INTRODUCTION

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THE CLEFT BETWEEN ADJACENT endothelial cells is the primary pathway for water and hydrophilic solutes across the wall of endothelial barriers. Within the cleft, a major barrier to the movement of water and hydrophilic solutes is the junctional strand (5, 14-16). Using serial section reconstructions in individually perfused capillaries of frog mesentery, Adamson and Michel (4) demonstrated that the junctional strands were not continuous but were interrupted by infrequent breaks that, on average, were 150 nm long, spaced 2-4 µm apart along the strand, and accounted for up to 10% of the length of the strand. At these breaks, the space between adjacent endothelial cells (average 20 nm) was as wide as that in regions of the cleft between adjacent cells with no strands. Adamson and Michel (4) were able to account for the measured hydraulic conductivities of continuous capillaries of frog mesentery by modeling water flow through the breaks when they considered the two-dimensional spreading of the water flows on either side of the breaks. Fu et al. (10, 11) extended this approach and developed a three-dimensional model of water and solute flows through the strand breaks in the presence of a surface fiber matrix (Fig. 1). They found that the observed break frequency was sufficient to account for the measured water flows and the permeability coefficients of solutes with a radius larger than 0.75 nm, but that the observed break frequency was too small to account for the measured permeability coefficients for solutes with a Stokes radius smaller than 0.75 nm. Fu et al. (10, 11) suggested that, in addition to the breaks described by Adamson and Michel (4), solutes with a radius smaller than 0.75 nm could cross through the strands via a very small pore system within the junctional strand, which excluded solutes with a radius larger than 0.75 nm. They suggested that this pathway may be formed by a narrow slit pathway 2 nm wide, which may represent a continuous ~2-nm translucent narrow slit along the outer leaflets in the tight junction revealed in the investigation of strand structure on a tilting stage. The model describing both large breaks and the putative pathway for small solutes is called the two-pathway model to distinguish it from the large-break model.

View larger version (28K): [in this window] [in a new window]   Fig. 1.   A: plane view of junction-orifice-matrix entrance layer model for interendothelial cleft (10, 11). Junction strand with periodic openings lies parallel to luminal front. L is total depth of cleft, L2 is depth of pores in junction strand, and L1 and L3 are depths between junctional strand and luminal and abluminal fronts, respectively. Lf is thickness of fiber matrix at cleft entrance. Distance between 2 adjacent breaks in junctional strand is 2D, and d is one-half width of large junctional breaks. At entrance of cleft on luminal side, surface glycocalyx structures are represented by a periodic square array of cylindrical fibers. Radius of these fibers is a, and gap spacing between fibers is . B: 3-dimensional sketch of model. Large-break only model: only 2d × 2B = 150 × 20-nm breaks in junction strand; 2-pathway model: a continuous small slit with width 2bs = 1.5 nm existing in parallel with 2d × 2B = 150 × 20-nm large breaks in junction strand, where B is one-half cleft width.

The aim of the present experiments was to test the hypothesis proposed by Fu et al. (10, 11) that a pathway for small solutes, separate from a pathway through larger breaks in the junctional strand, makes a measurable contribution to the transcapillary flux of the small solutes. One difficulty with the comparison made by Fu et al. (10, 11) was that the permeability coefficients used to test their models for solutes ranging in size from that of sodium chloride to that of albumin were not measured on the same population of microvessels. Furthermore, the values were measured using several different techniques. Thus one aim of these experiments was to make paired permeability measurements on each microvessel of frog mesentery for a small fluorescent solute (sodium fluorescein; mol wt 376, Stokes radius 0.45 nm), which would be representative of solutes assumed to cross the wall mainly through the putative very small pore pathway, and a larger solute (-lactalbumin; mol wt 14,176, Stokes radius 2 nm) labeled with FITC, which should not penetrate the very small pore pathway but should penetrate the vessel wall via the pathway formed by the larger breaks in the junctional strand. Another aim of the experiments was to determine whether experimental conditions that raised endothelial cell cAMP concentrations and lowered the basal hydraulic conductivities would also reduce the permeability coefficients to small and larger solutes. Specifically, Adamson et al. (3) demonstrated that elevation of endothelial cell intracellular cAMP concentrations by simultaneous adenylate cyclase activation (forskolin) and phosphodiesterase (PDE4) inhibition (rolipram) reduced capillary hydraulic permeability (L_p) to 43% of baseline values within 20 min. We argued that if both small and intermediate-sized solutes shared a common pathway with water, we should observe a reduction in the permeability for both solutes when the vessels were exposed to conditions that increase intracellular cAMP. On the other hand, if the pathway available for larger solute accounted for less than one-half the flux of small solutes, and if the main effect of increased cAMP was on the common solute-water pathway, then the proportional reduction in permeability for small solutes in vessels treated with increased cAMP was expected to be less than that measured for water and larger solutes.

