Abstract

The receptive field (RF) of neurons recorded from the lateral intraparietal area (LIP) was quantified using a rapid, computer-driven mapping procedure. For each neuron, the RF was mapped: (1) during attentive fixation and (2) during free visual exploration. RF location, size and internal structure were modulated by the mapping context in over two-thirds of the recorded neurons. The major trend was a proportionally larger amount of neuronal visual resources allocated to central space during fixation, and an attenuated center-to-periphery gradient in the visual field representation during free gaze. A population approach shows that these spatial modulations are accompanied by changes in the signal-to-noise ratio of the information carried in the RF substructure. We related these neurophysiological observations to behavior, by comparing the characteristics of saccades elicited during fixation and free gaze. Together, the results suggest that the dynamics of LIP visual RFs may characterize both the state of engagement of attention and the power of resolution of visual analysis: during fixation, the neural population is locked in a filter state concentrating the processing resources at the fovea, while during free gaze, the population shifts to a detector state spreading the resources more evenly across the visual field.

Introduction

The requirements of visual analysis are highly dependent upon the ongoing or intended behavior. One of the most intensively studied modulating parameter is attention, and several studies have reported the effects of manipulating its characteristics on the visual responses of neurons and on the structure of their receptive fields (RFs). Many single-unit recording studies reported enhancement and suppression phenomena in the known cortical visual areas: in the temporal lobe, in areas V4 (Moran and Desimone, 1985; Mountcastle et al., 1987, Motter, 1993, 1994; Connor et al., 1996) and IT (Richmond and Sato, 1983; Sato, 1989; Rolls and Tovee, 1995), in the parietal lobe, in areas LIP (Robinson et al., 1995), 7a (Mountcastle et al., 1981; Steinmetz et al., 1994) and MT and MST (Treue and Maunsell, 1996; Seidemann and Newsome, 1999; Treue and Maunsell, 1999), in the prefrontal lobe, in the FEF (Boch and Goldberg, 1989) and prefrontal cortex (Rainer et al., 1998), but also in early visual areas V1 and V2 (Motter, 1993). Experiments have been designed to characterize the range of effects that modulate RF structure as a function of attention (Moran and Desimone, 1985; Connor et al., 1996, 1997; Luck et al., 1997; Reynolds et al., 1999).

Attention is the process by which certain features of the world are selected with respect to others in analysis of the incoming stimuli (Fischer and Breitmeyer, 1987) and in the generation of purposive motor responses (Reuter-Lorenz et al., 1991). Its characteristics have been widely studied in the context of generating saccadic eye movements and more precisely in the well-known ‘gap paradigm’ (Fischer and Breitmeyer, 1987). One of the major results of these studies is the idea that selective attention is an oriented dynamic process that engages in and disengages from a particular spatial location (Braun and Breitmeyer, 1988). Because the lateral intraparietal area (LIP) has been shown to carry saccade-related signals (Gnadt et al., 1986; Barash et al., 1991; Duhamel et al., 1992) and to be modulated by selective spatial attention (Robinson et al., 1995; Colby et al., 1996; Gottlieb et al., 1998), it is a good candidate for the study of the mechanisms by which attention affects visuomotor processing at the neuronal level.

In the present study, we quantified the RF of neurons recorded in area LIP in two distinct behavioral contexts. The first is a central fixation and color discrimination task. This task requires both stable eye fixation and focused attention. The second is a free gaze condition in which no constraint is imposed on fixation or attention. In this condition, attention can shift from one location to another, or can be in an undetermined ‘unfocused’ state. A previous study by Mountcastle et al. compared the activity of parietal neurons during attentive fixation and during the rest interval between successive fixation trials (Mountcastle et al., 1981). They show a facilitation of the responses to visual stimuli falling at identical retinal locations during fixation with respect to alert wakefulness. They provide a conclusive range of arguments to suggest that this facilitation is specifically due to attentive fixation. However, this study did not focus specifically on the modulation of RF characteristics under those two conditions. Here we report that the visual responses recorded in different behavioral contexts cannot be characterized only by global variations of activity levels, but also by variations in the characteristic of their RFs in terms of size, location and substructure. Effects are described (i) at the single-cell level on individual visual RFs with respect to the spatial allocation of visual resources, and (ii) at the population level with respect to the information processing characteristics. We also investigated whether the modulations of the visual properties of LIP neurons were related to the preparation and execution of purposive, visually triggered saccades in each of these contexts. Preliminary results of this study have been reported previously (Ben Hamed et al., 1997).

Materials and Methods

Animal Preparation and Physiological and Histological Methods

This study includes cells recorded from three hemispheres of one rhesus and one fascicularis monkeys. All animal care, housing and surgical procedures were in accordance with European published guidelines (European Community Council Directive 86/609/ECC). Training, surgical, physiological and histological methods have been described previously (Ben Hamed et al., 2001). Briefly, a head-holding device, scleral search coils and a recording chamber (anchored flat to the skull at P 5 L 11) were implanted under general anesthesia (ketamine and Propofol) and embedded in dental acrylic. Tungsten-in-glass electrodes advanced by means of a hydraulic microdrive (Narishige Ltd.) were used for extracellular recording. Area LIP was identified by its location within the intraparietal sulcus and by its typical physiological response characteristics, with regard to the neighboring areas 7a, VIP and MIP. Recording sites within the first 2.5 mm of recording were considered area 7a. One animal is still used in ongoing experiments; in the other monkey detailed histological analysis verified that recording sites in the two hemispheres had been located either in the dorsal or ventral portions of area LIP.

Behavioral Tasks

Behavioral Conditions for the Mapping Procedure

RFs were mapped while the monkey performed two different tasks: (i) a standard fixation task during which the monkey gazed at a central green fixation point and was rewarded for holding eye position within a 2° wide window for 2300–3000 ms and for releasing a lever within 700 ms of fixation point dimming or change in color. (ii) A free gaze task, during which the monkey could freely move its gaze on the dark screen where no stimulus was present except for the mapping stimulus. During this task, the animal was given a liquid reward at regular intervals, and its degree of vigilance was monitored by an online analysis of its eye movements. All tasks were carried in an otherwise dark room, monkeys being head-fixed.

Three sets of controls were carried out in order to check that the observed modulations of the visual response of neurons during the free gaze task are not due to unmonitored parameters. (i) We checked that this task does not induce a drop of vigilance, by continuously recording eye movements (spontaneous saccades and slow drifts). (ii) Because this task does not constrain the oculomotor behavior of the monkey, we checked if the observed effect could be accounted for by the modulation of the visual responses by eye position in the orbit. This was done for a subset of neurons whose RF were mapped during fixation at five different orbital locations. (iii) We calculated the spatial distribution of eye fixations during free gaze mapping to determine whether there were any systematic biases or whether fixation positions were evenly distributed around the resting position.

