INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B REFERENCES

Vergence eye movements function to align both eyes on the same object and facilitate the binocular fusion of visual images. An important cue in this process is the slight difference in the locations of the two retinal images that arises from the slight difference in the viewpoints of the two eyes: binocular disparity. Most studies of disparity-induced vergence have examined the transfer of fixation between small targets presented at different distances and have reported latencies ranging from 150 to 200 ms in humans (Jones 1980; Mitchell 1970; Rashbass and Westheimer 1961; Westheimer and Mitchell 1956) and from 135 to 177 ms in monkeys (Cumming and Judge 1986). However, it has been shown that step changes in the horizontal disparity of a large pattern result in machine-like vergence responses with very short latencies: <60 ms in monkeys and <0.80 ms in humans (Busettini et al. 1996; Masson et al. 1997). It has been suggested that these disparity vergence responses are important for the rapid automatic correction of residual (i.e., small) vergence errors (Busettini et al. 1996). In line with this suggestion, these short-latency vergence responses have disparity tuning curves that resemble the derivative of a Gaussian, are well fit by odd (sine phase) Gabor functions and have a roughly linear servo region that extends only a degree or so on either side of zero disparity (Masson et al. 1997). It has recently been reported (Masson et al. 1997) that horizontal disparity steps applied to dense anticorrelated random-dot patterns (in which the patterns seen by the two eyes have opposite contrast so that each black dot in one eye is matched to a white dot in the other eye) also elicit short-latency vergence responses that are very similar to those observed with normal correlated patterns except that they are in the opposite direction. In line with the earlier observations of Cogan et al. (1993), Masson et al. also showed that all of their human subjects were able to discriminate between 1.2° crossed and uncrossed disparity steps applied to dense correlated patterns, but none was able to make these discriminations with dense anticorrelated patterns, which evoked strong binocular rivalry. Cumming and Parker (1997) have reported that monkeys too can make such discriminations with correlated patterns but not with anticorrelated patterns. These anticorrelated patterns therefore provide an interesting disparity stimulus in that they can support vergence eye movements but not depth perception.

It has often been suggested that disparity-induced vergence utilizes disparity-selective neurons to sense vergence errors, and such neurons have been recorded in various regions of the monkey cortex, including striate and extrastriate visual areas (Burkhalter and Van Essen 1986; Cumming and Parker 1999, 2000; Felleman and Van Essen 1987; Hubel and Livingstone 1987; Hubel and Wiesel 1970; Poggio and Fischer 1977; Poggio and Talbot 1981; Poggio et al. 1988; Prince et al. 2000; Smith et al. 1997; Trotter et al. 1996), as well as the middle temporal area (MT) (Bradley and Andersen 1998; Bradley et al. 1995; DeAngelis and Newsome 1999; DeAngelis et al. 1998; Maunsell and Van Essen 1983a), MST (Eifuku and Wurtz 1999; Roy et al. 1992), the posterior parietal area (Sakata et al. 1983), the lateral bank of the intraparietal sulcus (LIP) (Gnadt and Mays 1995), and the frontal eye fields (FEF) (Ferraina et al. 2000; Gamlin et al. 1996). Most of the earlier studies grouped cells according to the shapes of their disparity tuning curves using the classification scheme of Poggio and Fischer (1977), which recognized two general groupings of disparity-selective neurons, later termed "tuned" and "reciprocal" by Poggio et al. (1988). Tuned neurons had narrow tuning curves with either a peak ("tuned-excitatory" neurons) or a trough ("tuned-inhibitory" neurons) centered on the plane of fixation. Reciprocal neurons had asymmetric tuning curves and responded to a broad range of disparities in front ("near" neurons) or behind ("far" neurons) the plane of fixation. Subsequently, Poggio et al. (1988) recognized two additional tuned groups with peaks in front ("tuned near" neurons) or behind ("tuned far" neurons) the plane of fixation and this led to the renaming of the "tuned excitatory neurons" as "tuned zero neurons." Cumming and Parker (1997) recently showed that most disparity-selective neurons in cortical area V1 of monkeys also respond to the disparity of anticorrelated random-dot patterns, often with the opposite sign, e.g., neurons that had "tuned excitatory" disparity tuning curves with correlated patterns had "tuned inhibitory" tuning curves with anticorrelated patterns. Such responses are in line with the suggestion that these neurons act as purely local filters (Cumming and Parker 1997, 2000; Nomura et al. 1990; Ohzawa 1998; Ohzawa et al. 1990).

