The Journal of Neurophysiology Vol. 78 No. 6 December 1997, pp. 3283-3306
Copyright ©1997 by the American Physiological Society
Analysis of Primate IBN Spike Trains Using System Identification Techniques. II. Relationship to Gaze, Eye, and Head Movement Dynamics During Head-Free Gaze Shifts
Kathleen E. Cullen and
Daniel Guitton
Aerospace Medical Research Unit and the Montreal Neurological Institute, McGill University, Montreal, Quebec H3G 1Y6, Canada
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ABSTRACT |
Cullen, Kathleen E. and Daniel Guitton. Analysis of primate IBN spike trains using system identification techniques. II. Relationship to gaze, eye, and head movement dynamics during head-free gaze shifts. J. Neurophysiol. 78: 3283-3306, 1997. We have investigated the relationships among the firing frequency B(t) of inhibitory burst neurons (IBNs) and the metrics and dynamics of the eye, head, and gaze (eye + head) movements generated during voluntary combined eye-head gaze shifts in monkey. The same IBNs were characterized during head-fixed saccades in our first of three companion papers. In head-free gaze shifts, the number of spikes (NOS) in a burst was, for 82% of the neurons, better correlated with gaze amplitude than with the amplitude of either the eye or head components of the gaze shift. A multiple regression analysis confirmed that NOS was well correlated to the sum of head and eye amplitudes during head-free gaze shifts. Furthermore, the mean slope of the relationship between NOS and gaze amplitude was significantly less for head-free gaze shifts than for head-fixed saccades. NOS is a global parameter. To refine we used system identification techniques to evaluate a series of dynamic models in which IBN spike trains were related to gaze or eye movements. We found that gaze- and eye-based models predicted the discharges of IBNs equally well. However, the bias values required by gaze-based models were comparable to those required in our head-fixed models whereas those required by eye-based models were significantly larger. The difference in biases between gaze- and eye-based models was very strongly correlated to the mean head velocity (
) during gaze shifts [R = 
0.93 ± 0.15 (SD)]. This result suggested that the increased bias required by the eye-based models reflected an unmodeled input onto these cells. To pursue this argument further we investigated a series of dynamic models that included both eye velocity (
) and terms and this confirmed the importance of these two terms. As in our head-fixed analysis of companion paper I, the most valuable model formulation also included an eye saccade amplitude term (
E) and was given by B(t) = r0 + r1E + b1 + g1 where r0, r1, b1, and g1 are constants. The amplitude of the head velocity coefficient was significantly less than that of the eye velocity coefficient. Furthermore, in our population long-lead IBNs tended to have a smaller head velocity coefficients than short-lead IBNs. We conclude that during head-free gaze shifts, the head velocity signal carried to the abducens nucleus by primate excitatory burst neurons (EBNs; if EBNs and IBNs carry similar signals) must be offset by other premotor cells.
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INTRODUCTION |
Inhibitory burst neurons (IBNs) in the paramedian pontine reticular formation, caudal to the abducens motor nucleus, project to the contralateral abducens nucleus (ABD) and inhibit its activity during saccades (Hikosaka and Kawakami 1977
; Hikosaka et al. 1978, 1980; Scudder et al. 1988; Strassman et al. 1986; Yoshida et al. 1982). In the preceding companion paper (Cullen and Guitton 1997a) we analyzed, by using system identification techniques, the discharge characteristics of IBNs in the head-fixed primate. In this paper we are concerned with the discharge of these cells in the primate whose head is free to move. We define gaze = eye-in-space = eye-in-head + head-in-space.
IBNs are the inhibitory component of the saccade burst generator; the excitatory drive onto motoneurons (MNs) being provided by excitatory burst neurons (EBNs). EBNs project to IBNs and both cell types are thought to carry the same signals (see reviews by Fuchs et al. 1985; Hepp et al. 1989). Burst neurons (BNs) have been further subdivided into short- and long-lead bursters depending on the magnitude of the time interval by which the discharge leads movement. IBNs are thought to be gated by inhibitory projections from omnipause neurons (OPNs) (Evinger et al. 1982; Furuya and Markham 1982; Keller 1974; King and Fuchs 1977; Nakao et al. 1980). Investigations in the cat demonstrated that OPNs pause for the entire duration of head-free gaze shifts, rather than for the duration of the saccadic eye movement's contribution (Paré and Guitton 1990). The latter duration is usually shorter, especially in large gaze shifts that are bigger than the oculomotor range and for which the eye frequently remains immobile, at an eccentric orbital position, while gaze motion is carried by the head. There is also evidence that the pause in activity of primate OPNs may also be gaze related (Phillips 1993). Because the OPN pause disinhibits IBNs, it follows that IBNs should discharge during the entire duration of gaze shifts in both cat and monkey. We have seen this in the head-free cat; the duration of an IBN's burst was better correlated with gaze than with saccade duration (Cullen et al. 1993).
The first studies of BNs in the head-free primate classified short-lead BNs as "gaze related" or "saccade related" (Whittington et al. 1984). It was not known whether the neurons were IBNs or EBNs. Gaze-related BNs were defined as cells for which the total number of spikes (NOS) in a burst is the same for a given displacement of the visual axis irrespective of whether the head is fixed or free. Saccade-related BNs were defined as cells for which the total NOS in a burst is the same for eye movements of equal amplitude irrespective of whether the head is fixed or free. Gaze-related bursters were thought to be converted to saccade-related bursters by subtracting from the former a signal encoding head velocity (). Our studies regarding the cat (Cullen et al. 1993) demonstrated that the discharge of cat IBNs during combined eye-head gaze shifts differed from that of the prototypical saccade-related and gaze-related BNs. In the head-free condition, the total NOS in a burst was well correlated with gaze amplitude and generally poorly correlated with saccade amplitude. This is a property of gaze-related neurons, not saccade-related ones. However, in the head-fixed condition the slope of the relationship between the NOS in a burst and eye saccade amplitude was significantly higher than that between NOS and gaze amplitude measured during head-free gaze shifts. This is not a property of gaze-related BNs. In summary, IBNs in cats were neither the saccade- nor gaze-related neurons defined by Whittington et al. (1984); they were related to the movement of the visual axis in different ways depending on whether the cat's head was fixed or free. Put another way, the discharge characteristics of cat IBNs could not be extrapolated from head-fixed data to predict accurately either eye or gaze saccade amplitude in the head-free condition.
Recently a number of studies in primates have suggested that the nature of the signals carried by their IBNs may also be more complex than initially proposed. For example, Phillips et al. (1995) proposed what they called command, head, eye, and gaze BNs. By comparison, Tomlinson and Brance (1991) recorded saccade-related bursters in the IBN area of the head-free primate but surprisingly, these neurons also discharged throughout the duration of large gaze shifts when the eye was relatively immobile at an eccentric position in the orbit. The results of these analyses have not permitted a clear quantitative determination of whether BN discharges encode gaze, eye, or head. To address this issue we carried out dynamic analyses of IBN discharges in the totally head-free macaque monkey, using the objective system identification algorithms described in Cullen et al. (1996), and applied it to IBNs in the head-fixed primate as described in companion paper I (Cullen and Guitton 1997a).
