Department of Neuroscience, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6058
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ABSTRACT |
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Freed, Michael A..
Rate of Quantal Excitation to a Retinal Ganglion Cell Evoked by
Sensory Input.
J. Neurophysiol. 83: 2956-2966, 2000.
To determine the rate and statistics of light-evoked
transmitter release from bipolar synapses, intracellular recordings
were made from ON-alpha ganglion cells in the periphery of
the intact, superfused, cat retina. Sodium channels were blocked with
tetrodotoxin to prevent action potentials. A light bar covering the
receptive field center excited the bipolar cells that contact the alpha cell and evoked a transient then a sustained depolarization. The sustained depolarization was quantified as change in mean voltage (v), and the increase in voltage noise that
accompanied it was quantified as change in voltage variance
(
2). As light intensity increased,
v and
2 both increased, but their
ratio held constant. This behavior is consistent with Poisson arrival
of transmitter quanta at the ganglion cell. The response component
attributable to glutamate quanta from bipolar synapses was isolated by
application of 6-cyano-7-nitroquinoxaline (CNQX). As CNQX concentration
increased, the signal/noise ratio of this response component
(
vCNQX/
CNQX)
held constant. This is also consistent with Poisson arrival and
justified the application of fluctuation analysis. Two different
methods of fluctuation analysis applied to
vCNQX and
CNQX produced
similar results, leading to an estimate that a just-maximal sustained
response was caused by ~3,700 quanta s
1. The transient
response was caused by a rate that was no more than 10-fold greater.
Because the ON-alpha cell at this retinal locus has
~2,200 bipolar synapses, one synapse released ~1.7 quanta s
1 for the sustained response and no more than 17 quanta
s
1 for the transient. Consequently, within the ganglion
cell's integration interval, here calculated to be ~16 ms, a bipolar
synapse rarely releases more than one quantum. Thus for just-maximal
sustained and transient depolarizations, the conductance modulated by a single bipolar cell synapse is limited to the quantal conductance (~100 pS at its peak). This helps preserve linear summation of quanta. The
v/
2
ratio remained constant even as the ganglion cell's response saturated, which suggested that even at the peak of sensory input, summation remains linear, and that saturation occurs before the bipolar synapse.
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INTRODUCTION |
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A central neuron encodes a stimulus by integrating
transmitter quanta from multiple synapses. The rate at which quanta
impinge on a neuron and the statistics of their arrival times determine the neuron's signal/noise ratio. For example, if quanta arrive with
Poisson statistics, then the signal/noise ratio is proportional to the
square root of the mean rate (Laughlin 1989). Mean rate and the statistics of arrival also determine how many quanta overlap temporally. This sets the instantaneous synaptic conductance that limits the linearity of summation. For example, if a large synaptic conductance saturates the driving force on the ions that provide the
synaptic current, summation of quanta will be nonlinear (Freed et al. 1992
; Koch et al. 1982
; Martin
1955
; Rall 1959
). Despite their importance,
quantal rate and the statistics of arrival are relatively unknown for
central neurons during natural stimulation in an intact neural circuit.
In theory, rate and arrival statistics can be evaluated by counting
quanta. This approach works in culture where a neuron receives quanta
infrequently from a few synapses (Bekkers and Stevens
1995; Forti et al. 1997
; Isaacson and
Walmsley 1995
; Liu and Tsien 1995
). This
approach has not proved feasible in intact neuronal circuits because
quanta arrive from so many synapses at such high frequencies that
individual quanta merge in the macroscopic voltage. An alternative
approach has been to measure the mean and variance of the membrane
voltage. If for different stimulus intensities, the ratio of these two
measures is constant, then quantal arrival is consistent with Poisson
statistics (Dodge et al. 1968
; Katz and Miledi
1972
). This has been found in a vertebrate circuit (cone to
OFF bipolar cell) (Ashmore and Copenhagen
1983
). Assuming that quantal arrival is indeed Poisson,
measurements of mean and variance were used to calculate the quantal rate.
The present study used this method (measurement of voltage mean and
variance) to estimate the mean rate and arrival statistics of quanta
from bipolar cell synapses on the ON-alpha ganglion cell.
