During saccadic eye movements abducens motoneurons (ABD Mns) show a burst of
activity that encode the horizontal component of the movement. Very different
approaches have been used in order to account for how ABD Mns encode saccades
(Robinson, 1981; Fuchs, Kaneko and Scudder, 1985) and to define how the driving
signal of the saccade is generated in the brainstem. In this sense, a main diagram
has been proposed joining amplitude, maximun velocity and duration of saccadic
eye movements (Bahill and Stark, 1979). This main diagram defines the general
strategy for saccade generation, showing an exponential relation between amplitude,
maximum velocity and saccade duration. However, for the range of these variables
in the cat such a main diagram could be considered linear in a first approach
(Goldberg, 1980). Also, ABD Mns show an activity burst related with eye saccade
parameters that can be approached in very different ways: i) linear relationships
have been described between different parameters of saccadic eye movements and
parameters of the Mns firing rate burst, as maximum velocity versus maximum
firing rate (Robinson, 1970; Fuchs and Luschei, 1970; Delgado-García,
del Pozo and Baker, 1986; Gómez, Torres, B., Jiménez-Ridruejo
and Delgado-García, 1986a) and burst duration versus eye saccade duration
(Robinson, 1970; Fuchs and Luschei, 1970; Schiller, 1970); ii) a second approach
is to consider the second order differential equation proposed to relate Mns
activity and position, velocity and acceleration of the eye (Robinson, 1981),
where Mn firing rate encodes in a continuous form for the eye variables. This
model has been proved valid in monkey (van Gisbergen, Robinson and Gielen, 1981)
and cat Mns (Torres, Gómez and Delgado-García, 1986); iii) reconstruction
of possible Mns firing rate pattern by an inverse method using eye position
registers (van Opstal, van Gisbergen and Eggermont, 1985); and iv) the proposal
of a descriptive model of Mn burst during saccades. In fact it has been described
that the firing rate burst can be modelled by a couple of exponential equations
(rising and falling) (Pozo, Jiménez-Ridruejo, Delgado-García and
Zoreda, 1984; Jiménez-Ridruejo, Pozo, Gómez and Delgado-García,
All these approaches have shown some general roles in the eye saccadic coding
by Mns and saccadic generation strategy. Some of the more interesting are: with
known saccade amplitude, peak velocity and duration can be modelled (Afifi and
Azen, 1979); peak velocity is predicted by peak firing rate (Robinson, 1970;
Fuchs and Luschei, 1970; Schiller, 1970) and the previous intervals (Gómez
et al., 1986a); ocular mechanics can he predicted in a first approach as a second
order linear model (Robinson, 1981), and the firing rate burst should be considered
as a gradual firing rate increase instead of an abrupt jump (Jiménez-Ridruejo
et al., 1983; Pozo et al., 1984; van Opstal and van Gisbergen, 1985). However,
some questions still remain about the relationships between amplitude, velocity
and duration in the strategy of saccadic generation and their coding by Mns
(Evinger, Kaneko and Fuchs, 1981; King, Lisberger and Fuchs, 1986). Also, some
kind of asymmetry can be observed inside the eye saccade (Baloh et al., 1975)
(shorter in the rising than in the falling phase); how this asymmetry is coded
in Mns is a question that still remains. Other minor questions can be also addressed.
Finally, the validity of the descriptive double exponential model of Mns behavior
during saccadic should be tested.
For these reasons a kind of multivariate analysis, the principal component
analysis was applied to 27 parameters extracted during saccades from eye position
and velocity registers, from ABD Mns activity and from the double exponential
model. The goal of the principal component analysis is to reduce correlated
variables to a small set of statistically independent linear combinations (Afifi
and Azen, 1979; Frey and Pimentel, 1978). In a data set of P observations in
a N multidimensional space (N variables measured in each observation), it is
possible to produce a rotation of the axes that reduce the distance of the observations
to the axes of the N-dimensional space (the reduction of the distance is called
the explained variance). Also, it is possible to consider the N variables as
a function of the P observations, a P-dimensional space in this case, then a
rotation of the axes produces a reduction of the distance of the variables to
the axes of the P-dimensional space. The latter is the geometrical interpretation
used in present report. The analysis creates new axes (the principal components)
where the variable are situated by their coordinates (the loading factors).
So, the information contained in the actual data set can be reinterpreted by
the position of the variables in the new space, variables that are in the same
region covary directly and those situated in opposed regions covary inversely.
Also the different positions of the variables on the same axe permit to interpret
functionally the principal components.
MATERIALS AND METHODS
Under general anesthesia (35 mg/Kg, i.p), two adult cats were prepared for
the recording of the electrophysiological activity of antidromically identified
ABD Mns of the left ABD nucleus.
