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Department of Neuroscience, The Ohio State University College of Medicine, Columbus, Ohio
Submitted 26 January 2005; accepted in final form 24 November 2005
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ABSTRACT |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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; Byzov and Shura-Bura 1986).
Horizontal cells (HCs) also provide a signal back to cone photoreceptor cells (Baylor et al. 1971). Cones hyperpolarize to light with graded potentials, but when they are constantly stimulated with a central spot of light, they depolarize in response to annular stimulation. This phenomenon was called "negative feedback," and for many years, it was assumed that this feedback depolarization is due to some chemical inhibitory signal from HCs to cones (see Burkhardt 1993; Kamermans and Spekreijse 1999). However, this chemical hypothesis has still not been proven, and an alternative, electrical mechanism of negative feedback has also been proposed (Byzov 1977; Byzov and Shura-Bura 1986; Kamermans et al. 2001). The most intriguing feature of this electrical mechanism of negative feedback is the claim that HCs transfer electrical signals to cones in the absence of electrical synapses because there are no gap junctions between HCs and cones. In fact, this mechanism, in contrast to conventional electrical communication through gap junctions, has been proposed as unilateral (from HC to cone) and sign-reversing (HC hyperpolarization produces cone depolarization).
Byzov proposed that "electrical feedback is an intrinsic property of any chemical synapse" because the presynaptic membrane possesses a large local transmembrane conductivity. The unique architecture of the cone synaptic terminal might facilitate the generation of electrical feedback. In the cone pedicle, the dendrites of HCs, together with the dendrites of bipolar cells, invaginate 
1 µm inside the cone presynaptic terminal. As a result, the resistance of the restricted extracellular space for the current running from the entrance of the invagination to the tip of the horizontal cell dendrite might be much larger than the resistance of the extracellular space outside the synaptic region.
An electrical circuit representation of Byzov's electrical feedback model is shown in Fig. 1. The glutamate-gated cation channels are located on the HC postsynaptic membrane and determine the resistance of the HC dendrite (Rd, Fig. 1). The reversal potential of the glutamate channels is close to 0 mV, and the only variable current-generating element in the circuit is the battery of the membrane potential of the HC body (Eb, Fig. 1). Because the resistance of the synaptic cleft inside the invagination of the cone pedicle (Rf, Fig. 1) is a common element for both the HC and the cone, the potential generated across this resistance by the current caused by Eb influences the local membrane potential in the presynaptic region of the cone. This extracellular potential inside the cone pedicle is, in essence, the "feedback" potential (Vf) because it is equal to the value at which the cone presynaptic membrane potential (between points 3 and 2 in Fig. 1) is different from the membrane potential of the rest of the cone (between points 3 and 1 in Fig. 1, where point 1 is extracellular "ground"). An increase of Eb, which corresponds to a hyperpolarization of the HC, enhances the extracellular current through Rf, which in turn increases the feedback potential. The membrane potential of the cone measured between points 1 (ground) and 3 does not appreciably change (because the transmembrane resistance of the cone presynaptic membrane, Rs, is by far the largest resistance in the circuit), and consequently, the increase in the negative potential between point 2 and ground is associated with a decrease in the negative potential between points 2 and 3, i.e., a local depolarization of the cone presynaptic membrane. Formally, Rs is a variable resistor, because it includes Ca2+ voltage-gated channels. However, in the context of the electrical feedback hypothesis, the opening and closing of Ca2+ channels in the cone presynaptic membrane must have a negligible effect on the resistance of the cone presynaptic membrane, Rs. In fact, the very high resistance of the cone presynaptic membrane, and accordingly, the very small conductance of the Ca2+ channels in the cone presynaptic membrane, is an important condition for the electrical mechanism of negative feedback. Characteristically, in a recent version of the hemichannel-mediated electrical feedback hypothesis (see following text), the Ca2+ channels on the cone presynaptic membrane are presented as voltmeters (Kamermans and Fahrenfort 2004), i.e., a device with very high resistance.
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Rf) has never been demonstrated.