The solute permeability coefficient (P) was measured by using quantitative fluorescence microscope photometry (1, 12, 13). All experiments have been performed on individually perfused venular microvessels in frog mesentery. Each capillary was perfused via two micropipettes to enable the perfusate to be switched rapidly from a clear (washout) perfusate to one containing the fluorescently labeled test solute. This method enabled us to repeat measurements of the permeability coefficient of the capillary wall to more than one solute and to the same solute under more than one chemical treatment on each capillary. In addition, the permeability was measured by perfusing segments of the microvessels with fluorescently labeled solutes under conditions in which the transcapillary differences of solute concentration and hydrostatic pressure were known (13).

	MATERIALS AND METHODS

Top Abstract Introduction Materials & Methods Results Discussion Appendix References

General

The frog brain was destroyed by pithing, leaving the spinal cord intact. The abdominal cavity was opened, and the mesentery was gently arranged on the surface of a polished quartz pillar (1 cm in diameter; Heræus-Amersil, Fairfield, NJ) to maintain the circulation to the gut and mesentery of the animal. The upper mesentery was continuously superfused with frog Ringer solution at 14-18°C. Venular capillaries, generally 20-30 µm in diameter, were chosen for study. All vessels had brisk blood flow immediately before cannulation and had no marginating white cells. Each of the two arms of a Y-branched microvessel were cannulated with beveled glass micropipettes containing perfusion solutions. This arrangement allowed alternate perfusion of the downstream vessel with a washout solution (containing no fluorescent solute) or the test solution (containing the fluorescent solute). Each pipette was connected to a water manometer that enabled perfusion at known pressures. For these experiments the pressure in the capillaries was 5-8 cmH₂O as determined by balancing the interface between fluorescent and nonfluorescent solution within the nonflowing branch of the Y (13). This pressure range was chosen to minimize convectively coupled solute flux. In each vessel, P was determined for straight segments, 300-500 µm long, at least 100 µm downstream from the Y-branch junction point.

Frog Ringer solution was used for all dissections, perfusates, and superfusates. The solution composition was (in mM) 111 NaCl, 2.4 KCl, 1.0 MgSO₄, 1.1 CaCl₂, 0.195 NaHCO₃, 5.5 glucose, and 5.0 HEPES. The pH was balanced to 7.4 by adjusting the ratio of HEPES acid to base. In addition, both the clear washout solution and the fluorescent dye solution contained BSA (A4378, Sigma) at 10 mg/ml.

Fluorescent Test Solute Preparation

Sodium fluorescein. Sodium fluorescein (F6377, Sigma; mol wt 376, Stokes-Einstein radius ~0.45 nm) was dissolved at 0.1 mg/ml in frog Ringer solution containing 10 mg/ml BSA. The solution was made fresh on the day of use to avoid binding to the serum albumin (2).

FITC-labeled -lactalbumin. -Lactalbumin (L6010, Sigma; mol wt 14,176, Stokes-Einstein radius ~2 nm) was labeled with FITC (F7250, Sigma; mol wt 389.4) as follows (revised from Ref. 13). Protein (90 mg) was dissolved in 15 ml of borate buffer (0.05 M, pH ~9.3, 20°C) containing 0.4 M NaCl. The solution was placed in 18-mm-diameter dialysis tubing with a 3,500-mol wt cutoff (Spectrum Medical Industries) and was dialyzed for 12 h with constant stirring at 15°C against 50 ml of borate buffer containing FITC (0.5 mM). The labeled protein then was dialyzed against 2 liters of glucose-free frog Ringer solution twice, each time for 12 h. The dialysis procedure was repeated twice further with 2 liters of normal frog Ringer solution until there was no free dye. The influence of free dye on measured permeability to a labeled protein will be discussed in the APPENDIX. The FITC-labeled -lactalbumin was stored frozen and was used within 2 wk of preparation. On the day of use, unlabeled BSA was added to aliquots of the labeled protein. The final FITC--lactalbumin dye concentration used in the experiment was 2 mg/ml in frog Ringer solution. For this preparation, the fluorescence intensity of the free FITC dye was 1% of the solution, which was checked using the photometer at the same instrument settings used in our experiments.

