Neuroscience Vol. 93 No. 3, pp. 1063—1076, 1999
Copyright © 1999 IBRO. Published by Elsevier Science Ltd
Printed in Great Britain. All rights reserved
0306-4522/99 $20.00+0.00
VELOCITY RESPONSE PROFILES OF COLLICULAR NEURONS: PARALLEL AND
CONVERGENT VISUAL INFORMATION CHANNELS
W. J. WALESZCZYK, C. WANG, W. BURKE and B. DREHER
Department of Anatomy and Histology, Department of Physiology, Institute for Biomedical Research,
The University of Sydney, Sydney, NSW 2006, Australia
Abstract—We have recorded from single neurons in the retinorecipient layers of the superior colliculus of the cat. We distinguished
several functionally distinct groups of collicular neurons on the basis of their velocity response profiles to photic stimuli. The first group
was constituted by cells responding only to photic stimuli moving at slow-to-moderate velocities across their receptive fields (presumably
receiving strong excitatory W-type input but not, or only subthreshold, Y-type input). These cells were recorded throughout the stratum
griseum superficiale and stratum opticum and constituted 50% of our sample. The second group of cells exhibited excitatory responses
only at moderate and fast velocities (presumably receiving excitatory Y-type but not W-type tnput). These cells constituted only about 7%
of the sample and were located principally in the lower stratum griseum superficiale. The third group of cells was constituted by cells
excited over the entire range of velocities tested (1 —2000û/s) and presumably received substantial excitatory input from both W- and Ychannels. These cells constituted almost 26% of our sample and were located in the lower stratum griseum superficiale, stratum opticum
and the upper part of the stratum griseum intermediale. Overall, cells receiving excitatory Y-type input, i.e. the sum of group two and
group three cells, constituted about a third of the sample and their excitatory discharge fields were significantly larger than those of cells
receiving only W-type input. A fourth distinct group of collicular neurons was also constituted by cells responding over a wide range of
stimulus velocities. These cells were excited by slowly moving stimuli, while fast-moving photic stimuli evoked purely suppressive
responses. The excitatory discharge fields of these cells (presumably, indicating the spatial extent of the W-input) were located within
much larger inhibitory fields, the extent of which presumably indicates the spatial extent of the Y-input. These low-velocityexcitatory/high-velocity-suppressive cells were recorded from the stratum griseum superficiale, stratum opticum and stratum griseum
intermediale and constituted about 17% of the sample. The existence of low-velocity-excitatory/high-velocity-suppressive cells in the
mammalian colliculus has not been previously reported. Low-velocity-excitatory/high-velocity-suppressive cells might play an important
role in activating “fixation/orientation” and “saccade~’ premotor neurons recorded by others in the intermediate and deep collicular layers.
Overall, in the majority (57%) of collicular neurons in our sample there was no indication of a convergence of W- and Yinformation
channels. However, in a substantial minority of collicular cells (about 43% of the sample) there was clear evidence of such convergence
and about 40% of these (low-velocity-excitalory/high-velocity-suppressive cells) appear to receive excitatory input from the W-channel
and inhibitory input from the Y-channel. © 1999 IBRO. Published by Elsevier Science Ltd.
Key words: cat’s superior colliculus, excitatory responses. suppressive responses, superficial and intermediate layers, parallel channels,
convergence of W- and Y-channels.
The superior colliculus (SC), the principal retinorecipient
nucleus of the mammalian mesencephalon, plays an important role in the selection of targets for visually guided behaviour, integration of sensory information and initiation of
goal-directed orientation responses towards novel sensory
stimuli (for reviews see Refs 81, 82 and 93). The superficial
layers of the SC (stratum zonale; stratum griseum superficiale, SGS; and stratum opticum, SO) receive massive visual
inputs which originate either directly in the retinas or are
relayed mainly, but not exclusively, via the dorsal lateral
geniculate nuclei (LGNd) and a number of visual cortical
areas, again mainly but not exclusively in the ipsilateral
hemisphere (for reviews see Refs 34, 42 and 82). In the cat,
the species in which the connectional and functional
organization of the superficial collicular layers has been
studied most thoroughly, these layers receive their direct
retinal input from only two (the so-called W- and Ychannels) of the
HVE, high-velocity-excitatory cells; HVS. highvelocity-suppressive; LGNd, dorsal lateral geniculate nucleus;
LGNv, ventral lateral geniculate nucleus; LP, lateral posterior
nucleus; LyE, low-velocity-excitatory cells; RGCs, retinal ganglion
cells; RRZ, retinorecipient zone of the pulvinar; SC, superior
colliculus; 5g. suprageniculate nucleus; SGI, stratum griseum
intermediale; SGS, stratum griseum superficiale; SO, stratum
opticum.
Abbreviations:
three principal parallel information channels present in the
visual system of this species. 11,14a,20,38,52.71,83.87.90 The W-type
retinal ganglion cells (RGCs), especially the W-2 subtype,
which provide the principal retinal input to the SC,’0-’2’~ may
be involved in the detection of local motion in the
environment77 but respond poorly or not at all to fast-moving
photic stimuli. 18.19.50.55,87.88 Although Y-type RGCs, like the
W-2 subgroup of the RGCs, are presumed to be mainly
involved in processing information about motion, unlike Wcells they exhibit good responsiveness to photic stimuli moving
at high velocities and poor responsiveness to slowly moving
photic stimuli.25,29,32,50 There is very little overlap in the laminar
distribution of W-type and Y-type retinotectal terminals.
11,28,38,55,57.67
Furthermore, although there is a strong excitatory
convergence on single collicular neurons of retinal W-type
input and corticotectal input from the primary visual cortices,
only a small proportion of collicular neurons which receive Wtype retinal input also receives Y-type input via the
corticotectal projection.12 It is not clear therefore to what
extent, if any, the convergence of retinal and corticotectal
inputs onto single collicular neurons represents the convergence of different visual information channels. Indeed, despite
clear-cut differences in the receptive field properties of W-type
and Y-type RGCs (especially in the velocity sensitivity
profiles) it has been claimed in numerous studies that
1064
W. J. Waleszczyk et al.
the receptive field properties of collicular neurons throughout
the retinorecipient layers are rather homogeneous (for review
see Ref. 82).