Our purpose in the present study was to see if there are neurons in area MST of the macaque monkey that have the necessary properties to initiate the short-latency disparity-vergence responses described by Busettini et al. (1996) and Masson et al. (1997). A strong motivating factor came from preliminary evidence that bilateral lesions in MST cause a significant reduction in these vergence responses (Takemura et al. 1999, 2000). Our study was restricted to the initial (open-loop) neuronal responses that occur before the associated vergence responses have had time to modify the central neuronal responses via the disparity feedback loop. We here report that MST neurons can be activated by horizontal disparity steps applied to either correlated or anticorrelated random-dot patterns at latencies that are probably short enough for these neurons to have a causal role in producing even the earliest vergence responses. However, comparatively few of these neurons had disparity tuning curves that resembled the tuning curves for vergence and, when sorted using a fuzzy clustering algorithm, the curves fell into four major groups, corresponding roughly to classes of disparity-selective neurons described in the visual cortex (Poggio et al. 1988). Thus qualitatively at least, most individual tuning curves resembled those at earlier, overtly sensory, stages. Interestingly, when these curves were simply summed together, they fitted the tuning curves for the vergence responses elicited by both correlated and anticorrelated stimuli, indicating that the associated motor responses are encoded at the population level. Nonetheless, using a genetic algorithm, it was possible to identify subsets of neurons whose tuning curves, when summed together, gave an even better fit to the vergence tuning curves, though these subsets invariably included cells from all four groups. Additional analyses of the spike trains elicited by disparity steps revealed considerable variation across cells in the latency, amplitude, and time course of the changes in discharge rate. When all of the spike trains elicited by a given disparity step were summed together to give an average discharge profile for the whole population of cells, many were rather noisy, but others that were less so matched the temporal profile of the motor response, vergence velocity, quite well. Based on these findings, we hypothesize that the disparity-sensitive cells in MST each encode only some aspect(s) of the sensory input and/or motor output, but that the population of cells as a whole encodes the complete motor output (vergence velocity).

Preliminary results have been presented elsewhere (Takemura et al. 1997, 1998, 1999).

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B REFERENCES

We recorded single unit activity in the MST area of five adolescent Japanese monkeys (Macaca fuscata, 6-8 kg) in response to disparity steps applied to large random-dot patterns. Prior to any surgery, animals were trained to fixate small target spots on a tangent screen for a liquid reward using the dimming task of Wurtz (1969). After the completion of training, animals were anesthetized with pentobarbital sodium for the surgical implantation (under aseptic conditions) of 1) a pedestal, secured to the skull to permit the head to be fixed in the standard stereotaxic position during the experiments, 2) a cylinder, secured to the skull over the superior temporal sulcus for the chronic recording of single neuron activity, and 3) scleral search coils, around both eyes for recording eye movements (Judge et al. 1980). All experimental procedures were approved by the Electrotechnical Laboratory Animal Care and Use Committee and have been fully described elsewhere (Kawano et al. 1994).

Disparity stimuli

During recording sessions, which were each several hours long, the animal sat in a primate chair with the head secured and faced a translucent tangent screen onto which two identical random-dot patterns were back-projected. The screen was 50 cm in front of the eyes and subtended 90° along the vertical and horizontal meridia. Orthogonal polarizing filters in the two projection paths and in front of each eye ensured that each pattern was visible to only one eye. Mirror galvanometers in the two light paths were used to control the horizontal positions of the two images (binocular disparity). Using fluid reinforcement, animals were rewarded for fixating stationary red target spots, which were projected onto the patterns on the screen. Binocular disparity stimuli were applied to random-dot patterns that were either exactly matched at the two eyes (standard correlated patterns) or of opposite contrast (anticorrelated patterns).