For these cells in peripheral cat retina, the number of bipolar cell
synapses is known (Kier et al. 1995). Thus from the total quantal rate, one can derive the quantal rate per bipolar synapse. Because the alpha cell also receives amacrine synapses, special precautions were taken to restrict the analysis to glutamate quanta from bipolar cells. This was done by applying a glutamate antagonist, CNQX, and analyzing only those components of the voltage mean and variance that were sensitive to this antagonist.
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METHODS |
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Intracellular recording
Intracellular recordings were made from a superfused, flattened
preparation of the mammalian retina (Dacey and Lee 1994;
Jensen 1991
). Experimental procedures were approved by
the University of Pennsylvania Animal Care and Use Committee. A cat was
anesthetized with ketamine (10 mg/kg im) and then pentobarbital sodium
(50 mg/kg ip); an eye was removed, and the cat overdosed with
pentobarbital. A 1 × 0.5 cm rectangle, which included the ventral
retina, pigment epithelium, and sclera, was removed from the back of
the eye and placed in a chamber on the stage of an upright microscope.
The retina was superfused at 1-2 ml/min with tissue-culture medium (minimal essential medium, Life Technologies, Rockville, MD), which was bubbled with a mixture of 95% oxygen and 5% carbon dioxide and heated to 34°C. Pharmacological agents were kept in an array of
reservoirs, any of which could provide the superfusate. These agents
were tetrodotoxin (TTX; Sigma, St. Louis, MO),
6-cyano-7-nitroquinoxaline (CNQX),
L-(+)-2-amino-4-phosphonobutyric acid (L-AP4),
bicuculline methobromide, strychnine, and
N-(2,6-dimethylphenyl carbamoylmethyl) triethylammonium
bromide (QX-314; RBI, Natick, MA). Electrodes were filled with 1%
pyranine in 1 M KCl buffered with 0.1 M Tris (pH 7.3) and had tip
resistances of ~100 M
.
To visualize ganglion cells, a few drops of 0.001% acridine orange were added to the superfusate. This dye was taken up by ganglion cell somas, causing them to fluoresce when excited with near-ultraviolet (UV) light (400-440 nm). An alpha cell was identified by its large soma, and the tip of a microelectrode was advanced until it touched the soma. The illumination was turned off, and the microelectrode was advanced to impale the cell. During recording, the pyranine diffused into the soma and dendrites, confirming the cell's identity.
To create visual stimuli, the filter cube used for epifluorescence microscopy was replaced by a mirror. This reflected light (from a 50-W mercury arc lamp) passed through a rectangular aperture, then through a series of neutral density and interference filters, and finally onto the retina. The stimulus comprised wavelengths of 650 ± 15 nm and, when controlled by an electromagnetic shutter, had a rise time of ~2 ms.
The stimulus intensity was ~106 photons
µm2 s
1, which caused
~5,000 R* s
1 rod
1
(see calculation below) thus saturating the rod response (half saturation = 100 R* rod
1
s
1) (Schneeweis and Schnapf
1999
). The stimulus was presented for 1-2 s every 3-6 s.
Between stimuli, the retina was in dim red light (termed "dark" in
RESULTS; Kodak Safelight 1A, 440 nm cutoff), which allowed
the rod response to recover. Recordings from retinal neurons under
these conditions show that the initial 100-300 ms of the response has
both rod and cone components; the remaining response has only a cone
component (Freed et al. 1996
).
Membrane potential was amplified using an electrometer and stored on a frequency modulated recorder. For fluctuation analysis, recordings were digitized at 1 kHz using an anti-aliasing filter (4-pole Bessel, fc = 500 Hz). Electrode frequency response was measured by injecting white noise currents through the electrode into the bath, digitizing the resulting voltages at 10 kHz, and calculating the power spectrum. The frequency response was flat (±3 dB) from 1 to 500 Hz. At 500 Hz, the power spectral density of ganglion cell voltage noise was down by 40 dB from its peak value (Fig. 7) and was thus negligibly affected by the electrode frequency response or by the anti-aliasing filter used for fluctuation analysis.