It has been shown recently that contrary to previous assertions there is a substantial degree of excitatory convergence of
different information channels in different visual cortical areas
of mammals with well-developed visual systems such as cats
and macaque monkeys (for review see Ref. 16). In the present
study, in order to assess the proportion of collicular neurons in
which there is convergence (or lack of convergence) of
different visual information channels we have examined
quantitatively the velocity response profiles of single neurons
in the retinorecipient layers of the cat’s SC to photic stimuli.
Our results indicate that in almost half of the collicular
neurons there is a detectable convergence of different visual
information channels.
A preliminary report of this work has been published in
abstract form.26
EXPERIMENTAL PROCEDURES
Animals, anaesthesia and surgical procedures
All efforts were made to minimize animal suffering and to reduce
the number of animals used. Experiments adhered strictly to the
guidelines of the National Health and Medical Research Council of
Australia and all procedures were approved by the Sydney University
Animal Care and Ethics Commitee. Five adult, normally pigmented,
female cats weighing from 2.2 to 3.5 kg were provided by the
Laboratory Animal Services of the University of Sydney. The initial
surgery which included intravenous and tracheal cannulation, bilateral
cervical sympathectomy and craniotomy was carried out under 1—
1.5% halothane in N20/02 (67%/33%) gaseous mixture. During the
recording sessions, the animals were paralysed with gallamine
triethiodide at the rate of 7.5 mg/kg/h in a mixture of equal parts of
5% dextrose and sodium lactate (Hartmanns) solutions and artificially
ventilated. Anaesthesia was maintained with a gaseous mixture of
N20102 (67%/33%) and halothane (0.5%). Expired-CO2 was
maintained at 3.7-4.0% by adjusting the rate of the pulmonary pump.
Body temperature was maintained at about 37.50C. Heart rate and
electroencephalogram were monitored continuously. Each day
antibiotic (amoxycillin trihydrate, 75 mg), dexamethasone phosphate
(4 mg) and atropine sulphate (0.3 mg) were injected intramuscularly.
Furthermore, each day 10 ml of 25% solution of D-mannitol was
injected intravenously.
The corneas were protected with zero-power, air-permeable plastic
contact lenses. Pupils were dilated and accommodation paralysed with
1% atropine sulphate solution. The nictitating membranes were
retracted with 0.128% phenylephrine hydrochloride. Artificial pupils,
3 mm in diameter, were placed in front of the contact lenses. Correcting lenses were used, if required, to focus the eyes on a tangent screen
located 57 cm in front of eyes. The locations of the optic discs and the
areae centrales were plotted daily using a fibre-optic projector.
Recording
Craniotomy for recording the activity of single neurons in the
superior colliculus was made at Horsley-Clarke coordinates P2-A4
and L0-5. A plastic cylinder was mounted around the opening and
glued to the skull with dental acrylic to form a well around the hole. A
smaller opening in the dura was made above the recording site. A
platinum! iridium glass-coated microelectrode was lowered until its
tip was positioned 14mm below the cortical surface. The cylinder was
then filled with 4% agar gel and sealed with warm wax to reduce brain
pulsations. The microelectrode was advanced into the colliculus with
an hydraulic micromanipulator. The action potentials of single
neurons were recorded extracellularly and amplified conventionally;
triggered standard pulses were then fed to a microcomputer.
Photic stimulation and data analysis
The excitatory receptive fields (discharge fields) of recorded units
were first plotted with a hand-held light slit projector and remapped
with hand-held black bars and spots. The size of the excitatory
discharge field was defined as the area of visual space within which
moving bars, lighter or darker than the background elicited an increase
in the cell’s firing rate which was detectable by ear.5’23 The positions
and dimensions of receptive fields were corrected for tangential
distortion. The relative magnitude of the responses to photic stimuli
presented separately through either eye (occular dominance class) was
evaluated quantitatively by the analysis of the peristimulus time
histograms)’ Computer-controlled light slits or spots from a slide
projector, used for studying, quantitatively, the properties of the receptive fields. had a luminance of 15 cd/m2/m2 against a background
luminance of 0.9 cd!m2/m2. The peristimulus time histograms were
usually constructed by summing the responses to 30 successive stimulus sweeps at each test condition. The temporal base of each histogram
was divided into 150 bins. The bin width varied depending on
stimulus velocity, the amplitude of the sweep and the time the
stimulus remained stationary outside the receptive field (see Figs 2, 3,
4, 6,7). The responses were then smoothed using a Gaussian weighted
average over five neighbouring bins. The smoothed values were used
for peristimulus time histograms and evaluation of the peak discharge
rates.
Localization of recording sites
At the end of long penetrations microlesions were made with 20
µA current passing through the microelectrode for 20 s (electrode
negative). At the end of the recording session (lasting four to six days)
the animal was deeply anaesthetized with an intravenous injection of
120 mg of sodium pentobarbitone and perfused transcardially with
warm (370C) Hartmann’s solution followed by a 4% solution of paraformaldehyde in 0.1 M phosphate buffer (pH 7.4). The midbrains
were stereotaxically blocked and sectioned coronally at 50 ~.m on a
freezing microtome. mounted on gelatinized slides and counterstained
with Cresyl Violet. The reconstruction of the locations of the cells
studied by us was based on the depth recorded from the microdrive
and the positions of the microlesions.
Statistics
Statistical significance of differences between different groups of
cells was assessed using non-parametric tests: the Mann—Whitney Utest or χ2-test.80 Statistical differences were considered significant
when P at two-tailed criterion was 0.05 or less.
RESULTS
Binocularity and spatial characteristics of collicular neurons
All our electrode penetrations were through the central
part of the SC where, in the superficial layers at least, the
binocular part of the visual field is represented (Fig. lA; see
Refs 9,27 and 49). Consistent with this, as indicated in Fig.
1B, the great majority of cells (50/58; about 86%) in our
sample were binocular cells, that is, they could be activated by
stimuli presented via either eye. All monocular cells (8/58;
about 14%) in our sample could be activated by photic stimuli
presented via the contralateral, but not the ipsilateral, eye
(class I cells). Furthermore, the majority of binocular cells was
either dominated by the contralateral eye (class 2 cells) or
responded equally well to photic stimuli presented through
either eye (class 3 cells). Thus, the eye dominance distribution
in our sample is very similar to those reported in previous
studies of the cat’s collicular visual neurons, with receptive
fields located within the binocular part of the visual field (see
Refs 4, 9, 20, 36, 38, 56, 79 and 85). For all binocular cells the
velocity response profiles were virtually the same irrespective
of the eye through which the stimuli were presented.