Standard paradigm using correlated patterns. At the beginning of each trial, the patterns seen by the two eyes were identical, overlapped exactly (zero binocular disparity), and filled the screen. The patterns consisted of white dots on a black background (dots had a luminance of 0.8 cd/m², a diameter of 1.5° and covered 50% of the image space). Horizontal disparity steps (crossed and uncrossed, ranging in amplitude from 0.5 to 6.0°) were applied by displacing the two images equally in opposite directions. Because previous studies had shown that the vergence responses were subject to transient postsaccadic enhancement (Busettini et al. 1996), these steps were applied 50 ms after 10° leftward centering saccades guided by target spots projected onto the screen. The experimental situation was the same as that used by Busettini et al. (1996) in all essentials. Because we were interested only in the initial vergence responses, the disparity steps lasted only 230 ms, and, if there were no saccades during this time, then the data were stored on a hard disk and the animal was given a drop of water; otherwise, the trial was aborted and fluid was withheld. At this point, both images were blanked for 500 ms by mechanical shutters and then reappeared once more for the start of the next trial. Note that all experiments included control trials in which no steps were applied (saccade-only trials). By applying the disparity steps in the immediate wake of centering saccades, we ensured that the animal was alert during the steps, the stimulus pattern was always centered on the retina at the onset of the steps, and the vergence responses were subject to postsaccadic enhancement.

Paradigm using anticorrelated patterns. For this paradigm, the right eye saw the same white dots on a black background as when the binocular patterns were correlated, and the left eye saw a matching negative image (black dots on a white background). However, trials started with the screen a featureless gray (with the same space-averaged luminance as for the patterns), until 50 ms after a 10° leftward centering saccade (again, guided by projected target spots), at which time the anticorrelated random-dot patterns suddenly appeared with a fixed horizontal disparity. Here too the disparity stimuli were presented only briefly (230 ms) before the screen was blanked, ending the trial. This procedure for applying disparate anticorrelated stimuli was the same as that used by Masson et al. (1997) and was necessitated because disparity steps applied directly to anticorrelated patterns at best elicit only weak vergence eye movements (unpublished observations).

Data collection

The techniques for recording unit activity in MST were the same as previously described (Kawano et al. 1992, 1994) and will only be given in brief here. A hydraulic microdrive (Narishige Mo-9) was mounted on the recording cylinder, and glass-coated tungsten microelectrodes were used for the initial identification and mapping of the MT/MST region. Subsequently, a fixed grid system (Crist et al. 1988) was used to position a guide tube through which a flexible tungsten microelectrode was introduced into the MST area for single-cell recordings. The tip of the guide tube was positioned 3-5 mm above the MST. Neuronal activity was recorded using standard extracellular techniques. Spikes were detected with a time-amplitude window discriminator with a resolution of 1 ms. We selectively isolated neurons whose discharge was modulated by disparity steps applied to correlated patterns, and only after obtaining 40 samples of the responses to the complete set of disparity steps did we record responses to similar "steps" applied to anticorrelated patterns. Eye velocity signals were sampled at 500 Hz and all other analog signals at 250 Hz. All data were transferred to a work station (SunSparc) for quantitative analysis.

Data analysis

Horizontal vergence was computed by subtracting the horizontal position signal for the right eye from that of the left eye. We used the convention that rightward positions and velocities are positive, hence, crossed disparities and convergence were also positive. The latency of the vergence eye movements (and associated neuronal responses) was taken to be the time when the mean vergence acceleration (and the mean discharge rate) first exceeded the baseline noise by 2 SD. Vergence responses were quantified by measuring the change in vergence position over the 60-ms time period beginning 50 ms after stimulus onset, and disparity tuning curves were constructed by plotting these measures against the amplitude of the disparity step. To quantify the neuronal responses, we first constructed peristimulus time histograms (binwidth, 1 ms) from the responses to multiple presentations of each disparity step, computing a spike density function by convolving each spike with a Gaussian pulse whose standard sigma was 3 ms (MacPherson and Aldridge 1979; Richmond et al. 1987). These histograms were then used to compute the (average) instantaneous discharge frequency over time. The mean discharge frequency over the 60-ms period starting 40 ms after stimulus onset was computed for the responses to each disparity step, and these values were then plotted against the amplitude of the step: these plots will be referred to as disparity tuning curves. All data shown in the figures, including both eye movements and neuronal discharges, have had the responses on saccade-only trials (i.e., no disparity step applied) subtracted to eliminate any postsaccadic vergence drift and postsaccadic neuronal activity. This has the effect of forcing all the disparity tuning curves through the origin.

Fuzzy clustering analysis. It has been usual to group disparity-selective neurons according to the shape of their disparity tuning curve using a classification scheme described by Poggio and coworkers (Poggio and Fischer 1977; Poggio et al. 1988). This scheme has been very successful but relies on a subjective assessment. In an effort to classify the cells according to the shape of their tuning curve in an objective manner, we turned to clustering methods. These methods attempt to achieve an optimal partitioning of the data into groups. When visual inspection of the data reveals the presence of relatively tight and separate clusters, classic clustering algorithms successfully assign each datum to one of several discrete groups. But when a human observer is uncertain about the separation between groups, as was the case with our data set, these algorithms may not find any structure in the data. In this case, one can try fuzzy clustering algorithms, which retain much more information about the distribution of the data being clustered. We implemented the fuzzy c-means clustering algorithm of Bezdek (1981), and the technical details are given in APPENDIX A. Here, we provide only a brief outline of the general operations performed.