Tasks Used to Study the Effect of Fixation on Saccadic Eye Movements

The animals were asked to make visually triggered saccades towards briefly flashed stimuli (50 ms) in two different conditions, in an otherwise completely dark room. (i) Saccades from attentive fixation. The monkey initially fixated a point at the center of the screen. After 1500 ms, the fixation point was replaced by a saccade target briefly appearing at one of 40 possible locations on the screen in one of eight possible radial directions, 45° apart, at five eccentricities (3°, 6°, 9°, 12° and 15°). In order to take into account small variations in eye position during fixation, the position of the saccade target on the screen was calculated with respect to the actual position of the eyes in the few milliseconds preceding the flash. (ii) Saccades in a free gaze context. During the initial part of the task, the monkey was free to move its eyes and no stimuli appeared on the screen. At irregular intervals, a saccade target was flashed for 50 ms on the screen. The location of the saccade target was randomly selected from the same set as in the previous task and was placed on the screen with respect to the eye position sampled a few milliseconds before its appearance. The monkey was rewarded for making an accurate saccade within 600 ms of target onset. Saccade direction was varied pseudo-randomly throughout one block of trials, but not saccade amplitude. Eye position was stored at 250 Hz.

Mapping Procedure

In both conditions the RF of the neuron being recorded was mapped in two steps: (i) The spatial location of its RF was determined on the tangential screen with the use of a hand-held projector and the temporal characteristics of its visual response was estimated by flashing a visual stimulus at the center of its RF. (ii) The mapping parameters (stimulus duration, inter-stimulus interval, mapping grid location and mapping resolution) were derived from the temporal and spatial characteristics of the visual response of the neuron and stimulation cycles were repeatedly run on the screen, (a) during the pre-discrimination period of the fixation task, and (b) during intervals of steady fixation in the free gaze task. In the latter condition, the position of the mapping stimulus on the tangential screen was calculated online relatively to the actual eye position, so that it was determined with respect to the fovea (Fig. 1). A single cycle consisted in stimulating, once and in random order the center of each subregion of a 7 × 7 or 9 × 9 matrix totally encompassing the RF. The resolution of this matrix, i.e. the distance between two adjacent stimulus positions, varied between 1° and 6°, depending on the size of the RF of the neuron. The 1° wide achromatic mapping stimuli and the inter-stimuli intervals typically had a 100 ms and a 200 ms duration. Between 6 and 10 stimuli were presented between two successive liquid rewards. A complete stimulation cycle was thus obtained every five to nine trials and 7–12 stimulation cycles were run on a given unit. Stimulus order was reshuffled every time a new cycle began. Thus, each point of the stimulation grid was stimulated at least seven times, each time in a different spatial and temporal context.

Data Analysis

Receptive Field Data

RF maps were computed off-line by reverse correlation analysis as described by Duhamel et al. (Duhamel et al., 1997). For free gaze RF data, any stimulus occurring between 300 ms before the start and 300 ms after the end of a saccadic eye movement were discarded from the analysis. Several descriptive parameters were associated with the representation of RFs for each data set: (i) a maximum discharge rate referred to as the peak, (ii) the x and y locations of the peak in degrees of visual angle, relative to the center of the screen, (iii) the x and y locations of the center of gravity, i.e. of the center of mass of activity calculated over the whole matrix, and (iv) a width, in degrees, referring to the average extent of the RF, and defined as the square root of the surface of the interpolated RF whose activity is equal to or greater than half the peak discharge rate.

Latency of Visual Responses

Latency was calculated from the cumulated response of the cell to the mapping stimulus evoking the strongest response (i.e. the peak of the RF). It was defined as the time from stimulus onset for which the stimulus discharge frequency exceeded half the difference between the baseline activity of the cell and the maximum discharge of the cell to the considered stimulus. Latencies were computed by a semi-automatic procedure that enabled a control of the experimenter on the decision of the latency detection algorithm and eliminate possible artifacts.

Results

Characteristics of the Population of Neurons Studied

Pairs of RF maps were obtained for 128 neurons, 80.5% of which (103/128) were selected for further analysis, based on two criteria. (i) The neuron had to remain well isolated throughout the two mapping procedures. (ii) The pair of obtained RFs had to be largely encompassed by the mapping grid, and it had to have a significant activity with respect to the baseline in at least one of the two conditions (Mann–Whitney rank test between baseline activity and activity at the peak of the RF, P < 0.05).

Effect of Behavioral Context on RF Characteristics: a Cell-by-Cell Analysis

The Range of Modulatory Effects

RF modulations can be of several types. The level of discharge of the neuron can be affected locally or across the whole surface of the RF. The size of the RF can vary, as well as the spatial location of the peak, the center of mass, and the RF borders. Figure 2ac shows the RF of cell c191, during fixation (Fig. 2a) and free gazing (Fig. 2b). The main differences can be seen on horizontal sections through the two RFs at the level of the maximum of discharge of the RF during fixation (Fig. 2c). The RF during fixation has a foveal hot spot and its maximum level of discharge (pkFX = 77.5 spikes/s) is nearly twice that during the free gaze condition (pkFR = 40.5 spikes/s). The portion of the RF during fixation for which the level of discharge exceeds half the maximum level of discharge is relatively small (widthFX = 15.7°) with respect to that during free gaze (widthFR = 21.2°) and is located in the portion of the RF nearest to the central region of the visual field.

Cell c218 has a peripheral RF (Fig. 2df). During fixation, the peak of the RF is located at 7.5° to the right, and has a maximum level of discharge of 96.8 spikes/s. During free gaze, several phenomena are observed. First, the activity of the neuron in regions outside the RF increases from ~5 spikes/s to 40 spikes/s (Fig. 2f), suggesting a global inhibition of the cell's baseline activity in the presence of a fixation target. This is comparable to the observed increase in activity just before the appearance of the first mapping stimulus with respect to the intertrial interval during the fixation task (respectively 8 and 49 spikes/s), indicating that foveal stimulation exerts a tonic inhibitory influence on this neuron. Second, the maximum discharge level increases by a factor of two during free gaze (to 208.5 spikes/s). Finally, the peak of the RF is displaced towards the periphery (13.5°, 0°) as well as the whole RF. The net result is a relative enhancement of the representation of the periphery during free gaze with respect to fixation.

A third type of effect is shown by cell c127. This neuron has a RF located at (2°, –4°) which does not include the fovea during free gazing (Fig. 3ac). During fixation, the inner borders of the RF expand so as to encompass the central visual field. The growth of the RF is unidirectional, and both the maximum level of discharge, and the location of the peak are modified by the mapping context (Fig. 3c).

A last example is illustrated by Figure 3df. During fixation, the maximum level of discharge of cell c152 is higher and the RF narrower than during free gaze (pkFX = 103.6 spikes/s and pkFR = 51.3 spikes/s; widthFX = 6° and widthFR = 8.8°). These modulations are associated with a displacement of the location of the peak from (0°, 0°) to (5°, –3.8°) between fixation and free gaze. Thus, overall the shape of the RF is more central and more tuned during the former than the latter mapping condition.