The debate over the possibility of electrical feedback from HCs to cones was recently reinvigorated by the immunohistochemical demonstration that the tips of HC dendrites inside the cone pedicles of fish and turtle retinas express hemichannels (Janssen-Bienhold et al. 2001a,b). A hemichannel is half of a gap junction localized on the membrane of a cell without a counterpart on an adjacent cell. As a result, a hemichannel is open into the extracellular space. According to Kamermans and his colleagues (2001; for review, see Kamermans and Fahrenfort 2004), hemichannels could provide a sink for extracellular current and thus play the same role in electrical feedback as the glutamate-mediated current in Byzov's model. An advantage of hemichannel-mediated electrical feedback over the glutamate-mediated version is that the former would presumably not be modulated by light stimulation, at least over a short time scale. Again, the critical point of the Kamermans et al. (2001) model is the ratio between the transmembrane and extracellular resistances, that is, the ratio between the transmembrane resistance of the hemichannels on the HC dendrite and the extracellular feedback resistance. Kamermans and coworkers suggested that the ratio could be as low as 4:1, but they have likely significantly underestimated the hemichannel resistance (see following text).
The aim of this article is to investigate through computational means whether an electrical mechanism can provide the feedback signal from HCs to cones. The electrical model we used to evaluate electrical feedback from a HC to a cone is presented in Fig. 2 (for details, see METHODS). The circuit calculations were made using Kirchhoff's laws, which are generalized extensions of Ohm's law employed in network analysis. A computer program was custom-made to perform the calculations.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSREFERENCES |
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We used a "parallel shunt" model (Fig. 2) to evaluate electrical feedback from a HC to a cone. The only battery in the circuit is the battery of the potassium equilibrium potential (or reversal potential of the potassium channels, Ek), which is in series with the transmembrane potassium resistance, Rk. This potential-resistance element is localized in the HC body and shunted by other transmembrane resistances in the HC dendrites. Each dendrite has two transmembrane resistances arranged in parallel, the resistance of the glutamate-regulated channels, Rg, and the resistance of the hemichannels, Rh. There are no batteries for these transmembrane resistances because we accept following Byzov and Shura-Bura (1986) and Kamermans and colleagues (2001) that the reversal potential for both is 0 mV. Also each dendrite has two longitudinal resistances that are in series with the transmembrane resistances. One of these, the feedback resistance, Rf, represents the extracellular resistance of the invagination within the cone pedicle. The drop of potential across this resistance, Vf, is the main focus of our simulations because it is the feedback potential that is equal to the difference between the cone membrane potential in the presynaptic region and in the rest of the cone. The other radial resistance, Rr, represents the sum of the extra- and intracellular resistances that the current meets on its way from the cell body to the invagination through the extracellular space and back through the cytoplasm, excluding the resistance of the extracellular space inside the invagination, which was defined in the preceding text as Rf. As we will show, the value of Rr is likely to be comparable to Rf.
Rg is a variable resistance (indicated with an arrow) because the opening of glutamate-gated channels on the HCs is regulated by the light-induced release of glutamate from cones (for review, see Dowling 1987; Massey 1990). The effects of light stimulation are simulated in the model by changes in Rg, which is the only variable element in the circuit; all other elements are constant. Although changes in membrane potential can alter the conductance of many types of hemichannel, the voltage-dependent modulation of hemichannel conductance is relatively small; a 50-mV change in voltage under physiological conditions almost always changes hemichannel conductance by less than twofold (for review, see Harris 2001). Moreover, connexin26 (Cx26), which is located in fish HC dendrites (Janssen-Bienhold et al. 2001a, b), has a very low sensitivity to voltage. The steady-state junctional conductance of Cx26-containing hemichannels decreases by only 10% when a cell is depolarized from –100 to 0 mV (Barrio et al. 2000). We have therefore not included a voltage-dependent modulation of hemichannel conductance in our analysis, assuming instead that the hemichannels in HC dendrites remain as open in the depolarized (dark adapted) state as they are in a maximum hyperpolarized (saturated light) state, a condition that favors the hemichannel-mediated electrical feedback hypothesis.
For simplicity we have ignored a nonlinearity in Rk. In addition, because we were interested in the final amplitude of the potential, but not in its dynamics, membrane capacitance was not included in the circuit. We have also not included the conductances and batteries for other ions besides K+ in the cell body. It is known that in the absence of glutamate the membrane potential of HCs is determined almost exclusively by K+ (Tachibana 1981). Taking into account other ions would decrease the transmembrane resistance of the soma and reduce the potential of the battery, thus decreasing the possible electrical feedback potential. The inclusion of only the K+ battery in the analysis therefore maximizes the effect of electrical feedback. For the same reason, our idealized "horizontal cell" lacks an axon terminal.
Finally, electrical coupling between HCs was also not included in the analysis because we analyzed feedback from an individual HC to a cone. Our virtual "illumination" is always uniform and our modeled horizontal cell responds to light with its maximum possible hyperpolarization. Thus coupling cannot affect this response.
