1Neuroscience Research Institute, Electrotechnical Laboratory, National Institute of Advanced Industrial Science and Technology; 2Core Research for Evolutional Science and Technology, Japan Science and Technology, Ibaraki 305-8568; 3NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation, Kanagawa 243-0198; and 4Advanced Telecommunications Research Institute International, Kyoto 619-0288, Japan
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ABSTRACT |
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Takemura, Aya, Yuka Inoue, Hiroaki Gomi, Mitsuo Kawato, and Kenji Kawano. Change in Neuronal Firing Patterns in the Process of Motor Command Generation for the Ocular Following Response. J. Neurophysiol. 86: 1750-1763, 2001. To explore the process of motor command generation for the ocular following response, we recorded the activity of single neurons in the medial superior temporal (MST) area of the cortex, the dorsolateral pontine nucleus (DLPN), and the ventral paraflocculus (VPFL) of the cerebellum of alert monkeys during ocular following elicited by sudden movements of a large-field pattern. Using second-order linear-regression models, we analyzed the quantitative relationships between neuronal firing frequency patterns and eye movements or retinal errors specified by three parameters (position, velocity, and acceleration). We first attempted to reconstruct the temporal waveform of each neuronal response to each visual stimulus and computed the coefficients for each parameter using the least-square error method for each stimulus condition. The temporal firing patterns were generally well reconstructed [coefficient of determination index (CD) > 0.7] from either the retinal error or the associated ocular following response. In the MST and DLPN datasets, however, the fit with the retinal error model was generally better than with the eye-movement model, and the estimated coefficients of acceleration and velocity ranged widely, indicating that temporal patterns in these regions showed considerable diversity. The acceleration component is greater in MST and DLPN than in VPFL, suggesting that an integration occurs in this pathway. When we determined how well the temporal patterns of the neuronal responses of a given cell could be reconstructed for all visual stimuli using a single set of coefficients, good fits were found only for Purkinje cells (P- cells) in the VPFL using the eye-movement model. In these cases, the coefficients of acceleration and velocity for each cell were similar, and the mean ratio of the acceleration and velocity coefficients was close to that of motor neurons. These results indicate that individual MST and DLPN neurons are each encoding some selective aspects of the sensory stimulus (visual motion), whereas the P-cells in VPFL are encoding the complete dynamic command signals for the associated motor response (ocular following). We conclude that the sensory-to-motor transformation for the ocular following response occurs at the P-cells in VPFL.
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INTRODUCTION |
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Ocular following responses are
slow tracking eye movements evoked by sudden drifting movements of a
large-field visual stimulus in primates. These responses help to
stabilize the eyes on the visual scene. Experiments using monkeys have
revealed many features of ocular following (Kawano and Miles
1986; Miles and Kawano 1986
; Miles et al.
1986
). One of the most interesting features of ocular following
is that it has an observed latency of as short as 50 ms. Considering
the delays introduced in the retina and the ocular motor plant, the
intervening neural elements must be limited in sequential number,
suggesting that this system may be amenable to characterization at all
stages, from sensory input to motor output.
Previous studies have found that neurons in the medial superior
temporal (MST) area of the cortex (Kawano et al.
1994), the dorsolateral pontine nucleus (DLPN)
(Kawano et al. 1992
), and the ventral paraflocculus
(VPFL) of the cerebellum (Shidara and Kawano 1993
) of
the monkey respond with directional selectivity to movements of a
large-field visual stimulus. In most cases, their firing rate begins to
increase before the eye movement.
The MST sends strong projections to the DLPN (Brodal
1978; Glickstein et al. 1980
, 1985
;
Maunsell and van Essen 1983
; May and Andersen
1986
; Ungerleider et al. 1984
), and the DLPN
sends projections to the cerebellum, mainly to the flocculus
(paraflocculus) and lobules VI and VII of the vermis (Brodal
1979
, 1982
; Langer et al. 1985
). Recent
anatomical studies have shown that the DLPN sends only a light
projection to the flocculus. In contrast, DLPN projections to the VPFL
and dorsal paraflocculus are substantial (Glickstein et al.
1994
; Nagao et al. 1997
). Furthermore, lesion studies of the MST (Shidara et al. 1991
; Takemura
et al. 2000
), DLPN (Kawano et al. 1990
) and VPFL
(unpublished observations) have shown that injection of suppressive
chemicals into any of these regions produces a decrement in ipsilateral
ocular following responses. Evidence from these single-unit recordings
and focal chemical lesions have suggested that early ocular following
responses are mediated by a pathway that includes the MST, DLPN, and VPFL.
To understand what the temporal pattern of a Purkinje cell (P-cell) in
the VPFL represents, Shidara et al. (1993) and
Gomi et al. (1998)
used a linear time-series regression
analysis. They showed that the simple spike activities of the P-cells
during ocular following could be reconstructed by an inverse-dynamics representation. This successful reconstruction suggested that the
firing frequencies of the P-cells represent the dynamic motor command
used by downstream structures to elicit ocular following. However, the
transformation of visual information into motor commands for eye
movement has yet to be characterized.
To examine how the motor command is generated in the information-processing stream, we analyzed the temporal patterns of single units in the neural circuit for ocular following, specifically, the MST, DLPN, and VPFL. The purposes of this study are to understand what the temporal neuronal activities in the MST and DLPN represent and to understand the difference among the MST, DLPN, and VPFL.
To investigate the information represented in the discharges of MST and DLPN neurons and of P-cells in the VPFL from the viewpoint of motor command generation, we applied a second-order linear-regression model (the inverse-dynamics representation) using eye movement to reconstruct the temporal firing patterns. Conversely, to examine the neural discharges from the viewpoint of visual signal transformation, we used retinal error instead of eye movement in the model. Furthermore, to investigate the relationship between the firing patterns and retinal error/eye movement under a single condition or multiple conditions, we used local and global fitting, respectively. In the analyses, we focus on the differences between the fitting performances in global/local fittings from sensory/motor signals and the estimated coefficients representing characteristics of the neural discharges. Our results indicate that the information represented in the firing patterns of MST and DLPN neurons were similar to each other, but differed from those of P-cells in the VPFL. Based on our observations, we provide a hypothetical scheme of spatiotemporal and sensory-to-motor transformations for ocular following. Preliminary results from these analyses have been presented elsewhere (Takemura et al. 1996, 1999).
