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The Journal of Neurophysiology Vol. 80 No. 3 September 1998, pp. 1407-1426
Copyright ©1998 by the American Physiological Society
1 Graduate Group in Bioengineering, University of California at Berkeley, Berkeley, 94720; and 2 Smith-Kettlewell Eye Research Institute, San Francisco, California 94115
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ABSTRACT |
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 Abstract
 Introduction
Methods
Results
Discussion
References
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Edelman, Jay A. and Edward L. Keller. Dependence on target configuration of express saccade-related activity in the primate superior colliculus. J. Neurophysiol. 80: 1407-1426, 1998. To help understand how complex visual stimuli are processed into short-latency saccade motor programs, the activity of visuomotor neurons in the deeper layers of the superior colliculus was recorded while two monkeys made express saccades to one target and to two targets. It has been shown previously that the visual response and perimotor discharge characteristic of visuomotor neurons temporally coalesce into a single burst of discharge for express saccades. Here we seek to determine whether the distributed visual response to two targets spatially coalesces into a command appropriate for the resulting saccade. Two targets were presented at identical radial eccentricities separated in direction by 45°. A gap paradigm was used to elicit express saccades. Express saccades were more likely to land in between the two targets than were saccades of longer latency. The speeds of express saccades to two targets were similar to those of one target of similar vector, as were the trajectories of saccades to one and two targets. The movement fields for express saccades to two targets were more broad than those for saccades to one target for all neurons studied. For most neurons, the spatial pattern of discharge for saccades to two targets was better explained as a scaled version of the visual response to two spatially separate targets than as a scaled version of the perimotor response accompanying a saccade to a single target. Only the discharge of neurons with large movement fields could be equally well explained as a visual response to two targets or as a perimotor response for a one-target saccade. For most neurons, the spatial properties of discharge depended on the number of targets throughout the entire saccade-related burst. These results suggest that for express saccades to two targets the computation of saccade vector is not complete at the level of the superior colliculus for most neurons and an explicit process of target selection is not necessary at this level for the programming of an express saccade.
Research in the past three decades has demonstrated that the vectors of saccades are coded by neurons in the frontal eye fields (FEF), posterior parietal cortex, and deeper layers of the superior colliculus (DSC) (Andersen 1989
Animals and surgery
Neurons were recorded in the superior colliculi of two adolescent monkeys (Macaca fascicularis). All experimental protocols were approved by the Institutional Animal Care and Use Committee at the California Pacific Medical Center and complied with the guidelines of the Public Health Service policy on Human Care and Use of Laboratory Animals.
Training
After being allowed to recover from the effects of surgery, monkeys were trained to climb out of their cages into a primate chair designed to restrain the monkey during experiments. Training and subsequent experimental sessions took place four to five times per week, during which monkeys were given water as an experimental reward until satiated. Otherwise, the monkeys were water deprived. On days when training or experiments were not being performed, monkeys were allowed to drink water in their cages ad lib.
Monitoring of single-neuron activity
Single-neuron activity was recorded extracellularly using tungsten microelectrodes (Frederick Haer). With the use of an electrostatic device, insulation was blown off the tip to create an electrode with 0.5-1.5 M Eye movement monitoring, data collection, and stimulus presentation
Eye movement signals were obtained by placing the head-fixed monkey in horizontal and vertical magnetic fields that oscillated in temporal quadrature at 22 kHz. Electrical currents induced in the eye-coil wire by the magnetic fields were passed through a phase detector to yield separate horizontal and vertical eye movement signals. Phase-detector offsets were set to account for variability in position of the coil within the eye. Before the beginning of each experimental session, the monkey's eye position was calibrated by adjusting the gain and offset of an eye position signal amplifier while the monkey looked at visual targets projected at known locations.
Paradigm
On isolating a single neuron, the center of the neuron's movement field was coarsely estimated immediately before collecting data by observing discharge during 1T saccades. A variant of the standard saccade paradigm was designed to include presentations of one or two targets. Trials began with presentation of a fixation point, generally at the straight-ahead position. The monkey was required to fixate this point within 500 ms. After a variable period of fixation (400-800 ms), the fixation point disappeared, and one or two targets appeared and remained lit until the saccade terminated. To help elicit express saccades, a gap paradigm was used (Saslow 1967 Latency and accuracy requirements
To further prevent anticipatory saccades, we only rewarded saccades with latencies above a minimum reaction time of 50 or 60 ms. In most experimental sessions the maximum reaction time for saccade onset was set at 200-225 ms. We found that setting the maximum reaction time so that only express saccades were rewarded (i.e., at 100 ms) would often frustrate the monkey to the point where it did not make any express saccades. In 2T trials monkeys were rewarded for a short-latency saccade to a window surrounding both targets. This window had the shape of a radial arc with an inner radius of 0.75 × the radial amplitude of the two targets, an outer radius of 1.25 × the radial amplitude, and an angular extent of ~55°. To avoid introducing a more cognitive component to our task, we did not explicitly train the monkey to make averaging saccades. In 1T trials short-latency saccades to a small square window (4 × 4°) surrounding the single target were rewarded. Only data recorded when monkeys made saccades satisfying the latency and accuracy measures described above were analyzed.
Saccade detection
To enforce our saccade latency requirements, we detected saccade onset on-line. Eye velocity signals were obtained on-line with the use of a low-pass analog differentiator (cutoff: 170 Hz). Time of saccade onset was defined as the time when radial eye velocity (calculated on-line using the Pythagorean theorem) exceeded 20°/s. For data analysis, a digitally filtered eye velocity signal was filtered to obtain a more precise estimate of saccade latency. Using this off-line technique, saccade onset was defined as the time when radial eye velocity reached 10°/s. For a random sample of trials, this algorithm virtually always marked saccade onset within 2 ms of their onset as determined by visual inspection.
