1Research Unit Retinal Signal Processing, The Netherlands Ophthalmic Research Institute, and 2Department of Visual System Analysis, Graduate School Neurosciences Amsterdam, Academic Medical Center, University of Amsterdam, 1105 BA Amsterdam, The Netherlands
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ABSTRACT |
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Kraaij, D. A., H. Spekreijse, and M. Kamermans. The Open- and Closed-Loop Gain-Characteristics of the Cone/Horizontal Cell Synapse in Goldfish Retina. J. Neurophysiol. 84: 1256-1265, 2000. Under constant light-adapted conditions, vision seems to be rather linear. However, the processes underlying the synaptic transmission between cones and second-order neurons (bipolar cells and horizontal cells) are highly nonlinear. In this paper, the gain-characteristics of the transmission from cones to horizontal cells and from horizontal cells to cones are determined with and without negative feedback from horizontal cells to cones. It is shown that 1) the gain-characteristic from cones to horizontal cells is strongly nonlinear without feedback from horizontal cells, 2) the gain-characteristic between cones and horizontal cells becomes linear when feedback is active, and 3) horizontal cells feed back to cones via a linear mechanism. In a quantitative analysis, it will be shown that negative feedback linearizes the synaptic transmission between cones and horizontal cells. The physiological consequences are discussed.
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INTRODUCTION |
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The cone synaptic complex offers
a unique opportunity to study the properties of synaptic transmission
in the retina, since the stimulus of the presynaptic cell is well
defined and since in this synapse both the pre- and postsynaptic
signals can be recorded rather easily. Given the nonlinearity of the
processes involved in neurotransmitter release (Witkovsky et al.
1997), one would expect that the transfer functions are highly
nonlinear. However, under constant light conditions, the visual system
seems to be rather linear (see, for instance, Van der Tweel and
Reits 1998
). A quantitative description of the transfer
functions between photoreceptors and second-order neurons is
essential for understanding the effects of the nonlinearities in the
first step of visual signal processing for the visual system as a
whole. Various studies have addressed this question. However, in most
of these studies, salamander, toad, or xenopus was used (Belgum
and Copenhagen 1988
; Falk 1988
; Witkovsky
et al. 1997
; Wu 1998
; Yang and Wu
1996
). In contrast to fish, the horizontal cells (HC) in these
animals have a parallel rod and cone input, which complicates the
analysis. Also, fish and turtle retinae have been used (see, for
instance, Normann and Perlman 1979
), but in those
studies, the feedback signal could not be separated accurately from the
direct light response of the cones.
The feedforward synapse
The basic scheme of the events in the synapse between cones and
second-order neurons can be formulated as follows. In the dark, cones
rest at about 45 mV (Kraaij et al. 1998
). At that potential, the voltage-dependent Ca channels in the cone synaptic terminals are activated, causing a continuous Ca influx, resulting in a
continuous glutamate release. During light stimulation, cones hyperpolarize and consequently, the voltage-dependent Ca channels close, which leads to a reduction in Ca influx and to a reduction of
glutamate release (Ayoub et al. 1989
; Copenhagen
and Jahr 1989
; Witkovsky et al. 1997
). HCs, one
of the postsynaptic cell types, have
-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) -type
glutamate receptors (Lasater and Dowling 1982
;
Slaughter and Miller 1983
; Zhou et al.
1993
) and due to the continuous release of glutamate by the
cones, they rest in the dark at about
35 mV. During light
stimulation, the glutamate release by photoreceptors decreases and
consequently the AMPA-type glutamate channels in the HC membrane close,
leading to hyperpolarization of the HCs. Also, the bipolar cells (BCs)
receive input from the cones and depending on the type of glutamate
receptor (ionotropic or metabotropic), these cells will hyperpolarize
or depolarize in response to light (Ashmore and Copenhagen
1983
; Attwell et al. 1987a
; Kaneko and Saito 1983
; Nawy and Copenhagen 1987
;
Saito and Kaneko 1983
; Shiells et al.
1981
).
The feedback synapse
Besides this "feedforward" pathway, HCs feed back to cones by
directly modulating the Ca current in the cones (Verweij et al.