The above-described electrical circuit is an appropriate model of the cone-HC synapse because it consists of the most essential elements, the electrical values of its elements can be estimated reasonably well, and the circuit is able to reproduce HC light-induced activity and electrical feedback to cones. In darkness, when cones release glutamate, the glutamate-gated channels on HCs are open. As a result, Rg is minimal, the shunt of the HC membrane is maximal, and the transmembrane potential of the HC body (between points 1 and 4 in Fig. 2) is minimal. The HC is thus depolarized. When cones are illuminated, Rg in the HC dendrites that contact them increases, the shunt of the HC membrane decreases, the current across Rk diminishes, and the HC membrane potential shifts closer to Ek, i.e., the HC hyperpolarizes. This hyperpolarization increases the current across the dendrites that contact "nonilluminated" cones, and consequently, the feedback potential Vf across the extracellular resistance inside the invagination in the cone pedicle, Rf, increases. The increase in Vf is equal to the local depolarization of the cone presynaptic membrane. Thus the model reproduces electrical feedback from HCs to cones. The principal question is whether the feedback electrical signal is large enough to produce a significant effect on the cone presynaptic membrane.
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RESULTS |
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The values of the circuit elements can be estimated from the extant literature and especially from data provided by Kamermans and coauthors (2001, note 17). According to their measurements, when both glutamate channels and hemichannels were blocked, the HC membrane potential was equal to –82.7 mV. In this condition, the shunting conductance in the HC dendrites was eliminated, and the HC membrane potential was equal to the battery in the cell body, e.g., Ek = –82.7 mV. Because the average resting potential of HCs in the dark (i.e., when glutamate channels are open) is –34.7 mV, and blocking the glutamate-gated conductance leads to a hyperpolarization of –36.7 mV (to –71.4 mV) (Kamermans et al. 2001), we can conclude, based on Ohm's law, that the contributions of potassium, glutamate-gated, and hemichannel conductances to the total cell conductance are 42.0, 51.4, and 6.6%, respectively. The fact that the potassium and glutamate-gated cationic conductances are approximately equal and together provide most of the total HC membrane conductance is well known and enables the HC membrane potential to change from approximately –40 mV in the dark, when the glutamate channels are open, to about –80 mV in the light, when the glutamate channels are closed. It is also unlikely that the contribution of the hemichannels could be much larger than 6.6%. Because they are located at the tip of HC dendrites, the hemichannels provide a constant shunt that interferes with the postsynaptic current through the glutamate-gated channels. The larger the relative conductance of the hemichannels, the smaller the postsynaptic signal that can be generated in the HC. Figure 3A illustrates the relationship between the relative conductance of the hemichannels, Gh, shown as a percentage of the total HC transmembrane conductance and the amplitude of the changes in the membrane potential of the HC body, 
Vb, (% of maximum) which are produced by modulation of the postsynaptic glutamate-gated conductance. The conductance of the potassium channels is fixed at 42%, and the conductance of the hemichannels increases at the expense of the glutamate conductance. The response of the HC when the relative conductance of the hemichannels equals 0 is defined as 100%, and even a small constant shunt from the hemichannels significantly reduces Vb. If Gh = 6.6%, the glutamate-dependent change of the HC membrane potential is 75% of its maximum value, and if Gh = 18%, only half of the maximal Vb can be evoked. Thus it is unlikely that the hemichannels contribute more to the total membrane conductance than the estimated value of 6.6%. Otherwise, it would be in direct conflict with the synapse's main function, which is to transfer a signal from the cone to the HC.
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20 cones (23 for H1 type, and 17 for H2 type) (Stell and Lightfoot 1975). As a result, the portions of the total HC conductance provided by Rk and each individual Rg and Rh are 42, 2.57, and 0.33%, respectively. The absolute values of the resistors depend on the total resistance of the HC membrane, or the input resistance of the HC. For most calculations we have used an input resistance, Rin, equal to 50 M
. The input resistance is the total resistance of all the transmembrane resistors, consisting of Rk, 20 Rg, and 20 Rh, connected in parallel. As a result, Rk, Rg, and Rh have values of 119.05, 1945.53, and 15151.5 M, respectively. We have used these values in our calculations because a lower input resistance favors electrical feedback. In fact, the input resistance of goldfish HCs is likely not <100 M. Measurements of the input resistance of freshly isolated goldfish HCs obtained in our laboratory (K. E. Gavrikov and S. C. Mangel, unpublished observations) were always >200 M, which is similar to the calculated value of 307 M [the surface area of goldfish HC soma is 1,300 µm2 (Yagi and Kaneko 1988), the specific membrane resistance is 4,000 *cm2].
