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The Journal of Neuroscience, June 1, 2000, 20(11):3956-3963
Parallel Cone Bipolar Pathways to a Ganglion Cell Use Different
Rates and Amplitudes of Quantal Excitation
Michael A.
Freed
Department of Neuroscience, University of Pennsylvania,
Philadelphia, Pennsylvania 19104-6058
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ABSTRACT |
The cone signal reaches the cat's On-
(X) ganglion cell
via several parallel circuits (bipolar cell types b1, b2, and b3). These circuits might convey different regions of the cone's temporal bandwidth. To test this, I presented a step of light that elicited a
transient depolarization followed by a sustained depolarization. The
contribution of bipolar cells to these response components was isolated
by blocking action potentials with tetrodotoxin and by blocking
inhibitory synaptic potentials with bicuculline and strychnine.
Stationary fluctuation analysis of the sustained depolarization gave
the rate of quantal bombardment: ~5100 quanta sec
1 for
small central cells and ~45,000 quanta sec1 for
large peripheral cells. Normalizing these rates for the vastly different numbers of bipolar synapses (150-370 per small cell vs 2000 per large cell), quantal rate was constant across the retina, ~22
quanta synapse1 sec1. Nonstationary
fluctuation analysis gave the mean quantal EPSP amplitude: ~240 µV
for the transient depolarization and 30 µV for the sustained
depolarization. The b1 bipolar cell is known from noise analysis of the
On-
ganglion cell to have a near-maximal sustained release of only
approximately two quanta synapse1 sec1.
This implies that the other bipolar types (b2 and b3) contribute many
more quanta to the sustained depolarization (
46
synapse1 sec1). Type b1 probably
contributes large quanta to the transient depolarization. Thus, bipolar
cell types b1 and b2/b3 apparently constitute parallel circuits that
convey, respectively, high and low frequencies.
Key words:
quantal rate; ganglion cell; vesicular release; retina; parallel pathways; ribbon synapse
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INTRODUCTION |
Commonly in the CNS, a signal is
transmitted forward by multiple pathways operating in parallel. The
function of such parallelism is rarely apparent, and thus the pathways
are often considered merely "redundant." Yet redundancy is an
unlikely explanation because there is selective pressure for the brain
to use space efficiently (Panico and Sterling, 1995
; Hsu et al., 1998).
Possibly, parallel pathways might carry different components of the
overall signal. Here, I explore this hypothesis for a system of
parallel circuits in cat retina that connect cones to the On- (X)
ganglion cell.
Seventy percent of the synapses to the cell, known for its linear
response to light, are of the "ribbon" type from cone bipolar cells
(Kolb, 1979; McGuire et al., 1986). Three types of bipolar cell
contribute substantially; roughly half of the contacts are from type
b1, and the rest are from types b2 and b3 (Cohen and Sterling, 1992).
All three bipolar types collect from the same patch of cones, so they
must carry the same spatial and spectral information (Cohen and
Sterling, 1990). However, they might carry different temporal
information. Indeed, the response of the cell does exhibit two
temporal components, transient and sustained, that make it sensitive,
respectively, to high and low frequencies (Cleland et al., 1973; Victor
and Shapley, 1979; Frishman et al., 1987).
Type b1 is thought to convey the transient component of the cell
because b1 provides nearly all of the bipolar input to the On-
ganglion cell, whose transient component is large (Freed and Sterling,
1988). Types b2 and b3 are hypothesized to convey the sustained
component of the cell because they do not contribute to the cell but do contribute to the cell, whose sustained component is
large. To test this hypothesis, I analyzed the voltage noise of the cell in response to a light step. This analysis provided an estimate of
the rate and size of quantal EPSPs. Under the experimental
conditions, glutamatergic bipolar synapses provide virtually all of the
response, and a basic assumption of noise analysis, which asynchronous
quanta follow Poisson statistics, is well supported (Matsui et al.,
1998; Freed, 2000). Noise analysis of the ganglion cell had already
given the sustained quantal rate of the b1 bipolar cell (Freed, 2000).