1996). This pathway forms the basis for the surround response of the BCs (Hare and Owen 1992
; Kaneko
1970
; Saito and Kujiraoka 1988
). HC
hyperpolarization leads to a shift of the Ca-current activation
function to more negative potentials, which results in an increase in
Ca influx and consequently to an increase in glutamate release, which
makes this pathway a negative feedback pathway. Since the Ca current is
very small relative to the total conductance of the cones
(Kamermans and Spekreijse 1999
; Kraaij et al.
2000
; Verweij et al. 1996
), negative
feedback hardly modulates the cone membrane potential, whereas it
strongly modulates the synaptic output of the cone. This means that the
signal transmitted across this type of synapse is not primarily coded
in membrane potential but in changes in Ca concentration in the cone
synaptic terminal. Therefore, the transfer functions of this synapse
determined by measuring the pre- and postsynaptic membrane potentials
as was done by (among others) Normann and Perlman
(1979)
, Belgum and Copenhagen (1988)
, and
Wu (1991
, 1993
, 1998
) does not adequately describe the
signal flow over this synapse.
Nonlinearity of synaptic transmission
The synaptic transmission between photoreceptors and second-order
neurons has been reported to be highly nonlinear (Akopian et al.
1997; Attwell et al. 1987b
; Witkovsky et
al. 1997
; Wu 1998
) and to depend on the
activation of L-type-like Ca channels. These channels do not
desensitize at all and are activated at potentials more positive than
60 mV (Verweij et al. 1996
). Both properties make
these channels very suitable for their role in sustained synaptic transmission across the cone/HC synapse because they can
maintain a continuous Ca influx at the resting-membrane potential of
the cones. In the range of physiological membrane potentials, the Ca
current has an exponential behavior which might underlie the
nonlinearity of the synaptic transmission (Witkovsky et al. 1997
) .
On the other hand, various papers have shown that the modulation
response of HCs is linearly related to the modulation depth of the
light stimulus even for large modulation depths (Chappell et al.
1985; Naka et al. 1988
; Sakai et al.
1997a
; Sakuranaga and Naka 1985
;
Spekreijse and Norton 1970
). In other words, the transfer function from cones to HCs seems to be linear. Given the Ca
dependence of the glutamate release, a special mechanism would be
required to linearize the synaptic transmission. This mechanism has not
yet been described.
Rationale
The aim of this paper is to describe the
gain-characteristics between the cones and HCs in goldfish retina. One
has to realize that the cone/HC network is a closed loop network. Cones
feed into the HC network and HCs feed back to the cones. In previous studies, dealing with the transfer functions of the cone/HC synapse, this fact has been ignored but, as will be shown, it has significant effects on the gain-characteristics. Unfortunately, at this moment, there are no pharmacological tools available to open the loop between
cones and HCs by blocking the feedback pathway. Therefore, another
method was used to separate the feedforward from the feedback signal.
Since the negative feedback signal is slower than the feedforward
signal, the initial part of the HC response is dominated by the
feedforward signal (Fahrenfort et al. 1999;
Kamermans and Spekreijse 1999
; Piccolino et al.
1981
; Wu 1994
). This enables us to determine the
open-loop feedforward gain-characteristic. The sustained part of the
response contains both the feedforward and the feedback signal
(Kamermans and Spekreijse 1999
; Piccolino et al.
1981
; Wu 1994
). That transfer function gives
therefore the closed loop gain, which describes the behavior of the
system when it is adapted to the background illumination and is
modulated around that illumination level.
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METHODS |
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Goldfish (Carassius auratus; 12-16 cm) were kept at
20°C under a 12-h-light, 12-h-dark regime. Prior to the experiment,
the fish was kept in the dark for about 8 min to facilitate the
isolation of the retina from the pigment epithelium, while keeping the
retina still light adapted. Under dim red or infrared light
illumination ( = 920 nm), the fish was decapitated and pithed,
an eye was enucleated and hemisected, and the retina was removed.
Animal handling and experimental procedures were reviewed and approved by the ethical committee for animal care and use of the Faculty of
Medicine of the University of Amsterdam, acting in accordance with the
European Community Council directive of 24 November 1986 (86/609/EEC).
The retina was placed, with the receptor side upwards, in a superfusion
chamber, illuminated with infrared light ( > 850 nm; Kodak
wratten filter 87c), and viewed with a video camera (Philips, The
Netherlands). The superfusion chamber was continuously perfused at a
rate of about 1.5 ml min
1
with oxygenated Ringer solution.