The most important element of the model with respect to electrical feedback is the feedback resistance of the extracellular space within the invagination of the cone pedicle, Rf. Kamermans and colleagues (2001; note 20) estimated its value as 6–60 M. This estimate was based on morphometry data from goldfish retina (Vandenbranden et al. 1996) and seems high but reasonable. For the calculations here, we have used the highest value (60 M) estimated by Kamermans and colleagues to favor the possibility of electrical feedback. It should be noted, however, that if Rf was >60 M, it would have negative effects on transmission of the synaptic signal from cone to HC. Figure 3B shows the relationship between the resistance of the extracellular space within the invagination of the cone pedicle (Rf, M) and the amplitude of the maximum "light-induced" change in HC membrane potential (Vb, %). Increasing Rf to 100 M has little or no effect on the HC response, but when Rf increases to higher values, these resistors begin to isolate the dendrites from the body, and Vb is dramatically reduced.
The resistance of the extracellular space outside the invagination of the cone pedicle is much lower compared with Rf if it is calculated per 1 µm of dendritic length but has a larger, significant value when the entire length of the dendrite is considered. This extracellular resistance can be approximated from the geometry of the HC dendritic tree (diameter of the dendritic field is 50 µm, diameter of the cell body is 10 µm) (Stell and Lightfoot 1975), the thickness of the outer plexiform layer (5 µm), and the extracellular space volume fraction in the outer plexiform layer (11%) (Karwoski et al. 1985). Because our modeled "cell" has 20 dendrites to share the extracellular space and assuming the specific resistance of the extracellular fluid is the same as that which was used for the estimation of Rf, the total extracellular resistance per 1 dendrite of 20 µm length is 6 M. The intracellular resistance of the dendrite should be larger simply because the dendritic end is very thin. If the diameter of the dendrite at the entrance of the cone pedicle is 0.3 µm, it has a resistance of 8.5 M per 1 µm of length, assuming that the mobility of ions in the cytoplasm is the same as in the Ringer (It should be less because most intracellular anions are macromolecules with low mobility, the cytoplasm is filled with organelles, and the colloid density of the cytoplasm is apparently higher than that of the Ringer). Thus several micrometers of the most distal part of the HC dendrite can have a resistance that is comparable to the feedback resistance. We define the value of Rr, which represents the extracellular resistance outside the invagination of the cone pedicle and all the intracellular resistance, as 30 M. In fact, Rr is the element that is the most difficult to estimate, but as is apparent from Figs. 4 and 5, Rr has a very small impact on the results of the calculations.
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The feedback potential (Vf), which represents the extent that the potential of the cone presynaptic membrane is different from the membrane potential of the rest of the cone, depends on the resistance of the extracellular space within the invagination of the cone pedicle, which is defined here as the feedback resistance, Rf. Figure 4 demonstrates the relationship between changes in the feedback potential (Vf) and the feedback resistance Rf. Kamermans and colleagues believed that Vf could be as large as 10 mV (Kamermans et al. 2001; note 20). However, according to our calculations, a value of 10 mV can be reached only if Rf is 2,000 M (Fig. 4, —). A larger value of Rf interferes with the ability of HCs to respond to light-induced modulation of glutamate-gated channels (see Fig. 3B), and the feedback potential Vf decreases. Kamermans and his colleagues estimated that Rf was between 6 and 60 M (Kamermans et al. 2001), which is in agreement with our estimations, and in this range of Rf, the feedback potential Vf is between 0.1 and 1 mV (see Fig. 4, inset).
It is important to state that all of the calculations here were performed using the largest possible changes of the HC membrane potential. The largest changes of the membrane potential of our modeled HC occur when the glutamate channel resistances Rg of all but one dendrite—that which ends inside the cone targeted for feedback—increase from their standard "dark" value to infinity. This mimics the physiological condition in which the dark-adapted retina is stimulated in such a manner that the cones connected with the 19 dendrites of the HC are illuminated by a saturating light, but the cone targeted for feedback is not illuminated at all. Obviously, this is a purely theoretical situation that rarely, if ever, occurs in a real visual environment.
This result was obtained with Rr equal to 30 M, but did not change much when Rr = 300 M (Fig. 4, · · · ) and almost did not change when Rr = 0 M (Fig. 4, - - -). Thus the model is stable with respect to Rr, the intra- and extracellular resistance along the HC dendrite, the least reliably established parameter.