Digitized voltages were analyzed using a Macintosh computer and scientific analysis software (IGOR, Wavemetrics, Lake Oswego, OR). Intervals of voltage noise (~0.5 s long, as shown in Figs. 1, 2, and 5) were selected for analysis. The voltages within some of these intervals showed slight linear trends, due either to electrode drift or to a gradual decline of the cell's sustained depolarization (e.g., Fig. 9A). Before calculating variance and power spectra, the drift was corrected for by fitting a line to the voltages within the interval (regression fit) and subtracting this line from the voltages.
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Calculating error due to dispersion of quantal size
Dispersion of quantal amplitude (i.e., variation around the
mean) increases the variance of the voltage, causing an underestimate of quantal rate and an overestimate of quantal amplitude. Dispersion of
quantal amplitude could come from several factors, including variation
in vesicle size or filling, variation in the number of postsynaptic
receptors, and electrotonic decay along the dendritic arbor
(Bekkers et al. 1990; Frerking and Wilson
1996
). For retinal ganglion cells, electrotonic decay is a
small factor because their dendritic arbors are electrotonically
compact (Coleman and Miller 1989
; Freed et al.
1992
; Taylor et al. 1995
, 1996
;
Velte and Miller 1995
). Apparently other factors are
significant because the amplitudes of spontaneous excitatory
postsynaptic currents (EPSCs) recorded from retinal ganglion cells in
salamander have a 50% coefficient of variation (CV = SD/mean)
(Taylor et al. 1995
). Spontaneous PSCs in other neurons
vary by a similar amount (CV = 59%) (Frerking and Wilson
1996
). If stimulus-evoked quanta vary to the same extent as
spontaneous quanta, then fluctuation analysis would underestimate quantal rate and overestimate quantal amplitude by
(CV)2 (Katz and Miledi 1972
),
~25%. Thus to correct for dispersion, the estimated quantal rate was
multiplied by 1.25 and the estimated quantal amplitude was divided by
the same factor.
Rate of photoisomerizations within the ganglion cell's receptive field center
Under RESULTS, I calculate the contribution of
photon noise to the ganglion cell's light-evoked noise. This
calculation requires an estimate for the total photoisomerization rate
of all cones in the receptive field center. This calculation also
requires a determination of whether the rods are saturated by the
stimulus, which requires a similar estimation for a single rod. A cone
outer segment is ~17 µm long (Steinberg and Wood
1974), and its absorptivity at the wavelength of peak
sensitivity (556 nm) is 0.018 µm
1
(Harosi 1975
). Thus the outer segment absorbance
(absorptivity * length) equals 0.3 and its fractional absorbance
[1
log
1(
absorbance)] equals 0.5. Given a photon efficiency of 0.7 (Dartnall 1968
), each
incident photon at the cone's peak wavelength causes ~0.35
R* (fractional absorbance * photon efficiency). The cone absorption at the stimulus wavelength (650 nm) is 0.158 times that at
its peak sensitivity (Fig. 11 of Pflug et al. 1990
), so R* per incident photon is 0.055. The cross-sectional area of
the cone outer segment is ~3 µm2
(Steinberg and Wood 1974
), and the stimulus intensity
used for a just-maximal response was ~106
photons µm
2 s
1, so
photoisomerization rate per cone (R*
photon
1 * cross-sectional area * intensity) was
~1.7 × 105 R*
s
1 cone
1. About 10°
ventral to the area centralis, where the ON-alpha cells
were recorded, there are ~5,000 cones mm
2
(Fig. 6 of Steinberg 1973
). Thus the receptive field
center, ~300 µm in radius (personal observations; Peichl and
Wässle 1979
), encompasses ~1,400 cones. So the total
photoisomerization rate (R* s
1
cone
1 * number of cones) is ~2 × 108 R* s
1. A
similar calculation for the rods, based on an outer segment length of
30 µm, a cross-sectional area of 2 µm, and a relative absorption
(
650/
502) of 0.005 results in a photoisomerization rate per rod of 5,000 R*
s
1. These calculations neglect self-screening,
the waveguide properties of the cone inner segment, and tapetal
reflectivity. But these are minor factors because, as shown in
RESULTS, the calculated photon noise is six orders of
magnitude less than the total light-evoked noise.