Saccade classification
In accordance with a previous report from this lab (Edelman and Keller 1996 Neuron classification
The activity of 37 visuomotor burst neurons in the deeper layers of the SC was assessed using this paradigm. These neurons all displayed separate bursts of visual and perimotor activity when tested with a delayed paradigm, in which a single target was presented but the monkey had to continue fixating until the fixation point was turned off (see Edelman and Keller 1996 Spike density and summary of data analyses
To assist the quantitative analysis of DSC neurons' burst waveform, the raw spike trace was convolved with a Gaussian of 4 ms standard deviation to yield a spike density trace (Richmond and Optican 1987 Comparison of surface fits of movement fields
The spatial properties of 1T movement fields were estimated using a two-dimensional nonlinear surface fit with five free parameters. This process is illustrated in Fig. 2, and the detailed equations are described in the APPENDIX . The fields were fit as a product of a term expressing the peak discharge of the neuron, M, a log-Gaussian function along a curve of constant direction, P(), which is depicted in Fig. 2E, and a Gaussian function along a curve of constant radius,
Visuomotor analysis: derivation of motor and visual predictions and measures of goodness-of-fit of predictions
To determine how well discharge for express saccades to two targets resembled that of the perimotor discharge for 1T express saccades, we computed for each neuron the motor goodness-of-fit (MGF), a measure of how closely the 2T movement field resembled a surface proportional (of same shape, but scaled in magnitude) to the calculated 1T movement field fit. This procedure is illustrated in Fig. 3. This surface corresponding to the contour plot in Fig. 3C was obtained by calculating the movement field fit for saccades to one target (Fig. 3A), as described for Eq. 1 above
Saccade characteristics
We were concerned about possible differences in the speed or curvature of 1T and 2T saccades, because such differences would make the results of our single-cell recordings more difficult to interpret. We were also interested in the distribution of endpoints of 2T saccades relative to the positions of the two targets, and how this distribution depended on saccade latency. We therefore analyzed the eye movement data that we recorded while collecting neuronal data. We also analyzed data for regular saccades elicited by the gap paradigm.
SPEED AND CURVATURE OF 1T AND 2T SACCADES.
It is well established that, given the same stimulus conditions, saccade peak speed is strongly dependent on saccade amplitude and that peak speed shows a soft saturation for saccades larger than ~20° in amplitude (Becker 1991
RELATIONSHIPS BETWEEN NUMBER OF TARGETS, SACCADE ENDPOINT DISTRIBUTION, AND SACCADE LATENCY.
The number of targets had a small effect on saccade latency in the gap paradigm. This effect was of opposite sign for the two monkeys. For example, for saccades between 10 and 20° in amplitude with directions from right horizontal to 45° right and up, 2T saccades tended to have slightly longer latencies than 1T saccades for one monkey (GM) (1T: 87 ms, 2T: 98 ms; t-test, P < 0.001), but slightly shorter latencies for the other monkey (ME) (1T: 109 ms, 2T: 95 ms; t-test, P < 0.001).
Single-unit activity
In the following sections we describe the results of our analyses of single-unit data. The results can be summarized as follows: 1) The spatial profile of discharge for 2T express saccades depends not only on saccade vector but also on the number of targets that elicit the saccade. 2) This discharge accompanying 2T express saccades is more like a visual response to two targets than a motor response preceding 1T saccades; the VGF (see METHODS) is generally greater than the MGF. 3) The MGF and VGF are comparable only for neurons with movement fields broad in direction. 4) The spatial profile of discharge for 2T express saccades is different from that of 1T express saccades for the duration of the saccade-related burst. 5) The differences between MGF and VGF are significant for both averaging express saccades and nonaveraging express saccades.
DOES SINGLE-NEURON ACTIVITY AT SACCADE ONSET DEPEND ON TARGET CONFIGURATION?
In this section our sole aim is to provide evidence demonstrating that 1T and 2T movement fields are different. Across our sample of recorded neurons, express saccade movement fields were clearly dependent on target configuration. Movement fields were broader along the direction axis in the 2T case than in the 1T case for all neurons tested quantitatively (see below). Data for a neuron whose discharge was greatly dependent on the number of targets are shown in Fig. 7. This neuron discharged more for 1T than for 2T saccades when saccades landed close to the center of the neuron's movement field, as can be seen by comparing the brightness of spatially corresponding squares in Fig. 7, A and B. However, this neuron discharged much less for 1T saccades than for 2T saccades when saccades had a direction very different from that of the center of the movement field. In addition, for this neuron, 2T saccades were accompanied by more discharge when their directions were far from the movement field center than when they were close to the center. In the neuron whose discharge is portrayed in Fig. 8, such a spatially bimodal pattern was not so detectable, yet the discharge was clearly dependent on the number of targets. Figure 9 shows data for a neuron whose 1T and 2T movement fields were more similar, a finding seen for most of our neurons with larger 1T movement fields.
VISUOMOTOR ANALYSIS: DOES ACTIVITY FOR TWO TARGETS RESEMBLE A VISUAL RESPONSE OR A MOTOR PRELUDE?
Having determined that express saccade movement fields of visuomotor neurons were dependent on target configuration, we next asked whether the spatial profile of discharge for 2T express saccades could be better explained as the visual response to the two targets than as a motor prelude of a saccade with a particular vector.
IS THERE A SEPARATE CLASS OF NEURONS THAT CODES FOR THE SACCADE AND NOT THE TARGET CONFIGURATION?
Although the sample of neurons we recorded generally coded the target configuration better than they did saccade vector, we sought to determine whether some subset of neurons might show the opposite preference of coding. We hypothesized that visuomotor neurons with greater perimotor than visual responses during nonexpress saccades would have a greater MGF. To temporally separate visual from motor discharges for 31/37 neurons, we used a visually guided delayed saccade paradigm, in which a target appears but a saccade cannot be made until the fixation light is turned off 500-700 ms later (see Edelman and Keller 1996
DOES ACTIVITY BECOME MORE SACCADE DEPENDENT AS THE VISUOMOTOR BURST ACCOMPANYING EXPRESS SACCADES PROGRESSES?
We also determined whether the spatial profile of activity of visuomotor neurons during 2T saccades could become more like that for 1T saccades as the visuomotor burst continued. To do so we repeated elements of the analyses described above on specific epochs of express saccade-related activity. Because the saccades we elicited varied considerably in duration, we chose not to analyze epochs of fixed length locked to the onset of the saccade. Instead, we considered epochs whose length and position depended on saccade duration. For each saccade we defined t = 0 as 25 ms before the onset of the saccade, because the high-frequency burst of activity in visuomotor neurons begins ~25 ms before express saccades (Edelman and Keller 1996
DOES THE SPATIAL PROFILE OF ACTIVITY FOR 2T EXPRESS SACCADES DEPEND ON HOW CLOSE THE SACCADE LANDED TO A TARGET?