In the calculations in the preceding text, the glutamate channels in the HC dendrite inside the pedicle of the cone targeted for feedback were open (i.e., the cone was "in darkness") and served as the main sink for the current that was responsible for Vf. When these glutamate channels were closed (the cone targeted for feedback was "illuminated"), only the hemichannels provided a sink for the current. The conductance of the hemichannels is eight times less than the conductance of the glutamate channels (Kamermans et al. 2001; note 17), so changes in Vf were much smaller under these conditions (Fig. 4, - · -). At Rf = 60 M, the Vf was slightly more than 0.1 mV (see Fig. 4, inset).
The above-described results were obtained when the input resistance (Rin) of the "cell" was 50 M. In Fig. 5, Vf was plotted against Rin. Here and in all other calculations, Rf is constant and equal to 60 M. As was expected, lowering Rin increased Vf. However, the changes never exceeded 7 mV in calculations that took into account the intra- and extracellular resistances (Rr = 30 M, Fig. 5, —). When all the intra- and extracellular (except inside the synaptic invagination, Rf) resistances were ignored (Rr = 0), Vf could reach a value of 10 mV, but only when Rin was as low as 2 M (Fig. 5, - - -), a value that is two orders of magnitude smaller than the input resistance of HCs that has been measured experimentally (Tachibana 1981). When Rin = 50 M, which is probably its lowest reasonable value, the feedback signal Vf was 1 mV. Again, if the glutamate-gated channels were blocked and only the hemichannels supported electrical feedback, as would occur during light illumination, Vf was negligibly small (Fig. 5, - · -).
The results of the calculations presented in Figs. 3 and 4 suggest that when reasonable electrical parameters are used, individual HCs are able to produce only a very small electrical feedback potential, which can hardly serve as an effective feedback signal to the cone. Yet it has been noted that not one but several HC dendrites invaginate in the cone pedicle and that the extracellular currents generated by each of the dendrites could have an additive effect on the local membrane potential of the presynaptic area (Kamermans et al. 2001; note 20). However, to sum the feedback currents from several HCs, their dendrites have to share the same extracellular resistance, i.e., these dendrites have to end in the same invagination not just in the same pedicle. It is well known that only two HC dendrites are typically located in one invagination in a cone pedicle (Dowling 1987), constituting together with the bipolar cell dendrite a structure that is called the triad. Thus two HC dendrites in one invagination would double the size of the feedback current across Rf, generating a 2-mV feedback potential Vf, instead of the 1-mV feedback potential that one HC can produce under the most favorable "light stimulation " conditions, when the most favorable assumptions for the electrical characteristics of the system are used.
Light/dark adaptation state greatly influences electrical feedback
The conductance of the glutamate-gated channels is significantly larger than the conductance of the hemichannels (Kamermans et al. 2001; note 17) (see also Fig. 3A), and accordingly, the glutamate channels could support a larger feedback current than the hemichannels. But light reduces the glutamate conductance and the glutamate-mediated electrical feedback should therefore be most effective in darkness. To characterize the effectiveness of electrical feedback, we have used the ratio Vf/Vb, where Vf is the change in the feedback potential and Vb is the change in the membrane potential of the HC body. This ratio shows how large the electrical feedback signal is per 1-mV change in the membrane potential of the cell body. The effectiveness of negative feedback was calculated separately for glutamate-mediated (Fig. 6, —) and hemichannel-mediated (Fig. 6, - · -) mechanisms and was plotted against the reduction of the light-regulated glutamate conductance, which mimicked the increase in background illumination. As expected, Byzov's glutamate-mediated mechanism is most effective in darkness when all of the glutamate channels of the HC dendrite are open. In this situation, each 1-mV hyperpolarization of the HC body will locally depolarize the cone presynaptic membrane by 0.029 mV. The effectiveness of glutamate-mediated electrical feedback is reduced when the glutamate conductance is blocked by light. When 90% of the glutamate conductance is blocked, the glutamate-mediated mechanism is less effective than hemichannel-mediated electrical feedback, which is independent of light but able to produce only 0.004 mV Vf with 1 mV of membrane potential change in the HC body. These calculations indicate that electrical feedback is greatest under dark-adapted conditions. Consequently, the well-known experimental finding that negative feedback is most effective under light-adapted conditions (Baylor et al. 1971; Kamermans et al. 2001) cannot be explained by the hypothesized electrical mechanism.