These four examples illustrate various types of modulations of the RF structure of LIP neurons that are observed between the two conditions A two-way ANOVA on the RF pairs with mapping condition and stimulus grid as factors and firing rate as dependent variable was carried out in order to assess: (i) the presence of global differences between the two RFs, revealed by the main effect of mapping condition and (ii) the presence of local effects, revealed by the interaction between mapping position and stimulus location within the RF. A majority of the cells studied (65/101) showed significant effects on the analysis of variance at the P < 0.0002 level or better. For about two-thirds of these cells (n = 41) these modulatory effects affected local subregions within the neurons' RF, as indicated by the presence of a significant interaction (P < 0.0002 or less) between mapping condition and stimulus location. In the other neurons (n = 24), the observed modulations were of a more global nature with a significant main effect of the mapping task but no interaction. For these cells, activity within the RF was globally higher during fixation than during free gaze in half of the cases (12/24) and the reverse was true in the other half (12/24). The extreme cases were four cells that had a well-characterized RF during fixation but no definite RF structure during free gaze and two cells that showed the opposite pattern.

For cells with a significant interaction effect, a posteriori pair-wise comparisons were conducted in order to determine the preferential location of the modulation in the RF, for each stimulation location independently. Significant local differences at P < 0.01 were observed along the borders of the RF (18 cells), at the center (11 cells), and both along the borders and at the center (eight cells). Four cells showed no specific localized differences.

Effects of Behavioral Context on RF Characteristics: Location, Shape and Size

We have shown thus far a wide heterogeneity in the RF structure between the two mapping conditions. We next consider whether such variations correspond to systematic differences in the location of the peak and center of mass of the RFs, and in their size. The results are summarized in Table 1 for the subset of cells with significant effects (65 cells).

RF Location

RF eccentricity can be characterized by the location of the maximum of discharge (pk), or of the center of mass of activity (cm). The single-cell examples presented above indicate that the direction and magnitude of the effects on the location of the activity peak can vary from one cell to the next. Nevertheless, across the entire sample, the tendency is, on average, for RF peaks to shift eccentrically during free gaze relative to fixation, with a median peak eccentricity of 6.2° (mean = 7.2°, SD = 5.9°) during fixation and of 7.25° (mean = 8.8°, SD = 6.7°) during free gaze [t(1,65) = –2.03, P < 0.043]. The location of the maximum of discharge during free gaze was, on average, 1.62° more eccentric than during fixation. Values of shift ranged from –7.5° to 21.5° (negative value expressing a less eccentric peak during free gaze than during fixation).

By contrast, an alternative measure of RF center, the center of mass, does not vary between the two conditions (mean of 7.96° and 7.8° for fixation and free gaze, respectively). The range of variation of center of mass displacement between fixation and free gaze was smaller than for the peak (–6.8° to 5.27°, with a mean of 0.12°). In order to observe a significant shift of the center of mass, a rigid displacement of the entire RF would have to take place. The presence of a peripheral displacement of the local maximum of activity within the RF, in the absence of a significant change in the center of mass, suggests that the observed modulations correspond instead to a redistribution of the activity within the RF. The overall picture that emerges is a pattern of neural activity in their RF that weighs more strongly the outer (centrifugal) subregion during free gaze and the central (centripetal) subregions during fixation. While such modulations may modify only minimally the center of gravity of the RF, its resulting shape, and in particular its relative degree of asymmetry, may be altered, a possibility which is considered next.

RF Shape

A simple index for the degree of asymmetry of RFs is the distance D between the peak and the center of mass. For each cell, we set as limit for experimental significance of D the step used for projecting the stimuli during the RF mapping procedure. Forty-five cells out of 103 (44%) had a D-value in this category in at least one of the two conditions. Of these, 44% (21/45 cells) showed asymmetry on the RF map computed during fixation condition and 77% (35/45 cells) showed asymmetry on the RF map computed during free gaze. Thus RFs tend to be more often asymmetric when mapped during free gaze than during fixation.

To compare the magnitude of the asymmetry in the two mapping conditions, D-values were normalized with respect to RF size so as to eliminate the possible confound of a covariation of the asymmetry index with RF peak eccentricity and RF size. An analysis was thus carried out on the absolute magnitude of the RF asymmetry, expressed as a percentage of the total RF width. An asymmetry index of 0% indicates that peak and center of mass fall at the same location and an asymmetry value of 50% indicates that the distance between peak and center of mass is half the extent of the RF. Mean asymmetry values of RFs mapped during fixation and during free gaze differ significantly (respectively: mean = 32.4% and SD = 15.9%; and mean = 41% and SD = 20%, P < 0.05).

We finally considered the sign of the asymmetry, that is, whether the RF peak is more foveal or more eccentric than the center of mass. Figure 4 shows the relative location of the peak and center of mass for cells with asymmetrical RF profiles during free gaze and/or fixation, as a function of both mapping condition and RF eccentricity. During fixation, an almost constant ratio of cells showing a more foveal peak than center of mass is observed whatever the eccentricity of the RF (~2/3). During free gaze, this ratio is slightly decreased for cells whose RF center is located within the central 7°, but significantly so for cells with more eccentric RFs (χ2 = 8.04, d.f. = 3, P < 0.05).

To summarize, RF profiles show more frequent and more pronounced asymmetries during free gaze than during fixation, a characteristic which is most common in cells with RFs located outside the central field and which is expressed by an eccentric displacement of the peak with respect to the center of gravity of the RF.

RF Size and its Relation to Eccentricity

The width of RFs is significantly larger on maps from data collected during free gaze than during fixation (t(1,68) = –2.63, P < 0.01). A degree of dependency of size upon eccentricity is a general characteristic of RF organization throughout the visual system. The best linear fit for the distribution of width as a function of eccentricity during fixation is of the form: width = eccentricity × 0.84 + 6.7 (P < 0.05, R2 = 38%), whereas during free gaze, the best linear fit is of the form: width = eccentricity × 0.74 + 9.2 (P < 0.05, R2 = 28%). The higher intercept simply reflects the overall larger size of RFs computed in the latter condition. The two regression slopes are very close to each other, suggesting that the variation in size of RFs between the two conditions is independent of eccentricity and that task effect on RF size is uniformly distributed on the whole studied range.

RF Maximum Discharge Rate

There was no significant difference at the level of the population between the maximum discharge rate of the cells in fixation and in free gaze, although at the single-cell level, either an increase or a decrease in the maximum discharge rate of the neurons could be observed (see next section).

Visual Field Representation in LIP as a Function of Behavioral States: a Population Analysis

We have seen the range of modulations and the general observable trends in the population due to the RF mapping context. But how do these effects combine at the scale of the neural population to influence visual information processing? One way to address this question is to use a population coding approach.