Figure 1 shows an extension of the local feedback system for controlling head-fixed saccades (described in companion paper I Cullen and Guitton 1997a), to the control of gaze shifts in the head-free condition. As in companion paper I Fig. 1 demonstrates that the BN signal can be considered from either the upstream or downstream perspectives. This paper deals with the latter; the subsequent companion paper III (Cullen and Guitton 1997b) will consider the former. The schematic proposes that gaze shifts are controlled by a signal encoding gaze motor error (
g) produced by subtracting the angle the eye (E*) and head (H*) have rotated from the desired angular rotation (T); i.e., g = T E* H*. There is considerable agreement on this conceptual model (Fuller et al. 1983; Guitton and Volle 1987; Guitton et al. 1984, 1990; Laurutis and Robinson 1986; Pélisson and Prablanc 1986; Pélisson et al. 1988, 1989, 1995; Roucoux et al. 1980; Tomlinson and Bahra 1986a,b; Tomlinson 1990; see review by Guitton 1992). In our simplified schema illustrated, the BN pool (B) is shown in an ambiguous state, driven by g but itself only driving eye MNs. Furthermore, neck MNs are shown as being driven by an unknown source. We will show that the organization in Fig. 1 is inadequate. This has already been demonstrated for the cat where a modified version of this model was proposed by Galiana predicts movement trajectories and burst generator firing frequency profiles (Cullen et al. 1993; Galiana and Guitton 1992; Guitton et al. 1990). This model assumed that the cat burst generator is strongly coupled to both eye and head motor circuits (as suggested by the results of Grantyn and Berthoz 1987 and Guitton et al. 1990), but because this is uncertain in the monkey we have not included a link between B and neck MNs in Fig. 1. Our present analysis of monkey IBNs reveals strong analogies with our previous findings in the cat (Cullen et al. 1993).
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| FIG. 1.
Classic local feedback model for saccade generation (shown in Fig. 2 of companion paper I, Cullen and Guitton 1997a) extended to describe the control of head-free gaze shifts. E*, angular rotation of the eye since onset of gaze shift; obtained by integrating the burst neuron (BN) output here assumed (incorrectly as our analysis will show) to encode eye velocity. H*, angular rotation of the head in space (or relative to body) since onset of gaze shift; obtained by integrating the canal input (or from propioceptive feedback from the head plant). T, desired angular rotation of visual axis in space (or relative to body). Difference between (E* + H*) and T provides an estimate of gaze motor error [g(t)]. E(t) and H(t), actual eye and head movements generated as a result of motoneuron (MN) signals passing through plant dynamics of the eye and head plants, respectively. BNs are thought to be gated by inhibitory projections from omnipause neurons (OPNs). As discussed in companion paper I (Cullen and Guitton 1997a), BNs can be analyzed from upstream and downstream perspectives. In this study we focused exclusively on predicting inhibitory BN (IBN) firing frequency based on downstream signals (indicated by the dotted box). We have investigated a series of models in which the spike train dynamics of the IBNs were described in terms of eye, head, and gaze (eye + head) trajectories. B, BNs;  , neural integrator; ?, unknown origin.
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An important conclusion of our analysis is that IBNs in the head-free primate carry both eye velocity () and head velocity () signals to the ABD and that vestibular projections to this motor nucleus are necessary to offset the signal. A further conclusion of our analysis is that head-fixed models are not adequate for predicting the discharges of primate IBNs during head-free gaze shifts.
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METHODS |
The neurons described in this study were obtained from the same two monkeys (Macaca fascicularis) whose IBNs were studied in the head-fixed condition and described in companion paper I (Cullen and Guitton 1997a). The surgical preparation of the animals and the methods used for obtaining extracellular recordings from IBNs were identical to those previously described in that paper. The same cells are analyzed in the present study, and as described in companion paper I, these neurons were categorized as IBNs on the basis of their physiological responses during head-fixed saccades, vestibular nystagmus, smooth pursuit, and their location in the IBN area.
Data collection and analysis
After we collected data from a neuron during saccadic eye movements made by a monkey with its head restrained, we carefully released the animal's head and attempted to continue recording the activity of the same cell during active orienting gaze shifts made with the head completely unrestrained. If the neuron was lost at this stage in the experiment (which occurred regularly), we again restrained the head and attempted to locate another IBN in the head-fixed condition. For neurons that remained well isolated during the head-free recording period, data were recorded while the monkey oriented to 1) a target light that was stepped between positions ±10, 20, and 35° relative to the straight ahead position and 2) a fruit target that appeared unexpectedly on either side of an opaque screen placed in front of the monkey. Gaze and head positions were recorded by using the magnetic search coil technique and stored on digital audio tape (DAT) tape with the recorded unit activity sampled at 20 kHz. We corrected for the nonlinearity in recorded eye movements, which was inherent to the measurement system, during off-line analysis. In head-free recordings the action potential amplitude frequently varied during a movement, probably because of slight movement of the electrode tip relative to the cell. Hence, it was important to review the data off-line to carefully monitor the shape of the unit spike wave form to guarantee an uncontaminated single unit recording. Off-line, the level of a windowing circuit was set by visual inspection at an appropriate level to generate a pulse coincident with the rising phase of the action potential. This pulse was sent to the event channel of the intelligent CED1401 (Cambridge Electronic Design) peripheral device, with the result that the event times of the spikes were logged by the computer along with the position signals, low-pass filtered (250 Hz, 8 pole Bessel), and sampled at 1,000 Hz.
During off-line analysis using Matlab, the sampled gaze- and head-movement traces were digitally filtered at 125 Hz (Cullen et al. 1996). A spike density function, in which a Gaussian function with a width of 5 ms was convolved with the spike train, was used to represent the neural discharge. This procedure assured that the frequency content of the movement and spike density traces were similar (see Cullen et al. 1996). Eye position was calculated from the difference between the recorded gaze and head position signals. Gaze, head, and eye velocities were derived digitally from position data. We considered only those gaze shifts in which the vertical position component was less than one-third of the entire amplitude; this assured the analysis of only nearly horizontal gaze movements. The onset and offset of the ocular saccade and head movement components of the gaze shift and the gaze shift itself were defined by using a 20°/s eye velocity criterion. In cases where the head continued to move slowly, long after the end of the gaze shift (>100 ms; in all cases the neuron had ceased firing), the head movement offset was set to the time 100 ms after the termination of the gaze shift. Burst duration was defined as the time between the onset and offset of the burst. Burst onset was defined as when the first spike of the burst occurred. Because these neurons frequently generated a few additional spikes after a saccade or gaze shift, burst offset was defined as when 95% of the spikes in the burst had occurred.