Consistent with numerous previous reports9,20,22,36,56,75,85 all
neurons but one in our sample were characterized (at least at
some velocities, see further) by the presence of excitatory
discharge regions in their receptive fields. Thus, as the narrow
slit of light (or a light spot of small diameter) crossed the
Convergence of channels in superior colliculus
1065
Fig. 1. (A) The positions of electrode penetrations superimposed onto the dorsal view of cat’s SC with projections of horizontal and vertical meridians
and some of their parallels (modified after Ref. 27). Note that all penetrations were in that part of the colliculus in which the central part of the binocular
visual field is represented. Note also that only the most rostral penetrations encroach onto the representation of the ipsilateral visual field (indicated by
gray area in the rostral colliculus). HM, zero horizontal meridian; VM, zero vertical meridian. (B) Percentage histogram of eye dominance classes of the
present sample of collicular neurons. Class I cells are monocular neurons which respond only to photic stimuli presented via the contralateral eye; class
2 cells are binocular neurons which give stronger excitatory response when stimulated via the contralateral eye; class 3 cells are binocular neurons
which are excited equally strongly when stimulated through either eye; class 4 cells are binocular neurons excited more strongly when stimulated via the
ipsilateral eye. Note that there were few class 4 neurons and that monocular neurons which could be excited only via the ipsilateral eye (class 5 cells)
were not present in our sample.
excitatory discharge region there was a clear increase in the
cell’s firing rate (Figs 2A, B, C, 3B, D, F. 4B, D, F). This
increase in firing rate often consisted of a single peak in the
peristimulus time response histogram (Fig. 2A and B, top and
bottom histograms, respectively; Figs 3B, D. F, 4B, D, F). For
most cells, however, at least at certain stimulus velocities, the
peristimulus time response histograms comprised two or more
distinct peaks (Figs 2B, C, 4F; see Ref. 22) suggesting that
there were several discharge subregions that were partly or
completely separated from one another.
Most cells in our sample exhibited a degree of direction
selectivity, that is, they responded more vigorously to stimuli
moving across their receptive field in one (preferred) direction
than to stimuli moving in the opposite direction. However, for
a given cell the degree of direction selectivity was usually
velocity-dependent (Figs 2A, B, C, 3D, 4D, F; see Refs 22, 56,
85 and 89). Furthermore, at a given velocity some cells
exhibited a substantial degree of direction selectivity only
when short stimuli, not extending beyond the the excitatory
discharge regions, were applied (Fig. 3B, D) but not when the
photic stimuli extended well into the parts of the suppressive
fields which did not overlap the excitatory discharge region
(Fig. 3F). In other cells however the degree of direction selectivity was not dependent on the length of the photic stimuli
applied (Fig. 4D, F).
Based on their responses to photic stimuli moving at
various velocities across their receptive fields we have distinguished four classes of cells in our sample of collicular
neurons.
Cells responding only at low to moderate velocities
Low-velocity-excitatory cells. These cells gave their
strongest excitatory responses at stimulus velocities not
exceeding 400/s. They invariably appeared to have strong
suppressive regions in their receptive fields, at least partly
overlapping with the excitatory discharge regions and
responded poorly, if at all, to long (12-28û) bars moving across
their receptive fields (Fig. 3B bottom two histograms, Fig. 3F;
see Refs 4, 22, 56, 82 and 85). Indeed, in all neurons
constituting this group (28/58 cells, about 48% of our sample)
light bars much shorter than the width of the excitatory
discharge region evoked stronger responses than stimuli
approximating the width of the excitatory discharge region
(Fig. 3B, G; see Refs 22, 36 and 85).
Low-velocity-excitatory (LVE) cells responded well (as
indicated by a substantial increase in firing rate) to short-tomedium size (1-6û) bars moving at slow-to-moderate (l-l00û/s)
velocities, but poorly, if at all, to fast-moving short or long
bars or spots (over l000/s; Figs 2A, D, 3B, C, D, F, G).
Furthermore, most of the LVE cells (23/28 about 82%) gave
their strongest responses to short bars, or small diameter spots,
moving at velocities not exceeding 100/s (Figs 2A, D, 3D, G,
5A). Indeed, the mean preferred velocity for LVE cells was
9.60/s (± 8.80/s). Consistent with the velocity— response
profiles based classification of neurons in the mammalian
visual cortex developed by Orban68 we have found that LVE
collicular cells could be classified as either velocity-low-pass
(14/27; 52%) or low-velocity-tuned (13/27; 48% of the
sample). In several earlier studies of single neurons in the
superior colliculus of the cat (see Refs 22, 78 and 79) cells
with very similar velocity—response profiles constituted the
majority of cells recorded from the superficial layers.
As indicated in Fig. SB, LVE cells were characterised by:
(i) low “spontaneous” activities (mean 1.3 spikes/s; range 0—
6 spikes/s; see Ref. 22); and (ii) low-to-moderate peak
discharge rates (mean 19.7 spikes/s; range 5—47.2 spikes/s).
Furthermore, as indicated in Fig. SC, the excitatory discharge
regions of cells responding poorly to fast-moving stimuli
tended to be relatively small (mean area 42.9±46.2 deg2 mean
diameter 6.0±3.0 deg).
Finally, LVE cells constituted the majority of cells (17/25;
68%) recorded from the SGS and a large minority of cells
(11/28; about 39%) recorded from the SO (Fig. 9).
1066
W. J. Waleszczyk et al.
Fig. 2. Patterns of discharges of collicular neurons to photic stimuli moving at different velocities. In A, B and C are shown peristimulus time
histograms for three neurons. In each case only the responses to stimuli presented via the dominant eye are presented. In each histogram the stimulus (a
light bar) moves forwards and backwards across the receptive field. The angle of the bar and the direction of movement are indicated beneath the
bottom histogram. The velocity of movement of the bar is indicated above each histogram. The bar moves only during the time indicated by the filled
rectangles beneath the histograms and then remains stationary for 400 ma (at 40û/S and lOOû/s) or 800 ins (at velocities >1000/s), outside the receptive
field before moving back in the opposite direction (right half of each histogram). The period of time necessary to complete single forward and backward
sweeps plus delays is indicated on the right of each histogram. Each peristimulus histogram was compiled from responses to 30 successive stimulus
sweeps. In D are shown the graphs of peak response vs velocity for three LVE cells. These cells (including the cell whose responses are illustrated in A)
are low-pass or low-velocity-tuned cells (see Ref. 68). In E are shown the graphs of peak response vs velocity for three cells which respond only at
moderate and high velocities but not at low velocities. These cells (including the cell whose responses are illustrated in B) are velocity high-pass (HVE)
cells (see Ref. 68). In F are shown the graphs of peak response vs velocity for three cells which respond over a wide range of velocities. These cells
(including the cell whose responses are illustrated in C) are velocity broad-band (LVE/HVE) cells (see Ref. 68). In D, E and F the responses have been
corrected for “spontaneous” activity, the levels of which are indicated by the horizontal lines through the symbols at the bottom right of each graph. All
the graphs in D, E and F are based on the responses to stimuli presented via the dominant eyes.
