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The Journal of Neuroscience, March 15, 1999, 19(6):2224-2246
Visual Motion Analysis for Pursuit Eye Movements in Area MT of Macaque Monkeys
Stephen G. Lisberger1 and J. Anthony Movshon2 1 Howard Hughes Medical Institute, Department of Physiology, and W. M. Keck Foundation Center for Integrative Neuroscience, University of California, San Francisco, San Francisco, California 94143 and 2 Howard Hughes Medical Institute and Center for Neural Science, New York University, New York, New York 10003
ABSTRACT
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Abstract
Introduction
We asked whether the dynamics of target motion are represented in visual area MT and how information about image velocity and acceleration might be extracted from the population responses in area MT for use in motor control. The time course of MT neuron responses was recorded in anesthetized macaque monkeys during target motions that covered the range of dynamics normally seen during smooth pursuit eye movements. When the target motion provided steps of target speed, MT neurons showed a continuum from purely tonic responses to those with large transient pulses of firing at the onset of motion. Cells with large transient responses for steps of target speed also had larger responses for smooth accelerations than for decelerations through the same range of target speeds. Condition-test experiments with pairs of 64 msec pulses of target speed revealed response attenuation at short interpulse intervals in cells with large transient responses. For sinusoidal modulation of target speed, MT neuron responses were strongly modulated for frequencies up to, but not higher than, 8 Hz. The phase of the responses was consistent with a 90 msec time delay between target velocity and firing rate. We created a model that reproduced the dynamic responses of MT cells using divisive gain control, used the model to visualize the population response in MT to individual stimuli, and devised weighted-averaging computations to reconstruct target speed and acceleration from the population response. Target speed could be reconstructed if each neuron's output was weighted according to its preferred speed. Target acceleration could be reconstructed if each neuron's output was weighted according to the product of preferred speed and a measure of the size of its transient response.
Key words: smooth pursuit; eye movements; visual motion processing; temporal dynamics; gain control; models; MT; monkeys
INTRODUCTION
What we do is often guided by what we see. Sensory-motor systems must therefore transform visual signals into commands for accurate movement. Smooth pursuit eye movements provide an excellent opportunity to investigate the neural circuits that perform visual-motor transformations. The basic neuroanatomy of pursuit is known, the sensory inputs and motor outputs are well understood, and the behavior itself has been studied extensively. Eckmiller (1987)
, Lisberger et al. (1987)
The particular visual signals needed to control pursuit are related to the motion of visual targets (Rashbass, 1961
Pursuit is configured as a negative feedback control system; its visual input is target motion with respect to the (potentially moving) retina, defined as "image motion." As a result, the visual input for pursuit varies as a function of time according to the pattern illustrated in Figure 1. For this single-pursuit trial, the stimulus was a ramp of target position from an eccentric starting point, which provides a step of target velocity. After the onset of the step, the eye remained still for ~100 msec, accelerated for ~150 msec, and then oscillated around target velocity at a frequency of ~6 Hz. To estimate the image velocity, we subtracted eye velocity from target velocity. This reveals that the visual input during pursuit is, sequentially, a step increase in image velocity, constant image velocity for 100 msec, a ramp decrease in image velocity toward zero, and small oscillations around zero at ~6 Hz.
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Figure 1. Schematic diagram showing typical pursuit eye movements and the visual image motion that drives them. From top to bottom, the traces are as follows: superimposed eye and target position, superimposed eye and target velocity, image velocity computed as target velocity minus eye velocity, and image acceleration computed as the low-pass filtered derivative of image velocity. The image acceleration at the onset of target motion is represented by a brief square pulse that has been clipped as a reminder that it is an impulse of acceleration. The short horizontal dashed line below the eye position trace shows the position of a fixation point that went out when the eccentric tracking target started to move.
Several laboratories have made computer models that reproduce the eye movements illustrated in Figure 1 on a millisecond time scale. An issue that distinguishes many of these models is whether the dynamics of the biological system are generated by direct sensory drive or by feedback from motor computations. For example, the model of Krauzlis and Lisberger (1994)
The present experiments were designed to record the dynamics of visual motion signals in area MT, to determine whether those dynamics could represent image acceleration, and to explore ways to extract information about image velocity and acceleration from the population responses in area MT. Thus, we used trajectories of stimulus speed that varied in the same way as image velocity and acceleration vary during pursuit. Our recordings showed that many individual MT neurons have transient responses that can provide information about image acceleration. Individual neurons, however, do not carry an invariant acceleration-related signal across all image speeds, so the true value of image acceleration can be represented only by the activity of a population of MT cells. We developed a model of MT neuron responses that simulates the responses of the population of MT neurons for a variety of stimuli, and we used the model to visualize the distributed representation of target motion in MT and to reconstruct target velocity and acceleration from this distributed representation.
Parts of this paper have been published previously (Movshon et al., 1990
MATERIALS AND METHODS Surgical preparation and maintenance. We recorded the activity of single units in area MT in 10 hemispheres of eight macaque monkeys (six fascicularis and two nemestrina). The monkeys were prepared for acute single-unit recording using methods we have described in detail previously (Levitt et al., 1994
1 · hr
To minimize eye movements, paralysis was maintained with an infusion of vecuronium bromide (Norcuron, 0.1 mg · kg
Tungsten-in-glass microelectrodes (Merrill and Ainsworth, 1972
Physiological optics. The pupils were dilated, accommodation was paralyzed with topical atropine, and the corneas were protected with +2D gas-permeable hard contact lenses. When necessary, supplementary lenses were chosen by direct ophthalmoscopy to make the retinas conjugate with the display screen. The power of the lenses was then adjusted as necessary to optimize the visual responses of recorded units. Contact lenses were removed periodically for cleaning. At this time, the eyes were rinsed with saline and infiltrated with a few drops of ophthalmic antibiotic solution (gentamycin). At least once a day, the locations of the foveae were recorded using a reversible ophthalmoscope.
