegra magnetic resonance imaging (MRI) head scanner using a 16 cm birdcage coil (NMSC-023; Nova Medical, Wakefield, MA). A high-resolution, 0.5 x 0.5 x 0.5 mm anatomical scan of the whole brain was taken (magnetization-prepared rapid-acquisition gradient echo sequence; field of view, 128 x 128 mm; matrix, 256 x 256; repetition time, 2500 ms; echo time, 4.4 ms; flip angle, 8°). Figure 1A shows a surface reconstruction of the cortex with the studied area in brightened shading. Figure 1B shows a sagittal section through the motor cortex with the studied area again in brightened shading.
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Figure 1. Images of the brain of monkey 1 showing the studied area of cortex. A, MRI reconstruction of the cortical surface showing sulcal pattern. Studied region is in lightened shading. The white line indicates the section shown in B. B, Parasagittal section (0.5 mm thick) through the studied area of cortex. Studied region is in lightened shading.
To find the motor cortex before recording, the central and arcuate sulci were located by shining a bright light on the dura during the initial craniotomy surgery. Both sulci were clearly visible through the dura. The microdrive was then mounted to the recording chamber, and the locations of the visualized sulci were measured with the tip of the guide tube. In this way, the locations of the sulci were obtained in microdrive coordinates.After the craniotomy surgery, during the daily experiments, the measured location of the central sulcus was confirmed to within 0.5 mm by recording and stimulating to either side of the sulcus. Just posterior to the sulcus, in primary somatosensory cortex, we observed the expected small tactile receptive fields on the contralateral limb and also the expected rarity of effect of intracortical electrical microstimulation even with currents as high as 200 µA (negative leading biphasic pulses, 0.2 ms phase width, 200 Hz, 100–500 ms train durations, 5–200 µA current). Just anterior to the sulcus, we obtained neuronal responses during hand and arm movement and low microstimulation thresholds, typically <20 µA, sometimes as low as 5 µA, as expected from primary motor cortex. The location of the arcuate sulcus was confirmed by microstimulating just anterior to it and obtaining no skeletomotor movements, but instead obtaining stimulation-evoked saccadic eye movements presumably in the frontal eye fields.
The sites tested were located in the arm representation in motor cortex and were within the anterior bank of the central sulcus or on the cortical surface within 2 mm of the central sulcus. They therefore lay within the boundaries of traditional primary motor cortex. Additional information on the location of sites within the functional map was provided by the analyses of the joint angles to which the neurons were responsive, as described below.
Measurement of joint angles. The positions of points on the limb contralateral to the recording electrode were measured by means of an Optotrak 3020 system (Northern Digital, Waterloo, Ontario, Canada). This system tracks the three-dimensional position of infrared light emitting diodes (LEDs). Each LED could be separately tracked to a spatial resolution of 0.1 mm. The position was measured every 14.3 ms. To create a marker that could be detected by the Optotrak cameras from any angle, we glued five individual LEDs together to produce an omni-directional marker ball. A marker ball was taped to the monkey's forefinger on the dorsal surface so it would not interfere with grasping, on the thumb, again on the dorsal surface so it would not interfere with grasping, on the back of the hand between the knuckles of the third and fourth digits, on the lateral aspect of the elbow, and on the shoulder. In addition, 14 individual markers were taped in a double ring around the monkey's wrist, with seven markers per ring and a 1 cm spacing between the rings. A marker was taped to the side of the primate chair to calibrate the position of the monkey with respect to the chair. For the LEDs attached to the arm and hand, the wires were taped in a bundle to the underside of the arm and draped behind the monkey. The primate chair was open at the front and side, allowing for almost total range of movement of the arm. The monkey's other arm, ipsilateral to the electrode, was not studied with Optotrak markers. To ensure that this hand did not reach for the fruit rewards during trials or tear off the markers taped to the measured hand, the untested hand was fixed to the side of the chair in an arm holder.
The double ring of 14 markers around the wrist was subjected to a rigid body computation to calculate the location and spatial orientation of the wrist. In this computation, for each time point, a three-dimensional rigid model of the double ring of markers was fitted to the measured positions of the currently visible markers, using a least-squares method of optimal fit. The orientation and position of the model could then be used to estimate the orientation and center of the wrist. The center of the wrist was taken to be the mean position of the 14 points in the model.
The position of the shoulder in space was calculated by analyzing the position of the elbow over time. Over many time points, the elbow described a portion of a sphere, the origin of which was located at the shoulder joint. For each 3 min block of data, a shoulder position was calculated by fitting a sphere to the data using a least-squares best-fit algorithm and using the center of the sphere as the shoulder location. Because the shoulder is capable of small translational movements in addition to rotations, this method of estimating shoulder joint location is approximate but was sufficient for the purposes of this study. When the shoulder position was calculated multiple times over different time segments, it varied within <3 cm.
