it is widely accepted that the two-cell-layered epithelium of the ciliary body is responsible for the production of the aqueous humor that circulates through the chambers of the anterior segment of the eye and maintains intraocular pressure (IOP). Most investigators believe that a large fraction, if not all, of the aqueous humor is produced by a mechanism of secretion secondary to active ionic transport of the epithelial layer (12, 14, 21, 24). Thus, to reduce IOP in glaucoma, one common strategy is to target transport mechanisms to bring the secretion down to levels comparable to the reduced aqueous outflow.

To better understand how this can be accomplished, during the past 15 years several laboratories have developed techniques to study the transport properties of the isolated ciliary body to identify transporters, exchangers, and channels involved in this secretory process (3, 8, 16, 23, 26, 28, 29, 34, 35). Despite intensive research and the identification of several of the transport elements present in the ciliary epithelium, a satisfying model consistent with all the available experimental data is still elusive. There are, in our opinion, mainly three reasons for this situation: the complexity of this epithelium with two juxtaposed apical membranes, the contribution of the capillary pressure to aqueous humor secretion by ultrafiltration, and the possible variability in transport elements among the studied species. Despite a similar anatomic configuration and the presence of common transport elements in the rabbit and bovine ciliary epithelium, differences in transport properties were already apparent. While HCO${}_3^{-}$ transport from the blood to the aqueous side is present in the rabbit and accounts for the negative potential on the aqueous side (11, 23, 26), Cl⁻ transport in the same direction seems to account for the short-circuit current (I_sc) in the bovine tissue (14, 30). Very recently, Crook et al. (12) also described a net Cl⁻ transport as a component of the I_sc of the isolated rabbit ciliary epithelium. Because acetazolamide, an inhibitor of the carbonic anhydrase enzyme (CA), reduces the I_sc in the bovine preparation (unpublished observations), we thought that a transepithelial transport of HCO${}_3^{-}$ might also be present in the bovine ciliary epithelium. To examine this possibility, we measured the unidirectional transepithelial fluxes of HCO${}_3^{-}$ using a system adapted from Candia (5,6).

Another previous puzzling finding with the bovine ciliary epithelium was a net Cl⁻ flux that was consistently two to three times larger than the I_sc, without any other net ionic transport to account for the discrepancy. Here we report that we were unable detect any net flux of HCO${}_3^{-}$ across the isolated bovine ciliary epithelium. We also report that the endogenous conversion of CO₂ into HCO${}_3^{-}$ + H⁺ could account for the inhibition of theI_sc and net Cl⁻ flux by acetazolamide, by reducing the substrates available to parallel Na⁺/H⁺ and Cl⁻/HCO${}_3^{-}$ exchangers at the basolateral surface of the pigmented epithelium (PE). We propose a model similar to others in the literature (18, 24, 25, 32) that includes these findings and, in addition, explains why the net Cl⁻flux may be larger than the I_sc and why HCO${}_3^{-}$ removal from the aqueous side may paradoxically inhibit the I_sc. On the basis of a theoretical model in which the Na⁺-K⁺-pump activity and the K⁺ permeability of the basolateral side of the nonpigmented epithelium (NPE) are larger than those of the PE, a net movement of Na⁺ and K⁺ toward the aqueous side is apparent, resulting in a transcellular secretion of KCl and NaCl under short-circuit conditions.