Optical stimulator
The optical stimulator used has been described in detail
elsewhere (Fahrenfort et al. 1999; Kraaij et al.
2000
). In short, it consisted of two light beams from a 450 W
Xenon light-source, projected through electronic shutters (electronic
Uniblitz VS14, Vincent Associates), neutral density filters (NG Schott,
Germany), neutral density wedges (Barr and Strout, UK), band-pass
interference filters with a bandwidth of 8 ± 3 nm (Ealing
Electro-Optics), monochromators (Ebert), and lenses and apertures.
Throughout the paper, the intensity for white light stimuli of 4.0 × 103 cd
m
2
s
1 corresponds to an
intensity of 0 log.
Electrodes
In the experiments involving HCs, intracellular recording
techniques were used, whereas in the experiments involving cones, patch-clamp recording techniques were employed. For the intracellular experiments, micro-electrodes were pulled on a Sutter puller (P-80-PC; Sutter Instruments, San Rafael) using alluminosilicate glass
(AF100-53-15; Sutter Instruments) and had a resistance ranging from 80 to 200 M when filled with 4 M KAc. The intracellular voltages were
measured with a WPI S7000A electrometer (World Precision Instruments). For the patch-clamp experiments, the electrodes were pulled from borosilicate glass (GC150TF-10, Clark, UK) with a Sutter P-87 pipette
puller (Sutter Instruments). Currents or potentials were measured using
a Dagan 3900A Integrating Patch Clamp (Dagan). Data acquisition and
control of the patch-clamp and the optical stimulator were performed
with a CED 1401 AD/DA converter (Cambridge Electronic Design, UK) and
an MS-DOS-based computer system.
Liquid junction potential
The liquid junction potential was measured with a patch electrode, filled with pipette medium, positioned in a pipette medium containing bath. Then the potential was adjusted to zero and the bath solution was replaced with Ringer solution. The resulting potential change was considered to be the junction potential and all data were corrected accordingly.
Ringer solutions and pipette medium
The Ringer solution contained (in mM) 102.0 NaCl, 2.6 KCl, 1.0 MgCl2, 1.0 CaCl2, 28.0 NaHCO3, 5.0 glucose and was continuously bubbled with approximately 2.5% CO2 and 97.5% O2 yielding a pH of 7.8. The pipette medium contained (in mM) 20.0 KCL, 70.0 D-Gluconic-K, 5.0 KF, 1.0 MgCl2, 0.1 CaCl2, 1.0 EGTA, 5.0 HEPES, 4.0 ATP-Na2, 1.0 GTP-Na3, 0.2 3':5'-cGMP-Na, 20 phosphocreatine-Na2, and 50 units/ml creatine phosphokinase. The pH of the pipette medium was adjusted to 7.25 with KOH. All chemicals were obtained from Sigma-Aldrich.
Statistics
The mean amplitude of the responses is given as mean ± SE. Statistical significance was tested using a t-test with a significance level of 0.05.
Cell classification
Cones were selected under visual control and classified
according to their spectral sensitivity (Kraaij et al.
1998). Only L-, M-, and S-cones were found. HCs were classified
based on their spatial and spectral properties (Norton et al.
1968
). In this study, only monophasic HCs (MHCs) were used.
These HCs hyperpolarize over the whole visible spectrum.
