INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

To optimize visual perception, it is essential for foveated animals to precisely align their two visual axes on targets of interest. Therefore it is not surprising that the oculomotor system of these animals has developed sophisticated mechanisms to ensure the tight control of binocular positioning. More than a century ago, Hering (1868) proposed the elegant "theory of equal innervation" as a conceptual framework for the study of binocular control. When applied to eye movements between two immobile targets, for example, Hering's theory suggests that two separate neural subsystems should exist that control different aspects of these movements (Fig. 1). On the one hand, a conjugate saccadic subsystem would rapidly yoke the eyes in a given direction to generate movements between targets located at a constant depth but at different horizontal eccentricities. On the other hand, a slower and separate vergence subsystem would rotate the eyes by the same angle but in opposite directions to generate eye movements between targets located at different depths but at constant eccentricities. To date, the neural basis of these two subsystems has been extensively studied in isolation. Under these conditions, neuronal circuitry that are involved in generating conjugate saccades (reviewed in Moschovakis et al. 1996; Scudder et al. 2002) or slow symmetric vergence shifts (reviewed in Gamlin 1999; Mays 1995a) have been well characterized.

View larger version (28K): [in this window] [in a new window]   Fig. 1. Schematic representation of Hering's theory of equal innervation. Drive from the conjugate subsystem is sent directly to the abducens nucleus and indirectly to the oculomotor nucleus via abducens internuclear neurons. In turn, drive from the vergence subsystem is sent directly to both the abducens nucleus and the oculomotor nucleus. During disjunctive saccades, these 2 drives would summate. OMN, oculomotor motoneurons; AIN, abducens internuclear neuron; AMN, abducens motoneurons; III and VI, 3rd and 6th cranial nuclei; MR and LR, medial and lateral recti.

However, during our normal daily activities these two subsystems do not always function in isolation; we generate simultaneous conjugate and vergence eye movements anytime we rapidly reorient our eyes between targets located at different eccentricities and depths. During such eye movements, termed disjunctive saccades, the two eyes rotate by different angles and with different trajectories. Accordingly, a question that naturally arises is: does Hering's theory hold true during disjunctive saccades?

In fact, although Hering's theory is attractive in its simplicity and in the anatomical and physiological correlates that support it during pure conjugate or vergence movements, it cannot account for a number of observations made during disjunctive saccades. For example, a number of studies have clearly demonstrated that the straightforward linear summation of the conjugate and vergence components of eye motion predicted by the theory of equal innervation does not occur during disjunctive saccades (human: Collewijn et al. 1995, 1997; Enright 1984; Erkelens et al. 1989; Kenyon et al. 1980; Ono et al. 1978; Oohira 1993; Zee et al. 1992; monkey: Maxwell and King 1992). Rather, it was shown that the vergence component of the movement is dramatically accelerated when compared with a control pure vergence shift, while the saccadic movement is slowed down in comparison to control conjugate saccades, suggesting central interactions between the conjugate and vergence neural pathways. We have recently furthered the evidence supporting the central coupling between the conjugate and vergence premotor circuitry by describing synchronized oscillations in the conjugate and transient vergence of conjugate saccades and gaze shifts (Sylvestre et al. 2002).

Recent reports have also indicated that some neural structures previously assumed to form the conjugate saccadic system do not carry purely conjugate information during disjunctive saccades. For example, electrical perturbations of the superior colliculus during disjunctive saccades were shown to modify both the conjugate and the vergence trajectories (Chaturvedi and VanGisbergen 1999, 2000). Also, premotor saccadic burst neurons that are active only during saccadic eye movements (Sylvestre and Cullen 1999b; Zhou and King 1998) and nuclei prepositus/vestibular neurons (McConville et al. 1994; Zhou and King 1996) were found to preferentially encode the velocity and position of one of the two eyes (i.e., do not encode the conjugate eye position) during disjunctive saccades and disjunctive fixation, respectively. Thus these studies have provided convincing evidence that Hering's law is violated at the premotor level during disjunctive saccades. It is likely that these neurophysiological observations represent the substrate for the saccadic facilitation of vergence, where the faster vergence velocities are supplied through the saccadic circuitry (see Sylvestre et al. 2002).

Although we are now beginning to better understand the premotor mechanisms of binocular control during disjunctive saccades, surprisingly nothing is known about the actual signals that are generated by extraocular motoneurons to drive these eye movements. To date, all of our knowledge on motor patterns during disjunctive movements was obtained during slow, nonsaccadic eye movements (Gamlin et al. 1989; Gamlin and Mays 1992; Keller 1973; Keller and Robinson 1972; King and Zhou 2000; King et al. 1994; Mays and Porter 1984; Zhou and King 1996, 1998). Most of these studies were conducted on neurons in the abducens nucleus (ABNs), which contains two subpopulations of neurons: motoneurons (AMN) that project to the ipsilateral lateral rectus and internuclear neurons (AIN) that project to medial rectus motoneurons (OMNs) in the contralateral oculomotor nucleus (see Fig. 1; Delgado-Garcia 1986a,b). It was found that nearly all ABNs, including identified AMNs and AINs (Gamlin et al. 1989), encode similar signals during slow vergence eye movements. When the eyes symmetrically converge (i.e., both eyes move nasally), the discharges of ABNs decrease, while they increase during divergence (i.e., both eyes move temporally). In contrast, OMNs that drive the medial rectus muscles increase their discharges when the eyes converge (Gamlin and Mays 1992; King et al. 1994; Mays and Porter 1984). Thus the discharge patterns of AMNs and OMNs during slow disjunctive eye movements are modulated appropriately to drive the eye muscles to which they project, but those of AINs are modulated inappropriately to drive the contralateral eye to which they project. These results, overall, are consistent with Hering's theory of equal innervation (Mays 1998).