METHODS

Freshly enucleated bovine eyes were obtained from a local abattoir and used in our experiment. The detailed procedure of tissue preparation has been described elsewhere (14, 30). Briefly, a sector of intact bovine iris ciliary body was dissected and mounted in either of two types of modified Ussing chambers. Only the ciliary body was exposed to the chamber cavity with a cross-sectional area of 0.30 cm² in both chambers. The standard HEPES-buffered Ringer solution comprised (in mM) 113.0 NaCl, 4.6 KCl, 21.0 NaHCO₃, 0.6 MgSO₄, 7.5d-glucose, 1.0 glutathione (reduced form), 1.0 Na₂HPO₄, 10.0 HEPES, and 1.4 CaCl₂. To obtain HCO${}_3^{-}$-rich and HCO${}_3^{-}$-free solutions, we bubbled standard solutions with 95% O₂-5% CO₂ and air, respectively, for 15 min before use. All solutions were adjusted to pH 7.4. Electrical parameters such as potential difference (PD), I_sc, and electrical resistance (R) across the preparations were continuously monitored with the Dual Voltage Clamp-1000 (World Precision Instruments, Sarasota, FL). R was calculated as the change of PD when a known current was passed. For the measurements of electrical parameters and unidirectional Cl⁻ fluxes, a previously described chamber was used (30). Essentially, it consisted of two potential-sensing tubes that were connected to each other by a bypass arm through three-way stopcocks. At the beginning of the experiment, both the potential-sensing tubes and the bypass arm were filled with normal Ringer solution. The potential-sensing tubes were then fitted into the PD-sensing arms of the chamber. By switching the three-way stopcocks to a neutral position (A), any junction potentials between the 0.9% NaCl and Ringer solutions or associated with the Ag-AgCl electrodes could be nullified. The stopcocks were then switched back to a measuring position (B) to allow for the measurement of the electrical parameters across the preparation in the chamber. At that point, the fluid junction was exactly the same as inposition A (0.9% NaCl and Ringer solutions). The offset potential was checked frequently with the bypass arm and stopcocks throughout the experiment.

Measurement of radiolabeled Cl⁻ flux.

In the initial experiments, after a brief stabilization period, Ringer solution with acetazolamide was perfused to the preparation until its full effect on the I_sc was demonstrated. Later, a radiolabeled (hot) solution with that drug was perfused and allowed to equilibrate before the flux measurements, as described earlier (30), were performed. In the subsequent experiments, we loaded the drug together with the hot solution and skipped the drug-only treatment. The results were not different from those before, and the electrical parameters remained stable throughout the experiments.

The unidirectional Cl⁻ fluxes were determined under short-circuited conditions. To minimize the variability between individual eyes, we compared only those data from paired measurements (i.e., using the same eye). This was achieved by mounting two preparations from each eye: one preparation was for the measurement of influx (J_ba, blood to aqueous), and the other preparation was mounted in another identical chamber for back flux measurement (J_ab, aqueous to blood). The net flux was the difference between J_ba andJ_ab. In other words, a single net flux data point was obtained from each eye, and the calculation of the net flux, in both control and acetazolamide-treated preparations, is the subtraction of paired unidirectional fluxes. However, the comparison between the net fluxes in control and acetazolamide-treated preparations is not paired. After a 60-min equilibration period, perfusates from both half-chambers were collected separately with two scintillation vials. The samples were taken from each side at 12-min intervals until a stable flux was obtained. The radioactivity of all the samples was measured with a liquid scintillation counter (Wallac 1414 Winspectral DSA; Wallac, Helsinki, Finland) after the samples were mixed with 15 ml of a biodegradable scintillation cocktail (Amersham Radiochemicals, Amersham, UK).

Measurements of unidirectional fluxes of CO₂ and HCO${}_3^{-}$.

Because of the CO₂-HCO${}_3^{-}$ interconversion and possible loss of CO₂ from the bathing solutions to the atmosphere, the measurement of HCO${}_3^{-}$ fluxes across epithelia is a difficult technique that could produce misleading results. To circumvent this problem, we have developed and previously used a closed recirculating system to measure the combined fluxes of CO₂ + HCO${}_3^{-}$ (5, 6). Theoretical justification as well as a detailed description of the apparatus and protocols can be found in previous reports (5,6). The key to the method is having a closed system with well-mixed and recirculating gas and liquid phases. In this closed environment, in which the liquid and gas phases are well mixed, it can be shown that after addition of the radiolabeled HCO${}_3^{-}$, the specific activity of the CO₂and HCO${}_3^{-}$ are the same in steady state. Thus the label appearing in the cold side represents a true unidirectional flux of CO₂ and HCO${}_3^{-}$. The surface area of tissue exposed to the bathing solutions is 0.3 cm². The chamber compartments on each side of the tissue are filled with 13 ml of the appropriate solution. Labeled bicarbonate (H¹⁴CO${}_3^{-}$) is added to one bath (hot side), and 2-ml samples are taken from the opposite side (cold side) every 15–20 min and replaced with an equal volume of unlabeled solution. From the “hot” solution, 20-μl samples were sufficient. They were mixed with Ringer solution to make up to 2 ml. The samples were promptly mixed in a scintillation vial with 10 ml of scintillation cocktail and capped. The labeled HCO${}_3^{-}$ immediately interconverts to CO₂ and reaches the same ratio as the abundant species, which is determined by the solution pH. The unidirectional flux is calculated by conventional methods. In general, after a 30-min equilibration, five to six samples are taken to obtain four to five periods of baseline values. After this, and with the same tissue, five to six more samples are obtained after an experimental change, allowing for paired data comparison. In experiments in which the bathing solutions were bubbled with air to reduce the CO₂ concentration, the pH was ∼8.7, but this change did not affect the electrical parameters.