Therefore, this rate could be subtracted to give a lower limit of
average sustained rate for types b2 and b3: ~20-fold higher than for
type b1. Thus, types b2 and b3 provide nearly all quanta during the
sustained response, supporting the idea that parallel circuits convey
different temporal components of the overall signal.
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MATERIALS AND METHODS |
Detailed methods of intracellular recording have been described
previously (Freed, 2000). A cat, anesthetized with ketamine and
pentobarbital, was enucleated and then overdosed with pentobarbital. A
portion of the back of the eye, including neural retina, pigment epithelium, and sclera, was excised and placed in a chamber. The retina
was kept in tissue culture medium (minimal essential medium; Life
Technologies, Grand Island, NY), which was bubbled with a mixture of 95% oxygen-5% carbon dioxide, maintained at 34°C, and flowed at 1-2 ml/min. Pharmacological agents were introduced into the
medium; these included tetrodotoxin (Sigma, St. Louis, MO), bicuculline
methobromide (Research Biochemicals, Natick, MA), and strychnine
(Research Biochemicals).
Recording and staining. Intracellular electrodes were pulled
to tip resistances of 100-400 M
and filled with 2% neurobiotin in
3 M KCl buffered with 0.1 M Tris, pH 7.3, or
3% horseradish peroxidase (HRP) in 1 M KCl buffered with
0.05 M Tris, pH 8.6. Membrane voltages were obtained using
an electrometer and stored on an instrumental recorder. Recordings were
low-pass filtered (four-pole, Bessel, fc = 500) and digitized at 1000 Hz. A high gain (1V/mV) was used during
recording to ensure that voltage noise (~400 µV) ranged over
approximately seven bits. The baseline voltage in the dark was
subtracted from each response to keep voltages within the ranges of the
recorder and digitizer (10 V). Digitized voltages were analyzed using a
personal computer and scientific analysis software (IGOR; Wavemetrics,
Lake Oswego, OR). To compute power density spectra, time intervals of
512-2048 digitized points were multiplied by a Hanning window and were fast-Fourier transformed.
After recording, a cell was iontophoresed with either neurobiotin using
a pulsed +2 nA current (10 Hz, 50% duty cycle, 15 min) or HRP using a
continuous +5 nA current (1 min). The retina was then fixed with 4%
paraformaldehyde in phosphate buffer. Neurobiotin and HRP were
converted into dark reaction products using standard methods (Adams,
1977; Vaney, 1991, 1992), and filled cells were drawn using a camera
lucida and a 100× objective.
Photic stimulation. Light from a mercury or xenon arc lamp
illuminated a rectangular aperture that was focused on the retina. Light intensity was adjusted with neutral density filters and interrupted by an electromagnetic shutter. Light was monochromatic because of an interference filter (650 ± 15 nm). Light
intensity was ~106 photons
µm2 sec1, which caused ~5000
R* sec1 rod1 (Freed, 2000)
and saturated the rod response (half saturation, 100 R*
rod1 sec1) (Schneeweis and Schnapf,
1999). This stimulus was presented for 1-2 sec every 3-6 sec. Between
stimuli, the retina was in dim red light (termed "dark" in Results)
(Kodak Safelight 1A, 440 nm cutoff; Eastman Kodak, Rochester,
NY), which allowed the rod response to recover. Under these
conditions, the initial 100-300 msec of the response has both rod and
cone components; the remaining response had only a cone component
(Freed et al., 1996).
Potential sources of error. Several sources of noise
upstream of the bipolar terminal might modulate its quantal release and thus contribute voltage noise to the On- cell. This would cause overestimates of quantal size and underestimates of quantal rate (Wong
and Knight, 1980). Fluctuations in the current supplying the
illuminator caused small fluctuations in intensity but have been shown
to be insignificant (Freed, 2000). Poisson arrival of photons and
release of transmitter quanta from the photoreceptor terminals also
added noise but can be calculated (below) to be negligible.