Microscope and Photometer Preparation

P was calculated from the relationship

(1)

where I_f0 is the step increase in fluorescent light intensity as the test solute fills the capillary lumen, (dI_f/dt)₀ is the initial rate of increase in fluorescence light intensity after solute fills the lumen and begins to accumulate in the tissue, and r is the capillary radius (13).

Calibration Experiments

The results of experiments performed to test the assumption follow. In vitro calibrations were performed using a simple chamber constructed from coverslips (2). A large 24 × 50-mm coverslip formed the base of the chamber. Two small 22-mm² coverslips were laid on top of this base ~1 cm apart, and a third small coverslip was placed on top of those to form a chamber ~170 µm deep. Solutions of fluorescein were applied to the edge of the opening, and the chamber filled by capillarity. A new chamber was made for each concentration. I_f was measured from each concentration. These in vitro calibrations showed that the relationship between the concentration and fluorescence intensity was linear over the concentration range from 0.025 to 0.15 mg/ml for sodium fluorescein and from 0.5 to 3 mg/ml for FITC--lactalbumin.

In the in vivo calibration experiment, a capillary was cannulated and perfused as if for measurement of P. We recorded the step increase in I_f as the solute was perfused into the capillary. Perfusion time was <5 s during each run to minimize accumulation in the surrounding tissue. The procedure was repeated on the same capillary at each of four sodium fluorescein solute concentrations: 0.05, 0.1, 0.15 and 0.2 mg/ml. Step increase was plotted as a function of concentration. In a separate experiment, the step increase was recorded on a single vessel at each of four FITC--lactalbumin concentrations: 1, 2, 2.5, and 3 mg/ml. We also checked, in an in vivo experiment whether I_f was independent of the width of the measuring window when the capillary was aligned along the center line of the window. In vivo calibration results for the same concentration ranges as in the in vitro experiment are shown in Fig. 2. Figure 2A shows the results of an experiment to perfuse a capillary with four concentrations of sodium fluorescein. The capillary diameter was 30 µm, and the measuring window was 240 µm wide and 350 µm long. Figure 2B shows the results for FITC--lactalbumin in a capillary of 40-µm diameter. The measuring window was also 240 µm wide and 350 µm long. Both the 0.1 mg/ml sodium fluorescein and the 2 mg/ml FITC--lactalbumin concentrations used in all our measurements fell within the linear range of the calibration. In addition, the linear relationship between the fluorescence intensity and the concentration held for both solutes under the same instrument settings. We can therefore directly compare the results from different solutes on each capillary.

View larger version (11K): [in this window] [in a new window]   Fig. 2.   In vivo calibration experiments on a single capillary. A: fluorescence intensity of sodium fluorescein in a capillary of 30-µm diameter. B: fluorescence intensity of FITC--lactalbumin in a capillary of 40-µm diameter. Data are means ± SE.

Using in vivo experiments, we checked whether the initial step of I_f was independent of the width of the measuring window when the capillary was aligned along the center line of the window, provided that the window was wider than and up to 5 times the diameter of the vessel. This experiment showed that there was no contamination of our measuring window from dye leaked into the tissue during cannulation or diffused into the tissue from adjacent vessels. If there was contamination during the permeability measurement, the increase of I_f in the measuring window when the dye traveled out of the vessel and accumulated in the tissue would not be linear. We discarded the measurement when this happened.

We found in the in vitro photobleaching experiment that sodium fluorescein (0.1 mg/ml) and FITC--lactalbumin (2 mg/ml) I_f values fell to ~7 and 2% of their original values in 1 min, respectively. This 1-min period was typically two to four times as long as the exposure time required for an individual solute permeability measurement. The low degree of photobleaching was due to reduced excitation light intensity achieved with the use of the neutral density filter in our experiments. If this method were used for a larger molecule or in a tighter and smaller vessel, the exposure time to the fluorescence light for the individual permeability measurement would be longer than 30 s.

Experimental Protocol

To test the effects of rolipram and forskolin on sodium fluorescein and FITC--lactalbumin permeabilities, for each test solute, after making several control measurements when the washout pipette was filled with Ringer perfusate containing BSA (10 mg/ml) and the dye pipette was filled with the same perfusate, to which the test solute was added, we replaced both washout and test pipettes with new pipettes that also contained rolipram (10 µM) and forskolin (5 µM). The concentrations of rolipram and forskolin were chosen to be consistent with those used in L_p measurements by Adamson et al. (3). The test measurement during the treatment with rolipram and forskolin was performed once for every 2- to 5-min interval. The duration of the fluorescent light exposure was 10-30 s for each measurement. The treatment lasted ~20 min.