Rate of transmitter quanta from photoreceptors within the ganglion cell's receptive field center
In RESULTS, I calculate the contribution of quantal
release from photoreceptors to the ganglion cell's light-evoked noise. This calculation requires the rate of transmitter quanta within the
ganglion cell's receptive field center. In cat, each cone terminal has
~12 ribbon synapses (Sterling and Harkins 1990), and
each rod terminal has 1 ribbon synapse (Rao et al.
1995
). There are ~5,000 cones and 500,000 rods per
mm2 (Steinberg and Wood 1974
).
Thus within the receptive field center (300 µm radius) there are
~156,800 photoreceptor synapses. The sustained release rate of a
ribbon synapse in the dark is somewhere between 20 and 100 quanta
s
1 (Ashmore and Copenhagen 1983
;
Rao et al. 1994
; Rieke and Schwartz 1996
). The lower of these two estimates is chosen to
give an upper bound for noise from quantal release. This results in a
quantal rate for all photoreceptors within the receptive field center (nrc) of 3 × 106 quanta s
1.
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RESULTS |
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After impalement a ganglion cell was observed for several minutes;
if its dark potential was more negative than 50 mV and its action
potentials were larger than 40 mV, it was selected for further study
(Fig. 1A). Then, because action potentials obscured voltage
noise, TTX (20 nM) was applied (Fig. 1B).
The stimulus was a bar ~1 × 0.6 mm, which covered the receptive
field center and thus stimulated the bipolar cells presynaptic to the
alpha cell. The intensity of the stimulus was incremented until, by
visual inspection of the oscilloscope trace, the response was just
maximal. The intensity for maximal response was
~106 photons µm2
s
1.
The response consisted of an initial transient depolarization followed
by a sustained depolarization (Fig. 1B). The sustained response (v) was quantified by subtracting the mean
in the dark from the mean during the sustained depolarization and
averaged 3.5 ± 0.4 mV (mean ± SE; n = 13 cells). The sustained response was accompanied by an increase in
voltage noise. This noise increase (
2) was
quantified by subtracting the variance in the dark from the variance
during the sustained depolarization and averaged 0.11 ± 0.03 mV2.
Changing quantal rate did not alter 2/
v
For quanta whose arrival times have Poisson statistics, the ratio
of the voltage variance to the voltage mean
(2/
v) is
proportional to quantal amplitude (Katz and Miledi
1972
). Thus changing quantal rate should not alter this ratio.
The light-evoked quantal rate was increased by increasing stimulus
intensity. This increased both
2 and
v (Fig. 2, A-C). A plot of
2 versus
v was linear and
well fit by a regression line. The slope of this line varied from 6 to
33 µV, but the line always crossed near the origin (n = 5 cells; Fig. 2D). Thus the ratio
2/
v was constant, consistent
with quanta whose arrival times have Poisson statistics.
The light-evoked quantal rate was also changed pharmacologically to see
again whether the ratio 2/
v
remained constant. The light-evoked quantal rate was reduced by bath
application of the glutamate agonist L-AP4, which reduces the light response of ON-bipolar cells (Slaughter
and Miller 1981
). L-AP4 was applied in
concentrations from 1 to 10 µM, which incrementally reduced
v and
2 in the alpha cell
(Fig. 3A). A plot of
2 versus
v was linear
and well fit by a regression line. The slope of this line varied from
38 to 89 µV, but the line always passed close to the origin
(n = 3 cells; Fig. 3B). Thus the ratio
2/
v was again constant,
consistent with quanta whose arrival times have Poisson statistics.
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Changing quantal amplitude did not alter
vCNQX/
CNQX
For quanta whose arrival times have Poisson statistics, the
signal/noise ratio (v/
) is proportional to the
square root of quantal rate (Katz and Miledi 1972
). Thus
changing quantal amplitude should not alter this ratio. To reduce the
amplitude of quantal glutamate excitatory postsynaptic potentials
(EPSPs) from bipolar cells, CNQX was added to the bath. Then the
components of
v and
sensitive to CNQX
(
vCNQX and
CNQX) were analyzed to see whether the
signal/noise ratio
(
vCNQX/
CNQX)
had changed.