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RESULTS |
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First, the gain-characteristics of the feedforward pathway will be
determined: one in the "open-loop mode" and one in the "closed-loop mode." To obtain these functions, the R/log
I relations of cones and MHCs were determined early in the
response (between 34 and 46 ms after stimulus onset) to obtain the
gain-characteristic without the influence of feedback (open-loop mode)
and in the sustained phase of the response (between 434 and 494 ms
after stimulus onset) to obtain the gain-characteristic in the
closed-loop mode. These time-windows were chosen such that the early
window did not include the peak response of the HCs but still yielded a
relatively large amplitude, while the late window was positioned in the
sustained phase of the response. Figure 1
shows the light responses of an M-cone to 500-ms flashes of full-field
white light stimuli of various intensities. The response amplitude
increases with stimulus intensity and the slope of the onset response
becomes steeper with intensity (see inset). For the highest
intensities, the cone response starts to saturate, which leads to an
elongation of the response. The R/log I relations
of the initial and the sustained light responses of six cones were
determined with 500-ms flashes presented at an inter-stimulus interval
of at least 5 s. Since the maximal response amplitude and the
sensitivity of the cones varied slightly between individual cones, the
initial and the sustained light responses were normalized to the
maximal sustained response amplitude of each cone and shifted along the intensity axis such that the intensity needed to obtain the
half-maximal sustained light response (K) equals 1 cd
m2
s
1. These normalized
R/log I curves were averaged, interpolated in
steps of 0.02 log units, and scaled back to the mean maximal sustained
light response. The initial (solid curve
) and the sustained
R/log I relations (solid curve
) for these six
cones are shown in Fig. 2. Hill functions
(Eq. 1) were fitted through the R/log
I curves (dashed curves). The slope factor (n) of
the R/log I relation of the sustained response
was 0.69. Since the R/log I relation of the
initial response
did not reach a plateau phase, the fitted values
of n (0.34) and K (2041 cd
m
2
s
1) for this relation are
meaningless. However, since this fitted curve does describe the
experimental curve adequately in the intensity range between
2 log to
+3 log, this curve will be used later in the paper for further
analysis.
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(1) |
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The feedforward signal
Next, the responses of the HCs were studied using a similar
protocol as for the cones. To circumvent the spectrally coded pathways
in the outer plexiform layer, only full-field white light stimuli and
MHCs were used in these experiments. Note that all spectral cone types
responded equally to white light. Therefore, the input to the MHC can
be considered as one cone class for white light stimuli. Figure
3 gives the responses of an MHC to white light stimuli of 500 ms with an inter-stimulus interval of at least
10 s. The stimulus intensity was increased in steps of 0.20 log
units over a range of 3.00 log. Again, the response amplitude increased
with intensity, but in contrast to the cones, the shape of the HC
response changes strongly with intensity. For the middle intensities, a
pronounced roll-back is present in the HC response (arrow). The
R/log I relations of six MHCs were normalized to the maximal sustained response amplitude of each HC and shifted along
the intensity axis such that K for the sustained responses was 1 cd m2
s
1. Then the
R/log I curves were averaged, interpolated in
steps of 0.02 log units, and scaled back to the mean sustained response amplitude. Figure 4 gives the mean
R/log I relation of the initial (34-46 ms; curve
marked
) and the sustained (434-494 ms; curve marked
) HC
responses.
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Hill functions (Eq. 1) were fitted through both the
R/log I relations (dashed lines). The slope
factors of the initial and the sustained relation were 0.57 and 0.89, respectively, and the K value of the initial
R/log I relation was 1.22 cd
m2
s
1.
By assuming that the mean absolute sensitivities for the sustained light responses of the cones and the HCs are equal for white light,1 the intensity can be factored out, obtaining the gain-characteristic of the cone/HC synapse in the open-loop mode (Fig. 5A) and in the closed-loop mode (Fig. 5B). Figure 5A illustrates that the gain-characteristic in the open-loop mode is highly nonlinear, whereas Fig. 5B shows that the gain-characteristic in the closed loop mode is almost linear. The solid lines show the gain-characteristic based on the interpolated R/log I curves of Figs. 1 and 3 and the dashed lines show the gain-characteristics based on the fitted Hill functions of Figs. 2 and 4.
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One can define the
gain2 of the signal
transmission from cones to HCs as the slope of the gain-characteristic.
From Fig. 5, it is clear that in the open-loop mode, the gain is high
for depolarized cone membrane potentials and low for hyperpolarized
cone membrane potentials. In the closed-loop mode, on the other hand,
the gain is almost independent of cone polarization.