We also performed paired measurement of sodium fluorescein and FITC--lactalbumin permeabilities on single capillaries. In one set of measurements, we first measured the sodium fluorescein permeability and then changed the dye pipette to FITC--lactalbumin to measure its permeability under control conditions. Replacing washout and test pipettes with pipettes containing rolipram and forskolin, we measured sodium fluorescein permeability for 20 min and then changed the dye pipette to measure FITC--lactalbumin permeability for another 20 min. In the second set of these measurements, we used exactly the same procedure as in the first set but changed the order of measurements to FITC--lactalbumin first and sodium fluorescein second.

Reagents

Analysis and Statistics

	RESULTS

Top Abstract Introduction Materials & Methods Results Discussion Appendix References

Rolipram and Forskolin Effect on P to Sodium Fluorescein and FITC--Lactalbumin

FITC--lactalbumin

FITC--lactalbumin

View larger version (21K): [in this window] [in a new window]   Fig. 3.   Individual measurements showing time effect of rolipram and forskolin on capillary permeability (P) to sodium fluorescein (Psodium fluorescein). Perfusion was performed with 10 mg/ml BSA frog Ringer solution as control (). A: reperfusion with same solution also containing rolipram (10 µM) and forskolin (5 µM) (). B: sham experiment reperfusion with control solution (). Dashed lines are mean control values.

View larger version (18K): [in this window] [in a new window]   Fig. 4.   Individual measurements showing time effect of rolipram and forskolin on P to FITC--lactalbumin (PFITC--lactalbumin). Perfusion was performed with 10 mg/ml BSA frog Ringer solution as control (). A: reperfusion with same solution also containing rolipram (10 µM) and forskolin (5 µM) (). B: sham experiment reperfusion with control solution (). Dashed lines are mean control values.

Figure 5 summarizes the results from a series of individual measurements similar to those shown in Figs. 3 and 4. Mean results are shown for control measurements for P^{FITC--lactalbumin} in four vessels and for P^{sodium fluorescein} in five vessels. Test results are shown for both FITC--lactalbumin and sodium fluorescein when cAMP levels were elevated by rolipram and forskolin. P^test represents the test permeability at a specific time, and results are expressed as the ratio for the mean control value (P^test/P^control) for each single vessel. After the introduction of rolipram and forskolin, P^{FITC--lactalbumin} averaged over 17 vessels decreased from a mean control value of 3.5 (±1.5 SD) × 10⁶ cm/s to a mean value of 2.1 (±0.7 SD) × 10⁶ cm/s after 20 min, a reduction to 60%. This mean ratio was similar to the ratio P^test/P^control of 0.64 (±0.19 SD) measured on individual vessels. The range of individual ratios after 20 min was from 0.29 to 0.95. In 18 different vessels, P^{sodium fluorescein} decreased from a mean control value of 28.5 (±11.6 SD) × 10⁶ cm/s to a mean value of 18.3 (±5.7 SD) × 10⁶ cm/s after 20 min. The mean ratio of 0.64 was also similar to the ratio P^test/P^control measured on individual vessels, which was 0.67 (±0.17 SD) after 20 min. The range of individual ratios was from 0.36 to 1.0. The falls in P^{FITC--lactalbumin} and P^{sodium fluorescein} were highly significant at all times and were different from their control values (P < 0.01, Wilcoxon signed-rank test). Figure 5 also indicates that the temporal patterns of decreasing permeability under the treatment of rolipram and forskolin are the same for FITC--lactalbumin and sodium fluorescein (P > 0.5, Mann-Whitney U test). Thus increased cAMP reduces both small-solute and large-solute permeability to nearly the same extent. This result would not be expected if most of the small solute crossed the vessel wall via a pathway that was regulated by a mechanism different from those modulating water and larger-solute permeability.

View larger version (13K): [in this window] [in a new window]   Fig. 5.   P decreased as a function of time in response to treatment with rolipram and forskolin. , Control values with 10 mg/ml BSA frog Ringer perfusate for FITC--lactalbumin in 4 vessels; , control values for sodium fluorescein in 5 vessels; , test values with perfusate also containing rolipram (10 µM) and forskolin (5 µM) for FITC--lactalbumin in 17 vessels; , test values for sodium fluorescein in 18 vessels. Results are expressed as ratio of test value to control value (Ptest/Pcontrol) for each individual vessel, and data are means ± SE for each group.