Photon noise was calculated as follows. For shot noise (Rice, 1954),
the relationship between the mean v, duration of the shot event T, event rate n, and variance
2 is
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(1)
|
Small central cells had the smallest light-evoked variances,
so their estimated quantal rates would be most affected by photon noise
(Table 1). Their sustained
responses (i.e., change in mean, 
v) from the receptive
field center averaged 1 mV. The photon capture rate
nR* was calculated from the number of
photoreceptors in the receptive field center; the stimulus was an
elongated bar that covered a 60 µm strip through the center of a
400-µm-wide receptive field center
(4 * rc, where rc is measured as described by Freed and Nelson,
1994). Thus, this strip had an area of ~24,000
µm2 and contained ~10,800 rods and ~144 cones
(for photoreceptor densities see Steinberg et al., 1973). In the dark,
photon noise is negligible, and during the stimulus, the rod response
is saturated. Thus, virtually all photon noise in the ganglion cell
response comes from cones in the light. For a stimulus intensity of
106 photons µm2
sec1, the photon capture rate by a single cone is ~2 × 105 R* sec1 (for details of
calculation, see Freed, 2000). Thus, the total capture rate for all
stimulated cones (nR* = photon capture
rate * number of cones) is ~107. The duration of
the photon event, TR*, is ~100 msec
(Baylor et al., 1984). Thus, from Equation 1, the light-evoked voltage
variance attributable to photon events
(R*2) is
~1012 V2, which is negligible
compared with the total light-evoked variance measured in central
neurons (~108 V2).
Noise from quantal release from photoreceptor terminals in the dark was
also calculated using Equation 1. Again small, central cells would be
most affected. The lower bound of quantal rate, nrc, which results in an upper bound for
variance, was calculated from the number of photoreceptor synapses
within the receptive field center of the On- cell and their
estimated quantal rates. Because the stimulus rate was low enough
(~0.3 Hz) to allow rod responses to recover (see above), rods
contributed as well as cones. Because there were ~10,800 stimulated
rods (each with 1 synapse) (Rao et al., 1995) and ~144 cones (each
with 12 synapses) (Sterling and Harkins, 1990), ~12,500 stimulated
photoreceptor synapses provide input to bipolar cells that converge
upon the On- cell. The sustained quantal rate of a photoreceptor
ribbon synapse is between 20 and 100 sec1 (Ashmore and
Copenhagen, 1983; Rao et al., 1994; Rieke and Schwartz, 1996), so the
total quantal rate was >250,000 sec1. Because of filtering
by membrane capacitance, these quantal events have the same duration,
Trc, as events from quantal release at
bipolar terminals, ~10 msec. This results in a total variance, rc2, of
<1010 V2, which is negligible.
Another potential source of error is synaptic saturation, which can
occur if total quantal conductance approaches the cell's input
conductance (Koch et al., 1982; Freed et al., 1992). Then the response
would be reduced more than the associated change in voltage variance,
causing an underestimate of quantal rate. In the present study,
response saturation was minimized by holding the stimulus intensity
within the linear range.
The final potential source of error is a linear trend in the data as a
result of electrode drift or a gradual decline in the cell's sustained
depolarization. Uncorrected, a linear trend would add to the voltage
variance, causing an underestimate of quantal rate and an overestimate
of quantal amplitude. Linear trends were corrected by calculating a
regression fit to the data and then subtracting the regression slope
from this data. For analysis of stationary fluctuations, this
correction was applied to short intervals independently (see Results).
Thus, each interval was fully corrected for the particular linear trend
that it contained. For ensemble analysis, however, the regression fit
from the baseline data in the dark was applied to data during the
response. If the linear trend in baseline and response differed, then
correction of the response was incomplete. This caused an artifactual
increase in variance. Consequently, although ensemble analysis inflated quantal size, it did give relative size between transient and sustained
responses (see Results).
Adjustment for variation in quantal size. The greatest
source of error is variation in quantal size (Freed, 2000). The
coefficient of variation in ganglion cells is ~50% (Taylor et al.,
1995). This would cause the quantal rate to be underestimated and the quantal amplitude to be overestimated by ~25% (Katz and Miledi, 1972). Thus, the calculated quantal rates and amplitudes were adjusted
by this factor.