Simultaneousy the horizontal eye position was recorded by
the search coil technique during spontaneous saccadic eye movements in the alert
cat (Delgado-García et al., 1986; Gómez et al., 1986a). Recordings
were stored on magnetic tape for subsequent analysis. Neuronal electrical activity
was passed through a window discriminator and converted into a point process
temporally correlated with occurring spikes (Gómez, Canals, Torres and
Delgado-García, 1986b). Pulse trains and eye position recordings were
digitized and then stored in a computer. A computer program was carried out
to display on the screen the frequency histogram, the eye position and eye velocity
(Fig. 1). The program provided two cursors to select the register positions
chosen to calculate the parameters. This program permitted obtaining a series
of 27 parameters defining the position and eye velocity, the Mn burst firing
rate and the double exponential model describing rising and falling phases of
the burst (Fig. 1A-C). Some of the parameters were calculated manually by positioning
of the cursors as described above. Others were calculated by algorithms implemented
in the program. The parameters of the descriptive model were calculated by fitting
exponential equations to the rising and falling phase of the burst. The parameters
of each exponential equation, time constant and asymptotic value, were fixed
by hand. The values of the couple of exponential equations were calculated by
the computer and compared by linear regression methods with the firing rate
values stored during the burst. Afterwards, a new couple of exponential equations
was automatically calculated changing the exponential equation parameters. Finally,
the program selected as the valid couple of exponential equations those that
reached the highest score in the linear correlation coefficient between exponential
equation values and actual firing rate values. This iterative method permits
to avoid possible distortions in the regression produced by the neccesary logarithmic
transformation of the data to fit an exponential model. Given the few points
used to calculate the regression inside the burst (4-10), the distortion could
be significant if a standard linear regression model were used. If none of the
calculated couple of exponential equations reached a minimum of 0.8 in the correlation
coefficient value when plotted against firing rate burst values, that particular
saccade was discarded for subsequent analysis.
From Mn firing rate the parameters considered were (Fig. 1C, bottom): Ric,
firing rate previous to the burst; R, peak firing rate; If, firing rate increase
in the burst; Rfc, firing rate at the end of the burst; Af, firing rate increase
of the step; Dd, burst duration; Ts, rising time of the burst (time between
peak firing rate and the time when firing rate falls 90% of the firing rate
burst increase); Rps, slope of the firing rate rising phase; Nsu, number of
spikes in the rising phase of the burst and Nba, number of spikes in the falling
phase of the burst. The parameters considered from the double exponential model
were (Fig. 1B, bottom): Asu, asymptotic value of the rising exponential; Bsu,
time constant of the rising exponential; Aba, asymptotic value of the falling
exponential; Bba, time constant of the falling exponential; Tsc, duration of
the rising exponential. The parameters obtained from the horizontal eye register
were (Fig. 1A and 1 B): P1, eye position before the saccadic movement (by convention
negative values were from central eye position in the orbit to the left, and
conversely positives to the right); P2, eye position after the saccadic movement;
As, saccadic amplitude; Vmd, mean velocity; Vmax, maximum velocity; S, duration
of the accelerating phase of the saccade: B, duration of the decelerating phase;
Ds, duration of the saccade and A1, inverse of the time between two saccades,
Le frequency of saccades, this parameter has been used as an alertness level
index (Evinger et al., 1981). The latencies considered were (Fig. 1C): Lmv,
latency between the onset of the burst and the onset of the saccadic movement;
Tvf, latency between the peak firing rate of the burst and the peak velocity
of the saccadic movement.
All these variables were analyzed using the principal component analysis (Afifi
and Azen, 1979, Frey and Pimentel, 1978). Data in present analysis were obtained
from 10 ABD Mns antidromically identified, where a number from 30-60 spontaneous
saccades were analyzed (a total of 400 saccades were analyzed). All the values
of the variables were standardized. The coil system used in the present experiments
permits the recording of horizontal eye position, therefore saccades analysed
in the present report should be considered as putative oblique saccades. The
parameters of each saccade were stored in files created in the computer where
a standard program of principal component analysis was applied (KM from the
BMDP statistical library).
In Fig.1C (bottom) is shown the firing rate pattern of an ABD Mn, showing the
typical pattern of burst activity during saccades proportional to eye velocity
(Fig. 1C top), and the steady state phase proportional to eye position during
eye fixation (Fig. 1A bottom).
Figure 1. A. Description of eye saccade parameters on an eye saccade diagram
(top) and eye position recording (bottom). E, eye position; L, left; R, right.
B. Description of eye velocity parameters on an velocity diagram (top) and double
exponential model (bottom) fitting motoneuron burst (see introduction and methods)
. E, eye velocity; . FR, firing rate. C. Eye velocity register (top) and motoron
firing rate (bottom). Variable abbreviations appear in the methods section.
