Journal of Neurophysiology

The Open- and Closed-Loop Gain-Characteristics of the Cone/Horizontal Cell Synapse in Goldfish Retina

D. A. Kraaij, H. Spekreijse, M. Kamermans

Abstract

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, and3) 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.

INTRODUCTION

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 α-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), andWu (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.

METHODS

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 (λ = 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 (λ > 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 1with 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 2s 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 MΩ 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.

RESULTS

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/logI 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 1shows 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 m 2s 1. These normalizedR/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 ➁) and the sustainedR/log I relations (solid curve ➀) for these six cones are shown in Fig. 2. Hill functions (Eq. 1 ) were fitted through the R/logI 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 ➁ did not reach a plateau phase, the fitted values of n (0.34) and K (2041 cd m 2s 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.V=VmaxInIn+Kn Equation 1where V is the response amplitude (mV),V max is the maximal response amplitude (mV), I is the light intensity (cd m−2 s−1), K is the intensity yielding half-maximal response (cd m−2 s−1), andn is the Hill coefficient.

Fig. 1.

Light responses of an M-cone to 500-ms full-field white light flashes with intensities indicated in the figure. The stimulus intervals were at least 5 s. The scaling, timing, and intensities are indicated in the figure. Inset: normalized cone onset-response for various intensities of the same cone as illustrated in the main figure showing that the slope at light onset becomes steeper with intensity.

Fig. 2.

Mean intensity-response relations of six cones. The solid line, marked as ➁, represents the normalized, mean, interpolated amplitude of the initial light response (between 36 and 46 ms after light onset) as a function of the relative stimulus intensity. The solid line, marked as ➀, represents the normalized mean, interpolated amplitude of the sustained cone light response (between 434 and 494 ms after light onset) as a function of the relative stimulus intensity of the same cones. The dashed lines are Hill equations (Eq. 1 ) fitted through the data points.

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. Figure3 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). TheR/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 m 2s 1. Then theR/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 meanR/log I relation of the initial (34–46 ms; curve marked ➁) and the sustained (434–494 ms; curve marked ➀) HC responses.

Fig. 3.

Light responses of an MHC to 500-ms white light flashes with intensities indicated in the text. The inter-stimulus intervals were at least 10 s. The scaling, timing, and intensities are indicated in the figure. The arrow points to the “roll back” in the MHC response.

Fig. 4.

Mean intensity-response relations of 6 MHCs. The solid line, marked as ➁, represents the normalized, mean, interpolated amplitude of the initial light response (between 36 and 46 ms after light onset) as a function of the relative stimulus intensity. The solid line, marked as ➀, represents the normalized, mean, interpolated amplitude of the sustained light response (between 434 and 494 ms after light onset) as a function of the relative stimulus intensity based on the same MHCs. The dashed lines are Hill equations (Eq. 1 ) through the data points.

Hill functions (Eq. 1 ) were fitted through both theR/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 initialR/log I relation was 1.22 cd m 2s 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.5 A) and in the closed-loop mode (Fig. 5 B). Figure 5 A illustrates that the gain-characteristic in the open-loop mode is highly nonlinear, whereas Fig. 5 B 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/logI curves of Figs. 1 and 3 and the dashed lines show the gain-characteristics based on the fitted Hill functions of Figs. 2 and4.

Fig. 5.

The “open loop” (A) and “closed loop” (B) gain-characteristic functions from cone to horizontal cells (HC) (solid lines). This solid curve is based on the measured R − log (I) relations of Figs. 2 and 4 and the dashed lines are the gain characteristic based on the fitted curves of Figs. 2 and 4. The open-loop gain-characteristic is highly nonlinear, whereas the closed-loop gain characteristic is nearly linear.

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.ICa=(VmECa)gCa11+exp(VmKCa)nCa Equation 2where I Ca is the current (pA),Vm is the holding potential (mV),E Ca is the reversal potential of Ca current (mV), g Ca is the maximal conductance of Ca current (mS), K Ca is the potential for half-maximal activation of Ca-current activation function (mV), and n Ca is the slope factor of Ca-current activation function (mV).

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.K Ca in Eq. 2 is the half-activation potential and n Ca is the slope factor of the Ca current. The curves of Fig. 6 were fitted with a set of parameters in which K Cawas the only parameter that changed with intensity. The mean values ofK Ca,n Ca,g Ca, andE Ca were −23.7 ± 7.6 mV, 8.7 ± 1.5 mV, 1.7 ± 1.1 nS, and 135 ± 151 mV, respectively. In Fig. 7,K Ca 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 feedbackR/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 2s 1 and of the feedback signal 9.2 ± 0.5 (n = 9) log cd m 2s 1. The difference of 0.1 log does not differ significantly from zero.