As mentioned previously, the endpoints of saccades elicited by the presentation of two targets were quite variable with respect to the locations of the two targets. Could the dependence of visuomotor neuron activity on movement vector and target configuration depend on whether a saccade elicited by two targets was averaging or nonaveraging? Because of the generally small sample sizes, few of the five-parameter nonlinear regressions were successful for the averaging or nonaveraging saccade data. Therefore we only repeated the visuomotor analysis for the comparison of 1T with averaging saccades and then 1T with nonaveraging saccades. Analysis for the 40-ms epoch centered on saccade onset showed that the differences between the MGF and VGF were smaller for the nonaveraging saccade comparison than for the averaging saccade comparison, although the difference between MGF and VGF for nonaveraging saccades was still large (Table 2). This finding suggests the idea that nonaveraging saccades are coded in a manner intermediate to that of 1T and averaging saccades.
Activity in the deeper layers of the superior colliculus accompanying express saccades to two targets
Edelman and Keller (1996) Relation to previous work on spatial coding in the DSC for saccades to two targets
Previous investigators studying the neural activity underlying saccades to two targets used more complicated tasks than the one used here, apparently because in monkey the conventional visually guided saccade paradigm elicited saccades that landed on one target or the other and not in between. Van Opstal and Van Gisbergen (1990) Role of DSC visuomotor burst neurons in saccade generation
Robinson (1972) Saccade spatial commands, target selection, and the visual grasp reflex
Previous work has supported the idea that a vector of an impending saccade is represented by a particular distribution of neural activity on the motor map of the DSC. While recent work has demonstrated that the vector of the saccade may be modified by other signals related to the memory of target (Stanford and Sparks 1994
INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References
; Goldberg and Segraves 1989; Sparks and Hartwich-Young 1989). Neurons in these saccade-related areas also have sensory properties, suggesting that they play a role in analyzing the array of sensory input and determining the location in visual space to which the saccade will be made.
; Findlay 1982; Ottes et al. 1984). It is unclear where in the saccadic pathway the processing of such an array of sensory input to yield a saccade vector is complete. Indeed, the command to make such a saccade may only be evident at a level, such as at that of the excitatory burst neurons in the brain stem, where saccades are coded temporally, not spatially.
). Such neurons have both receptive and movement fields, receptive fields being the region of visual space in which presentation of a target modulates a neuron's response, and movement fields being the loci of endpoints of saccades accompanied by neural discharge. The two-dimensional shape of receptive and movement fields refers to the dependence of cell discharge on target location or saccade vector, respectively.
described three hypotheses of where in the saccadic system saccades to two targets are programmed relative to the DSC. The upstream hypothesis claims that averaging saccades are programmed in "upstream" areas that project to the DSC, such as the FEFs and posterior parietal cortex. This hypothesis predicts that, by the time the saccade generating signals pass through the DSC, they should be independent of target configuration and depend only on saccade vector. Discharge in the DSC for saccades to one target and two targets should be identical, and thus a neuron's activity should only depend on saccade vector (Fig. 1, C and D). The downstream hypothesis claims that saccades to two targets are spatially programmed in saccade-related regions downstream of the DSC, or else that they are merely a consequence of the spatiotemporal processing downstream of the DSC. The most extreme version of this hypothesis would predict that the spatial distribution of perisaccadic activity in the DSC is identical to the spatial distribution of the visual response in the DSC, so that a neuron's discharge should only depend on target configuration (Fig. 1, E and F). Thus, according to this hypothesis, the impending saccade vector is never represented explicitly at the level of the DSC. The collicular hypothesis claims that sensorimotor transformations underlying saccades to two targets occur within the DSC. This hypothesis predicts that while a saccade to two targets is programmed and executed, discharge in the DSC will at first depend on target configuration and then later have discharge identical to that for saccades to one target of the same vector. Some previous work has partially addressed the question of what role visuomotor neurons in the DSC play during saccades to two targets.
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FIG. 1.
Cartoon illustrating predictions of the upstream and downstream hypotheses. A: cartoon of superior colliculus (SC) motor map depicts recording of a neuron located on the horizontal meridian of the motor map at a position corresponding to 20° rightward saccades. B: cartoon of location in visual space corresponding to location on motor map of recorded neuron. C and D: cartoon illustrating prediction of upstream hypothesis. C: cartoon of relation of activity on motor map and neural discharge of a single neuron for 2-target (2T) saccades given that activity only depends on saccade vector. Each map of visual space depicts a saccade of a particular vector, whereas the accompanying SC motor map depicts the activity (grayish area) in the SC that would accompany this saccade. Small square on the map depicts the location in the SC of the recorded neuron. Each pair of maps is connected by a dashed line to a data point in D corresponding to discharge of this neuron for this saccade. D: taken together, these data points depict the relation between neural discharge and saccade direction. E and F: cartoon illustrating prediction of downstream hypothesis. E: cartoon of relation of activity on motor map and neural discharge recorded from a single neuron for saccades to 2 targets given that activity only depends on the locations of the 2 targets. Each map of visual space depicts a particular 2T configuration, whereas the accompanying SC motor map depicts the activity (grayish area) in the SC that would accompany this target configuration. Small square on the map depicts the location in the SC of the recorded neuron. Each pair of maps is connected by a dashed line to a data point in F corresponding to discharge of this neuron for this target configuration. F: taken together, these data points depict the relation between neural discharge and average target direction. See text for details.
showed that simultaneous electrical stimulation of two sites in the DSC elicited saccades with a vector average of the saccades elicited by stimulation of each site alone. If we assume that electrical stimulation activates the output elements of the DSC, this result suggested that saccade areas downstream of the DSC can spatially average DSC activity. This result partially corroborates the downstream hypothesis and furthermore suggests that the resultant saccade vector is dependent on the "center of mass" of activity in the DSC and not on the total amount of activity in the DSC. However, just because the collicular-brain stem interface has the ability to create averaging saccades does not prove that saccades elicited by two visual stimuli are programmed in the same way.
used a double-step paradigm, in which two targets were presented close together in space but separated in time, to elicit saccades that landed between the two targets. They showed that neurons in the DSC discharged less for two-target (2T) saccades than they did for one-target (1T) saccades to the same location, but also demonstrated that saccades elicited by the double-step paradigm were slower than saccades to a single target. Using a more complicated paradigm in which a monkey had to make a saccade to one of two target locations depending on the color of the fixation point and after a delay period, Glimcher and Sparks (1993) found that saccades that by mistake landed in between the two locations were coded in the DSC similarly to 1T saccades with the same vector.