In four vessels in which control P^{sodium fluorescein} was 25.1 (±12.3 SD) × 10⁶ cm/s, treatment with rolipram and forskolin decreased permeability to 17.3 (±10.6 SD) × 10⁶ cm/s in 20 min. After perfusion for 20 min with control solution, the final P^{sodium fluorescein} was 17.9 (±10.0 SD) × 10⁶ cm/s. In a separate group of four vessels, rolipram and forskolin induced a fall in P^{FITC--lactalbumin} from 3.7 (± 1.4 SD) to 1.8 (±0.4 SD) × 10⁶ cm/s. Perfusion for a final 20 min with control solution did not change P^{FITC--lactalbumin} [1.8 (±0.3 SD) × 10⁶ cm/s]. Therefore, both groups exhibited a sustained and stable permeability decrease over the time course of our experiments.

Paired Measurements of P^{sodium fluorescein} and P^{FITC--lactalbumin} on Single Capillaries

FITC--lactalbumin

We first report the results of paired measurements of P^{sodium fluorescein} and P^{FITC--lactalbumin} in the control state (i.e., without rolipram or forskolin). Paired measurements of P^{FITC--lactalbumin} and P^{sodium fluorescein} in 26 vessels are listed in Table 1. In 15 microvessels, FITC--lactalbumin was the first test solute and sodium fluorescein was the second. In the other 11 vessels, the order of the perfusion was reversed. The mean values from 26 individual capillaries are P^{FITC--lactalbumin} = 3.73 (±1.40 SD) × 10⁶ cm/s (range from 1.10 to 6.47 × 10⁶ cm/s), P^{sodium fluorescein} = 34.4 (±14.5 SD) × 10⁶ cm/s (range from 12.36 to 60.70 × 10⁶ cm/s), and the mean ratio P^{sodium fluorescein}/P^{FITC--lactalbumin} = 10.55 (±6.20 SD) (range from 3.10 to 26.45). There was some tendency for the ratio of permeability coefficients to be lower in vessels in which sodium fluorescein was measured first, suggesting that there was some tendency to overestimate the second permeability measurement in a pair.

View this table: [in this window] [in a new window]   Table 1.   Paired control measurements of PFITC--lactalbumin and Psodium fluorescein on single capillaries

In 17 of the 26 vessels in which paired measurements of solute permeability were performed, we also measured paired permeability coefficients after exposure to rolipram and forskolin. Results for our paired measurements of P^{sodium fluorescein} and P^{FITC--lactalbumin} on single capillaries are shown in Fig. 6, A and B. As demonstrated in one representative capillary (Fig. 6A), we first measured P^{FITC--lactalbumin} and then P^{sodium fluorescein} under control conditions. After both washout and dye pipettes were replaced with perfusates containing rolipram and forskolin, we continuously measured P^{FITC--lactalbumin} at intervals of 2-5 min for 20 min. Replacing the dye pipette with sodium fluorescein solution containing rolipram and forskolin, we measured the P^{sodium fluorescein} for another 20 min in the same manner. We successfully completed eight experiments in the order shown in Fig. 6A. We also completed an additional nine experiments with the order of the solute perfusion reversed (Fig. 6B). The time-dependent decreasing patterns of P^{sodium fluorescein} and P^{FITC--lactalbumin} in these representative experiments are similar to those in nonpaired measurements.

View larger version (22K): [in this window] [in a new window]   Fig. 6.   Individual paired measurements of Psodium fluorescein and PFITC--lactalbumin (apparent permeability) and their changes with time in response to treatment with rolipram (Roli) and forskolin (Forsk) on same vessel. A: PFITC--lactalbumin measured first. B: Psodium fluorescein measured first.

A summary of these paired permeability measurements is shown in Fig. 7. Results are described as P^test/P^control for the same capillary. The mean results are shown for measurement of P^{FITC--lactalbumin} first and P^{sodium fluorescein} second in eight vessels. The results are shown for measurement of P^{sodium fluorescein} first and P^{FITC--lactalbumin} second in 9 vessels. After 20-25 min, P^test/P^control with paired measurements on 17 vessels was 0.62 (±0.16 SD) for FITC--lactalbumin and 0.64 (±0.16 SD) for sodium fluorescein. These values are similar to those (0.64 and 0.67) measured in the nonpaired experiments as previously described. Statistical analysis of these data shows that there is no significant difference in decreasing patterns of P^{sodium fluorescein} and P^{FITC--lactalbumin} over time when the order of the measurement is switched (P > 0.4, Mann-Whitney's U test). Furthermore, as shown in Fig. 8, for paired permeability measurements before and after treatment with rolipram and forskolin, there was no systematic variation in the magnitude of the reduction in permeability with the magnitude of the initial permeability coefficient.