Three shoulder angles were computed: the elevation, the azimuth, and the "twist" or internal/external rotation of the shoulder joint. We also calculated the flexion of the elbow, the pronation of the forearm, the extension of the wrist, the adduction of the wrist, and the grip aperture. In total, eight degrees of freedom were calculated for the arm. This model of the arm was verified by applying forward kinematics to estimate the position of the hand. This calculated position of the hand matched the actual, measured position of the hand within 1.5 cm.
Description of movements in the dataset. During testing of a neuron, the monkey was allowed to move its contralateral arm freely to touch and explore parts of the primate chair, to reach for small pieces of fruit held out on the end of forceps, to bring food to its mouth, to retrieve food from its mouth, to hold and examine food in central space, and to rotate and explore food items. Occasionally, the monkey also scratched at its skin, scratched rhythmically at a portion of the monkey chair, or attempted to scratch the experimenter with a fast semi-ballistic arm movement. The movement of the arm was recorded through all of these behaviors. Different types of behaviors were not separated in the analysis, partly because one type of behavior tended to grade into another type and the distinction between behaviors could only be made subjectively and partly because the purpose of the study was to include all arm movements in as large and naturalistic a range as possible given the constraints of the primate chair.
For each neuron, the position of the hand in three-dimensional space was measured every 14.3 ms during a continuous time interval ranging from 10 to 30 min. The hand position data were smoothed using a cubic spline with a smoothing coefficient of 0.05. The instantaneous hand speed was then calculated using a three-point running average to obtain a smoothed speed profile. Separate movements were extracted from the dataset on the basis of a speed analysis. Minima in the speed were identified and the intervals between minima were flagged as potential separate movements. To enter the final dataset, the movement had to be at least 150 ms in duration and the peak speed had to be at least 20 cm/s. These parameters seemed to successfully divide the data into discrete segments that matched our subjective impression of separate hand movements. The average speed profile is further described in Results (see Speed tuning I).
The various analyses in this report focus on the neuronal activity associated with periods of arm movement as defined by the velocity analysis described above. We originally attempted to analyze both the periods of movement and the interleaved periods of non-movement but found that neurons were frequently inactive during periods of hand stasis between movements. This lack of activity may be related to the spontaneous nature of the movements. There may have been little planning between movements. Sometimes the arm was relaxed or braced against a part of the chair between movements, and this state of relaxed stasis could not be distinguished from more active stasis in the recorded data. Often the animal performed a mouth movement or a foot movement between arm movements, perhaps drawing attention and motor planning to a different body part. These reasons may have contributed to a reduction in and a variability of neuronal activity between movements. The analyses reported here are therefore focused on the periods of arm movement.
Figure 2A shows a typical movement set collected during the testing of a neuron. This set shows 514 separated movement segments that densely sampled the workspace of the hand. Vertically, the movements ranged from 29.7 cm below the mouth to 7.8 cm above the mouth. Horizontally, the movements ranged from 19.4 cm on the contralateral side (same side as the studied arm, opposite side to the electrode) to 16.6 cm on the ipsilateral side. In depth (direction along the monkey's forward line of sight), the movements ranged from 7.5 cm behind the level of the mouth (such as when the monkey reached to its flank or to its ear) to 20.2 cm in front of the mouth (normal for a fully extended reach). The range of movement starting points was not significantly different from the range of ending points.
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Figure 2. Range of movements in the naturalistic movement set. A, Front view of 514 hand movements made during 10 min of testing one neuron. Each trail of dots is equivalent to one movement measured at 14.3 ms intervals. Frame is 45 cm tall. B, Correlations among the final positions of the eight degrees of freedom among the recorded movements. Degrees of freedom are as follows: 1, shoulder azimuth; 2, shoulder elevation; 3, shoulder internal/external rotation; 4, elbow extension; 5, forearm pronation; 6, wrist extension; 7, wrist adduction; 8, grip aperture. Units on x- and y-axes of each plot are degrees of joint angle, except for degree of freedom 8, which is expressed in centimeters.
The average ± SD length of a movement was 8.0 ± 4.9 cm. The average ± SD duration was 351 ± 133 ms. The average ± SD hand speed was 23.74 ± 9.9 cm/s. Each movement had a peak speed, and the average ± SD peak speed among all movements was 40.7 ± 20.4 cm/s. The average time between movements was 4.06 s. This pause between movements ranged from <1 s (40% of pauses, representing brief periods of stasis during ongoing arm movement) to longer than 10 s (15% of pauses, representing periods when the monkey had stopped making arm actions and was stationary or engaged in movement of other body parts).For each movement, we calculated a standard curvature metric as follows. The straight-line distance between the start and end of the movement was found. The total path length of the movement was found. The ratio of these two quantities provided a curvature metric in which 1.0 corresponds to no curvature and smaller numbers correspond to increasingly curved movements. The average ± SD curvature was 0.91 ± 0.09, indicating that the movements tended to be straight. In Figure 2A, some movements appear to be highly curved. This appearance is a result of collapsing a three-dimensional movement into a two-dimensional depiction in which the long axis of the movement is not fully shown.