In both chambers the PD, I_sc, and Rrecorded were similar. Most of the experiments measuring the changes in electrical parameters were done by the continuous perfusion-type chamber (30).

Radiolabeled isotopes and pharmacological agents.

The radioactivity was measured with a liquid scintillation counter (Wallac 1414 Winspectral DSA). The radiolabeled isotopes [¹⁴C]sodium bicarbonate and [³⁶Cl]sodium chloride were purchased from Amersham Radiochemicals. The HCO${}_3^{-}$-free solution was prepared by replacing the HCO${}_3^{-}$ in the bathing solution with gluconate ion. Acetazolamide and DIDS were purchased from Sigma Chemical (St. Louis, MO).

RESULTS

Fluxes of labeled CO₂ + HCO${}_3^{-}$were measured with and without CO₂ bubbling of the hot-side bathing solution. Whereas in the first case the label appearing in the cold side represents the transepithelial movement of HCO${}_3^{-}$ and CO₂, in the latter case it only represents the transcellular and paracellular movement of HCO${}_3^{-}$.

Table 1 shows the results of nine experiments in which the effects of acetazolamide (10⁻⁴ M in both bathing solutions) on the unidirectional fluxes of labeled CO₂ + HCO${}_3^{-}$ and electrical parameters were examined. The control values in Table 1 show that there is no net flux of the label or, consequently, of HCO${}_3^{-}$. The small 0.028 μeq · h⁻¹ · cm⁻² net flux is statistically not significant and is also opposite to the expected direction to drive fluid into the posterior chamber. In all but one experiment, acetazolamide produced a small (∼6%) increase, which was statistically significant as paired data but still inconsequential. The possible reasons for this increase will be discussed later. Acetazolamide, however, had a clear inhibitory effect on theI_sc (except for 1 experiment) amounting to an average decrease of 38%. In our existing database of 21 experiments, acetazolamide inhibits the I_sc from 11.7 ± 1.29 to 7.6 ± 0.83 μA/cm², a 35% decrease. Thus, by an undetermined mechanism, acetazolamide must be inhibiting the Cl⁻ transport, which is the main component of theI_sc. Further confirmation that the bovine ciliary body lacks a HCO${}_3^{-}$ transport mechanism was given by two additional experiments in which DIDS (10⁻⁴ M) had no effect on the control unidirectional fluxes of ∼0.20 μeq · h⁻¹ · cm⁻² (data not shown).

In three other experiments, after control values were established in HCO${}_3^{-}$-rich solutions bubbled with 5% CO₂, replacing the bubbling with air produced a reduction in the unidirectional fluxes of ∼0.070 μeq · h⁻¹ · cm⁻², indicating that ∼75% of the label moves as HCO${}_3^{-}$. However, much of this fraction may be paracellular in view of the lack of a net transport. Furthermore, acetazolamide had no effect on baseline fluxes measured in two preparations bathed in HCO${}_3^{-}$-rich solution bubbled with air in which the CO₂ concentration was negligible.