View larger version (12K): [in this window] [in a new window]   Fig. 7.   Paired measurement results expressed as Ptest/Pcontrol (control: 10 mg/ml BSA frog Ringer perfusate). PFITC--lactalbumin was measured first () and Psodium fluorescein was measured second () in 8 vessels. Psodium fluorescein was measured first () and PFITC--lactalbumin was measured second () in 9 vessels. Data are means ± SE.

View larger version (19K): [in this window] [in a new window]   Fig. 8.   Paired measurements of Psodium fluorescein and PFITC--lactalbumin on same 17 vessels as in Fig. 7 in control state () and after 20-25 min of treatment with rolipram (10 µM) and forskolin (5 µM; ).

Evaluation of Methods: Free Dye Associated With FITC-Labeled -Lactalbumin

6

FITC--lactalbumin

6

6

FITC--lactalbumin

	DISCUSSION

Top Abstract Introduction Materials & Methods Results Discussion Appendix References

The results of these experiments do not appear to support the hypothesis that the small fluorescent test solute, sodium fluorescein, crosses the walls of frog mesenteric microvessels via a pathway different from that available to the large solute, -lactalbumin. The first argument against a significant contribution from a very small pore pathway is that, on average, the permeability coefficients for sodium fluorescein were only 10.6 times larger than permeability coefficients for -lactalbumin measured on the same capillary. This difference is within the range of values predicted by the model described by Fu et al. (10, 11) for diffusion through breaks in the junctional strand observed by Adamson and Michel (4) and when there was a fiber matrix at the cleft entrance. Thus the contribution of a pathway available to sodium fluorescein, but not to -lactalbumin (e.g., a pathway formed by a narrow slit, 2 nm wide along the junction strand), was smaller than could be detected with these measurements. We will evaluate this result in more detail below. The second line of evidence against a separate pathway for sodium fluorescein is that the permeability coefficients for both sodium fluorescein (Stokes radius 0.45 nm) and -lactalbumin (Stokes radius 2 nm) are reduced to the same extent relative to their controls in microvessels exposed to conditions that lower basal permeabilities. We expected this result when the same mechanisms reduced permeabilities to both solutes. Some possible mechanisms to change the permeability coefficients for both solutes are evaluated below. As we shall discuss, these results do not definitively rule out the presence of a second pathway for solutes smaller than sodium fluorescein, but they place much tighter constraints on the properties of such a pathway than were available from the previous analysis (10, 11). Before we discuss these results further, it is useful to evaluate the possible errors in the method used to measure permeability coefficients.

Free Dye Influence on P^{FITC--lactalbumin}

Solvent Drag Contribution to P^{FITC--Lactalbumin}

6

(2)

(3)

(4)

FITC--albumin

FITC--albumin

7

7

1

1

6

6

View this table: [in this window] [in a new window]   Table 2.   Solvent drag effect on PFITC--lactalbumin under control and rolipram/forskolin treatment conditions

Taking into account both the free dye and solvent drag effects on measured P^{FITC--lactalbumin}, we estimated a corrected mean P^{FITC--lactalbumin} of 2.85 × 10⁶ cm/s. This value is only slightly larger than the previously measured data for TRITC--lactalbumin, which was 2.1 × 10⁶ cm/s (1, 13). One reason for the slightly larger value may be that all microvessels used in our study were venular capillaries, which tend to have higher permeability than the population of venular, true, and arterial capillaries used previously (1, 13).

Influence on P^{sodium fluorescein} From Fluorescein Concentration at Cleft Exit

P^{sodium fluorescein} decreased in response to treatment with rolipram and forskolin. Because the degree of underestimation of P^{sodium fluorescein} will always be larger for the control case when permeability is larger than that when cAMP was elevated in the test case, the corrected ratio P^test/P^control should be smaller than the measured value of 67%.

It follows from the above that the measured mean P^{sodium fluorescein} of 34.4 (±14.5 SD) × 10⁶ cm/s (range 12.4 to 60.7 × 10⁶ cm/s) would increase after the concentration increase in the extravascular space is taken into account. If the underestimation of P^{sodium fluorescein} due to buildup of extracellular solute is as high as a factor of 2, the corrected mean P^{sodium fluorescein} will be roughly 68.8 × 10⁶ cm/s. With this estimate, the mean ratio of corrected P^{sodium fluorescein} to corrected P^{FITC--lactalbumin} in single capillaries is increased from the measured value of 10.6 to a value of 27.6.