). For such saccades there may be little time to create an explicit spatial representation of saccade vector on the DSC motor map before saccade initiation. On the other hand, if the coding of such short-latency saccades does not depend on target configuration, it is unlikely that saccades of longer latencies would be so dependent.
described above.
METHODS
Abstract
Introduction
Methods
Results
Discussion
References
and modified by Judge et al. (1980); 2) a stainless steel recording chamber above the stereotactically determined location of the superior colliculus; and 3) two hollow bars transversely above the skull anterior to the recording chamber and a third diagonally, posterior to chamber, for use with a head-holding device. The recording chamber and transverse bars were fixed to the skull by embedding them in dental acrylic applied as liquid to the exposed skull. The dental acrylic mount was firmly anchored to the skull by the use of titanium self-tapping screws.
impedance when tested at 1 kHz. On days of recording, the stainless steel recording chamber was opened and thoroughly cleaned under aseptic conditions. A double-eccentric micropositioning device was inserted into the chamber. A hole drilled in this device could be placed at any location within the 12-mm-diam chamber, allowing the electrode to access arbitrary but reproducible positions within the chamber. The dura mater was penetrated using a sharpened cylindrical guide tube, through which the electrode was subsequently driven hydraulically. Action potentials were detected by passing the raw neural signal through a spike discriminator (Mentor).
), in which there was a temporal "gap" between fixation point disappearance and target spot reappearance. Depending on the animal's performance, gaps were adjusted in length from 80 to 150 ms to prevent anticipatory saccades. In one-third of our trials, two targets of identical radial amplitude and separated in direction by 45° were presented. We chose this value because we found that larger separations dramatically reduced the yield of express saccades. To discourage formation of the strategy of repeatedly making a saccade to the same of two targets as well as to gather normative data for 1T saccades, single targets were presented in two-thirds of the trials. Single targets were presented randomly at one of nine possible positions near and flanking the center of the neuron's movement field. The nine possible positions were arranged in a 3 × 3 polar grid, so that each position could be of one of three radial eccentricities and of three directions. The directions were spaced by 22.5°, whereas the radial eccentricities were spaced differently from neuron to neuron depending on the radial extent of its movement field. For two target trials, the targets were presented so that the radial eccentricity and average direction of the two targets was of one of the nine positions selected randomly. If the monkey was still well-motivated and the neuron still well-isolated after sufficient data had been obtained for each of the nine positions (~15 total trials per position), targets were presented at additional positions flanking the original nine positions.
) express saccades were classified as those saccades with latencies between 65 and 90 ms, and regular saccades were classified as those saccades with latencies between 120 and 200 ms. The averaging saccades were defined as those saccades that landed closer to the midpoint of two targets than to either target; nonaveraging as those that landed closer to either target.
), or during regular saccades. During or just before a saccade of optimal vector, the activity of these neurons peaked at >250 spikes/s then dropped during the saccade. Neurons with this temporal profile of activity have been referred to as clipped and partially clipped burst neurons (Waitzman et al. 1991), or burst neurons (BNs) (Munoz and Wurtz 1995). However, a few of our neurons also discharged at a low-frequency several hundred milliseconds before a saccade, a characteristic of the buildup neurons (BUNs) described by Munoz and Wurtz (1995). We applied the criterion of Munoz and Wurtz (1995) (discharge of >30 spikes/s in the 100-ms time interval beginning 200 ms before saccade onset for the saccades of the optimal vector in a delayed saccade paradigm) to the 31/37 neurons for which we collected data during a delayed paradigm, to determine how many of the neurons would be classified as BUNs. By this test we found 9/31 (~29%) tested neurons were BUNs. We have argued elsewhere that this criterion does not separate DSC into two distinct classes (Anderson et al. 1998).
, the neurons we recorded would be classified neurons as visuomotor neurons because our neurons all had visual responses. In their scheme this class of neurons is distinct from burst neurons without a visual response, which they termed saccade-related burst neurons (SRBNs), although it is unclear from their classification whether or not neurons with visual responses below a certain small criterion level would be called SRBNs. In a larger sample of neurons recorded in the SC more recently in our lab, 139/145 recorded neurons had a separate visual response (Anderson et al. 1998). This neural population consisted both of BNs and BUNs, as described above.
).
(), which is depicted in Fig. 2D. The form of the equation of the fit is
where
(1)
is the predicted neural discharge (spikes/s); 
is the saccade radial amplitude (deg); 
is the saccade direction (zero is right and horizontal; deg); and the five free parameters are 1) M, the magnitude of response at center of movement field (spikes/s); 2) c, the radial eccentricity of center of movement field (deg); 3) c, the direction of center of movement field (deg); 4) s, the spread of surface along radial dimension [unitless]; and 5) s, the directional standard deviation, or spread, of surface (deg). A three-dimensional plot of such a surface is shown in Fig. 2B, and the contour plot of the surface is shown in Fig. 2C.
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FIG. 2.