Because we could not detect an effect of acetazolamide on HCO${}_3^{-}$ fluxes, we tested its effect on Cl⁻fluxes, which seem to support the I_sc. These results are shown in Table 2. Acetazolamide in either bathing solution clearly decreases the blood-to-aqueous Cl⁻ flux (J_ba) while having a smaller, not significant, inhibitory effect on the opposite flux. The decrease in J_ba by acetazolamide on the aqueous side was statistically significant. The reduction in the net flux amounted to 42% but had a borderline significance of P = 0.12. The effect of acetazolamide on the blood side was less pronounced, and a significant net flux was detected.

In the rabbit ciliary body, where transport of HCO${}_3^{-}$seems to be present in the blood-to-aqueous direction (4, 11, 33,35), removal of HCO${}_3^{-}$ from the blood bathing solution decreases and reverses the I_sc, whereas removal of HCO${}_3^{-}$ from the aqueous side increases theI_sc by favoring the net movement of HCO${}_3^{-}$ from the blood side. To demonstrate that a net transport of HCO${}_3^{-}$ is not present in the bovine ciliary body, we effected similar protocols of unilateral removal of HCO${}_3^{-}$ in this isolated tissue. The results are shown in Table 3. Removal of CO₂ + HCO${}_3^{-}$ from the blood bathing solution had no effect on the electrical parameters, whereas the additional removal of CO₂ + HCO${}_3^{-}$from the aqueous bath had the inhibitory effect of reducing theI_sc and PD with no significant change inR. To confirm these effects, we implemented removal of CO₂/HCO${}_3^{-}$ from the solutions in the reverse order (Table 3). A large reduction inI_sc and PD was observed upon the unilateral removal of CO₂ + HCO${}_3^{-}$ from the aqueous side, whereas additional removal from the blood side produced a small improvement in the I_sc. These effects are paradoxical because, if HCO${}_3^{-}$ were transported in the blood-to-aqueous direction, it should have increased theI_sc, as occurs in the rabbit ciliary epithelium, and because the change is larger than can be expected by any possible contribution of HCO${}_3^{-}$ transport. Table 3 shows that the effect of bicarbonate removal was partially reversible. This suggests, as with the effect of acetazolamide, that it is due to an indirect effect on Cl⁻ transport. Indeed, in 10 experiments in which we tested the effect of CO₂/HCO${}_3^{-}$ removal from the aqueous solution on Cl⁻ fluxes, J_abincreased from the control 5.20 ± 0.30 to 6.20 ± 0.24 μeq · h⁻¹ · cm⁻² with little effect on J_ba and reducing the net Cl⁻ flux by 58%.

Because changes from a HCO${}_3^{-}$-rich to a HCO${}_3^{-}$-free Ringer solution included changing the bubbling from 5% CO₂ to air, it is possible that the decreased solution CO₂ produced a reduction in cell CO₂ and, consequently, a reduction in endogenously produced HCO${}_3^{-}$, resulting in a lesser activity of the PE and NPE HCO${}_3^{-}$/Cl⁻ exchangers that supply part of the Cl⁻ uptake that subsequently exits the NPE and contributes to the I_sc. However, as shown in Table 4, changing the bubbling from 5% CO₂ to air (which increases the solution pH to 8.7) did not reduce the I_sc; on the contrary, a small increase was observed. The effect was reversible, because the electrical parameters returned to control values when 5% CO₂ bubbling was reintroduced. Thus CO₂ removal was not the cause of the I_sc reduction. When CO₂ and HCO${}_3^{-}$ were unilaterally removed from the aqueous bathing solution, as shown in Table 4, the typical large inhibition of I_sc was observed, which cannot be reverted by simply bubbling 5% CO₂ to the HCO${}_3^{-}$-free solution. Thus it is the removal of HCO${}_3^{-}$ and not CO₂ that causes theI_sc inhibition.

It is possible that the effects of the absence of HCO${}_3^{-}$ in the aqueous solution and acetazolamide may be related. Thus we studied the sequential effects of these two protocols, which are shown in Table 5. Although the effect of HCO${}_3^{-}$ removal from the aqueous solution on the I_sc is much larger in the presence of acetazolamide, it is also evident that HCO${}_3^{-}$ removal produces a larger inhibition than acetazolamide regardless of the sequence. Thus it seems possible that the two effects are independent of each other and affect the I_sc by different mechanisms. Because acetazolamide acts on CA and probably reduces the rate of conversion of endogenously generated CO₂ to HCO${}_3^{-}$ + H⁺, another mechanism must underlie the inhibitory effect of aqueous HCO${}_3^{-}$removal.