Characterization of receptive fields and stimulus presentation. We initially mapped the receptive fields of single MT neurons by hand on a tangent screen using small black-and-white geometric targets. For each neuron, we recorded the location and size of the minimum response fields and determined its selectivity for the direction of motion. With the exception of a small group clustered around 30° eccentric, our neurons had receptive field centers that were fairly evenly distributed between 1 and 17° from the fovea. After receptive fields had been determined, we positioned a mirror to place the preferred eye's receptive field on the face of a display oscilloscope that subtended 10-15° at the monkey's eye. For most experiments, textures consisting of several hundred randomly placed bright dots were generated and moved with 100% coherence under computer control. The mean luminance of the random-dot displays was between 5 and 10 cd/m2, and the frame rate was 128 or 250 Hz. In some experiments, we also used a separate display generated by a raster frame buffer to measure responses to drifting gratings or plaid patterns. Methods for generating these stimuli are detailed elsewhere (Levitt et al., 1994
Before starting quantitative analysis, we attempted to optimize the stimulus to elicit strong and reliable responses to stimuli moving at the optimal speed and direction. Many cells responded much better if dots moved through a small window inside a surround of stationary dots; this often meant presenting a surround of stationary dots around dots that moved through a window over the classical receptive field. For the remainder of the paper, the moving texture will be called a "target," and we will refer to target speed and acceleration even though these attributes actually belong to the individual dots within the moving part of the texture stimulus. Because our recordings were made in anesthetized monkeys, target and image motion are interchangeable; this would not be the case during pursuit in awake monkeys.
Stimuli were presented as a series of trials with durations that ranged from 1024 to 3072 msec with intertrial intervals of ~1 sec. Target motions consisted of steps and ramps of target speed of different final speeds and durations, double pulses of target speed at different interpulse intervals, and sinusoidal variation of target speed around baselines ranging from zero to several times the neuron's preferred speed. Trials were blocked by stimulus type to generate coherent, controlled experiments while keeping each block small enough so that we would obtain useful data for at least part of our series if neuronal isolation were lost. Each block of trials was repeated 8-32 times, and the order of trials was shuffled between blocks. The seed used to initiate the pseudorandom sequence that placed the random dots was changed, and the dots were replotted for each trial; we cannot reconstruct the locations of the dots because we did not record the seed for each trial. Early experiments were controlled by a PDP11 computer, and later experiments were controlled by an 80486 personal computer using a DSP board with 16-bit DACs to generate random dots. Data were analyzed after the experiment by aligning the responses to identical target motions and compiling average response histograms. Details of the data analysis are provided in the descriptions of the relevant figures.
Reconstruction of recording sites. During recording, small electrolytic lesions were produced at locations of interest along the electrode tracks by passing DC current (2 µA for 2-5 sec; tip negative) through the electrode. At the end of the experiment, the monkeys were killed with an overdose of Nembutal and perfused through the heart with 2 l of 0.1 M PBS followed by 2 l of a solution containing 4% paraformaldehyde in 0.1 M PBS. Blocks containing the region of interest were stored cold overnight in a post-fix solution of 4% paraformaldehyde and 30% sucrose, after which 40 µm sections were cut on a freezing microtome. Sections were stained for Nissl substance with cresyl violet or for myelin using the methods of Gallyas (1979)
RESULTS Experimental results
Our results are presented in separate experimental and simulation sections. In the experimental results, we show first that MT cells vary substantially in the dynamics of their responses to motion. Some cells encode only target velocity, whereas others have large transient responses to changes in target motion. We will conclude that the distribution of transient responses across the population of MT cells has the potential to provide information about target acceleration, although no individual cell does. Second, we use paired pulses of target velocity at short intervals to characterize the mechanism that controls the time course of transient responses. We will conclude that a class of mechanisms that falls under the general term "adaptation" is responsible for the transients, although our data could be accounted for by any of several specific cellular or neural mechanisms. Third, we describe the responses of MT cells for sinusoidal oscillation of target speed at frequencies normally seen during pursuit eye movements.
Responses to steps of target speed
It is well known that MT cells are tuned for the direction and speed of target motion. Our first step was to look for dynamic features in the responses to target motion by measuring the time course of neuronal firing for target motions that had instantaneous onsets. Figure 2 shows the responses of two cells to steps of target speed for stimuli that moved in the neurons' preferred directions. For these experiments, the target initially was visible and stationary for 256 msec, then moved at one of 8-10 speeds for 512 msec, and finally stopped and remained stationary for 256 msec. For the cell in Figure 2A, steps of target speed evoked a large transient pulse of activity followed by a sustained response. Both the transient and sustained responses were tuned for speed, with a preferred speed of ~9°/sec for the transient response and ~5°/sec for the sustained response. The offset of target motion caused only a slight transient response, in contrast to the large transients emitted by this cell for the onset of motion. For the cell in Figure 2B, a step of stimulus speed caused little or no transient response at the lower speeds, only a small transient response at speeds >19°/sec, and a clear sustained response with a preferred speed of ~19°/sec. In our sample of ~100 cells, we always observed a speed-tuned sustained response, but we observed a range of transient responses. The example in Figure 2A is near one end of the range, whereas that in Figure 2B is in the middle of the population.