Models for BN firing rate
The goal of this analysis was to determine whether IBN discharges were best linked to gaze, eye, or head trajectories or a combination thereof. We employed system identification techniques (Cullen et al. 1996) to objectively analyze different models that relate the dynamics of spike trains to quantities describing gaze, eye, or head trajectories (e.g., velocity). The specific models are considered in RESULTS. The methods for parameter estimation were the same as those used in companion paper I (Cullen and Guitton 1997a). The gaze, eye, and head movements that occurred between the onset and offset of the gaze shift were used in our analysis. Model fits were carried out over the entire duration of the gaze shift, because IBNs continued to discharge throughout the gaze shift, even during the end portion where the eye had stopped moving and/or had reversed direction (Figs. 2 and 3). For each model, optimal fits were made to an ensemble of ~40 gaze shifts of different amplitudes between 10 and 70°. Models were ranked by noting whether a model provided an increase in the variance accounted for (VAF) as well as a simultaneous decrease in a cost index (the Bayesian information criterion, BIC) whose value will decrease for an increasingly complex model only when the addition of parameters is warranted.
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| FIG. 2.
Behavior of typical short-lead IBN (SLIBN; L0702) during 3 combined eye-head gaze shifts in the ipsilateral direction. Gaze position (G) = visual-axis-in-space = eye-in-head (E) + head-in-space (H). Note that the neuron continued firing throughout entire duration of gaze shift, even during periods in which eye (E) was stationary in orbit and/or had reversed direction. Dotted vertical lines, onset and offset of gaze shift; SD, spike density;  , , and , gaze, eye and head velocity, respectively.
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| FIG. 3.
Behavior of typical long-lead IBN (LLIBN; H0409) during three combined eye-head gaze shifts in ipsilateral direction. LLIBNs, like SLIBNs, continued to discharge throughout entire duration of a gaze shift. Abbreviations are the same as those used in Fig. 2.
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RESULTS |
In this study we consider the same population of 28 IBNs whose activity during saccadic eye movements made by the head-fixed monkey was presented in companion paper I (Cullen and Guitton 1997a). Here we specifically investigate the nature of the relationship among the discharge of these cells and the eye, head, and gaze movements generated during voluntary combined eye-head gaze shifts.
General discharge characteristics
We retained the same classification of short-lead IBNs (SLIBNs; n = 16) and long-lead IBNs (LLIBNs; n = 12) used in companion paper I (Cullen and Guitton 1997a), so as to be compatible with our analysis in that paper and with Scudder et al. (1988). Recall that the mean period between the onset of the first spike and the onset of eye velocity during head-fixed saccades was taken as 
15 ms for SLIBNs and >15 ms for LLIBNs. In this paper we will use the same example neurons as in companion paper I.
Figure 2 demonstrates the discharge of our typical SLIBN (L0702) that accompanied gaze shifts made with coordinated eye and head movements by the head-free monkey. As determined in companion paper I (Cullen and Guitton 1997a), during head-fixed saccades the first spike in this neuron's discharge led ipsilateral saccadic eye movements on average by 15 ms; the duration of its burst was tightly correlated with saccade duration (slope = 1.0; correlation coefficient R = 0.94); and the total NOS generated during a burst was well correlated with the amplitude of the horizontal component of eye saccades (slope = 0.95; R = 0.79). During head-free gaze shifts this cell's discharge led ipsilateral gaze movements on average by 14 ms, and the duration of the burst was better correlated with the duration of the entire gaze shift than with the duration of the ocular saccade(R = 0.97 vs. 0.84). The strong correlation between burst and gaze duration is particularly evident in the middle column of Fig. 2. The cell continued to fire until the gaze shift had ended even though the eye movement reached a position limit (plateau) where the eye velocity was near zero (i.e., the rapid ocular saccade had ended) and the final portion of the gaze shift was generated by the head movement alone. In other gaze shifts this cell continued firing until the end of the gaze shift, despite the fact that the eye movement actually reversed its direction before gaze stabilized.
Figure 3 illustrates the behavior of our typical LLIBN (H0409) during three example head-free gaze shifts. In the head-fixed condition, this IBN generated a burst of firing whose first spike led ipsilateral saccadic eye movements by 51 ms; the total NOS generated during a burst was proportional to the horizontal component of the saccade (slope = 1.0; R = 0.85) and the duration of its burst was correlated with the duration of the saccade (slope = 0.88; R = 0.57). During head-free gaze shifts, the first spike in this cell's discharge led ipsilateral gaze movements on average by 54 ms, and the duration of the entire discharge (prelude + burst) was as well correlated with the duration of the entire gaze shift as with the duration of the ocular saccade component (R = 0.77 vs. 0.76). The inability of discharge duration to specify whether gaze or eye is being encoded by this LLIBN is typical of these cells and, as will be seen later, is due to "noise" created by the prelude discharge. In the three examples illustrated in Fig. 3, the cell continued to fire until the gaze shift ended even in the plateau phase when eye velocity was near zero. This result was similar to the SLIBN described previously. Indeed, all the IBNs we recorded discharged during the plateau phase of the eye movement and throughout the terminal portion of the gaze shift where the eye movement actually reversed its direction.
As noted in companion paper I (Cullen and Guitton 1997a), the IBNs we recorded burst most robustly for ipsilateral "ON-direction" (OND) saccades and discharged far less, if at all, during pure vertical and contralateral "OFF-direction" (OFFD) saccades. Figure 4 compares, by using the same scale, the gaze OND and OFFD responses for neurons L0702 and H0409, introduced in Figs. 2 and 3, and neuron H0925, to be considered in a subsequent section. The former two cells had negligible OFFD discharges in both the head-fixed and -free conditions. The latter neuron was unusual in that its direction tuning curve was located well above zero during contralaterally directed saccades. This cell had the best OFFD responses in our population for both the head-fixed and head-free conditions. Note in Fig. 4 the clear correlation for this cell between firing frequency and gaze velocity in the ONDs and OFFDs. We will consider this phenomenon more quantitatively in a subsequent section.
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| FIG. 4.
IBN firing rate during ON-direction (OND) and OFF-direction (OFFD) gaze shifts for 3 example IBNs (SLIBN L0702 and LLIBNs H0409 and H0925). A and B: units L0702 and H0409 were typical of 1/2 of the cells in our population. There was a strong similarity between trajectories of neurons' firing frequency and horizontal gaze velocity during gaze shifts directed ipsilateral to the recording site in the cell's OND. In contrast, these cells discharged few, if any, spikes during contralateral gaze shifts in cell's OFFD. C: by comparison, unit H0925 demonstrated robust OFFD response that resembled an attenuated version of OND response. Response of this cell was a particularly striking example of behavior of the other1/2 of cells in our population that demonstrated a substantial OFFD response. Abbreviations are the same as in Fig. 2. Vertical calibration bar denotes 400 spikes/s, 400°/s, and 40°.