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METHODS |
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Data were collected from nine adolescent Japanese monkeys
(Macaca Fuscata), weighting 5-9 kg. All animals had been
trained previously to fixate on a small target spot on a tangent screen for a liquid reward (Wurtz 1969). A cylinder for chronic
recording of single neuron activity was implanted under aseptic
conditions into each monkey under pentobarbital sodium anesthesia. A
fixture was attached that allowed the head to be fixed in the standard stereotaxic position during the experiments. Scleral search coils were
implanted into both eyes to record eye movements according to the
technique of Judge et al. (1980)
. Eye position was
monitored by an electromagnetic induction technique (Fuchs and
Robinson 1966
). The coil output voltages were calibrated for
eye position by having the animal fixate on small light-emitting diode
(LED) targets at known positions along the horizontal and vertical
meridians. All experimental protocols were approved by the
Electrotechnical Laboratory Animal Care and Use Committee.
Behavioral paradigms and visual stimuli
The behavioral paradigms and visual stimuli used in this study
were identical to those of Shidara and Kawano (1993) and
are described elsewhere (Kawano et al. 1992
, 1994
;
Shidara and Kawano 1993
). In brief, during the recording
sessions, the monkey sat in a primate chair with its head secured to
the chair facing a translucent screen (85 × 85°) located 235 or
500 mm in front of the animal. The visual stimulus was back-projected
onto the screen as a ramp movement of a randomdot pattern.
Each ramp started 50 ms (in some cases, 100-300 ms) after the end of a
saccade directed toward the central part of the screen. The stimulus
lasted 250-300 ms, then the screen went blank for 0.5-2 s while the
animal remained in the dark. The ramps were presented at five speeds
(10, 20, 40, 80, and 160°/s) and in eight directions (right, left,
up, down, and the 4 diagonal directions). The monkeys were given an occasional drop of fruit juice to help them remain alert and to facilitate fast saccades.
Recording technique
Single-unit activities were recorded using tungsten
microelectrodes implanted in the MST, DLPN, or VPFL. A hydraulic
microdrive (Narishige Mo-9) was mounted on the recording cylinder, and
glass-coated tungsten microelectrodes were used to initially identify
and map each region and its neighboring structures. A fixed grid system (Crist et al. 1988) was then used to introduce and fix
in place a stainless steel guide tube through the dura. The tips of the guide tubes were positioned 3-5 mm above the MST, DLPN, or VPFL. Flexible tungsten electrodes were used to record through the tube.
Acquisition of behavioral and unit data
Our previous studies indicated that neurons in the MST and DLPN
and P-cells in the VPFL discharge during brief, sudden movements of a
large-field visual stimulus that elicits ocular following (Kawano et al. 1992, 1994
; Shidara and Kawano
1993
). Most of these neurons increase their firing rate before
the eye movements begin. To further characterize the response
properties of neurons involved in sensory-to-motor information
processing for ocular following, we first selected neurons according to
their discharge sensitivity to a moving visual scene that elicited
ocular following. After isolating a single unit, we observed its
responses to a visual scene moving at 80°/s in eight directions. We
selected neurons in which the activity was modulated by one of these
stimuli (the preferred direction). We then moved the visual scene in
the preferred direction and recorded the neuronal and ocular responses
at five different speeds.
During the ocular following response, the mirror velocity and the
horizontal and vertical components of eye position and velocity (measured with the search coils and filtered with a 6-pole analog Bessel filter using a cutoff frequency of 100 Hz), were recorded at 500 Hz. The speed of the random-dot pattern on the screen was proportional
to the mirror velocity. The single-cell activity of each region was
isolated using a time-amplitude window discriminator and was
simultaneously recorded at 1,000 Hz. Some of the data presented here
were taken from prior studies (Kawano et al. 1992, 1994
;
Shidara and Kawano 1993
) and were reanalyzed.
Data preparation
We selected neurons whose responses to each stimulus were recorded for more than 30 trials under each condition. The firing frequency of each neuron and the eye movement during 30 trials under the same stimulus conditions were ensemble averaged for each cell after excluding trials with saccadic intrusion (35 MST neurons, 32 DLPN neurons, and 20 P-cells). The responses were aligned with the stimulus onset (time 0), and the eye acceleration profiles were obtained by digital differentiation of eye-velocity profiles after averaging. Retinal errors as a visual motion signal were obtained by subtracting eye movements from mirror movements. To align the filtering delays, the ensemble average firing pattern (i.e., the firing frequency temporal pattern) was low-pass filtered with a 6-pole Bessel digital filter using the same cutoff frequency (100 Hz) as that of the analog filter for the eye movements. For reasons that we shall go into later, all data were low-pass filtered with the same cutoff frequency to avoid an estimation error (the Butterworth filter cutoff was 50 Hz).
Analysis method (linear-regression models of firing rate)
To quantitatively analyze the relationship between sensory/motor
information and neural activity, we used a linear time-series regression method (Gomi et al. 1998; Shidara et
al. 1993
). We applied the same linear-regression model to the
neuronal activity of each region using acceleration, velocity, and
position of sensory or motor information (retinal errors shown in Fig.
1B; eye movements shown in
Fig. 1C). Figure 1 shows the temporal patterns of each retinal error component as input and eye movements as output, with the
temporal pattern of an MST neuron. The equation used for the analysis
is as follows
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(1) |
|
The coefficient of determination index (CD) (Gomi et al.