Genetic algorithm. In examining the correlation between the single-unit activity and the vergence eye movements elicited by disparity steps, we attempted to identify the subset of cells whose disparity tuning curves when summed together best matched the disparity tuning curve for vergence. However, if the number of units recorded in a given animal is n, then 2ⁿ subsets are possible. In the present study, for example, we obtained disparity tuning curves for 49 units from one animal, and we estimate that our current computers would require hundreds of years to examine all 2⁴⁹ subsets. After reviewing the options, we decided to use a genetic algorithm (GA). The rationale behind this choice is that for problems in which there is a large number of binary variables (as here), GAs are known to outperform all other methods (computation time being equal): unlike other optimization algorithms, GAs sample several regions of the solution space in parallel. The technical details are given in APPENDIX B and only a brief outline of the general operations performed is provided here.

Histology

At the conclusion of recordings in a given monkey, that animal was deeply anesthetized with pentobarbital and perfused through the heart with saline followed by 10% Formalin. The animal's brain was removed, and frozen sections were cut at 50 µm in the sagittal plane, mounted on microscope slides, and stained with cresyl violet for cell bodies and with a modified silver stain (Gallyas 1979) for myelinated fibers. Electrolytic lesions facilitated histological reconstruction of the electrode tracks, and recording sites were verified using both Nissl and myelination. Sample electrode tracks were verified to pass through the MST using X-rays, and neurons were assumed to be in the MST based on their physiological characteristics (such as preferred speed and receptive field size).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B REFERENCES

Initial vergence responses to disparity steps (correlated patterns)

Horizontal disparity steps applied to large-field, correlated, random-dot patterns elicited vergence eye movements at short latency that were, in all essentials, like those described by Busettini et al. (1996) and Masson et al. (1997). Latency estimates for the five monkeys, based on the responses to the optimal disparity steps, were 73 ms (monkey H, +2°), 68 ms (monkey L, +2°), 65 ms (monkey M, 2°), 58 ms (monkey N, +1°), and 59 ms (monkey Q, +1°).¹ Although no attempt was made to obtain formal estimates of latencies to nonoptimal stimuli, the vergence velocity temporal profiles suggested that for a given animal, latency was largely independent of the stimulus amplitude: see, for example, the sample profiles from monkey H in Fig. 1, those in A showing responses to crossed disparity steps, and those in B responses to uncrossed disparity steps, the stimuli ranging in amplitude from 0.5 to 6°. The profiles in Fig. 1A reach a peak and then decline, often before the closing of the disparity feedback loop (twice the response latency), whereas the profiles in Fig. 1B have a more varied time course and some fail to reach a peak within the time window shown (150 ms after the disparity step). The initial responses to small (<2°) steps were always compensatory in that they operated to reduce the seen disparity: small crossed steps elicited increases in the vergence angle and small uncrossed steps the converse. Responses were generally maximal with steps of 1-3° and declined with larger steps, sometimes showing reversal (Fig. 1B). These trends are evident from the disparity tuning curves in Fig. 1C, in which the change in vergence position (measured over the time period of 50-110 ms) is plotted against the amplitude of the disparity step. These plots indicate that the system showed appropriate servo-like behavior only for small disparity steps. That is, increases in the input resulted in roughly proportional increases in the output (in the compensatory direction) only for steps of less than a degree or so. (Note that the amplitude and direction of the responses of any given monkey to the largest steps were generally independent of whether the steps were crossed or uncrossed and showed considerable variation from one animal to another.) The disparity tuning curves resembled the derivative of a Gaussian and were well fit by a Gabor function: the parameters for the least squares best fits are listed for all five monkeys in Table 1. To evaluate the goodness of the fit, we computed the fraction of the disparity-induced variation in the data accounted for by the fit, r², as previously done by others (e.g., Cumming and Parker 1999). We found that r² ranged from 0.88 to 0.99, indicating that 88-99% of the variation in the data were captured by the fit. (Note that the Gabor functions for monkeys N and Q are plotted as the continuous lines in Fig. 6, A and B.)