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We employed the same technique, as those used in our head-fixed analysis, to obtain an accurate measure of each IBN's optimal direction with respect to the direction of both the ocular component of the saccade and the entire gaze shift (Fig. 5). Each neuron's optimal direction was calculated by fitting a nonlinear function to relate the NOS in the unit discharge to polar angle of the gaze and eye movements. The gaze shift amplitudes used to determine the preferred direction ranged from 30 to 40°. Example fits are illustrated for LLIBN H0409 in the inserts in Fig. 5, A and B (eye and gaze, respectively). As in the case of head-fixed saccades, the IBNs fired most strongly in relation to eye movements directed ipsilaterally and closely aligned with the horizontal plane (Fig. 5A). Likewise, IBNs fired preferentially for gaze shifts aligned with the horizontal plane (Fig. 5B). The mean OND of the IBNs was 3.5 ± 21.1° (SD) and 1.9 ± 18.8° with respect to eye and gaze movements, respectively. This result can be compared with the value 1.0 ± 15.2° found in the head-fixed condition. In the present analysis the calculated preferred directions (relative to either gaze or eye movements) varied somewhat more than in the head-fixed analysis (gaze: 51° upward to 68° downward); however, this additional variance was accounted for by only two neurons (7% of our sample). As in the previous study (Cullen and Guitton 1997a) the population average of preferred directions approximated well the ipsilateral horizontal; consequently, the subsequent analyses in this study were confined to gaze, eye, and head movements directed horizontally or nearly so (see METHODS).
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| FIG. 5.
Preferred direction of each of the IBNs in our population is illustrated in polar coordinates; the length of the vector indicates the sensitivity of each IBN measured in spikes/deg as indicated by scale to left of each panel. A: average preferred direction (heavy arrow) of our sample of IBNs was aligned with ipsilateral eye movements that were directed 4° above horizontal. Inset: direction tuning of example IBN (LLIBN H0409) is illustrated by a plot of the number of spikes (NOS) vs. eye movement direction. B: average preferred direction (heavy arrow) of the entire sample of IBNs was aligned with 2° of ipsilateral gaze displacement. Inset: direction tuning of LLIBN H0409 is illustrated by a plot of the NOS vs. gaze direction. Gaze shifts included in analysis ranged from 30 to 40°. Optimal direction for this cell was determined by fitting data to a sum of 2 sinusoids by using nonlinear least squares.
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Estimation of lead time
The time by which a BN's discharge led a gaze shift was calculated by the two methods used in companion paper I (Cullen and Guitton 1997a). Briefly, lead time was determined by 1) calculating the period between the onset of the first spike and the onset of gaze velocity and 2) shifting the unit discharge in time td until an optimal model fit (i.e., the maximal VAF) was obtained for the simple dynamic model
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(1)
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where r is a bias term, b1 is a gain term, and 
is the input that can either be eye, head, or gaze velocity.
Figure 6 shows the results of applying the latter procedure to cell L0702. The relationship among VAFs obtained by Eq. 1 and lead times used relative to td are illustrated. The values of optimal dynamic latency td for this cell were 12, 11, and 13 ms for the eye-, head-, and gaze-based model fits, respectively. The figure shows that a clear maximum VAF can be identified for eye-, head-, and gaze-based versions of Eq. 1. It is important to note that correlations between the entire profile of the temporally shifted burst and the gaze or eye movement trajectories, not only the beginning of the burst, were used to determine the optimal value of td. Lead times on each trace are indicated that would be coincident with the onset of the burst relative to the indicated movement (
).
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| FIG. 6.
Decreasing variances accounted for (VAFs) that arise when burst is shifted by times other than the optimal. Data are illustrated for cell L0702. Optimal dynamic lead time td is defined as value for which maximal VAF is obtained using model 2d (Eq. 1) to fit the firing frequency profile. Values of td for this cell were 12, 11, and 13 ms for eye-, head-, and gaze-based models 2d, respectively. A clear optimal lead time value (latency = 0 on the abscissa) can be identified for each eye, head, and gaze model. Arrow, lead times that would correspond to the burst not being shifted in time relative to each component.
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The onset of gaze and eye movements are coincident in most gaze shifts because the early portion of the gaze shift is dominated by the eye movement. Therefore the onset of gaze and eye velocity can be considered to be equivalent. The distributions of lead times determined from the difference in timing between the onset of the first spike and the onset of gaze (or eye) velocity are shown in Fig. 7A. The distributions of the dynamic lead times that were estimated by using either eye or gaze velocity, respectively, as input to Eq. 1 are illustrated in Fig. 7, B and C. A comparison of the histograms in Fig. 7, C and B, with that in Fig. 7A reveals that the dynamic lead times have a much narrower distribution than those based on the first spike.
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| FIG. 7.
Histograms illustrating lead time by which IBN discharges led head-free gaze shifts. Lead times were obtained via 2 methods. A: time between onset of 1st spike and onset of gaze shift. By using this method, the onset of 1st spike led the onset of gaze shift by 21.0 ± 11.4 ms. B and C: to obtain an estimate of IBNs' dynamic lead time, unit discharge wasshifted in time until an optimal model fit was obtained for model 2d, [B(t) =R + b1], where = eye velocity in B and gaze velocity in C. By usingthis method, the BN discharge led gaze velocity and eye velocity by 12.6 ±2.9 ms and 13.7 ± 3.6 ms, respectively. Measures of dynamic lead time in (B) and (C) provided, in general, lower values of lead time than conventional method that utilized the onset of 1st spike (A). N, total number of neurons.
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Table 1 shows a comparison of the average lead times for SLIBNs and LLIBNs obtained by the first-spike and dynamic lead time methods. These numbers can be compared either along rows (for each neuron group, the first-spike method vs. the dynamic method) or along columns (for each method the difference between SLIBNs and LLIBNs). Let us first consider the rows in Table 1. In our accompanying head-fixed study, lead times for LLIBNs determined by the onset of the first spike were significantly longer than dynamic lead times. The values were comparable for SLIBNs. For head-free gaze shifts, the dynamic lead times (both gaze and eye velocity based) were significantly less (P < 0.005) for both SLIBNs and LLIBNs than mean lead times determined from the onset of the first spike. For the combined SLIBN and LLIBN groups, the first spike in the discharge led head-free gaze shifts on average by 21.0 ± 11.4 ms, (see also Fig. 7A) whereas the dynamic lead time analysis gave 12.6 ± 2.9 ms (Fig. 7B) and 13.7 ± 3.6 ms (Fig. 7C) for eye and gaze inputs, respectively. For the columns in Table 1, as in the case of head-fixed saccades, the estimated dynamic lead times (either gaze or eye velocity based) for SLIBNs were significantly less (P < 0.005) than those estimated for LLIBNs (gaze input, 11.7 ± 2.4 vs. 16.5 ± 3.1; eye input, 11.1 ± 2.7 vs. 14.8 ± 2.1).