Construction of Population Response Fields (PRFs)

In order to preserve information about the coding of both angular location and eccentricity, we used a two-dimensional weighted averaging approach. Population Response Fields (PRFs) were calculated for a large number of simulated stimuli locations with a one-degree step. The PRF was constructed by pooling left hemisphere data and right hemisphere data reflected onto it, so as to obtain a full representation of a single (right) visual hemifield. For a given stimulus, and for each cell, we calculated from the actual data the response the cell would have had to that stimulus, and assigned it to the horizontal and vertical locations of the peak of the RF. Neuronal responses to the points that were never actually stimulated during the RF mapping were inferred by linear interpolation. In Figure 5, each needle represents a cell, the base of the needle corresponds to the position of the RF peak projected on the XY plane, and the height of the needle corresponds to the response of the cell for the considered stimulus. This response is normalized so that the maximum response of each cell is taken as 1. The plots in Figure 5a,b show the PRF for the fixation condition, constructed for two distinct hypothetical stimuli, at (0°, 0°) and (+ 10°, –10°), respectively. The population of active neurons shifts down and to the right from the center of the visual field between the two PRFs. In Figure 5c,d, the needle plots are substituted by a Gaussian fit taking as parameters the mean and the standard deviation of the needle distribution. The peak of activity shifts from Fig. 5c to Fig. 5d, but its amplitude is also smaller, due to the sparser representation of the visual periphery relative to the foveal region in this neural population.

Coding of Spatial Location by the Weighted PRF

The population response represents quite accurately the angle of the stimulus with respect to the meridians (Fig. 6a). The relation between true eccentricity and its coding by the population can be fitted by linear regression: Coded = 0.52 + True × 0.144 during fixation and Coded = 0.54 + True × 0.134 during free gaze (Fig. 6b). We depart from a 1:1 proportionality between coded and true eccentricity. Again, this bias may be due to the relatively larger weight in the PRF of the foveal representation as compared with the peripheral field representation, because of the cortical magnification factor and of a possible over-representation of the central visual field in our sample. Nevertheless, the linear fit accounts for 87% of the variability in both mapping conditions, indicating that, with a differently weighted ‘read-out’ algorithm, the eccentricity of a stimulus can be predicted quite accurately from the weighted population activity.

Information Processing

For several stimuli, we can construct the PRF in both fixation and free gaze conditions. Figure 7a,b shows the one-dimensional PRF along the horizontal meridian constructed for a stimulus at (0°, 0°) and at (25°, 0°) respectively, for each of the two conditions. Two major points can be noted: (i) The maximum level of the fixation PRF is higher and its width narrower than those of the free gaze PRF. (ii) The PRFs in both conditions have higher maxima and have a higher spatial resolution for central stimuli than for peripheral stimuli. These two observations hold for all tested stimulus locations (data not shown). One way to address these differences quantitatively is by measuring the tuning of the PRFs, for both conditions and for all possible eccentricities of stimuli, and taking the ratio of the mean of the PRF for a given stimulus by the associated standard deviation (μ/σ, Fig. 7c). This ratio is an estimate of the precision with which LIP population codes a location. The distribution corresponding to fixation can be fitted by: μ/σ = 0.023 – 0.005 × log(Eccentricity). For free gaze, the best logarithmic fit is: Signal-to-noise = 0.011 – 0.002 × log(Eccentricity). Three main points can be noted: (i) The μ/σ ratio is higher for central than for peripheral stimuli. (ii) The μ/σ ratio is always higher during fixation than during free gaze. For central stimuli, this ratio is 2.2 times higher during fixation than during free gaze. For peripheral stimuli, this value drops to 1.4. (iii) The gradient of μ/σ ratio between center and periphery is higher during fixation than during free gaze. During fixation, the μ/σ ratio is 3.2 times higher for central stimuli than for stimuli at 25° of eccentricity. During free gaze, this factor drops to 2.

Task Effects on Saccade Characteristics

Eye movements to a peripheral flashed target were measured in one of the recorded monkeys in two different conditions: visually triggered saccades from fixation and visually triggered saccades when the monkey is gazing at a blank screen. Latencies were significantly longer for saccade from fixation than during free gaze [F(1,9693) = 454.5, P < 0.001]. Saccade latencies also became shorter as target eccentricity increased [F(4,9693) = 286.3, P < 0.001] and a significant interaction effect between task and saccade amplitude was noted [F(4,9693) = 15.8, P < 0.001] (Fig. 8a). A posteriori comparisons reveal that while the latency differences between fixation and free gaze are significant at all target eccentricities, the center to periphery gradient is more pronounced during fixation than free gaze. Since the target was a brief flash, it was no longer visible after completion of the saccade, and secondary corrective saccades could not take place. We used variable saccadic deviation, normalized with respect to saccade amplitude, as an index of saccadic accuracy. There was a significant task effect [F(1,9692) = 73.2, P < 0.001], expressing diminished accuracy during the free gaze condition with respect to fixation and a significant effect of saccade amplitude [F(4,9692) = 500.2, P < 0.001], with poorer accuracy for saccades made to central than to eccentric targets (Fig. 8b). The best fit of the data is logarithmic both during fixation [saccadic error = –0.097 × log(Saccade amplitude) + 0.326, accounting for 94% of the variability] and during free gaze [saccadic error = –0.089 × log(Saccade amplitude) + 0.329, accounting for 88% of the variability]. There was only a small, non-significant correlation (r = 0.33) between saccade latency and saccade error in our data set.

To summarize, saccadic behavior shows two major effects on latency and accuracy. The first is characterized by slower and less accurate saccades to perifoveal targets than to targets located in the near periphery. The latency gradient in particular seems to be more pronounced for saccades made from a fixation target than during free gaze. The second effect is a speed–accuracy trade-off, which is characterized by faster initiation but lower accuracy for saccades made during free gaze, as compared to those made from fixation.

Latency of Visual Responses during Fixation and Free Gaze

Across the neuron population studied, latencies of visual responses were significantly shorter during free gaze than during fixation (respectively, mean = 89.5 ms, SD = 18.8; and mean = 94.2 ms and SD = 22.2, P<0.005). However, it should be noted that the magnitude of the difference (4.7 ms) is smaller than the average difference in saccade latency between the two conditions (22 ms). Therefore the faster initial processing of visual stimuli by LIP neurons during free gaze could only account for ~20% of the observed gain in saccadic reaction time in this condition. There was no correlation between latency differences in the two tasks and eccentricity of the RF of the cell (R2 = 0).

Controls for the Free Gaze Condition

Free Gaze is not a Vigilance State but a Behavioral State

A drop in vigilance is characterized by an upward drift of the resting position of the eyes, sometimes accompanied by a spontaneous nystagmus. Online control of the eye position enabled us to monitor the state of vigilance of the monkey. The free gaze condition mapping was embedded in time within other tasks, and lasted at most 4 min. This time interval is too short to allow for a drop in vigilance during the course of the task and no evidence of drifts or nystagmus was ever observed during these periods. A more subtle indicator of a drop in alertness is a decrease in the frequency of spontaneous saccades. The monkey executed on average 1.33 saccades per second during free gaze RF mapping. For comparison, eye movements were monitored during several other visual scanning conditions (Table 2). Saccade frequency during free gaze was closest to the saccade frequency during scanning of low contrast naturalistic scenes.