1998; Hines and Montgomery 1972
) expressed in
the Eq. 2 was used to evaluate the performance of the model
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(2) |
Local and global fitting
Previous studies demonstrated that the magnitude of ocular
following is strongly dependent on stimulus speed (Miles et al. 1986). Recent experiments also demonstrated that different
temporal patterns of firing frequency could be induced by different
stimulus speeds. That is, neural responses are also strongly dependent on stimulus speed (Kawano et al. 1992
, 1994
;
Shidara and Kawano 1993
). To investigate the
relationship between firing pattern and sensory/motor information under
the single-stimulus condition, we used local fitting (Gomi et
al. 1998
). By applying the model to the firing pattern at one
of the five speeds, a local relationship between the neuronal firing
pattern and retinal errors or ocular responses can be examined. The
temporal firing patterns in response to the five stimulus speeds in the
preferred direction of a neuron were reconstructed by each set of
parameters. This yielded five sets of parameters calculated per neuron.
On the other hand, we used global fitting to test whether the model
could be applied independently of stimulus speed such that all five
responses could be reconstructed together using a single set of
parameters from retinal errors or eye movements (Gomi et al.
1998
). To investigate the characteristics of the neural
activities, we focused on the reliable parameters using the Student's
t-test, in which the P values of the
t-test indicate the probability of the null hypothesis (that
the coefficient of each component is 0). The model's applicability was
evaluated by Cp statistics. The technical details and results are
described in the APPENDIX.
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RESULTS |
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We successfully recorded the activities of single units in the MST, DLPN, and VPFL, all of which represent different stages of the information-processing stream, from sensory input to motor output for ocular following. To investigate the relationship between neuronal activity and retinal errors or eye movements under single (local fitting) or multiple (global fitting) stimulus conditions, we used Eq. 1 to quantitatively analyze temporal firing patterns during ocular following responses in the preferred directions.
Fitting performances of the retinal error model
The traces in Fig. 2, A
and B, summarize the results of reconstructing the firing
patterns of an MST neuron from retinal errors under local
(A) and global fitting (B). In Fig. 2,
A and B, each pair of traces shows the firing
patterns aligned with the onset of the ramp motion. Within each pair,
the thick trace (labeled "reconstruction") shows the reconstructed
firing patterns from retinal acceleration, velocity, and position under
local (Fig. 2A) and global fitting (Fig. 2B). The
thin trace (labeled "observed data") in each pair shows the
observed firing pattern, which is based on the same data at the same
stimulus speed as in Fig. 2, A and B. As shown in
Fig. 2A (local fitting), all reconstructed firing patterns
were very close to the observed data within each pair. Their CDs were
between 0.82 and 0.94 (mean value, 0.85), indicating extremely good
reconstruction at each of the five stimulus speeds. Under local
fitting, the linear-regression model for retinal errors was applicable
to most of the data from the MST [shaded area of Fig. 2C;
CD 0.7 (131/175, 75%)]. On the other hand, as shown in Fig.
2B (global fitting), the reconstructed firing patterns were
quite different from the observed data in each of the pairs. The
calculated CD was 0.35, indicating a failed reconstruction of the five
temporal patterns from retinal errors using a single set of parameters.
The CDs for a large percentage of MST neurons (88%, 27/35) were lower
than 0.7 (blank area of Fig. 2D) under global fitting,
indicating that the firing patterns of most MST neurons were not
adequately reconstructed from retinal errors using only a single set of
parameters.
|
The results obtained from DLPN neurons were similar to those obtained
from MST neurons. Most of the data from the DLPN (71%, 114/160) were
satisfactorily reconstructed by the retinal error model under local
fitting (CD 0.7). Under global fitting, however, the CDs for a
large percentage of DLPN neurons (75%, 24/32) were <0.7.
Figure 3 summarizes the results of
reconstructing the firing patterns of a P-cell from retinal errors
under local (A) and global fitting (B). As shown
in Fig. 3A (local fitting), all reconstructed firing
patterns were close to the observed data within each pair. The
CDs were between 0.72 and 0.96 (mean value, 0.87), indicating a good
reconstruction at each of the five stimulus speeds. Most of the data
from P-cells (89%, 89/100) were satisfactorily reconstructed from
retinal errors under local fitting (CD 0.7, in shaded area of
Fig. 3C). On the other hand, as shown in Fig. 3B
(global fitting), the reconstructed firing patterns were quite
different from the observed data in each of the pairs. The CD was 0.68, indicating a failed reconstruction of the five temporal patterns from
retinal errors using a single set of parameters. Global fitting was
accurate only for a small percentage of the VPFL P-cells [CD
0.7 (7/20, 35%), in the shaded area of Fig. 3D].
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From the preceding analyses, the following features common to MST, DLPN, and VPFL neurons were evident. The firing patterns of most neurons were successfully reconstructed by local fitting. However, reconstruction was unsatisfactory using retinal error during global fitting.
Estimated parameters of the retinal error model
To investigate the information represented in the temporal firing
patterns, we focused on the reliable coefficients of acceleration, velocity, and position of retinal errors under local fitting. After
applying a threshold (0.7) to the CDs of the local fittings, we
performed a statistical analysis in which the significance of each
coefficient was examined by the t-test for the null
hypothesis (that the coefficient of each component is 0). The number of
datasets that fell under a particular t-test P
value is shown in Table 1A. In
most datasets from MST and DLPN neurons (67.2%, 88/131 and 76.3%,
87/114, respectively), the null hypothesis for the acceleration
component was rejected. On the other hand, in only one-fifth of the
datasets from VPFL P-cells (21.3%, 19/89), the null hypothesis for the
acceleration component was rejected. These results indicate that the
necessity for the acceleration component to be presented in P-cell
firing patterns is less than that for the MST and DLPN neuronal firing
patterns. Meanwhile, the small P value for the other
components (i.e., velocity, positional, and bias components) indicates
that these components are necessary for adequate reconstruction in all
regions.