For each MT cell, speed tuning and direction tuning were similar for the transient and sustained responses. Figure 3A illustrates speed-tuning curves for the transient (open symbols) and sustained (filled symbols) responses of the typical MT cell whose responses to steps of target speed are shown in Figure 2B. For each speed, the size of the sustained response was computed as the mean firing rate in the interval from 256 to 512 msec after the onset of target motion. The size of the transient response was estimated as the largest mean firing rate in a 24 msec window within 120 msec of the onset of target motion. The spontaneous firing (Fig. 3A, horizontal dashed line) was taken as the sustained firing rate for a target that remained stationary throughout the trial. We fitted each speed-tuning curve (with spontaneous firing subtracted) with the function:
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Figure 2. Representative responses of MT cells to steps of target speed. A, Responses of a neuron (321r10) with one of the largest transient responses we recorded. B, Responses of a neuron (324r4) with a more typical transient response. Each histogram shows the accumulated response of the neuron to steps of target speed from zero to the final speed indicated at the left of A. The histogram labeled stationary shows each neuron's response to the appearance of a stationary dot field that did not move. Bin width was 8 msec. The traces at the bottom of the figure show the time course of target speed, which always started at zero. Histograms were accumulated from nine repeats of each stimulus in A and eight repeats in B.
where Rs is the response at each speed, a is the amplitude, b is the preferred speed, c is the tuning bandwidth, d is a parameter controlling the skew of the curve, and s is target speed. As shown in Figure 3B, there was a strong correlation between the preferred speeds of the transient and sustained responses (r = 0.92), with a tendency for the preferred speed for the transient response to be slightly higher than that for the sustained response.
(1)
We computed the transient/sustained ratio as aT/aS, where aT and aS are the fitted values of a for the transient and sustained responses, respectively. For the two cells illustrated in Figure 2, the transient/sustained ratio was 7.8 and 1.9. Among 104 cells that were studied during steps of target speed, the transient/sustained ratio varied from 1.08 to 9.4 with a median of 1.77 and a mean of 2.1. The size of the transient/sustained ratio was not correlated with any of the other parameters we measured, including laminar location of the recorded neurons, preferred speed, sustained response strength, spatial or temporal tuning for sine wave gratings, or pattern versus component characteristics during stimulation with moving "plaids" (Movshon et al., 1985
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Figure 3. Quantitative analysis of the responses of 104 MT neurons to steps of target speed. A, Firing rate plotted as a function of target speed for neuron 324r4, which also appears in Figure 2B. Open and filled symbols show the transient and sustained responses, respectively. The horizontal dashed line shows the spontaneous firing in the presence of stationary dots. The solid curves show the best-fitting function based on Equation 1. The vertical arrows labeled aT and aS are positioned at the preferred speeds of the transient and sustained responses, respectively, and show the peak responses, which were used to compute the transient/sustained ratio. B, Comparison of preferred speed for the transient and sustained response. Each symbol summarizes the response of one MT neuron. C, Representative speed-tuning curves showing the range of preferred speeds of the sustained responses. The curves were normalized so that each is plotted on the scale shown by the calibration bar on the lower right but were shifted vertically to facilitate viewing. The horizontal dashed line at the right of each curve shows the baseline for that neuron, and the number next to the curve gives the amplitude of the sustained response at the preferred speed. The three vertical dashed lines were drawn at speeds of 1, 10, and 100°/sec to facilitate comparison of the different tuning curves.
Latency of response
We measured the latency of the neuronal response for steps of target speed; to avoid contaminating our data with noise, we did not make measurements if a stimulus evoked sustained firing that was <10% of the sustained response at the preferred speed. Latencies were measured manually from histograms with 4 msec bin widths by following the rising phase of the averaged response back in time until the average firing was within the fluctuations in spontaneous rate. Because of the low or absent spontaneous rates and the brisk rises of the initial responses to steps of target speed, this procedure almost always yielded an estimate of latency that had an error of 8 msec or less. In 80% of the responses, the manual analysis yielded latencies in perfect agreement with those obtained by an objective procedure that found the time after which the firing rate remained >1 SD above the base rate. We elected to use the manual analysis throughout, however, because it was clearly superior to the objective analysis in the remaining 20% of responses, in which the objective analysis was unreliable because of response variability. In almost all cells, the latency was quite long for low target speeds, decreased with increases in target speed, and became as short as 40 msec at the highest speeds. We have plotted the latency of response as a function of the inverse of target speed (Fig. 4A) because straight lines in these graphs have a clear functional interpretation if response latency has two componentsa variable component that requires the target to traverse a given distance before the response is initiated and a fixed delay affecting all responses. The y-intercept latency from the linear model estimates the fixed minimum latency. The slope of the line has the units of degrees, estimating a "space constant" that measures the distance the target has to traverse before a response is initiated. We have not analyzed the linear model rigorously, but linear fits were generally excellent for speeds as low as 0.5°/sec (Fig. 4A). Latency often failed to follow the linear model for speeds <0.5°/sec, which we excluded from the linear regression for this reason.
The regular relationship between latency and inverse speed appeared to be robust despite wide variations in response strength across speed. For example, note the difference in latency between the weak responses of each of the example neurons to targets of low and high speeds. The fixed component of latency showed no convincing (or statistically significant) relationship to either the transient/sustained ratio (Fig. 4C) or the preferred speed (Fig. 4D), suggesting that cells preferring different speeds did not differ in their temporal properties. In contrast, the graph in Figure 4B shows that the space constant was larger for cells that had higher preferred speeds. This relationship can be understood by noting that neurons with different speed preferences can be constructed by variation in either their spatial or temporal properties. In agreement with the previous finding that cells responding well to high speeds tend to prefer lower spatial frequencies (Levitt et al., 1988
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Figure 4. Determinants of response latency in MT neurons. A, Plots of latency versus 1/speed for three representative MT cells. Symbols show the measurements, and the straight lines show the result of regression analysis with the equation: latency = b + a/speed, where a is the space constant and b is the fixed, minimum latency. B, Space constant (a converted to minutes of arc) plotted as a function of preferred speed of the transient response. C, Intercept latency (b) plotted as a function of the transient/sustained ratio for steps of target speed. D, Intercept latency (b) plotted as a function of preferred speed of the transient response. In B-D, each symbol shows the response of one MT neuron.
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Figure 5. Distribution of response latency for MT neurons with measurable responses at three selected speeds: 1, 8, and 64°/sec. Vertical arrows show the median latency for each speed.