The Effect of the Two Tasks on RF Structure is Not Explained by an Eye Position Effect

LIP is an area in which neuronal activity can be influenced by the position of the eyes in the orbit (Andersen et al., 1985, 1990; Bremmer et al., 1997). We checked whether eye position effects could account for the modulation in shape of the RF reported between free gaze and fixation conditions.

We found that during free gaze mapping, the eyes were most frequently located within a 10° cone centered slightly to the right of and above the primary position [horizontal and vertical average position = (3.9°, 4.1°), and standard deviation = (4.8°, 3.6°)]. This systematic bias is present in both monkeys, whatever the location of the RF with respect to the screen and the recorded hemisphere. Its origin is unclear and could be due to the configuration of the experimental room that accessed though a door situated on the monkey's right side.

Eye position effects in area LIP are distributed evenly across the orbital range such that the mean discharge rate balances out at the population level (Bremmer et al., 1998). Seventy-one per cent of a representative subset of 27 cells from our sample are modulated by eye position (P < 0.05). We compared the main characteristics of RFs at the central fixation and at a fixation closest to the mean fixation positions during free gaze. No significant difference were observed on: average peak firing rate = 238 spikes/s vs 243 spikes/s; mean eccentricity of peaks = 3.73° vs 3.70°; mean eccentricity of center of mass = 3.64° vs 3.61°; mean width = 10.23° vs 10.16°, for fixations at (0°, 0°) and (4°, 4°), respectively.

This suggests that having used the primary position as a reference fixation condition did not introduce systematic biases as compared to a fixation location closer to the average eye position spontaneously adopted during free gaze. This does not preclude, however, that single cells might be affected by this factor. We have shown that individual RFs are significantly different between fixation at (0°, 0°) and free gaze. These differences are maintained for a fixation at (4°, 4°): in the same subset of 27 cells, 21 originally showed significant variations when tested against fixation at (0°, 0°). When tested against fixation at (4°, 4°), an interaction effect appeared in four cells, and four cells lost it. One cell gained a global effect. For the 18 remaining cells, the significant interaction found at (0°, 0°) was maintained and the spatial distribution of the effects remained unchanged.

In summary, eye position effects were present in our sample and may have ‘contaminated’ the observed effects of mapping condition for slightly less than a third of the cells. However, they could have resulted both in a systematic overestimation or an underestimation of the observed differences between fixation and free gaze RFs. Second, free gaze RFs differ qualitatively from fixation RFs (Figs 2 and 3) in a manner which cannot usually be interpreted as an overall gain change of visual responses across the RF, which is the main defining characteristic of eye position effects.

Comparing RF Fitting Methods

The analysis of the form of RFs is a difficult and yet crucial issue. Several authors have addressed it, favoring a Gaussian fit (Gnadt and Breznen, 1996, Platt and Glimcher, 1997, 1998, 2000). We compared the fitting method used in the present study (where the experimental discharge rates of the neuron are retained in the final RF model) to a Gaussian model on the RFs presented in Figures 2 and 3 and observed the following: (i) The Gaussian fits vary, for a given cell, as a function of the task. The location of their center and their width are modulated in the same way as observed with our fitting method. (ii) The Gaussian fits overlook the asymmetry of the RFs (which we have shown to be a robust characteristic of some LIP neurons) and fail to account for the fine structure of the fixation RF of unit 191 and the free gaze RF of units 152 and 218. (iii) For the remaining cells, Gaussian fits are either centered on the center of mass of the RF as calculated by our method, or on an intermediate value between the peak and the center of mass. In all cases, this model yields lower maximum rates than the actual maximum discharge rate of the neurons and wider RF structures.

The Gaussian model is thus reliable in the case of symmetrical RFs. It is adequate to analyze the distribution of RFs in a given area and their global task-dependent variations. The method used in this study, because of its higher spatial sensitivity, is more adapted to the analysis of the fine structure of RFs and their fine task-dependent modulations.

Discussion

Considerations about the Two Behavioral Paradigms Used

The principal requirement of a fixation task is to keep the eyes still but it can also be made attentionally demanding by varying the degree of detectability of a critical event, such as a change in luminance or color at the fixated location. By contrast, free gaze imposes no constraints on oculomotor behavior or visual attention. An analysis of the patterns of eye movements indicates that the oculomotor behavior of the monkey is close to visual exploration of a familiar environment with an average of 1.33 saccades/s. However, the free gaze task is not equivalent to visual scan, and the mapping stimuli are not relevant to the monkey's behavior. No overt signs of a drop in vigilance were observed. This is likely due to the fact that RF mapping during free gaze is achieved in just a few minutes, and is always embedded in an experimental protocol comprising other tasks (fixation, memory-guided saccades). The free gaze condition undoubtedly leads to uncontrolled volitional, attentional and behavioral variance, however any of these variables is assumed to be evenly distributed over the explored space. The hypothesis underlying this study is thus that, other things being equal, the differential requirements in the fixation and free gaze conditions will affect the visual processing both at the single-cell level and at the population level. We expected visual resources to be biased towards the fovea during the central discrimination task and to be more evenly distributed from fovea to periphery during free gaze.

Tasks Effects at the Single-cell Level

The task is shown to affect visual excitability in 65% of the studied cells. These effects can take place at the center, at the borders and/or outside the RF, and is indicative of the extent of the redistribution of the visual responsiveness inside the RF. Quantitatively, this can be related to displacements in the location of the maximum of activity in the RF or of the center of gravity of this activity, a change in the size of the RF, a modification in the absolute level of discharge of the neuron, or a combination of all of these elements. The single-cell examples depicted by Figures 2 and 3 show the wide polymorphism of this phenomenon.

RF Shape and Asymmetry

We have shown that the shape of the RF could substantially vary from a symmetrical shape, making it difficult to completely account for it using standard mathematical, e.g. Gaussian, functions. This asymmetry is task dependent: 42% of the cells tested show a repositioning of their peak with respect to their center of mass between the two tasks. Whereas during fixation, two-thirds of the cells have a more foveal peak than center of mass, during free gaze, this tendency is inverted for the more peripheral RFs (7° of eccentricity). This suggests that peak and center of mass are informational and raises the potential concern that RF fitting may in some cases induce a loss of information with respect to the parameters being manipulated by the experimental paradigm. Such task-dependent asymmetries have been described in the RFs of other cortical areas such as area V4 (Connor et al., 1996, 1997).