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The t-test analysis suggests that the information on retinal
errors represented in the temporal firing patterns of the MST and DLPN
neurons is similar but differs from that of P-cells. To characterize
the temporal firing patterns of the three regions, we investigated
reliably estimated parameters (coefficient of acceleration, velocity,
and position). We first examined whether the distributions of the
estimated coefficients were different in the three regions. Figure
4 shows the relationships between the
acceleration and velocity parameters, which were both reliably estimated (CD 0.7 and P < 0.05) by the retinal
error model under local fitting. As shown in Fig. 4, the MST and DLPN
neurons (represented by
and
, respectively) were more widely scattered than
P-cells (represented by
). There were various cell
types (acceleration- or velocity-dominant cells) in the MST and DLPN.
Their temporal pattern characteristics were very different from each
other. The means of the acceleration coefficients for the MST and DLPN
neurons and the VPFL P-cell datasets were 0.032 ± 0.036, 0.025 ± 0.034, and 0.009 ± 0.022 (spikes/s)/(°/s2), respectively. The magnitudes
of the acceleration coefficients of the MST and DLPN neurons were
approximately threefold greater than those of the VPFL P-cells.
Furthermore, differences in the distributions of the acceleration
coefficients were significant at the P < 0.0015 level
between the MST and VPFL and at the P < 0.01 level
between the DLPN and VPFL, respectively (by Wilcoxon's rank-sum test).
The difference in the distributions of the acceleration coefficients
between the MST and DLPN, however, was not significant (P = 0.24).
|
The means of the velocity coefficients for the MST and DLPN neurons and the VPFL P-cell datasets were 3.81 ± 4.04, 3.24 ± 3.18, and 2.50 ± 1.69 (spikes/s)/(°/s), respectively. The magnitudes of the velocity coefficients in the firing patterns of the MST and DLPN neurons and P-cells were similar. The differences in their distributions were not significant (P = 0.71 for the MST vs. DLPN, P = 0.59 for the DLPN vs. VPFL, and P = 0.41 for the MST vs. VPFL, by Wilcoxon's rank-sum test).
The means of the position coefficients were 5.61 ± 13.54 (spikes/s)/° for the MST neuron datasets, 8.06 ± 35.38 (spikes/s)/° for the DLPN neuron datasets, and 7.16 ± 27.19 (spikes/s)/° for the VPFL P-cell datasets. The distribution of the
DLPN positional components was significantly different from that of the
MST and VPFL (P < 0.00005 for the MST vs. DLPN,
P < 0.05 for the DLPN vs. VPFL, and P = 0.85 for the MST vs. VPFL, by Wilcoxon's rank-sum test).
We next examined whether the relationship between the stimulus speed and the goodness of fit (CD) under local fitting differed among the three regions. However, we will first review the directional and speed sensitivities of the MST and DLPN neurons and the P-cells. The neurons analyzed in this study were direction-selective. Therefore their neuronal responses increased for stimuli moving in their optimal direction. To understand the temporal neuronal activities in MST and DLPN neurons and P-cells, we studied their temporal firing patterns using stimuli moving in their optimal direction at 10-160°/s. There were also speed-selective neurons, as shown in Figs. 2 and 3. The temporal firing patterns of these neurons were of different magnitudes, depending on stimulus speed.
To determine the optimal speed for each neuron, we measured the magnitudes of the neuronal responses over the time period analyzed by the linear-regression method. Some MST neurons (13/35, 37%) showed their best response at high stimulus speed (160°/s), whereas others (19/35, 54%) showed their best response at a moderate stimulus speed (40 and 80°/s). Most of the DLPN neurons (25/32, 78%) and P-cells (15/20, 75%) showed their best responses at high stimulus speed (160°/s). Significant differences were observed between the speed preferences for the MST and DLPN/VPFL (P < 0.002 for the MST vs. DLPN and MST vs. VPFL, by Wilcoxon's rank-sum test). However, no significant difference was observed between the speed preferences of the DLPN and VPFL (P = 0.94).
Because we were interested in the relationship between the optimal
speed and fitting performance, we first normalized the stimulus speed
to the optimal speed [log2 (stimulus speed/optimal speed)]. Figure 5 shows the average CD
as a function of the normalized stimulus speed for 35 MST neurons
(A), 32 DLPN neurons (B), and 20 P-cells
(C). As shown in Fig. 5A, the fitting performance
(CD) of the MST was significantly reduced as the stimulus speed moved away from the preferred speed regardless of whether it was faster or
slower. On the other hand, the fitting performance of the DLPN and VPFL was not significantly reduced over the range 2 to +2 (Fig.
5, B and C). These results indicate that the
temporal firing patterns of MST neurons represented information on
retinal errors only near their optimal speed.
|
Fitting performances of the eye-movement model
Figure 6 summarizes the fitting
performances of the eye-movement model under local (A) and
global (B) fitting for the same MST neurons that were used
in Fig. 2. As shown in Fig. 6A, the CDs were between 0.41 and 0.79 (mean value, 0.65), indicating that the firing patterns at
lower stimulus speeds were relatively well reconstructed. In Fig.
6B, the traces in each pair show that the MST firing
patterns were not adequately reconstructed under global fitting. The CD
was 0.58, indicating a nonlinear relationship between MST firing and
ocular responses through multiple stimulus speeds. Under local fitting
(Fig. 6C, ), 57% of the data from the
MST (99/175) were reconstructed relatively well from eye movements. Under global fitting, however, the reconstructed firing patterns were
not able to approximate the observed firing patterns of most MST
neurons (71%, 25/35; Fig. 6D,
).
|
The results obtained from DLPN neurons were similar to those obtained
from MST neurons. Under local fitting, 55% of the data from the DLPN
(88/160) was reconstructed relatively well from eye movements, whereas
global fitting produced a CD of 0.7 in a small percentage of the DLPN
neurons (31%, 10/32). It is clear from these results that the
eye-movement model accounted for the different neuronal responses of
only a small portion of neurons in the MST and DLPN under multiple
stimulus speeds and using a single set of parameters.
On the other hand, the traces in Fig. 7
summarize the results of reconstructing the firing patterns of the same
P-cell as in Fig. 3 from eye movements under local (A) and
global fitting (B) at five different speeds. In Fig.