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RESULTS |
Voltage noise from bipolar cell synapses
On- ganglion cells were identified by their medium somas (~25
µm diameter in peripheral retina, ~15 µm near the central area) and their bushy dendritic arbors (Fig.
1A). Thirteen cells
were analyzed in detail (Table 1); all were selected for their large action potentials (>35 mV) and resting membrane potentials more negative than 
50 mV. The stimulus was a 1 sec, 400-µm-wide bar that
stimulated all the bipolar cells presynaptic to the cell (because
their receptive fields are in register) (Cohen and Sterling, 1990).
Stimulus intensity was adjusted (while observing the oscilloscope trace) to produce a near-maximal center response. This response consisted of a transient depolarization and a burst of spikes, followed
by a sustained depolarization and a train of spikes (Fig. 1B). The membrane voltage fluctuated between spikes,
and when these were blocked with TTX (30 nM), this voltage
noise could be seen more clearly (Fig. 1C).
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Figure 1.
Fluctuation analysis of synaptic noise in On-
cell. A, Camera lucida drawing of stained cell 13. B, Response to step of light. C, Responses during
application of TTX (cell 6). Top trace, Application of only
TTX; bottom trace, application of TTX plus bicuculline and
strychnine. Note that light increases voltage noise. Heavy
line shows intervals used for fluctuation analysis. This cell had
a relatively large transient depolarization; all other cells had a
smaller transient (B) (Fig. 4A).
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To isolate noise caused by bipolar input, amacrine input was blocked
with the GABAA antagonist bicuculline (50 µM)
and the glycine receptor antagonist strychnine (0.5 µM).
This caused a nonspecific decrease in voltage noise both in darkness
and during the sustained response to light (Fig. 1C).
However, these antagonists did not significantly affect the
light-evoked noise, nor did they significantly affect the magnitude of
the sustained response (as has been found before for this cell type)
(Caldwell et al., 1978; Saito, 1981, 1983; Bolz et al., 1985).
GABAB and GABAC antagonists were omitted
because the On- cell lacks the corresponding receptors (Cohen et
al., 1994).
Fluctuation analysis of sustained depolarization
The sustained response and its accompanying light-evoked noise
were analyzed to obtain the sustained rate of quantal bombardment on a
ganglion cell. As an example, consider cell 13, whose morphology and
response are shown in Figure 1. The sustained depolarization of this
cell (v) was 3.0 mV, and the variance averaged over 1 sec
intervals was 5.1 102 mV2 in
the dark (d2) and 6.7 × 102 mV2 in the light
(l2). The difference between these
two variances, i.e. the variance evoked by light
(2), was 1.6 × 102
mV2. The time constant of the postsynaptic event,
, was derived from the power spectrum of the light-evoked noise
(Fig. 2), which was fit with a Lorentzian
function taken to the power k:
|
(2)
|
The parameter A is a scaling constant. The best fit to
the spectrum resulted in of 4.3 msec and k = 1.2.
With these parameters, Equation 2 approximates a simple Lorentzian
function (i.e., K = 1). Thus, they are consistent with
a quantum whose decay is exponential and whose form is f(t) = aet/
, where a is the peak
amplitude (Katz and Miledi, 1972). Given this form of
quantal event, one can calculate the total quantal rate upon the
cell (Katz and Miledi, 1972) as
|
(3)
|
The calculated light-evoked rate, adjusted for variation in
quantal size by multiplying by 1.25 (see Materials and Methods), was
88,000 quanta sec1.
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Figure 2.
Spectral analysis. A. Power spectra
from cell 4 of noise before stimulus ( ) and during sustained
depolarization ( ). B, Power spectrum of light-evoked
noise. This is the difference between two spectra in A,
smoothed by averaging over three points below 20 Hz and otherwise over
five points. The spectrum is fit with Equation 2 (solid
line; see Results), which resulted in k = 1.2, thus approximating a Lorentzian. C, D, Spectra for cells 8 and 10.