For head-free gaze shifts, the relationships among the dynamic lead times that were calculated on the basis of gaze and eye velocity and those determined by the onset of the first spike are compared for each neuron in Fig. 8. The dynamic lead time was better correlated with the lead time of the first spike when the dynamic model was gaze velocity based (R = 0.87) than when it was eye velocity based(R = 0.78). Furthermore, the slope of the linear regression line was <1 because, as also shown in Fig. 7, the range of dynamic lead times was much less than that based on the onset of first spike.
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| FIG. 8.
Relationship between lead time values obtained by 2 separate methods used in this study (see text). Dynamic lead times calculated by using both eye- ( ) and gaze- ( ) based models were well correlated with lead times determined with onset of 1st spike (R = 0.78 and 0.87, respectively). This result indicates that neurons that began to fire just before gaze shifts tended to have shorter dynamic lead times than those IBNs with longer preludes.
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When the onset of the first spike was used to determine lead times, the values determined for head-free gaze shifts were well correlated (R = 0.89) but significantly larger (P < 0.005) than those determined for head-fixed saccades across our sample of neurons (Table 1). However, the significantly greater first-spike lead time during head-free versus head-fixed gaze shifts was not accompanied by corresponding differences in the estimated dynamic lead times. A comparison of the lead times calculated in head-fixed and -free conditions for each unit further revealed that the head-free dynamic lead time was not particularly well correlated with the head-fixed value(R = 0.54, gaze-based model; R = 0.66, eye-based model). This observation probably reflects the fact that the estimated values of dynamic lead times (gaze- and eye-based) for all neurons were rather similar and consistently covered a small range (~12 ms) compared with the broad range (~52 ms) determined by using the onset of the first spike.
Relationships between IBN activity and saccade metrics
For the head-fixed condition we reported significant relationships between NOS in the IBN burst and saccade amplitude and between burst duration and saccade duration. We now consider analogous relationships in the head-free condition. These relationships are summarized in Table 2 and Fig. 9 and to facilitate comparison, data from the head-fixed analysis of the same population of neurons are included in the table.
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| FIG. 9.
Relationships among burst duration and duration of ocular component of gaze shift (A), duration of head movement (B), and duration of entire gaze shift for our population of SLIBNs (C; see Table 1). Heavy lines, average regression fit for all SLIBNs. Inset: data for example SLIBN L0702. Relationship among burst duration and duration of ocular component of gaze shift (D), duration of head movement (E), and duration of entire gaze shift for our population of LLIBNs (F). Heavy lines, average regression fits for all LLIBNs (see Table 1). Inset: data for example LLIBN H0409.
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BURST DURATION VERSUS EYE, HEAD, OR GAZE DURATION.
Figure 9, A-C shows regression plots of burst duration versus ocular saccade duration, head movement duration, and gaze shift duration for each SLIBN. Insets show data for SLIBN L0702. Table 2 shows average values. In general, burst duration (DB) was well correlated with both gaze (Dg) and (De) eye saccade duration (mean R = 0.90, range = 0.73-0.98; R = 0.90, range = 0.61-0.99, respectively) whereas the correlation between head (Dh) and burst duration was significantly poorer (R = 0.63, range = 0.39-0.86). The mean intercept values calculated in the head-free analysis of burst duration versus either gaze (19.8) or eye saccade (10.0) duration were not significantly different from the intercept value (10.6) calculated in the head-fixed analysis of burst versus eye saccade duration. Furthermore, the average slope of the SLIBN burst-gaze saccade duration relationship (0.81) was not significantly different from that observed during head-fixed saccades (0.87). By comparison, the mean slope of the relationship between burst duration and head-free saccadic eye movement duration (0.95) was significantly higher (P < 0.005) than that observed during head-fixed saccades. In summary, according to these tests the head-free relation between burst and gaze shift duration was statistically similar to the head-fixed SLIBN burst eye saccade duration relationship.
The results obtained for LLIBNs are shown in Table 2 and Fig. 9, D-F. Insets show data for cell H0409. As was the case for SLIBNs, LLIBN burst duration was well correlated with both gaze and eye saccade duration (mean R = 0.85, range = 0.68-0.97; R = 0.85, range = 0.71-0.95, respectively), whereas the correlation between head movement and burst duration was significantly poorer (R = 0.58). The mean slope of the burst-gaze saccade duration relationship (0.80) was significantly smaller (contrary to that found for SLIBNs), and the mean slope of the burst eye saccade duration relationship (1.07) was significantly larger than that observed during head-fixed saccades (0.97; P < 0.005). The intercept calculated in the head-free analysis of burst versus eye saccade duration (26.2) was closest to the head-fixed intercept (26.5). In summary, for LLIBNs no head-free relations were statistically similar to the head-fixed relations.
When the entire population of IBNs was considered, the slope of the relationship between burst and eye saccade duration head-fixed (0.91) was halfway between the head-free gaze (0.80) and eye (1.00) slopes. The population head-free eye intercept was the most similar to the head-fixed value. We conclude, from our analysis of burst duration, that this quantity does not indicate clearly whether IBNs as a population discharge for the duration of either saccadic gaze or eye motion. This ambiguity is due to the noise attributable to the preamble discharge in LLIBNs and the very similar durations of the eye and gaze saccades. However, when a clear distinction is available between the end of the eye saccade and gaze saccade, as in the middle panel of Fig. 2, then the burst clearly continues for the duration of the gaze shift and exceeds saccade duration.
NOS VERSUS EYE, HEAD, OR GAZE AMPLITUDE.
In our head-fixed analysis of IBNs we reported a robust correlation between NOS in the discharge and the horizontal amplitude of the ocular saccade. Figure 10 illustrates for the head-free condition the relationship between NOS and the amplitudeof the eye (ocular; top), head (middle), and gaze (bottom) components of gaze shifts for SLIBNs (Fig. 10, A-C) and LLIBNs (Fig. 10, D-F). Insets show data for the examples SLIBN (L0702) and LLIBN (H0409). Table 2 gives mean values. For SLIBNs, the NOS was best correlated with the amplitude of the entire gaze shift (mean R = 0.73) than with the amplitude of the eye (R = 0.62) and head (R = 0.59) components. Indeed, the NOS in a burst was better related to gaze than eye amplitude for 82% of the cells in this study. In addition, it is interesting to note that the NOS generated by SLIBNs was nearly as well related to gaze amplitude during head-free gaze shifts as to saccade amplitude during head-fixed saccades (mean R = 0.73 vs. 0.79, respectively). Note that the mean slope (0.89 NOS/deg) of the relationship between NOS and gaze amplitude was significantly less than that observed for saccades made head-fixed (1.1 NOS/deg, P < 0.005). By comparison the mean slope of the relationship between NOS and the amplitude of the ocular component of a head-free gaze shift (1.3 NOS/deg) was significantly larger than that observed during head-fixed saccades. The intercept values calculated in the head-free analysis of NOS versus gaze amplitude and NOS versus eye amplitude were similar and significantly greater (P > 0.005) than that calculated in the comparable head-fixed analysis.