Responses to ramps of target speed
In this section, we show that the firing rate of some MT neurons is influenced by target acceleration. The data do not support a conclusion that the firing of individual MT neurons encodes target acceleration. Instead, these data provide the basis for the final section of the paper, in which we demonstrate that target acceleration can be reconstructed from the population response in MT. To determine whether the firing of MT cells was influenced by target acceleration and how, we used stimuli in which the target either accelerated or decelerated through a given range of speeds. Figure 6 shows the time course of firing rate during these stimuli for the two cells whose responses to steps of target speed appear in Figure 2. As shown by the target speed traces at the bottom of the figure, the target was initially stationary and visible for 256 msec. Target speed then increased at a constant rate for 128 msec up to final speeds indicated by the numbers at the left of each histogram in Figure 6A, moved at constant speed for 512 msec, decelerated at a constant rate for 128 msec back to zero velocity, and finally remained stationary and visible for 256 msec. In our later experiments, the entire sequence of constant acceleration, constant speed, and constant deceleration was presented in single trials like those illustrated in Figure 6. In our earlier experiments, we presented the accelerations and decelerations in separate trials and then spliced the averages together. The results were identical for the two methods.
In principle, the response of a cell to this stimulus could be determined entirely by the sequence of speeds traversed by the target during ramp accelerations and decelerations, or it might also be influenced by features of motion other than target speed. If a ramp acceleration took target speed from zero through the cell's preferred speed to a final speed well above preferred speed, then we would expect to see a large transient response because of the speed tuning of the cell. However, we would expect to see approximately the same transient as ramp deceleration took target speed from well above preferred speed back through preferred speed down to zero. Thus, MT cells that give symmetric responses to ramp increases and decreases in target speed probably do not provide information that could be used to determine target acceleration. On the other hand, an asymmetric response to ramp increases and decreases in speed would show that a cell's response could carry information about target acceleration as well as speed. The cell whose responses appear in Figure 6A shows one extreme of a continuum of neuronal behavior for ramp increases and decreases in target speed, whereas the cell in Figure 6B is near the median. For all six final ramp speeds shown here, the cell in Figure 6A showed a pronounced transient response during ramp increases in target speed and either none or much less of a transient during ramp decreases in target speed. The cell in Figure 6B showed a clear transient response during ramp increases in target speed to 74°/sec as well as to other speeds >18°/sec. However, this cell also emitted a large transient for ramp decreases to zero target speed from these higher speeds. Thus, inspection of the histograms demonstrates, at least for ramps of target speed that started at zero, that the firing of the cell in Figure 6A differentiates between target acceleration or deceleration for all final speeds, whereas the firing of the cell in Figure 6B did so only over a middle range of speeds. Inspection of Figure 6, A and B, reveals that the latency of the peak response during ramp increases in target speed becomes shorter as final target speed increases. This suggests that the transients of firing during ramp increases in target speed occur as the target passes through the cell's preferred speed and leads to the question (addressed below) of why similar transients are not always evident for ramp decreases in target speed. We quantified the asymmetry in each cell's responses to ramps of target speed by measuring the peak firing rates over a 24 msec window in the two 256 msec intervals starting at the onset of the ramp increases and decreases in target speed (Fig. 6, intervals marked by vertical dashed lines). The analysis intervals always included the peak of the responses without including other peaks that occasionally occurred later. The results of this analysis appear in Figure 7 for the two example cells in Figure 6. Figure 7, A and B, plots the peak firing during ramp increases (open symbols) and decreases (filled symbols) in target speed as a function of the magnitude of target acceleration. As was clear in the histograms, the cell in Figures 6A and 7A showed a large asymmetry, whereas that in Figures 6B and 7B shows a consistent but smaller asymmetry. To gain an impression of the size of the asymmetry in relation to each cell's sustained and transient responses to steps of target speed, we computed the difference between the peak firing for target accelerations to and decelerations from a given target speed and plotted the difference firing rate as a function of target acceleration (Fig. 7C,D). For the cell in Figure 7C, the difference firing between ramp acceleration and deceleration increased consistently as a function of target acceleration up to an asymptote of ~320 impulses/sec. The asymptote was much larger than the peak of the sustained response to steps of target speed (Fig. 7C, bottom horizontal dashed line). For the cell in Figure 7D, the difference firing rate was clearly tuned and reached a peak that was less than the maximal sustained response for steps of target speed. Comparison with the maximal sustained response is useful because it reveals the size of the asymmetry, which may provide information about target acceleration, relative to the size of the same neuron's responses to sustained speed. We conducted this analysis on all 89 cells that were studied during steps and ramps of target speed, and for each cell, we fitted the difference firing with Equation 1, with speed supplanted by acceleration. Examples of the fits are shown by the smooth curves in Figure 7, C and D.
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Figure 6. Representative averaged responses of MT neurons to ramp increases and decreases in target speed. A, MT neuron (also shown in Fig. 2A) that had one of the largest transient responses and one of the largest asymmetries and that was recorded between ramp increases and decreases in target speed. B, MT neuron (also shown in Fig. 2B) that fell approximately in the middle of our sample in terms of transient response and asymmetry between ramp increases and decreases in target speed. For each neuron, the different firing rate histograms show responses for ramp increases to and decreases from different target speeds, given by the numbers at the left of A. Target speed always started at zero. The traces at the bottom of A and B show the time course of target speed. The vertical dashed lines delimit two analysis intervals in the first 256 msec after the onsets of ramp increases and decreases in target speed. Histograms were accumulated from 9 repeats of each stimulus in A and 16 repeats in B. Bin width is 8 msec.