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An alternative method of estimating quantal rate makes no assumption
about the shape of the quantal event (Wong and Knight, 1980). According
to this method, the spectrum of the light-evoked noise was
inverse-Fourier transformed to give the autocorrelation function, which
was then normalized to its value at t = 0 (Fig. 3). The integral of this function
estimates the quantal duration T to be 10 msec. The rate was
then calculated as
|
(4)
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and multiplied by 1.25 to adjust for variation in quantal size
(see Materials and Methods). The result was 70,000 quanta sec1, close to the rate calculated from Equation 3.
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Figure 3.
Normalized autocorrelation function of
light-evoked quanta. This is the inverse-Fourier transform of the
light-evoked spectrum in Fig. 2D, normalized to its value at
t = 0.
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Analyzing 13 cells, I found that both methods invariably gave similar
values (t test, df = 12, p = 0.68)
(Table 1). Therefore, in the following description, the results of both
methods are averaged for each cell. For all cells (except cell 1),
Equation 2 was best fit to the power spectrum of the light-evoked noise when the parameter k was close to one, justifying the
assumption of exponential quantal decay.
Small dendritic arbors have lower total quantal rates
Cell 13, analyzed above, was located in peripheral retina and had
a relatively broad dendritic arbor (240 µm diameter) (Fig. 1, Table
1). Eight additional cells from the periphery also had broad arbors and
similar rates of sustained, quantal bombardment. The average for all
nine cells was ~45,000 quanta sec1 (Table 1). Four cells
were located in central retina and had much smaller dendritic arbors
(30-70 µm diameter) (Table 1). These small central arbors had
quantal rates that were similar to each other, averaging ~5100 quanta
sec1. Thus, the rate for small arbors was lower by
approximately ninefold.
Sustained release rate at a bipolar cell synapse is invariant
across retina
The density of bipolar synapses on the arbor is invariant
across the retina (28/100 µm2 membrane area), and
thus the number of synapses on a arbor depends on its size (McGuire
et al., 1986; Cohen and Sterling, 1992; Kier et al., 1995). In the
present study, small central (3-7°) arbors had diameters of 30-70
µm (Boycott and Wässle, 1974) (Table 1) and consequently
received 150-370 bipolar synapses (Cohen and Sterling, 1992; Kolb and
Nelson, 1993). Large peripheral (18-35°) arbors had diameters of
150-290 µm (Fig. 1A, Table 1), ~7000
µm2 of membrane area (Kier et al., 1995), and
consequently received ~2000 bipolar synapses. Dividing the total
sustained rates for small and large cells by their respective numbers
of synapses gave average rates per synapse, respectively, of 21 and 23 quanta synapse1 sec1. Thus, the average
rate per synapse (nsyn) for central and
peripheral cells was not significantly different (t test,
df = 11, p = 0.76).
Quantal amplitude during the sustained response is invariant
across retina
The sustained response and accompanying noise were analyzed to
obtain the amplitude of a single quantal response. Since the power
spectra show that a quantum follows a simple exponential decay, its
amplitude can be calculated (Katz and Miledi, 1972):
|
(5)
|
The result was divided by 1.25 to adjust for variation in quantal
size (see Materials and Methods). For central and peripheral cells
quantal amplitudes were, respectively, 23 ± 5 and 33 ± 8 µV. These amplitudes were similar (t test, df = 11, p = 0.33), suggesting that quantal amplitude for
bipolar cell synapses is constant across the retina. The average
quantal amplitude for both center and periphery was 30 ± 6 µV.
To compare this quantal voltage to the spontaneous EPSCs in other
mammalian ganglion cells, I calculated the integral of the quantal
current (Freed, 2000):
|
(6)
|
where Ri is the input resistance, ~36
M for the On- cell (Freed and Nelson, 1994), and E is
the synaptic voltage for glutamate at the dark potential, ~50 mV.