The stimulus was presented repeatedly while the concentration of CNQX
was increased stepwise (Fig.
4A). At each step, CNQX hyperpolarized the membrane potential and reduced the response amplitude. The variances before the response and during the sustained depolarization were both reduced, as was their difference,
2 (Fig. 4B). The same result was
obtained from 4 ON-alpha ganglion cells (Fig.
5). Then
v at the highest
CNQX concentration was subtracted from the same measure at each CNQX
concentration to give the component of
v sensitive to
CNQX (
vCNQX). The component of
2 sensitive to CNQX
(
CNQX2) was derived in similar fashion, and its
square root gave
CNQX.
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As CNQX concentration increased,
vCNQX and
CNQX both decreased, and a plot of
vCNQX versus
CNQX was linear and well fit by a
regression line. The slope of this line averaged 6.6 ± 0.6, and
the line always crossed close to the origin (n = 4 cells; Fig. 6). Thus the ratio
vCNQX/
CNQX
was constant, consistent with quanta from bipolar cells arriving with
Poisson statistics.
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Total quantal rate from bipolar synapses
The total quantal rate arriving from all bipolar synapses to the
ON-alpha cell during its sustained response was calculated by two methods. In the first method, the form of the quantum
f(t) was represented by the impulse response of a
k-stage low-pass filter (Ashmore and Falk
1982; Taylor et al. 1996
; Wong and Knight 1980
)
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(1) |
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(2) |
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(3) |
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The second method of calculating quantal rate made no assumptions about
the shape of the event (Wong and Knight 1980). For the
same four cells, the power spectrum of the CNQX-sensitive noise was
inverse-Fourier transformed and then divided by its value at
t = 0 to give the normalized autocorrelation function. The integral of this function estimated quantal duration T
and averaged 16 ± 4 ms. The rate
n was then
calculated as
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(4) |
In theory, the basal rate in darkness and the peak rate during the
light-evoked transient could also be estimated because CNQX reduced
mean voltage and variance in darkness and also reduced the transient
(Figs. 4 and 5). However, these measures in darkness drifted too much
over time to estimate the basal rate. Similarly, a single transient was
too brief to allow its fluctuations to be averaged over time
(fluctuation analysis), and the recording time (30 min) was too brief
to allow averaging over transients (ensemble analysis). Nevertheless,
because the largest transients were ~10-fold larger than the
sustained depolarization (Figs. 1B, 2B,
5A, and 9A), and because quantal summation during
the transient is probably linear (see DISCUSSION), a
10-fold higher rate sets an upper bound of 37,000 quanta
s1.
Peak amplitude of quantal voltage
Given that the quantal voltage has a simple exponential decay, its
peak amplitude a was estimated as
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(5) |
This amplitude for an evoked quantum can be compared with the size of a
spontaneous EPSC in other mammalian ganglion cells. This has a peak
conductance of ~100 pS (Tian et al. 1998) and a decay
time constant of ~1-6 ms (Protti et al. 1997
;
Tian et al. 1998
); therefore the integral of its
conductance is ~100-600 pS ms. Consider that the
ON-alpha cell's quantal conductance
g(t), in parallel with its input conductance
G, and in series with the synaptic voltage E,
causes a quantal voltage f(t). The quantal voltage may outlast the quantal conductance, due to membrane
capacitance, but the integrals of quantal voltage and quantal
conductance are related by Ohm's law
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(7) |
The ON-alpha cell's macroscopic light-evoked conductance
Glight can be calculated as the
product of quantal rate and the quantal conductance integral
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(8) |
Possible contributions of upstream and downstream noise sources to
2
Conceivably, noise sources upstream of the bipolar synaptic
terminal might modulate its vesicular release (Fig.
8). Also, noise sources downstream of the
bipolar terminal might be modulated by bipolar release. Either upstream
or downstream modulation would add to the ganglion cell's
2. Therefore the contributions of the main
upstream and downstream noise sources were examined.
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LAMP NOISE.