For each movement, we calculated a direction by connecting the start point to the end point and obtaining the azimuth and elevation angles. The distribution of these directions was then examined. The directions appeared to be relatively evenly distributed. The sphere of all possible directions was divided into 20 equal sectors, and the movement directions were distributed over these 20 sectors with all sectors represented. Thus, the unstructured movement set was well behaved, followed expected characteristics of normal movement, and included a diverse range in terms of workspace, length, speed, and direction.
Inevitably, the movement set included some non-uniformities in the distribution of hand positions and joint angles. For example, hand positions near the face were overrepresented. Hand positions in lower space were less well represented. Because the movement sets were spontaneous, we were not able to enforce an even distribution of all types of movement. As a result, there is some concern whether the dataset is diverse enough, and the movement parameters independent enough, to allow for meaningful regression analyses. One approach to this issue is addressed in Results (see Simulated neurons). We simulated noisy neurons that were tuned in a variety of ways, calculated the expected response of these neurons during the actual recorded movement sets, and then applied the regression models to the results. We found that the movement sets were sufficiently diverse to allow the regression analyses to uncover the correct tuning curves.
Non-uniformities in the movement set present a particular problem for separating the effect of direction tuning from the effect of hand-position tuning. For example, if a neuron is tuned to upward motion of the hand, it may appear to prefer an upper hand location simply because that location in space can only be reached by upward motion. This possible confound was addressed partly through the use of the simulated neurons (simulated direction-tuned neurons did not evidence a high degree of tuning to hand position) and partly by means of the analysis of neuronal data in Results, showing that the preferred direction does not easily account for the hand-position tuning (see End-point tuning).
Non-uniformities in the movement set may also result in correlations among the different joints of the arm. Such interjoint correlations would be problematical particularly in the analysis for neuronal tuning to final posture. A neuron may actually be related to one joint but, because of interjoint correlations, appear to be related to other joints as well. It was therefore important that the movement set contain enough independence among joints that the contributions of each joint could be separated through regression analysis. Figure 2B shows the correlations among the joint angles reached at the end of the movements. The joints were not tightly coupled. Some showed correlations with each other, as expected given the known covariance of joints during movement, but the scatter was easily sufficient to allow a regression analysis to separate the different contributions. This lack of any strong coupling among joints was probably caused by the great diversity of movements in the set and is presumably the reason for the success of the simulated neuron analysis in which simulated tuning functions could be successfully recovered using our regression analyses. This issue is further addressed in Results.
Preliminary analysis to specify somatotopic location. To further confirm the somatotopic portion of motor cortex that was studied, we performed a preliminary analysis on each neuron. Using a stepwise regression, we obtained the degree of correlation between the neuronal activity and the velocity of each of the eight measured joints. If we were recording primarily in a distal representation, we would expect to find significant regressions with distal joints including hand aperture, wrist flexion, wrist adduction, and forearm pronation. If we were recording primarily in a proximal representation, we would expect to find significant regressions with proximal joints, including elbow flexion and the three degrees of shoulder rotation. Given the known overlap in motor cortex somatotopy, we expected to find neurons related to both proximal and distal joints. The results indicated that 89% of the neurons were significantly related to the proximal joints and 67% were significantly related to the distal joints. These results indicate that the studied neurons were in the forelimb representation in a region that emphasized the proximal joints over the distal joints but represented both.
Regression models. Each neuron was tested for a range of possible tuning functions. Each model of a tuning function was compared with the behavior of the neuron by means of a regression analysis. Some models, such as tuning to speed, involved one free parameter. Other models, such as tuning to posture, involved several free parameters. To avoid inflating the R2 value with the addition of more parameters, we used the standard adjusted R2 metric that takes into account the number of regressors (Cohen et al., 2003
For all regression models described below, we followed a standard procedure in which we offset the movement data from the neuronal spike data by a latency. In this procedure, the kinematic data were taken from the movement period defined by the velocity analysis and the neuronal spike data were taken from an equivalent time period offset by a latency. We tested latencies between –286 and 286 ms at 14.3 ms increments (the temporal resolution of the movement data) and used the result of the regression analysis to choose the latency that optimized the R2 between neuronal activity and movement. The reason for this approach is that, in general, a latency will exist between the activity of a cortical neuron and the movement of the arm, and different neurons may have different latencies. This analysis differs from the analysis we described previously (Aflalo and Graziano, 2006
In most analyses, the neuronal firing rate was averaged over the duration of each movement, and therefore no additional smoothing of the neuronal data was required. However, for the analyses of hand speed, the instantaneous neuronal firing rate was required. For these analyses, we smoothed the firing rate data using a 10 Hz upper cutoff. The reason for using this frequency cutoff was to ensure that our results were directly comparable with previous studies that used a similar technique (Moran and Schwartz, 1999
The four main regression models used in this paper are described below, and other models are described in the relevant subsections of Results.