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The electrical parameters that generate electrical negative feedback inevitably also produce positive electrical feedback (Byzov and Shura-Bura 1986; Kamermans et al. 2001). In the case of negative feedback, the feedback potential Vf increases because hyperpolarization of the HC membrane outside of the invagination enhances the current through the dendrite in which the transmembrane resistance does not change. It mimics the physiological condition during which the cone that is targeted for feedback does not experience changes in illumination, but the cones around it are illuminated. When the cone targeted for feedback is illuminated, it decreases its release of glutamate, and the resistance of the glutamate channel in the HC dendrites postsynaptic to this cone (Rg) increases. Reduction of the transmembrane shunt leads to hyperpolarization of the HC. But in this case, the current through the dendrite and consequently the feedback potential Vf decreases. The decrease in Vf produces a more positive potential on the outside of the cone terminal membrane, which is equivalent to a local hyperpolarization of the cone presynaptic membrane (see Fig. 1). Thus a light-induced hyperpolarization of the cone leads to a hyperpolarization of the HC, which in turn produces an additional hyperpolarization of the cone, i.e., positive electrical feedback is established.
One important feature of electrical positive feedback in the cone pedicle is that its effectiveness should always be higher than the effectiveness of electrical negative feedback because of a simple electrophysiological reason. For both negative and positive feedback, the key element that defines the amplitude of the feedback potential is the resistance of the extracellular space (Rf) inside the synaptic invagination within the cone pedicle. But the other resistor with which Rf divides the potentials is different for negative and positive feedback. As was explained earlier, the negative feedback potential depends on the ratio of Rf and the transmembrane resistance, Rd, of the tip of the HC dendrite, which consists of the resistance of glutamate-gated channels, Rg, and the resistance of the hemichannels, Rh, connected in parallel (see Figs. 1 and 2). In contrast, positive feedback depends on the ratio of Rf and the resistance of the entire HC membrane, except for the one synaptic terminal that generates the changes in current. This resistance, Rb (see Fig. 1), is obviously lower than the resistance of one dendrite Rd because it consists of the resistances of other dendrites and the resistance of the HC body connected in parallel. Consequently, the ratio Rf/Rb, which determines the extent of positive feedback, is larger than the ratio Rf/Rd, which determines the extent of negative feedback. As a result, the negative feedback potential generated by illumination of all the cones connected with the HC, except for the cone targeted for feedback (Fig. 7, - - -), is about the same or even smaller (with Rh >100 M) than the positive feedback potential generated by illumination of only one cone (Fig. 7, · · · ). In addition, the light-induced decrease in glutamate conductance reduces the effectiveness of negative feedback (see Fig. 6). When all of the cones that contact the HC are equally illuminated, the extent of positive feedback greatly exceeds that of negative feedback and the total electrical effect on the cone presynaptic membrane is a hyperpolarization (solid line in Fig. 7).
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DISCUSSION |
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; HC input resistance: 1–1,000 M) and that incorporated values for these electrical parameters that favor electrical negative feedback, our calculations were performed to quantitatively determine whether an electrical mechanism could be effective enough to account for negative feedback from HCs to cones. An effective electrical feedback mechanism in any of its variations is possible only if one condition is met: the extracellular resistance inside the synaptic invagination in the cone pedicle (Rf) must be comparable in value to the transmembrane postsynaptic resistance (the total resistance of the glutamate channels in one synaptic terminal of the horizontal cell (Rg) in Byzov's model (Byzov 1977; Byzov and Shura-Bura 1986) or the total resistance of the hemichannels (Rh) in one synaptic terminal of the horizontal cell in the model of Kamermans et al. (2001)). If Rf is small compared with Rg or Rh, the electrical mechanism is not effective. Although one might speculate that Rf is relatively large and/or that Rg or Rh are relatively small, our analysis shows that this is unlikely. In addition, our calculations show that the values of the extracellular and transmembrane resistances must be within specific narrow ranges because they are limited by the necessity of preserving adequate cone to HC signal transfer. The conditions under which electrical negative feedback could and could not occur are discussed in the following text.