The selection of curves in Figure 8A shows the diversity of the asymmetries among the cells that had the largest responses to ramp acceleration and deceleration. These examples were selected from the 40 cells that had transient/sustained ratios of 1.8 or larger during steps of target speed and that were studied during ramps of target speed. Each curve plots the difference firing rate described in the previous paragraph, normalized for the largest transient response evoked by steps of target speed, as a function of the value of the ramp acceleration. We chose to normalize for the largest transient response during steps of target speed so that most of the normalized points would have values between 0 and 1 and different cells could be compared easily. The curve labeled e in Figure 8A is from the neuron that was used to construct Figure 7, A and C, and shows an asymmetry evident across the full range of accelerations we tested. Curve g in Figure 8A is from the neuron used to construct Figure 7, B and D, and shows an asymmetry tuned for a middle range of accelerations. Other cells showed tuning for a narrow range (Fig. 8A, curve h) or a broad range (curve f) of accelerations or had high-pass characteristics with positive values of difference firing rate starting at low (curves c, d), medium (curve b), or high (curve a) accelerations. None of the 39 cells that were tested with target accelerations as low as 0.9°/sec2 showed low-pass characteristics. The presence of large differences in the response to ramp accelerations and decelerations demonstrates that the firing of some MT cells is influenced by target acceleration. The diversity of the tuning across the population suggests that target acceleration across different speed ranges is probably represented by different MT cells.
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Figure 7. Quantitative analysis of the asymmetry between responses to ramp increases and decreases in target speed. A, B, Open and filled symbols plot the peak firing rate in the first 256 msec after the onset of ramp increases and decreases, respectively, in target speed as a function of the magnitude of target acceleration. The horizontal dashed lines show the maximum sustained firing rate, computed as the maximum sustained response plus the spontaneous firing rate. C, D, Open symbols plot the difference between the peak firing rates for ramp increases and decreases in target speed as a function of target acceleration. The solid curves plot the best fit obtained with Equation 1, with target acceleration substituted for target velocity. The two horizontal dashed lines show the largest transient and sustained responses for steps of target speeds, with spontaneous firing subtracted. A, C, Data are for cell 321r10, which also appears in Figures 2A and 6A. B, D, Data are for cell 324r4, which also appears in Figures 2B, 3A, and 6B.
Two facts argue against the possibility that the transient responses of MT neurons to accelerating and decelerating targets might arise because the apparent contrast of rapidly moving stimuli is lower than that of stationary targets. First, this effect should be the same for both increases and decreases in target speed, because MT cells usually respond equally to increases and decreases in contrast (Maunsell and Van Essen, 1983
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Figure 8. Asymmetry between responses to ramp increases and decreases in target speed. A, Family of curves showing the relationship between the difference firing rate (peak during acceleration minus peak during deceleration) and the magnitude of target acceleration for eight MT neurons. Difference firing rates are normalized to the peak transient response for steps of target speed and are plotted according to the calibration bar on the lower right of the graph. The curves for different cells have been shifted vertically to facilitate viewing. The horizontal dashed lines show difference firing rates of zero. Curves e and g are from the two neurons that appear in Figure 7. B, Comparison of the transient/sustained ratio for ramps and steps. C, Comparison of individual neurons' preferred stimulus acceleration for ramps and preferred speed for steps of target speed. The solid line is the type 2 regression line for the neurons plotted with open circles. In B and C, open circles are for cells with transient/sustained ratios for ramps >1.8, and small x symbols are for cells with transient/sustained ratios <1.8. Because the ramp increases in target speed always started from zero and were always 128 msec in duration, the two y-axes in C are proportional and differ only by the factor of 0.128
Comparison of responses to ramps and steps of target speed
To summarize the ramp asymmetry for each cell, we computed the transient/sustained ratio for ramps, defined as (aR + aS)/aS, where aR is the peak value of the curve fitted to the difference firing rate from graphs like Figure 7, C and D, and aS is the peak value of the curve fitted to the sustained firing rate during steps of target speed. The transient/sustained ratio for ramps of target speed was 4.9 for the cell in Figures 6A and 7, A and C, and was 1.6 for the cell in Figures 6B and 7, B and D. Figure 8B shows that the transient/sustained ratio for steps and ramps of target speed agreed well for almost every cell we recorded (r = 0.87). The different symbols indicate cells with transient/sustained ratios for ramps greater than and less than 1.8 (compare Fig. 8C). Type 2 regression analysis on the log10 of the data in Figure 8B, under the assumption that the two values of transient/sustained ratio were equally well estimated from the data, gave a slope of 0.74. As expected, there was also excellent agreement between the peak sustained responses for steps and ramps of target speed (r = 0.96; type 2 regression slope = 1.19). Figure 8C illustrates that there was also a correlation between the preferred speed of the transient response to steps of target speed and the preferred acceleration from the fits to the difference curves for ramps of target speed. The values plotted along the y-axis (Fig. 8C) were all obtained for 128 msec ramps from zero to final speed, creating a proportionality between the final speed (left y-axis) and the acceleration of the preferred ramp (right y-axis). The scatter plot suggests a more consistent relationship for neurons with transient/sustained ratios >1.8 (Fig. 8C, open circles, r = 0.61) than for those with smaller transient/sustained ratios (small x symbols, r = 0.16). For the neurons with transient/sustained ratios of 1.8 or greater, type 2 regression analysis on the log10 of the data in Figure 8C (solid line) revealed a regression slope of 1.0, indicating that the derived values on the y- and x-axes are proportional. The constant of proportionality of approximately four implies that most cells could contribute most effectively to a distributed representation of target acceleration when the target accelerates from zero to final speeds higher than the cell's preferred speed.Responses to spatially restricted targets
To establish the generality of the response characteristics that we measured in MT cells stimulated with speed steps and ramps for random-dot texture targets, we studied the responses of 38 of the cells to the same motion trajectories of small spots and textures. These experiments were complex to design and execute, because the use of small targets mandated that we explore the effect of varying the receptive field position at which steps and ramps of target speed occurred. The analysis was similarly complex, because the sensitivity profile of the neuron's receptive field had to be taken into account in evaluating the responses. We do not present a detailed analysis of these experiments here, but the results showed that the important dynamic features of MT cells' responses to textures could also be discerned in their responses to small targets. We are therefore confident that our measurements with textures represent adequately the response of MT cells for the small targets normally used to study pursuit eye movements.Effect of base velocity and ramp duration on the responses to target acceleration
The results in Figures 7 and 8 imply that many MT cells could provide information about the direction and possibly the magnitude of target acceleration for targets that are initially stationary and accelerate smoothly through the range of speeds to which the cell is sensitive. However, individual MT cells cannot signal acceleration for all initial target speeds. Figure 9A-D shows the responses of an example MT neuron to different combinations of acceleration and initial target speed. This cell had large transient responses during 128 msec ramps of target speed from 0 to 2.25, 4.5, or 9°/sec (Fig. 9A-C). The transient response was completely absent when the ramp started at the preferred speed for the sustained response, which was ~4.5°/sec for this cell, and increased to 9°/sec (Fig. 9D). Thus, a target acceleration of 35°/sec2 caused a large transient in firing when the target speed started at 0°/sec (Fig. 9B) and no transient when the target speed started at 4.5°/sec (Fig. 9D). We obtained the same result on all 15 cells that were tested. The converse experiment, of varying ramp duration and therefore target acceleration while keeping the initial and final target speed the same, also emphasized the nature of the relationship between firing rate and target acceleration. When the initial target speed was 0°/sec and the final target speed was 9°/sec, the response of the cell in Figure 9 was essentially the same when the target acceleration was 2240°/sec2 (Fig. 9H, ramp duration 4 msec), 560°/sec2 (Fig. 9G, ramp duration 16 msec), 280°/sec2 (Fig. 9F, ramp duration 32 msec), 140°/sec2 (Fig. 9E, ramp duration 64 msec), or 70°/sec2 (Fig. 9C, ramp duration 128 msec). These results show that individual MT neurons can contribute to a distributed representation of target acceleration only for a limited range of target speeds.