7A, the reconstructed firing patterns under local fitting
were very close to the observed data within each pair. The CDs were
between 0.87 and 0.94 (mean value, 0.91), indicating good
reconstruction at each of the five stimulus speeds. In addition, in
Fig. 7B, the reconstructed firing patterns under global
fitting were also very close to the observed data in all pairs. The CD
was 0.89, again indicating good reconstruction at each of the five
stimulus speeds using only a single set of parameters. These results
indicate a linear relationship between P-cell firing and ocular
responses at multiple stimulus speeds. The linear-regression model
(Eq. 1) for eye movement was inapplicable in only a small
number of P-cell firing patterns under both local and global fitting
(Fig. 7, C and D, , 15/100 and 3/20,
respectively; CD < 0.7).1
|
As illustrated in Fig. 8, comparing the
fitting performances of temporal firing patterns from eye movements for
the MST and DLPN neurons and for the VPFL P-cells revealed distinct
differences. In this figure, the CDs are displayed for global fitting
(the abscissa) and for local fitting (the ordinate). The fitting
performances of the VPFL P-cells () are
distributed in the right top quadrant of Fig. 8, indicating that the
temporal firing patterns of the P-cells were satisfactorily
reconstructed from eye movement components using the linear-regression
model for both local and global fitting [CD
0.7 in 85/100
datasets of the VPFL (85.0%) in local fitting; CD
0.7 in 17/20
P-cells (85%) in global fitting]. On the other hand, fitting
performances of the DLPN (
) and MST neurons (
) were distributed above the slope line 1. This indicates that we were
able to attain a relatively good fit under local fitting [CD
0.7 in 99/175 datasets of the MST (56.6%) and 88/160 datasets of the
DLPN (55.0%)]. When we used global fitting for the MST and DLPN
neurons, however, the model adequately reproduced the firing patterns
for only a small number of neurons [CD
0.8 in 3/35 MST (8.6%)
and 1/32 DLPN neurons (3.1%); CD
0.7 in 11/35 MST (33.3%) and
10/32 DLPN neurons (31.3%)]. On the other hand, as demonstrated in
the preceding text, global fitting was accurate for most of the P-cells
[CD
0.8 in 9/20 (45%); CD
0.7 in 17/20 P-cells
(85%)]. In Fig. 8, frequency histograms of the CDs for the MST, DLPN,
and VPFL datasets under both local and global fitting clearly show the
similar tendencies of the MST and DLPN. Figure 8 also reveals the
difference between the VPFL and upstream structures (the MST and DLPN).
|
From the preceding analyses, the following differences between MST and DLPN neurons and P-cells were evident: the temporal firing patterns of the MST and DLPN neurons were successfully reconstructed under local fitting for one-half of the neurons but for only one-third of the neurons under global fitting, but the temporal firing patterns of the P-cells were satisfactorily reconstructed from eye movements under both local and global fitting.
Estimated parameters of the eye-movement model
After applying a threshold (0.7) to the CDs of local
fittings, we performed the t-test analysis. In local
fitting, the number of datasets that could be classified under a
particular t-test P value is listed in Table
1B. The null hypothesis for the eye acceleration component
was rejected (0.005 > P) in most datasets from all
three regions [92.9% (92/99) for the MST, 97.7% (86/88) for the
DLPN, and 94.0% (78/83) for the VPFL]. The P values for the other components (i.e., eye velocity and positional components) were also small, and the null hypothesis for these components was
rejected (P < 0.05). This indicates that all of the
components in Eq. 1 make a significant contribution to
describing the relationship between temporal firing patterns and eye
movements. We investigated the estimated coefficients for the datasets
at different speeds. Figure 9 shows the
relationship between the acceleration and velocity parameters, which
were both reliably estimated (CD
0.7 and P < 0.05) by the eye-movement model under local fitting. As shown in this
figure, the MST data (Fig. 9A,
) and the DLPN data (Fig. 9B,
) are more widely scattered than
the VPFL data (Fig. 9C,
). Each symbol
represents the coefficients of acceleration and velocity of a neuron at
the slowest stimulus. These parameters for a neuron at different
stimulus speeds are connected (
); the lines in Fig. 9, A
and B, extend further than those in Fig. 9C.
|
There are three implications of the data presented in Fig. 9. First, the magnitudes of the acceleration and velocity coefficients varied at different speeds and in different cells, especially in the MST and DLPN (Fig. 9, A and B). Second, the magnitudes of the velocity coefficients for slow stimuli were frequently larger than those for fast stimuli (the y axis in Fig. 9), especially in the MST and DLPN. Third, the magnitudes of the acceleration coefficients for slow stimuli were often larger than those for fast stimuli in the DLPN (the x axis in Fig. 9).
In summary, the firing frequencies of the MST and DLPN neurons were reconstructed successfully for one-half of the datasets by the eye-movement model under local fitting. In MST and DLPN neurons, the coefficients for different cells and for different stimulus speeds within a cell were different and widely scattered. On the other hand, the firing frequencies of the VPFL P-cells were reconstructed successfully for most datasets, and their coefficients were similar to each other.
As was the case with local fitting, the results of global fitting also demonstrated that the temporal firing patterns in the MST and DLPN were different from those in the VPFL. We examined the reliability of estimated parameters that had a high CD (>0.7) by the eye-movement model under global fitting. The significance of each coefficient was <0.02 in all units, except one P-cell (11/11 MST neurons, 10/10 DLPN neurons, and 16/17 P-cells).
The mean lead-time of the neuronal response with respect to the
onset of eye movement was 11.8 ± 3.6 (SD) ms for MST neurons and
11.9 ± 6.9 ms for DLPN neurons. These values agree with those of
previous studies on the relative latency to the onset of the stimulus
of MST neural activity (Kawano et al. 1994) and DLPN neural activity (Kawano et al. 1992
) during ocular
following. The mean time delay of VPFL P-cells was 7.7 ± 5.1 ms,
which is near the latency period for electrical-stimulation-evoked eye movements (Shidara and Kawano 1993
).