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(2) |
The feedback signal
Up to now the feedforward gain-characteristics from cones to HCs
have been determined. To obtain a complete description of the signal
flow between cones and HCs, the gain-characteristic of the feedback
pathway has to be derived. The HCs feed back to cones in a rather
special way. Negative feedback from HCs to cones shifts the activation
function of the cone Ca current, without a substantial change in the
cone membrane potential. This shift in activation function in cones can
be determined directly. Plotting the shift in Ca-activation function as
a function of the HC-membrane potential yields the gain-characteristic
of the HC to cone feedback synapse. To isolate the feedback signal in
cones from the feedforward signal, cones were continuously saturated
with a 65-µm-diameter white spot of 0 log and at the same time the
retina was stimulated with a full-field stimulus. During full-field
stimulation, the cone's holding potential was ramped from 70 to 0 mV
within 500 ms (Fig. 6). This protocol was
repeated for a series of intensities of the full-field stimulus. The
curves were leak subtracted, and, after leak subtraction, Eq. 2 was fitted through the data points. KCa in Eq. 2 is the
half-activation potential and nCa is
the slope factor of the Ca current. The curves of Fig. 6 were fitted
with a set of parameters in which KCa
was the only parameter that changed with intensity. The mean values of
KCa,
nCa,
gCa, and
ECa were
23.7 ± 7.6 mV,
8.7 ± 1.5 mV, 1.7 ± 1.1 nS, and 135 ± 151 mV, respectively. In Fig. 7,
KCa is plotted as a function of the
stimulus intensity yielding the R/log I curve for
the feedback signal. This relation could be fitted with a Hill equation
(Eq. 1) with a slope factor of 0.73. The gain-characteristic
of the feedback signal is the relation between the HC-membrane
potential and the shift in the cone Ca-current activation function.
Fortunately, since both the feedforward and the feedback
R/log I relation could be determined in the same
cone, the difference in intensity needed to obtain the half-maximal
response amplitude for both the feedforward and the feedback signals
could be determined without any additional assumptions. The absolute
values of K for the feedforward signal was 9.3 ± 0.4 (n = 9) log cd
m
2
s
1 and of the feedback
signal 9.2 ± 0.5 (n = 9) log cd
m
2
s
1. The difference of 0.1 log does not differ significantly from zero.
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Having both the R/log I curves of the sustained HC response (Fig. 4) and of the feedback signal (Fig. 7), the intensity was factored out, and the gain-characteristic of the feedback pathway was obtained (Fig. 8). The solid line is the gain-characteristic based on the interpolated data and the dashed line is the one based on the fitted Hill equation. This gain-characteristic is almost linear, showing that in this range of the HC potentials, the gain of the feedback pathway (millivolt shift in cone Ca-current activation function per millivolt HC polarization) is nearly independent of the HC-membrane potential. Only the gain-characteristic of the sustained part of the responses was determined because the feedback signal is almost absent in the initial phase of the response.
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The effect of feedback on the output of the cones
The shift in half-activation potential of cone Ca current will
affect the output of the cones. The question now arising is whether we
can obtain an estimate of the change in cone output due to feedback
from HCs. This estimate is an important parameter since feedback from
HCs to cones is thought to be the source of the surround response of
the BCs (Kaneko 1970, 1973
; Saito and Kujiraoka
1988
). Full-field light stimuli hyperpolarize the cones, which
leads to hyperpolarization of the HCs and consequently to a shift in
the activation function of the Ca current in cones to more negative
potentials. This causes an increase in the glutamate release by the
cones. Due to this increased transmitter release, HCs will depolarize
slightly. This depolarization is the secondary depolarizing phase or
roll-back in the HC response (see Fig. 2) (Fahrenfort et al.
1999
; Kamermans and Spekreijse 1995
;
Piccolino et al. 1981
) and was used as an estimate of
the effect of feedback on the output of the cones.
In Fig. 9A, the mean
R/log I relation of the sustained response of
four MHCs is given and in Fig. 9B, the difference between the peak and the plateau phase of the response of the same HCs is
plotted as a function of intensity. Both curves are obtained after
normalization of the intensity of the sustained R/log
I curves. This figure indicates that the roll-back in the HC
response is maximal in the middle intensity range (K = 1 cd m2
s
1), suggesting that
negative feedback is small at low and high intensities and maximal in
the middle intensity range. This is an unexpected result since the
R/log I relations of the cone, the HC, and the
feedback signal measured in cones are monotonic relations. In the
discussion, a hypothesis accounting for these seemingly contradictory
observations will be offered.
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DISCUSSION |
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In this paper, we have determined the R/log I curves of cones, HCs, the feedback signal in the cones, and the effect of the feedback on the HC responses. Based on these curves, the gain-characteristics from cones to HCs, and from HCs to cones were derived and the efficiency of the feedback signal was estimated.