Maximum Level of Discharge

At the population level, we show no significant systematic increase or decrease of the maximum discharge rate of the neurons from fixation condition to free gaze. This is somewhat different from previous studies in the parietal lobe that mainly describe a predominance of enhancement over suppression (Mountcastle et al., 1981, 1987; Robinson et al., 1995). The most plausible interpretation is that in the present study we are comparing absolute maximum discharge rates, which can be located in different RF subregions in the two conditions, and not responses for a given fixed stimulus location.

Task Effects at the Population Level

In order to examine the combined effects of these different factors we used a population coding approach.

Coding of Spatial Location

We find that the population very reliably codes for angular deviations of the stimulus with respect to the horizontal meridian and the eccentricity of the stimulus in both behavioral conditions. The location of the peak of PRFs was not affected by the ongoing task, while other changes in the overall aspect of PRFs did take place. As it is highly desirable that representational maps remain in some way independent of the behavioral state, peak of PRFs could be the encoded variable for that. The mechanism by which this constancy is maintained at the population level is yet to be determined.

Signal Processing

Single-cell Level.

Early studies point out a variation in signal-to-noise ratio as a function of vigilance states (Livingstone and Hubel, 1981). This observation deduced from neurons of V1 corresponds to a decrease in the baseline discharge of neurons during awake states with respect to sleeping states, together with an increase in the response to visual stimuli. In the present study, there was no such systematic trend between one condition and the other at the single-cell level. Modulations were mostly observed on the response itself, reflecting specific (attention) rather than unspecific (arousal) mechanisms.

Population Level.

At the level of the population there was a major effect of the task on the shape of the PRF. The three characteristics of μ/σ ratio (a higher ratio during fixation, a higher ratio for central stimuli in both conditions and a higher center-to-periphery gradient of the ratio during fixation) and given the fact that there is no systematic variation in single-cell levels of discharge from one condition to the other, suggest a differential information processing both as a function of spatial location of the stimulus and as a function of the behavioral context. This is, to our knowledge, the first time that such a trend is described at the neural level, in a parietal area.

Task Effect on the Latency of Visual Responses

Visual latencies have been studied in several sub-cortical and cortical areas [for a review see Nowak and Bullier (Nowak and Bullier, 1997)]. Anesthetized (Nowak et al., 1995) and sleeping states (Livingstone and Hubel, 1981) versus awake behaving state do not have a significant effect on the visual latencies of neurons in V1. In area LIP, we found a significant variation in visual response latencies, which were shorter when the monkey is engaged in a free gaze task than when performing a fixation task. The visual stimulation and the oculomotor state are equivalent in the two conditions. However, during the fixation task, a stimulus is continuously present on the fovea. This could affect the visual response pattern to the mapping stimulus for cells whose classical or sub-liminar RF included the fovea. But because there is no correlation between latency differences between the two conditions and eccentricity, this hypothesis can be rejected. Another possibility is that attentive fixation, in addition to modulating the spatial structure of the visual RFs, also plays a temporal gating function on visual input.

Correlation between Behavioral and Neuronal Observations

The potential relevance of the task effects observed at the neural level are revealed by saccadic behavior measured with targets having the same temporal and spatial characteristics as the stimuli used during the RF mapping.

Effect on Latencies

Saccade latencies are longer for perifoveal targets than for peripheral targets in both task conditions, a phenomenon thought to related to saccade programming itself and not to target detection which is optimal around the fovea (Kowler, 1990). During free gaze, saccade latencies are on average 22 ms shorter than during fixation condition, the difference being most pronounced for short (3°–6°) saccades. This result presents a parallel with the so-called ‘gap paradigm’ (Fischer and Breitmeyer, 1987; Braun and Breitmeyer, 1988; Reuter-Lorenz et al., 1991). Saccades made to a target presented some time after the disappearance of a fixation point have shorter latencies than saccades to a target appearing before or at the time of fixation point extinction. The difference in latencies increases with gap duration and typically reaches a maximum of 30–35 ms for gap intervals of 200 ms (Dorris and Munoz, 1995; Weber and Fischer, 1995) and is more pronounced for central than for peripheral stimuli (Fischer and Boch, 1983). The gap effect has been interpreted as an early visual–attentional modulation (Fischer and Breitmeyer, 1987) or as premotor process (Reuter-Lorenz et al., 1991), thought to facilitate the disengagement of attention from the fovea. Its decays to ~20–25 ms for prolonged gap durations and uncertain target locations (Weber and Fischer, 1995; Dorris and Munoz, 1995), suggesting that attention cannot stay disengaged for long but could spontaneously oscillate between engaged and disengaged states (Braun and Breitmeyer, 1988). The similarity of the results obtained in the present study with those obtained in gap paradigms suggests that the free gaze RF mapping context used hereby can be viewed as a prolonged gap condition, during which attention may be alternatively engaged at some point of space or disengaged. Very close to our own observations, saccades to flashed targets in the absence of a fixation point have reproduced the gap effect in humans (Fendrich et al., 1999).

Effect on Precision

Saccades accuracy made from a fixation point is consistent with previous reports (Kowler, 1990). Accuracy diminished in the free gaze condition with respect to saccades from fixation. This observation could be related to the lower overall σ/μ ratio in the population activity in the former condition, which might reflect a relative loss of spatial resolution. An alternative interpretation is that the source of saccadic error lies in a trade-off between response latency and accuracy such that the shorter latencies in free gaze might be associated with a somewhat less extensive sensorimotor processing of saccade targets.

The relations between the above behavioral observations and the neuronal observations on area LIP suggest the following tentative interpretations.

Distribution of Analysis Resources over the Visual Field.

The analysis of RF distribution and the population analysis suggest that during fixation, visual resources favor the central part of the visual field whereas during free gaze they are more evenly distributed over the whole field. A psychophysical correlate of this is observed on saccadic latencies: a more pronounced functional gradient between center and periphery seems to entail a higher threshold for attentional disengagement as indicated by the longer saccadic latencies in the fixation condition.

Information Processing.

The μ/σ ratio is more pronounced during fixation than during free gaze for all parts of the visual field, indicating a more contrasted analysis of space in this state. The better saccade precision in this condition with respect to free gaze could be related to this differential analysis of space. The μ/σ ratio is relatively higher for central portions of the visual field than for peripheral portions during fixation with respect to free gaze, indicating that during fixation, a greater processing load is placed at the center of the visual field where discrimination is required by the behavior.

Filter vs Detection.

During fixation, the μ/σ ratio is increased and is maximum for central stimuli. Saccades towards perifoveal targets are more strongly inhibited than those towards the visual periphery. The system is in a state comparable to a filter monitoring a local event. During free gaze, μ/σ ratio is decreased across the whole visual field and processing resources are less biased towards the central field. Saccade latency is decreased as the system is more prompt to react to stimuli appearing anywhere in the visual field. Saccades towards central targets are comparatively quicker to process than during fixation state. The system is thus in a state comparable to a detector which enables the eye to move to a novel stimulus whatever its position in the visual field. Foveation at this point doesn’t need to be very precise.