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| FIG. 10.
A-C: SLIBNs. Relationships among NOS in a burst and amplitude of ocular component of gaze shift (A), amplitude of head movement (B), and amplitude of gaze shift (C). Heavy lines, average regression fit for all SLIBNs (see Table 1). Inset: data for example SLIBN (unit L0702). D-F: LLIBNs. Relationships among NOS in a burst and amplitude of ocular component of gaze shift (D), amplitude of head movement (E), and amplitude of gaze shift (F). Heavy lines, average regression fit for all LLIBNs (see Table 1). Inset: data for example LLIBN (unit H0409).
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Results obtained from the analysis of LLIBNs (Fig. 10, D-F) yielded similar results. The NOS in a burst was best correlated with the amplitude of the entire gaze shift (R = 0.68) and more weakly correlated with the amplitude of the eye and head components (R = 0.60 and 0.53, respectively). The NOS gaze amplitude correlation was not as good as that obtained head-fixed. The slope of the relationship between NOS and gaze amplitude (0.65 NOS/deg) was significantly less than that between NOS and the amplitude of saccades made head-fixed (0.95 NOS/deg, P < 0.05). Unlike SLIBNs, however, there was no significant difference in the slopes of the relationship between NOS versus ocular saccade amplitude during head-free gaze shifts and head-fixed saccades.
When data from the entire population of IBNs were combined, NOS was best related to gaze amplitude (R = 0.71, range = 0.26-0.86) and more weakly correlated with eye amplitude (R = 0.61, range = 0.15-0.87) and head amplitude (R = 0.57, range = 0.21-0.84). Furthermore, the slope of the relationship NOS versus amplitude was significantly lower for gaze (0.79 NOS/deg) and higher for eye amplitude (1.14 NOS/deg) than it was in the corresponding head-fixed relationship (1.03 NOS/deg). We conclude from our analysis of NOS that this quantity is best correlated to head-free gaze shift amplitude, and furthermore the correlation coefficients for head-free gaze and head-fixed eye saccades are nearly the same. These results suggest that NOS encodes gaze amplitude, but note that the slope NOS/deg for head-free gaze is less than that for head-fixed eye.
NOS VERSUS EYE AND HEAD AMPLITUDE.
In general, the results of the foregoing analysis of the relationships between primate IBN discharges and the metrics of head-fixed saccades and head-free gaze shifts bear a striking resemblance to our previously published results in the cat (Cullen et al. 1993). We can probe further the question of whether the discharges of our IBNs were gaze related by carrying out a multiple regression analysis. For this analysis we fit the following equation
where a, b, and g are constants and E and H represent the amplitude of the eye and head components at the end of the gaze shift, respectively. The results of this analysis are illustrated in Table 2. If the IBNs in our study were gaze related, then the values of b and g should be nearly equal. We found that this was, in fact, the case; there was no significant difference between the values of b and g estimated for either SLIBNs (1.00 ± 0.58 vs. 0.78 ± 0.39), LLIBNs (0.77 ± 0.31 vs. 0.54 ± 0.44), or the entire population of cells (0.90 ± 0.49 vs. 0.68 ± 0.42). In addition, there was only a slight improvement in the correlation coefficient (Table 2, mean R = 0.75) versus the value obtained in our prior analysis of the relationship between NOS and gaze amplitude (Table 2, mean R = 0.71). Finally, there was no significant difference between the values of the y-intercept obtained from this multiple regression analysis (Table 2, 14.0 ± 9.3) and that obtained from the comparable head-fixed relationship, NOS versus saccade amplitude (Table 2, 10.4 ± 4.2). Taken together, these findings lend support to the hypothesis that the discharges of IBNs are gaze related during head-free gaze shifts. This hypothesis is examined in more detail in the next section and the implications of these findings are addressed in the DISCUSSION.
Dynamic models of IBN discharge during head-free gaze shifts
GAZE- VERSUS EYE-BASED DYNAMIC MODELS.
We investigated the same downstream models as those studied in companion paper I (Cullen and Guitton 1997a), but now IBN spike train dynamics were estimated by using either gaze, eye, or head movement trajectories as inputs. We will show in a later section that head movement parameters were poor (as might be concluded from the poor relationship between head movement amplitude and NOS shown in the previous analysis) at predicting burst dynamics, so we focused on the link between burst and either eye or gaze parameters. Three representative models along with the average parameter values associated with either gaze or eye motion as inputs are listed in Tables 3 (models 1d, 2d, and 7d). The numbering of each model corresponds to that of the comparable model tested in companion paper I (Cullen and Guitton 1997a). The parameter estimation methods were described in detail elsewhere (Cullen et al. 1996). In the analysis of all models that were tested we found that there were no notable differences between the averaged VAF and BIC values for the subpopulations of SLIBNs and LLIBNs. Therefore in our description of model fits we will consider average values for the entire population of IBNs.
The simplest model: is firing frequency proportional to eye or gaze velocity? The results of applying the most simple model in our series of downstream models (Table 3, model 1d) to the analysis of head-free IBN discharges are illustrated in Fig. 11 for cell L0702. For this neuron and all others in our study model 1d was much better at predicting the dynamics of IBN firing when gaze velocity, rather than eye velocity, was the model input. The IBN continued firing throughout the entire gaze shift (onset and offset indicated by vertical dotted lines) although eye velocity sometimes approached 0°/s
the so-called plateau phasemore than 100 ms before the gaze shift ended. This is particularly evident in the middle column where eye velocity also reversed direction just before the gaze shift ended. The firing rate predicted from eye velocity was much too low, starting particularly from the middle of the gaze shift onward.
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| FIG. 11.
Examples of model fits to SLIBN (L0702) firing frequency during head-free gaze shifts. Shaded trajectories, unit firing frequency profiles; superimposed curves, fit produced by each model. Top panel: simple modelB(t) = b1 produced significantly better fit (heavy line) of the actual firing rate (shaded curve) than the model B(t) = b1 (2nd panel). Values of parameters, estimated by using >40 gaze shifts, provided below each model fit for this neuron. Bottom traces: accompanying gaze and eye velocity trajectories shifted in time by estimated optimal dynamic lead time td.