Light source intensity fluctuated due to instability of the power
supply voltage (signal/noise ratio 50). If this added to the
light-evoked noise increase, then it would decrease the signal/noise
ratio of the sustained response. However, light ON increased noise in ON-alpha cells (Fig. 1) by the same
amount as light OFF increased noise in
OFF-alpha cells. Consequently, their signal/noise ratios
were not significantly different (
v/
= 16 ± 2 for 4 OFF cells and 15 ± 2 for 13 ON
cells). Because
v/
was independent of whether the
stimulus was on or off, fluctuations in lamp intensity could not have
contributed significantly to
2.
PHOTON NOISE.
A single photon absorbed by a rod can affect spiking in a profoundly
dark-adapted ganglion cell (Barlow et al. 1971;
Mastronarde 1983
). This suggests that at any light
level, a photoreceptor is capable of transmitting photon noise to the
ganglion cell. However, in the dark, photon noise was negligible, and
during the bright stimulus, the rod response was saturated (see
METHODS). Thus virtually all photon noise in the alpha cell
came from cones.
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(9) |
NOISE FROM PHOTORECEPTOR RELEASE UPON BIPOLAR CELLS.
Light reduces quantal release by photoreceptor terminals. Because
bright light also reduces noise in bipolar cells (including those types
that contact the ON-alpha cell) (Nelson et al.
1981; R. Taylor, personal communication), quantal release from
photoreceptors is apparently the bipolar cell's main noise source.
Thus photoreceptor release would contribute indirectly to the
ON-alpha cell's
2. Because
stimulus rate (~0.3 Hz) was low enough to allow rods responses to
recover (see METHODS), the rods must repolarize between stimuli and resume quantal release. Thus rods would contribute to
quantal noise as well as cones. Therefore the total contribution of
both photoreceptors was calculated by rearranging Eq. 3
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(10) |
NOISE FROM AMACRINE RELEASE ONTO THE GANGLION CELL.
Quanta released by bipolar cells might modulate the amacrine cell's
release and thus contribute indirectly to the ON-alpha cell's 2. Most amacrine cells employ GABA
or glycine as a transmitter (Marc et al. 1995
;
Strettoi and Masland 1996
), and the postsynaptic ON-alpha cell has GABAA and glycine
receptors (but not GABAB or GABAC receptors) (Cohen et al.
1994
). The contributions of GABA and glycine to
2 were evaluated (in separate experiments)
by adding their respective antagonists bicuculline and strychnine to
the bath in concentration known to effectively block the respective
currents in the ON-alpha cell (Cohen et al.
1994
). Bicuculline (20 µM) increased the transient, and
strychnine (0.5 µM) increased basal noise, but neither significantly affected
v or
2 (Fig.
9). Apparently, under the conditions of
the main experiment, neither GABA nor glycinergic amacrine cells add to
2.
|
NOISE FROM VOLTAGE-GATED CHANNELS.
Although TTX blocked the alpha cell's voltage-gated sodium channels,
it seemed possible that the sustained depolarizing response might
activate other types of voltage-gated channel
(K+, Ca2+) that might
contribute to 2. Therefore steps of
positive current (50-100 pA) were injected into three cells to cause
depolarizations similar in amplitude to
v (3-10 mV; Fig.
10). For all three cells, the
light-evoked variance was not significantly different from zero
(Student's t-test; P > 0.65). Thus in the
presence of TTX, voltage-gated channels do not add to
2.
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DISCUSSION |
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The key conclusion is that a stimulus of just-maximal intensity to
the ganglion cell's receptive field center evokes sustained release
from bipolar cells of ~3,700 quanta s1.
Before discussing the implications of this conclusion, it is necessary
to treat the main assumptions on which it rests.
The conclusion derives from standard fluctuation analysis, which
assumes quanta arrive with Poisson statistics (Dodge et al. 1968; Katz and Miledi 1972
). If arrival is
Poisson, then the variance/mean ratio remains constant as the rate
changes. This held true when quantal rate increased with increasing
stimulus intensity (Fig. 2D), and when quantal rate
decreased with L-AP4 (Fig. 3B). If arrival is
Poisson, then the signal/noise ratio remains constant as quantal
amplitude changes. This also held true when quantal amplitude decreased
with CNQX antagonism (Fig. 6). Poisson statistics are found where
spontaneous quanta arrive at low rates on the ganglion cell
(5-200 s
1) (Gao et al.