View larger version (29K): [in this window] [in a new window]   Fig. 1. Vergence responses: dependence on the amplitude and direction of the disparity step (correlated stimuli). A: traces show vergence velocity over time in response to crossed disparity steps. B: traces show the same for uncrossed steps. Upward deflections denote increased vergence and the numbers on the traces indicate the magnitudes of the steps in degrees. C: the mean change in vergence position in degrees, measured over the 60-ms period starting 50 ms after the disparity step (see the horizontal bars in A and B), is plotted against the magnitude of the step in degrees, for each of the 5 monkeys: disparity tuning curves. Continuous lines are spline interpolations with values at +6° disparity replicated at disparities of +9 and +12°, and values at 6° disparity replicated at disparities of 9 and 12°, and external knots at values with disparities of 18, 15, +15, and +18°. This method was preferred to classic spline interpolation (or cubic interpolation) because it dampens oscillations between absolute disparities of 3 and 6° (where there were no data). Error bars, 1 SD.

Initial neuronal responses to disparity steps (correlated patterns)

We recorded the activity of 586 MST neurons in seven hemispheres of five monkeys while horizontal disparity steps were applied to correlated large-field random-dot patterns. About 20% of the neurons (122) responded to disparity steps at short latency, and the changes in discharge rate ranged from very transientsome lasting little more than 20 msto tonic. This is evident from the sample responses in Fig. 2, which shows the discharge rate temporal profiles of 20 units recorded from monkey N in response to 2° crossed-disparity steps. If a neuron has a response latency of L_n ms, and the associated vergence has a latency of L_v ms, the earliest time at which the neuronal response could be affected by the decrease in retinal disparity secondary to the vergence response would be L_n + L_v ms (after the disparity step). The estimated latency of the vergence response (see METHODS) in Fig. 2 was 59 ms (indicated by the dashed vertical line), which means that only neurons with a latency of <51 ms could have been affected by the closing of the disparity-feedback loop within the time window shown (110 ms after the disparity step). Seven of the neurons in Fig. 2 had a short enough latency to have been so affected (see *), but even in those cases, the loop wouldn't have closed until long after the neurons' initial burst of activity had ended. This is apparent from the estimated time of closure of the disparity feedback loop for those seven cells (indicated by  on the relevant traces in Fig. 2). A similar scrutiny of the entire population of cells indicated that the discharges of ~60% had a phasic component, which in every case was independent of the closure of the disparity feedback loop. The histograms in Fig. 3 show the distributions of the latency estimates for the neurons that met the response-onset criterion (2 SD above the mean control level: see METHODS). The estimates in Fig. 3A are given with respect to the onset of the disparity steps (n = 71; median, 55 ms; range 43-86 ms), whereas those in Fig. 3B are given with respect to the (measured) onset of the vergence responses. The onset of the neuronal responses preceded the onset of the vergence eye movements in 43/50 units (86%) by 24 ms (median lead, 9 ms). Note that the measures in Fig. 3 were all obtained from the response profiles elicited by the stimulus that was optimal for the cell (see METHODS).

View larger version (12K): [in this window] [in a new window]   Fig. 2. Time course of the neuronal responses (correlated stimuli). Top: the changes in mean discharge rate over time in response to 2° crossed disparity steps for each of the 20 units that modulated most with this stimulus (ranked in descending order of their mean discharge rates over the period 30-110 ms after the step). Bottom: the changes in vergence velocity over time; the vertical dashed line shows the estimated latency of the vergence response (59 ms). Seven of the units (*) had response latencies <51 ms; , the estimated times at which the closing of the disparity feedback loop could first influence the discharges of these units (see text). The response latencies of the remaining units were too long for the disparity-feedback loop to close during the 110 ms time window shown. Calibration bars: 500 imps/s, 5°/s. Data from monkey N.

View larger version (35K): [in this window] [in a new window]   Fig. 3. Latency of onset of discharges (correlated stimuli). Histograms show the distribution of latencies with respect to the onset of the stimulus (A) and the onset of the associated vergence eye movements (B). For the latter, negative times indicate that the discharge preceded the vergence response.