In the present study, our primary objective was to determine whether the signals carried by ABNs during disjunctive saccades are appropriate to drive the motion of the eye to which they project. Since AMNs ultimately drive the extraocular muscles of the ipsilateral eye, the conjugate and vergence-related premotor inputs that they receive during disjunctive saccades might be combined, on a neuron-by-neuron basis, to generate motor signals that are exclusively related to the movements of that eye. Alternatively, single neurons might encode mixed signals that get sorted out at the population level, such that the overall ABN drive to the ipsilateral eye is appropriate. Finally, the convergence of conjugate and vergence-related premotor signals on ABNs might be incomplete or inappropriate, such that the discharge patterns of AMNs would not account entirely for the movements of the ipsilateral eye. In this scheme, additional mechanisms at or downstream to the abducens nucleus, for example co-contraction of the agonist and antagonist muscles, would be required to fine tune the eye movements. A secondary goal of this study was to determine whether ABNs encode conjugate and vergence signals similarly during disjunctive saccades and disjunctive fixation. As we described above, there is evidence that the source of the vergence-related premotor signals differs in these two conditions. Consequently, there are no a priori reasons to assume that, for example, a neuron that encodes conjugate signals during disjunctive saccades will also encode conjugate signals during disjunctive fixation. Some of the results have been reported in abstract form (Sylvestre and Cullen 1999b).

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Two rhesus monkeys (Macaca mulatta) were prepared for chronic extracellular recording using the aseptic surgical procedures described elsewhere (Sylvestre and Cullen 1999a). To briefly summarize, a stainless steel post that allowed the complete immobilization of the animal's head was attached to the animal's skull with stainless steel screws and dental acrylic. Two stainless steel recording chambers oriented stereotaxically toward the abducens nucleus on the right and left side of the brain stem, respectively, were also anchored in the implant. An eye coil (3 loops of Teflon coated stainless steel wire, 18-19 mm diam) was implanted in each eye (Judge et al. 1980) to allow recordings of binocular eye movements with the magnetic search coil technique (Fuchs and Robinson 1966). All procedures were approved by the McGill University Animal Care Committee and were in compliance with the guidelines of the Canadian Council on Animal Care.

Behavioral paradigms

Both monkeys were trained to follow a target light in a dimly lit room for a juice reward. Only eye movements restricted to the horizontal plane will be discussed in the present report. To elicit conjugate eye movements, a red HeNe laser target was projected via a system of two galvanometer controlled mirrors onto a cylindrical screen located 55 cm away from the monkey's eyes (isovergent, 3.5° convergence). Ipsilaterally and contralaterally directed conjugate saccades (±5-30°) were elicited by stepping the target between horizontal positions in a predictable and an unpredictable sequence. In addition, smooth pursuit eye movements were obtained using a sinusoidally moving target (40°/s peak velocity, 0.5 Hz).

An array of 16 computer-controlled red light emitting diodes (LEDs; with intensities comparable to that of the laser target) were utilized to elicit different types of vergence eye movements. First, symmetric (pure) vergence eye movements were obtained using four LEDs (convergence angles: 17°, 12°, 8°, and 6°) and a laser target that were aligned with the monkey's mid-sagittal plane. Second, disjunctive saccades were generated using a variety of paradigms. In a first configuration, the target jumped from one of the mid-sagittal LEDs described above to an eccentric laser target (i.e., right or left of the mid-sagittal plane). During this paradigm, monkeys made disjunctive saccades with conjugate components 5-30° in amplitude in both directions and converging or diverging vergence components with amplitudes 4-13°. Disjunctive saccades were also obtained using LEDs that were positioned in a configuration similar to the Müller paradigm (see Ramat et al. 1999 for examples). More specifically, four LEDs were aligned with the left eye at an angle of 45° to the right of the mid-sagittal plane, and four other LEDs were aligned with the right eye at an angle of 45° to the left of the mid-sagittal plane. This paradigm elicited disjunctive saccades during which the left or the right eye barely moved, respectively. Finally, to enrich the variety of disjunctive eye movements in our data set (and the monkey's viewing experience), we also performed trials in which any of the LEDs and laser targets were randomly presented.

Data acquisition procedures

During the experiment, the head-restrained monkey was comfortably seated in a primate chair. The monkey's head was restrained for the duration of the experiment. The horizontal and vertical positions of both eyes were recorded using the magnetic search coil technique (Fuchs and Robinson 1966). Extracellular single unit activity was recorded using enamel insulated tungsten microelectrodes (7-10 M impedance, Frederick Haer; for details, see Sylvestre and Cullen 1999a). Targets, data acquisition, and on-line data displays were controlled using real-time experimentation system (REX), a QNX-based real-time acquisition system (Hayes et al. 1982).

The abducens nucleus was identified as previously described (Sylvestre and Cullen 1999a). Because of the invasiveness of implanting an electrode in the abducens nerve for antidromic activation (Delgado-Garcia et al. 1986a,b) and/or a recording electrode in the lateral rectus for spike triggered averaging (Fuchs et al. 1988), we elected to physiologically identify putative AMNs and AINs using an approach modified from Sylvestre and Cullen (1999a) (see also Broussard et al. 1995). Specifically, Fuchs et al. (1998) found that identified AINs and AMNs formed fairly distinct clusters when their eye velocity sensitivities during sinusoidal smooth pursuit were plotted as a function of their eye position thresholds (see Fig. 8 of Fuchs et al. 1988). In fact, only a small area of their scatter plot showed overlap of the two neuron types. This area of overlap can be easily defined using an upper border (R = 2.0  0.033 × Threshold) and a lower border (R = 1.4  0.033 × Threshold). Here, we obtained a similar scatter plot for the neurons in our sample and used the borders described above to separate putative AMNs from AINs. Neurons that were plotted above the top border and below the lower border were labeled as putative AINs and AMNs, respectively, while those that were plotted between the upper and lower borders could not be identified and were labeled as ABNs.

When a neuron was properly isolated, unit activity, horizontal and vertical positions of the right and left eyes, target position, and table velocity were recorded on a digital audio tape (DAT). The isolation of each unit was re-evaluated off-line during playback. An abducens neuron was considered to be adequately isolated only when individual action potential waveforms could be discriminated using a windowing circuit (BAK) during saccades (e.g., see Fig. 1 in Sylvestre and Cullen 1999a), during fixation and during smooth pursuit. Right eye, left eye, and target position signals were low-pass filtered at 250 Hz (analog 8-pole Bessel filter) and sampled at 1 kHz. Subsequent analysis was performed using custom algorithms (Matlab, The MathWorks).