“Suppressed-by-contrast” cell. One of the cells in our
sample had a relatively high spontaneous firing rate (22
spikes/s) which was always reduced, rather than increased, by
the introduction into the receptive field of any sort of photic
stimulus (stationary flashing light spots or slits, slowly or
moderately but not fast-moving light or dark spots or bars).
This cell was recorded from the border of the SGS and SO
(Fig. 9) and responded only to photic stimuli presented via the
contralateral eye.
High-velocity-excitatory cells
A small number of the cells which constituted this group
(4/58; about 7% of the sample) did not respond to slowly (110û/s) moving photic stimuli but exhibited clear-cut excitatory
responses at moderate (2O-4Oû/s) and high velocities (l00-
2000û/s; Fig. 2B, E). These cells did not exhibit strong
suppressive regions within and/or around the excitatory
discharge regions and could be classified as velocity
high-pass cells (see Ref. 68). High-velocity-excitatory
(HVE) cells were recorded from the lowest part of the
lower SGS or from the SO (Fig. 9).
Low-velocity-excitatory/high-velocity-excitatory cells
Cells constituting this group (15/58; about 26% of the
sample) gave clear-cut excitatory responses over a very wide
range of stimulus velocities employed by us 1-2OOOû/s;
Fig. 2C, F). Although some of these cells were tuned for
Convergence of channels i n superior colliculus
1067
Fig. 3. Characteristics of LVE cells. A and E show outlines of the excitatory discharge fields for two LVE neurons, units 104.17 and 104.16.
respectively. Note that the nearest border of the excitatory discharge field of cell 104.17 (A) is located about 50 from the area centralis (AC, center
indicated by 0) while the excitatory discharge field of cell 104.16 (E) encompasses the area centralis (AC, center indicated by®). B shows peristimulus
time histograms of responses of unit 104.17 to light bars of different length moving at 40/s across the cell’s receptive field. The peak discharge rates of
unit 104.17 to bars of different length moving in the preferred direction at 4û/s across the cell’s receptive field are graphed in C. Note that responses
illustrated in B and C are strongest for the shortest bar (1.2û length x 1û width) and progressively weaken as the bar is lengthened until at a length of 120
(10 width) the response disappears. Note also that responses to the shorter bars (1.20 and 30) are clearly direction selective while those to longer bars
are not. The responses of cell 104.16 to a short bar (30x1û) moving at progressively increased velocities (from 4û/s to 400û /s) are illustrated in D. The
responses of the cell in D to a long bar (220x1û) moving at progressively increased velocities are illustrated in F. The amplitudes of responses of unit
104.16 to narrow bars of different length (indicated) moving at different velocities are graphed in G. Note that at all velocities the responses of unit
104.16 are substantially weaker for the longer bars, and for both the short and long bars the response diminishes with increase in stimulus velocity. In
each case only the responses to stimuli presented via the dominant eye are illustrated. For other details see legend of Fig. 2.
particular velocities (Figs 2C, F, 4D, F, G) in general these
cells could be classified as velocity broad-band cells (see Ref.
68). In a significant proportion of cells constituting the third
group, there were also strong suppressive regions within
and/or around the excitatory discharge regions (Fig. 4).
Nevertheless, all LVE/HVE cells gave clear-cut excitatory
responses not only to fast-moving (l00-2000û/s) short-tomedium (1-6û) bars (Fig. 4D, G) but also to fast-moving long
(l2-28û) bars (Figs 2C, F, 4F, C).
As indicated in Fig. 9, LVE/HVE cells were recorded
mainly (12/15) from the SO and the deepest part of the SGS
with only an occasional cell of this kind recorded from the
upper part of the lower SGS or the uppermost part of the
stratum griseum intermediale (SGI). The laminar distribution
of LVE/HVE cells was significantly different from that of
LVE cells (P<0.05; χ2-test).
Overall, the majority (12/19) of cells which were excited at
high stimulus velocities (combined HVE and LVE/HVE cells)
responded optimally at velocities exceeding 100û/s (Fig. 5A).
Not surprisingly, the preferred velocities of cells excited at
high velocities (mean 450±693û/s) were significantly
(P<0.0001; Mann—Whitney U-test) higher than those of LVE
cells.
As indicated in Fig. SB, HVE and LVE/HVE cells taken
together were characterized by: (i) moderate-to-high spontaneous activities (mean 12.8 spikes/s; range 0.4—35 spikes/s;
see Ref. 22); and (ii) moderate-to-high peak discharge rates
(mean 74.8 spikes/s; range 10.3—165.2 spikes/s). Thus, cells
responding to higher stimulus velocities differed significantly
in these parameters from LVE cells (in either case P<0.000l;
Mann—Whitney U-test). Furthermore, despite the fact that the
receptive fields of cells responding at high stimulus velocities
were located at the eccentricities not significantly different
from those of the receptive fields of the LVE cells (P>0.12;
Mann—Whitney U-test) the excitatory discharge regions of
HVE and LVE/HVE cells (mean area 185.1±248.7 deg2 mean
diameter 11.7±7.5 deg) were significantly (P<0.002;
Mann—Whitney U-test) larger than those of LVE cells (Fig.
5C).
Low-velocity-excitatory/high-velocity-suppressive cells
Cells constituting this group had rather unusual receptive
field properties and as far as we know collicular neurons with
such properties have not been described before. In particular:
(i) presentation of slowly moving (2-10û/s) short-to-medium
(2-6û) or long (12-28û) bars or small (2-4û in diameter) spots
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W. J. Waleszczyk et al.