DISCUSSION

The ciliary epithelium that lines the posterior chamber side of the ciliary body is a complex epithelium with two cell layers juxtaposed by their apical side. Many of its transport characteristics and components including channels and transporters have been identified (1, 12, 15, 19, 20, 31). It is widely known that the composition of the aqueous humor of different species varies, particularly with regard to its Cl⁻ and HCO${}_3^{-}$ concentrations (9, 10, 13, 22). In humans, for example, Cl⁻ concentration is higher and HCO${}_3^{-}$ concentration is lower in the posterior chamber than in the plasma, whereas in the rabbit, the reverse is true (9, 10, 13, 22). Most of the transport work with the isolated rabbit ciliary epithelium has obtained results consistent with the in vivo higher-than-plasma concentration of HCO${}_3^{-}$in the aqueous humor (7, 23, 25). Even in the recent paper by Crook et al. (12), bumetanide only inhibited 43% of the I_sc, the remainder of which may be net HCO${}_3^{-}$ flux. In the isolated bovine ciliary body, however, previous findings show a net Cl⁻ transport toward the aqueous humor (14, 30), which is consistent with a higher-than-plasma concentration of Cl⁻ in the aqueous humor, as found in humans. Despite these differences, inhibitors of CA reduce aqueous Cl⁻ concentration in humans and HCO${}_3^{-}$ concentration in rabbits with a concomitant reduction of IOP in both (2, 17, 32). The question arises as to how a drug with a very specific action on CA can have the same final effect on IOP in two apparently different systems.

In this work we have shown that there is no noticeable transport of HCO${}_3^{-}$ across the bovine ciliary epithelium and that acetazolamide has no influence on its unidirectional fluxes. We present a model that could explain most of our results, including the effect of acetazolamide on Cl⁻ fluxes andI_sc, and the reasons for the discrepancy between net Cl⁻ transport and I_sc.

We have previously shown the reliability of our system for the measurement of CO₂ + HCO${}_3^{-}$ fluxes. Indeed, in frog skin, one of us found a substantial net flow that was attenuated with acetazolamide and PGF_2α (6). In the present experiments, baseline fluxes were very stable, equal in both directions, and unaffected by acetazolamide and DIDS. These findings support the notion that there is no bicarbonate transporter and channels working in unison to produce a net transepithelial flux and that the inhibitory effect of acetazolamide must be on Cl⁻ fluxes. The small increase in both unidirectional CO₂ and HCO${}_3^{-}$ fluxes by acetazolamide (Table 1) could be explained by a time-dependent increase in paracellular permeability. This is unlikely since the increase was not observed in experiments with solutions bubbled with air. Another possibility is that part of the labeled CO₂ that diffuses into the tissue is quickly converted and trapped as HCO${}_3^{-}$ in the cell. With acetazolamide, this process is slowed down, and more of the labeled CO₂ can traverse the tissue. This also implies that the label crosses the epithelium transcellularly as CO₂ but as HCO${}_3^{-}$ mainly via the paracellular pathway. The suggestion that little HCO${}_3^{-}$ crosses the epithelium as such is justified by the fact that the only pathways known to exist in this tissue are Cl⁻/HCO${}_3^{-}$ exchangers that direct HCO${}_3^{-}$ out of the cell. In contrast, bicarbonate uptake mechanisms mediated by Na⁺-(n)HCO${}_3^{-}$ cotransport and Na⁺-dependent Cl⁻/HCO${}_3^{-}$exchange have been described in the rabbit ciliary epithelium (4,33, 35).

Regardless of the possibility that H⁺ and HCO${}_3^{-}$ are endogenously produced from metabolically generated CO₂, calculation of unidirectional fluxes does not include species that are not part of the “hot solution” compartment and thus do not contribute to transepithelial fluxes.