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The VAF and BIC for model 1d are listed in Table 4 for short-lead, long-lead, and the combined population of IBNs. (The values for the parameters in Table 3 will be considered in the DISCUSSION where we will evaluate their physiological significance as well as their relation to the head-fixed data.) A comparison of the VAF values indicates, not surprisingly after viewing Fig. 11, that the gaze velocity-based model 1d provided a substantially better prediction of IBN firing than the eye velocity-based model (population meansVAF = 0.04 vs. 0.35, respectively). Note, however, the negative VAFs. Thus in spite of the better gaze prediction, as in the case of head-fixed saccades, this simple model was objectively poor at predicting the firing behavior of IBNs. Indeed, the negative VAF, for both SLIBNs and LLIBNs, when either gaze or eye velocity were the model inputs, indicates that the fit was worse than that about a constant mean value.
Importance of a bias term to gaze and eye velocity-based models. The addition of a bias term (r) to model 1d resulted in model 2d (Table 3) and greatly improved the prediction of IBN firing in both gaze and eye velocity-based models. This result is the same as that found in our preceding analyses of these neurons during head-fixed saccades. Comparison of Fig. 12 with Fig. 11 illustrates for cell L0702 the improvement in the fit of this SLIBN's firing rate that accompanied the addition of a bias term when either gaze or eye velocity was the input to the model. (Note the different bias values in these 2 cases.)
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| FIG. 12.
Model fits to SLIBN (L0702) activity for same 3 example gaze shifts illustrated in Fig. 11. When bias term was added to model illustrated in Fig. 11 there was a significant improvement between goodness of the model fit when either gaze (top panel) or eye (2nd panel) velocity were used as inputs to model. Values of the parameters, estimated by using >40 gaze shifts, provided below each model fit. Gaze- and eye-based models provided comparable fits to data; however, bias term estimated when gaze velocity was input was similar to that estimated for the head-fixed data (for this example neuron, mean 184 vs. 175) (see companion paper I Cullen and Guitton 1997a), whereas that estimated when eye velocity was input was significantly larger (255).
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The VAF increased substantially from 0.04 to 0.20 for the gaze velocity-based model 2d, and from 0.35 to 0.22 for the eye velocity-based model (Table 4). There was no significant difference between the ability of the gaze and eye velocity-based models to predict the firing discharge of IBNs. In effect, the addition of a bias to the model effectively permitted the velocity term in the eye velocity-based model to contribute to predicting the modulation of the IBNs discharge once the eye had reversed direction toward the end of the gaze shift (Fig. 12). Model 2d provided a fit of the IBN spike trains that was as good, on average, as that described by a correlation coefficient (R) of 0.46 in a linear regression analysis. The accompanying relatively important decrease in the average BIC value between models 1d and 2d [population means 10.07 vs. 9.54 (gaze) and 10.56 vs. 9.50 (eye)] states that the addition of a bias term to both the eye and gaze models was warranted. It should be noted, however, that whereas the bias value estimated for the gaze model was comparable to that determined for head-fixed saccades (222.9 ± 96.6 vs. 222.6 ± 64.6, respectively), the bias value estimated for the eye model was significantly larger (279.3 ± 107.9; P < 0.005). The reasons for this are due to the influence of head velocity and will become evident in the DISCUSSION.
Importance of acceleration, higher-order nonlinear and position terms. As was the case in the dynamic analysis of IBN discharges during head-fixed saccades, the addition of acceleration, higher-order velocity, and position terms to model 2d had little effect on increasing the VAF (or decreasing the BIC) of either gaze or eye velocity-based head-free models for the population of IBNs. The addition of an acceleration term to model 2d resulted in no change in the VAF (0.20 for gaze-based models; 0.22 for eye-based models). Furthermore, when higher-order terms (squared and cubed velocity terms) as well as an acceleration term were added to model 2d (to approximate the nonlinearity proposed by Van Gisbergen et al. (1981) the VAF only increased very slightly (0.22 for gaze-based models; 0.24 for eye-based models). Finally, the addition of a position term to model 2d did not produce a marked improvement in model fits for either gaze- or eye-based models (VAF = 0.21 and 0.23, respectively). Consequently, as in the case of the head-fixed analysis, in downstream head-free models it appears that the bias term is much more critical than either acceleration, higher-order velocity, or position terms for representing IBN discharges.
Estimation of pole term, initial conditions, and variable bias. The addition of a pole term (the derivative of the IBN firing rate) and acceleration term to model 2d improved the model fits slightly when initial conditions (ICs) were taken directly from the data parameters (VAF = 0.25 for gaze-based models; 0.27 for eye-based models). However, the ability of this model to estimate IBN discharges improved considerably when ICs were estimated as parameters(VAF = 0.43 for gaze-based models; 0.43 for eye-based models). Such a model is comparable to model 6d in our investigation of head-fixed models (companion paper I, Cullen and Guitton 1997a). It is important to note that this model required a large number of additional parameters, because a separate IC was estimated for each gaze shift. As was the case in our accompanying investigation of head-fixed model 6d, an important limitation of the pole-term model was that the estimated bias was highly variable and most often a large negative value (mean bias = 2,147 ± 4,314 vs. 1,166 ± 3,145 for gaze- and eye-based models, respectively). As discussed in companion paper I, it is unlikely that such a large negative bias has any physiological significance.
The value of model 6d in companion paper I (Cullen and Guitton 1997a) was that it led to model 7d and ultimately to 8d. Accordingly, we also tested model 7d using eye or gaze inputs (Table 3). For this model the bias term was estimated separately for each gaze shift. The method of parameter estimation was less complex than it was for models that include a pole term for which the ICs are estimated as parameters (see Cullen et al. 1996), although the number of parameters is comparable. Model 7d provided significantly better fits than model 2d (Table 4: VAF = 0.40 for gaze-based models; 0.40 for eye-based models). Comparison of Fig. 13 with Figs. 11 and 12 illustrates for cell L0702 the impressive fit of IBN firing rate that accompanied the addition of a variable bias by using model 7d. As was the case for model 2d, the mean bias value estimated for the gaze-based model was comparable to that determined for head-fixed saccades (209.2 ± 91.1 vs. 222.5 ± 65.3, respectively), whereas the bias value estimated for the eye-based model was significantly larger (274.5 ± 109.4; P < 0.005).
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| FIG. 13.
Model fits to SLIBN (L0702) activity for same 3 example gaze shifts illustrated in Figs. 11 and 12. When model included velocity and variable bias terms there was significant improvement between goodness of the model fit when either gaze (top panel) and eye (2nd panel) velocity was input to model. Gaze- and eye-based models provided comparable fits to data. Values of parameters, estimated by using >40 gaze shifts, provided below each model fit. Values of rk listed represent the bias estimated for each of 3 gaze shifts. Mean of the variable bias term estimated when gaze velocity was input was similar to that estimated from the head-fixed data (for this example neuron mean 181 vs. 169) (see companion paper I, Cullen and Guitton 1997a), whereas mean bias estimated when eye velocity was input was significantly larger (244).