Fig. 4. Characteristics of LVE/HVE cells. A and E show outlines of the excitatory discharge fields for two LVE/HVE neurons, units 104.12 and 104.15
respectively. Note that the nearest border of the excitatory discharge field of cell 104. 12 (A) is located about 40 from the area centralis (AC, center
indicated by ®) while the excitatory discharge field of cell 104.15 (E) encompasses the area cent rails (AC, center indicated by ®). B shows
peristimulus time histograms of responses of unit 104.12 to light bars of different length moving at 4û/s across the cell’s receptive field. The peak
discharge rates of unit 104.12 in the preferred direction to bars of different length moving at 4û/s across the cell’s receptive field are graphed in C. Note
that responses illustrated in B and C are strongest for the shortest bar (3û length x10 width) and weaken as the bar is lengthened; however a substantial
response remains for the bars of l20x10 and 220x 10. The responses of cell 104.15 to a short bar (30x 1û) moving at progressively increased velocities
(from l00/s to l0000/s) are illustrated in D. The responses of the same cell as in D to a long bar (220 x1û) moving at progressively increased velocities are
illustrated in F. The peak responses of unit 104.15 to narrow bars of different length (indicated) moving at different velocities are graphed in G. Note
that although at most velocities the peak responses of unit 104.15 for long and short bars are quite different, the overall shape of the velocity-response
curves as well as the range of best velocities for the long and short bars are very similar. .As in Figs 2 and 3 in each case only the responses to stimuli
presented via the dominant eye are illustrated. For other details see legend of Fig. 2.
revealed excitatory discharge regions in their receptive fields
(Figs 6A, B, 7A, B, C); (ii) most of the cells responded poorly
or not at all to photic stimuli moving across their receptive
fields at moderate velocities (20-40˚/s; Figs 6A, 7A, B); (iii)
both long and short bars moving at high velocities (over
100˚/s) evoked purely suppressive responses which tended to
be non-direction selective (Figs 6A, B, C, D, 7B, C): (iv)
photic stimuli moving slowly outside the excitatory discharge
region did not evoke any responses (Fig. 6C and D upper
histograms); (v) suppressive, but not excitatory, responses
could be evoked by fast-moving stimuli which were
positioned well outside the excitatory discharge regions (Fig.
6C and D, lower histograms); and (vi) while there could be
some axis-of-movement preference in the excitatory responses
to slowly moving stimuli (Fig. 7C, upper histograms) such
preferences were not apparent in the suppressive responses to
fast-moving stimuli (Fig. 7C, lower histograms).
As indicated in Figs SB, 6 and 7, LVE/high-velocitysuppressive (HVS) cells were characterized by moderate
background activities (mean 11.0 spikes/s; range 7-17
spikes/s) and moderate peak discharge rates (mean 26.8
spikes/s; range 15-43.3 spikes/s).
Consistent with the fact that in all five cats we have
recorded from the central part of the superior colliculi where
in the superficial layers the central 20-25˚ of the visual field
are represented (Fig. 1A, see Refs 9, 27 and 49) the excitatory
discharge regions of a substantial proportion (3/10) of our
LVE/HVS cells were centered or encroached on the area
centralis (Fig. 8). Furthermore, the excitatory discharge
regions of all our LVE/HVS cells were either centered or at
least encroached on the vertical and/or horizontal meridians
(Fig. 8).
The excitatory discharge regions of LVE/HVS cells were
located at eccentricities not significantly different from those
of the excitatory discharge regions of the LVE cells (P>0.7;
Mann—Whitney U-test). Similarly, the sizes of the excitatory
discharge regions of LVE/HVS cells (mean area 48.6±28.6
deg2 mean diameter 6.8±2.3 deg) were not significantly
different (P>0.3; Mann—Whitney U-test) from those of LVE
cells (Figs 5C, 8). At the same time the suppressive regions
had diameters six to eight times those of the excitatory
discharge regions and invariably included a portion of the
visual hemifield contralateral to the excitatory discharge
regions (Figs 6, 7).
Cells constituting the LVE/HVS group (10/58; about 17%
of the sample) were recorded in the deep SGS, SO or the
upper part of the SGI (Fig. 9) of all five animals studied by us.
However, one LVE/HVS cell was recorded above the deepest
part of the SGS (Fig. 9).
Convergence of channels in superior colliculus
1069
Fig. 5. Properties of collicular neurons of different classes. (A) Percentage histogram of preferred velocities of LVE, HVE and LVE/HVE neurons. Note
that while over 85% of LVE cells responded maximally at velocities not exceeding l00/s, only 20% of LVE/HVE cells responded maximally at such
velocities. Note also that all HVE cells and over 53% of LVE/HVE cells responded optimally at velocities exceeding 1000/s. (B) Peak discharge rate to
presumably optimal stimulus vs level of “spontaneous” activity. Note that cells with higher spontaneous activity tend to respond more strongly (higher
peak discharge rates) to photic stimuli. Note also that LVE neurons exhibit very little or no spontaneous activity and tend to respond weakly (low peak
discharge rates) to photic stimuli. (C) Excitatory receptive field areas of collicular neurons vs distance of the centre of the excitatory discharge region
from the area centralis (AC). Note lack of clear correlation between the receptive field size and the distance from the AC. In each case the data are based
on the responses to stimuli presented via the dominant eyes.
DISCUSSION
Parallel information channels in superior colliculus.
Low-velocity-excitatory cells. In view of the clear preference
of LVE cells (constituting almost 50% of cells in our sample)
for slowly moving stimuli and their lack of responsiveness for
fast-moving photic stimuli, it appears that these cells receive
their principal visual input from the W-channel and do not
receive a significant excitatory input from the Y-channel.
There are additional lines of evidence which support this
conclusion. First, about 75% of collicular neurons which
receive W-type input as indicated by the conduction velocity
of their retinal afferents respond poorly or not at all to photic
stimuli moving at velocities exceeding l000/s.20,38,79 Second, all
but three cells recorded from that part of the SGS where Wbut not Y-type RGCs terminate (between 200 and 600 p.m
from the collicular surface; Fig. 9), like W-type RGCs, not
only responded poorly to fast-moving photic stimuli but had
low spontaneous activities, low peak discharge rates and
contained strong suppressive regions in their receptive fields.
18.19,77.87,88
Third, the velocity low-pass cells recorded from
area 19 (which receive their principal thalamic input from the
W-type cells23) are also characterized by low spontaneous
activities, low peak discharge rates and in most cases
contained strong suppressive regions in their receptive fields
(hypercomplex or end-stopped cells, see Refs 23, 41 and 68).