Coordinate conventions

The eyes are referred to as either ipsilateral or contralateral based on their location relative to the recording site. Positive and negative values indicate eye positions that are to the right and left of the central position (i.e., straight ahead), respectively. Each eye was calibrated separately by having the monkey fixate monocularly (i.e., one eye masked) on a variety of targets at different eccentricities and depths.

The motion of the eyes is also reported in terms of conjugate and vergence coordinates

(1a)

(1b)

The left eye and right eye inputs to Eq. 1 could be either position or velocity signals. For the conjugate position signal (Eq. 1a), positive and negative values correspond to the right and left of the mid-sagittal plane, respectively. For the vergence position signal (Eq. 1b), larger positive values indicate greater angles of convergence. Note that vergence position signals are always positive, but that vergence velocity signals can be either positive (during convergence) or negative (during divergence).

Analysis of abducens neuron discharges

Before analysis, recorded eye position signals were digitally filtered with a 51st order finite-impulse-response (FIR) filter with a Hamming window, using a cutoff at 125 Hz. The position signals were digitally differentiated to produce eye velocity profiles. Zero-phase forward and reverse digital filtering was employed to prevent phase distortion. A spike density function in which a Gaussian function was convolved with the spike train (SD of 5 ms for saccades, 10 ms for smooth pursuit and fixation) was utilized to represent the neuronal discharges (Cullen and Guitton 1997; Cullen et al. 1996; Sylvestre and Cullen 1999a,b).

Horizontal saccades were defined as having vertical amplitudes <10% of their horizontal amplitudes. Conjugate saccades had changes in vergence angles <2.5°, and were directed either ipsilaterally ("ON" direction) or contralaterally ("OFF" direction) to the recording site. Disjunctive saccades during which both eyes moved either in the direction ipsilateral or contralateral to the recording site, and for which one eye moved at least twice more than the other (mean vergence: 6.2 ± 1.3°), were selected for the analysis. Note that for each neuron analyzed, the numbers of converging and diverging disjunctive saccades were matched. Fixation periods were defined as time intervals having peak conjugate and vergence velocities <10°/s. All analyzed fixation intervals had conjugate positions ipsilateral to the neuron's threshold.

The dynamic eye position and velocity sensitivities of a neuron during saccades were estimating using linear optimization techniques that have been described in detail elsewhere (Sylvestre and Cullen 1999a). The rationale for using this technique as opposed to a more conventional metric-based analysis approach is described in the APPENDIX. The specific linear regression models utilized in this study are described in RESULTS. The goodness-of-fit of a given model to the data were quantified using the Variance-Accounted-For {VAF =1  [var (mod  fr)/var (fr)], where mod represents the modeled firing rate and fr represents the actual firing rate}. For the estimation of linear models (like those utilized in this report), the VAF is mathematically equivalent to the correlation coefficient R². A VAF value of 1 indicates a perfect fit to the data, and a value of 0 indicates a fit that is equivalent to a mean value. Note that the VAF can be utilized for the direct comparison of the goodness-of-fit of model estimations and predictions. The dynamic lead time of individual neurons (t_d) was determined during conjugate saccades as described in Sylvestre and Cullen (1999a).

Statistical analysis of model parameters

In this study, the residuals of the multiple regression model utilized for the analysis of the discharge dynamics of ABNs during disjunctive saccades (see model Est-ic-all in RESULTS) were not always normally distributed. Therefore standard statistical tests could not be performed on the parameter estimates because the assumptions inherent to these tests were invalid. To compensate for this limitation, we estimated the probability distribution of the model parameters in Est-ic-all (and also Est-cv-all, see RESULTS) using a nonparametric bootstrap approach. This analysis method is described in Carpenter and Bithell (2000). It is particularly well suited for small samples with unknown probability distributions (Carpenter and Bithell 2000; Press et al. 1997; Richmond et al. 1987).

Briefly, the final model parameters in model Est-ic-all (see RESULTS) were estimated from an original data set of N (usually >40) disjunctive saccades (where 1/2 were divergent and 1/2 were convergent; both eyes moved in the "ON" direction). Then 1,999 "new data sets" of N saccades were obtained by randomly re-sampling with replacement from the original data set. Every new data set differed from the original due to saccade repetitions and omissions, and from the other new data sets due to the randomness of the re-sampling process. Preliminary tests conducted on 10 neurons selected randomly indicated that 1,999 re-samplings were sufficient to obtain stable distributions (i.e., yielded the same mean and SD as when using 2,999 or 3,999 re-samplings). The model parameters were then estimated on each of the new data sets.

Following the re-sampling process, 95% confidence intervals were computed for each model parameter (as well as for more complex statistics such as the VAF; Sokal and Rohlf 1995) using the parameter values obtained across the 1999 iterations (Bca method, Carpenter and Bithell 2000). Parameters with 95% confidence intervals that overlapped with zero were not statistically significant and were removed from the model (e.g., see Fig. 4). Parameters with 95% confidence intervals that overlapped with one another were statistically identical and were replaced by conjugate parameters in the model (e.g., see Fig. 7). Note that the parameters were removed one at a time, starting with the parameter(s) that showed the most overlap, and that the parameters of the reduced model were estimated after each removal. This approach prevented removing important parameters whose numerical values were biased by the inappropriate parameters included in the original model.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

The discharge dynamics of 50 abducens nucleus neurons (36 from Monkey B, 14 from Monkey J) were analyzed during conjugate and disjunctive saccades. Our analysis approach was as follows: first, we assessed whether we could predict the discharge dynamics of individual neurons during disjunctive saccades based on their discharge properties during conjugate saccades; second, we directly estimated the sensitivity of individual neurons to the velocity and position of either the right/left eyes or the conjugate/vergence traces on the same data set of disjunctive saccades. Based on this analysis, the neurons were sorted in five categories according to the type of eye velocity-related signals that they encoded during disjunctive saccades: monocular with a preference for the ipsilateral eye, monocular with a preference for the contralateral eye, binocular with a preference for the ipsilateral eye, binocular with a preference for the contralateral eye, or conjugate (i.e., equally encoding the motion of both eyes). The eye velocity sensitivity was chosen as the criterion because velocity signals are dominant during saccades (Sylvestre and Cullen 1999a).