The key element of an electrical feedback model is the resistance of the extracellular space inside the synaptic invagination in the cone pedicle (Rf). We show in Fig. 4 that Rf must be very large (3 G) to support an electrical mechanism that produces significant (
10 mV) negative feedback and that this occurs only under dark-adapted conditions when the glutamate-gated conductance is at its maximum. Under bright illumination when the glutamate-gated conductance is blocked and the hemichannel conductance, which we assume is not suppressed by light, dominates the HC dendritic tip, electrical negative feedback is small in size (<3 mV) even when Rf is very large (3–10 G). However, it is very unlikely, that Rf is as large as 3 G. The value of Rf can be estimated with confidence based on the well-known morphology of the cone pedicle. The electrical resistance of the extracellular space has routinely been estimated elsewhere in the CNS based on morphology, and these estimates have agreed with direct electrical measurements and with measurements that used diffusible extracellular space markers (see Nicholson and Sykova 1998). In the retina, measurements of electrical resistance were used to determine the volume fraction of the extracellular space in different retinal layers (Karwoski et al. 1985). Our calculations indicate that the extracellular space inside the invagination in the cone pedicle has a resistance of 10 M, which is close to Byzov's estimation (15 M) (Byzov and Shura-Bura 1986) and is in the range (6–60 M) suggested by (Kamermans et al. (2001). A much larger Rf would occur only if the extracellular space inside the invagination in the cone pedicle included a special structure such as tight junctions, but such structures have never been observed in the cone pedicle of any species. More importantly, our calculations show that if Rf exceeded 100 M, it would produce a significant obstacle for current, leading to electrical isolation of the HC dendritic tip and a compromise in signal transfer from cone to HC (Fig. 3B).
In the hemichannel-mediated variant of the electrical hypothesis, the effectiveness of feedback depends on the ratio Rf/Rh, where Rh is the resistance of the hemichannels in one dendritic tip. Kamermans and coauthors have estimated Rh as 24–240 M (Kamermans et al. 2001; note 20), but if this was the case, the HC input resistance would be improbably small. That is, if the resistance of the hemichannels is 240 M, then the resistance of the glutamate channels in the same HC dendrite would be 30 M because the resistance of the glutamate channels is about eight times less than the resistance of the hemichannels. Consequently, the total resistance of the glutamate channels in 20 HC dendrites would be 1.5 M. Because the glutamate channels provide about half of the total HC transmembrane conductance (see Derivation of values for the circuit elements in RESULTS), the input resistance of the HC would be <1 M, which is more than two orders of magnitude lower than the input resistance that has been measured experimentally (Tachibana 1981). In our analysis, Rh was calculated based on the following properties of the HCs: 1) the input resistance of the horizontal cell is 50 M, a value that is several times smaller than has been experimentally measured (Tachibana 1981), but one that is more favorable for effective electrical feedback; 2) the hemichannels are responsible for 6.6% of the total transmembrane conductance of the cell (see Derivation of values for the circuit elements in RESULTS); and 3) the hemichannel-mediated conductance is distributed among 20 HC dendrites. Using these three properties, a realistic estimate of Rh is 15,000 M, and as a result, the ratio Rf/Rh is too small to generate a significant electrical feedback signal, as suggested previously (Schwartz 2002). In fact, this resistance corresponds to a conductance of 66 pS, suggesting that the hemichannels are mostly in a closed state. Moreover, it should be noted that even in this low conductive state the hemichannels represent a significant transmembrane shunt that diminishes the glutamate-mediated response of HCs by 25% (Fig. 3A). An increase in the hemichannel conductance would further compromise cone to HC synaptic transfer. For example, reduction of Rh by even a factor of four from 15,000 to 3,750 M, which corresponds to a conductance of 260 pS, would reduce the size of HC light responses to one third of their maximum value.
Thus our calculations show that the hemichannels that are located at the tips of HC dendrites likely do not generate significant electrical negative feedback. Even if it is assumed that the resistance of the extracellular space in the synaptic invagination within the cone pedicle is as large as 60 M and the input resistance of HCs is as small as 50 M, the feedback current through the sink provided by the hemichannels can locally depolarize the presynaptic membrane of the cone by only 0.10–0.15 mV (Fig. 4, inset) when the HC is maximally hyperpolarized by saturating illumination of all cones connected with it except for the cone targeted for the feedback.
The glutamate-gated channels in the dendritic tips of HCs can support a larger current for the generation of a negative feedback potential, compared with the hemichannels because the glutamate channels have about eight times smaller resistance than the hemichannels (Kamermans et al. 2001). However, using realistic electrical values (see preceding text), the effectiveness of the feedback mechanism mediated by the glutamate channels would still be only 3%, e. g. a 30-mV HC hyperpolarization would depolarize the local cone presynaptic membrane by only 1 mV. Moreover, glutamate-mediated electrical negative feedback would be most effective under dark-adapted conditions when the glutamate-gated channels are open and their resistance is lowest (Fig. 6). This feature of glutamate-mediated electrical negative feedback directly contradicts the experimental data that show that feedback from HCs to cones is greatest under light-adapted conditions (Baylor et al. 1971; Kamermans et al. 2001).