Because a averaged 30 µV and averaged 6 msec (Table
1), the resulting conductance integral (
g(t)dt) is 100 pS-msec. Spontaneous EPSCs in mouse ganglion cells have a peak
conductance of 100 pS (Tian et al., 1998) and a decay time constant of
1-6 msec (Protti et al., 1997; Tian et al., 1998). Thus, their
conductance integral is 100-600 pS-msec, similar to the conductance
integral calculated here for the On- cell.
Quantal amplitude is larger during the
transient depolarization
Quantal amplitudes during the transient and sustained
depolarizations were compared by analysis of nonstationary fluctuation ("ensemble analysis") (Sigworth, 1981). Consider cell 7 as an example; the average response (v) was computed from 41 responses to a repeated stimulus (Fig.
4A). The transient
depolarization (t 
1 sec) was 5.5 mV, and the
sustained depolarization (t = 1.8-2.0 sec) was ~3.5
mV. The light-evoked ensemble variance (2) at
each of these time points was computed across responses, which resulted
in a value for the transient of 4.2 mV2 and for the
sustained depolarization of 0.27 mV2 (Fig.
4B). Substituting these values into Equation 5 and dividing by 1.25 to adjust for variation in quantal size gave quantal amplitudes for the transient and sustained depolarizations of 1.2 mV and 120 µV
(Fig. 4C). This analysis, repeated for three additional peripheral cells, gave average values for the transient and sustained quantal amplitudes of 1.1 ± 0.3 mV and 130 ± 10 µV.
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Figure 4.
Analysis of nonstationary fluctuations from cell
7. A, The average of 41 responses minus the average baseline
voltage in the dark (v). B, The difference between
individual responses and the average response (14 of 41 responses
shown). C, Point-by-point calculation of the variance minus
the average baseline variance in the dark and smoothed over 101 points
(2). D, Point-by-point calculation from
Equation 5 of quantal amplitude (a).
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By ensemble analysis, quantal amplitude during the sustained
depolarization is approximately fourfold larger than by fluctuation analysis. The difference is attributable to incomplete correction for
linear trends in the ensemble data (see Materials and Methods). Although ensemble analysis is inaccurate for the absolute quantal size,
it does give relative quantal size for the transient and sustained
depolarizations. Because the quantal amplitude during the transient is
greater by approximately eightfold, its absolute value can be estimated
as eight times the absolute value of the sustained quantal amplitude
(8 × 30 µV), ~240 µV. In theory, ensemble analysis could
also be used to calculate quantal rate during the transient
depolarization. However, the transient proved too brief to allow
accurate calculation of the necessary decay time constant from a power spectrum.
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DISCUSSION |
The fluctuation and ensemble analyses applied here assume that
quanta arrive at the ganglion cell with Poisson statistics. Supporting
this assumption, spontaneous quanta from both amacrine and bipolar cell
synapses in the presence of TTX show an exponential distribution of
intervals (Gao and Wu, 1998; Matsui et al., 1998; Dr. Masao Tachibana,
personal communication). In addition, for sustained EPSPs from
bipolar cells, the ratio of mean to variance remains constant (Freed,
2000). An exponential distribution of intervals and a constant ratio of
mean to variance are hallmarks of Poisson statistics; therefore, the
assumption of Poisson arrival seems justified.
It is natural to wonder whether Poisson processes upstream of the
bipolar-to-ganglion cell synapse might contribute significantly to the
voltage noise of the ganglion cell. Such processes include photon
absorption and quantal transmitter release from photoreceptors, shown
to be insignificant for the On- cell (see Materials and Methods).
Such processes also include quantal release from amacrine cells onto
ganglion cells and amacrine feedback control of bipolar cell release,
analyzed in detail for the On- cell and also shown to be
insignificant (Freed, 2000). This suggests that most of the voltage
noise of the cell was caused by Poisson release at the bipolar
ribbon synapse.
An empirical test of the present approach is whether the calculated
amplitude of the quantal EPSP matches the amplitude of the quantal
inward current EPSC that caused it. An approximate comparison was made
by calculating the time integral of the quantal current based on
previous measurements of input resistance and dark potential. There was
a good match to published values of glutamatergic quantal EPSCs in
mouse and rat (Protti et al., 1997; Tian et al., 1998). Given that the
key assumptions for the fluctuation and ensemble analyzes are justified
and that a key result is corroborated by a more direct method, I now
consider the possible matches of quantal size and rate with different
types of cone bipolar cell (Fig. 5).