Because an HCO${}_3^{-}$ flux does not contribute to theI_sc, the inhibitory effect of acetazolamide on the current must be on the net Cl⁻ transport, which accounts for more than the measured I_sc. Indeed, Table 2 shows a net Cl⁻ flux from blood to aqueous humor as well as its inhibition by acetazolamide. Even though the net Cl⁻ flux persists in the two experimental conditions, it is smaller by 42 and 21%, respectively. More importantly, the decrease in J_ba is statistically significant for acetazolamide on the aqueous side, whereas the decrease inJ_ab is not. A logical conclusion is that acetazolamide reduces I_sc by inhibiting theJ_ba Cl⁻ flux.

Also, the inhibition of the I_sc produced by HCO${}_3^{-}$-free solutions on the NPE side must be due to a reduction in the net Cl⁻ flux. Indeed, we have found a 58% net Cl⁻ flux reduction in HCO${}_3^{-}$-free solutions compared with HCO${}_3^{-}$-rich control solutions. Because the decrease in the net Cl⁻ flux was due to an increase in the back flux J_ab with little effect on J_ba, the paracellular pathway should be involved. A decrease in transcellular J_basimultaneous with an increase in its paracellular component will leave this unidirectional flux unchanged, while increasing the oppositeJ_ab flux and thus reducing the net. If so, this would also preclude the detection of resistance changes. The possibility that the effect of aqueous HCO${}_3^{-}$ removal is due to a decreased net Cl⁻ flux was confirmed with experiments in which electrical parameters were measured. As shown in Table 3, the effect of HCO${}_3^{-}$ removal, which is reversible, is exclusively due to the lack of HCO${}_3^{-}$ on the NPE side. This very reproducible effect is difficult to explain because removal of HCO${}_3^{-}$ from the NPE side should create a gradient that would favor the movement of HCO${}_3^{-}$ toward that side, thereby increasing theI_sc, as occurs in the rabbit. Because no net transport or diffusional transcellular pathways could be found for HCO${}_3^{-}$, it is logical to assume that its effect should be indirect. In most of the experiments, when HCO${}_3^{-}$was replaced with another buffer, the bubbling was also changed to air. Thus it was possible that it was CO₂ diffusing out of the cell with less cellular conversion to HCO${}_3^{-}$ that produced the effect by slowing down the Cl⁻/HCO${}_3^{-}$ exchanger. The experiments in Table 4 disproved this hypothesis: changing the bubbling from CO₂ to air, leaving HCO${}_3^{-}$ in the solution, did not produce the inhibition but produced a small stimulation. Furthermore, bubbling 5% CO₂ on the HCO${}_3^{-}$-free aqueous side did not restore the controlI_sc but reduced it further. Clearly, it is HCO${}_3^{-}$, not CO₂, that is responsible for the effect.

We tried to establish whether there was a direct relationship between the inhibitory effects of acetazolamide and the removal of HCO${}_3^{-}$ from the aqueous side. Although the experiments in Table 5 are not conclusive, they seem to indicate that their effects can be separated. Acetazolamide undoubtedly decreases the endogenously produced HCO${}_3^{-}$ that fuels the Cl⁻/HCO${}_3^{-}$ exchangers, which in turn reduce the Cl⁻ exit at the basolateral side of the NPE. As indicated before, this interpretation cannot be applied to the HCO${}_3^{-}$ effect, since it is opposite to what is expected. We can only assume that removing aqueous-side HCO${}_3^{-}$ acidifies the cell (27). If so, such acidification may decrease Cl⁻ and K⁺permeability with a larger effect on Cl⁻, thus reducing the I_sc. In addition, cell acidification, which is known to close gap junctions, will reduce theI_sc across this tissue (34).

We propose a model (shown in Fig. 1) of the ciliary epithelium that includes channels and transporters well-characterized in bovine and rabbit tissues. This model is similar to those previously proposed by several investigators (14, 24,32). We should note, however, that our previously proposed model (14) has been modified. The interpretation of new data in the present study compels us to include the parallel Cl⁻/HCO${}_3^{-}$ and Na⁺/H⁺ exchangers. The reduction inI_sc by acetazolamide can only be explained by an inhibition of the uptake by the exchangers.