Previous Models for Capillary Permeability and Hydraulic Conductivity

6

FITC--lactalbumin

6

FITC--lactalbumin

FITC--lactalbumin

Figure 9 shows the permeability coefficients predicted by a model of either the junctional strand containing only the large breaks or the junctional strand containing large breaks plus an additional 2-nm-wide narrow slit pathway as a function of solute radius (10, 11). Also shown are the current experimental data using quantitative fluorescence microscope photometry to measure P^{sodium fluorescein} and P^{FITC--lactalbumin} on the same single capillaries, with uncorrected and corrected P values. The relationship between the measured permeability P and the structural components of the interendothelial cleft pathway is described by a three-dimensional model proposed previously (11) as

(5)

where D⁽¹⁾ and D⁽³⁾ are the effective solute diffusion coefficients in regions 1 and 3 of the interendothelial cleft (see Fig. 1A). D⁽¹⁾ and D⁽³⁾ include the influences from the cleft wall and the fiber matrix. B is the half cleft width, L is the cleft depth, d is one-half the width of the large junctional break, and 2D is the spacing between adjacent large breaks. L_jt is the total cleft length (total cell perimeter) per unit capillary surface area. K is a complete elliptic integral of the first kind. The first term in Eq. 5 is the contribution to P from the large breaks; the second term, P_s, which has a complicated form, is the contribution from the possible small continuous ~2-nm slit in the tight junction strand. The first subterm in the large-break contribution term (Eq. 5) is dependent on the fiber matrix composition (fiber radius a, volume fraction S_f, and its ordering manner), the cleft width, and the solute properties. The second subterm is the cleft width. The third subterm is dependent on the break size and the cleft depth. The fourth subterm is dependent on the frequency of the breaks in one cleft and the frequency of the clefts per unit capillary surface area.

View larger version (22K): [in this window] [in a new window]   Fig. 9.   P as a function of solute radius for a large 150 × 20-nm-break only (dashed line) and a 2-pathway model (continuous line) with an additional 2bs = 1.5 nm narrow continuous slit (11). Lps is contribution to hydraulic conductivity (Lp) from narrow slit, and Lpl is contribution from large breaks. Total Lp is fixed at 2.0 × 107 cm · s1 · cmH2O1, which is normal Lp value in experiment. Symbols represent experimental data for frog mesenteric capillaries: , data for other solutes from a variety of studies referred to in Ref. 11; , measured Psodium fluorescein and PFITC--lactalbumin on same vessels using quantitative fluorescence microscope photometry in current study; , corrected Psodium fluorescein for extravascular concentration influence and corrected PFITC--lactalbumin for free dye and solvent drag influence from experimental values. Sf (0.017) is periodic matrix. Fiber radius a = 0.6 nm. All lengths are expressed in nanometers, and units of Lp are × 107 cm · s1 · cmH2O1.

Figure 9 shows that both the corrected and uncorrected measured P^{sodium fluorescein} and P^{FITC--lactalbumin} fall close to the curve predicted by the large-break model. We do not need an additional small slit to explain the data from the paired experiment for P^{sodium fluorescein} and P^{FITC--lactalbumin}. Furthermore, because we measured a proportional reduction in the permeability coefficients to sodium fluorescein and -lactalbumin in the presence of elevated cAMP, we could account for the data in the lower-permeability state induced by rolipram and forskolin simply by sliding the curve vertically without changing its shape. According to Eq. 5, P should be changed in the same proportion for different-sized solutes as long as the first subterm, which is determined by the fiber matrix properties, and the second term, the cleft width, are unchanged under the treatment of rolipram and forskolin. Thus the possible candidates for change induced by rolipram and forskolin are the large-break frequency and size, and the cleft depth.