The feedforward gain-characteristics
It was found that the open-loop synaptic transmission from cones
to HCs is nonlinear. Although little data about the transmission between cones and second-order neurons is available, our data are
consistent with the data concerning the transmission between rods and
second-order neurons (Akopian et al. 1997; Belgum
and Copenhagen 1988
; Falk 1988
;
Witkovsky et al. 1997
; Wu 1998
;
Yang and Wu 1996
). All these studies show a strong
nonlinearity. This nonlinearity can be accounted for by the shape of
the I-V relation of the cone Ca current in the physiological
membrane potential range of the cones. Our results are, however, not in
agreement with the work of Naka and co-workers (Naka and
Carraway 1975
; Naka and Ohtsuka 1975
;
Naka et al. 1974
; Sakai et al. 1997a
-c
; Sakuranaga and Naka 1985
), who found that cone to HC
synaptic transmission is linear. When discussing this point, one should realize that the two sets of data are based on different sets of
experiments. The conclusion that the transmission is nonlinear is
mainly based on HC flash responses recorded in the dark or on a dim
background light, whereas the later conclusions are based on white
noise modulated stimuli. Sakai et al. (1997a
-c
)
suggested that in the "white noise" stimulus used in their
experiments, high frequencies are less prominent compared with the
flash stimuli used by others. Another difference is that the
experiments of Sakai et al. are performed under a relative steady state
condition, whereas the flash experiments are not. As obvious from Fig.
5, negative feedback from HCs to cone linearizes the
gain-characteristic from cones to HCs. Since feedback has a longer time
constant than the feedforward signal, this linearization will be most
prominent in steady state conditions. This might be the reason for the
discrepancy between the white noise experiments and the flash
experiments. For full-field, low-frequency stimuli, the transmission
between cones and HCs will be rather linear, whereas for high
frequencies and small spots, it is likely to be nonlinear.
In this analysis, the assumption was made that the mean absolute
sensitivity (1/K value) of the sustained light response of the cones and MHCs are equal for white light. To investigate the dependence of the gain-characteristics on this assumption, K
of the HC R/log I curves was varied from +0.5 log
to 0.5 log in steps of 0.25 log. The resulting gain-characteristics
are presented in Fig. 10. In panel
A, the gain-characteristics based on the early responses are
plotted, and in panel B, the gain-characteristics of the
sustained responses are plotted. As is clear from this figure, the
general conclusion that feedback linearizes the gain-characteristics holds for almost a range of ±0.5 log units variation in the
K values. This range is about the reported range of
sensitivity differences in literature (Fuortes and Simon
1974
; Normann and Perlman 1979
).
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The feedback gain-characteristic
The gain-characteristic of the feedback signal turns out to be almost linear. It was not possible to polarize HCs with light far enough to show the saturation of the feedback signal other than due to the saturation of the HC response. Thus, in the range of physiological membrane potentials, HCs feed back to the cones in a linear manner. The finding that HCs feed back linearly to the cones is consistent with the finding that HCs feedback to cones via an electrical feedback mechanism (Kamermans, personal communication).
The estimates of the gain-characteristic for large HC hyperpolarizations are less reliable than for small HC hyperpolarizations because to hyperpolarize HCs strongly, high light intensities were needed, which could have adapted the cones and HCs, introducing an additional variable. Briefer flashes could not be used in these experiments because the feedback and the HC response would not have been in their sustained phase. Taken together, HCs feed back to the cones in a linear way, at least in the physiological membrane potential range of the HCs.
Now the question arises as to how a linear feedback function can
linearize the nonlinear open loop gain-characteristic. The responsible
mechanism is illustrated schematically in Fig.
11A. In the open-loop mode,
the Ca current does not shift with stimulus intensity. The result is
that the gain-characteristic from cones to HCs is dominated by the
nonlinearity of the Ca current (solid arrow). However, in the
closed-loop mode, the Ca current does shift. The higher the intensity,
the more the Ca-current activation function has shifted to negative
potentials. The result is that the gain-characteristic from cones to
HCs in the steady state becomes linear (dashed arrow). Based on this
mechanism, one could simulate the open- and closed-loop
gain-characteristics. Starting with the mean R/log
I curves of the early and late cone responses, the mean
R/log I curve of the feedback signal, and the
estimate of the Ca current (ECa = +135
mV, KCa = 27.5 mV,
nCa = 6.5), one can calculate the
early and late R/log I curves of the Ca current.