The principal component analysis program used (KM from BMDP) provides a table
of the explained variance (VP) by the calculated principal components (Table
I), and the cumulative proportion of variance explained by each of the principal
components (VA). Table I shows that the first 4 components account for 70% of
the variance. 70% is a value of cumulative variance typical for not considering
more loading factors in the interpretation of the analysis (Afifi and Azen,
1979; Frey and Pimentel, 1978). However, given that the two first components
account for 52% of the total variance, and in order to simplify the interpretation
results, only the first two axes were considered. For identical reasons the
same criterion was used in the other 9 analyzed Mns. Also in Table 1 appear
the calculated new coordinates (loading factors) of the variables for each component.
The loading factor values permit plotting of the eye saccade, Mns and model
parameters in an ideal plane formed by the orthogonal intersection of the ideal
calculated axes (Fig. 2).
The plot of the loading factors for components I and II for the Mn analyzed
in table I is shown in Fig 2. When the same analysis was performed for all the
Mns registered, a similar position and grouping of the variables was obtained.
For this reason, curves were traced by hand in order to group the set of variables
that i) appear in the same area of the plane traced by componente I and II in
all the analized Mns, and ii) their positions were constant in this plane in
at least 8 of the analized Mns. Three groups ( 1,2,3) of variables appear in
defined positions in the plots (Fig. 2). Group 1 include parameters from the
eye saccade as As, Vmax, Vmd and S, but also parameters from the burst as If
and Af. The variables included in group 2 are exclusively variables from the
burst as R, Rfc and Rps. The group marked as the 3 included variables from the
eye saccade as P1, B, and Ds, from the Mn firing rate as Nsu, Dd and Ts and
also contains some parameters from the exponential model as Tsc and Bsu. Other
variables appear outside these groups, P2 from the eye saccade, Tb, Ric and
Nba from the Mn firing rate and Asu, Aba and Bba from the exponential model.
The latency variables Lmv and Tvf and the alertness measure (Al) also appear
outside these groups.
The principal component analysis program ( P4M) also provides the linear correlation
matrix of the considered variables. The linear correlation matrix of variables
for Mn shown in Fig. 1 and Fig. 2 is presented in table II. The absolute values
whose linear correlation coefficient was consistently .5 in the 10 analyzed
Mns are marked by an asterisk in table II. The sign of the linear correlation
can be interpreted considering the variables in the horizontal file of the matrix
as the abcissa and the variables in the vertical row of the matriz as the ordinate.
In any case, results from the correlation matrix will be used only to support
conclusions that are not obvious from the variable arrangement plot provided
by the principal component analysis program.
A total of 400 Mn firing bursts were tested by the double exponential model
(see methods). 18% were discarded for subsequent analysis because the relationship
between Mn firing rate and the calculated double exponential did not reach the
.8 level explained in the methods section.
The most powerful use of principal component analysis arise from the possibility
of grouping variables by their coordinate proximities in the ideal orthogonal
axes created by the analysis (Afifi and Azen, 1979; Frey and Pimentel, 1978).
The variables that are situated in the same area of this ideal space are variables
that covary, which means that they should have the same proximal cause or that
some of the variables could be the cause of the others. In addition, the variable
distribution along the axes could give some physiological significance to the
mathematically calculated axes. With this perspective the 3 groups of variables
found in eye saccades, Mns burst and the descriptive model will be discussed.
Group 1 reflects the known fact that amplitude (As) and peak velocity (Vmax)
are linearly related (Goldberg, 1980), and that peak velocity of saccades (Vmax)
is also linearly related with firing rate increase (If) in the burst (Robinson,
1970; Fuchs and Luschei, 1970; Schiller, 1970; Delgado-García et al.,
1986; Gómez et al., 1986a). Also this group 1 associates the firing rate
increase in the step (Af) with variables defining eye saccade and burst increase
parameters, a fact expected from current models of saccadic generation that
assume a step command calculation from the mathematical integration of the pulse
signal generated by burst neurons (Robinson, 1981; Fuchs et al., 1985). In addition,
the presence in this group of the saccade mean velocity (Vmd) with maximun velocity
(Vmax) is coherent with results in oblique saccades of cats, monkeys and humans
(Evinger et al., 1981; King et al., 1986), where they found a linear relationship
between peak and average component velocity. It can be concluded that the amplitude,
peak velocity and average velocity of the saccade are coded by the step and
pulse commands (Robinson, 1970). The presence of the accelerating phase duration
(S) in group 1 supports the Evinger conclusion (1981) that this period of time
should be critical in determining saccade amplitude.
Figure 2. Principal component diagram of the first two ares. Variable coordinates
are obtained from the unrotated factor loading table. Variable abbreviations
appear in the methods section.