In the following sections, we begin by demonstrating our analysis approach on a typical monocular ABN that preferentially encoded movements of the ipsilateral eye. We then contrast the results with those of a typical conjugate ABN. Next, we describe in detail the distribution of our sample of neurons across the categories described above. We also characterize the responses of ABNs during OFF direction disjunctive saccades. Finally, we compare the discharge properties of individual ABNs during disjunctive saccades and disjunctive fixation.

Example monocular ABN with ipsilateral eye preference

We first estimated a neuron's sensitivity to eye movements during conjugate saccades. Recall that during these movements, the two eyes rotate by the same amplitude and move with highly comparable trajectories. The bias, conjugate eye position, and velocity sensitivities of the neurons were estimated using the following dynamic model, which we have previously shown provides an adequate description of ABN discharge dynamics during conjugate saccades (Sylvestre and Cullen 1999a)
where FR(t) is the neuron's instantaneous firing rate, b_CS, k_CS, and r_CS are constants and represent the neuron's firing rate at eye position zero, the neuron's conjugate eye position, and eye velocity sensitivities, respectively (_CS refers to conjugate saccades), CJ(t) and C(t) are instantaneous conjugate position and velocity, respectively, and t_d is the neuron's dynamic lead time.

The model fits obtained for a typical ABN, unit B72_2, are shown in Fig. 2 for two conjugate saccades. This first-order model of eye position provided a good fit of the neuron's firing rate (Fig. 2, Est-CS; VAF_Est-CS = 0.58; mean population VAF_Est-CS ± SD = 0.68 ± 0.12, see Table 1).

View larger version (16K): [in this window] [in a new window]   Fig. 2. Discharge patterns of unit B72_2 during conjugate saccades. Neuron's firing rate is shown as the gray shaded area (top row). Model fit obtained using Est-CS is shown as the thick black curve superimposed on the firing rate. Note the good fit to data. Also shown are ipsilateral eye (IE), contralateral eye (CE), and conjugate (CJ) velocity (2nd row) and position (4th row) traces, and vergence (VG) velocity (3rd row) and position (bottom row) traces. Note the different line styles utilized for each trace. Vertical dotted lines denote saccade onsets and offsets (20°/s criterion), and horizontal dotted lines represent 0 velocity.

We next determined whether the conjugate model estimated above could be utilized to predict the neuron's activity during disjunctive saccades. During converging disjunctive saccades, the contralateral eye moves more than the ipsilateral eye (e.g., Fig. 3A), while the ipsilateral eye moves more than the contralateral eye during diverging saccades (e.g., Fig. 3B). Note that during these movements, not only do the velocity profiles of the ipsilateral and contralateral eyes peak at different values, but often they also exhibit differences in their dynamics. Therefore a good fit from the conjugate predictions would indicate that the neuron equally encodes the motion of both eyes (i.e., encodes conjugate eye movements).

View larger version (29K): [in this window] [in a new window]   Fig. 3. Discharge patterns of monocular unit B72_2 during (A) 2 converging disjunctive saccades and (B) 2 diverging disjunctive saccades. Top row: neuron's firing rate with the model fit obtained with Pred-CS. Note the particularly poor fit to data. 2nd row: same firing rate traces (duplicated for clarity), but with the model fits obtained using Est-ic-all (black curve) and Est-ic-red (dark gray curve; equation is also shown). Both fits were virtually identical and modeled equally well the firing rate. 3rd-6th rows: velocity and position traces recorded during these disjunctive saccades.

The first indication that unit B72_2 did not encode conjugate eye movements came from the poor conjugate predictions shown in the top row of Fig. 3 (Pred-CS; VAF_Pred-CS = 0.45). Such low prediction VAFs were observed for all monocular units (e.g., mean VAF_Pred-CS = 0.45 ± 0.20, for the monocular ipsilateral eye preference category; see Table 1). Another characteristic of monocular units was that the conjugate predictions tended to overshoot the firing rate when the preferred eye (in this example the ipsilateral eye) moved less (Fig. 3A), and to undershoot the firing rate when the preferred eye moved more (Fig. 3B). Thus the conjugate-based prediction analysis suggested that unit B72_2 did not encode the conjugate movements of the eyes but rather that it exhibited a marked preference for the movements of the ipsilateral eye.

To directly quantify the sensitivity of individual ABNs during disjunctive saccades, we used the following two approaches. First, we described neuronal discharges as a function of the movements of each eye. This approach was motivated by recent studies of premotor neurons in the saccadic burst generator (Sylvestre and Cullen 1999b; Zhou and King 1998). Second, we utilized a conjugate/vergence based model to describe the activity of the same neurons during the same disjunctive saccades. This model structure follows from the proposal of Hering (1868) and is described in a subsequent section.

When applied to unit B72_2, the ipsilateral/contralateral eye movements-based approach first involved estimating the parameters of the following model on the sample of disjunctive saccades gathered for this neuron

where b_DS, k_i-DS, k_c-DS, r_i-DS, and r_c-DS are the bias, ipsilateral eye position, contralateral eye position, ipsilateral eye velocity, and contralateral eye velocity sensitivities of the neuron, respectively (_DS, _i, and _c refer to disjunctive saccades, ipsilateral eye, and contralateral eye, respectively; ic in the model name indicates the ipsilateral/contralateral eye based approach), and IE(t), CE(t), I(t), and C(t) are instantaneous ipsilateral and contralateral eye positions and instantaneous ipsilateral and contralateral eye velocities, respectively. This model is the binocular expansion of Est-CS. Model fits obtained using Est-ic-all for unit B72_2 are shown in the second row of Fig. 3, A and B (thick black curve). Clearly, this model fit was far superior to the conjugate model predictions (VAF_Est-ic-all = 0.66 vs. VAF_Pred-CS = 0.45; mean VAF_Est-ic-all = 0.60 ± 0.15 vs. mean VAF_Pred-CS = 0.45 ± 0.20, for the monocular ipsilateral eye preference category, Table 1). Although this observation strongly supports the idea that unit B72_2 did not encode conjugate eye movements, it does not provide enough information to determine if it solely encoded the movements of one eye or a weighted mixture of both eyes' movements.