Possible Mechanisms for the RF Modulation

The effects of manipulating object-based attention or spatial attention have mostly been described in terms of enhancement and suppression. These effects have been reported in the temporal lobe, in V4 (Moran and Desimone, 1985; Mountcastle et al., 1987; Motter, 1993, 1994; Connor et al., 1996) and IT (Richmond and Sato, 1983; Sato, 1989; Rolls and Tovee, 1995), in the parietal lobe, in LIP (Robinson et al., 1995) and 7a (Steinmetz et al., 1994), in the prefrontal lobe, in the FEF (Boch and Goldberg, 1989) and PF (Rainer et al., 1998), but also in the visual areas V1 and V2 (Motter, 1993). However, an apparent enhancement or suppression at a given position can in fact result from a wide variety of modulations of the visual responsiveness of the neuron. Moran and Desimone (Moran and Desimone, 1985) originally suggested that the effects observed in area V4 reflect a modulation of the RF characteristics under specific attentional constraints, a phenomenon that recent studies have addressed directly (Connor et al., 1996, 1997). Several models have also been proposed to account for low-level and top-down attentional mechanisms on visual processes (Anderson and Van Essen, 1987; Olshausen et al., 1993; Salinas and Abbott, 1997).

A limitation of the present study is that it did not involve instructed shifts of focused attention between spatial locations. Nevertheless, it provides evidence for modulatory mechanisms of the structure of RFs in the range of the predictions formulated by theoretical models (Olshausen et al., 1993). Indeed, authors predict shifts in RFs spatial location, and widening and shrinkage of their spatial extent as a function of size and of the location of the attentional window. They also predict that gating-like mechanisms would have a major role in these modulatory mechanisms. These attentional gain fields are expected to be independent from spatial location and structure of RFs (Olshausen et al., 1993; Salinas and Abbott, 1997). Such phenomena have partly been described in the ‘what’ ventral visual stream (Connor et al., 1996, 1997). To our knowledge, this is the first time that such multiple trends are documented in the dorsal visual stream. Further experiments controlling precisely the locus and the extent of spatial attention will have to be carried out to complement the present report.

Notes

We thank Alexandre Pouget for helpful suggestions. This work was supported by grants from the European Community (HCM: ERBCHRXCT- 930267), the Human Frontier Science Program (RG71/96B) and the French Foundation for Medical Research.

Table 1

Effects of mapping context (fixation and free gaze) on the spatial characteristics of LIP RFs: mean and SD of the eccentricity of peak, of the eccentricity of center of mass and of the width

 Fixation mean (SD) Free gaze mean (SD) Mean of variation (min, max) 
The last column gives the mean variation of these parameters between the two tasks as well as the minimum and maximum variations. Variation of peak and center of mass are taken as EccentricityFree – EccentricityFix. Variation of width is taken as 100×(WidthFree – WidthFix)/ (WidthFree + WidthFix
Peak  7.2° (5.9°)  8.8° (6.7°)  1.62° (–7.5°,21.5°) 
Center of mass  8° (4.9°)  7.8° (5.1°) –0.12° (–6.8°,5.27°) 
Width 13.4° (6.6°) 15° (7.1°)  5.6% (–46%,44%) 
 Fixation mean (SD) Free gaze mean (SD) Mean of variation (min, max) 
The last column gives the mean variation of these parameters between the two tasks as well as the minimum and maximum variations. Variation of peak and center of mass are taken as EccentricityFree – EccentricityFix. Variation of width is taken as 100×(WidthFree – WidthFix)/ (WidthFree + WidthFix
Peak  7.2° (5.9°)  8.8° (6.7°)  1.62° (–7.5°,21.5°) 
Center of mass  8° (4.9°)  7.8° (5.1°) –0.12° (–6.8°,5.27°) 
Width 13.4° (6.6°) 15° (7.1°)  5.6% (–46%,44%) 
Table 2

Frequency of eye movements during visual exploration

Explored visual scene Mean SD 
Mean and standard deviation of eye movements frequency (in saccades/s) displayed by one monkey during the exploration of (a) a blank screen during the mapping procedure; (b) a completely blank screen in a dimly lit room; (c) a low-contrast photograph of rising sun; (d) a low-contrast photograph of a female macaca monkey with child; (e) a high-contrast cartoon of the Marsupilami, a French cartoon character; (f) a high contrast cartoon of Jim the cat. 
(a) Blank screen during mapping procedure 1.33 0.9 
(b) Blank screen 1.04 1.19 
(c) Low contrast picture of rising sun on sea 1.18 1.06 
(d) Low contrast picture of female monkey with child 1.38 1.47 
(e) Cartoon of Marsupilami 1.45 0.78 
(f) Cartoon of Jim the cat 1.47 1.10 
Explored visual scene Mean SD 
Mean and standard deviation of eye movements frequency (in saccades/s) displayed by one monkey during the exploration of (a) a blank screen during the mapping procedure; (b) a completely blank screen in a dimly lit room; (c) a low-contrast photograph of rising sun; (d) a low-contrast photograph of a female macaca monkey with child; (e) a high-contrast cartoon of the Marsupilami, a French cartoon character; (f) a high contrast cartoon of Jim the cat. 
(a) Blank screen during mapping procedure 1.33 0.9 
(b) Blank screen 1.04 1.19 
(c) Low contrast picture of rising sun on sea 1.18 1.06 
(d) Low contrast picture of female monkey with child 1.38 1.47 
(e) Cartoon of Marsupilami 1.45 0.78 
(f) Cartoon of Jim the cat 1.47 1.10 
Figure 1.

Experimental design of the two behavioral tasks. (a) Central fixation associated with a color discrimination. Six to eight mapping stimuli were flashed in sequence during the pre-discrimination fixation period. (b) Free gaze. Mapping stimuli were presented throughout the trial and before the reward distribution. Their position was calculated with respect to the fovea using an online monitoring of eye position.

Figure 1.

Experimental design of the two behavioral tasks. (a) Central fixation associated with a color discrimination. Six to eight mapping stimuli were flashed in sequence during the pre-discrimination fixation period. (b) Free gaze. Mapping stimuli were presented throughout the trial and before the reward distribution. Their position was calculated with respect to the fovea using an online monitoring of eye position.

Figure 2.

The RF of cell c191: (a) during the fixation condition [location of the maximum discharge = (9.5°, 6°), location of the center of mass of the activity inside the RF = (14°, 4.6°), width = 15.7°, maximum discharge rate = 77.5 spikes/s]; (b) during the free gaze condition [location of the maximum discharge = (14°, 4.5°), location of the center of mass of the activity inside the RF = (19.8°, 2.9°), width = 21.2°, maximum discharge rate = 40.5 spikes/s]; (c) sections through the fixation RF (in red) and the free gaze RF (in blue) at the level of the short white mark on panels (a) and (b). Standard errors are indicated by the vertical lines. The RF of cell c218: (d) during the fixation condition [location of the maximum discharge = (7.5°, 0°), location of the center of mass of the activity inside the RF = (9.4°, –1.6°), width = 15.9°, maximum discharge rate = 96.8 spikes/s]; (e) during the free gaze condition [location of the maximum discharge = (13.5°, 0°), location of the center of mass of the activity inside the RF = (14.8°, –3.1°), width = 23.9°, maximum discharge rate = 208.5 spikes/s]; (f) same representation as in (c).