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Dependence of ICs and/or biases on gaze shift metrics. In our head-fixed investigation we demonstrated that for 50% of our cells the estimated ICs in model 6d (Table 2, companion paper I, Cullen and Guitton 1997a) and the estimated bias terms in model 7d (Table 2, companion paper I) were correlated with the metrics of saccades. In the head-free analysis of these neurons we found a similar phenomenon; the estimated ICs and/or biases were correlated with the metrics of eye and gaze saccades, for gaze-based models in 5 of 16 SLIBNs and 9 of 12 LLIBNs (
50% of the whole population). Seventy-one percent of the cells (5 of 9 SLIBNs and 5 of 5 LLIBNs) that demonstrated head-fixed correlations between saccade metrics and ICs (and/or variable biases) also demonstrated correlations between eye and gaze saccade metrics and these parameters in the head-free models 6d and 7d. The best correlations were between the bias term of the gaze-based model (rkg) and eye and gaze saccade amplitudes. Significant correlations were also found with peak eye and gaze saccade velocity, but it is well known that eye-gaze amplitude and velocity are correlated during gaze shifts. By comparison, the estimated ICs or biases were correlated with the metrics of ocular and gaze saccades for eye-based head-free models 6d and 7d in only 2 of 16 SLIBNs and 4 of 12 LLIBNs (21% of the population).
Some of these relationships are illustrated in Fig. 14 for the same example IBN (H0925) shown in companion paper I (Cullen and Guitton 1997a). For this neuron the estimated bias term (rkg) in gaze velocity-based model 7d was well correlated with eye and gaze saccade amplitudes (Figs. 14, A and B; , amplitudes >10°; R = 0.54 and 0.57, respectively) but much less to peak gaze velocity (Fig. 14C; R = 0.39). By comparison, the bias term (rke) in eye velocity-based model 7d was only weakly correlated with eye amplitude (Fig. 14D; R = 0.33) and even more poorly related to peak eye velocity (not shown, R = 0.13). The filled symbols in Fig. 14, A and B are for gaze shifts accompanied by some head motion(), generally for gaze amplitudes >10°. We also analyzedsmaller gaze shifts (<10°) for which the head, although completely unimpeded, did not move. These points (open symbols) lie near the head-fixed line [- - -; taken from our analysis in companion paper I (Cullen and Guitton 1997a)] for this cell, suggesting a nonlinear bias versus gaze amplitude relationship related to the nonlinear contribution of head motion to gaze amplitude. This finding is further addressed in the following section.
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| FIG. 14.
Analysis of relationship between multiple biases (in model 7d) for LLIBN H0925 during head-free gaze shifts. Estimated bias term (rkg) in gaze velocity-based model 7d was correlated with eye (A) and gaze (B) amplitudes but much less to peak gaze velocity (C). In contrast, the bias term (rke) in eye velocity-based model 7d was only weakly correlated with eye amplitude (D). Filled squares and circles, bias values for gaze shifts accompanied by some head motion; open square, bias values for small gaze shifts in which the head did not move; solid line, fit through filled squares and circles; dashed line, taken from Fig. 13C of companion paper I (Cullen and Guitton 1997a) and shows bias values in head-fixed condition. Note that the open square lie near this line. Majority of cells (71%) that demonstrated head-fixed correlations among saccade metrics and variable biases also demonstrated correlations between eye and gaze saccade metrics and biases in head-free condition.
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We also investigated the relationships between the estimated ICs and/or biases and the position of either gaze or eye immediately before and after the saccade. Only two IBNs demonstrated a relationship; this was between ICs or biases (models 6d and 7d, gaze and eye velocity-based) and the initial position of the eye before the onset of the gaze shift.
EYE- AND HEAD-BASED DYNAMIC MODELS.
We showed in the previous section that only model 1d showed a significant difference in VAF between gaze-based and eye-based models (Table 4; VAF = 0.04 vs. 0.35, respectively). However, the mean VAF values that were obtained using model 1d were negative, indicating that neither gaze- nor eye-based models provided a useful description of IBN discharges. In models that included a bias term, including models 2d and 7d, the bias value estimated for gaze-based models was comparable to that in our head-fixed analysis, whereas that estimated for the eye-based models was significantly larger. One possible explanation for this result is that the increased bias required in the eye-based models reflected an unmodeled head velocity input onto these neurons. To further investigate this possibility, the difference in bias obtained in gaze- and eye-based models (model 7d) was compared with the mean head velocity during each gaze shift. We found that, for our sample of cells, the difference in biases was very strongly correlated with the mean head velocity during each gaze shift (R = 0.93 ± 0.15). This relationship is demonstrated for a typical neuron in Fig. 15. Based on these results we investigated a second series of models that include linear combinations of separate eye and head velocity terms (Table 5). These models address objectively the issue of whether IBNs carry both eye and head velocity signals during head-free gaze shifts.
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| FIG. 15.
Difference between biases (rk, model 7d) estimated in gaze- and eye-based models plotted as function of mean head velocity during gaze shift for LLIBN H0925. This cell was typical of all cells in the study in that difference between estimated biases was very well correlated with the mean head velocity (R = 0.93).
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Simplest model: is firing frequency described by sum of independent eye and head velocity inputs? The results of applying the most simple model, based on the sum of independent eye and head velocity inputs (model 1d), is listed in Tables 5 and 6. In this model the estimated head velocity coefficient (1.37 ± 0.52) was significantly larger than the estimated eye velocity coefficient (0.96 ± 0.28; Table 5). In addition, the estimated head velocity coefficient was more variable across the cell population than was the estimated eye velocity coefficient. Although model 1d predicted better the dynamics of IBN firing when a linear combination of eye and head velocity were used (Table 6; VAF = 0.03) than when either gaze or eye velocity was the only input to the model (Table 4; VAF = 0.04 vs. 0.35, respectively), the mean VAF for model 1d with independent eye and head velocity terms was nearly zero. This result indicated that the fit of model 1d was not much more effective than a fit about a constant mean value.
Importance of bias term to models with independent eye and head velocity inputs. The addition of a bias term (r) to model 1d resulted in 2d (Table 5) and greatly improved the ability of models that include linear combinations of independent eye and head velocity terms to predict IBN discharges (Table 6; VAF = 0.23). This result is consistent with our preceding analyses of these neurons during head-fixed saccades (companion paper I Cullen and Guitton 1997a) and during head-free gaze shifts using gaze-based and eye-based models (see GAZE- VERSUS EYE-BASED DYNAMIC MODELS). In contrast to model 1d, the estimated head velocity coefficient (0.17 ± 0.42) was significantly less and more vari
Abstract
Introduction
Abstract