Fourth, as mentioned in the introduction, although most, if not
all, neurons in the SGS which receive W-type excitatory input
from the retina receive also excitatory input from the visual
cortex, this input is not of the Y-type. 12 Fifth, although cells
responding poorly to fast-moving photic stimuli were also
encountered in the deeper part of the SGS and the SO which
receive substantial Y-type retinotectal and corticotectal inputs,
the receptive field properties of those cells were indistinguishable from those of their counterparts in the upper part
of the SGS. Furthermore, the majority of morphologically
identified neurons encountered in the deeper part of the SGS
receive W-type but not Y-type inputs.67 Indeed, this finding is
consistent with earlier findings of Berson12 that not all Wdriven cells in the lower SGS and SO receive Y-type input.
In view of the fact that the excitatory discharge regions of
collicular neurons with W-type excitatory input are substantially larger than those of W-type retinal ganglion
cells18,19,76,77,87,88 it appears that there is a substantial excitatory
convergence of W-type RGCs on single collicular neurons.
Since ablation of the ipsilateral visual cortices does not affect
the size of the collicular excitatory discharge fields75,92 it is
unlikely that the large size of the excitatory discharge fields of
collicular cells reflects the convergence of corticotectal fibers.
However, a word of caution is needed here. Thus, lack of
responsiveness to fast-moving photic stimuli does not necessarily imply that LVE cells receive only W-type excitatory
input. First of all, in view of the fact that area 17 which is
dominated by X-input (see Refs 23 and 86) provides strong
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W. J. Waleszczyk et al.
Fig. 6. Responses of a LVE/HVS cell. The hatched oval in the centre of the diagram shows the excitatory discharge field (ellipsoid hatched area) which
is embedded in the much larger suppressive field (grey), the outer boundary of which has not been accurately determined. Note however that the
suppressive field involves not only a large part of the visual field ipsilateral to the excitatory discharge field but also extends into the visual field
contralateral to the excitatory discharge region. AC, area centralis; ® indicates the center of the area centralis. (A) The peristimulus time histograms on
the left show the responses to a long bar (200 x1.20 moving forward and backward across the entire receptive field. Note the excitation at low velocities
(40/s and l00/s) and a clear suppression at high velocities (1000/s or more) with virtually no response at the intermediate (400/s) velocities. (B) A short
light bar (about 40, similar to the width of the excitatory discharge field) produces strong excitation at a low velocity (100/s) and clear suppression at a
high velocity (2000/s). (C and D) When the long bar is moved outside the excitatory discharge region there is no response at low velocities (l00/s) but
again a clear suppression at high velocities (2000/s). As in Figs 2, 3 and 4 all illustrated responses are responses to stimuli presented via the dominant
eye. As in Figs 2 and 3 in each case only the responses to stimuli presented via the dominant eye are illustrated. Other conventions as in Figs 2. 3 and 4.
non-Y corticotectal input to the superficial collicular layers12,34
it is very likely that LVE cells also receive some excitatory
input from the X-channel. Second, lack of responsiveness to
fast-moving photic stimuli does not necessarily imply that
LVE cells do not receive any excitatory input from the Ychannel. Indeed, 20—25% of cells in the primary visual
cortices of the cat (areas 17 and 18) which receive excitatory
Y-type input as indicated by the conduction velocity of their
retinogeniculate afferents respond poorly to photic stimuli
moving at velocities exceeding 1000/s.23 Similarly, about 10%
of collicular neurons which receive excitatory Y-type Input
via the ipsilateral visual cortex respond poorly to photic
stimuli moving at velocities exceeding 1000/s.20,38 Furthermore, in 40% of layer V cells recorded from area 17 of the cat,
blockade (with lignocaine) of visuotopically corresponding
parts of layer V of area 18 revealed responses to high-velocity
photic stimuli which were ineffective before the blockade.2
The suppressed-by-contrast cell recorded by us is strongly
reminiscent of the W-type “suppressed-by-contrast” or
“uniformity detectors” ganglion cells described in the cat’s
retina. 19,74.76,88 A few collicular cells with such properties have
been reported previously (see Refs 22, 35, 36 and 38).
Taking into account the laminar distribution of collicular
cells projecting to the cat’s dorsal and/or ventral lateral geniculate nuclei (LGNd and LGNv) and/or the retinorecipient
zone of the pulvinar1,33 and the fact that geniculate cells in
those regions which receive collicular input as well as cells in
the retinorecipient zone of the pulvinar (RRZ) exhibit W-like
properties (see for reviews Refs 30 and 86) it is likely that
collicular neurons receiving W- but not Y-input project to the
LGNd, LGNv and the RRZ.
High-velocity-excitatory cells. HVE cells which constituted
about 7% of the sample appeared to receive Y-type but not Wtype inputs. Unlike cells receiving only W-input these cells
were characterized by: strong excitatory responses to fastmoving photic stimuli; poor, if any, responses to slowly
moving photic stimuli; moderate-to-high spontaneous activity;
moderate-to-high peak discharge rates; and absence of strong
suppressive regions in their receptive fields. All these cells
were located in the deep SGS or SO where there is a strong Ytype input coming directly from the retina and/or indirectly via
the visual corticesi.13,20,38 Indeed, it has been reported by
Hoffmann38 that virtually all collicular neurons which receive
Y-type input directly from the retina respond vigorously at
stimulus velocities exceeding 2000/s. Again, a word of caution
is needed here. Thus, despite the lack of responses to the
slowly moving photic stimuli a subthreshold W-input to HVE
cells is a distinct possibility.
Convergence of channels in superior colliculus
1071
Fig. 7. A further example of receptive field organization of LVE/HVS cells. (A) Shows graphs of the change in discharge rate vs velocity of bar
movement for three cells which show excitation at low velocities and suppression at high velocities (0, no change in cells’ ongoing discharge rates;
positive values, increase in discharge rates; negative values, decrease in discharge rates). B and C show responses of a cell when stimulated via the
contralateral eye (B) or via the ipsilateral eye (C; excitatory discharge field and surround from stimulation of this eye). C. illustrates the fact that the
excitatory discharge region is axis-of-movement-selective (low velocities), while the suppressive region is not (high velocities). Further explanations in
text. Other conventions as in Figs 2, 3, 4 and 6.
Convergence of different information channels
part of the LP complex.