DISPARITY TUNING CURVES OF SINGLE CELLS. Neuronal responses were quantified by measuring the mean discharge frequency over the 60-ms period starting 40 ms after the disparity step. Of the 122 MST neurons that showed sensitivity to horizontal disparity steps at short latency, 102 yielded sufficient data to allow complete disparity tuning curves to be plotted. These curves showed a variety of forms and, after normalization, we used the fuzzy c-means algorithm to organize them into groups based on their shapes (see METHODS). This algorithm sorted the curves into four clusters, and we then assigned each curve to one of four groups based on the cluster in which each curve had its largest membership. We chose to partition the curves into four groups because this was the largest number to yield a consistent grouping when the algorithm was run multiple times (50).

View larger version (62K): [in this window] [in a new window]   Fig. 4. Disparity tuning curves for the individual cells (correlated stimuli). Top 4 graphs: mean change in discharge rate over the 60-ms period starting 40 ms after the disparity step is plotted against the magnitude of the disparity step; curves are normalized and arranged in 4 groups based on the outcome of the fuzzy c-means clustering algorithm. Bottom: the disparity tuning curves for the vergence responses of the two monkeys that yielded most of the data (N and Q). Traces are spline interpolations (see legend of Fig. 1 for details).

View larger version (81K): [in this window] [in a new window]   Fig. 5. Rank ordering of disparity tuning curves based on their membership values from the fuzzy clustering analysis (correlated stimuli). Top: membership values; each point along the abscissa represents an individual unit, whose four membership values (1 for each of the 4 clusters) are plotted along the ordinate; each unit is placed in the group that corresponds to the cluster in which it has its highest membership (group 1 have their highest memberships in cluster 1, group 2 their highest in in cluster 2, etc) and, within each group, each unit is ranked according to its membership in an adjacent cluster. Units in group 1 are ranked in ascending order of their memberships in cluster 2, units in group 2 are ranked in ascending order of their memberships in cluster 3, units in group 3 are ranked in ascending order of their memberships in cluster 4, and units in group 4 are ranked in descending order of their memberships in cluster 3. Triangles, cluster 1; stars, cluster 2; squares, cluster 3; circles, cluster 4. Bottom: disparity tuning curves; each point along the abscissa corresponds to the unit whose membership value is plotted above, and its disparity tuning curve is shown in a color-coded form in accordance with the scale shown at the right (increases in discharge rate, in imp/s, are shown in red and decreases are shown in blue) with the amplitude of the disparity steps represented along the ordinate.

DISPARITY TUNING CURVES FOR (SUMMED) POPULATIONS OF CELLS. A characteristic feature of the disparity tuning curves for vergence in Fig. 1C is that they are roughly odd functions, that is, f(x) = f(x), with a linear segment passing smoothly through zero disparity defining the critical servo range over which changes in the input (binocular disparity) elicit roughly proportional changes in the output (vergence eye movement). It is significant that very few cells had disparity tuning curves with this exact same feature: The tuned inhibitory group 2 cells have rather flat curves in the vicinity of zero, conveying little information about disparity in this range, and the tuning curves for most other cells undergo a substantial change in slope near zero disparity. Exceptions are small numbers of cells in the tuned near group 4 and tuned far group 1, with positive and negative slopes, respectively, extending on either side of zero disparity. (Given appropriate excitatory or inhibitory connections, neurons with either positive or negative slopes could make a positive contribution to the vergence responses. That the tuning curves for vergence had a positive slope around zero disparity was determined solely by our sign convention.) To obtain an estimate of how well the vergence responses were encoded in the discharges elicited in individual MST cells, we fitted the disparity tuning curves of the individual cells to the tuning curves for vergence, the only free parameters being gain and y offset. We assumed that all neurons made a positive contribution to the vergence responses elicited by disparity steps in the important servo range, ±1° and so reversed the sign of those curves that had negative slopes over that range: this involved 29/102 cells, including all 28 in the tuned-far group 1 and 1 in the tuned inhibitory group 2. The least-squares best fits ranged widely (r²: mean, 0.51; range, 0.009-0.92), but the very best of the fits were good enough to raise the possibility that some cells might be more properly regarded as "vergence-related" rather than "disparity-related." We will revisit this issue later when we describe the responses of these cells to anticorrelated stimuli.

View larger version (26K): [in this window] [in a new window]   Fig. 6. Spatial coding of vergence by populations of cells (correlated stimuli). Disparity tuning data for vergence (*) and for the least-squares, best-fit summed activity () for monkey N (A and C) and monkey Q (B and D). For the top plots (A and B), the individual unit curves with negative slopes around zero disparity were inverted before summing and for the bottom plots (C and D), no curves were inverted. Curves are the least-square, best-fit Gabor functions for the vergence data () and the summed activity data (- - -).