1997
; Matsui et al. 1998
; M. Tachibana, personal communication), and the present findings suggest that, as the rate
rises due to stimulation, arrival statistics remain constant. Poisson
statistics have also been found by measuring the variance/mean ratio
for the OFF-bipolar cell at very high stimulated rates
(9,200 quanta s
1) (Ashmore and
Copenhagen 1983
).
Constant ratios of variance/mean and signal/noise could also be
consistent with a doubly Poisson process (Teich
1981). This would result if Poisson noise sources
upstream of the bipolar cell modulated the bipolar cell's
quantal release. One consequence of such modulations would be an
increase in light-evoked noise in the ON-alpha cell. Yet,
negligible additions to
2 were found from
the main upstream sources (photon absorptions, photoreceptor
transmitter release, and amacrine cells) implying that these do not
modulate the bipolar cell's transmitter release. Furthermore, were the
bipolar cell's release modulated by upstream noise, the power spectrum
of the ganglion cell's voltage noise would be attenuated at lower
frequencies and peak at higher frequencies (Wong and Knight
1980
), but this was not observed (Fig. 7B).
Doubly Poisson statistics might also result if bipolar cell release modulated Poisson noise sources downstream, again increasing light-evoked noise. Normally, sodium channels would be activated by the sustained depolarization and would provide a large source of downstream noise. However, these were blocked with TTX, and injecting depolarizing current ruled out possible contributions from other voltage-activated channels. Amacrine cell release on the ON-alpha cell might be modulated by bipolar cells, but, as evident in the null effects of bicuculline and strychnine, amacrine cells contribute insignificantly to the ON-alpha cell's sustained light-evoked noise.
The present analysis assumes that CNQX affects noise solely by antagonizing glutamate quanta released by bipolar cells onto the ON-alpha cell. CNQX probably also antagonizes glutamate quanta released by bipolar cells onto amacrine cells. This would reduce both amacrine release onto the ON-alpha cell and, because amacrine cells feed back on the bipolar cell, would increase the rate of bipolar release onto the ON-alpha cell (Fig. 8). Because quantal rate is proportional to the square of the signal/noise ratio (Eq. 3), an alteration in rate would alter the signal/noise ratio. Yet no such alteration was observed. Because quantal rate was estimated from this signal/noise ratio, any contribution of amacrine cells to this estimate was negligible.
The analysis also assumes that the ON-alpha cell sums
quanta linearly. This is consistent with finding that as quantal rate increased, the variance/response ratio remained constant (Fig. 2D). The variance/response ratio is proportional to the
amplitude of the quantal voltage (Eq. 5), and thus the
quantal voltage must have been constant. If summation were nonlinear,
increasing quantal rates would have caused successively smaller quantal
voltages. Finally, fluctuation analysis yielded a value for both the
quantal and the macroscopic conductances that are close to those
measured directly. Thus 3,700 quanta s1 seems a
reasonably good estimate, and I now consider some implications.
Release rate from a single bipolar cell synapse
The sustained release rate evoked by light from a single bipolar
cell synapse can be obtained by dividing the total quantal rate (3,700 quanta s1) by the number of bipolar synapses on
the ON-alpha ganglion cell. This number can be extrapolated
from the smaller ON-alpha cells in the area centralis that
have 550 synapses (Freed and Sterling 1988
) to the
larger ON-alpha cells of the present study recorded at
10° eccentricity. The density of bipolar synapses on the membrane is
constant, and cells at 10° have fourfold greater membrane area (Kier et al. 1995
), so they should have ~2,200
synapses. Thus the sustained rate at a single bipolar synapse is ~1.7
quanta s
1. Given that the alpha cell's
transient depolarization is no more than 10-fold larger than the
sustained depolarization, an upper bound for the transient release rate
is ~17 quanta s
1. This number seems
reasonable given that peak rates >20 quanta s
1
have been reported for other ribbon synapses by capacitance
measurements (Rieke and Schwartz 1996
; von
Gersdorff et al. 1996
) and by noise analysis (Ashmore
and Copenhagen 1983
).