The maximal feedback-induced shift in the activation function of the Ca
current was 10 mV. The parameters chosen do not differ significantly
from the estimated values. To translate the Ca current into the
HC-membrane potential, one has to make some assumptions about the
glutamate release and the glutamate receptors on the HCs. It was
assumed that the glutamate concentration in the cleft is linearly
related to the Ca current (Witkovsky et al. 1997
), that
the glutamate receptors on the HCs have a cooperativity of 2, and that
the glutamate receptors on the HCs are activated for about 55% in the
dark (Gaal et al. 1998
). Since the Ca current ranged
from
10.5 to about 0 Ca-current units, to obtain such activation in
the dark, the dissociation constant
(KGlu) had to be about
9 Ca-current
units. To transform Ca-current into glutamate concentration in the
HC-membrane potential, Eqs. 3 and 4 were used.
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(3) |
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(4) |
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Figure 11B shows the normalized HC-membrane potential as a function of the cone-membrane potential. The simulated open-loop gain-characteristic is highly nonlinear (solid line) and the simulated closed-loop one is almost linear (dashed line). Since the capacitance of the HCs is not included in this model, only the shape of the gain functions and not the absolute amplitude can be estimated. Therefore, only the shape of the early and late gain functions can be compared. The resemblance between Figs. 5 and 11B is striking. For the gain functions of Fig. 5, it was assumed that the sustained response amplitude of the cones and of the MHCs are equally sensitive for white light. For the gain-characteristic of Fig. 11B, on the other hand, only assumptions were made about the relation between ICa, the glutamate receptor on the HC, and the relative value of the glutamate conductance in the HC. The resulting curves are almost identical.
This analysis depends strongly on the estimation of the Ca current in
the cones. In this study, we determined the I-V relation of
the Ca current using a leak subtraction protocol. The same strategy was
used by, for instance, Taylor and Morgans (1998). Wilkinson and Barnes (1996)
studied the properties of
the Ca channel in isolated salamander cones. They also found that the
half-activation potential of the Ca current in cones in isolated retina
is relatively negative. Known L-type Ca-channel blockers, such as
nisoldipine and nefedipine, were only partly effective in blocking the
Ca current. Similar results were obtained by us (unpublished
observations). Since blocking or reducing the Ca current in cones in
the isolated retina will lead to hyperpolarization of HCs, and thus to
the modulation of the activation function of the Ca current in the cones, an estimate of the half-activation potential of the Ca current
of the cones in the isolated retina cannot be made using these
pharmacological tools. Therefore, we had to rely on the leak
subtraction protocol.
Feedback efficiency is the largest for middle-range intensities and for full-field stimuli
The size of the secondary depolarization in the HCs was taken as
an estimate of the effect feedback has on the output of the cones. The
intensity response relation of the secondary depolarization is a
bell-shaped curve which peaks around 1 cd
m2
s
1 (Fig. 9B).
This result is surprising given the finding that the feedback
gain-characteristic is linearly related to the HC-membrane potential
and that the R/log I function of HCs is
sigmoidal. How then can the effect of feedback on the cone output be
bell-shaped?
Basically, Fig. 9B shows the change in HC response as a
function of intensity due to the feedback-induced change in the Ca current in cones. It suggests that, at high intensities, feedback is
reduced. As is obvious from Fig. 7, the feedback-induced shift in the
Ca current increases monotonically with intensity. However, does the
effect of this shift on the output of the cone also increase monotonically with intensity? Cones release glutamate in a Ca-dependent manner and the release is linearly related to the Ca current
(Witkovsky et al. 1997). This means that the size of the
Ca current is a first approximation of the glutamate release by the
cones. Based on the initial R/log I curve of the
feedback-induced shift in Ca current in the cones (Fig. 8) and the
parameters of the Ca current in cones in the dark (Fig. 6), one can
calculate the relation between the change in Ca current and the light
intensity of the surround stimulus for various cone membrane potentials
(Fig. 12). Figure 12 shows that for
depolarized cone membrane potentials (solid line), the feedback-induced
change in Ca current is much larger than for hyperpolarized cone
membrane potentials (dashed lines). The efficiency of the feedback
signal to modulate the cone output depends strongly on the cone
membrane potential: i.e., high efficiency at depolarized cone membrane
potentials and low efficiency at hyperpolarized cone membrane
potentials.