The main improvements in this model are the quantification of all vectorial fluxes and its dynamic nature that allows for the changes in one vector to be transmitted to all others so that a new steady state is attained. This is accomplished by the use of spreadsheet software (e.g., QPRO or Excel) in which two basic principles are preserved:1) the net ionic current is the same at each limiting membrane and is equal to the I_sc; and2) the total flux of an ion leaving the cell compartment is equal to the total flux entering the cell compartment for each ion. Descriptions of the equations in the spreadsheet cells are provided inappendix .

Figure 1 shows the control condition with the average values of theI_sc and vectorial fluxes compiled from many experiments during the past five years. Notice that the net Cl⁻ flux emerging from the NPE (27.0 μA/cm²) is 3.23 times larger than the I_sc. This was a consistent finding difficult to explain up to the present time. The model shows that the difference is due (at the aqueous side) to the pump-originated Na⁺ flux and the net K⁺ efflux. For simplicity we have chosen two vectors to be variable inputs to the system: the Cl⁻ entering the cell from the blood side via the two transporters. The relative value of these two vectors was selected on the basis of previous results indicating the inhibition of DIDS and furosemide on Cl⁻ fluxes. Obviously, it could be modified. All the other vectors are interconnected in such a way that the two enunciated principles are respected. At the bottom of the model, the relative activity of the two oppositely directed Na⁺-K⁺ pumps, the relative permeability of the NPE and PE K⁺ channels, and the relative contribution of the aqueous-side Cl⁻/HCO${}_3^{-}$ exchanger are indicated. The Cl⁻ permeability of the basolateral Cl⁻ channel of the NPE is considered to be 1 in the control condition but can be changed.

The “0.70” value means that 70% of the Na⁺ entering the epithelium from either side will leave the cell via the NPE pump; likewise for the K⁺ flux (72%). These values were chosen on the basis of the effects of ouabain and K⁺ channel inhibitors (26). It was found that the effects were larger at the aqueous side. These values also can be changed; this will not affect the Cl⁻ fluxes but will change theI_sc and some of the other vectors. Also shown in the model inside the cell is a nonvectorial production of H⁺ and HCO${}_3^{-}$ (Fig. 1, H and B, respectively). This can originate from endogenous as well as exogenous (bubbling) CO₂ catalyzed by CAII. Because H⁺can only exchange with Na⁺, and HCO${}_3^{-}$ with Cl⁻, they must be equal to each other at the basolateral membranes. Although we have chosen the Cl⁻ flux exchanged for HCO${}_3^{-}$ at the PE to be an input, this is arbitrary and can be changed at will. Again, the only inputs to the model are the Cl⁻ fluxes at the PE basolateral membrane, 21.0 and 6.0 μA/cm². All the other values are results of well-established relations necessary to satisfy the defined conditions and steady state. To test this model, we can analyze the effect of acetazolamide on the I_sc and Cl⁻fluxes. In the model shown in Fig. 2, we have reduced the production of H⁺ and HCO${}_3^{-}$ (an expected effect by acetazolamide) by simply reducing the Cl⁻ entering the cell via the Cl⁻/HCO${}_3^{-}$ exchangers to zero, since Cl⁻ entry is coupled to available HCO${}_3^{-}$. This results in a reduction of the net Cl⁻ flux to 21 and the I_sc to 5.95 μA/cm², which is consistent with the observed experimental results. In this example, we reduced the H⁺ and HCO${}_3^{-}$production to zero, but lesser inhibition can also be simulated. Other examples of the utilization of this spreadsheet model are given inappendix .

Going back to Fig. 1, we can see that under short-circuit conditions, there is a net secretion of NaCl and KCl with a small HCO${}_3^{-}$ component. The difference between the negative and positive ions (8.36 μA/cm²) is compensated by theI_sc.

In summary, we have presented results indicating that HCO${}_3^{-}$ is not transported across the isolated bovine ciliary epithelium and that acetazolamide can inhibit the Cl⁻ fluxes and I_sc by reducing the available HCO${}_3^{-}$ to be exchanged with Cl⁻, which contributes in large measure to the I_sc. We chose a model in which the ratio of Cl⁻ entering the PE via the 2Cl⁻-K⁺-Na⁺ cotransporter to the that entering via the Cl⁻/HCO${}_3^{-}$exchanger is ∼3.5.