To address this limitation, we estimated 95% confidence intervals for each of the model parameters in Est-ic-all using the bootstrap technique described in METHODS. Figure 4 shows the parameter estimates (vertical arrows) of Est-ic-all for unit B72_2 (left, eye velocity parameters; right, eye position parameters), as well as the bootstrap distributions (histograms) and the 95% confidence intervals (thick horizontal bars) for each parameter. Two important observations can be made from the 95% confidence intervals. First, for both the velocity and the position parameters, the parameter values estimated for the ipsilateral (r_i-DS and k_i-DS) and contralateral (r_c-DS and k_c-DS) eyes were statistically different (i.e., the confidence intervals did not overlap). This confirmed that unit B72_2 did not encode conjugate signals. Second, both the position and velocity parameters for the contralateral eye had confidence intervals that overlapped with zero (i.e., were not statistically different from 0). Therefore these parameters played no significant role in modeling the neuron's discharge dynamics.

View larger version (29K): [in this window] [in a new window]   Fig. 4. Results of the bootstrap analysis for monocular unit B72_2. Left: results for eye velocity sensitivity of this neuron. Right: results for eye position sensitivity. Histograms represent the distribution of parameter values obtained with the bootstrap analysis using Est-ic-all for the ipsilateral (black bars) and contralateral (white bars) eye. Vertical arrows indicate mean value for each parameter. Thick horizontal bars below histograms indicate the 95% confidence intervals associated with each parameter (black bar, ipsilateral eye; white bar, contralateral eye).

When the position and velocity terms relating to the contralateral eye (r_c-DS and k_c-DS) were removed from Est-ic-all and the remaining model parameters were estimated for this reduced model
the obtained fit was nearly identical to that of the full ipsilateral/contralateral eye-based model (Fig. 3, A and B, 2nd row, Est-ic-red, thick gray curves). Indeed, the goodness-of-fit of this reduced monocular model was the same as that of the full ipsilateral/contralateral eye-based model (VAF_Est-ic-red = VAF_Est-ic-all = 0.66). The model parameters of Est-ic-red for unit B72_2 are shown in Table 2, in the monocular ipsilateral eye category. Note that the parameter values estimated for the "meaningless" eye were appropriately replaced by zeros. Also note that Est-ic-red will not be the same for all neurons (see Example conjugate ABN). Altogether, the prediction-based and estimation-based analyses clearly demonstrated that during disjunctive saccades, unit B72_2 encoded signals related to the motion of the ipsilateral eye only.

Example conjugate ABN

Figures 5-7 show the results of the same analysis of a typical conjugate ABN, unit B27_1. This neuron discharged a vigorous burst of action potentials during conjugate saccades that could be well described using Est-CS (Fig. 5; VAF_est-CS = 0.69). However, in marked contrast to unit B72_2, the conjugate predictions of the neuron's discharge during disjunctive saccades provided a fairly good fit to the data (Fig. 6, A and B, top rows, Pred-CS, thick black curve; VAF_Pred-CS = 0.54). This result, which was consistent across the category of conjugate ABNs (mean VAF_Pred-CS = 0.51 ± 0.16; Table 1), provided strong indications that unit B27_1 encoded conjugate position and velocity signals and hence was equally sensitive to the motion of both eyes.

View larger version (16K): [in this window] [in a new window]   Fig. 5. Discharge patterns of a 2nd example neuron, unit B27_1, during conjugate saccades. Model fit obtained using Est-CS, which provided a good fit to data, is shown as the thick black curve superimposed on firing rate.

View larger version (26K): [in this window] [in a new window]   Fig. 6. Discharge patterns of conjugate unit B27_1 during (A) 2 converging disjunctive saccades and (B) 2 diverging disjunctive saccades. Note the good fit to data provided by PredCS (top row). Also shown are the model fits obtained using Est-ic-all (black curve) and Est-ic-red (dark gray curve; equation is also shown). For this neuron, Est-ic-red had the same structure as Pred-CS.

View larger version (29K): [in this window] [in a new window]   Fig. 7. Results of the bootstrap analysis for conjugate unit B27_1. Left: results for eye velocity sensitivity of this neuron. Right: results for eye position sensitivity, using the same conventions as for Fig. 4.

The estimation of Est-ic-all confirmed this conclusion. First, the goodness-of-fit provided by Est-ic-all was only marginally better than that provided by the conjugate predictions (Fig. 6, A and B, 2nd row, Est-ic-all, thick black curve; VAF_Est-ic-all = 0.57; mean VAF_Est-ic-all = 0.58 ± 0.11, for the conjugate category; Table 1). Second, as is shown in Fig. 7, for both the eye velocity (left) and eye position (right) sensitivities of the neuron, the estimated parameter values (vertical arrows) were very similar for the ipsilateral and contralateral eyes. Indeed, the bootstrap distributions (histograms) and the 95% confidence intervals (thick horizontal bars) overlapped for the ipsilateral and contralateral eye parameters (i.e., r_i-DS = r_c-DS, and k_i-DS = k_c-DS, at 95% confidence), but did not overlap with zero. It can be concluded from these results that unit B27_1 was equally sensitive to the position and velocity of the two eyes, and hence that it encoded conjugate position and velocity signals.

As for the monocular unit described previously, this conclusion was strengthened by replacing the monocular position and velocity signals in Est-ic-all by conjugate signals [i.e., Est-ic-red for this neuron: FR(t) = b_CS + k_CSCJ(t  td) + r_CS J(t  td)]. This reduced model (Fig. 6, A and B, 2nd rows, thick gray curve) provided a goodness-of-fit that was identical to that of Est-ic-all (VAF_Est-ic-red = VAF_Est-ic-all = 0.57; mean VAF_Est-ic-red = 0.57 ± 0.11, for the conjugate category; Table 1). Furthermore, the parameter values (Table 2) that were estimated using Est-ic-red were comparable to those estimated during conjugate saccades (P > 0.5, paired t-test). Note that in Table 2, the parameter values for neurons with conjugate ocular preferences are represented as their monocular equivalent (see Eq. 2). Thus, when taken together, the prediction-based and estimation-based analyses clearly demonstrated that unit B27_1 encoded conjugate signals during disjunctive saccades.