Direction tuning. Each neuron was tested for direction tuning in the following manner. For each movement, we calculated a mean firing rate of the neuron (spikes per second during the movement, offset by a latency as described above). Each hand movement was assigned a direction in Cartesian space based on the vector connecting the beginning and end point of the movement. Firing rate was modeled as a function of the angular deviation (
) between this movement vector and a preferred direction: firing rate = A cos (
Direction tuning that rotates with the start position of the hand. Each neuron was also tested with a second direction-tuning model. In this model, the preferred direction vector (PD) was obtained using a cosine tuning model of neuronal firing rate, as above. However, PD was not assumed to be fixed in all regions of the workspace. Instead, it was assumed to vary depending on the start position of the arm. The start vector (ST) was defined as the vector pointing from the shoulder to the position of the hand at the start of the movement. The direction of ST was described by two parameters: the start azimuth
. PD was assumed to vary linearly with ST. In this model, the azimuth of PD was linearly related to the azimuth of ST with a slope defined by the parameter AZ, and the elevation of PD was linearly related to the elevation of ST with a slope defined by the parameter EL. Thus, if both AZ and EL are 0, then PD is indeed independent of ST and always points in the same direction regardless of starting position. If AZ and EL are both 1,then PD rotates exactly in tandem with ST, remaining at afixed spatial relationship with respect to the arm. In this model, the equation for PD as a function of AZ,
where PD0 indicates the preferred direction when the hand is located at
End-point tuning. For this model of neuronal tuning, all data concerning the direction or trajectory of the movement was discarded and only the end point of the movement was considered. Firing rate was modeled as a Gaussian function of these end points in Cartesian space. In the following equation, x1, x2, and x3 refer to the three Cartesian coordinates of the end point of the movement, P1, P2, and P3 refer to the coordinates of the peak of the Gaussian, the SDs of the Gaussian around that peak are indicated by
1,
End-posture tuning. This model followed the same general equation as the end-point model except that it involved the eight dimensions of arm-posture space (x1 through x8) rather than the three dimensions of Cartesian space. Firing rate was modeled as a Gaussian function that had a peak at a specific, preferred posture. Again, a nonlinear regression technique was used to fit the model to the data for each neuron:
Results
Speed tuning I
We first tested whether previous standard methods of obtaining speed tuning from motor cortex neurons would also reveal speed tuning in the present, unconstrained movement set. In the first test of speed tuning, we used a procedure based partly on that of Moran and Schwartz (1999)Figure 3 shows the results for one example neuron. The data on the changing position of the hand through time was segmented into separate movements (for details, see Materials and Methods). Because of the unconstrained nature of the animal's behavior, different movements were of different durations. To average across movements, we first normalized the length of movements by dividing each movement into 20 time bins. For each time bin, the instantaneous firing rate and the hand speed were calculated. These numbers were then averaged across the 321 movements tested for this neuron. The thin line in Figure 3A shows the average hand speed rising and falling during the movement in a smooth, bell-shaped velocity profile typical of normal movement. The thick line shows the average neuronal activity, also rising and falling during movement.
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Figure 3. Speed tuning of motor cortex neurons. A, Firing rate and hand speed averaged over 321 movements for one example neuron. When neuronal data were shifted forward by 71 ms (the optimal time lag for this neuron), the two curves matched closely with an R2 of 0.87. B, Frequency histogram of R2 values for all 64 neurons tested as in A. C, Firing rate versus hand speed for 9018 time bins during hand movement studied for one example neuron. The two variables showed a small but highly significant correlation (R2 = 0.03; p = 1.5 x 10–17). D, Frequency histogram of R2 values for all 64 neurons tested as in C.
We performed a regression analysis to compare the average hand speed with the average firing rate. Following a standard method, we used a fixed time window of kinematic data that corresponded to the hand movement and used a time window of equal duration but adjustable start time for the neuronal data. The temporal offset between the neuronal and kinematic data were then optimized to yield the maximum R2 value. A similar offset optimization was used for all analyses (see Materials and Methods). For this neuron, the regression analysis returned the largest R2 value at a temporal offset of –71 ms with neuronal activity preceding movement. The R2 value for this example neuron was 0.87, and the regression was highly significant (p = 3.5 x 10–9).Figure 3B shows a histogram of R2 values for all 64 cells tested in this manner. The mean R2 value was 0.71, and 93% of the neurons had a statistically significant regression against speed (0.05 significance level, corrected for the number of neurons using the Bonferroni method). These findings approximately match the findings of Moran and Schwartz (1999)
The above method of testing for speed tuning has a limitation. The method involves averaging across many movements to obtain relatively smooth, well behaved curves from which the between-movement variance has been removed. If the averaging is not performed and therefore the full range of neuronal variance is left in the analysis, what percentage of the total variance will be attributable to speed tuning? This question is addressed in the next section.