Illustration of 5-parameter Gaussian/log-Gaussian curve-fitting procedure. A: plot of movement field of a single neuron from our data set for 1T saccades. Each square represents discharge for a single saccade. Horizontal and vertical axes represent horizontal and vertical saccade displacement, respectively. Brightness of square represents mean discharge (spikes/s) in a 40-ms window centered on saccade onset. The brighter the square, the greater the activity. B: 3-dimensional mesh plot of movement field fit. C: contour plot of this same movement field fit. Center of contour is the center of the movement field, described by polar coordinates ( c, c), representing the directional center and the radial center of the movement field, respectively. D: slice of the movement field along an isoradial line (depicted in inset). Actual discharge corresponding to saccades with a radial amplitude close to that of the center of the movement field (c) is superimposed on the isoradial slice of the movement field fit. The height of this curve is M, the magnitude or peak discharge of the movement field fit. The width of this curve is described by 
, the directional spread of the movement field fit. This curve is a Gaussian. E: slice of the movement field along an isodirectional line (depicted in inset). Actual discharge corresponding to saccades with a direction close to that of the center of the movement field (c) is superimposed on the isodirectional slice of the movement field fit. The width of this curve is reflected in the unitless parameter, s, which describes the radial spread of the movement field fit. This curve is a log-Gaussian. See text for details. The parameter estimates and 95% confidence intervals of the parameter estimates of the curve-fit for this neuron are M: 375 ± 43 spikes/s; c: 8.8 ± 0.25°; s: 0.144 ± 0.02 [unitless]; c: 141 ± 1.6°; : 11.6 ± 1.5°; R2: 0.83.
). Regressions were termed successful if over multiple iterations they mathematically converged on a stable value for each of the five parameters. We also computed the coefficient of determination (R2), a measure of goodness-of-fit for each successful regression (Glantz and Slinker 1990).
The subscript 1Tm indicates that the value is associated with the data for the 1T saccades. Next, we linearly regressed the neural discharge for the 2T data, z2T, against P1Tm()·
(2)
1Tm() to yield the coefficient, M2Tm. Multiplying this coefficient by P1Tm()·1Tm() yields the motor prediction
The subscript 2Tm indicates that these values of z are associated with the motor prediction. Note that this surface is a scaled version of the 1T movement field fit (Eq. 2). An isoradial slice through this surface passing through the center of the movement field is shown in Fig. 3D.
(3)
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FIG. 3.
Illustration of the visuomotor analysis procedure; calculation of motor goodness-of-fit (MGF). Data are from same neuron whose properties are illustrated in Fig. 2. A: movement field for 1T saccades. Conventions as in Fig. 2A. B: movement field for 2T saccades. Data corresponding to saccades within the white arc, which straddles the center of the neuron's movement field is depicted in D. Other conventions as in Fig. 2A. C: contour plot of 1T movement field fit. Equation displayed is Eq. 2, which describes the movement field fit. Dashed line is isoradial slice through the center of the movement field. Other conventions as in Fig. 2C. D: depiction of goodness-of-fit. The curve shown is a slice through the motor prediction ( 2Tm; Eq. 3) along the dashed line shown in C. The motor prediction is a scaled version of the movement field fit. MGF reflects how well the motor prediction fits the 2T neural discharge. The comparison between the motor prediction and the 2T discharge is shown graphically for the saccades that landed in the white arc shown in B, although the MGF was calculated using all trials. MGF for this neuron: 
0.68.
2Tm, the goodness-of-fit is calculated as
where the added subscript i refers to the value for each saccade in the neuron's data set and
(4)
2T is the mean neural discharge for all 2T saccades in the neuron's data set. The MGF for the neuron in Fig. 3 is 0.68.
where all notation is the same as in Eq. 1. The subscript 1Tv indicates that the parameters are those for the visual receptive-field fit of the 1T data. A contour plot of this surface is shown in Fig. 4C. The 1T receptive fields were fit using the same procedure used for that of the 1T movement fields, substituting radial target displacement and direction for saccade radial amplitude and direction, respectively. As for movement fields, spike density was measured using a temporal epoch aligned with saccade onset.
(5)
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FIG. 4.
Illustration of the visuomotor analysis procedure; calculation of visual goodness-of-fit (VGF). Data are from same neuron whose properties are illustrated in Figs. 2 and 3. A: receptive field for 1T presentations. Because targets were only presented at 13 different locations, the average discharge for each location is represented by each square. Other conventions as in Fig. 3A. B: receptive field for 2T presentations. The location of each square corresponds to the average in polar coordinates of the 2 target locations. Data corresponding to target presentations within the white arc which straddles the center of the neuron's receptive field are depicted in E. Other conventions as in Fig. 3B. C: contour plot of 1T receptive-field fit. Equation displayed is Eq. 5, which describes the receptive-field fit. Other conventions as in Fig. 3C. D: contour plot of sum of receptive fields corresponding to 2 targets (Eq. 8). Dashed line is isoradial slice through the center of the receptive field. E: depiction of goodness-of-fit. The curve shown is a slice through the visual prediction ( 2Tv; Eq. 9) along the dashed line shown in D. The visual prediction is a scaled version of the equation shown in D. VGF reflects how well the visual prediction fits the dependence of 2T neural discharge on the average direction of the 2 targets. The comparison between the visual prediction and the 2T discharge is shown graphically for the targets with average target locations in the white arc shown in B, although the VGF was calculated using all trials. VGF for this neuron: 0.72.
where the subscript CCW refers to the shifting of the 1T receptive-field surface in direction by 22.5° counterclockwise and
(6)
refers to the average direction of the two targets. (Note that the clockwise target's correspondence to a counterclockwise shift in the receptive field follows from the inverse relationship between discharge on the SC map and the receptive field of a SC neuron). Similarly, the receptive field due to the counterclockwise target is
where the subscript CW refers to the shifting of the 1T receptive-field surface in direction by 22.5° clockwise. The detailed versions of Eqs. 6 and 7 are in the APPENDIX .
(7)
A contour plot of this surface is shown in Fig. 4D. Note how each "mound" of the surface is shifted in direction relative to the surface portrayed in Fig. 4C. Finally, we linearly regressed the neural discharge, z2T, against P1Tv()·(
(8)
CCW() + CW()) to yield the coefficient, M2Tv. Multiplying this coefficient by (CCW() + CW()) yields what we will refer to as the visual prediction
The symbols are defined analogously to those in Eq. 3. Note that this surface is a scaled version of that described by Eq. 8. An isoradial slice through this surface passing through the center of the neuron's receptive field is shown in Fig. 4E.
(9)
The VGF for the neuron in Fig. 4 is 0.72. The MGFs and VGFs were calculated for each neuron's data and then compared across our sample of neurons using the Wilcoxon signed-rank test.
(10)
RESULTS
Abstract
Introduction
Methods
Results
Discussion
References
). We determined that this relationship held for both 1T and 2T saccades, and that the speed of 2T saccades was virtually identical with that of 1T saccades for most saccade amplitudes (Fig. 5).