Population distributions

The parameter values obtained for each ABN in our sample using Est-ic-red are shown in Table 2. Neurons are grouped in five categories according to the eye velocity-based criteria described below. Average parameter values (±SDs) are included for each category and for the entire sample. To quantify the "ocular-preference" of a given neuron, ratios of ipsilateral and contralateral eye velocity (Ratio_vel) and eye position (Ratio_pos) parameters were calculated as follows using the parameter values from Table 2 (Est-ic-red)
To indicate which eye yielded the larger parameter (par.) value, each Ratio value is accompanied by an _i or a _c, for the ipsilateral (ipsi.) or contralateral (contra.) eye, respectively. The Ratio_vel values were utilized to sort neurons in the categories shown in Tables 1 and 2, and can be interpreted as follows

Hence, monocular unit B72_2 shown in Figs. 2-4 had a Ratio_vel = 0i, while conjugate unit B27_1 shown in Figs. 5-7 had a Ratio_vel = 1 (note that in this case, the _i or _c character was omitted because both parameters had equal values). This Ratio index was chosen because its interpretation is more intuitive than that of other indexes utilized in previous studies. For example, for the index utilized in the present study, values of 0.1i and 0.5i simply represent ratios of ipsilateral to contralateral eye parameters of 10:1 and 2:1, respectively. On the other hand, the same values of 0.1 and 0.5 for a common index ([ipsi. eye  contra. eye]/[ipsi. eye + contra. eye]; see for example Zhou and King 1998) represent ratios of ipsilateral to contralateral eye parameters of 1.22:1 and 3:1, respectively.

A graphical summary of the Ratio values is presented in Fig. 8, where the distributions of Ratio_vel (Fig. 8A) and Ratio_pos (Fig. 8B) for our sample of neurons are shown. With respect to the eye velocity sensitivity of ABNs during disjunctive saccades, many ABNs in our sample (44%; light and dark red bars, Fig. 8A) exhibited monocular velocity sensitivities (i.e., Ratio_vel = 0). Of these monocular ABNs, 73% preferred the ipsilateral eye (light red bars, Fig. 8A). Furthermore, 30% of the ABNs in our sample equally encoded the velocity of both eyes (i.e., conjugate, Ratio_vel = 1; blue bar, Fig. 8A). The remaining 26% of ABNs encoded the motion of both eyes (light and dark green bars, Fig. 8A), of which 77% favored the ipsilateral eye (light green bars, Fig. 8A). Only two neurons encoded opposite ON directions for the two eyes (Ratio_vel < 0). The distribution of Ratio_pos (Fig. 8B) was similar to that of Ratio_vel. Most neurons in our sample (70%) exhibited monocular preferences. Of these monocular ABNs, 63% preferred the position of the ipsilateral eye. In addition, 24% of all ABNs tested were equally sensitive to the position of both eyes. Only one neuron had a negative Ratio_pos. The main difference between the distributions of Ratio_pos and Ratio_vel was that slightly more units were binocular with respect to their velocity sensitivity than to their position sensitivity (24% vs. 6%, velocity and position sensitivities, respectively).

View larger version (19K): [in this window] [in a new window]   Fig. 8. A: distribution of Ratiovel during disjunctive saccades for our sample of abducens nucleus neurons (ABNs). Columns marked with asterisks indicate neurons that had a vergence sensitivity greater than one-half their conjugate sensitivity. Red, blue, and green bars denote monocular, conjugate, and binocular units, respectively. B: distribution of Ratiopos during disjunctive saccades for our sample of ABNs. The conventions utilized were the same as in A. C: coherence of the preferred eyes for the position and velocity sensitivities of ABNs during disjunctive saccades. The x and y axes plot the 3 preferred eye categories (ipsilateral eye, Ipsi; contralateral eye, Contra; or conjugate, Conj) for the position and velocity sensitivities, respectively. Black columns indicate coherence (i.e., the eye position and the eye velocity preferred eyes of a neuron were the same), and gray bars indicate absence of coherence.

We conclude that during disjunctive saccades, our sample of ABNs is dominated by a subpopulation of neurons that monocularly encodes the motion of the ipsilateral eye (i.e., "monocular with ipsilateral eye preference"; Fig. 8) and by a second less pronounced subpopulation that encodes the conjugate motion of the eyes (i.e., "conjugate"; Fig. 8). As a result of this distribution, the average sensitivity to the velocity of the ipsilateral eye for our sample of ABNs was 1.5 times larger than that for the contralateral eye. The average eye position sensitivity of our sample of ABNs to the ipsilateral eye was also 1.5 times larger than that of the contralateral eye.

Coherence of the "preferred eye" for the position and velocity coefficients

For each neuron in our sample, our analysis approach identified a "preferred eye" (defined as the eye that yielded the largest parameter value) for both the position and the velocity sensitivities. Here, we asked whether the preferred eye for the position and velocity sensitivities of ABNs were matched on a neuron-by-neuron basis. To do so, we regrouped our data under three general categories: ipsilateral eye preference category (grouping the "monocular with ipsilateral eye preference" and "binocular with ipsilateral eye preference" cell types; Table 2), contralateral eye preference category (grouping the "monocular with contralateral eye preference" and "binocular with contralateral eye preference" cell types; Table 2), and conjugate category (Table 2). Hence, a total of nine permutations represent all the possible combinations of preferred eyes for the position and velocity sensitivities.