Speed tuning II
To examine speed tuning in the raw data without using averaging to remove variance, we used a technique based partly on that of Ashe and Georgopoulos (1994)Figure 3D shows the R2 values for all 64 cells tested. The mean R2 was 0.01, and 98% of the neurons had a statistically significant regression (0.05 significance level, corrected for the number of neurons using the Bonferroni method). These results show that almost all neurons are tuned to hand speed and that this tuning accounts for a small proportion of the total neuronal variance.
Many different analytic methods can be used to test for speed tuning. We tested two additional regression analyses with similar results. We compared the peak speed of each movement (hand speed during the 14.3 ms time bin around the peak speed) with the firing rate associated with that peak speed (during the 14.3 ms time bin offset from the peak speed by a latency optimized for each neuron). This regression returned a mean R2 value of 0.03. We also compared the mean speed during each movement with the mean firing rate associated with the movement (during a time window of the same duration as the movement and offset by a latency optimized for each neuron). This regression returned a mean R2 value of 0.02. All of these methods converged on a similar result: the neuronal firing rate varies from movement to movement, and 1–3% of this variance is attributable to speed tuning. Only when the between-movement variance is removed by averaging (as above, Speed tuning I) will the remaining variance be well correlated with hand speed. These results do not show that neurons have no real speed tuning. Rather, they are genuinely speed tuned, accounting for a small proportion of the total neuronal variance. Previous studies report that motor cortex neurons are tuned to both speed and direction. Can a large proportion of the remaining variance be attributed to direction tuning? The following sections examine tuning to direction and also to velocity.
Direction tuning I: local
Figure 4A shows 26 movements selected from the 320 spontaneous movements performed by the monkey during the testing of one example neuron. These 26 movements were selected from the full set of movements on the basis of start location (within a central ball of space with radius 5 cm) and length (between 6 and 15 cm). These movements therefore roughly approximated the center-out movement set commonly used to test direction tuning in motor cortex neurons (Georgopoulos et al., 1986
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Figure 4. Direction tuning of motor cortex neurons. A, Front view of 26 selected hand movements made during 10 min of testing one neuron. Each trail of dots is equivalent to one movement measured at 14.3 ms intervals. Frame is 45 cm tall. Each movement shown originated within a 5 cm radius sphere of central space and was between 6 and 15 cm in length. B, Tuning of an example neuron to direction, based on selected movement set. x-Axis shows angular difference between the direction of each movement and the preferred direction; y-axis shows mean firing rate during each movement; for cosine tuning to direction, R2 = 0.43, p = 0.0001. C, Frequency histogram of R2 values for all neurons tested as in B. D, Front view of full set of 320 hand movements made during testing of one neuron. E, Direction tuning of an example neuron (same neuron as in B), based on full movement set. R2 = 0.05, p = 0.00008. Note that a new preferred direction was obtained by regression, and therefore the data points shown in B do not plot to the same location on the x-axis as in E. F, Frequency histogram of R2 values for all neurons tested as in E.
Figure 4B shows the result of this analysis for an example neuron. On average, the firing rate was high during movements near the preferred direction (thus with lowFigure 4C shows the R2 values for all cells tested. The mean R2 value was 0.42, and 68% of the cells showed a significant fit to the cosine model of directional tuning (0.05 significance level, corrected for the number of neurons using the Bonferroni method). The present results are therefore similar to previous results using a center-out task, in that most neurons showed a significant fit to a cosine tuning function.
Just as in the case for speed tuning, the R2 values obtained for the present analysis showing strong direction tuning must be interpreted cautiously. The movement set is limited such that the direction of movement represents a main source of variance and thus results in a relatively high R2. Other sources of variance, including differing starting positions, starting postures, and movement distances, although present in this selected dataset, are minimized. If the entire range of movements were used and, thus, all sources of variance were admitted to the data, how much of the total variance would be attributable to direction tuning? This question is addressed in the next section.
Direction tuning II: global
Figure 4D shows the full set of 320 movements performed by the monkey during the testing of one example neuron. We performed a regression analysis to determine how well the neuronal firing during the full range of movements fit a cosine model of direction tuning. Figure 4E shows the result for the same example neuron shown in Figure 4B. The regression fit to the cosine model was highly significant (p = 0.00008). The R2 value for the global movement set, however, was 0.05. Thus, direction tuning accounted for onlyThese results show that most neurons in motor cortex are indeed direction tuned, but by itself direction tuning accounts for only
Direction tuning III: rotation of preferred direction with changes in starting hand position
The previous section examined whether each neuron was tuned to a single preferred direction. One possibility, however, is that a single preferred direction might not capture the full extent of direction tuning for a typical neuron. Perhaps direction tuning would capture a greater share of the total neuronal variance if we used a more sophisticated tuning model in which the preferred direction rotates systematically as the starting position of the hand changes.Caminiti et al. (1990)
We analyzed each neuron as follows (for equations, see Materials and Methods). First, for each movement, we defined the start vector to be the straight-line vector from the monkey's shoulder to the position of the hand at the start of the movement. The direction of this start vector was defined by a specific start azimuth angle and start elevation angle. We then fit the neuronal data to a regression model that included a cosine tuning to a preferred direction but in which the preferred direction rotated in the azimuth in a manner linearly related to the start azimuth angle of the arm and also rotated in elevation in a manner linearly related to the start elevation angle of the arm. The ratio between the rotation of the preferred vector of the neuron and the start vector of the arm was parameterized by two numbers, AZ for the azimuth ratio and EL for the elevation ratio. For example, if the regression settled on an AZ = 0, this result would indicate that the preferred direction for the neuron remained constant in different regions of space and did not rotate in the azimuth regardless of the start vector. If the regression returned an AZ > 0, this result would indicate that the preferred direction of the neuron tended to rotate in the same direction as the starting vector of the arm. An AZ = 1 would indicate that the preferred vector rotated exactly in tandem with the start vector of the arm. An AZ < 0 would indicate that the preferred vector rotated in the opposite direction as the start vector of the arm. Given the noisy nature of neuronal signals, a range of AZ values was expected, and a null result would emerge as a distribution of AZ values centered around 0. Similar relationships would pertain to the elevation of the preferred vector and the elevation of the start vector, characterized by the parameter EL.