To compare the component data obtained from MST and DLPN neurons and
P-cells with corresponding data from motor neurons (Keller 1973), we calculated the ratios of the acceleration, velocity, and position coefficients (Table 2). The
mean ratios of the acceleration coefficient to the velocity coefficient
(b/a) of MST (36.5) and DLPN neurons (24.7) differed from those of
motor neurons (67.4). This was because the acceleration coefficient
tended to be larger than that of the motor neurons. On the other hand,
as reported previously (Gomi et al. 1998
; Shidara
et al. 1993
), the mean ratio of the acceleration
coefficient to the velocity coefficient (b/a) of P-cells (50.1) was
close to that of motor neurons (67.4). Thus the acceleration
coefficient of MST and DLPN neurons tended to be larger than that of
the P-cells. Meanwhile, the mean ratio of the acceleration coefficient
to the position coefficient (c/a) differed between the MST, DLPN, and
VPFL, and was of negative sign.
|
Comparison of the performances in local and global fittings from retinal error and from eye movement
The boxes in Fig. 10 summarize the fitting performance (i.e., the CD values) of all regression analyses (left, local and global fitting by the retinal error model; right, eye-movement model). In the retinal error model (left), the differences between the distributions of CDs under local and global fitting were significant (P < 0.0001) in all three regions (the Mann-Whitney U tests of nonparametric tests). This indicates that neuronal responses in the MST, DLPN, and VPFL represent information on retinal errors under a single or narrow stimulus range. Additionally, in the eye-movement model, the differences between the distributions of CDs under local and global fitting (right) were also significant for the MST and DLPN neurons, (P = 0.0001 and P = 0.0014, respectively). However, as shown in Fig. 10F, this difference was not significant for VPFL P-cells (P = 0.15), and their firing patterns were frequently reconstructed well from eye movements. These results indicate that only neuronal responses in the VPFL represented motor command information independent of the stimulus conditions.
|
By comparing performances in the retinal error model and eye-movement model under local fitting, the features of MST and DLPN neurons become clearer. Under local fitting, the differences between the CD distributions in the retinal error and eye-movement models were significant (P < 0.0001) for both the MST and DLPN neurons (left boxes in A vs. B and C vs. D). On the other hand, this difference was not significant (P = 0.14) for the VPFL P-cells (left boxes in E vs. F). These results indicate that the retinal error model describes the temporal firing patterns of the MST and DLPN neurons more accurately than the eye movement model. These results also indicate that the firing patterns of VPFL P-cells were well reconstructed both from retinal errors and from eye movements under local fitting.
On the other hand, by comparing the performances in the retinal error and eye-movement models under global fitting, the features of P-cells become clearer. Under global fitting, the fitting performances in the eye-movement model were better than those in the retinal error model for the MST, DLPN, and VPFL (these differences were significant at P < 0.002, P < 0.04, and P = 0.0002, respectively), although the performance of the eye-movement model for most MST and DLPN neurons was still insufficient. As described in the preceding text, sufficient performance by the eye-movement model under global fitting was only obtained for the P-cells in the VPFL.
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DISCUSSION |
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Description of the relationship between sensory/motor information and neuronal activity
As shown in the preceding analyses, we quantified the relationship among the temporal firing patterns for single neurons in the MST, DLPN, and VPFL and eye movements or retinal errors. The advantage of this method is that by applying both local and global linear regression analyses, we can both argue the global linearity and global characteristics of the cell firing and examine the local representation of the cell firing within a limited stimulus range. The ability to perform linear-regression analyses and compare the estimated coefficients obtained by local and global analyses for the three regions (MST, DLPN, and VPFL) has made it possible for us to consider signal transformation in the process of eye motor command generation.
Instead of taking the "piecewise linear" analysis approach, one
could try to consider nonlinearities concealed in the relationships between sensory/motor information and neuronal firing patterns. Previous studies (Kawano et al. 1992, 1994
) and our
preliminary analysis suggest that three nonlinear factors should be
considered in characterizing the "global" MST and DLPN activities
and speed preference in each neuron. First, even in a particular
neuron, the neuronal response latencies differ according to stimulus
speed. Second, the sensitivity of the acceleration and velocity
components varies according to the stimulus speed. Third, there is a
difference between the sensitivity changes of the acceleration and
velocity components according to stimulus speed. To consider all of
these nonlinear factors for global fitting, however, we need to use a
complicated nonlinear model, which may be hardly justified and does not
give any clear view without sufficient data analysis to characterize
these nonlinear factors. Further experiments using various visual
stimuli having complex profiles are needed to capture the
nonlinearities between retinal errors and neural responses under the
global condition.
Another interesting point is the effect of eye movement on the neuronal
activities in each region. Several studies have reported continuous
neuronal activities in the MST (Bradley et al. 1996; Newsome et al. 1988
; Sakata et al. 1983
;
Squatrito and Maioli 1996
), DLPN (Mustari et al.
1988
; Suzuki and Keller 1984
; Thier et
al. 1988
), and VPFL (Lisberger and Fuchs
1978a
,b
; Miles and Fuller 1975
) without a visual
target during smooth pursuit eye movements. Previous studies of the
ocular following response, however, have demonstrated that the
discharges of MST and DLPN neurons and P-cells increase before eye
movement (Gomi et al. 1998
; Kawano and Shidara
1993
; Kawano et al. 1992
, 1994
; Shidara and Kawano 1993
; Shidara et al. 1993
) and
abruptly decay when the moving visual scene is blanked (Gomi et
al. 1998
; Kawano et al. 1992
). Thus the
closed-loop portion of the temporal firing patterns during the ocular
following responses in this study need not be considered an effect of
eye movement on neuronal activity (extra-retinal information).