The fraction of neurons that fell within each of the nine possible categories are illustrated in Fig. 8C, where the x and y axes represent the three preferred eye categories for the position and velocity sensitivities, respectively, and the z axis represents the percentage of neurons that fell within each category. As is shown by the black columns, the majority of neurons (58%) exhibited coherence between their preferred eye for the position and velocity sensitivities (i.e., had the same preferred eye). Of those neurons, 62% preferred the ipsilateral eye, 17% preferred the contralateral eye, and 21% were conjugate. With the exception of noncoherent neurons that encoded ipsilateral position/conjugate velocity eye preferences and were equally numerous as those that exhibited conjugate coherence, no trend could be identified for the other categories of noncoherent neurons; they were approximately uniformly distributed over the remaining five combinations of preferred eyes (gray columns). Thus during disjunctive saccades, a majority of ABNs exhibited coherence in their preferred eye for the position and velocity sensitivities.

Testing the alternative conjugate/vergence approach

In our second approach, we utilized a conjugate/vergence based model to describe the activity of the same neurons

where _cj and _vg refer to conjugate and vergence-related parameters, respectively, cv in the model name indicates the conjugate/vergence based approach, and CJ(t), VG(t), J(t), and G(t) are instantaneous conjugate and vergence eye positions and velocities, respectively. As for Est-ic-all, we estimated the parameters of this model on our entire data set of neuronal activities and computed bootstrap confidence intervals for all of the parameters. The latter were then used to reduce the model to its simplest form (Est-cv-red; note that this model can vary from neuron to neuron).

In its nonreduced form, Est-cv-all is mathematically equivalent to Est-ic-all. Accordingly, the VAF values obtained with both models were identical on a neuron-by-neuron basis. Furthermore, when the parameters of Est-cv-all were converted to those of Est-ic-all using the following relationships (shown for a neuron recorded to the left of the midline)

(2a)

(2b)

the parameters obtained with either model were all statistically identical (paired t-tests, P > 0.05). However, because Est-ic-all and Est-cv-all are not always equivalent after one or more parameters have been removed and because the parameters in these models can take markedly different numerical values and have an inherent variability (i.e., have confidence intervals with nonnegligible widths), it was not possible to utilize Eq. 2 to derive Est-cv-red from Est-ic-red. Stated differently, we could not assume that if the bootstrap confidence intervals of the ipsilateral and contralateral eye parameters in Est-ic-all overlapped slightly (which we interpreted as conjugacy), the confidence interval of the vergence term in Est-cv-all would automatically overlap with zero. Hence, we properly evaluated Est-cv-red by independently computing bootstrap confidence intervals for the conjugate/vergence based model Est-cv-all on all the neurons in our sample.

Figure 9 shows the results of this conjugate/vergence analysis for our population of neurons. Note that to allow direct comparisons of these results with those described in the previous sections, we processed the parameters of Est-cv-red with Eq. 2 to obtain the equivalent parameter values in ipsilateral/contralateral eye coordinates, and then computed Ratio_vel and Ratio_pos indexes as described above. As illustrated in Fig. 9 by the axis labels between square brackets, a conjugate unit (vergence-related parameters nonsignificant) will yield a Ratio index of 1, a vergence unit (conjugate-related parameters nonsignificant) will yield a Ratio of 1, and a "monocular" unit (conjugate-related parameters twice bigger than the absolute vergence parameters; see Eq. 2) will yield a Ratio of 0. The distribution in Fig. 9A shows the Ratio_vel values calculated using Est-cv-red. This distribution can be directly compared with that obtained with Est-ic-red (Fig. 8A). A first important observation was that the main features of the two distributions were similar in that both showed two predominant peaks [i.e., monocular (Ratio = 0) and conjugate (Ratio = 1) peaks]. Similar results were also observed for the Ratio_pos values (compare Figs. 9B and 8B). However, the distributions obtained with the two types of reduced models differed in that the number of monocular versus conjugate units was less based on the conjugate/vergence approach. The number of units with binocular tuning for their eye position and velocity sensitivities was also higher using the conjugate/vergence approach.

View larger version (15K): [in this window] [in a new window]   Fig. 9. A: distribution of Ratiovel during disjunctive saccades obtained with Est-cv-red for our sample of ABNs. Ratio indexes are equivalent to those in Fig. 8 (see text for details). The axis labels between square brackets illustrate the relationship between the Ratio values and the conjugate/vergence parameter values. Conventions for red, blue, and green bars are as in Fig. 8. B: distribution of Ratiopos during disjunctive saccades obtained with Est-cv-red for our sample of ABNs. The conventions utilized were the same as in A.

Because the analyses using models Est-ic-all and Est-cv-all yielded slightly different results, we sought to determine which of the two provided the most appropriate description of ABN discharges. To do so, we analyzed the VAF values generated by these two models. For 64% of the neurons in our sample, Est-ic-red yielded VAF values that were clearly larger than those obtained with Est-cv-red (7 ± 11%). In contrast, for the remaining neurons, the VAF values obtained with Est-cv-red were only slightly larger than those obtained with Est-ic-red (2 ± 2%). Hence, for almost two-thirds of the neurons in our sample, model Est-ic-red provided markedly better goodness-of-fits than model Est-cv-red, while the latter model only provided marginally (if at all) better fits for the remaining neurons. Furthermore, and consistent with these results, the VAF values obtained with Est-ic-red were, on average, only 1% smaller than those obtained with Est-ic-all, while those obtained with Est-cv-red were 5% smaller than those obtained with Est-cv-all [recall that VAF(Est-ic-all) = VAF(Est-cv-all)]. Thus removing conjugate or vergence parameters from Est-cv-all (based on the bootstrap statistics) was far more detrimental to the goodness-of-fit than removing ipsilateral or contralateral eye parameters from Est-ic-all. We conclude that ipsilateral/contralateral eye based models were better suited for our analysis than conjugate/vergence based models.