Figure 5A shows the results of this regression for all neurons. The black bars show the results for the azimuth. The AZ values peaked near 1. The mean AZ value was 0.88, and the distribution was significantly more than 0 (t = 3.87; p = 0.00039). This result replicates the finding of Caminiti et al. (1990)
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Figure 5. Rotation of preferred direction with starting hand position. A, A preferred direction model was tested in which the preferred direction of a cell was not fixed but instead could rotate as the start position of the hand rotated. Frequency histogram shows AZ and EL values for all cells tested. The AZ rotation index indicates the ratio between the starting azimuth angle of the arm and the azimuth angle of the preferred direction of the neuron. The peak in AZ near 1 indicates that the preferred direction of most neurons tended to rotate in the same direction and by a similar amount as the starting angle of the arm. Similarly, the EL rotation index indicates the ratio between the starting elevation angle of the arm and the elevation angle of the preferred direction of the neuron. B, Frequency histogram of R2 values for all cells tested with this model of a rotating preferred direction.
The experiment of Caminiti et al. examined changes in start position in the azimuth only. Here we were able to examine changes in both azimuth and elevation, and the open bars in Figure 5A show the result for elevation. The mean EL value was 0.54, and the distribution was significantly more than 0 (t = 2.28; p = 0.029). This result indicates that the preferred direction tended to rotate in elevation in the same direction that the start vector rotated. However, the distribution was not as clearly shifted toward 1 for elevation as it was for azimuth.These results show that the preferred direction that best fits a neuron, as extracted by regression analysis, tends to be one that changes depending on the start position of the hand, rotating approximately in tandem with the arm. This trend is more clear and highly significant for rotations in the azimuth and is less clear although still significant for elevation. Figure 5B shows the distribution of R2 values obtained with this model of a rotating preferred direction. The mean R2 value is 0.13. This mean R2 value is significantly greater than the mean R2 of 0.08 obtained with the previous, simpler model of a fixed preferred direction and shown in Figure 4F (comparison of the two R2 distributions, t = 3.5; p = 0.00072).
Direction tuning IV: changes of preferred direction with changes in initial posture
Scott and Kalaska (1995For each neuron, we performed the following analysis. We analyzed the posture of the arm at the start of each movement. We focused on two aspects of arm posture: the elevation angle of the shoulder and the internal rotation angle of the shoulder. We constructed a single parameter, the "raised elbow" parameter, in which both of these shoulder angles varied together. A high value of raised elbow indicates that the shoulder elevation was high and the shoulder was internally rotated, essentially bringing the arm to a "chicken wing" posture with the elbow in upper space. Likewise a low value of raised elbow indicates that the shoulder elevation was low and the shoulder was externally rotated, essentially bringing the elbow to a low position. All movements were divided into two equal groups along a median split: those with a high raised elbow value at the start of the movement, and those with a low raised elbow value at the start of the movement. For each group of movements, we separately calculated a preferred direction using a regression analysis as above (see Direction tuning I). We then compared the two preferred directions by calculating the angular difference between them.
Figure 6A shows the result for one example neuron. The preferred direction was different for the trials with a high value of raised elbow than for the trials with a low value of raised elbow, with a change in preferred direction of 62° (Fig. 6A, thin vertical line). Is this change in preferred direction the result of the change in arm posture, or is it merely the result of noise in measuring an unreliable preferred direction? To address this question, we took the same total movement set and divided it in half randomly, calculating a preferred direction for each half and then finding the difference between the two preferred directions. We performed this random division of the data 200 times. The results are shown in the histogram in Figure 6A. When the movements were randomly assigned to two groups, the difference in preferred direction tended to be small, with a mean difference of 24°. When the movements were assigned to two groups on the basis of arm posture, the difference obtained was far from the randomized mean, with a Z score of 2.81. For this particular cell, the start posture of the arm had a significant effect on the preferred direction, beyond that expected by chance (p = 0.0051). This example neuron was not typical; it showed an unusually clear effect.