Finally, the electrical circuitry characteristics that generate negative feedback in the cone-HC synapse, namely, the very high resistance of the extracellular space inside the synaptic invagination within the cone pedicle and the relatively low transmembrane resistance of the HC dendritic tips, also produce positive feedback from HCs to cones. Moreover because the positive feedback at the cone-HC synapse appears to be much more effective than the negative feedback, it would manifest itself more prominently than the negative feedback. In other words, the electrical characteristics of the cellular elements in the cone pedicle necessitate that any increase in the extracellular space resistance will increase positive feedback more than negative feedback. It should also be noted that in contrast to negative feedback, which utilizes both glutamate-gated channels and hemichannels proportionally to their conductances, positive feedback relies only on glutamate-gated channels. Potentially, hemichannels could indirectly diminish positive feedback because their presence in the postsynaptic membrane of HC dendritic tips produces a constant electrical shunt that diminishes HC light-induced responses. Thus if such hemichannel-mediated reduction of positive feedback occurs, it would only be at the expense of reducing HC light-induced activity, and negative feedback would also be reduced.
The presence of strong positive feedback is a feature that is difficult to associate with the gradual character of cone and HC light responses. When positive feedback occurs, a system tends to respond in an "all-or-nothing" manner. Thus if positive feedback was present, a small light-induced cone response would generate a maximal response in the HC dendrite. However, the experimental data show that there is no such positive feedback in the cone pedicle. The probable explanation of the absence of positive feedback in the cone-HC synapse is that the actual electrical characteristics of the circuit are not as favorable for electrical feedback as they were in our calculations. For example, if Rf has a value of 10 M, rather than 60 M as used in our calculations, the positive feedback potential would not exceed 0.1 mV when the glutamate-gated conductance maximally changed. Accordingly, the negative feedback potential is probably even smaller than was estimated in our calculations.
Thus according to the computational analysis performed here, it seems doubtful that an electrical mechanism could be responsible for negative feedback from HCs to cones. Hemichannel-mediated, compared with glutamate-mediated, electrical feedback appears to be especially problematic, and experimental data offered in support of the hemichannel hypothesis are not convincing. As has been noted, in the best case, an electrical feedback mechanism can only produce a local depolarization of the cone presynaptic membrane, a phenomenon that cannot be measured when an intracellular electrode monitors the cell body of the cone. Thus the effects of the gap junction blocker carbenoxolone on the depolarizing response of a cone evoked by surround illumination (Kamermans et al. 2001) cannot be used as evidence for or against the electrical model. Moreover, carbenoxolone produces several other effects in addition to blocking gap junctions. For instance, carbenoxolone inhibits the Na+-K+-ATPase (Zhou et al. 1996), and in retina, it has been shown that carbenoxolone reduces the light-evoked responses of photoreceptors (Verweij et al. 2003). Most importantly, inhibitory effects of the drug on Ca channels in photoreceptors have recently been demonstrated (Vessey et al. 2004). The carbenoxalone-induced block of the Ca channels in the photoreceptor presynaptic terminal results in the cessation of glutamate release and may explain why the drug hyperpolarizes HCs and significantly reduces their light-evoked responses (Kamermans et al. 2001; Pottek et al. 2003; Vessey et al. 2004). When HC light-evoked responses are reduced, negative feedback from HCs to cones should also be decreased. Hirasawa and Kaneko have also pointed out that changes in the I-V relationship of the cone calcium current evoked by surround illumination are inconsistent with the purely parallel shift toward a negative potential that is predicted by the electrical hypothesis (Hirasawa and Kaneko 2003). Finally, it should also be noted that the presence of hemichannels in the HC dendritic tip might produce additional problems because of leakage of various molecules, including neurotransmitters, directly into the synaptic cleft (Schwartz 2002).
To summarize, it is unlikely that an electrical mechanism plays a significant role in negative feedback from HCs to cones. The nature of the negative feedback mechanism thus still remains to be defined. One possibility, which recently received strong experimental support (Hirasawa and Kaneko 2003; Vessey et al. 2005), is that protons mediate negative feedback from HCs to cones. Consistent with this idea is the finding that the circadian clock in the retina decreases retinal pH to its lowest level at night, when negative feedback from HCs to cones is weakest (Dmitriev and Mangel 2000, 2001).
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Address for reprint requests and other correspondence: A. Dmitriev, Dept. of Neuroscience, The Ohio State University College of Medicine, 333 W. 10th Ave., Columbus, OH 43210 (E-mail: dmitriev.4{at}osu.edu)
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). The presence of hemichannels in the HC dendritic tip compromises the synaptic terminal's main function, which is to transfer a signal from the cone to the HC. Rin = 50 M