Group 2 includes variables exclusively from the Mn, with a high linear correlation
coefficient between all the variables in the group (R, Rfc, Rps ). It should
be considered that the slope of Mns increase of firing rate during the burst
(Rps) is related with maximum firing rate (R) and with the initial firing rate
(Ric) but not with the absolute value of firing rate increase (If). This fact
could be related with a higher excitability of Mns or by a more abrupt input
from pontine burst neurons if the Mn has been previously depolarised. It is
impossible with the present set of data to decide between the two hypotheses.
However, present data suggest that direct experimentation on intracellular register
of ABD Mns should be neccesary to prove a possible higher excitability of membranes
if the Mn has been previously depolarized. Research on intracellular ABD Mns
has not checked this question (Barmack, 1974; Grantyn and Grantyn, 1978). On
the other hand, the high linear correlation of final firing rate (Rfc) with
the other two variables in the group should be interpreted by the fact that
a higher firing rate end state is more probable if a high peak frequency is
Group 3 mainly is a group where duration variables from the burst and from
the eye saccade appear. In fact, from the 7 duration variables considered in
the present study, Ds, S and B from the saccade; Dd, Ts and Tb from the burst
and Tsc from the exponential model, 5 of them (Ds, B, Dd, Ts and Tsc) lie in
group 3, and S and Tb are the only variables situated outside this group. First
of all, a high linear relationship appears between Mn burst duration and eye
saccade duration, a basic result previously described in ABD Mns studies (Fuchs
and Luschei, 1970; Schiller, 1970; Henn and Cohen, 1973). Given that cat pontine
burst neurons do not code the duration of the horizontal component of eye saccade
in the burst duration (Kaneko, Evinger and Fuchs, 1981) , some coupling mechanism
should exist between cat pontine burst neurons and ABD Mns in order to match
burst Mn duration and the desired eye saccade duration. On the other hand, saccade
profile skewness is a known fact (Baloh, Sills, Kumley and Honrubia, 1975),
where the accelerating phase is shorter than the decelerating phase of the saccade.
Present results show that the rising time of the burst (Ts) and the accelerating
phase of the saccade (S) do not lie in the same group of variables and there
is no significant correlation between them. In the same sense, falling time
of the burst (Tb) and decelerating phase of the saccade (B) do not lie in the
same group, although a better correlation is found between them. However, in
the 10 registered Mns the ratios Ts/Tb and SB are less than 1 (ranges 0.4-0.7
and 0.4-0.9 respectively, data not shown). This result suggests that saccade
skewness is coded by Mn firing rate skewness, but the irregularity in the particular
time when peak firing rate is reached blurs the possible relationships between
Ts with S and Tb with B. In group 3 the eye position before the saccade (P1)
also appears. This result can be interpreted by the positive correlation of
the eye position with the variables in this group, and the negative relationship
with variables in group 2 plus Ric. This negative relationship between P1 and
Ric is due to the convention used (right eye position positive, left eye position
negative and Mn recording site in the left abducens). Presence of Nsu in group
3 can be explained by its tight relatric fixation of the desired saccade amplitude
by duration and maximum velocity suggests the possibility that the saccade coding
could be parametric and not continuously generated by the motor error signal
as present saccade generation models propose (Robinson, 1981; Fuchs et al.,
1985). Present analysis of eye and Mn parameters cannot by itself demonstrate
the latter suggestion but it shows a deep parametric structure in the encoding
of saccades by Mns.
With respect to the descriptive double exponential model (Jiménez-Ridruejo
et al., 1983; Pozo et al., 1984) for the firing rate burst of Mns checked in
the present report, its validity as a good predictor of Mn firing rate during
the burst is confirmed by the fact that 82% of analyzed saccades bursts was
accepted for subsequent analysis with the 8 linear correlation coefficient level
described in methods. In addition, validity can be tested by the correlation
between the model parameters and their corresponding Mn burst parameters. In
this sense, time duration of the rising exponential (Tsc) is correlated with
the rising time of the burst (Ts); the time constant of the rising phase of
the exponential (B su) is inversely related with the slope of the burst rising
phase (Rps); asymptotic value of the rising exponential (Asu) is related with
the peak firing rate (R) and asymptotic value of the falling exponential (Aba)
with the final firing rate (Rfc). All these results suggest as valid the proposed
(Jiménez-Ridruejo et al., 1983; Pozo et al., 1984) double exponential
model. Such a modulation has been proved to occur in ABD Mns 11 and to be neccesary
to explain saccade profiles (van Opstal and van Gisbergen, 1985). For these
reasons the exponential firing rate modulation should be incorporated in simulation
models of the oculomotor system (Bahill and Stark, 1979; Fuchs et al., 1985;
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