We think that the bovine ciliary epithelium may be a good model to study the mechanisms of aqueous secretion and to understand the effects of pharmacological agents used to reduce IOP in humans.

For those interested in reproducing the model to try different variations, the equations for the relevant spreadsheet cells are indicated below.

	A3 = (A4 − C5 − C7 + C8 − C9 + A12 − C13 + A15 + C17 − A18)
	A4 = (D11)
	A12 = (1 − B21)*(C5 + C9)
	A15 = (1 − B22)*(F13 + C7 + C13)
	A18 = (C17)
	C5 = (A4)
	C7 = (0.5*C8)
	C8 = (A8*F22)
	C9 = (C7)
	C13 = (0.6666*A12)
	C17 = (A17*F22)
	D10 = (D11)
	D11 = (A18 + H18)
	F13 = (0.6666*H12)
	F17 = (H18)
	H3 = (H8 + F13 + H18 − H12 − H15 − F17)
	H8 = (C8 + C17 + F17)
	H12 = (B21*(C9 + C5))
	H15 = (B22*(F13 + C7 + C13))
	H18 = (F21*A18*F22)
	J5 = (H8 − F17)
	J6 = (H18)
	J7 = (H12)
	J8 = (H15 − F13)

The necessary inputs are in cells A8, A17, B21, B22, F21, and F22.

We give three examples for the utilization of the spreadsheet model presented in the discussion with cells identically defined as in the legend to Fig. 1 and in appendix.

We can observe what happens if the relative K⁺ permeability of one of the sides is changed, for example, by Ba²⁺blockade of the PE or NPE side. In Fig.3, a blockade of the NPE K⁺channels is simulated, which results in an increase of theI_sc without a change in the Cl⁻fluxes. A similar effect of less magnitude is obtained by ouabain on the NPE side. On the contrary, Ba²⁺ or ouabain on the PE side will decrease the I_sc. These effects have been observed experimentally (26).

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In another example (Fig. 4), we can simulate the effect of reducing the permeability of the Cl⁻ channel on the aqueous side of the NPE by changing the control value of 1 to 0.6. By simply restricting the output of Cl⁻, the model gets unbalanced unless the Cl⁻influx across the transporters in the PE is also restricted. This is accomplished by making the Cl⁻ fluxes across the transporters (cells C8 and C17) equal to their respective inputs (cells A8 and A17) multiplied by the Cl⁻ permeability. Figure 4then simulates the effect of HCO${}_3^{-}$ removal from the aqueous side on Cl⁻ flux and I_sc.

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We can also explain our previously reported results that reducing Cl⁻ concentration in the bathing solutions to 60 mM abolished the I_sc (14). Further reduction produced a reversal of the I_sc. We can speculate that at this Cl⁻ concentration, the Na⁺-K⁺-2Cl⁻ cotransporter is dominated by the large K⁺ gradient from cell to bath and reverses direction [Cl⁻(60:15)2 + Na⁺(136:15) < K⁺(140:4.6)], where 15, 15, and 140 are assumed millimolar cellular concentrations of Cl⁻, Na⁺, and K⁺, respectively. We have represented this situation in Fig.5, in which we reduced the activity of the Cl⁻/HCO${}_3^{-}$ exchanger to 2 and induced a reversed Cl⁻ flux across the Na⁺-K⁺-2Cl⁻ cotransporter of −3.00. This reduced the I_sc to near zero and produced an absorption of KCl across the NPE. One must realize that the values in the model are only approximations because possible changes in electrical potentials are not considered. Nevertheless, the model is self-consistent and is a useful aid in interpreting and predicting experimental results.

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FOOTNOTES

• Address for reprint requests and other correspondence: O. A. Candia, Dept. of Ophthalmology, Mount Sinai Medical Center, One Levy Place, New York, NY 10029–8574 (E-mail:oscar.[email protected]edu).

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