Fig. 6.

The I-V relation of a cone, of which the membrane potential was ramped from −70 to 0 mV within 500 ms. At the same time, the cone was saturated with a 65-μm white spot and in addition a 3000-μm white full-field stimulus of 3 intensities was applied. As is obvious from this figure, the full-field stimuli shift the activation function of the Ca current to more negative potentials in an intensity-dependent manner.

Fig. 7.

The feedback-induced mean shift of the Ca-current activation function as a function of the relative full-field stimulus intensity. The filled circles represent the feedback induced shift in the activation function of the Ca current in 9 cones. The solid line shows the best fitting Hill equation (Eq. 1 ) through these data points, and the dotted lines show the 95% probability interval of this function.

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.

Fig. 8.

The gain-characteristic from HCs to cones. This is the feedback-induced shift of the calcium current activation function as function of the sustained monophasic HCs (MHC) membrane potential. The solid line is based on the data points of sustained part of the response of Figs. 4and 7, whereas the dashed line is based on the fitted curves of sustained part of the response of Figs. 4 and 7.

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. 9 A, the meanR/log I relation of the sustained response of four MHCs is given and in Fig. 9 B, 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/logI curves. This figure indicates that the roll-back in the HC response is maximal in the middle intensity range (K = 1 cd m 2s 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 theR/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.

Fig. 9.

Intensity response relation of the roll-back in the response of 4 MHCs.A: the mean R/log Irelation of the MHC sustained (between 434 and 494 ms after light onset) response. The curves were normalized, shifted along the intensity axis such that the half-maximal response amplitude equaled 1 cd m 2 s 1, and scaled back to the mean maximal response amplitude. B: the difference between the peak and the plateau phase of the response of the same 4 MHCs as a function of the relative stimulus intensity. These curves where shifted along the intensity axes similarly as the curves in A.

DISCUSSION

In this paper, we have determined the R/logI 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. 1997ac;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. (1997ac) 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, Kof 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 panelA, 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 theK values. This range is about the reported range of sensitivity differences in literature (Fuortes and Simon 1974; Normann and Perlman 1979).

Fig. 10.

The open loop (A) and closed loop (B) gain-characteristics from cone to HC for different sensitivities of the HCs. The solid lines are the curves from Fig. 5. The dashed and dotted lines are the gain-characteristics for different values ofK as indicated in the figure. The open-loop gain-characteristic remains highly nonlinear and the closed-loop gain-characteristic remains almost nearly linear for the different values of K.

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.11 A. 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/logI curves of the early and late cone responses, the meanR/log I curve of the feedback signal, and the estimate of the Ca current (E Ca = +135 mV, K Ca = −27.5 mV,n Ca = 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 (K Glu) 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.gcat=ICa2ICa2+KCa2 Equation 3 VHC=gcatEcat+gnsEnsgcat+gns Equation 4where g cat is the cation conductance (=1.0), E cat is the reversal potential of the cation conductance (=0 mV),g ns is the lumped nonsynaptic conductances (=0.5), and E ns is the lumped reversal potential of nonsynaptic conductances (= −65 mV).

Fig. 11.

A: schematic Ca-current I-V relations with various strengths of feedback. The effect of feedback on the light-induced change in Ca current is illustrated. During small spot stimulation, the cone hyperpolarizes, which causes a reduction of the Ca current (solid arrow). This reduction is exponentially related to the intensity. However, for full-field stimuli in addition to hyperpolarization of the cone membrane potential, the Ca-current activation function shifts to more negative potentials. The result is that the relation between reduction of the Ca current and the cone membrane potential becomes more linear (dashed arrow).B: cones to HCs gain-characteristic based on the data of Figs. 2, 7, and 8. The solid line represents the open loop and the dashed line represents the closed loop gain-characteristic.

Figure 11 B 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 11 B 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. 11 B, on the other hand, only assumptions were made about the relation betweenI Ca, 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 m 2s 1 (Fig. 9 B). 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. 9 B 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.

Fig. 12.

Simulated feedback-induced change of the Ca current for various cone membrane potentials. At depolarized cone membrane potentials, the same feedback-induced change in Ca-current activation function results in a larger change in Ca influx than at hyperpolarized potentials. Feedback is most efficient at depolarized cone membrane potentials.

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 theeffect 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.

Acknowledgments

This work was supported by the Human Frontier Science Program (HFSP) and the Netherlands Organization for Scientific Research (NWO).

Footnotes

  • 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, whereasFuortes 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.

REFERENCES

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