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FIG. 5.
Relationship of peak velocity to amplitude for all 1T and 2T saccades produced by monkey GM (A) and monkey ME (B). Saccades were placed in amplitude bins 2.5° in width. Only bins for which at least 10 trials of both 1T and 2T trials were obtained are shown. Error bars indicate standard errors of the mean for each bin for each class of saccade. Asterisks mark amplitude bins for which 1T saccades were significantly faster than 2T saccades at 
= 0.05 (t-test).
). The average curvature for all saccades between 10 and 20° in amplitude and 0 and 45° in direction (right to up and right) was small and only slightly greater for 2T saccades, although this difference was statistically significant (monkey GM: 1 target, 0.044; 2 targets, 0.057, t-test: P < 0.001; monkey ME: 1 target, 0.038; 2 targets, 0.049, t-test: P < 0.001).
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FIG. 6.
Transition in saccade directional distribution with increasing latency in monkey GM (A) and monkey ME (B). Histograms of saccade endpoint direction during all 2T trials for saccade latencies between 50 and 200 ms are shown. Direction is normalized so that saccades at "up" (+) landed on the higher target, at "down" ( ) landed at the lower target (targets were never presented symmetrically about the vertical axis), and at "pure averaging" landed halfway between the 2 targets. Note that the normalized locations of the 2 targets were always ±22.5°.
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FIG. 7.
Spatial profile of activity for a neuron with a 2-peaked movement field for 2T saccades. A: plot of movement field for 1T saccades. Horizontal and vertical axes represent horizontal and vertical saccade displacements (deg). Mean discharge rate (spikes/s) in the 40-ms epoch centered on saccade onset and averaged across all saccades landing in a 1 × 1° bin (in Cartesian coordinates) is represented by the luminance of each square. Plots in C were constructed by using saccades landing in 1 of 3 labeled sectors. Each sector spanned 22.5° in direction and a range of saccade amplitude close to the center of the neuron's movement field. The fixation point is represented by a plus sign. B: same as A but for 2T saccades. C: rasters and spike density traces for 1T saccades. Each of the 3 plots are aligned on saccade onset (dashed line). Each horizontal tick mark represents 25 ms. Vertical bar on the left represents 250 spikes/s. All saccades landing in labeled sectors, 1, 2, and 3, in A were used to construct the corresponding plots in C. D: rasters and spike density traces for 2T saccades. Same conventions as C. See text for details. The parameter estimates and 95% confidence intervals of the parameter estimates of the curve-fit for this neuron are, for the 1T data, M: 564 ± 40 spikes/s; c: 9.6 ± 0.2°; s: 0.188 ± 0.0188 [unitless]; c: 51.4 ± 1.26°; : 11.3 ± 0.92°; R2: 0.87. The regression was not successful for the 2T data.
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FIG. 8.
Spatial profile of activity for a neuron whose 2T movement field did not show 2 distinct peaks, but did show a difference in comparison with the 1T movement field. Conventions same as in Fig. 7, except that because we were able to collect more data from the periphery of the movement field we plot rasters and spike density traces for 4 bins instead of 3. Parameters of the curve-fit for this neuron are, for the 1T data. Parameter estimates and 95% confidence intervals of the parameter estimates of the curve-fit for this neuron are, for the 1T data, M: 691 ± 39.2 spikes/s; c: 8.2 ± 0.32°; s: 0.267 ± 0.03 [unitless]; c: 163 ± 0.83°; : 13.9 ± 1.1°; R2: 0.88. For the 2T data, M: 413 ± 50.5 spikes/s; c: 7.6 ± 0.34°; s: 0.241 ± 0.04 [unitless]; c: 161 ± 5.3°; : 28.7 ± 6.9°; R2: 0.50.
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FIG. 9.
Spatial profile of activity for a neuron whose 2T movement field was similar to that for 1T saccades. Conventions same as in Fig. 7, except that, because we were able to collect more data from the periphery of the movement field, we plot rasters and spike density traces for 4 bins instead of 3. Parameter estimates and 95% confidence intervals of the parameter estimates of the curve-fit for this neuron are, for the 1T data, M: 576 ± 56.5 spikes/s; c: 13.7 ± 1.2°; s: 0.46 ± 0.1 [unitless]; c: 11.1 ± 3.5°; : 27.4 ± 3.8°; R2: 0.63. For the 2-target data, M: 518 ± 79.7 spikes/s; c: 15.0 ± 2.6°; s: 0.47 ± 0.17 [unitless]; c: 15.0 ± 5.5°; : 29.1 ± 7.3°; R2: 0.45.
) and magnitude (M) parameters (Table 1A). The nonlinear regressions of the 1T data were successful for 35/37 neurons. Regressions of the 2T data were successful for 25 of these 35 neurons. The 2T saccade movement field regressions had a value of directional spread () greater than that for 1T saccades for all 25 neurons (Fig. 10A). This trend held both for the 11 confirmed BNs and the 6 confirmed BUNs that had successful regressions. For 22/25 neurons the 2T directional spread () was greater than the upper 95% confidence limit of the estimate of 1T directional spread (). For 20/25 neurons, 1T saccade regressions had higher peak responses values (M) than those for 2T saccades. This trend held for BNs but not for BUNs. For 17/25 neurons, the 2T peak response was smaller than the lower 95% confidence limit of the estimate of the 1T peak response. There were no statistically significant differences between the 1T and 2T fits for the other three parameters. The quality of the fits, as measured by the coefficient of determination (R2) was generally much higher for 1T data than for 2T data (Table 1A).
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TABLE 1.
Gaussian/log-Gaussian curve fits
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FIG. 10.
Comparison of the directional spread parameter ( ) for 1T and 2T saccades found using the Gaussian/log-Gaussian surface-fit procedure. A: express saccades. Data points corresponding to the 5 neurons that had > 50° are shown as hexagons at = 50°. B: same as C but for regular saccades. See text for details.
) between one and two target saccades, although this difference was not nearly as large as that found for express saccades. We could not find statistically significant differences for the other four parameters (Fig. 10B; Table 1B).
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FIG. 11.