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Figure 9. Examples showing that MT neurons are sensitive to target acceleration only for some stimulus trajectories. Each panel shows a histogram of firing rate obtained from nine repeats of the target speed trajectory shown by the lower trace. The column of histograms shows the responses for different initial and final target speeds. The row of histograms shows responses to different accelerations produced by different duration ramps between zero and twice the preferred speed. A, 0-2.25°/sec in 128 msec. B, 0-4.5°/sec in 128 msec. C, 0-9°/sec in 128 msec. D, 4.5-9°/sec in 128 msec. E, 0-9°/sec in 64 msec. F, 0-9°/sec in 32 msec. G, 0-9°/sec in 16 msec. H, 0-9°/sec in 4 msec.
Responses to double pulses of target velocity at different interpulse intervals
Our data on responses of MT cells to steps and ramps of target speed (Figs. 2, 6) revealed that many neurons have large transient responses with complex dynamics. Because the size and time course of these transients are dependent on stimulus speed and acceleration, such simple transient-forming mechanisms as linear high-pass temporal filters (e.g., spike frequency adaptation) probably cannot provide a complete account of the data. To account for these complex dynamics, we guessed that neuronal excitability might be influenced by a time-dependent adaptation of the responses to a given stimulus. Adaptation might arise either from complex synaptic or cellular mechanisms or from neurons outside those providing excitatory input to the cell. We conducted the following experiments to probe adaptation, even though we realize that they do not distinguish possible mechanisms rigorously and that adaptation could be implemented by division or subtraction. Thus, we use the term adaptation to encompass a number of possible neural and cellular mechanisms. As an initial probe of adaptation, we used a series of condition-test experiments in which we measured the response to a test pulse of target speed as a function of time after an identical conditioning pulse. As shown in Figure 10, targets were stationary and visible for 256 msec before undergoing one or two 64 msec pulses of motion of the preferred speed and direction. In Figure 10, top, for example, the histogram (Firing rate) shows the response of one cell to two 64 msec pulses of target speed that were separated by 64 msec. As a control, the solid firing rate trace shows the response of the same cell to a single pulse of target speed. The response to the second pulse can then be estimated by subtracting the response to the first pulse from the response to two pulses (Fig. 10, middle, Difference firing rate).
Figure 11 shows two examples that relate the results of the two-pulse condition-test experiments and the responses of MT cells to steps of target speed (traces labeled Step). The data in Figure 11A came from a cell that had a clear transient response to 512 msec steps of target speed, whereas the data in Figure 11B came from a cell whose response was almost purely tonic. For each cell, the traces labeled Pulse (Fig. 11) show the response to the test pulse alone, and the traces labeled with different times show the responses when the onset of the test pulse followed the offset of the conditioning pulse by the specified delay. For each histogram in the left columns of Figure 11, A and B, the companion histogram in the right columns shows the difference firing rate, obtained by subtracting the response to the conditioning pulse from the response to two pulses and aligning the differences on the onset of the test pulse. For the response to the test pulse alone (Fig. 11, Pulse), the difference histograms were obtained by subtracting the spontaneous firing recorded during presentation of a stationary texture.
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Figure 10. Example histograms showing the experimental design and data analysis for experiments that presented two pulses of target speed at different interpulse intervals. Top, The histogram shows the accumulated response to 10 repeats of two 64 msec pulses of target motion in the neuron's preferred direction at its preferred speed with an interpulse interval of 64 msec. Bin width is 8 msec. The solid trace superimposed on the histogram is the average response of the same neuron to 40 repeats of just the first pulse. Middle, The difference firing rate in the histogram shows the response to two pulses minus the response to the first pulse. Bottom, The solid and dashed traces show the time course of target speed for the double- and single-pulse stimuli, respectively.