Low-velocity-excitatory/high-velocity-excitatorv cells. Over
a third (12/34) of the cells recorded from the lower part of the
lower SGS and SO as well as one cell recorded from the SGI
and two cells recorded in the upper half of the lower SGS
were LVE/HVE cells characterized by good excitatory
responses over a wide range of stimulus velocities (Fig. 9).
Those cells appear to have received their excitatory visual
inputs from both W- and Y-channels. Further support for this
conclusion comes from the fact that up to 25% of collicular
neurons which receive direct excitatory input from W-type
retinal ganglion cells responded not only to photic stimuli
moving at slow-to-moderate velocities but also quite clearly to
stimuli moving at velocities exceeding 100û/s.38,79 Like other
cells receiving excitatory Y-input (see above) cells responding
well over a wide range of stimulus velocities were
characterized by moderate-to-high spontaneous activities;
moderate-to-high peak discharge rates and usually weak
suppressive regions in their receptive fields. Furthermore, their
excitatory receptive fields tend to be larger than those of the
LVE neurons (see above). The laminar distribution of these
cells suggests that their Y-type input originates directly from
the retina and/or is relayed via the visual cortex. Note that a
substantial degree of excitatory convergence of different
information channels is apparent in all visual cortical areas of
the cat so far studied (see for review Ref. 16).
Taking into account: (i) the laminar distribution of collicular cells projecting to the suprageniculate nucleus (Sg37,47)
and/or lateral posterior nucleus of the cat (LP17,48,54); (ii) a
clear preference for high-velocity motion of Sg cells8 and
many LP neurons,1 it is likely that collicular neurons receiving
excitatory Y-input project to the Sg and/or the tectorecipient
The receptive field sizes versus velocity response profiles of
low-velocity-excitatory cells, high-velocity-excitatory cells and
low-velocity-excitatory/high-velocity-excitatory cells
At any given eccentricity the excitatory discharge regions
of collicular cells presumably receiving Y-input (HVE and
Fig. 8. Plots of the excitatory receptive fields of LVE/HVS cells.
Although only the receptive fields plotted through the dominant eye
are illustrated, all 10 cells could be activated through either eye. Note
that the excitatory receptive fields of three LVE/HVS cells encroach
onto the area central is and that the receptive fields of all cells
encroach on the horizontal and/or vertical meridian. Note also that the
excitatory receptive fields of four cells encroach onto the ipsilateral
visual field. X indicate the positions of the centres of two excitatory
receptive fields which were not completely outlined.
1072
W. J. Waleszczyk et al.
Fig. 9. Depth and laminar distribution of the present sample of collicular neurons. The anatomical subdivisions shown at right are: SAl, stratum album
intermediale; SGI, stratum griseum intermediale; SGP, stratum griseum profundum; SGS1, stratum griseum superficiale lower; SGSu, stratum griseum
superficiale upper; SO, stratum opticum; SZ, stratum zonale. The laminar distributions of the W- and Y-terminals from the retina are shown under
“retinotectal input”, while the laminar distribution of the corticotectal terminals (Y and non-Y) originating from a number of the ipsilateral visual
cortices is shown under “corticotectal input’ to the right (after Refs 10, 11, 14a, 28, 38, 45, 55, 57, 67 and 84).
LVE/HVE cells) are substantially larger than these of cells
presumably receiving only W-input (LVE cells). Similar
positive eorelations between the size of the excitatory receptive fields of collicular neurons and their responsiveness to the
fast moving photic stimuli were observed in earlier reports.22,70
Thus, one might argue that in order to excite the cell the
stimulus has to spend some minimal time in the cell’s
receptive field. To a certain extent it might be so. However,
the differences in the sizes of the excitatory receptive fields of
the HVE and LVE/HVE cells vs those of LVE cells are
probably not sufficient to account for the good responses of
HVE and LVE/HVE cells to stimuli moving at velocities
exceeding 100û/s. There are several other lines of argument,
indicating that the positive correlation between the size of the
excitatory discharge field and the responsiveness to fastmoving stimuli is not generally applicable to the visual system
at least in the cat. Thus, although at a given eccentricity
receptive fields of W-type retinal ganglion cells are at least as
large as those of the Y-type RGCs (see for review Ref. 86),
the W-type ganglion cells, unlike Y-type cells, respond poorly
or not at all to fast-moving photic stimuli.18,19,50,55,87,88 Second,
although the excitatory receptive fields of neurons in cat’s
visual cortical area 2la are at any excentricity substantially
larger than those of area 18 neurons, hardly any area 2la
neurons respond to fast-moving (over l000/s) photic stimuli24
while a very high proportion of area 18 neurons does so.23,24,68
Low-velocity-excitatory/high-velocity-suppressive cells. In
a distinct group of collicular cells (about 17% of the sample)
there appears to be a special type of convergence of the Wand Y-channels. Activation of the W-channel (by slowly
moving photic stimuli) resulted in excitation (increase in firing
rate) while activation of the Y-channel (by fast-moving photic
stimuli) resulted in inhibition (reduction in firing rate). Poor
responsiveness of these cells to stimuli moving at moderate
velocities suggests that the two inputs act in an antagonistic
manner. Furthermore, the suppressive fields revealed by the
activation of the Y-input were much larger than those revealed
by the activation of the W-input and in addition to the large
visual field ipsilateral to the excitatory discharge field the
suppressive field usually included a region of the visual field
contralateral to the excitatory discharge field of the cell.