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The bell-shaped curve can now be accounted for in the following way. Two opposing processes are functioning. The first is that the feedback-induced change in Ca current increases with intensity, and the second one is that with hyperpolarization of the cone the effect of the shift of the Ca-current activation function on the output of the cone reduces because the cone membrane potential comes in a less steep part of the Ca-current I-V relation. Low-stimulus intensities yield small cone and HC responses and consequently feedback from HCs to cones will hardly shift the Ca-current activation function. Therefore, the effect of feedback on the cone output will be small. High-stimulus intensities, on the other hand, evoke large cone and HC responses, and thus, feedback from HCs to cones will shift the Ca-current activation function substantially. However, because the cones are hyperpolarized, the effect of this shift will have little effect on the cone output. Thus, at high intensities, feedback will hardly influence the output of the cones. Only in the middle intensity range the HC response is large enough to generate a substantial shift in the Ca-current activation function and since the cone will not have been hyperpolarized much, this shift will result in a substantial change in Ca current and thus in cone output.
Wu (1991) concluded that feedback in salamander retina
was most prominent in the middle-intensity range. However, his analysis was based on the assumption that HCs feedback to cones via a GABAergic pathway. In his analysis, he argued that hyperpolarization of the cones
drives the cone membrane potential closer to the reversal potential of
the GABA-gated Cl current. This makes the modulation of the GABA-gated
channel less effective in modulating the cone membrane potential. At
least in goldfish, HCs do not feed back to the cones by modulating a
GABA-gated channel (Verweij et al. 1996
). As shown in
the present paper, the potential dependence of the feedback response in
the cones can be fully attributed to the nonlinearity of the Ca current
in the cones.
Bipolar cell surrounds
In this paper, we have indicated that the strength of the feedback
signal from HCs to cones depends strongly on the cone-membrane potential. This would mean that the surround response of the BCs depends strongly on the membrane potential of the cones driving the
BCs. Is there evidence for such a feature of the BC surround? Skrzypek and Werblin (1983) stimulated cones with a
small spot of different intensities and flashed an annular stimulus in
addition. At low intensities of the center spot, the annulus-induced
response was very small, presumably, as suggested by the authors, due
to scatter from the annulus to the center. For middle intensities of
the center spot, the annulus-induced response increased due to the
reduction of the scatter. For high intensities of the center spot, the
surround response disappeared, which is completely consistent with the
data presented in the present paper.
For full-field stimuli, this means that the feedback-mediated signal in
BCs is maximal in the middle intensity range. However, one has to
realize that this only holds for full-field stimuli. The BC-surround
response due to annular stimulation without direct stimulation of the
center will be maximal for the highest intensity, which is confirmed by
the experiments of Saito and co-workers (Saito et al.
1981), among others.
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ACKNOWLEDGMENTS |
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This work was supported by the Human Frontier Science Program (HFSP) and the Netherlands Organization for Scientific Research (NWO).
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FOOTNOTES |
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Address for reprint requests: M. Kamermans, Research Unit Retinal Signal Processing, The Netherlands Ophthalmic Research Institute, Meibergdreef 47, 1105 BA Amsterdam, The Netherlands (E-mail: m.kamermans{at}ioi.knaw.nl).
1 One could argue that such an assumption is not necessary, since one could have made simultaneous recordings from HCs and cones. One has to realize that HCs receive input from hundreds of cones, directly or indirectly via the gap-junctions. The cones projecting to one HC do have different spectral sensitivities and do not necessarily have the same response shape and/or adaptational state. Therefore, we have chosen to determine the mean intensity response curves of the cones and HCs and use these curves to calculate the gain-characteristics.
Normann and Perlman (1979) showed that the sensitivity
of the cones was about 0.5 log less than that of the HCs, whereas
Fuortes and Simon (1974)
showed that HCs were slightly
less sensitive than the cones. These experiments indicate that there is
not a large difference between the sensitivities of cones and HCs.
2
This definition of gain differs from the one
used by Shapley and Enroth-Cugell (1987). In those
studies, gain is defined in millivolts per quanta. In the present
study, gain is defined as millivolts postsynaptic response per
millivolts presynaptic response.
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 14 December 1999; accepted in final form 18 May 2000.
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REFERENCES |
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