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Figure 6. Change in preferred direction with starting arm posture. A, Results for one neuron. All movements were divided on a median split according to a raised elbow parameter (see Results, Direction tuning IV: changes of preferred direction with changes in initial posture). The preferred direction was calculated separately for the two sets of movements, and the difference in preferred direction (
Figure 6B shows the distribution of Z scores obtained for all neurons. If the posture of the arm had no significant effect on direction tuning, then the Z scores should be equally distributed about 0. The distribution is broad and extensively overlaps 0 but is significantly more than 0 (mean of 0.51; t = 2.89; p = 0.0057). Thus, the effect of starting posture on the preferred direction is variable from neuron to neuron but across the population of neurons is statistically significant. These results replicate the finding of Scott and Kalaska (1995Direction tuning V: velocity tuning
The above sections explore speed tuning and direction tuning separately. It has also been shown that motor cortex neurons are tuned to velocity or to the combination of speed and direction (Moran and Schwartz, 1999First, we performed the same regression as above (see Direction tuning II: global), but the direction vectors in the regression equation were replaced by velocity vectors (the velocity vector for each movement was defined as the mean hand velocity during the movement, whose components were the mean x, y, and z hand velocity). The regression model returned a preferred velocity vector for each neuron with a cosine tuning to that preferred velocity. This model of velocity tuning resulted in a mean R2 value of 0.09, not significantly different from the value obtained for regression against direction alone (0.08).
Second, we performed the same regression as above (see Direction tuning III: rotation of preferred direction with changes in starting hand position) but again with the direction vectors in the regression equation replaced by hand velocity vectors. This regression model returned a preferred velocity vector that could rotate depending on the start position of the hand. This model of velocity tuning resulted in a mean R2 value of 0.11, also not significantly different from the value obtained for regression against direction alone (0.13).
Direction tuning VI: modulation by a hand-position signal
The activity of motor cortex neurons is modulated not only by the direction of a reach but also by the position of the hand (Kettner et al., 1988We examined a model of this type that took into account both direction and hand position. We began with the regression equation from above (see Direction tuning III), in which the preferred direction was allowed to rotate depending on the starting position of the hand. This model, as described above, resulted in a mean R2 value of 0.13. It was the best of the direction tuning models in the sense that it captured the greatest percentage of the variance. We then modified the regression in two ways. The A term in the model (see Materials and Methods) was replaced by a term that depended linearly on the x, y, and z starting position of the hand. In this manner, the gain of the direction tuning response could be modulated by hand position. Likewise, the B term in the model was replaced by a term that depended linearly on the x, y, and z starting position of the hand, thereby allowing the baseline of the direction tuning response to be also modulated by hand position. This model therefore examined the amount of neuronal variance that could be attributed to a combination of direction tuning and a linear effect of starting hand position. Because the model took into account more than direction tuning, it was expected to capture more of the neuronal variance than did direction tuning alone.
The mean R2 value for this combined regression was 0.16. One interpretation is that direction tuning has improved by taking linear hand-position trends into account. This interpretation, however, is not correct. The model is not a direction-tuning model; it is a mixed model. The 16% of the variance is not attributable to direction tuning alone. Instead, the results indicate that direction tuning captures
End-point tuning I: Gaussian tuning
In a standard test of direction tuning, the hand begins in a central location and reaches to a variety of peripheral targets. The movements therefore differ in both direction and final hand position. Many studies have examined whether the tuning obtained in these tasks is truly a tuning to direction or instead a tuning to the final position of the hand (Georgopoulos et al., 1985To test for end-point tuning, we modeled the firing rate of the neuron as a Gaussian function of end point in which the Gaussian was peaked at a preferred spatial location of the hand (see Materials and Methods). Movements that ended near that preferred end point should be associated with high firing rates, and movements that ended far from that preferred end point should be associated with low firing rates. For each neuron, we obtained an R2 value indicating how well this end-point model fit the neuronal data. Figure 7A shows the distribution of R2 values for the population of neurons. On average, the end-point model accounted for 22% of the total neuronal variance.
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Figure 7. Tuning of neurons to hand end point. A, Each neuron was tested with a tuning model in which the neuron fired most during movements that terminated with the hand at or near a specific location in space and fired progressively less during movements for which the hand terminated progressively farther from the preferred location. The graph shows a frequency histogram of R2 values for all cells tested with this end-point model. B–D, Preferred hand positions as determined by the end-point tuning model, displayed from three perspectives. The schematic monkey drawing indicates approximate scale and orientation.