Mechanism of linear summation
At low to moderate stimulus intensities, a ganglion cell's
response is proportional to stimulus flux (Barlow 1953;
Cleland and Enroth-Cugell 1968
). The mechanisms for this
linear summation have not been established. For a ganglion cell to
linearly sum the voltages generated by successive or adjacent quanta,
the quantal conductance must be small relative to the dendritic input
conductance (Freed et al. 1992
; Koch et al.
1982
; Martin 1955
; Rall 1959
). Otherwise the voltages generated by each successive or adjacent quantum
would be smaller. Also, the quantal EPSP must be small relative to the
potential difference driving the permeant ions, otherwise each quantum
would reduce the driving force for generating successive currents.
A multicompartment model of the ON-alpha cell suggested
that, if the light-evoked conductance applied by a single synapse were
low enough (~100 pS), summation would be linear (Freed et al.
1992). The present results and recordings from other mammalian ganglion cells indicate a peak quantal conductance of ~100 pS (Tian et al. 1998
); thus if quanta were to overlap in
time, the total synaptic conductance would exceed 100 ps, causing
nonlinear summation. However, 1.7 quanta s
1
implies ~0.03 quanta per integration interval (T = 16 mS). It follows from Poisson statistics that quanta overlap rarely
(P = 0.0004). Even at the highest rate (17 quanta
s
1) during the transient, quanta would overlap
rarely (P = 0.036).
Other mechanisms to preserve ganglion cell linearity have been
described. One mechanism uses the nonlinear voltage dependency of the
N-methyl-D-aspartate (NMDA) current to cancel
saturation of the non-NMDA current (Mittman et al.
1990). Another mechanism uses voltage-gated conductances to
clamp the membrane potential, preventing saturation of the synaptic
driving force (Diamond and Copenhagen 1995
). If this
mechanism were to serve the ON-alpha cell, then TTX, by
relieving this clamp, should augment its response. TTX did augment the
transient depolarization but actually reduced the sustained
depolarization (Fig. 1), suggesting that this mechanism is limited to
the transient.
Mechanism for saturation
At higher stimulus intensity, the alpha cell's response begins to saturate (Fig. 2C). This saturation could occur anywhere between the photoreceptor and, where voltages were recorded, the alpha soma (Fig. 8). If saturation occurred at the ON-alpha cell dendrites, due to exceeding the synaptic conductance consistent with linear summation, then the quantal EPSP amplitude would be reduced. Yet, during saturation, the alpha cell's variance/mean ratio remains constant (Fig. 2D). Because this ratio is proportional to quantal amplitude (Eq. 5), this constancy implies that quantal EPSP amplitude must have been constant. Thus saturation apparently is caused by a curtailing of quantal release from bipolar synapses and could originate anywhere upstream of these synapses.
Natural quantal rates on other neurons
Where the natural quantal rate impinging on a single neuron has
been measured, it appears to be low. In the present case, a mammalian
ganglion cell during visual stimulation receives ~3,700 quanta
s1 from ~2,200 synapses distributed across
the dendritic tree. This rate is low in that only ~60 quanta overlap
temporally during the sustained depolarization (3,700 quanta
s
1 * 16 ms). The low rate plus the modest
quantal conductance reduce interactions between quanta, allowing their
linear summation. Similarly, a spinal interneuron during natural
patterned motor activity receives ~100 quanta
s
1 or only about five overlapping quanta from
an unknown number of synapses (Raastad et al. 1996
).
However, the spinal neuron differs in that individual quantal
conductances are large compared with the input conductance and thus
could cause brief, but significant, nonlinearity (Raastad et al.
1998
).
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ACKNOWLEDGMENTS |
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The author is grateful for thoughtful discussions with R. Nelson and R. Smith. Special thanks to P. Sterling for carefully reading this manuscript and making excellent suggestions.
This work was supported by National Eye Institute Grant R01 EY-11138.
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 10 May 1999; accepted in final form 18 January 2000.
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REFERENCES |
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