Adamson et al. (3) have begun to investigate ultrastructural changes in the cleft of microvessels treated with rolipram and forskolin under the same experimental conditions used in the present experiments. In the vessels studied, Adamson et al. (3) found that the mean decrease in L_p of frog mesenteric microvessels after 20 min of exposure to rolipram and forskolin was 43%. These investigators have not yet made detailed analyses of changes in the size and frequency of breaks in the junctional strand, but they have observed that reduced permeability is associated with an increase in the number of junctional strands per cleft from an average of 1.7 to 2.2 (3). This change occurred with no change in the average cleft length. Although the change in number of strands is small, the addition of strand is expected to reduce the effective area available for diffusion through breaks in the junctional strand and to increase the diffusion distance for solutes within the cleft (3). The actual reduction in L_p is larger than the 33-36% reduction measured for the diffusible solutes. The reason for this difference has not been investigated in detail and may not be significant because of the variation from vessel to vessel. However, it is instructive to compare the expression for the L_p of the junctional pore-fiber matrix model with the corresponding relationship for diffusive exchange in Eq. 5. The L_p is given by the relationship (11)

(6)

Here µ⁽¹⁾ and µ⁽³⁾ are effective fluid viscosities in regions 1 and 3 of the cleft. L_ps is the contribution from the small slit. It is noted that the terms describing the effects of breaks in the junctional strand are the same in Eqs. 5 and 6. The biggest difference is that L_p depends on mean cleft width to the third power and not as a simple proportion, as for diffusion. Thus, in the simplest case, a change in break size or frequency is expected to have similar effects on L_p and solute permeabilities. However, a larger reduction in L_p relative to diffusion would not be unexpected if there were a small reduction in mean cleft width after exposure to cAMP.

Another way to analyze these results is to note that, according to the model in which solutes with a radius smaller than 0.75 nm cross the capillary wall via both the large breaks and a narrow slit pathway, nearly 70% of the flux of sodium fluorescein might have been expected to cross the vessel wall via the very small pathway, whereas 100% of the -lactalbumin and close to 75% of the water was expected to cross via the larger breaks. If these values were correct, and if the primary effect of raising cAMP was through an action on the large breaks, the reduction in P^{FITC--lactalbumin} and L_p to values close to 50% of control would have been associated with a reduction in P^{sodium fluorescein} to only 85% of control. Alternatively, if increased cAMP were to effectively close the narrow slit as well as modify the larger breaks, the reduction in P^{sodium fluorescein} would have been much larger, to as low as 15% of control values. These extreme values were not observed. We note, however, that theoretically it may be possible for a mechanism that effectively closes part of both pathways to cause reductions in the permeability of both small- and large-pore pathways within the ranges we measured. One such mechanism may involve additional junctional strands, as observed by Adamson et al. (3), which change the geometry of the diffusion pathways for both solutes.

An important caveat to the conclusion that our results do not support the hypothesis that a very small pore pathway is present is that sodium fluorescein may not be as good a probe of the putative small-pore pathway as we originally expected. We note that the corrected value of P^{sodium fluorescein}, ~69 × 10⁶ cm/s, is close to the value measured by Adamson et al. (2) using confocal microscopy. However, it is only one-half the mean value of P^sucrose (143 × 10⁶ cm/s) measured previously using osmotic transients (sucrose mol wt 342 vs. sodium fluorescein mol wt 376) (7). Furthermore, for even smaller solutes, Na⁺ and K⁺, the measured permeability coefficients are 440 × 10⁶ (7) and 670 × 10⁶ cm/s (6), respectively. For the smallest solutes the large-break model underestimates the measured permeabilities by up to one order of magnitude. Thus a conservative interpretation of our results is that, although they do not support the hypothesis that there is a significant flux of sodium fluorescein across a very small pore pathway, they do not rule out such a pathway for solutes smaller than sodium fluorescein. This would be the case if the additional pathway for smaller solutes had a size cutoff smaller than the 0.75- nm radius threshold proposed by Fu et al. (10, 11). This possibility needs further exploration with the use of both venular microvessels, as used in the present experiments, and true capillaries. One problem with such experiments is that it will be difficult to design experiments in which the same method is used to measure the permeability coefficients to small and large solutes because sodium fluorescein is one of the smallest fluorescent solutes available for use within the visible spectrum. Thus more refined methods to investigate the modulation of permeability properties of the capillary wall to very small solutes are needed to overcome possible limitations of the effectiveness of sodium fluorescein as a probe of putative pathways for very small solutes across the junctional strands.

In summary, the combined results from experiments using the best-understood methods to measure sodium fluorescein and -lactalbumin permeability coefficients on microvessels in both the control state and after permeability is reduced do not support the hypothesis that a separate pathway across the tight junction is available for solutes with a radius as large as 0.75 nm. If such a pathway is present, its cut-off size is smaller than the size of sodium fluorescein. Furthermore, the proportional reduction in the permeability of both sodium fluorescein and -lactalbumin is also consistent with the hypothesis that a mechanism involving a change in the number of tight junction strands within the cleft reduces the permeability of microvessels under conditions in which intracellular cAMP levels are increased.