Figure 7B–D shows the distribution of preferred hand positions for the tested neurons, as obtained with the end-point tuning model. These preferred hand positions were dispersed through the space around the animal. For some neurons, the regression analysis found a preferred hand position at the edge of the normal range of the workspace. In such a case, the neuron essentially had a monotonic tuning to hand position, preferring one extreme side of the workspace over the other. Most neurons, however, had a preferred hand position inside the workspace and therefore had a nonlinear response function that fell off to either side of the preferred location. The tuning functions were generally broad: the mean width of the Gaussian tuning curve at half-height was 18 cm, approximately half the range of the workspace. Because of the broadness of these tuning curves, the end-point tuning is unlikely to be a major source of signal in experiments that test a small part of the workspace in front of the monkey. If only a small volume of the workspace is tested, most neurons will have a preferred hand position outside that tested region, and the tuning to end point will either be missed (if the tested part of space happens to overlap a relatively flat part of the tuning curve) or will be measured as a graded, monotonic preference for one side of the tested space over the other (if the tested part of space overlaps with the rising slope of the tuning curve).Figure 8A1 shows data from an example neuron. First, the end-point tuning was found using the regression analysis described above. This analysis obtained a Gaussian surface in three-dimensional space for which the peak of the Gaussian corresponded to the preferred end point of the neuron. In this graph, the x-axis represents the distance in centimeters between the end point of each movement and the preferred end point of the neuron. The y-axis represents the firing rate of the neuron during the movement. On average, movements that terminated near the preferred end point (distance of 0) had higher firing rates, and movements that terminated progressively farther from the preferred end point had progressively lower firing rates. This trend is noisy for two reasons. First, only
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Figure 8. End-point tuning of three example neurons. A1–A3, Mean firing rate of example neurons 1–3 during each movement as a function of the distance (centimeters) between the end of the movement and the preferred end point determined by regression analysis. The neurons fired more during movements that terminated closer to the preferred end point. B1–B3, Same data as in A but with the x-axis replotted in units of the SDs of the Gaussian tuning curve, displaying the tuning to end point more clearly. C1–C3, Rasters showing high neuronal activity of example neurons 1–3 during the 10% of movements that terminated nearest to the preferred end point and low neuronal activity during the 10% of movements that terminated farthest from the preferred end point. Red tic marks indicate start and end of movement.
Figure 8C1 shows rasters of neuronal activity for the same example neuron. Each line in the raster display shows spike data during the analysis window for a single movement. Because different movements were of different durations in the naturalistic movement set, these lines in the raster display are of different lengths. The first raster display shows data from the 10% of movements that terminated nearest to the preferred position; the second raster display shows data from the 10% of movements that terminated farthest from the preferred position. These rasters show that the firing rate was variable from movement to movement but that the neuron tended to fire more during movements that terminated near the preferred hand position (mean ± SD of 49.8 ± 20.6 spikes per second) and tended to fire less during movements that terminated far from the preferred hand position (mean ± SD of 13.9 ± 12.4 spikes per second) with a significant different between these two firing rates (t = 11.3; p = 4 x 10–20).Is the tuning to final hand position merely an artifact of direction tuning? The region of final hand positions that the neuron appears to prefer may have been approached predominantly from the preferred direction. For example, a neuron that prefers upward movements might appear to prefer an upper location in space. This explanation, however, is unlikely for several reasons. First, it predicts that the preferred hand locations should cluster systematically around the edges of the workspace, but, as shown in Figure 7, the neurons preferred a range of final positions including many within the workspace. Second, as described below (see Simulated neurons), we simulated a direction-tuned neuron and tested it on the actual movements measured from the monkey. The simulated neuron performed well on a direction-tuning model and showed little tuning to final hand position. A neuronal signal that is known to be direction tuned, therefore, does not produce an artifactual hand-position tuning.
Finally, Figure 9 shows a third analysis to address this question. Figure 9A1 contains data from one example neuron. The dots show the final hand positions for the 10% of movements that terminated closest to the preferred hand position. Figure 9B1 shows the directions of the movements that terminated in those locations. This movement set included a range of directions and did not approach the end points from predominantly one direction. We used this limited movement set to obtain a preferred direction (using a standard cosine tuning model as above, see Direction tuning I). The direction-tuning R2 value was 0.18. (The relatively low R2 value, below the mean of 0.42 obtained for local direction tuning in Direction tuning I, probably reflects the fact that these movements, although more local than a full movement set, are nonetheless more dispersed than in our test of local direction tuning.) The preferred direction among these movements, plotted as a thick line in Figure 9A1, was aimed down and to the left, whereas the preferred hand location was up and to the right. For this neuron, the preferred direction was pointed the wrong way to account for the preferred hand location. Figure 9 also shows a second example cell. In general, the preferred direction had no obvious relationship to the preferred position. Thus, although neurons are to some degree direction tuned (as outlined in the previous sections) and are to some degree tuned to the end point of the movement, the preference for a particular final position of the hand apparently cannot be explained as a consequence of a preference for a particular direction of motion. This question is further addressed in the next section.
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Figure 9. Direction tuning does not explain end point tuning. A1, A2, Data from two example neurons. The dots show the final hand position for the 10% of movements that terminated closest to the calculated preferred position. The line shows the preferred direction of movement as calculated using the same local set of movements. The blue dot shows the end of the movement vect