Information represented in the neuronal activities of the MST and DLPN
In the analyses shown in the preceding text, several common characteristics can be found in the firing patterns of MST and DLPN neurons. First, the temporal firing patterns were accurately described by the models under local rather than global fitting. In addition, under local fitting, the temporal firing patterns of the MST and DLPN neurons were modeled better by retinal errors than by eye movements. These results suggest that the temporal pattern of each neuron in the MST and DLPN represents retinal error information within the limited stimulus range. Second, under local fitting using the retinal error model, the acceleration and velocity coefficients of the MST and DLPN were broadly distributed, whereas those of the VPFL were more compact (Fig. 4). This suggests that the MST and DLPN neurons encode a variety of dynamic visual properties and that some are dominated by the acceleration component, some are dominated by the velocity component, and others are indifferent. Furthermore, the acceleration component of retinal errors contributed more significantly to the temporal firing patterns of MST and DLPN neurons than it did for P-cells. From these results, it may be inferred that information on retinal errors is integrated to represent the appropriate temporal firing patterns of P-cells to drive eye movements.
As for the similarity in the neuronal responses of the MST and DLPN
neurons, it has been reported (Kawano et al. 1992, 1994
) that there are no significant differences in directional preference (ipsiversive/contraversive or up/down) in these regions. It has also
been reported that most direction-selective neurons show their
strongest responses at high stimulus speeds, but the remainder show
their strongest responses at low stimulus speeds. In the present study,
we observed a significant difference in preferred speeds between the
MST and DLPN. Furthermore, in the MST, the best CD was related to
"preferred speed." Thus when a neuron preferred faster speeds, its
CD tended to be higher at faster speeds, and when a neuron preferred
slower speeds, its CD tended to be higher at slower speeds. These
results suggest that the temporal patterns of MST neurons represent
information on retinal errors around the preferred stimulus. Previous
reports have shown that there is a wide range of receptive field sizes
in the MST, whereas DLPN neurons have large receptive fields
(Suzuki et al. 1990
; Thier et al. 1988
).
These studies suggested that there is spatial integration of
information from the MST to the DLPN. Even so, in this study, no clear
difference was observed between MST and DLPN neurons in temporal firing
patterns. It is possible that information on retinal errors may be
integrated spatially (i.e., receptive field and preferred speed) rather
than temporally from the MST to the DLPN.
A recent study on disparity-induced vergence eye movements suggests
that the discharges of individual MST neurons encode some limited
aspect(s) of the stimulus disparity and/or the vergence motor response,
whereas the summed activity of the population encodes the entire
vergence velocity response (Takemura et al. 2001). In
this study, to see how well the discharges of the entire population of
MST or DLPN neurons encoded the motor command for the ocular following
responses, we had to analyze the temporal firing patterns of neurons in
response to a given direction and speed in the same monkey, regardless
of the preferred stimulus of the neurons. Since we only have data on
the response to the preferred stimulus for each cell in this study, we
are unable to determine whether the neuronal population average
represents the motor command for the ocular following response.
Information represented in the activities of the VPFL P-cells
Our results show that the temporal firing patterns of VPFL P-cells
can be described by the eye-movement model under global fitting,
suggesting that P-cells have the appropriate global characteristics for
motor command. Previous studies have shown that VPFL P-cells have
different response properties than MST and DLPN neurons to visual
stimuli like those in the ocular following response (Kawano et
al. 1996). First, the distribution of their preferred
directions during the ocular following response has clearly divided the
VPFL P-cells into two classes: horizontal P-cells, which preferred ipsiversive movement, and vertical P-cells, which preferred downward movement. Second, P-cells showed their best responses at high stimulus
speeds. Most MST and DLPN neurons also showed their best responses at
high stimulus speeds, although some neurons preferred lower stimulus
speeds. These results indicate that P-cells increase their discharge
rate in response to a wide range of stimulus speeds and do so in
proportion to the stimulus speed. Third, a linear relationship between
neuronal firing patterns and eye movements was observed. This study
demonstrated that P-cells already encode the dynamic component of the
motor command for ocular following. They do so under multiple stimulus
conditions, which agrees with the observations of previous studies.
As for the positional component of eye movements, it has been reported
that VPFL P-cell activities show a weakly positive correlation or no
correlation with eye position (Krauzlis 2000; Krauzlis and Lisberger 1994
; Miles et al.
1980
). In this study, VPFL P-cell activities during ocular
following negatively correlated with eye position. Furthermore, the
magnitudes of these correlations were not negligible. Gomi et
al. (1998)
have already discussed in detail how the position
components have a reversed sign relative to eye movements.
Additionally, Kitama et al. (1999)
used the acceleration, velocity, and position of eye movements in cats to
analyze the temporal firing patterns of simple spikes from P-cells
during optokinetic response (OKR). When they controlled the
initial eye position to examine the contribution of eye position to the
firing pattern, the absolute eye position was not encoded in the
temporal firing pattern during OKR. Furthermore, we attempted to
determine whether these discrepant findings might have been caused by
the omission of the slide component, which shows the time decay
component of the firing rate (Krauzlis 2000
). To explain the time decay of P-cell firing, Eq. 3 was used.
Equation 3 is equivalent to the model proposed by
Goldstein and Robinson (1986)
and Optican and
Miles (1985)
and can be written as
![]() |
(3) |
In the retinal error model, the temporal firing patterns of VPFL P-cells were not described under global fitting. Under local fitting, the firing of P-cells fitted better than that of MST and DLPN neurons under local fitting (Fig. 9, A, C, and E, left). These results can be explained as follows: P-cells receive the visual information from the DLPN and MST, and DLPN and MST neurons have a narrow range of preferred stimulus speeds, so their temporal firing patterns encode the local representation of retinal errors. Since the local visual information converges on a P-cell, the temporal firing patterns do not relate to retinal errors globally. On the other hand, the temporal firing patterns at every stimulus speed relate to retinal errors locally.