For the cell with a transient response to steps of target speed (Fig. 11A), there was a clear effect of the time between the pulses on the response to the second pulse. The second response was attenuated for interpulse intervals <64 msec and returned to control values when the interpulse interval reached 256 msec. The gradual return of the amplitude of the response to the second pulse can be seen in the histograms of the responses to two pulses (Fig. 11A, left column of histograms) but is clearer in the difference firing rates obtained by subtracting the response to the first pulse (Fig. 11A, right column of histograms). The difference firing rates are aligned on the time of onset of the second pulse, revealing that the latency of the response to the second pulse (Fig. 11A, vertical dashed line) did not vary consistently as a function of the interpulse interval. Note also that these difference rate histograms suggest that the response to the second pulse at short interpulse intervals is a scaled-down replica of the unconditioned response (Fig. 11A, top traces); these scaled replicas are a characteristic signature of a mechanism that controls response gain and are quite different from the abbreviated ("iceberg") responses that would result from delivering double-pulse stimuli to a linear high-pass filter. For the cell that lacked a transient response to steps of target speed (Fig. 11B), the two-pulse experiment yielded a different result. The response to the second pulse did not depend strongly on the interpulse interval and was nearly the same as that of the control even for interpulse intervals as short as 32 msec. To quantify the relationship between the attenuation of the response to the second pulse at short interpulse intervals and the transient responses of MT cells to steps of target speed, we determined the latency of the response to a single pulse, defined the next 64 msec as an analysis interval, and measured the mean difference firing rate in the analysis interval for each of the six condition-test intervals. We then computed a "response attenuation index" defined as the mean difference firing rate for an interpulse interval of 32 msec divided by the average of the firing rates for interpulse intervals of 128 and 256 msec. Figure 12 shows the relationship between the transient behavior of firing rate for steps of target speed and the amount of attenuation revealed in two-pulse experiments. Each point in this plot shows results from one of the 22 cells studied using two pulse stimuli. The x-axis plots the response attenuation index derived above, and the y-axis plots the transient/sustained ratio for steps from stationary to the target speed used for the two-pulse experiment. In general, cells that had little or no transient response for steps of target speed also had attenuation indices near 1.0 for two pulse stimuli, indicating no attenuation. Cells with large transient responses for steps of target speed had attenuation indices as small as 0.1. Although we have elected not to show the data here, we obtained very similar results from the same cells when we tested them with a 64 msec pulse of target speed at different intervals after the offset of a 512 msec step of target speed. We interpret the correlation between the existence of a transient response to steps of target speed and attenuation of responses at short interpulse intervals as evidence that adaptation shapes the transient responses of MT cells. The recovery of the response to the test pulse at longer interpulse intervals reflects recovery from adaptation. In a later section of the paper, we will implement adaptation as divisive gain control to create transient responses in a model that reproduces the dynamics of MT cell responses.
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Figure 11. Comparison of transient behavior during steps of target speed with response attenuation in two-pulse experiments for two representative neurons. A, A neuron with a large transient during steps of target speed and strong attenuation of the response to the second pulse at short interpulse intervals. B, A neuron with no transient and no attenuation of the response to the second pulse. In A and B, the histogram labeled Step shows the accumulated firing for a 512 msec step of target speed to the same speed used for the two-pulse experiments. For the histogram labeled Pulse in A and B, the left column is the accumulated firing for a single pulse of target speed, and the right column is the same response with the spontaneous firing for a stationary dot pattern subtracted. For the lower six rows of A and B, the left column shows the response histogram for two pulses of target speed at the interval indicated by the number to the left of the histogram. The right column shows the difference firing rate obtained by subtracting the response to the first pulse and aligning the resulting histograms on the onset of the second pulse of target speed. The vertical dashed line shows the approximate start of the response. Bin width is 16 msec for the response to steps of target speed and is 8 msec in all of the other histograms. The traces below each histogram show the time course of target speed. For each neuron, we performed this experiment for pulses of target speed that were near the preferred speed. The pulses and step of target speed were 2°/sec in A and 4°/sec in B. In A, the step and single-pulse responses were obtained from 40 repeats of each stimulus, and the other histograms were from 10 repeats. In B, the step and single-pulse responses were obtained from 60 repeats of each stimulus, and the other histograms were from 16 repeats.
To determine whether the influence of the conditioning pulse was direction selective, we tested seven cells with a variant of the double-pulse experiment in which the first 64 msec pulse of target speed provided motion in the null direction and the second pulse was in the preferred direction. Figure 13 shows one example of the responses, for the same cell whose responses are also shown in Figure 11A. This cell gave a brisk response to a 64 msec pulse of target motion in the preferred direction (Fig. 13, top pair of traces labeled On-direction) and was inhibited slightly when the same pulse of target speed was delivered in the null direction (trace labeled Null-direction). The histograms of firing rate for the double pulse stimuli reveal that this cell responded well to the pulse of target speed in the preferred direction for the shortest condition-test intervals, even though the same cell showed almost complete attenuation of the response to the second pulse at short intervals when the two pulses were in the same direction (see Fig. 11A). We again isolated the response to the second pulse by computing the difference between the responses to two pulses and to the test pulse alone and aligning the difference firing rate on the onset of the second pulse.
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Figure 12. Quantitative analysis of the relationship between response attenuation in two-pulse experiments and the transient behavior for steps of target speed. Each point shows the response of one MT neuron. The x-axis plots the response attenuation index for two-pulse experiments: the mean firing rate for an interpulse interval of 32 msec divided by the average of the responses for interpulse intervals of 128 and 256 msec. The y-axis plots the transient response divided by the sustained response for a step from zero to the target speed used for the two pulse stimuli. Note that this is different from the transient/sustained ratio computed earlier as the peak transient response divided by the peak sustained response across target speeds.
In each of the seven cells tested, conditioning motion in the null direction affected responses to subsequent test motion in the preferred direction, but in a different way than did conditioning motion in the preferred direction. There was no response attenuation at short latencies. Instead, the dynamics of the response were affected. In Figure 13, for an interpulse interval of 0 msec, the response to the preferred-direction pulse was delayed by almost 24 msec and had a sharper time course and a larger amplitude than did the response to the control pulse (histogram labeled On-direction). The effect on the latency of the response to the preferred direction was absent when the interpulse interval increased to 96 msec. But inspection of Figure 13 hints that null-direction motion may have had a rather long-lasting effect on the shape and amplitude of this cell's responses to subsequent motion in the preferred direction, even for an interpulse interval of 256 msec. We have confirmed this effect with more detailed observations on a larger sample of cells (Priebe et al., 1998). However, our limited sample of seven cells provided enough data to show that the adaptation in MT cells is direction selective.