Goodness-of-fits for motor and visual predictions of 2T saccade activity for 4 neurons. The pair of plots in each row shows data for 1 neuron superimposed on the motor prediction of 2T activity (left column) and on the visual prediction of 2T activity (right column). Plots show a cross-section of the motor prediction (left column; see Fig. 3D) or visual prediction (right column; see Fig. 4E). The plotted discharge was the mean discharge in the 40-ms epoch centered on saccade onset. For the left column, each dot represents the average discharge for saccades landing in direction bins of 5.625 (180/32)° width. Saccade direction is normalized with respect to the direction of the center of the 1T movement field ( c1Tm). Solid lines are plots of an isoradial slice of the motor prediction at an amplitude equal to the center of the 1T movement field. As in Figs. 3D and 4E, only data corresponding to saccades with amplitudes close to the center of the 1T movement field are plotted. Error bars for discharge are not shown because only rarely did >1 saccade occupy each direction bin. Conventions for the right column are the same except that the variable on the abscissa is target direction normalized with respect to the center of the 1T receptive field (c1Tv), visual predictions are used in place of motor predictions, and bars representing standard errors of the mean are shown. Target direction for the data is defined as the average direction of the 2 targets.
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FIG. 12.
Summary data for MGF and VGF for all neurons. VGF is plotted against MGF for both the 1T and 2T data. Each dot represents 1 neuron. Dotted line represents the locus of points for which the 2 goodness-of-fit measures are equal. A: summary for express saccade data. B: summary for regular saccade data. See text for details.
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TABLE 2.
Visuomotor analysis
). For the six neurons in which we did not use the delayed saccade paradigm, we recorded activity during saccades of longer than 120 ms latency. We calculated a motor-visual index (MVI) for each neuron by comparing the perisaccadic activity of each neuron to its visual response for saccades close to the center of the neuron's movement field
where VIS is the magnitude of the peak spike density of the visual response during the epoch 50-100 ms after target onset and MOT is the magnitude of the peak spike density of the perimotor response during the epoch 40 ms centered on saccade onset. Thus a neuron that only discharged perisaccadically in the delayed saccade task would have a MVI = 1; a neuron that only discharged in response to the visual target would have a MVI =
1. Therefore, if neurons whose discharge was almost purely saccade related coded for saccade vector, whereas neurons whose discharge was almost purely a visual response coded for target configuration, then MGF should increase and VGF should decrease with increasing MVI.
0.22, P > 0.1; Fig. 13A). Overall, neurons with the greatest MVIs had comparable values of VGF and MGF (Fig. 13A).
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FIG. 13.
Summary of dependence of each neuron's MGF and VGF for express saccades on motor-visual index (A; MVI) and the directional spread parameter (B; ) for 1T saccades. For details, see text.
) increased as MVI increased (r = 0.35, P < 0.04), a result consistent with the finding of Mohler and Wurtz (1976) that movement field size and the ratio of saccade-related to target-related discharge were positively correlated. Could this result explain the dependencies of MGF and VGF on MVI? Note that if the directional spread () is small then we would expect a great difference between the motor prediction, 2Tm, and the visual prediction, 2Tv, for a given neuron. These predictions are shown for simulated data (Fig. 14A). In contrast, if directional spread () is large then the motor and visual predictions should become much more similar (Fig. 14B). If discharge depended completely on target configuration, then the MGF should increase with and VGF should not depend on .
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FIG. 14.
Illustration of decrease in difference of goodness-of-fit measures as neuron's directional spread ( ) parameter increases, assuming that discharge is completely dependent on target configuration. Simulated discharge data are superimposed on cross-sections of motor and visual predictions from 2 hypothetical neurons, one (A) with ( = 15°), the other (B) with ( = 30°) (bottom). Discharge values were generated by adding noise to values of the visual prediction. For simplicity and to allow the visual and motor predictions to be plotted on the same graph, saccade direction is set to target direction (as though every saccade was a pure averaging saccade). See text for details.
) (r = 0.63, P < 0.001; Fig. 13B), whereas VGF remained nearly constant with increasing (r = 0.08, P > 0.5; Fig. 13B). These results suggest that MGF and VGF become more comparable as the movement fields and receptive fields become larger. Thus MGF may get better with increasing MVI simply because the motor prediction more resembles the visual prediction with increasing directional spread (), not because the neurons have stronger perimotor than visual responses. Therefore our data do not support the idea that a separate class of visuomotor neurons exists that codes for the saccade vector of express saccades to two targets.
). For each saccade we defined t = 1 as 15 ms before the termination of the saccade, because the activity of visuomotor neurons during express saccades often reaches a minimum ~15 ms before the end of the saccade, before occasionally increasing (unpublished observations). We conducted the analyses for three epochs, t = 0 to t = 0.333, t = 0.333 to t = 0.666, and t = 0.666 to t = 1.0, which we will refer to as the early, middle, and late epochs.
) would decrease across epochs for 2T saccades. On the contrary, we found that for all three epochs directional spread () was greater for 2T saccades than for 1T saccades (Table 3; Fig. 15A). The difference in directional spread () between fits for 1T and 2T saccades changed little over time, and the small decrease observed resulted primarily from an increase in directional spread () for 1T saccades rather than from a decrease in directional spread () for 2T saccades (Table 3).
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TABLE 3.
Directional standard deviation across epochs (express saccades)
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FIG. 15.
A: relation between the directional spread ( ) parameter of the Gaussian/log-Gaussian fits for 1T and 2T saccades as the express saccade-related activity progresses. Conventions are the same as in Fig. 10A. B: relation between MGF and VGF as the saccade-related activity progresses. Measures for 2T data are represented by filled circles, for 1T data by unfilled circles. Other conventions are the same as in Fig. 12A. See text for details.
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TABLE 4.
Visuomotor analysis across epochs
DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References
demonstrated that what has been considered the visual and premotor responses of visuomotor burst neurons merge during express saccades (see also Dorris et al. 1997). The experiments described here ask whether the bimodal or broadly tuned distribution of sensory activity resulting from presentation of two targets spatially coalesces into the unimodal or more sharply tuned profile of activity that is seen for saccades to a single target. By using the gap paradigm (Saslow 1967), we elicited saccades to two targets of express latency. The saccades had a high degree of endpoint scatter relative to the locations of the two targets, allowing us to dissociate saccade vector from the locations of the targets. We found evidence that the discharge of visuomotor neurons was more dependent on target configuration than on saccade vector for the duration of the saccadic burst. The neurons that coded most similarly for 1T and 2T saccades tended to have very broad movement fields for 1T saccades.