Transformation of visual input into eye motor commands
In this study, we were unable to determine whether the neurons we
observed in the MST and DLPN send signals to the next stage of
information processing. These neurons could just function as local
interneurons or could project to regions unrelated to ocular-following eye movements. However, neurons in the DLPN, which is the next stage
after the MST, share many characteristics with neurons in the MST
(Figs. 4 and 8). This suggests that there is little possibility that
only MST neurons that fitted well with eye movements project to the
DLPN. Furthermore, it has also been reported that the visual response
properties of visual mossy fibers in the VPFL are similar to those of
DLPN and MST neurons (Kawano and Shidara 1993;
Shidara et al. 1993
). The temporal firing patterns of
visual mossy fibers were also similar to those of DLPN and MST neurons
and were modeled from eye movements under local fitting but not under
global fitting (unpublished data). This suggests that the neuronal
signals observed in the DLPN project as the inputs to the VPFL;
therefore it is unlikely that only well-fitted neurons in the DLPN
project to the VPFL.
Glickstein et al. (1994) reported that there is a sparse
but definite projection to the VPFL but that the major visual pontine projection is to the dorsal rather than ventral paraflocculus. To study
the role of the dorsal paraflocculus during the ocular following
responses, single-unit recording and quantitative analysis are
required. Although, evidence from focal chemical lesions of the MST,
DLPN, and VPFL suggests that the MST, DLPN, and VPFL play a role in the
early phase of the ocular following response. The temporal firing
pattern characteristics observed in this study and the visual
properties found in previous studies support the following ideas.
1) Single cells in the MST encode limited visual information
extracted by the visual cortex in their temporal firing patterns. They
do so only when a visual stimulus is given in the receptive field with
the preferred direction and speed. 2) Single cells in the
DLPN receive spatially integrated visual information (e.g., receptive
field, preferred speed) from MST neurons. Here the temporal firing
patterns in the MST and DLPN do not yet represent the dynamic component
of the motor command. Rather they represent the dynamic properties of
the visual stimulus in a limited range by various combinations of the
acceleration, velocity, and position components of retinal errors. MST
and DLPN neurons vary somewhat in their properties. However, as a
whole, they encode the dominant acceleration component that is probably
integrated prior to the VPFL P-cells' firing patterns. And
3) single P-cells receive spatially and temporally
integrated visual information (e.g., preferred direction) from DLPN
neurons, mediated by visual mossy fibers. The temporal firing pattern
of P-cells analyzed in this study was the simple spike, which results
from the synaptic action of granule cell axon terminals. The granule
cells receive mossy fiber inputs from the brain stem and send axons up
to the molecular layer, where they bifurcate and traverse as parallel
fibers, making numerous serial contacts with P-cell dendrites. In this
study, it is conceivable that the retinal error information encoded in the temporal patterns of DLPN neurons converges on a P-cell in the
VPFL. Thus a potential explanation is that every single P-cell receives
a large number of inputs with various time delays, and these inputs are
summed together into the temporal firing pattern of a P-cell. Therefore
the temporal firing patterns of the P-cells represent temporally
integrated visual information. At the same time, the P-cells' firing
represents the dynamic motor command independent of the stimulus speed.
We conclude that sensory-to-motor transformation for ocular following
occurs at the P-cell.
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APPENDIX |
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Modeling check (Cp statistics)
To find the model that best represented the observed firing
patterns, we examined several models that had combinations of acceleration, velocity, and position terms with bias and delay. The
best model was evaluated using Cp statistics, which test whether the
increased parameter can be traded for the goodness of model fit
(Gomi et al. 1998; Hines and Montgomery
1972
). The equation used for finding the Cp-statistics value
was as follows
![]() |
(A1) |
Representation of retinal error model
We analyzed the temporal firing patterns using the retinal error
model in Eq. 1. It is possible, however, that another model with fewer parameters may be sufficient for fitting the temporal firing
patterns. In other words, one of the parameters in Eq. 1
might be unnecessary to accurately represent temporal firing patterns.
For this reason, we examined all models that combined acceleration,
velocity, and position terms with bias and delay
![]() |
(A2) |
![]() |
(A3) |
![]() |
(A4) |
![]() |
(A5) |
![]() |
(A6) |
![]() |
(A7) |
Representation of eye-movement model
In local fitting, the Cp-statistics' value was lowest for Eq. 1 among all of the models we tested in most of the datasets: 75.8% (75/99) for the MST, 81.8% (72/88) for the DLPN, and 90.4% (75/83) for the VPFL. Additionally, in global fitting, for all the neurons except one P-cell (11/11 in the MST, 10/10 in the DLPN, and 16/17 P-cells), the Cp-statistics value was lowest for Eq. 1. These results indicate that all of the components of eye movements in Eq. 1 are required to represent the temporal firing patterns. Therefore the model in Eq. 1 was the best among those we tested, in both local and global fitting.
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ACKNOWLEDGMENTS |
---|
We are grateful to Dr. F. A. Miles for comments while preparing the manuscript. We thank Drs. M. Shidara, Y. Kodaka, and K. Miura for valuable advice and Dr. S. Yamane for continuing encouragement. We also thank M. Okui-Uchiyama, A. Kameyama, and T. Takasu for technical assistance and Y. Yaguchi and S. Inoue for secretarial assistance.
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FOOTNOTES |
---|
Address for reprint requests: A. Takemura, Neuroscience Research Institute, AIST, 1-1-1, Umezono, Tsukuba, Ibaraki 305-8568, Japan (E-mail: a.takemura{at}aist.go.jp).
1
In this paper, we focus only on the neuronal responses
to the preferred directions because the MST and DLPN neurons showed little response (neither an increase nor a decrease in firing rate) to
nonpreferred directions. In addition, we used the low-pass filter to
compare the temporal firing patterns of different regions (see
METHODS). These differences in methods between previous
studies (Gomi et al. 1998; Kitama et al.
1999
; Shidara et al. 1993
) and our study
resulted in a high CD for P-cells in this paper, under both local and
global fitting using eye movement.
Received 16 April 2001; accepted in final form 5 July 2001.
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REFERENCES |
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