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Figure 5.
Bipolar cell types b1, b2, and b3 form parallel
circuits from cone to On- ganglion cell. Type b1 contributes ~55%
of bipolar synapses () to the On- cell, and types b2 and b3
contribute the rest (). Present results indicate that type b1
contributes large quantal EPSPs in the ganglion cell during
initial transient depolarization of ganglion cell and thus contributes
to high-frequency responses. Types b2 and b3 cause small quantal EPSPs
during subsequent sustained depolarization and thus contribute to
low-frequency responses (diagram after Cohen and Sterling, 1992).
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Transient and sustained release from different bipolar types
The mean quantal amplitude is eightfold larger during the
transient depolarization than during the sustained depolarization. This
suggests that different bipolar types might predominate for each
component. Type b1, which contributes half of the bipolar synapses of
the On- cell (Cohen and Sterling, 1992), is known to depolarize
transiently to a light step (Nelson and Kolb, 1983). Furthermore, it
releases quanta at a low rate during the sustained depolarization (~2
quanta synapse1 sec1) and a much higher
rate during the transient (Freed, 2000). It follows that the type b1
may contribute a quantal EPSP that is larger than those from the other
bipolar types.
Quanta comprising the sustained component probably arise mainly from b2
and b3 bipolar cells because the b1 release rate during a sustained
stimulus is less than 2 quanta synapse1
sec1 (Freed, 2000). Given that b2 and b3 contribute only
about half of the bipolar synapses to the cell, their sustained
rate must be higher than 22 synapse1
sec1 calculated for the whole population. If quanta from
different cell types had different amplitudes (Gao and Wu, 1998), the
average rate would be weighted by the quantal size for each type and
its proportion of synapses. Using the average rate from fluctuation analysis (nsyn = 22), it is possible to
calculate (see Appendix; Fig. 6) that the
sustained quantal rate for b2 and b3 must be at least 46 quanta
synapse1 sec1 and might be higher.
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Figure 6.
Determining minimum value for b2 and b3 average
quantal rate per synapse (n2). Curve was
generated from Equation 10 substituted as follows:
nsyn = 22, quanta sec1,
p1 = 0.55, p2 = 0.45. The
average quantal rate per synapse for b2 and b3
(n2) has a minimum when c = 1, i.e., when quantal sizes for b1 and b2/b3 are equal, but any
disparity in quantal size makes n2 larger. Thus,
n2 is at least 46 quanta sec1
synapse1, but may be higher.
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This value for sustained quantal release (46 quanta
synapse1 sec1) resembles sustained rates
obtained by other methods at other ribbon synapses. Thus, capacitance
measurements show that a salamander rod terminal containing seven
ribbons (Townes-Anderson et al., 1985) releases ~400 quanta
sec1 (Rieke and Schwartz, 1996), for a sustained rate of 60 quanta synapse1 sec1. Similarly, noise
analysis shows that an Off bipolar cell in turtle retina is bombarded
by 9200 quanta sec1 from cones estimated to contain ~500
ribbons (Ashmore and Copenhagen, 1983). Thus, the turtle cone can
sustain release of greater than 20 quanta synapse1
sec1. Optical measurements of goldfish bipolar cell terminals
indicate a sustained release rate of ~9001
sec1 (Rouze and Schwartz, 1998) from ~50 ribbons (von
Gersdorff et al., 1996), indicating ~18 quanta
synapse1 sec1.
Ganglion cell bandwidth and the function of parallel
bipolar circuits
That a given patch of cones connects to the cell via multiple
types of bipolar cell (McGuire et al., 1986; Cohen and Sterling, 1992)
is puzzling because the bipolar cells apparently convey the same
spectral and spatial information. Similarly, in primate retina, bipolar
types DB2 and DB3 both contact the Off parasol cell (Calkins et
al., 1995). To explain parallel bipolar pathways, it was proposed that
these bipolar cell types convey different temporal information (Cohen
and Sterling, 1992). This hypothesis receives support from the present results.