, which predicts that 1T and 2T express saccades with similar metrics are coded by different spatial distributions of activity in the DSC. That visuomotor burst neuron discharge depends on target configuration rules out the upstream hypothesis, which predicts that saccade-related discharge in the DSC should depend purely on saccade vector. That the dependence on target configuration persists for the entire duration of the burst runs counter to the prediction of the collicular hypothesis, as this hypothesis states that the DSC should become purely dependent on saccade vector at some point during the burst.
). In our analysis we modeled such an interaction as a global inhibition that resulted in a decrease in activity proportional to the amount of discharge present in the sum of spatially separated responses (Eq. 9).
used a double-step paradigm to elicit saccades that landed between the two sequentially presented targets. Such stimulus presentation complicates the spatial analysis of visuomotor burst neuron activity. Indeed, the authors' conclusions were limited to the statement that the DSC was active for averaging saccades.
used a two-target delayed saccade paradigm that required monkeys to saccade to a target defined by color. The 5% of saccades to two targets that terminated in between the correct and incorrect targets were deemed "averaging." They did not find a statistically significant difference between the spatial profiles of one and two target saccade movement fields at = 0.05 for any individual neuron. The difference between the results of Glimcher and Sparks and ours may have been due to the difference in our tasks. Because their task required selection of one of the two targets, their averaging saccades may merely have resulted from an error in target selection. If such an error resulted from discharge in areas upstream of the DSC, then the activity of the DSC would reflect these errors, and 1T and 2T saccades would be coded in a similar manner at the level of the DSC. More generally, it may be that only short-latency 2T express saccades to suddenly appearing targets are coded differently from 1T saccades. Saccades with longer latencies may be coded identically.
and Lee et al. (1988) provided evidence that saccades are coded by a vector average of collicular activity, such that the discharge of each neuron is associated with a saccade vector, and the ensemble of collicular activity produces a saccade that is a weighted average of these vectors. A subsequent model of the DSC implemented this idea (Van Gisbergen and Van Opstal 1989). With respect to 2T saccades, our data add support to the vector average hypothesis by showing that the two regions of activity corresponding to each of the targets produce a saccade with a vector that is approximately a spatial average of the saccade vectors that would be produced by each region acting alone.
). Our experiments indicate that such a profile of activity on the DSC motor map can accompany saccades elicited with visual targets.
; Scudder et al. 1996). With respect to the SC classification scheme of Munoz and Wurtz (1995), both BNs and BUNs project to the brain stem, although it is unclear where exactly each SC subpopulation projects to (Istvan et al. 1994). It is also unclear, with respect to the SC classification scheme of Sparks and Hartwich-Young (1989), whether both visuomotor neurons and SRBNs project to the EBN region of the PPRF, although since work in our lab has shown that an overwhelming majority of neurons with saccade-related bursts also have visual responses and thus can be classified as visuomotor neurons, it is most likely that visuomotor neurons project to this region. But again, it is unknown whether the probability that a visuomotor neuron projects to EBNs depends on the strength of the visual response of the neuron or the size of its movement field. Such anatomic data would be crucial in interpreting our results because we found evidence that neurons in the DSC that showed the most similarity in discharge for 1T and 2T saccades had large movement fields. It has been found that BUNs have larger movement fields in direction than BNs (Anderson et al. 1998). Thus, if only BUNs, or more particularly, neurons with large movement fields, code for saccade metrics, then SC discharge coding for saccade metrics could be very similar for saccades to one and two targets. It is tempting to speculate that this could explain the lack of averaging responses when the two targets are much more widely separated than the 45° used here (Ottes et al. 1984); in such a case the spatial distribution of the sum of two spatially separated regions of 1T activity would look very different from that of a single region of 1T activity, even for neurons with the broadest 1T movement fields described here. It may be that the spatial profile of BUNs or neurons with large movement fields for 1T and 2T saccades must be similar for averaging saccades to occur.
), the velocity of the target (Keller et al. 1996), and saccade adaptation (Frens and Van Opstal 1997), such work still supports the idea that the discharge of neurons in the DSC codes for a specific saccade command. The present data showing that the saccade-related activity in the DSC is dependent on the number of targets and not just their location suggests that at least for express saccades an explicit representation in the DSC of an impending saccade is not present for all neurons with saccade-related activity.
). These authors suggested that the subject resolves the evidently conflicting demands of speed and accuracy by first making a short reaction time movement to land in the neighborhood of the stimuli, and only then selecting and making a saccade to the correct target. This suggestion supports the hypothesis that averaging saccades to two targets are generated by a "visual-grasp reflex" (Becker 1991). Our results suggest that target selection has not occurred at the level of the DSC for express saccades to two targets, whether the saccades are averaging or nonaveraging, although one may argue that immediately after the onset of the visual stimuli the saccadic system construes the two lights as a single target with a large spatial extent. Indeed, express saccades may occur too quickly to take advantage of the segregation of suddenly appearing visual stimuli into distinct targets for the saccadic system.
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ACKNOWLEDGEMENTS |
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The authors thank J. P. Gottlieb, M. E. Goldberg, M. Pare, and the anonymous reviewers for helpful criticisms and discussions.
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APPENDIX |
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Equations used for movement and receptive-field fits
The detailed form of log-Gaussian and Gaussian components of Eq. 1 are
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(A1) |
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(A2) |
).
Components of visual prediction
The components of the visual prediction are
|
(A3) |
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(A4) |
t arg is defined as the average direction of the two targets. The other symbols are defined in Eqs. 5-7 in METHODS.
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FOOTNOTES |
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Address for reprint requests: J. A. Edelman, Laboratory of Sensorimotor Research, National Eye Institute, Bldg. 49, Rm. 2A50, Bethesda, MD 20892-4435.
Received 24 December 1997; accepted in final form 5 June 1998.
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REFERENCES |
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Abstract
Introduction
Methods
Results
Discussion
References
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