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Figure 13. Example of a two-pulse experiment showing the effect of conditioning motion in the null direction on subsequent responses to target motion in the preferred direction. The same neuron's responses are also shown in Figure 11A. For the histograms labeled On-direction, the left column is the response histogram for a single pulse of target speed in the preferred direction, and the right column is the same response with the spontaneous firing for a stationary dot pattern subtracted. The histogram labeled Null-direction shows the response to a single pulse of preferred target speed in the null direction. For the lower six rows, the left column shows the accumulated firing for two pulses of target speed at the interpulse interval indicated by the number to the left of the histogram. The right column shows the difference firing rate obtained by subtracting the response to the first, null-direction pulse and aligning the resulting histograms on the onset of the second, preferred-direction pulse of target speed. The vertical dashed line shows the approximate start of the response to a single pulse. The traces below each histogram show the trajectory of target speed, which was 2°/sec for this experiment and was close to the neuron's preferred speed in all experiments. In all histograms, the bin width is 8 msec. The on-direction and null-direction histograms were accumulated from 40 repeats of the same stimulus; the other histograms were from 10 repeats.
Responses to sinusoidal modulation of target speed
Traditional approaches to understanding dynamics have often relied on sinusoidal-forcing functions to obtain estimates of response gain and phase as a function of frequency. In a linear system, such analysis provides the same information as the time domain analysis we have presented so far. In this instance, however, it seemed useful to analyze the responses of MT cells to sinusoidal modulation of target speed, partly because their responses are clearly nonlinear and partly to obtain data relevant to the performance of the smooth pursuit system, which has been analyzed frequently with sinusoidal target motion (e.g., Fuchs, 1967
Figure 15 shows data from a cell that exemplifies all the basic features of the responses to sinusoidal modulation of target speed. When the baseline speed was zero (Fig. 15A, DC = 0), firing rate was strongly modulated at frequencies up to 8 Hz. Modulation of firing rate increased somewhat as the frequency of target speed oscillation increased from 1 to 8 Hz but was small at 16 Hz. The attenuation of modulation at 16 Hz is verified by the cycle histograms on the upper right of each long histogram. The cycle histograms were constructed with 24 bins per cycle by averaging the responses across the last second of sinusoidal modulation. For all frequencies, MT neurons emitted a pulse of firing for the first cycle of target motion at DC = 0. When target speed oscillated between zero and the preferred speed (Fig. 15B, DC = 0.5), the modulation of firing rate was considerably weaker than when target speed oscillated around a baseline speed of zero. Again, there were responses at 1, 2, 4, and 8 Hz, but it is difficult to see any modulation of firing rate at 16 Hz in spite of an increase in the sustained firing of this MT cell.
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Figure 14. Schematic diagram of the experimental design for presenting sinusoidal modulation of target speed on different base speeds. The graph on the right plots target speed on the y-axis, with preferred-direction motion upward, and sustained firing rate on the x-axis, with increased firing rate plotted to the right. The curve shows a schematic speed-tuning curve for an MT neuron. The four sine waves on the left of the figure show target speed as a function of time. The speed calibration for the sine waves is the same as that for the speed-tuning curve at the right. The sine waves labeled DC = 0, DC = 0.5, DC = 1, and DC = 2 show schematically the situation we tried to achieve when we selected the baseline speeds and amplitudes of modulation of target speed used to study the responses of each MT cell.
When the baseline target speed was above the preferred speed so that target speed oscillated on the descending limb of the relationship between firing rate and target speed (Fig. 15C, DC = 2), the response of the cell was again modulated. As expected, the phase of the neuronal responses was now reversed relative to DC = 0 and DC = 0.5. For example, at 1 Hz, increased firing occurred during the upward deflection of the sinusoidal component of target speed for DC = 0 and DC = 0.5 but during the downward deflection for DC = 2. The single-cycle histograms illustrate the effects of oscillation frequency on phase shift. At each frequency, the response phase is similar for DC = 0 and DC = 0.5 but reversed for DC = 2, just as described above for oscillations at 1 Hz. For Figure 15, A-C, response phase lag increases with frequency, as expected of a response with a latency that is a substantial fraction of the period of the higher frequency oscillations. Responses for DC = 1 were quite small and, when present, were dominated by the second harmonic of the oscillation frequency (data not shown). For target speed oscillation around a base speed of zero, the relationship between the modulation of firing rate and the frequency of oscillation varied widely from neuron to neuron. Figure 16A plots the modulation of neuronal response as a function of the frequency of oscillation of target speed for 10 example cells. The examples were selected by ordering the 31 cells tested with sine waves according to the maximum modulation of firing rate at any frequency and plotting every third cell. For each cell, we normalized response modulation at all frequencies to the maximum. In Figure 16A, the functions are plotted on the normalized scale defined by the calibration bar on the bottom right of the graph but at arbitrary positions on the y-axis to facilitate viewing. The short horizontal dashed line on the right end of each curve shows zero modulation for that curve and demonstrates that the normalized modulation of neuronal firing at 16 Hz was always <0.1. Inspection of Figure 16A shows that many cells had increases in response modulation as the
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Figure 15. Responses of a representative MT neuron to sinusoidal modulation of target speed. The figure consists of 15 pairs of target velocity traces and histograms accumulated from six repeats of the same target motion. The inset on the right above each histogram is a cycle histogram showing the modulation of firing rate averaged over the last second of the sinusoidal speed modulation; the baseline of these cycle histograms has a duration equal to one period of the sinusoid. Cycle histograms have 24 bins per cycle. Full-stimulus histograms have a bin width of 10 msec. A, The amplitude of modulation of target speed was 3°/sec, and the base speed was zero. B, The amplitude of modulation was 1.5°/sec, and the base speed was 1.6°/sec. C, The amplitude of modulation of target speed was 10.5°/sec, and the base speed was 13.5°/sec. The preferred speed of this neuron was 3.2°/sec. From top to bottom in A-C, the frequency of the sine wave was 1, 2, 4, 8, and 16 Hz. Data are from neuron 405r09.