The response of the cell to a time-varying light peaks at ~10 Hz
but persists at lower frequencies (Cleland et al., 1973; Victor and
Shapley, 1979; Derrington and Lennie, 1982; Frishman et al., 1987). The
high-frequency response is apparently carried by large amplitude EPSPs
evoked transiently from the b1 bipolar cell, whereas the low-frequency
response is probably carried by smaller EPSPs evoked at high sustained
rates from b2 and b3 bipolar cells. The ganglion cell also responds
optimally at ~10 Hz, probably because of its strong input from b1
(Freed and Sterling, 1988). However, it responds more weakly at lower
frequencies, probably because it lacks input from b2 and b3. It will be
interesting to learn whether broad bandwidth requires multiple,
parallel lines in other neural circuits.
Some bipolar types apparently cause larger quantal EPSPs than others.
Because all three types of synapse distribute evenly across the
dendritic tree (Cohen and Sterling, 1992), the difference cannot be
explained by differential electrotonic attenuation, and because they
are received in the same neuron, they cannot be attributable to
differences in input resistance. Perhaps the synaptic vesicles of b1
release more glutamate, or the postsynaptic receptors are more numerous
or have a greater single-channel conductance. It will be interesting to
learn which of these strategies has been selected to accomplish the
extra boost required to create the transient response.
The sensitivity of the cell to a point stimulus is highest for
small cells in the central area and falls ~10-fold as the cells
enlarge toward periphery (Linsenmeier et al., 1982). The density of the
dendritic arbor of the cell (membrane per unit area of retina) is
also highest for small central cells and declines similarly toward the
periphery (Kier et al., 1995). This suggested that the denser central
arbor catches a denser accumulation of synapses, so more are activated
by a point stimulus (Kier et al., 1995). If quantal rate or voltage
were vastly different for small and large cells, this would alter the
relationship between dendritic density and sensitivity. Thus, the
present finding that quantal rate and quantal voltage are nearly
constant for small and large cells supports the hypothesis that
dendritic pattern sets sensitivity.
| |
FOOTNOTES |
Received Jan. 10, 2000; revised March 10, 2000; accepted March 14, 2000.
This work was supported by National Institutes of Health Grants
EY11138, EY00828, and MH48168. I thank Ralph Nelson and Robert Smith
for technical advice and support and Peter Sterling for thoughtful
editorial suggestions. I am grateful to Sharron Fina for preparing this manuscript.
Correspondence should be addressed to Dr. Michael A. Freed, Department
of Neuroscience, University of Pennsylvania, Philadelphia, PA
19104-6058. E-mail:
michael{at}retina.anatomy.upenn.edu.
| |
APPENDIX |
To derive an expression for the average quantal rate for the
synapses of b2 and b3, these types and the b1 can be treated as two
separate classes. Each class contributes a portion of the synapses of
the On- cell (px), response
(vx), and light-evoked variance
(x2); each class has an average
peak quantal amplitude (ax) and rate (nx). Because power spectra of the
light-evoked noise lacked obvious inflections and were fit by single
Lorentzians (Fig. 3), the two classes have quanta with the same time
constant (t).
The measured response and light-evoked variance is the simple sum of
responses and variances from individual bipolar cell classes, so
the estimated average quantal rate at a single synapse is
|
(7)
|
where subscripts 1 and 2 refers to the b1 bipolar cell and the
remaining types, respectively.
Campbell's theorem (Rice, 1954) specifies that v = nf(t)dt and that 2 = nf2(t)dt. The quanta have the form
f(t) = aet/, therefore
f(t)dt = at and
f2(t)dt = a2t.
Substituting these expressions into Equation 7 gives
|
(8)
|
Substituting the expression c = a1/a2 into this equation gives
|
(9)
|
Solving this last equation for n2
gives
|
(10)
|
| |
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ABSTRACT
INTRODUCTION