View larger version (13K): [in this window] [in a new window]   Fig. 7. Spatial coding of vergence by the subsets of cells selected by the genetic algorithm (correlated stimuli). Disparity tuning data for vergence (*) and for the summed activity of the subsets of cells (selected by the genetic algorithm) that gave the very best fits to the vergence data () for monkey N (A) and monkey Q (B). Curves are the least-squares best-fit Gabor functions for the vergence data () and for the summed unit data (- - -).

View larger version (19K): [in this window] [in a new window]   Fig. 8. Temporal coding of vergence velocity by populations of cells (correlated stimuli). A and B: plots of average vergence velocity () and the least-squares, best-fit summed activity (- - -) over time for monkey N (A) and monkey Q (B) in response to 1° crossed-disparity steps; gain and offset were free parameters for these fits, which were obtained for a range of x shifts (time shifts, at 1-ms intervals), and the data shown are for the x shifts that gave the very best fits. C and D: the dependence of the goodness of these best fits (r2) on the time shift is plotted for monkey N (C) and for monkey Q (D); a negative time shift indicates that the summed activity has been moved forward in time with respect to the vergence response; both peak at negative values (18 ms in A, 23 ms in B), indicating that the summed activity preceded the vergence response and had to be moved forward to get the very best fit.

Initial vergence responses to disparity steps (anticorrelated patterns)

The vergence responses elicited by disparity steps applied to anticorrelated patterns were recorded from two animals (monkeys N and Q). As previously reported by Masson et al. (1997), these vergence responses were comparable in latency with those produced by the same steps applied to correlated patterns but were often in the opposite direction. This is apparent from the sample data from monkey N shown in Fig. 9, which has a layout identical to Fig. 1. Thus the disparity tuning curves showed a negative slope in the immediate vicinity of zero disparity, though it is clear that the curve for monkey Q is shifted appreciably to the left of the curve for monkey N. The peak-to-peak amplitudes of the (interpolated) disparity tuning curves for the anticorrelated data were smaller than those for the correlated data: by 33% for monkey N and by 44% for monkey Q. The tuning curve data were well fit by a Gabor function (r² was 0.99 and 0.98 for monkeys N and Q, respectively), and the parameters of the least-squares best fits are listed in Table 1: see also the continuous lines plotted in Fig. 12, A and B. Of particular interest among the parameters of the Gabor functions is the difference in the phase of the cosine terms for the correlated and anticorrelated data: 177° for monkey N and 169° for monkey Q. This reinforces the impression that, to a first approximation, the disparity tuning curves obtained with anticorrelated stimuli were inverted versions of those obtained with correlated stimuli. The above-mentioned shifts, however, are evident in the x shifts of the best-fit Gabor functions, which differed for the correlated and anticorrelated data, especially for monkey Q: this parameter was always zero for the correlated data and negative for the anticorrelated data (Table 1). In fact, the tuning curves obtained with anticorrelated stimuli were quite well fitted by the tuning curves obtained with correlated stimuli when the latter were inverted provided that the x shift was a free parameter (in addition to gain and y offset): r² values for the least-squares best fits for monkeys N and Q were 0.86 and 0.97, respectively, and the corresponding x shifts were 0.05 and 0.61°.

View larger version (26K): [in this window] [in a new window]   Fig. 9. Vergence responses: dependence on the amplitude and direction of the disparity stimulus (anticorrelated stimuli). Traces in A show vergence velocity over time in response to crossed disparity steps, and traces in B show the same for uncrossed steps. C: the mean change in vergence position in degrees, measured over the 60-ms period starting 50 ms after the disparity step), is plotted against the magnitude of the step in degrees, for each of the 2 monkeys: disparity tuning curves. All conventions as for Fig. 1.

Initial neuronal responses to disparity steps (anticorrelated patterns)

Neurons that were still well isolated after we had finished recording their responses to disparity steps applied to correlated patterns were then recorded while the same steps were applied to anticorrelated patterns. The activity of 56 MST neurons in three hemispheres of two monkeys was so recorded (25/49 units from monkey N and 31/31 units from monkey Q), and all gave significant responses to the anticorrelated stimuli (P < 0.005, 1-way ANOVA). Neuronal response latencies to anticorrelated stimuli were roughly comparable to those obtained with correlated stimuli.