Figure 2.

The RF of cell c191: (a) during the fixation condition [location of the maximum discharge = (9.5°, 6°), location of the center of mass of the activity inside the RF = (14°, 4.6°), width = 15.7°, maximum discharge rate = 77.5 spikes/s]; (b) during the free gaze condition [location of the maximum discharge = (14°, 4.5°), location of the center of mass of the activity inside the RF = (19.8°, 2.9°), width = 21.2°, maximum discharge rate = 40.5 spikes/s]; (c) sections through the fixation RF (in red) and the free gaze RF (in blue) at the level of the short white mark on panels (a) and (b). Standard errors are indicated by the vertical lines. The RF of cell c218: (d) during the fixation condition [location of the maximum discharge = (7.5°, 0°), location of the center of mass of the activity inside the RF = (9.4°, –1.6°), width = 15.9°, maximum discharge rate = 96.8 spikes/s]; (e) during the free gaze condition [location of the maximum discharge = (13.5°, 0°), location of the center of mass of the activity inside the RF = (14.8°, –3.1°), width = 23.9°, maximum discharge rate = 208.5 spikes/s]; (f) same representation as in (c).

Figure 3.

The RF of cell c127: (a) during the fixation condition [location of the maximum discharge = (1.5°, –2°), location of the center of mass of the activity inside the RF = (1.3°, –2°), width = 4.6°, maximum discharge rate = 132.8 spikes/s]; (b) during the free gaze condition (location of the maximum discharge = (2°, –4°), location of the center of mass of the activity inside the RF = (2.3°, –4.2°), width = 2.8°, maximum discharge rate = 160 spikes/s]; (c) sections at two different levels through the fixation (in red) and free gaze (in blue) RFs (at –1° in continuous lines, horizontal section at –4° in dashed lines). The RF of cell c152: (d) during the fixation condition [location of the maximum discharge = (0°, 0°), location of the center of mass of the activity inside the RF = (0.3°, –0.5°), width = 6°, maximum discharge rate = 103.6 spikes/s]; (e) during the free gaze condition [location of the maximum discharge = (5°, –3.8°), location of the center of mass of the activity inside the RF = (3.6°, –2.7°), width = 8.8°, maximum discharge rate = 51.3 spikes/s]; (f) same representation as in Figure 2c.

The RF of cell c127: (a) during the fixation condition [location of the maximum discharge = (1.5°, –2°), location of the center of mass of the activity inside the RF = (1.3°, –2°), width = 4.6°, maximum discharge rate = 132.8 spikes/s]; (b) during the free gaze condition (location of the maximum discharge = (2°, –4°), location of the center of mass of the activity inside the RF = (2.3°, –4.2°), width = 2.8°, maximum discharge rate = 160 spikes/s]; (c) sections at two different levels through the fixation (in red) and free gaze (in blue) RFs (at –1° in continuous lines, horizontal section at –4° in dashed lines). The RF of cell c152: (d) during the fixation condition [location of the maximum discharge = (0°, 0°), location of the center of mass of the activity inside the RF = (0.3°, –0.5°), width = 6°, maximum discharge rate = 103.6 spikes/s]; (e) during the free gaze condition [location of the maximum discharge = (5°, –3.8°), location of the center of mass of the activity inside the RF = (3.6°, –2.7°), width = 8.8°, maximum discharge rate = 51.3 spikes/s]; (f) same representation as in Figure 2c.

Figure 4.

Relative position of peak and center of mass as a function of the eccentricity of the center of mass, for cells with asymmetric RF shapes in the fixation and free gaze conditions. In black, the cells for which the peak is more foveal than the center of mass. In gray, the cells for which the peak is more eccentric than the center of mass.

Figure 4.

Relative position of peak and center of mass as a function of the eccentricity of the center of mass, for cells with asymmetric RF shapes in the fixation and free gaze conditions. In black, the cells for which the peak is more foveal than the center of mass. In gray, the cells for which the peak is more eccentric than the center of mass.

Figure 5.

Normalized PRF responses (a) for a stimulus at the fovea and (b) at 10° to the right and 10° down. Gaussian fit of the same PRFs in (c) and (d).

Figure 5.

Normalized PRF responses (a) for a stimulus at the fovea and (b) at 10° to the right and 10° down. Gaussian fit of the same PRFs in (c) and (d).

Figure 6.

Population coding (a) of angular deviation and (b) of eccentricity of processed stimuli in the fixation condition (black dots) and free gaze (gray dots) for a range of simulated azimuths and eccentricities.

Figure 6.

Population coding (a) of angular deviation and (b) of eccentricity of processed stimuli in the fixation condition (black dots) and free gaze (gray dots) for a range of simulated azimuths and eccentricities.

Figure 7.

Superposition of normalized PRF responses obtained for the fixation (solid line) and for free gaze (dashed) conditions in response to a simulated stimulus presented (a) at 0° of eccentricity and (b) at 25° of eccentricity. (c) Distribution of the ratio μ/σ as a function of eccentricity for all possible simulated stimulus positions, collapsed with respect to azimuth for fixation (black) and free gaze (gray). For each condition, the best logarithmic fit of the data is shown.

Figure 7.

Superposition of normalized PRF responses obtained for the fixation (solid line) and for free gaze (dashed) conditions in response to a simulated stimulus presented (a) at 0° of eccentricity and (b) at 25° of eccentricity. (c) Distribution of the ratio μ/σ as a function of eccentricity for all possible simulated stimulus positions, collapsed with respect to azimuth for fixation (black) and free gaze (gray). For each condition, the best logarithmic fit of the data is shown.

Figure 8.

(a) Mean latency of saccades as a function of the eccentricity of the saccade target during fixation condition (black circles) and during free gaze (gray circles). Standard error intervals are shown for each condition. (b) Saccadic accuracy expressed as the ratio between mean saccade deviation and mean saccade amplitude as a function of saccade eccentricity, during fixation condition (black circles) and free gaze condition (gray circles). The logarithmic fits are represented in both conditions.

Figure 8.

(a) Mean latency of saccades as a function of the eccentricity of the saccade target during fixation condition (black circles) and during free gaze (gray circles). Standard error intervals are shown for each condition. (b) Saccadic accuracy expressed as the ratio between mean saccade deviation and mean saccade amplitude as a function of saccade eccentricity, during fixation condition (black circles) and free gaze condition (gray circles). The logarithmic fits are represented in both conditions.

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