In view of the fact that the region of LVE/HVS receptive
field which appears to receive the Y-input is very large and
invariably extends into the ipsilateral visual hemifield, it is
likely that morphological counterparts of our LVE/HVS cells
located in the lower SO and upper SGI (6/10 cells in our
sample of LVE/HVS cells) are “medium-sized trapezoid
radiating”, or “T type” efferent cells present in these layers of
cat’s superior colliculus.7,60 Indeed, the dendritic trees of the T
cells located in the lower SO or upper SGI are: (i) very large
in the dorsoventral axis (600—1 600 p.m) with dendrites
extending into the SGS7,60; and (ii) extend to over a 1000 p.m
mediolaterally and rostrocaudally.7,60 The W-type input to
these cells is likely to be relayed via the dendrites in the SGS,
while the Y-input might be relayed not only via their dendrites
in the SOS and SO but also more directly
1073
interneurons, two types of premotor (usually tectoreticular and
tecto-reticulo-spinal) cells described in the intermediate and
deep collicular layers of alert cats and macaque monkeys:
(i) cells which discharge tonically when the visual axis is
approximately stationary reduce their discharge before the
onset of the saccade which breaks the fixation and pause for
most of the saccade; and (ii) “saccade” neurons which
discharge before and during saccades to a specific region in
the visual field and pause during visual fixation.31,53,61-66,69 The
premotor cells which discharge tonically when the visual axis
is stationary have been subdivided into two subclasses:
(i) “fixation” neurons which have visual receptive fields that
include the area centralis and discharge maximally when the
animal fixates attentively the target of interest; and (ii) “orientation” neurons whose receptive fields do not include the area
centralis.63 We would argue that slowly moving photic stimuli
which evoke the excitatory responses of the LVE/HVS cells
would in the case of the LVE/HVS cells with excitatory
receptive fields involving the area centralis evoke excitatory
responses in “fixation” neurons. In the case of the LVE/HVS
cells with excitatory receptive fields not encroaching onto the
area centralis slowly moving stimuli would evoke excitatory
responses in “orientation” neurons. At the same time the
LVE/HVS cells excited by slowly moving stimuli would inhibit, presumably via interneurons, the “saccade” neurons. By
contrast, fast-moving photic stimuli by suppressing the
ongoing activity of the LVE/HVS cells would in turn reduce
the ongoing activity of inhibitory interneurons innervating
saccade neurons. There is emerging evidence that at least in
macaque and ferret the reciprocal inhibition between fixation
and saccade-related neurons is mediated by interneurons
located in the intermediate and deep collicular layers58,64 and
indeed some of the LVE/HVS neurons in our sample were
located in the SHI. However, most of the LVE/HVS cells in
our sample were located in the superficial layers. contrary to
some previous assertions, small groups of cells in the
superficial collicular layers project to the intermediate and
deep layers (see Ref. 6). Furthermore, a recent study of Lee
and co-workers51 indicates that, at least in the tree shrew, cells
in the superficial collicular layers directly excite cells in the
underlying intermediate layers. It has been postulated that
some of the so-called retinal-slip neurons in the nucleus of
optic tract, which have receptive field properties very similar
to those of LVE/HVS collicular neurons (excitatory responses
to slowly moving photic stimuli and suppressive
nondirectional responses to fast-moving stimuli) and are
believed to drive the ocular following components of
optokinetic nystagmus, function as blockers of “ocular
following in response to the visual disturbances caused by
saccades”.43
Convergence of channels in superior colliculus
via the Y-type retinal and cortical terminals in the 561 (see
Fig. 9). Furthermore, Y-input to LVEIHVS cells is presumably relayed via inhibitory interneurons and indeed, GAB Aergic neurons are plentiful in both the superficial and deep
layers of cat’s SC (see for review Ref. 59).
Another possibility, especially in relation to the LVE/HVS
cells located in the upper SO and the 565 is that the suppressive Y-input to these cells is relayed via a pretectocollicular
projection. Indeed, the pretectal complex, especially the
nucleus of the optic tract, is characterized by a large proportion of non-direction-selective cells with large receptive fields
and responding well (or exclusively) to fast-moving photic
stimuli (see Refs 39 and 79). Furthermore, the pretectal
complex projects to both the superficial and, to a lesser extent,
the intermediate collicular layers (see Ref. 42). Many of the
pretectal neurons which project to the superior colliculi are
GABAergic.3 Finally, cells with receptive field properties very
similar to these LVE/HVS collicular cells are present in the
pretectal nucleus of optic tract of cats,40 macaque monkeys39
and diprotodont marsupials-tammar wallabies.43,44
Cells with excitatory input activated by the W-channel and
inhibitory input activated by the Y-channel might be more
common than our data would suggest. In particular, the inhibitory input would be revealed by our procedures only when
the cell had a substantial spontaneous activity in the absence
of specific photic stimuli. However, most of the cells responding preferentially at low stimulus velocities but not increasing
their firing rates when fast-moving stimuli were presented had
very low, if any, background activity. Further support for the
idea that collicular cells with very extensive suppressive fields
comes from the study of Rizzolatti and his colleagues72,73 in
which they reported that in the great majority of neurons
recorded from the retinorecipient layers of the superior colliculus of the cat the magnitude of responses to a photic stimulus moving across the cell’s excitatory discharge field was
significantly (but only transiently for 2—3 s) decreased by a
second stimulus moving at 30—1000/s in a region 300 to 1200
from the border of the excitatory discharge region.72,73 When
the second stimulus was introduced into the field ipsilateral to
the cell’s excitatory receptive field the decrease of the
response was stronger and apparent in 95% of cells, while
introduction of the second stimulus into the field contra-lateral
to the excitatory receptive field produced a statistically
significant decrease of the response in only 77% of the cells
tested.
In many neurons in the intermediate and deep layers of
superior colliculi of cats and macaque monkeys there is a
substantial cross-modality excitation (see for recent review
Ref. 91) and, to a lesser degree, cross-modality suppression
(see for recent review Ref. 46). It is possible that LVE/HVS
neurons recorded by us in the intermediate layers also receive
a convergent auditory and/or somatosensory inputs. If so, the
nature of interactions between the visual and other sensory
modalities (excitatory vs suppressive) might depend on the
velocity of the photic stimuli applied.
Functional role
suppressive cells
of
low-velocity-excitatory/high-velocity-
Cells with excitatory input activated by the W-channel and
inhibitory input activated by the Y-channel might play a
unique functional role. One possibility is that these cells
innervate, with presumable involvement of some
CONCLUSIONS
In the majority (57%) of collicular neurons in our sample
of cells recorded from the retinorecipient layers there was no
indication of convergence of W- and Y-channels. However, in
about 43% of the cells there was clear evidence of convergence of W- and Y-channels. Furthermore, over 15% of collicular neurons (about 40% of these which receive convergent
input from both W- and Y-channels) appear to receive excitatory input from the W-channel and inhibitory input from the
Y-channel (LVE/HVS cells). We postulate that the LVE/HVS
cells (which constitute a new class of collicular neurons) play
1074
W. J. Waleszczyk et al.
an important role in activating “fixation/orientation”
and‘saccade” premotor neurons recorded by others in the
intermediate and deep collicular layers. Acknowledgements—
The work was supported by a grant from the National Health
and Medical Research Council of Australia. We would like to
thank anonymous reviewers for their helpful comments.
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(Accepted 25 March 1999)