DISPARITY TUNING CURVES OF SINGLE CELLS. Figure 10 shows the normalized disparity tuning curves for all 56 units whose responses to anticorrelated stimuli were recorded, and is organized like Fig. 4, with cells placed in the same four groups. That is, cells that were in group 1 in Fig. 4 were also placed in group 1 in Fig. 10, and so forth. Again, we fitted the disparity tuning curves of the individual cells to the tuning curves for vergence (gain and y offset, free parameters) and assumed that the contribution of any given cell to the vergence response would always have the same sign regardless of the stimulus used to drive it. Accordingly, cells whose contributions had been inverted for the earlier analysis of the correlated data were again inverted here. (For monkey N, 7/25 curves were inverted and for monkey Q, 7/31 curves were inverted, all in group 1.) As for the correlated data, the least-squares best fits for the anticorrelated data ranged widely (r²: mean, 0.39; range, 0-0.97) and some were clearly good enough to be considered vergence-related rather than disparity-related. However, no single cell had responses that fitted the vergence responses obtained with both correlated and anticorrelated stimuli with an r² value >0.67: Fig. 11 shows a plot of the individual r² values obtained with correlated stimuli against those obtained with anticorrelated stimuli, and there is a relative paucity of cells in the upper right quadrant, which is where pure vergence-encoding cells would be expected.

View larger version (65K): [in this window] [in a new window]   Fig. 10. Disparity tuning curves for the individual cells (anticorrelated stimuli). Top 4 graphs: mean change in discharge rate over the 60-ms period starting 40 ms after the disparity step plotted against the magnitude of the disparity step for the data from 2 monkeys (N, data in red; Q, data in blue); curves are normalized and each has been assigned to 1 of 4 groups (the curve for a given cell being assigned to the group to which that cell's curve was assigned in Fig. 4); thick gray traces in each of the 4 graphs show the (inverted) median tuning curves obtained for the same groups of cells with correlated stimuli. Bottom graph: thick colored traces, the disparity tuning curves for the associated mean vergence responses of the 2 monkeys; thin colored traces, the (inverted) vergence tuning curves obtained from the same 2 monkeys with correlated stimuli. Traces are spline interpolations (see legend of Fig. 1 for details).

View larger version (22K): [in this window] [in a new window]   Fig. 11. Coding of vergence by individual cells (correlated and anticorrelated stimuli). The disparity tuning curves of the individual cells were fitted to the disparity tuning curves of the associated vergence responses and r2 values for the least-squares, best fits were computed. This graph plots the r2 values for the data obtained with correlated patterns against those obtained with anticorrelated patterns. No cell had r2 values that exceeded 0.67 for both stimuli (indicated by the - - -). Also shown (indicated by their identifying letters), are the r2 values for the fits between the summed activity and the vergence responses for the 2 monkeys, N and Q (from which all the unit data plotted here were obtained).

DISPARITY TUNING CURVES FOR (SUMMED) POPULATIONS OF CELLS. We saw earlier that, when correlated patterns were used, the disparity tuning curves for the summed activity of the population of cells matched the tuning curves for the associated vergence responses quite well. We now sought to determine if the same was true for the data obtained with anticorrelated stimuli. We again summed all of the rawthat is, nonnormalizedtuning curves for each of the two monkeys separately and then determined how well these population responses fitted their respective tuning curves for vergence when gain and y offset were the only free parameters. We assumed that the contribution of any given cell to the vergence response would always have the same sign regardless of the stimulus used, and cells whose contributions had been inverted for the earlier analysis of the correlated data were again inverted here. Figure 12, A and B, shows that the disparity tuning data for the summed activity () again matched those for the associated vergence responses (*) quite well (r²: 0.96 and 0.95 for monkeys N and Q, respectively). Once again, failure to invert the contributions of the relevant cells before fitting led to significantly worse fits (r²: 0.77 and 0.57 for monkeys N and Q, respectively), though the effects on the fits were not as dramatic as reported above for the data obtained with correlated patterns. In the case of monkey N, this is perhaps in part because a somewhat smaller proportion of the curves obtained with anticorrelated stimuli were inverted: 28% (7/25), compared with 35% (17/49) of those obtained with correlated stimuli. There was one cell from monkey N whose tuning curve matched the vergence as well as the curve for the summed activity did (r² = 0.97) but the mean r² for all cells from this monkey was only 0.47. None of the single units from monkey Q had tuning curves matching its vergence responses as well as its summed activity did and the highest r² for any individual unit from this monkey was 0.88 (mean r²: 0.32).