Responses during off-direction disjunctive saccades

In good agreement with our previous findings (Sylvestre and Cullen 1999a), the majority of ABNs in our sample (82%) were driven into inhibitory cutoff (i.e., "paused") during all OFF direction conjugate saccades. Similarly, most ABNs (64%) were also driven into inhibitory cutoff during all OFF direction disjunctive saccades. Whether the saccade was divergent or convergent did not affect the pausing behavior of these ABNs. Discharge patterns from a representative neuron in this category, unit J66_1, are shown in Fig. 10A during converging and diverging OFF-direction saccades. For the remaining ABNs, the amplitude of the conjugate movement appeared to be the main determinant of their pausing behaviors, since the neurons' discharges were comparable during converging and diverging saccades. Of these neurons, the majority (67%) paused completely for disjunctive saccades with conjugate components >10°. In turn, 33% paused only for disjunctive saccades with conjugate amplitudes >20°. Figure 10B shows example disjunctive saccades from a neuron in this latter category (unit B76_1). Note that the neuron clearly paused for large amplitude converging and diverging saccades (right). Also note that, as for all neurons that did not always reach inhibitory cutoff, there was nevertheless a significant decrease in firing rate when the neuron did not pause. Thus the pausing behavior of ABNs is generally similar during conjugate and disjunctive saccades, with the exception that for movements of small amplitudes, slightly more ABNs pause during conjugate saccades.

View larger version (25K): [in this window] [in a new window]   Fig. 10. ABN discharge patterns during OFF-direction disjunctive saccades. A: 2 smaller (left pair; first is diverging, second is converging) and larger (right pair; first is diverging, second is converging) disjunctive saccades for a typical ABN, unit J66_1. The same conventions as Fig. 2 were utilized (note that for clarity, only position traces are shown). As for most units in our sample, this neuron completely ceased firing (paused) for disjunctive saccades of all amplitudes. Whether the saccade was divergent or convergent did not affect the pausing behavior (e.g., compare left and right small amplitude saccades). B: example saccades from another neuron, unit B76_1, that only paused for larger amplitude disjunctive saccades. Note that the neuron's firing rate decreased during smaller amplitude disjunctive saccades (left), but not sufficiently to reach cutoff.

Comparison of disjunctive saccades and disjunctive fixation

We next addressed whether individual ABNs retain the same preferred eye during disjunctive saccades and disjunctive fixation. For each neuron, we fitted its average firing rate as a function of the average ipsilateral and contralateral eye positions during intervals of disjunctive fixation. We next computed a Ratio_FIX value for each neuron using the same procedure as defined above for calculating Ratio_POS during disjunctive saccades.

Figure 11A shows the distribution of Ratio_FIX during disjunctive fixation. This distribution was similar to the distribution of Ratio_pos observed during disjunctive saccades (compare Figs. 11A and 8A). The main difference between the two distributions was that a greater proportion of ABNs encoded the position of both eyes during disjunctive fixation versus disjunctive saccades. As a consequence, during disjunctive fixation, fewer ABNs (48%) encoded the position of a single eye (of which 75% preferred the ipsilateral eye), while a comparable number of ABNs (26%) encoded the conjugate position of the eyes. Thus at the population level, ABNs generally encode the position of the two eyes in a similar manner during disjunctive saccades and disjunctive fixation. For our sample of ABNs, the average sensitivity to the ipsilateral eye position during disjunctive fixation was 3.1 times larger than that of the contralateral eye. This ratio is larger than that observed during disjunctive saccades (1.5) because the parameter values estimated during fixation were larger than those estimated during disjunctive saccades. This result is consistent with our previous finding that the eye position sensitivities of ABNs decrease as the eye velocity increases (Sylvestre and Cullen 1999a). We attributed this observation to the changes in antagonist/agonist muscle interactions that occur at different eye velocities.

View larger version (25K): [in this window] [in a new window]   Fig. 11. A: distribution of Ratiopos during disjunctive fixation for our sample of ABNs. Conventions for red, blue, and green bars are as in Fig. 8. B: coherence of the preferred eyes for the position sensitivities of ABNs during disjunctive saccades and disjunctive fixation. The x and y axes plot the 3 preferred eye categories for the eye position sensitivities during fixation and saccades, respectively. The other conventions are the same as for Fig. 8C.

On a neuron-by-neuron basis, ABNs exhibited good coherence between their preferred eye (eye position sensitivity) during disjunctive saccades and disjunctive fixation. This is illustrated in Fig. 11B, where for each neuron in our sample, the preferred eye during disjunctive fixation was plotted versus the preferred eye (position sensitivity) during disjunctive saccades. The majority of ABNs (60%) exhibited coherence between their preferred eye during these two behavioral conditions (black columns). No consistent pattern could be recognized for the remaining neurons. Thus these results clearly demonstrate that ABNs have similar ocular preferences during fixation and saccadic behaviors.

Putative motoneurons versus internuclear neurons

Figure 12 shows the relative distribution of preferred eye position and velocity sensitivities for the putative AMNs (abducens motoneurons) and AINs (internuclear neurons) in our sample. Note that eight neurons (labeled ABN in Table 2) could not be classified as AINs or AMNs using the identification criteria described in METHODS and were excluded from the following analysis. With respect to the eye position sensitivities (Fig. 12, left), our results suggest that a slightly greater proportion of AINs than AMNs (61% vs. 50%) preferentially encoded the position of the ipsilateral eye. In turn, a greater proportion of AMNs encoded the conjugate position of both eyes (29% vs. 17%, AMNs vs. AINs, respectively). These trends were more pronounced for the eye velocity sensitivities (Fig. 12, right). However, for our samples of putative AMNs and AINs, their relative distributions across the five categories of preferred eye shown in Table 2 were not statistically significant (² test on a 2 × 5 contingency table; P > 0.50 and P > 0.10, for position and velocity sensitivities, respectively). Thus we conclude that putative AMNs and AINs encode eye movements in a similar manner during disjunctive saccades.

View larger version (22K): [in this window] [in a new window]   Fig. 12. Distribution of eye position (left) and eye velocity (right) sensitivities of putative abducens motoneurons (AMNs; top row) and abducens internuclear neurons (AINs; bottom row). Conventions for red, blue, and green bars are as in Fig. 8.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX REFERENCES

In this report, we provide the first characterization of abducens nucleus neuron discharges during disjunctive saccades. The analysis approach that we utilized allowed us, for each neuron, to reduce a generic ipsilateral/contralateral eye-based model of ABNs firing rate (i.e., Est-ic-all) to a model that only included the terms that significantly modulated the neuron's discharge dynamics (i.e., Est-ic-red).